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Journal of Automation, Mobile Robotics and Intelligent Systems A peer-reviewed quarterly focusing on new achievements in the following fields: • Fundamentals of automation and robotics • Applied automatics • Mobile robots control • Distributed systems • Navigation • Mechatronic systems in robotics • Sensors and actuators • Data transmission • Biomechatronics • Mobile computing Editor-in-Chief

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Articles

Journal of Automation, Mobile Robotics and Intelligent Systems Volume 14, N° 2, 2020 DOI: 10.14313/JAMRIS/2-2020

Contents 50

Chaotic Path Planning for Grid Coverage Using a Modified Logistic-May Map Eleftherios Petavratzis, Lazaros Moysis, Christos Volos, Hector Nistazakis, Jesus Manuel Muñoz-Pacheco, Ioannis Stouboulos DOI: 10.14313/JAMRIS/2‐2020/13 10

Realization, Programming and Controlling of the Stewart‐Gough Platform Dawid Owoc, Krzysztof Ludwiczak, Robert Piotrowski DOI: 10.14313/JAMRIS/2‐2020/14 15

Adaptive Fuzzy-Sliding Mode Controller for Trajectory Tracking Control of Quad-Rotor Lahcen Simoud, Boufeldja Kadri, Ismail Khalil Bousserhane DOI: 10.14313/JAMRIS/2‐2020/15 25

Active Power Loss Reduction by Novel Feral Cat Swarm Optimization Algorithm Kanagasabai Lenin DOI: 10.14313/JAMRIS/2‐2020/16 30

Preface to Special Issue on Recent Advances in Machine Learning and its Applications Piotr A. Kowalski, Szymon Łukasik, Piotr Kulczycki DOI: 10.14313/JAMRIS/2‐2020/17 32

On Wavelet Based Enhancing Possibilities of Fuzzy Classification Methods Ferenc Lilik, Levente Solecki, Brigita Sziová, László T. Kóczy, Szilvia Nagy DOI: 10.14313/JAMRIS/2‐2020/18 42

Categorization of Persons Based on Their Mentions in Polish News Texts Maciej Pachocki, Anna Wróblewska DOI: 10.14313/JAMRIS/2‐2020/19 Articles

Supporting Decisions on the Forex Market Using Fuzzy Approach Przemysław Juszczuk, Lech Kruś DOI: 10.14313/JAMRIS/2‐2020/20 63

Non-Contact Video-Based Remote Photoplethysmography for Human Stress Detection Sergii Nikolaiev, Sergii Telenyk, Yury Tymoshenko DOI: 10.14313/JAMRIS/2‐2020/21 74

Radon-Wavelet Based Novel Image Descriptor for Mammogram Mass Classification Sk Md Obaidullah, Sajib Ahmed, Teresa Gonçalves, Luís Rato DOI: 10.14313/JAMRIS/2‐2020/22 81

Segregation of Songs and Instrumentals – a Precursor to Voice/accompaniment Separation From Songs in Noisy Scenario Himadri Mukherjee, Sk Md Obaidullah, K.C. Santosh, Teresa Gonçalves, Santanu Phadikar, Kaushik Roy DOI: 10.14313/JAMRIS/2‐2020/23 91

The Method of Selecting the Interval of Functional Tests Taking into Account Economic Aspects and Legal Requirements Jan Piesik, Emilian Piesik, Marcin Śliwiński DOI: 10.14313/JAMRIS/2‐2020/24 99

Three Level Fuzzy Signature Based Decision Methodology for Packaging System Design Kata Vöröskői, Gergő Fogarasi, Adrienn Buruzs, Péter Földesi, László T. Kóczy DOI: 10.14313/JAMRIS/2‐2020/25

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Chaotic Path Planning for Grid Coverage Using a Modified Logistic-May Map Submitted: 19th September 2019; accepted: 2nd April 2020

Eleftherios Petavratzis, Lazaros Moysis, Christos Volos, Hector Nistazakis, Jesus Manuel Muñoz-Pacheco, Ioannis Stouboulos DOI: 10.14313/JAMRIS/2-2020/13 Abstract: A simple and efficient method for creating a motion trajectory is presented with an aim to achieve sufficient coverage of a given terrain. A chaotic map has been used in order that the motion trajectory should be unpredictable. The chaotic path generator which has been created, is used for implementing a robot’s movement in four and eight directions. The path generator is tested in various scenarios and the results are discussed. After thorough examination, the proposed method shows that the motion in eight directions gives better and very satisfactory results. Keywords: Logistic-May map, path planning, chaos, grid coverage

1. Introduction In recent years, robots are used in our lives more than ever. Especially, in industry the need for developing efficient robotic systems is increasing vastly, because they can perform tasks that for humans are unreachable [1, 2]. Some of them can be presented in space missions [3, 4], in firefighting [5–8] and more [7, 9, 10]. In military [11–13], they can be used for patrol missions, or to find explosives or other dangerous materials. In all of these missions, the robots should recognize both their initial position and also the target’s position in the workspace, in order to update the workspace’s map instantly. These goals could be achieved with the use of a sufficient path planning method which will create a trajectory, that gives the robot the opportunity to cover a given workspace. However especially in patrolling missions [14–17], it is crucial for the robot to move randomly [18–20]. For that reason, nowadays, chaotic systems are used in order to control the motion of the robots. Chaotic systems have rich dynamic behavior and find a variety of applications in many fields such as engineering, cryptography, communication and many others [21–24]. Their advantages rely in the fact that they are very sensitive to initial conditions, which means that by a slight change the system will produce a completely different trajectory. This characteristic is crucial because it will be impossible for the system to produce the same motion sequence twice.

For that reason, many researchers have used chaotic systems in path planning [18, 25–33]. For the purpose of achieving randomness in the motion trajectory in discrete grids, many researchers have used chaotic random bit generators. These generators are used for moving the robot in discrete directions, four or eight, and their results are tested with appropriate statistical tests. The disadvantage of this approach is that it requires the generation of more than three times the number of iterations for the algorithm in order to obtain a statistical random motion. In our work, a completely different approach has been used. Instead of creating a chaotic random bit generator, we divide the interval [0, 1] into equally spaced subintervals. Τhen, a chaotic motion command is generated based on which interval the value of the chaotic map belongs to. This is considered for motion in 4 or 8 directions. The chaotic system that is used in our method, is a modification of a Logistic and May map [34]. With the use of modulo tactics two main goals are achieved. Firstly, robot’s motion is programmed in Matlab in a short and readable code. Secondly, it produces sufficient results for grid coverage and is more efficient than the methods based on chaotic random bit generation. This happens because it does not use the de-skewing method for producing random bits sequences as the chaotic random bit generators requires. So we do not have extra iterations in our code. The rest of the paper is organized as follows. In Section 2, the chaotic path planning generator for controlling our robot as well as some simulation results by using the proposed method and its analysis are presented. Section 3 includes the conclusion of our work and a discussion of future aspects.

2. The Proposed Chaotic Path Generator In [34], the authors proposed the following Logistic-May chaotic map

= x i +1

( x e( i

r + 9)(1− xi )

)

− ( r + 5) x i (1 − x i ) mod1 (1)

where ri ∈ [0, 1] and r ∈ [−6.8, 19.6]. This map was constructed as a combination of the Logistics map, given by

= x i +1 rx i (1 − x i )

(2) 3

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where xi ∈ [0, 1] and r ∈ [0, 4], and the May map, given by x i +1 = x i e a (1 − x i ) where xi ∈ [0, 10.9] and a ∈ [0, 5].

(3)

(

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)

x i +1 = dx i e ( r + 9)(1− xi ) −( r +5) xi (1− xi ) mod1 (4)

where d is a positive parameter, chosen here as d = 100 and r = 4. The bifurcation diagram of the proposed Logistic-May map is shown in Fig. 2. The Histogram of 2,000,0000 iterations for the modified map for r = 4 is presented in Fig. 3. Now, an even distribution of the map values on the interval [0, 1] is observed.

2.2 Chaotic Path Planning in 4 Motion Directions

In order to generate the chaotic path for a robot moving in 4 directions (up, down, left, right), the interval [0, 1] has been divided in 4 equal subintervals. Based on this partition, the following tactic is used Fig. 1. Histogram for 2,000,0000 iterations of the Logistic-May map (1)

Fig. 2. Bifurcation diagram of proposed Logistic-May map

Fig. 3. Histogram for 2,000,000 iterations of the modified Logistic-May map (4)

The Histogram for 2,000,000 iterations of the Logistic-May map (1) for r = 4 is shown in Fig. 1. Here, an uneven distribution of the values in the integral [0, 1] is shown. This is something we want to improve, since our proposed path generator is based on dividing the interval [0, 1] to subintervals of equal length. Thus, the following modified Logistics-May map is proposed Articles

 up , x i ∈ [0,0.25)  right , x i ∈ [0.25,0.5) mi =  down, x i ∈ [0.5,0.75)  x i ∈ [0.75,1]  left ,

(5)

where mi denotes the robot movement in the i-th iteration of the map. A simulation of the proposed chaotic motion is shown in Fig. 4. Here, a 100 x 100 grid, thus having 1002 discrete spaces (or cells) for the robot to cover is considered. In each iteration of the algorithm, a movement is generated, which the robot follows. If the generated movement is not acceptable, like moving outside the defined limits or facing obstacles, then the robot remains in its place and awaits for the next motion command. In Fig. 4, the robot starts from position (1, 1)T and performs 40,000 iterations. Also, Fig. 5 shows a color coded graph showing the number of visits in each step.

Fig. 4. Grid coverage for 40,000 steps in the case of 4 motion directions

2.2 Chaotic Path Planning in 8 Motion Directions The use of four directions for the motion of the robot is somewhat limited. In general, we can assume that a robot can also move in eight directions, so the diagonal motions can be used in order to make the robot

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 up ,  up − right ,  right ,  down − right , mi =  down,   down − left ,  left ,  up − left , 

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x i ∈ [0,0.125) x i ∈ [0.125,0.25) x i ∈ [0.25,0.375) x i ∈ [0.375,0.5) x i ∈ [0.5,0.625) x i ∈ [0.625,0.75) x i ∈ [0.75,0.875) x i ∈ [0.875,1]

2020

(6)

where mi denotes the robot movement in the i-th iteration of the map.

Fig. 5. Color-coded grid coverage showing the number of visits for 40,000 steps in the case of 4 motion directions

Fig. 8. Color-coded grid coverage showing the number of visits for 50,000 steps in the case of 4 motion directions

Fig. 6. Grid coverage for 20,000 steps starting from positions (1 ,1)T (blue), (50 , 50)T (red), (50 , 100)T (black), in the case of 4 motion directions

Fig. 9. Grid coverage for 40,000 steps in the case of 8 motion directions

Fig. 7. Grid coverage with obstacles for 50,000 steps in the case of 4 motion directions to move in more directions. In this case, the interval [0, 1] is divided in 8 equal subintervals and the proposed tactic is used

The simulation of the proposed method is shown in Fig. 9. We consider the same grid as the previous one and also the same starting position. The behavior of the robot is studied for 40,000 iterations and the colored map in Fig. 10 shows the number of visits in each cell. The improvement in the coverage is obvious. The robot with the insertion of 4 more motions managed to visit cells that they were uncovered. The size of the black areas which represent unvisited cells is reduced and in their place shades of blue are appearing, which represent visited cells. Fig. 11 shows the grid coverage starting from different initial positions. Articles

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grid coverage in the case of motion in 8 directions. It can be noticed that the coverage percentage is improved compared to the 4 direction motion. Also, the mean number of visits is reduced because of the use of diagonal motions. These diagonal motions gives the opportunity to move in cells that the robot has not visited many times. The result is also plotted in Fig. 12 where it is clear, that motion in 8 directions leads to better coverage result.

Fig. 10. Color-coded grid coverage showing the number of visits for 40,000 steps in the case of 8 motion directions

Fig. 13. Grid coverage with obstacles in the case of 8 motion directions, for 50,000 steps

Fig. 11. Grid coverage for 40,000 steps starting from positions (1 ,1)T (blue), (50 , 50)T (red), (50 , 100)T (black) for motion in the case of 8 motion directions

Fig. 14. Color-coded grid coverage showing the number of visits for 50,000 steps in the case of 8 motion directions

3. Conclusion Fig. 12. Grid coverage percentage for 4 (blue) and 8 (red) motion commands

Moreover, the problem of a grid with obstacles for 50,000 movements of the robot is studied. The results are shown in Figs. 13 and 14. The case that was studied, was an 8 direction motion. Although there were 5 obstacles, the robot managed to cover large amount of the given space. Finally, Table 1 shows the average Articles

In this paper, the problem of the efficient coverage of a given space, by a mobile robot, was studied. The method that was proposed, used a modified Logistic-May map for creating a “random” motion trajectory. The method was tested in two cases. The first one produced a motion trajectory which used 4 directions and in the second one, the diagonal motions were inserted. Both cases were tested in the same environment and with the same starting positions. In Fig. 12 it can be noticed that, the use of 4 more directions can improve the behavior of the robot, both in coverage

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Tab. 1. Average Grid Coverage and Mean Number of Visits in the Cases of 4 and 8 Motion Directions Steps x103

Average Grid Coverage %

Mean number of visits

Steps x103

Average Grid Coverage %

Mean number of visits

4.6

3.7

9.6

9.1

4.4

10.5

4.9

4.1

5.5

4.7

6.1

5.5

6.8

6.2

45 55 60

69 77 78

77 82 86

5.8

6.5 7.2 7.7

5.8

115

12.1

11.4

6.7

120 125

94 95 96

96 98 98

11.7 12.6 13

10.9 12.1 12.3

130

13.6

12.7

7.8

140

14.4

13.9

15.4

8.7

8.2

9.2

110

10.9

10.5

10.9

11.5

7.4

9.5

8.2 8.6

10.1

87 90

105

80 82

100

65 70

8.7

135 145 150

97 97 98

98 99

14.9

13.2 14.2 14.6

percentage and in the reduction of the number of visits of same cells. As a further improvement a pheromone method can be used for better covering of the given workspace. In future works the method could be used and tested in non-square spaces. Also, different discrete chaotic maps can be combined with the modulo tactics in order to generate the chaotic path. Finally, the implementation of the method on an actual mobile robot is crucial in order to study its behavior in real time.

Jesus Manuel Muñoz-Pacheco – Faculty of Electronic Sciences, Benemérita Universidad Autónoma de Puebla, Mexico, e-mail: jesusm.pacheco@correo.buap.mx.

AUTHORS

[1] H. Abdellilah, B. Mohamed, M. Abdellah, M. Youcef and A. M. Réda, “Depth advanced control of an autonomous underwater robot”, International Journal of Modelling, Identification and Control, vol. 26, no. 4, 2016, 336–344, DOI: 10.1504/IJMIC.2016.081134.

Eleftherios Petavratzis* – Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece, e-mail: elpetavr@physics.auth.gr. Lazaros Moysis – Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece, e-mail: lmousis@physics.auth.gr.

Christos Volos – Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece, e-mail: volos@physics.auth.gr.

Hector Nistazakis – Department of Electronics, Computers, Telecommunications and Control. Faculty of Physics, National and Kapodistrian University of Athens, Athens, Greece, e-mail: enistaz@phys.uoa.gr.

Ioannis Stouboulos – Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece, e-mail: stouboulos@physics.auth.gr. * Corresponding author

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path planning of a mobile robot using flatness controller”, Chaos, Solitons & Fractals, vol. 118, 2019, 366–375, DOI: 10.1016/j.chaos.2018.12.002.

[29] E. K. Petavratzis, C. K. Volos, I. N. Stouboulos, H. E. Nistazakis, K. G. Kyritsi and K. P. Valavanis, “Coverage Performance of a Chaotic Mobile Robot Using an Inverse Pheromone Model”. In: 2019 8th International Conference on Modern Circuits and Systems Technologies (MOCAST), 2019, 1–4, DOI: 10.1109/MOCAST.2019.8741542.

[30] C. K. Volos, I. M. Kyprianidis and I. N. Stouboulos, “A chaotic path planning generator for autonomous mobile robots”, Robotics and Autonomous Systems, vol. 60, no. 4, 2012, 651–656, DOI: 10.1016/j.robot.2012.01.001.

[31] C. K. Volos, I. M. Kyprianidis and I. N. Stouboulos, “Experimental investigation on coverage performance of a chaotic autonomous mobile robot”, Robotics and Autonomous Systems, vol. 61, no. 12, 2013, 1314–1322, DOI: 10.1016/j.robot.2013.08.004.

[32] C. K. Volos, “Motion direction control of a robot based on chaotic synchronization phenomena”, Journal of Automation, Mobile Robotics and Intelligent Systems, vol. 7, no. 2, 2013, 64–69.

[33] L. Moysis, E. Petavratzis, C. Volos, H. Nistazakis and I. Stouboulos, “A chaotic path planning generator based on logistic map and modulo tactics”, Robotics and Autonomous Systems, vol. 124, 2020, DOI: 10.1016/j.robot.2019.103377. [34] K. M. Ali and M. Khan, “Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps”, International Journal of Theoretical Physics, vol. 58, no. 9, 2019, 3091–3117, DOI: 10.1007/s10773-019-04188-3.

Articles

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VOLUME 2020 VOLUME 14,14, N°N°22 2020

REALIZATION, PROGRAMMING AND CONTROLLING OF THE STEWART‐GOUGH PLATFORM Submitted: 9th July 2019; accepted: 7th January 2020

Dawid Owoc, Krzysztof Ludwiczak, Robert Piotrowski DOI: 10.14313/JAMRIS/2‐2020/14 Abstract: This paper presents realization, programming, and con‐ trolling of a low cost Stewart‐Gough platform (SGP) with rotary actuators. The realized SGP is applied in a ball & plate control system. Developed dedicated soft‐ ware consists of embedded and application software for both the SGP positioning system and the ball & plate con‐ trol system. A ball position is being obtained using com‐ puter vision. The paper contains tests results for both an SGP positioning accuracy and a control quality of the ball & plate control system. Keywords: Stewart‐Gough platform, ball & plate, compu‐ ter vision

1. Introduction This paper presents a real implementation of the design of the Stewart‑Gough platform (SGP) [3], [8] presented in the paper [6]. It describes realization, programming and controlling of the SGP. The realized SGP is applied in a ball & plate control system. A ball & plate system is an expanded version (two degrees of freedom) of a ball and a beam system. In this paper, a ball position is being obtained using computer vision. Utilizing an SGP in a ball & plate cont‑ rol system is common. For example, the paper [1] des‑ cribes building of an educational kit of this type. The paper is organized as follows. In Section 2, a re‑ alization process with photos of the assembled system is presented. In Section 3, developed software is illus‑ trated. In Section 4, test results are provided. Section 5 contains project summary and conclusions.

2. Realization of the Platform

Fig. 1. A wooden board with all of the electronics and six servo motors for testing

Having designed the electronic subsystem in EAGLE environment [7], all the electronic parts were �ixed to a wooden board. In the begining, a 10 A

Fig. 2. A fully assembled SGP

Fig. 3. A complete ball & plate control system research station

AC circuit breaker, an AC/DC power supply, and two step‑down voltage converters were �ixed. At the early stage of the realization, six servo motors (PowerHD HD‑1235MG) were �ixed to the board for testing. The wooden board is presented in �ig. 1. After testing, the servo motors were moved to their target place ‑ the base. Next, a per�board with soldered electronic cir‑ cuit was �ixed. Every single servomotor was safeguar‑ ded with a dedicated fuse. Last two elements that were �ixed to the board were� servo controller (Pololu Micro Maestro) and Arduino UNO. Having designed the mechanical subsystem in In‑ ventor environment [5] all mechanical parts were ag‑ gregated. Metal elements such as servo motors moun‑

Journal Mobile Robotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation, Mobile

ting brackets and horns were made using laser cut‑ ting. The base and the moving platform with the plate for the ball were made with wood. Having all of the parts, the main assembling were started. In the begi‑ ning, the base was �ixed to a bigger rectangular plate. Next, horns were �ixed to the servomotors. The servo‑ motors were �ixed with mounting brackets that ensure them not to move even at high load. Assembling required high precision because every error during assembling woud have a big impact on the SGP’s geometry and as a result on a correctnes of the inverse kinematics problem (IKP) solution [6]. Having assembled the base, the assembly of the moving platform and connecting it to the rotary actu‑ ators with six legs was started. An important attribute is the range of angle of the ball joints. If the maximum angle was too low it would reduce the workspace of the SGP. The ball joints used in the assembled SGP has a maximum angle of 40◦ which is suf�icient. The last part of the realization process involved creating the ball & plate control system research sta‑ tion. A camera was hung on a tripod. All of the devices were connected to the Personal Computer (PC). Fig. 2 presents a fully assembled SGP and �ig. 3 presents a complete research station.

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Fig. 5. A flowchart of the ball vision application algorithm (one iteration)

3. Programming of the Platform

Fig. 4. A flowchart of the embedded software algorithm All software was developed in C++. The software consists of embedded software and PC software. The embedded software runs on Arduino UNO with an AVR microcontroller. The PC software runs on Debian ope‑ rating system (OS). In order to facilitate the process of building the ap‑ plication, CMake environment [4] was used. CMake is an open‑source, cross platform build system. The embedded system is the lowest abstraction layer of the system. It is the only one that has a direct access to rotary actuators. It calculates the IKP [6] and provides safety functions to prevent danger conditi‑ ons, e.g. trying to force a position and/or orientation beyond the workspace. A �lowchart of the algorithm of the embedded software is presented in �ig. 4. The PC software allows a user to position the SGP using command line interface (CLI) and high abstract

Fig. 6. Screenshots presenting view from the camera ‐ raw and with ball detected commands, e.g.: –set‑platform –pitch ]10 –roll 25 to [ rotate the SGP to R = 0 10◦ 25◦ . External ap‑ plications can bene�it from this software using a li‑ brary with relevant Application Programming Inter‑ face (API) that it provides. For tracking a ball, a computer vision application was developed. A color detection method was used. The application is based on OpenCV [2], which is an Articles

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test cases are presented in tabs. 1‑2. Testing the ball & plate control system was con‑ ducted with trajectory of reference values. The mea‑ sured ball position were downloaded from ball vision application. The results are shown in �igs. 10‑11. Tab. 1. SGP positioning accuracy test number 2

Fig. 7. A flowchart of the control application algorithm open‑source computer vision library. OpenCV puts strong focus on performance and real‑time applica‑ tions. Developing computer vision applications using OpenCV library is convenient because OpenCV deli‑ vers all needed subroutines and has a built‑in support for range of cameras available on the market. A �low‑ chart of the algorithm of the application is shown in Fig. 5. A vision is being obtained from a 30 frames per second (FPS) webcam. View from the camera both raw and with detected ball is presented in �ig. 6. Using a color detection method is appriopriate only in case where the detected object color is signi�i‑ cantly different than a color of surroundings. The hue, saturation, value color model (HSV) was used. Using the HSV model eases the process of �inding the boun‑ daries values. A tool which helps choosing the color boundaries values was also developed. All of the software is interconnected by another ap‑ plication which was developed. It implements a cont‑ rol loop. It uses subroutines provided by the software described above. It also implements proportional‑ integral‑derivative controller (PID) and provides very simple C�I, that allows i.e. to enter PID gains. A �low‑ chart of this application is shown in Fig. 7. The embedded system and PC software communi‑ cate with each other using Modbus communications protocol. Modbus has become a standard communica‑ tion protocol in industry. Open‑source implementati‑ ons of Modbus that exist for both PCs and AVR micro‑ controllers were used.

4. Verification Tests

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Conducted veri�ications tests checked� 1) the accu‑ racy of positionig the SGP, and 2) ball & plate system quality of control. Testing an accuracy of positioning the SGP invol‑ ved three test cases which test variety of pitch and roll combinations. Results of one out of three test cases are shown in Figs. 8‑9. The results of the remaining two Articles

Pitch Ref. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Roll Ref. ‑25.0 ‑23.0 ‑21.0 ‑19.0 ‑17.0 ‑15.0 ‑13.0 ‑11.0 ‑9.0 ‑7.0 ‑5.0 ‑3.0 ‑1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25.0

Pitch m. 1.0 0.5 0.5 0.5 0.5 0.5 0.5 1.0 0.5 1.0 1.0 1.0 1.0 1.0 0.5 0.5 1.0 0.5 1.0 0.5 1.0 1.0 0.5 0.5 0.5 0.5

Roll m. ‑23.0 ‑20.0 ‑19.0 ‑16.0 ‑15.5 ‑13.0 ‑12.0 ‑10.0 ‑9.0 ‑4.5 ‑4.0 ‑0.5 0.5 0.5 3.5 5.5 7.0 9.5 11.0 13.5 15.0 19.0 20.0 21.0 24.5 25.0

5. Conclusion The SGP has been realized and programmed. The SGP has been effectively used in the ball & plate con‑ trol system. The obtained test results proved a good quality of control. According to the project division presented in [6], it was evaluated how much time was spent on each module. The time allocation is presented in tab. 3. The results presented in tab. 3 show that the most cost effective tasks were related to assembly (35%) and 3D CAD model (25%). The research works for further improvement are de�ined as follows� ‑ Reimplementation of embedded software to provide handling of real values of pitch, roll, and ∆z (now it only supports integer values).

‑ Optimisation of all software to provide better per‑ formance in time domain. ‑ Use of faster camera ‑ more than 30 FPS.

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Fig. 8. Accuracy of positioning the SGP (pitch)

Fig. 9. Accuracy of positioning the SGP (roll)

Fig. 10. Response of of ball & plate system reference trajectory (x‐axis)

Fig. 11. Response of of ball & plate system reference trajectory (y‐axis) ‑ �se of sign�l �iltr�tion.

‑ Further tuning of PID controllers. Articles

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of Automation, Automation,Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of

Tab. 2. SGP positioning accuracy test number 3 pitch ref. ‑25.0 ‑23.0 ‑21.0 ‑19.0 ‑17.0 ‑15.0 ‑13.0 ‑11.0 ‑9.0 ‑7.0 ‑5.0 ‑3.0 ‑1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25.0

roll ref. ‑25.0 ‑23.0 ‑21.0 ‑19.0 ‑17.0 ‑15.0 ‑13.0 ‑11.0 ‑9.0 ‑7.0 ‑5.0 ‑3.0 ‑1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25.0

pitch m. ‑20.0 ‑20.0 ‑18.0 ‑15.0 ‑14.5 ‑12.0 ‑11.0 ‑9.5 ‑8.0 ‑6.0 ‑3.0 ‑2.0 0.5 1.0 3.0 6.0 7.5 9.0 11.0 14.5 16.0 18.0 21.0 23.5 25.5 27.0

roll m. ‑20.0 ‑20.0 ‑18.0 ‑16.0 ‑14.5 ‑12.5 ‑11.5 ‑9.5 ‑7.5 ‑4.0 ‑2.0 0.5 1.0 1.5 3.5 6.5 8.5 10.0 13.0 14.0 16.0 19.0 20.5 22.0 25.0 26.5

Tab. 3. Division of time spent on each module Module 3D CAD model electronics SGP positioning system ball & plate control system computer vision assembly

Time spent 25% 10% 10% 10% 10% 35% 100%

AUTHORS Dawid Owoc∗ – Gdansk University of Technology Fa‑ culty of Electrical and Control Engineering, Naruto‑ wicza 11/12, 80‑233 Gdansk, Poland, e‑mail: dawido‑ woc6@gmail.com. Krzysztof Ludwiczak – Gdansk University of Techno‑ logy Faculty of Electrical and Control Engineering, Na‑ rutowicza 11/12, 80‑233 Gdansk, Poland, e‑mail: kr‑ zysztof_ludwiczak07@wp.pl.

Robert Piotrowski – Gdansk University of Techno‑ logy Faculty of Electrical and Control Engineering, Na‑ rutowicza 11/12, 80‑233 Gdansk, Poland, e‑mail: ro‑ bert.piotrowski@pg.edu.pl.

∗

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Corresponding author Articles

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REFERENCES [1] H. Bang and Y. S. Lee, “Implementation of a Ball and Plate Control System Using Sliding Mode Con‑ trol”, IEEE Access, vol. 6, 2018, 32401–32408, 10.1109/ACCESS.2018.2838544. [2] G. R. Bradski and A. Kaehler, Learning OpenCV: computer vision with the OpenCV library, Software that sees, O’Reilly: Beijing, 2011.

[3] V. E. Gough, “Contribution to discussion of papers on research in automobile stability, control and tyre performance”, Proc. of Auto Div. Inst. Mech. Eng., vol. 171, 1957, 392–395. [4] K. Martin and B. Hoffman, Mastering CMake: A Cross‑Platform Build System, Kitware, Inc.: Clifton Park, NY, 2008. [5] P. Munford and P. Normand, Mastering Autodesk Inventor 2016 and Autodesk Inventor LT 2016, John Wiley & Sons, Inc: Indianapolis, Indiana, 2016.

[6] D. Owoc, K. Ludwiczak, and R. Piotrowski, “Me‑ chatronics Design, Modelling and Controlling of the Stewart‑Gough Platform”. In: 2019 24th In‑ ternational Conference on Methods and Models in Automation and Robotics (MMAR), 2019, 76–80, 10.1109/MMAR.2019.8864694. [7] M. Scarpino, Designing Circuit Boards With EAGLE: Make High‑Quality PCBs at Low Cost, Prentice Hall: Upper Saddle River, NJ, 2014.

[8] D. Stewart, “A Platform with Six De‑ grees of Freedom”, Proceedings of the In‑ stitution of Mechanical Engineers, 2016, 10.1243/PIME_PROC_1965_180_029_02, Sage UK: London, England.

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Adaptive Fuzzy-Sliding Mode Controller for Trajectory Tracking Control of Quad-Rotor Submitted: 3rd December 2018; accepted: 18th March 2020

Lahcen Simoud, Boufeldja Kadri, Ismail Khalil Bousserhane

DOI: 10.14313/JAMRIS/2-2020/15 Abstract: This paper deals with the design of an adaptive-fuzzy-PD-Sliding mode controller to achieve stabilization of a quadrotor aircraft in the presence of wind disturbance. Firstly, the dynamic system modeling is carried out using Euler-Lagrange formalism. Then, an adaptive PD-sliding mode control system with an integral-operation switching surface is investigated for quadrotor desired trajectory tracking. Finally, an adaptive fuzzy-PD-sliding mode controller is proposed to achieve control objectives and system stabilization where the fuzzy logic system used to dynamically control parameters settings of the PD-sliding mode equivalent control law. Effectiveness and robustness of the proposed control scheme is verified through simulation results taking into account external disturbances. The simulation results of a quadrotor aircraft control with the proposed controller demonstrate the high performance during flight such as null tracking error and robustness in the presence of external disturbances. Keywords: Quadrotor UAV, Sliding mode control, Adaptive PD-Slidng mode controller, Fuzzy PD-sliding mode

1. Introduction Unmanned aerial vehicles (UAVs) already have a wide area of possible applications in military and civilian purposes such as surveillance, traffic monitoring, inspection, law enforcement, search and rescue, among others [1]. Continuous evolution of robotic vehicles technology also offer a remarkable growth in the market of unmanned helicopters, which nowadays includes vehicles of various types, sizes and operational capabilities. While many possible types of small UAVs exist, one very promising vehicle with respect to size, weight and maneuverability is the so called quadrotor [1-4]. The quadrotor is classiﬁed as a powered rotary wing vertical take-off and landing (VTOL) aircraft. It is consisting of ﬁxed-pitch rotors mounted at the four ends of a simple cross configuration, as well as the direction of rotation of the rotors implies that front and the rear motor rotate clockwise, the left and the right motor rotate counter-clockwise (Fig. 1) [1-4].

The quadrotor is an interesting alternative to the classical helicopter because is mechanically simpler than a regular helicopter since it does not require a swash plate or teeter hinges and has several advantages in terms of maneuverability, motion control and cost. Because of the fixed pitch and its symmetric structure, this Omni-directional helicopter is dynamically excellent and its mathematical model is quite simple [4-6]. The dynamics of a quadrotor are a simplified form of helicopter dynamics that exhibit the basic problems of rotorcraft including under actuation, multi-input/multi-output (MIMO) design, and unknown nonlinearities and the states are highly coupled [3-6]. The movement of the quadrotor is caused by the resultant forces and moments of four independent rotors. Therefore the control algorithms designed for a quadrotor could be applied to a helicopter with relatively straightforward modifications, so that the quadrotor serves as a suitable, more tractable, case study for rotorcraft controls design [4-6]. The system we consider is an under actuated and has six degrees of freedom (DOF) with only four control inputs consisting of thrust and the three rotational torque inputs; characteristics which can make the platform difficult to control. To deal with this system, many modelling approaches have been presented [2, 3, 4, 7, 8] and various types of controllers have been proposed such as feedback linearization method [9, 10], backstepping control technique [11, 12], sliding mode control [8, 10, 11, 13], backstepping-sliding mode control [7, 14] and adaptive control [15, 16, 17, 18]. The authors of [17] have proposed an adaptive backstepping sliding mode control algorithm to stabilize the attitude. Considering the under-actuation, strong coupling properties of the aircraft, a nested double-loops control structure is designed in [17] and the adaptive estimation and sliding mode approach are used in the design procedure. In [5, 6], Madani and Benallegue divided the quad-rotor into three interconnected subsystems and developed a backstepping controller based on the Lyapunov stability theory in order that the aircraft tracks the desired trajectories. Bonna and Camino proposed a nonlinear control design based on feedback linearization for the quadrotor that guarantees the convergence trajectory to a given reference trajectory [9]. Zemalache and al. [13] a four rotors helicopter is studied and controlled using cascade-sliding mode control. In [13], the stabiliz-

Journal of Automation, Mobile Robotics and Intelligent Systems

ing/tracking control problem for the three decoupled displacement of the quadrotor has been considered. Furthermore, much research effort has been directed towards design of intelligent hybrid controllers using fuzzy logic. The authors of [18] studied a trajectory tracking of quadrotor unmanned aerial vehicle using a self-tuning fuzzy proportional integral derivative controller. The main idea of [18] is the design a fuzzy system tuning gains of the proportional-integral-derivative controller to stabilize the quadrotor. In this paper, a fuzzy PD-sliding mode controller is developed for quadrotor dynamics trajectory control. The proposed controller, which combines the merits of the sliding mode control and the fuzzy inference system, is derived to overcome the drawback of sliding mode control. In this scheme, a fuzzy logic controller is used to dynamically control parameters settings of the PD-sliding mode equivalent control law. The new adaptive fuzzy PD-sliding mode controller has been achieved, fulfilling the robustness criteria specified in the sliding mode control and yielding a high performance in implementation to Control of Quad-Rotor. The rest of the paper is organized as follows: The modeling of the four-rotor rotorcraft based on Lagrange approach is presented in section II. The adaptive PD-sliding mode controller (A-PD-SMC) and the proposed adaptive fuzzy-PD-sliding mode controller (A-F-PD-SMC) development for quadrotor trajectory tracking are summarized in section III. Some simulation results are given and discussed in section IV. Finally, some conclusions are drawn in Section V.

2. Dynamic of the Quadrotor UAV The quadrotor configuration consists of a rigid body equipped with four rotors which generate the propeller forces Fi (i = 1, 2, 3, 4). In this type of helicopters the front and the rear motors (1 and 3) rotate clockwise while the other two motors (2 and 4) rotate counter-clockwise as shown in Fig. 1 [1-6]. The quadrotor rotorcraft does not have a swash plate  f4

 f1

 f2

 f3

G mg

Ex O Fig. 1. Basic representation quadrotor unmanned aerial vehicle 16

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as standard helicopters. The main thrust is the sum of the thrusts of each motor. Pitch movement is accomplished by increasing (reducing) the speed of the rear motor while reducing (increasing) the speed of the front motor. The roll movement is obtained similarly using the lateral motors. The yaw movement is achieved by increasing (decreasing) the speed of the front and rear motors while decreasing (increasing) the speed of the lateral motors [1-3]. This should be done while maintaining the total thrust constant. The dynamic model of a quadrotor mini-aircraft derived using Euler-Lagrange formulation can be expressed as follows [1-5, 19]   − sθ   0       mξ u  cθ sϕ  +  0  =     cθ cϕ   −mg        τ θ      ℑ−1 (τ − C (η ,η )η ) τ ϕ  = η =     τψ    

(1)

where x and y are the coordinates in the horizontal plane, and z is the vertical position (see Fig. 1). ψ is the yaw angle around the z axis, θ is the roll angle around the (new) x axis, and f is the pitch angle around the (new) y axis. The control inputs u3, tθ, tf and tψ are the total thrust or collective input (directed out the bottom of the aircraft) and the new angular moments (rolling moment, pitching moment and yawing moment). Here, the quadrotor rotational dynamics can be expressed as follow [13, 19, 20]: θ = u4  (2) ϕ = u5  ψ = u6 and the translational dynamics are given by:

mx = −Sθ u3   = Sϕ Cθ u3 my  = mz Cθ Cϕ u3 − mg (3)

3. Adaptive Fuzzy PD-Sliding Mode Control of the Quadrotor Rotorcraft 3.1. Sliding Mode Control Variable structure control (VSC) with sliding mode (SMC) is one of the effective nonlinear robust control approaches because it provides system dynamics with an invariance property to uncertainties once the system dynamics are controlled in the sliding mode [8, 10, 11, 13, 21-23]. The first step of SMC design is to select a sliding surface that models the desired closedloop performance in state-variable space. The control is then designed such that the nonlinear system-state trajectories are driven on a specified user-chosen

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 <0 surface in state-space (phase plan). The system state k1a es < 0 k2a es k3a s < 0 = = = k ; k ; k3  1 2   trajectory in the period of time before reaching the  >0 k1b es > 0 k2b es k3b s > 0 sliding surface is called the reaching phase. Once the system trajectory reaches the sliding surface, it reIn this work, only the proportional and derivamains on it for all subsequent time and slides to the tive terms are used to design equivalent control law origin. The most important feature of sliding mode uequ for SMC control of the quadrotor with modified control is the insensitivity of the controlled system to hard-switching parameters and the controller strucuncertainties, but not during the reaching phase. ture can be defined as: Without loss of generality, the possible choice of de the nonlinear control law in the SMC can be defined u = us + k1 ⋅ e + k2 (9) dt as [8, 10, 11, 21-23] where (4) u= ueq + k ⋅ sgn ( s ) k Where ueq is called the equivalent control; k is 1a if es > ε  a constant design parameter, representing the maxi = (10) k1 k1b if -ε ≤ es ≤ ε mum controller output required to overcome param eter uncertainties and disturbances; sign is the sigk1c if es < −ε num function and s is called the switching function. In the conventional SMC design, a second-order system s  >ε k2a if es is chosen in the state-space by the following scalar   ≤ε = function [22]: k2 k2b if -ε ≤ es (11)  r −1  < −ε ∂  k2c if es s = + λ  ⋅ e (5) ∂ t   e: is a small positive gain. Where e = xd – x denotes the tracking position and xd is the desired state; l is a positive constant and r is 3.2. Adaptive PD-Sliding Mode Control of Quadrotor the order of the sliding surface. To ensure that the system trajectories move toThis section describes the design procedure of the ward and remain on the sliding surface s = 0, the folrobust nonlinear control via the adaptive PD-SMC for lowing sliding mode condition must be guaranteed quadrotor trajectory tracking and stabilization with [21, 22]: external disturbances handling. The objective of this controller is to obtain the quadrotor control laws so ss ≤ −σ ⋅ s ⇒ ss ≤ −σ ⋅ sgn ( s ) s ⇒ s ⋅ sgn ( s ) ≤ −σ as to achieve high-quality position and altitude per(6) formance. The overall control structure of the quadWhere s is a positive constant that ensures a finite rotor aircraft using adaptive PD-sliding mode and time convergence to s = 0. adaptive fuzzy-PD-sliding mode is depicted in Fig. 2. In practice, the main obstacle for application of The vertical input force u3 is used to stabilize the alsliding mode control is chattering phenomenon due titude of the quadrotor. The desired reference values to the using a sign function. This phenomenon can be of roll (θd) and pitch (fd) are formed on the rotationreduced by introducing a boundary layer around the al controller by the position subsystem. The rotation switching surface, such as [13, 21-22]: controller is used to stabilize the quadrotor with control inputs u3, u4, u5 and u6. The design of the proposed sliding mode controller for the quadrotor rotorcraft (7) us= k ⋅ sat s ζ trajectories control involves the following steps: Where the constant factor ζ defines the thickness of the boundary layer x, y , z For simplification reason in the development of u3 the equivalent control law in the sliding mode control Quadrotor aircraft x d , y d , z d Position model and to make the design task very easy for practical controller u x , u y Equations (17) u , u , u Desired Rotation 4 5 6 engineers, Nandam and Sen [24, 25] have proposed ψr trajectories controller an equivalent control action based on proportional θ , φ ,ψ and derivative law. The major advantage of this design method is its ability of nonlinear systems control Fig. 2. Basic control structure of the quadrotor with any dependency on system parameters. Y. Li and al. [26] extends this control strategy by incorporating Altitude control. The altitude can be controlled an integration term and to form a generic controller by the adaptive PD-sliding controller (see Fig. 3). structure given by: Through the equation of the following movement

( )

u = k1 ⋅ e + k2 ∫ e.dt + k3 ⋅

(8)

dt with the parameters ki (i = 1, 2, 3) are given by ageneralized hard-switching law as:

mz= Cϕ Cθ u3 − m[ g + a3 z ]

The tracking error is defined is: e= zd − z z

(12) (13)

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And the sliding surface can be given by the following linear function: s= ez + λz ez z

(14)

The control of the vertical position can be obtained by using the following control input:

= u3

m [ z + g + a3 z ] Cϕ Cθ

(15)

Fz With a3 = , disturbances a long of position z. m And the expression of z can be given by  z= k z ⋅ sat( s z ) + uzequ

And the equivalent control trol is defined by:

uzequ

uzequ = k pz ⋅ ez + kdz ⋅

(16) for altitude con-

dez

(17) dt Where kpz and kdz are positive constants and are obtained using Eq. 10 and Eq. 11, as follow:

And

k pza if ez s z > ε  = k pz k pzb if − ε ≤ ez s z ≤ ε  k pzc if ez s z < −ε

(18)

kdza if ez s z > ε  = kdz kdzb if − ε ≤ ez s z ≤ ε (19)  kdzc if ez s z < −ε From Eq. 15, Eq. 16 and Eq. 17 it follows that the output altitude tracking control can be given as:

m u3 = Cϕ Cθ

Desired trajectories

 dez   k z ⋅ sat( s z ) + k pz ⋅ ez + kdz ⋅ dt   zd + −

SMC controller

   + g + a3 z   

(20)

Quadrotor aircraft model

Fig. 3. Adaptive PD-Sliding mode control on z direction Linear x and y motion control. From the model Eq. 3 we can see that the motion through the axes x and y depends on u3. In fact u3 is the total thrust vector oriented to obtain the desired linear motion. If we considered ux = –sθ and uy = cθ sf the orientations of u3 responsible for the motion through x and y axis respectively, we can then extract the roll and pitch angle necessary to compute the control ux and uy (Fig. 2). Now, let denote the reference speeds in x and y directions by x d and y d respectively. Then, the tracking error is given by: x d − x x e= (21)  y d − y e= y

Then, the sliding surfaces for this step can be given such as: Articles

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e x + λx e x  s= x  e y + λ y e y  s= y The control laws can be obtained as follow:

 = ux    uy = 

2020

(22)

 m  de x    k x ⋅ sat( s x ) + k px ⋅ e x + kdx ⋅  + a1 x  u3   dt  

 m  de y    k y ⋅ sat( s y ) + k py ⋅ e y + kdy ⋅  + a2 y  u3   dt  

(23) Fy Fx With a1 = and a2 = : disturbances a long m m positions x and y. The reference roll and pitch angles can be computed by the following expressions:   m de x   = θ d arcsin   k x ⋅ sat( s x ) + k px ⋅ e x + kdx ⋅  dt    u3     m   dey   = ϕd arcsin  u c  k y ⋅ sat( s y ) + k py ⋅ e y + kdy ⋅ dt     3 θ  (24) where kx and ky are positive design parameter. Parameters kpx, kdx, kpy and kdy are positive constants which can be obtained by the same manner used in Eq. 18 and Eq. 19. Attitude control (ψ). Attitude control is the heart of the control system because it keeps the 3D orientation. From the equations of dynamic model Eq. 18, the altitude subsystem containing vertical force input u6 is given by:

ψ = u6

(25)

The first step in adaptive PD-sliding control design is to consider the tracking error, such as:

e= ψ d −ψ (26) ψ We define also the sliding surface for the variable ψ as follows:

sψ= eψ + λψ eψ (27) The vertical force input u6 can be obtained by the same way as above. Then the equivalent control law u6equ is given by:

deψ (28) dt And the switching control law for the altitude controller is defined as: u6equ = k pψ ⋅ eψ + kdψ ⋅

u6sψ= kψ ⋅ sat( sψ )

(29)

θd − θ θ e=  ϕd − ϕ ϕ e=

(30)

Roll and Pitch control (θ, f). The same steps are followed to extracted u4 and u6. The control laws are derived using adaptive PD-sliding technique to control the quadrotor in (x, θ) and (y, f) directions. The tracking errors for θ and f are defined as:

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Then, the sliding surfaces for θ and f are given by:

eθ + λθ eθ  s= θ  eθ + λθ eθ  s= θ The control laws are then:

(31)

deθ   u4 =θ =kθ ⋅ sat ( sθ ) + k pθ ⋅ eθ + kdθ ⋅ dt  (32)  u =ϕ =k ⋅ sat ( s ) + k ⋅ e + k ⋅ deϕ pϕ dϕ ϕ ϕ ϕ  5 dt

Desired xd + trajectories −

SMC controller

θd +

eθ −

SMC controller

Quadrotor aircraft model

Fig. 4. Adaptive PD-Sliding mode control on (x, θ) direction

3.3. Adaptive Fuzzy PD-Sliding Mode Controller In this section, hybridization between the fuzzy logic and the sliding mode control is proposed in order to adapt the parameters of the equivalent component ueq (Eq. 17) by two fuzzy logic controllers. In this approach, the fuzzy logic controllers are used to generate, in a soft way, the equivalent control law parameters given by (Eq. 18 and Eq. 19). So, the fuzzy logic controllers are designed to replace the inequalities which determine the parameters of the equivalent control action. The key idea of this controller is that instead of inequalities used to compute the parameters kpz and kdz. In this proposed adaptive fuzzy-PD-sliding mode control scheme, the sliding surface (s), the error e and its time derivative e form the inputs of the fuzzy implications of the switching rules. The first FLC, which is responsible for tuning kpz, has two inputs (s and e) whereas the second FLC which generate kdz has s and e as inputs. The basic structure of the adaptive fuzzy PD-sliding mode controller is depicted in Fig. 5. The membership functions of the FLC1 inputs and output are shown in Fig. 6, whereas the membership functions of the FLC2 inputs and output are depicted in Fig. 7. The membership functions of the inputs are chosen triangular whereas the output membership functions are singleton. We note here that the triangular membership functions for the input variables are taken for their simplicity. The singleton parameters are taken equal to the kpz and kdz values (for example: B = 51, M = 50 and S = 49 (see fig. 6)). After several tests, identical method is adopted for the membership output of the second regulator of kdz tuning. Five fuzzy values are selected for linguistic expression of s, e and e inputs of the controllers: BN, MN, ZE, MP and BP. Big negative is represented as NB, medium negative as NM, zero as ZE, medium positive as PM and big positive as PB. For linguistic expression of outputs kpz and kdz of the controller, three fuzzy values are selected: B, M, and S. Big are represented as B, medium as M and small as s.

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With the fuzzy implications, kpz and kdz have become nonlinear switched parameters, and the fuzzy inference mechanism can therefore replace the hard switching law generated by the ‘if’ conditioning of the adaptive PD-sliding mode controller. This new smooth nonlinear switching of the parameters of the sliding mode control works in such way that when (s and e) are in the positive direction kpz has a positive value (red sub-tables) and when (s and e) are in the negative sense, kpz has a negative value (blue sub-tables). And for the second parameter kdz, the same logic is used to generate its values using s and e as inputs variables. The resulting rule bases for the two output variables (kpz and kdz) are presented in Table I. Likewise, the same design method has been applied for the other controller of translation (x and y) and rotational positions (θ, f and ψ). All these controllers have the same membership functions for the input variables (s, e and e ) as shown in Fig. 6 and Fig. 7. However, their membership functions for the output variables can take different values as shown in Figs. 8-12. d dt

19.62

K pz ez + K dz

dez dt

k ⋅ sat (s ξ )

u1 − mg Model along z

Fig. 5. Basic structure of the proposed adaptive Fuzzy-PD-SMC for quadrotor trajectories tracking (in z direction)

Fig. 6. Membership functions of the surface s, error e and variable kpz

4. Simulation Results In order to verify the validity and the effectiveness of the proposed adaptive fuzzy-PD sliding mode controller, the designed controller has been tested for quadrotor trajectory tracking by numerical simulation using Matlab/Simulink software. The model parameters values of the quadrotor are given in table 2. Articles

Journal of Automation, Mobile Robotics and Intelligent Systems

Fig. 7. Membership functions of s, e and variable kdz

Fig. 8. Membership function of output variable kpz /kdz

Fig. 9. Membership functions of output variable kpz /kdz

A chosen trajectory, arc curves, is performed for the quadrotor to illustrate the operation of the proposed control scheme and its robustness against external disturbances. The performances of adaptive PD-sliding mode controller are compared with the Articles

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Fig. 10. Membership functions of output variable kpθ /kdθ

Fig. 11. Membership functions of output variable kpf /kdf

Fig.12. Membership function of outputvariable kpψ /kdψ performances of the adaptive fuzzy PD-Sliding mode controller. To test the robustness of the controllers for arc curve tracking, the simulation has been done con-

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sidering an external disturbance as wind influence along all directions (Fz = 2N at 15s, Fx = 1.5N at 25s and Fy = 2N applied at 40s). Inaddition, the desired ψ has been fixed at p/3. Tab. 1. Fuzzy rulesof kpz, kdz e s BN

MN ZE

Tab. 2. Quadrotor model parameters

Parameter

Value

Units

Ixx

2224931 × 10–7

Kg ⋅ m2

325130 × 10–7

Kg ⋅ m2

Iyy Ixx Ixx KM

0.23

222611 × 10–7 10–5

9 × 10–6

Kg ⋅ m2 N ⋅ s2

N ⋅ s2 ⋅ m

Fig. 14. Tracking errors according to (z, x, y) directions in case of the AF-PD-SMC, A-PD-SMCand SMC application

Fig. 13 shows the flying trajectory of the quadrotor stabilizing for arc curves tracking in case of adaptive fuzzy PD-sliding mode and adaptive fuzzy PD-Sliding mode control application. In this figure, the quadrotor flying response of the proposed controllers is clearly observed to present good performance for trajectory tracking and more robustness (minimal steady-state error against load force application). The errors on translation displacement positions in (x, y and z) directions and rotational positions (θ and f) of the quadrotor are shown in Fig. 14 and Fig. 15 respectively, for the two types applied controllers (APD-SMC and AF-PDSMC). It should be noted that, with the two proposed control scheme, the displacement errors converge to zero. However, we can note here that the proposed adaptive fuzzy-PD-Sliding mode controller presents good transient performances and it’s more robust than the adaptive PD-Sliding mode controller for trajectory tracking (i.e. minimal error tracking). From Fig. 14, we observe that rotational positions (θ and f)

Fig. 15. The Pitch, Roll and Yaw angles (θ, f, ψ) of the quadrotor for the AF-PD-SMC, A-PD-SMCand SMC Fig. 13. Response of quadrotor for arc curves tracking trajectory with A-PD-SMC and AF-PD-SMC

are converging to desired values (i.e. zero) after some transient affectation during transient variation on the directions which prove the stabilization of the quadroArticles

Journal of Automation, Mobile Robotics and Intelligent Systems

Fig. 16a. Variation in proportional gains values of the equivalent control laws (translational subsystem)

Fig. 16b. Variation in proportional gains values of the equivalent control laws (rotational subsystem)

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Fig. 17a. Variation of the derivative gains values of the equivalent control laws (translational subsystem)

Fig. 17b. Variation of the derivative gains values of the equivalent control laws (rotational subsystem)

Journal of Automation, Mobile Robotics and Intelligent Systems

tor along all directions. Moreover, Fig. 16 depicts the proportional gains of the different equivalent control laws kpx, kpy, kpz, kpθ, kpf whereas Fig. 16 shows the derivative gains kdx, kdy, kdz, kdθ, kdf for the two types applied controllers (A-PD-SMC and AF-PD-SMC). From Fig. 16 and Fig. 17, it can be observed that the adaptive fuzzyPD-SMC has lower value gains in comparison with the adaptive PD-SMC. In addition, we can notice that these gains vary smoothly in nonlinear form for the AF-PDSMC whereas they vary as a signum function for the A-PD-SMC. This performance allowed the proposed controller to reduce the chattering phenomenon with good transient tracking errors. In addition, it has been exploited to mitigate the variation caused by external disturbances. The control input signals (u3, u4, u5 and u6) are illustrated in Fig. 18. We notice that the inputs u4 and u5 converge to zero in steady-state after the quadrotor stabilization to its desired orientation. Furthermore, we notice here that the control inputs (u3, u4, u5 and u6) have minimal values and smooth signal in AF-PD-SMC compared to those in case of A-PD-SMC (see zoomed responses in Fig. 18).

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5. Conclusion In this paper, we have demonstrated the application of a novel hybrid adaptive fuzzy based PD sliding mode controller for stabilization and trajectories tracking of a quadrotor rotorcraft. The main control objective of the proposed controllers is to allow the quadrotor to track desired trajectories under external disturbance variation. First, dynamical model of the quadrotor has been developed and presented using Euler-Lagrange formulation. Then, an adaptive PD-Sliding mode controller was studied and developed for quadrotor control and stabilization. After that, fuzzy logic controllers have been introduced for designing a robust and adaptive PD-sliding mode control for trajectory tracking of the quadrotor. The combination between fuzzy logic and adaptive PD-sliding mode control has been successfully implemented and simulation. This combination allowed us to improve the control performance of the quadrotor and provide more robustness regarding to the external disturbance variation. The simulation results shown clearly that the proposed AFPDSM controller provides high precision trajectory tracking and good stabilization performance can be achieved enabling the rotorcraft to stabilize on desired values. Note also that the values of the amplitudes and periods of the AF-PD-SMC controller’s coefficients vary according to the amplitudes and periods of the applied signals, whereas the A-PD-SMC controller’s coefficients vary in period and the amplitudes remain fixed. These variations ensure a good follow-up of the trajectories.

AUTHORS

Lahcen Simoud – Smart-Grids and Renewable Energies Laboratory, University of Tahri MohammedBéchar, Algeria.

Boufeldja Kadri – Smart-Grids and Renewable Energies Laboratory, University of Tahri MohammedBéchar, Algeria. Ismail Khalil Bousserhane* – Smart-Grids and Renewable Energies Laboratory, University of Tahri MohammedBéchar, Algeria, e-mail: bou_isma@yahoo.fr. * Corresponding author

References

Fig. 18. Control effort signals for the two types of controllers AF-PD-SMC and A-PD-SMC

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[3] P. Castillo, A. Dzul and R. Lozano, “Real-time stabilization and tracking of a four-rotor mini rotorcraft”, IEEE Transactions on Control Systems Technology, vol. 12, no. 4, 2004, 510–516, DOI: 10.1109/TCST.2004.825052. [4] T. Hamel, R. Mahony, R. Lozano and J. Ostrowski, “Dynamic Modelling and Configuration Stabilization for an X4-Flyer”, IFAC Proceedings Volumes, vol. 35, no. 1, 2002, 217–222, DOI: 10.3182/20020721-6-ES-1901.00848.

[5] T. Madani and A. Benallegue, “Control of a Quadrotor Mini-Helicopter via Full State Backstepping Technique”. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, USA, 2006, 1515–1520, DOI: 10.1109/CDC.2006.377548.

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[10] Z. Fang, Z. Zhi, L. Jun and W. Jian, “Feedback linearization and continuous sliding mode control for a quadrotor UAV”. In: 2008 27th Chinese Control Conference, Kunming, Yunnan, China, 2008, 349–353, DOI: 10.1109/CHICC.2008.4605334.

[11] S. Bouabdallah and R. Siegwart, “Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor”. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005, 2247–2252, DOI: 10.1109/ROBOT.2005.1570447. [12] M. A. Mohd Basri, A. R. Husain and K. A. Danapalasingam, “Enhanced Backstepping Controller Design with Application to Autonomous Quadrotor Unmanned Aerial Vehicle”, Journal of Intelligent & Robotic Systems, vol. 79, no. 2, 2015, 295–321, DOI: 10.1007/s10846-014-0072-3. [13] K. M. Zemalache, L. Beji and H. Maaref, “Control of a drone: study and analysis of the robustness”, Journal of Automation, Mobile Robotics and Intelligent Systems, vol. 2, no. 1, 2008, 33–42. 24

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[25] Y. Li, K. C. Ng, D. J. Murray-Smith, G. J. Gray and K. C. Sharman, “Genetic algorithm automated approach to the design of sliding mode control systems”, International Journal of Control, vol. 63, no. 4, 1996, 721–739, DOI: 10.1080/00207179608921865.

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Active Power Loss Reduction by Novel Feral Cat Swarm Optimization Algorithm Submitted: 16th May 2019; accepted: 3rd April 2020

Kanagasabai Lenin

DOI: 10.14313/JAMRIS/2-2020/16 Abstract: In this paper Feral Cat Swarm Optimization (FCS) Algorithm is proposed to solve optimal reactive power problem. Projected methodology has been modeled based on the activities of the feral cats. They have two main phases primarily “seeking mode”, “tracing mode”. In the proposed FCS algorithm, population of feral cats are created and arbitrarily scattered in the solution space, with every feral cat representing a solution. Produced population is alienated into two subgroups. One group will observe their surroundings which come under the seeking mode and another group moving towards the prey which will come under the tracing mode. New-fangled positions, fitness functions will be calculated subsequent to categorization of feral cats for seeking mode and tracing mode, through that cat with the most excellent solution will be accumulated in the memory. Feral Cat Swarm Optimization (FCS) Algorithm has been tested in standard IEEE 30 bus test system and simulation results show the projected algorithm reduced the real power loss considerably. Keywords: optimal reactive power, Transmission loss, Feral Cat Swarm Optimization Algorithm

1. Introduction React i ve power problem plays a significant role in secure and economic operations of power system. Various methods [1-6] have been utilized to solve the optim a l reactive power problem. Nevertheless several scientific difficulties are found due to an assortment o f constraints. Evolutionary techniques [7-16] are applied to solve the reactive power problem. This paper proposes Feral Cat Swarm Optimization (FCS) Algorithm to solve optimal reactive power problem. Proposed approach has been modeled based on the deeds of the feral cats. They had two phases called as “s e eking mode”, “tracing mode”. In the projected FCS a l gorithm, population formed and capriciously dispersed in the solution space, with every feral cat symbo l ize a solution. Engendered population is alienated into two subgroups. One group will keep an eye o n their surroundings which comes under the seeki n g mode and another group moving towards

the prey which comes under the tracing mode. Subsequent to discovery of the prey although in latent mode (seek i ng mode), feral cat make a decision for quick movem e nt and a way based on the prey’s location and progression. Normally cats use diminutive time in tracing mode, so in the subgroup of tracing mode must b e small. By means of the mixture ratio (MR) it ha s been defined. New-fangled positions, fitness functions will be calculated subsequent to categorization of feral cats for seeking mode and tracing mode, through that cat with the most excellent solution will be accumulated in the memory. Until the end criterion reached these steps are repeated. Proposed Feral Cat Swarm Optimization (FCS) Algorithm has been tested in standard IEEE 30 bus test system and simulation results show the projected algorithm reduced the real power loss effectively.

2. Problem Formulation Reduction real power loss is the objective function of the problem and mathematically written as

F == PL Σ( k∈Nbr ) gk (Vi2 + V j2 − 2ViV j cosθ ij ) (1) with reference to voltage deviation it has been written as F = PL + ωv × Voltage Deviation (2) Npq

∑ Vi − 1

Voltage Deviation =

Constraint (Equality)

i =1

P= PD + PL G Constraints (Inequality)

min max Pgslack ≤ Pgslack ≤ Pgslack

Q gimin ≤ Q gi ≤ Q gimax , i ∈ N g Vi

min

≤ Vi ≤ Vi

min

≤ Ti ≤ Ti

Qcmin

max

, i ∈N

, i ∈ NT

≤ Qc ≤ QCmax ,

i ∈ NC

(3) (4)

(5)

(6) (7) (8) (9)

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3. Feral Cat Swarm Optimization Algorithm Feral Cat Swarm Optimization (FCS) Algorithm has been modeled based on the deeds of the feral cats. They had two phases mainly “seeking mode”, “tracing mode”. In the projected FCS algorithm, population of feral cats are formed and capriciously dispersed in the s o lution space, with every feral cat indicating a solution. Engendered population is alienated into two subgroups; one group will keep an eye on their surroundings which comes under the seeking mode and another group moving towards the prey which come under the tracing mode. Normally cats use diminutive time i n tracing mode, so in the subgroup of tracing mode m ust be small. By means of the mixture ratio (MR) it has been defined [17]. New-fangled positions, fitness functions will be calculated subsequent to categorization of feral cats for seeking mode and tracing mode, through that cat with the most excellent solution will be accumulated in the memory. Until the end criterion reached these steps are repeated. Seeki n g Mode; During this mode the feral cat is resting condition but keeping an eye on the surroundings. Feral cat make a decision for its subsequent move when there is any danger or prey found. Four param e ters are used in the modeling [17]: seeking memor y pool (SMP; sum of the copies organized of every cat in the seeking procedure), seeking range of the selected dimension (SRD; highest difference between the new-fangled and old values in the dimension c hosen for mutation), counts of dimension to change (CDC; number of dimensions will be mutated), and self-position consideration (SPC; Boolean variable which point out the present position of the cat as a candidate position for movement) [17]. Step a . Construct SMP replica of each feral cati. When S PC has true value, SMP-1 copies are formed and present position of the feral cat be as one among the copies made. Step b. With reference to CDC compute a new-fangled position for each copy by the following equation,

Ycn = (1 ± SRD × R ) × Yc (10) Ycn – indicate the new fangled position; Yc – present positions; R – random number.

Step c . Calculate the fitness values (FS) for new-fangled positions. For all candidate points When FS values are precisely equal for all then fix selecting probability as 1. Or else compute the selecting probability of every candidate point by using Equation (11). Step d . By utilizing roulette wheel, arbitrarily choos e the point to shift from the candidate points, and swap the position of feral cati. FS i − FS b

= Pi FS maximum − FS minimum

0<i < j

(11)

Pi – probability of present candidate feral cati; FSi – feral cati fitness value; FSmax fitness function maximum value; FSmin fitness function minimum value; Articles

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FSb = FSmax for optimal reactive power problem (minimization problem) Tracing Mode; it simulates action of the feral cat hunting the prey. Subsequent to discovery of the prey altho u gh in latent mode (seeking mode), feral cat make a decision for movement speed and way based on the prey’s location and speed vlk ,d= vlk ,d + r1 × c1 (Ybest ,d − Yk ,d )

(12) By means of velocity, the feral cat progress in the decision space and it informs about each new-fangled position it acquires. When the velocity of the feral cat is superior to the highest velocity- it will be fixed as maximum velocity. Then the new-fangled position of each feral cat is calculated by

Yk= Yk ,d ,old + vlk ,d ,d ,new

(13)

A new - fangled modified search equation is projected for tracing mode

Yk ,d ,new = (1 − β ) * Yk ,d + β * Pg + vlk ,d (14) Yk,d,new – Most excellent position attained by kth cat in dth dimension, Yk,d – present position of the kth cat in dth dimension, vlk,d old velocity of the kth cat. To perk up the diversity of the projected algorithm, parti c ularly in tracing mode, a new-fangled velocity modernized equation is proposed as,

Yk ,d ,new = vlk ,d + β ( Pg − Yk ,d ) + α * ε (15) α and β perform as control parameters to balance the exploration and exploitation procedure

α max − α min  *t t max  

α= (t ) α max − 

 πt    t max 

β ( t ) =β min + ( β max − β min ) sin 

(16) (17)

In th i s projected algorithm local search method has been implemented in order to direct the exploring direction and to attain the optimum solution in exploration space. Local optima problem has been avoided by collecting the neighborhood information. Exploring mechanism is employed to the present global best solut i on (Ygbest), and then the neighborhood of best solution can be described by n

(18) Ygb  =Ygbest − r ,Ygbest + r  r – boundary of neighborhood, Ygb – present most excellent solution, n – population number

Local search method will go to all N number of populations in all iterations

 Y L k −1 d ≠ L L (19) Ygb ( k ) = Y L ( kgb−(1) + r )* cx d d = L gb  Most e xcellent agent during the exploration can be selected in all iterations by

1 Ygb ( k ) = Minimum{Ygb ( k ) ,...,YgbL ( k ) ,...,Ygbn ( k )}

(20)

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Procedure of Feral Cat Swarm Optimization Algorithm

Step 1. Engender the preliminary population of feral cats and scatter them in the solution space (yi,d) and capriciously allocate velocity in the range to maximum velocity value vli,d for each feral cat. Step 2. Allocate a flag to each feral cat in order to sort them into the seeking, tracing phase assign each cat a flag to sort them into the seeking or tracing mode process with reference to the mixture ratio (MR). Step 3. By computation of the fitness value of each feral cat then the feral cat with most excellent fitness function is found and it will be saved. Position of the most excellent cat (Ybest) symbolizes the most excellent solution so far obtained. Step 4. Apply the cats into the seeking, tracing phase based on their flags. Step 5. Employ the Local search procedure Step 6. modernize the position of feral cats and global position Step 7. If the end criteria is satisfied, then stop the procedure or else replicate the step from 2 to 5. Commence Initialization of the parameters Feral cat population, SPC are initialized While (end criterion is not reached or I < Imax) For all feral cats compute the fitness function values and classify them = feral cat with the most excellent solution For = 1: N If SPC = 1 then commence the seeking mode Or Else commence the tracing mode Apply the Local search procedure Renew the position of feral cats and global position End if End for “i" End while Output the results End

4. Simulation Study Feral Cat Swarm Optimization (FCS) Algorithm has been tested in standard IEEE 30 Bus system [18]. Table 1 shows the constraints of control variables, Table 2 shows the limits of reactive power generators and comparison results are presented in Table 3. Figure 1 gives the Comparison of real power loss and Figure 2 gives the Reduction of real power loss (%) with reference to base case value.

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Tab. 2. Constrains values of the reactive power generators System type

List of Variables

Value of Q Minimum (PU)

Value of Q Maximum (PU)

-40

-10

IEEE 30 Bus

-40

40 40

-6

Tab. 3. Simulation results of IEEE − 30 system List of Control variables

Base case value

MPSO [19]

PSO [19]

EP [19]

SARGA [19]

FCS

1.045

1.101

1.086

1.100

1.072

NR*

1.097

NR*

1.094

1.018

1.010

1.057

1.048

1.033

1.053

1.059

1.010

VG−1

1.060

VG−5

1.010

VG−2 VG−8

VG−12

1.082

Tap-11

0.978

Tap-15

0.932

QC-10

0.19

VG-13

1.047

1.048

1.038

1.049

1.039

1.018

1.058

1.092

1.099

1.027

0.987

1.01

0.99

0.940

1.071

1.068

1.080

0.969

1.023

1.015

0.968

0.988

1.012

QC-24

0.043

0.119

0.128

QG (Mvar)

133.9

130.83

130.94

NR*

130.27

8.4

7.4

6.6

8.3

19.18

17.55

16.07

16.25

16.38

16.09

14.183

Tap-12 Tap-36

PG (MW)

Reduction in PLoss (%) Total PLoss (Mw)

300.9

NR* – Not reported.

0.983 1.020

0.077 299.54

1.091 1.03

1.099 1.03

1.020

1.07

0.98

0.077

0.19

0.99 0.04

299.54

NR*

0.96 0.04 NR*

1.032 0.911 0.904 0.916 0.094 0.108

298.19

Tab. 1. Constraint values of the control variables System type

IEEE 30 Bus

List of Variables

Minimum value (PU)

Maximum value (PU)

Transformer Tap

0.9

1.1

Generator Voltage VAR Source

0.95 0

1.1

0.20

Fig. 1. Comparison of real power loss Articles

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IEEE Transactions on Power Systems, vol. 5, no. 4, 1990, 1447–1454, DOI: 10.1109/59.99399.

[4] S. Granville, “Optimal reactive dispatch through interior point methods”, IEEE Transactions on Power Systems, vol. 9, no. 1, 1994, 136–146, DOI: 10.1109/59.317548. [5] N. Grudinin, “Reactive power optimization using successive quadratic programming method”, IEEE Transactions on Power Systems, vol. 13, no. 4, 1998, 1219–1225, DOI: 10.1109/59.736232. Fig. 2. Reduction of real power loss (%) with reference to base case value

5. Conclusion In this work optimal reactive power problem has been solved by Feral Cat Swarm Optimization (FCS) Algorithm in efficient mode. In the projected FCS algorithm, population of feral cats are formed and capriciously dispersed in the solution space, with every feral cat indicated a solution. New-fangled positions, fitness functions will be calculated subsequent to categorization of feral cats for seeking mode and tracing mode, through that cat with the most excellent solution will be accumulated in the memory. Proposed Feral Cat Swarm Optimization (FCS) Algorithm has been tested in standard IEEE 30 bus test system and simulation results show the projected algorithm reduced the real power loss considerably. Around 19.18 % reduction of real power loss have been attained.

AUTHOR Kanagasabai Lenin – Department of Electrical and Electronics Engineering, Prasad V. Potluri Siddhartha Institute of Technology, Vijayawada, India, e-mail: gklenin@gmail.com.

References [1] K. Y. Lee, Y. M. Park and J. L. Ortiz, “Fuel-cost minimisation for both real-and reactive-power dispatches”, Transmission and Distribution IEE Proceedings C – Generation, Transmission and Distribution Conference, vol. 131, no. 3, 1984, 85–93, DOI: 10.1049/ip-c.1984.0012. [2] N. I. Deeb and S. M. Shahidehpour, “An Efficient Technique for Reactive Power Dispatch Using a Revised Linear Programming Approach”, Electric Power Systems Research, vol. 15, no. 2, 1988, 121–134, DOI: 10.1016/0378-7796(88)90016-8.

[3] M. Bjelogrlic, M. S. Calovic, P. Ristanovic and B. S. Babic, “Application of Newton's optimal power flow in voltage/reactive power control”, Articles

[6] R. Ng Shin Mei, M. H. Sulaiman, Z. Mustaffa and H. Daniyal, “Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique”, Applied Soft Computing, vol. 59, 2017, 210–222, DOI: 10.1016/j.asoc.2017.05.057. [7] G. Chen, L. Liu, Z. Zhang and S. Huang, “Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints”, Applied Soft Computing, vol. 50, 2017, 58–70, DOI: 10.1016/j.asoc.2016.11.008.

[8] E. Naderi, H. Narimani, M. Fathi and M. R. Narimani, “A novel fuzzy adaptive configuration of particle swarm optimization to solve large-scale optimal reactive power dispatch”, Applied Soft Computing, vol. 53, 2017, 441–456, DOI: 10.1016/j.asoc.2017.01.012. [9] A. A. Heidari, R. Ali Abbaspour and A. Rezaee Jordehi, “Gaussian bare-bones water cycle algorithm for optimal reactive power dispatch in electrical power systems”, Applied Soft Computing, vol. 57, 2017, 657–671, DOI: 10.1016/j.asoc.2017.04.048. [10] N. R. H. Abdullah, M. Morgan, M. Mustafa, R. Samad and M. H. Sulaiman, “Benchmark studies on Optimal Reactive Power Dispatch (ORPD) Based Multi-Objective Evolutionary Programming (MOEP) using Mutation Based on Adaptive Mutation Operator (AMO) and Polynomial Mutation Operator (PMO)”, Journal of Electrical Systems, vol. 12, 2016, 121–132. [11] R. N. S. Mei, M. H. Sulaiman and Z. Mustaffa, “Ant lion optimizer for optimal reactive power dispatch solution”, Journal of Electrical Systems – Special Issue AMPE2015, 2016, 68–74.

[12] P. Anbarasan and T. Jayabarathi, “Optimal reactive power dispatch problem solved by symbiotic organism search algorithm”. In: 2017 Innovations in Power and Advanced Computing Technologies (i-PACT), 2017, DOI: 10.1109/IPACT.2017.8244970.

[13] A. Gagliano and F. Nocera, “Analysis of the performances of electric energy storage in residential applications”, International Journal of Heat and Technology, vol. 35, Special Issue 1, 2017, S41–S48, DOI: 10.18280/ijht.35Sp0106.

[14] M. Caldera, P. Ungaro, G. Cammarata and G. Puglisi, “Survey-based analysis of the electrical

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energy demand in Italian households”, Mathematical Modelling of Engineering Problems, vol. 5, no. 3, 2018, 217–224, DOI: 10.18280/mmep.050313.

[15] M. Basu, “Quasi-oppositional differential evolution for optimal reactive power dispatch”, International Journal of Electrical Power & Energy Systems, vol. 78, 2016, 29–40, DOI: 10.1016/j.ijepes.2015.11.067.

[16] G.-G. Wang, S. Deb and Z. Cui, “Monarch Butterfly Optimization”, Neural Computing and Applications, vol. 31, 2015, 1995–2014, DOI: 10.1007/s00521-015-1923-y. [17] P. Mohapatra, S. Chakravarty and P. K. Dash, “Microarray medical data classification using kernel ridge regression and modified cat swarm optimization based gene selection system”, Swarm and Evolutionary Computation, vol. 28, 2016, 144–160, DOI: 10.1016/j.swevo.2016.02.002.

[18] “Power Systems Test Case Archive”. University of Washington, Electrical & Computer Engineering – Richard D. Christie, https://labs.ece.uw.edu/ pstca/. Accessed on: 2020-08-09. [19] A. N. Hussain, A. A. Abdullah and O. M. Neda, “Modified Particle Swarm Optimization for Solution of Reactive Power Dispatch”, Research Journal of Applied Sciences, Engineering and Technology, vol. 15, no. 8, 2018, 316–327, DOI: 10.19026/rjaset.15.5917.

Articles

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Preface to Special Issue on Recent Advances in Machine Learning and its Applications

DOI: 10.14313/JAMRIS/2-2020/17 This special issue of the Journal of Automation, Mobile Robotics and Intelligent Systems (JAMRIS) is aimed to inform the readers about selected issues of contemporary Computer Science, in particular, Machine Learning in both theoretical and practical aspects. The papers contained in this issue of the journal have been introduced in their preliminary version between 2-5 July, 2018, during the 3rd Conference on Information Technology, Systems Research and Computational Physics (ITSRCP’18), as well as the 6th International Symposium CompIMAGE’18 – Computational Modeling of Objects Presented in Images: Fundamentals, Methods, and Applications (CompIMAGE’18), which were organized by the Faculty of Physics and Applied Computer Science of the AGH University of Science and Technology and co-organized by the Systems Research Institute of the Polish Academy of Sciences in Warsaw, Poland. The idea behind this second special edition volume was to create a specific section containing a number of interesting cutting edge scientific articles. Inside, one can find contributions dealing with computational algorithms, data mining, classification, time series analysis, as well as some aspects of image analysis. The contributions raise problems of well-known machine learning methods such as fuzzy logic, wavelet analysis and neural networks. The previous special issue of JAMRIS, which was dedicated selected aspects of Contemporary issues of Computer Science, Physics, Economy and Applied Mathematics, was published in vol. 13 no. 3 in 2019. This issue contains the following original papers in their special, extended versions. The first paper is entitled On Wavelet based Enhancing Possibilities of Fuzzy Classification Methods, and was authored by Ferenc Lilik, Levente Solecki, Brigita Sziová, László T. Kóczy, Szilvia Nagy. It introduces a new class classifier based on synergy of fuzzy logic and wavelet analysis. Some computational examples of two fuzzy classification schemes to show the improvement caused by wavelet analysis are also discussed. Maciej Pachocki and Anna Wróblewska, in their work entitled Categorization of Persons based on their Occurrences in Polish News Texts, provide a method of categorizing the occurrences of persons in Polish news texts. Based on the statistical evaluation and in accordance with tests that were conducted on own and chosen solutions from literature, and by applying the use of six classifiers, a new model based on the categorization method was suggested and numerically verified.

The work entitled Supporting Decisions on the Forex Market Using Fuzzy Approach, by Przemysław Juszczuk and Lech Kruś, proposed a new conceptualization of the multi-criteria fuzzy trading system using technical analysis. The proposed system treats all considered indicators jointly through applying the multi-criteria approach wherein binary information is extended with the use of the fuzzy approach. An experimental comparison of the proposed method, with the traditional crisp trading system, was shown. Herein, the numerical testing procedure is based on different sets of real-world data for different types of trading: short-term, medium and long-term. Sergii Nikolaiev, Sergii Telenyk and Yury Tymoshenko authored the paper Non-contact Video-based Remote Photoplethysmography for Human Stress Detection. In this paper, the authors present the experimental results for a stress index calculation using information technology developed by the authors for non-contact remote human heart rate variability (HRV) retrieval under various conditions from a video stream using common date derived from wide-spread web cameras with minimal frame resolution of 640x480 pixels at average frame rate of 25 frames per second. The use-cases of measuring stress index in a wide variety of situations starting with vehicle operators at work, and finishing with students passing exams, are presented and analyzed in detail. The results of the experiments show that the rPPG system is capable of deriving stress level data that is in accordance with the actual feelings of the experiments’ participants.

The paper entitled Radon-Wavelet based Novel Image Descriptor for Mammogram Mass Classification was written by the team consisting of Sk Md Obaidullah, Sajib Ahmed, Teresa Goncalves and Luis Rato. The article is devoted to the analysis of a very important issue – that of classifying mammogram images. For this issue, some machine learning tools are proposed, but in the paper before the reader, a novel image descriptor that is based on the idea of radon and wavelet transform is put-forward. The performance of the method is subsequently evaluated by way of applying six different classifiers namely: Bayesian network, linear discriminant analysis, logistic, support vector machine, multilayer perceptron and random forest so as to choose the best outcomes. What is interesting, the

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experimental results show the highest accuracy for the proposed solution when using only the carniocaudal view, as compared to when using only the mediolateral oblique or combining both approaches.

Himadri Mukherjee, Sk Md Obaidullah, K.C. Santosh, Teresa Goncalves, Santanu Phadikar and Kaushik Roy, in their work entitled Segregation of Songs and Instrumentals – a Precursor to Voice/Accompaniment Separation from Songs in Noisy Scenario, provide a system to be first able to detect whether a piece of music contains vocals or not prior to attempting source separation. In this work, the Authors were challenged to perform source separation from audio that is contaminated with noise. Included in the work are some computational examples based on a database of more than 99 hours of instrumentals and songs wherein six different classifiers were applied during tests and which show the proper and high quality results of the proposed methodology.

In a contribution entitled The Method of Selecting the Interval of Functional Tests, Taking into Account Economic Aspects and Legal Requirements written by Jan Piesik, Emilian Piesik and Marcin Ś� liwiński, some discussion is made on the problem of choosing the optimal frequency of functional tests, bearing in mind reliability and legal requirements, but also the impact of business aspects. Here, the authors propose a solution for selecting the interval of functional tests of safety elements and the necessity for additional machine protection measures as a compromise to achieve satisfactory results in terms of safety, performance and legal requirements. Finally, Kata Vöröskői, Gergő Fogarasi, Adrienn Buruzs, Péter Földesi, László T. Kóczy, provide a paper entitled Three Level Fuzzy Signature-Based Decision Methodology for Packaging System Design. The study focuses upon three different fuzzy signatures connected by fuzzy rules modelling the packaging-choice decisions as based on logistics expert opinions, in order to support the decision making process of choosing the right packaging system. Two real life examples are also given, one in the field of customer packaging and one in industrial packaging. We would like to thank all those who participated in, and contributed to the Conference program, as well as all the authors who had submitted their papers. We also wish to thank all our colleagues and the members of the Program Committee, both for their hard work during the review process and for their cordiality and outstanding efforts in the local organization of the Conference. Editors: Piotr A. Kowalski Systems Research Institute, Polish Academy of Sciences and Faculty of Physics and Applied Computer Science, AGH University of Science and Technology Szymon Łukasik Systems Research Institute, Polish Academy of Sciences and Faculty of Physics and Applied Computer Science, AGH University of Science and Technology Piotr Kulczycki Systems Research Institute, Polish Academy of Sciences and Faculty of Physics and Applied Computer Science, AGH University of Science and Technology

Articles

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ON WAVELET BASED ENHANCING POSSIBILITIES OF FUZZY CLASSIFICATION METHODS Submitted: 20th October 2018; accepted: 2nd June 2020

Ferenc Lilik, Levente Solecki, Brigita Sziová, László T. Kóczy, Szilvia Nagy DOI: 10.14313/JAMRIS/2‐2020/18 Abstract: If the antecedents of a fuzzy classification method are derived from pictures or measured data, it might have too many dimensions to handle. A classification scheme based on such data has to apply a careful selection or processing of the measured results: either a sampling, re‐ sampling is necessary. or the usage of functions, transfor‐ mations that reduce the long, high dimensional observed data vector or matrix into a single point or to a low num‐ ber of points. Wavelet analysis can be useful in such cases in two ways. As the number of resulting points of the wavelet ana‐ lysis is approximately half at each filters, a consecutive application of wavelet transform can compress the me‐ asurement data, thus reducing the dimensionality of the signal, i.e., the antecedent. An SHDSL telecommunication line evaluation is used to demonstrate this type of appli‐ cability, wavelets help in this case to overcome the pro‐ blem of a one dimensional signal sampling. In the case of using statistical functions, like mean, variance, gradient, edge density, Shannon or Rényi en‐ tropies for the extraction of the information from a pic‐ ture or a measured data set, and they don not produce enough information for performing the classification well enough, one or two consecutive steps of wavelet analy‐ sis and applying the same functions for the thus resulting data can extend the number of antecedents, and can dis‐ till such parameters that were invisible for these functi‐ ons in the original data set. We give two examples, two fuzzy classification schemes to show the improvement caused by wavelet analysis: a measured surface of a com‐ bustion engine cylinder and a colonoscopy picture. In the case of the first example the wear degree is to be deter‐ mine, in the case of the second one, the roundish polyp content of the picture. In the first case the applied statisti‐ cal functions are Rényi entropy differences, the structural entropies, in the second case mean, standard deviation, Canny filtered edge density, gradients and the entropies. In all the examples stabilized KH rule interpolation was used to treat sparse rulebases. Keywords: Fuzzy classification, wavelet analysis, fuzzy rule interpolation, structural entropy

1. Introduction

32 32

Real‑life control or classi�ication problems are of‑ ten solved by fuzzy methods, as fuzzy inference is usu‑ ally practically more ef�icient, �lexible and close to the human way of thinking than classical, crisp decision schemes. As the digital measuring and picture taking

devices become more and more widespread, the me‑ asured data becomes larger, contains more informa‑ tion bout the measured or photographed objects, but most of the such acquired information disturbs an automatic control or classi�ication scheme. For trai‑ ning a neural network or other, nature based learning method, however, very large number of measurement with time and resource consuming pre‑processing is often needed, thus in some cases it is not possible to use them. Digital measuring devices sample either in time, like in the case of an oscilloscope or temperature monitoring system; in frequency, like in the case of spectrum analysers; or in space, like in the case pictu‑ res or 3D scanners. The results of such measurements often consist of several hundreds or thousands or even millions of points, but such large data sets are not suit‑ able for serving as the antecedent set for a fuzzy deci‑ sion or classi�ication scheme. The measured data has to be made processable by a fuzzy inference system of reasonable size and complexity, mostly by decreasing the amount of data with the condition of keeping as much information as possible. The simplest step to achieve this may be re‑ sampling: selecting only a few from the measured va‑ lues as representatives of the whole data set. A more sophisticated method would be averaging. However, both lead to loss of information. From image and data compression it is well known that wavelets are suita‑ ble for distilling a lot of the available information and achieving a large compression ratio, thus it seems to be reasonable to try wavelet transform for achieving suitable compression rate as well as suf�iciently small information loss. In case of telecommunication line insertion loss over frequency functions, this method proved to be effective. Instead of wavelet‑based compression of the mea‑ surement results, its useful information content can be extracted by calculating statistical parameters, like its mean value, standard deviation, average gradient or gradient direction, some kind of shape‑related quan‑ tity or its entropy, or entropies, if Ré nyi’s generalisa‑ tion of the de�inition of entropy is used. In the case of pictures edge densities or colour elated parameters might be also necessary. Ré nyi’s generalised entropies can be combined into such quantities that characterise the shape or topology of the measured distribution, too, this step can map the measured data into a cou‑ ple of points. This scheme is useful especially in the case of two‑ or three‑dimensional measured data, as the number of measured points is usually too high, and

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Fig. 1. Crisp and fuzzy membership function of a measured variable the number of the remaining points is still too high af‑ ter wavelet‑based compression. In many cases, using only entropies, or other, similar functions leads to cri‑ tically high information loss, thus a method for regai‑ ning some of the information should be introduced. As the high‑pass �ilter outputs of the wavelet transform distill the �ine details from the original data and the low‑pass outputs behave as a kind of averaging, ap‑ plying the same functions – the previously mentioned statistical parameters and entropies – on the wavelet transformed versions of the images leads to other in‑ formation. This step can enhance the performance of an inference system without increasing the number of antecedents too much. This scheme proved to be ef�i‑ cient in signi�icantly increasing the effectiveness of a classi�ication scheme in surface roughness and colo‑ rectal polyp content characterisation. These two approaches are studied in the following considerations. As a �irst step, in Sec. 2a summary about fuzzy classi�ications is given completed with a section of fuzzy rule interpolation. Next the intro‑ duction of wavelet transforms is given in Sec. 3. Sec. 4 gives the generalization of the Shannon entropy and its use in the characterisation of shapes of functions or distributions. The applicability of the �irst approach is demonstrated in Sec. 5, and the usage of wavelet trans‑ form for increasing the information content is given in Sec. 6 and Sec. 7. A conclusions to be found in the last section.

2. The Fuzzy Component of the Approach 2.1. Fuzzy Sets

In set theory L.A. Zadeh came forth with a new con‑ cept in 1965. According to his idea [1], an element can not only be fully member of a set, or fully not mem‑ ber of it, but there can be in�inite many possibilities inbetween. This concept is closely related to the hu‑ man way of thinking, as there is a smooth transition between a tea being hot or cold, or a dog breed being small, medium‑sized or large. Zadeh’s fuzzy sets do not only allow membership values of exclusively 0 or 1 (like with the traditional, crisp sets), but any value in the [0, 1] unit interval. A measured value can have a membership degree in a fuzzy set, thus it also be‑ comes a fuzzy quantity, as it can be seen in Fig. 1 Ba‑ sed on such fuzzy sets, decisions can be made, like “IF

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the water level is low”, “THEN �ill the water tank with a small amount of water”, or “IF the temperature is high”, “THEN classify it to the highest class”. In the case of multiple conditions, like “IF the gasoline concentra‑ tion is high AND the pressure is high” it is necessary to re‑de�ine he operators “AND” and “OR”. Zadeh de�ined “AND” as the lowest of the membership values (called nowadays rather t‑norm), and “OR” as the highest (cal‑ led s‑norm or t‑conorm). 2.2. Fuzzy Inference

Using the fuzzy membership functions a rather �lexible control systems can be built. �amdani propo‑ sed [2] the �irst concept for carrying out fuzzy cont‑ rol (and decisions), which was a computationally more ef�icient implementation of the �ompositional Rule of Inference method also proposed by Zadeh [3]. His con‑ cept used multiple input variables, i.e., antecedents. For each of the outputs, i.e., consequents, he de�ined a set of rules, consisting of membership functions for all the antecedents. The consequent fuzzy set arises as the s‑norm (e.g., maximum) of the results for conse‑ quents, and the results for a consequent is the t‑norm (e.g., minimum) of the rules belonging to that conse‑ quent, as it can be seen in Fig. 2. The rules are generated from measured data, either using statistics or some intelligent learning al‑ gorithm. This means that there must be some measu‑ rements, where not only the antecedents, but also the consequents are known, moreover, it is useful to have such data for testing the inference system. In our ex‑ amples very simple rules are used: the membership function of each antecedent for each consequent is a triangle, with the minimum and maximum of the me‑ asured data forming the support of the membership function and the mean forming the core, the peak of the triangle, as seen in Fig. 3. 2.3. Fuzzy Rule Interpolation

In measurements it often happens that the rule‑ base does not completely cover the space of the pos‑ sible measured data, i.e., sparse rulebases are genera‑ ted. In this case, making the other measured data eva‑ luable can be carried out by rule interpolation. Stabi‑ lized KH interpolation [4], [5], [6] inf{Bα∗ } sup{Bα∗ }

∑2n (

1 dαL (A∗ ,Ai )

∑2n (

1 dαU (A∗ ,Ai )

i=1

∑2n ( i=1

i=1

∑2n

i=1

inf{Biα } (1) )k

1 dαL (A∗ ,Ai )

(

sup{Biα } ,(2) )k

1 dαU (A∗ ,Ai )

give very good results in our examples, too.

3. The Wavelet Component of our Approach Wavelet analysis [7] developed from several bran‑ ches of signal processing and numerical mathematics in the late 1970s‑early 1980s. Up till now its main use is image compression, from �ingerprint databases Articles

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µ1,1 1

µ y1

µ 2,1 A 1,1

0.5

µ1,2 1

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w1,1 x1

A 2,1

x µ 2,2

y1 µ y2

w1 w2

A 2,2 w2,2

µy

A 1,2

0.5 w1,2

w2,1

B∗ y∗

ydefuzz

w2 x2

Fig. 2. Mamdani’s fuzzy consequent from a two‐dimensional antecedent and two consequent sets. The rules are denoted by the membership values Ai,j of the variable xi , the consequent sets by Byj , and the final consequent set by B ∗ . The final consequent is usually defuzzified, thus one value ydefuzz becomes the result of the inference. Arbitrary units a grid of smaller grid distance, while the rougher re‑ solution levels have lower, wider basis functions over grids with larger grid distance, as it can be seen from the following de�initions of the basis functions at reso‑ lution level j and shift position k

ϕjk (x) = 2j/2 ϕ(2j x − k).

xmin

xaverage xmax

Fig. 3. A simple rule generation method from the measured values of the training set. The statistics of the measured data is represented by the histogram of the plot, while the resulting fuzzy rule by the triangle‐shaped membership function. Arbitrary units through the Mars rover [8] to the JPEG2000 image co‑ ding standard [9]. It is also possible to suppress noise, enhance edges, or retrieve special types of patterns from images by wavelet transform, moreover, simi‑ larly to Fourier transform [10], wavelets are used to simplifying differential equations, too [11].

These basis functions ϕjk of the embedded subspa‑ ces are called scaling functions. Wavelets are also similar basis functions: they pro‑ vide the way between two resolution levels. The spa‑ ces completing a rougher resolution level subspace to the next, �iner resolution subspace are the detail spa‑ ces, and their basis functions are the wavelets, de�ined as (4) ψjk (x) = 2j/2 ψ(2j x − k).

This subspace setup means, that any function of any resolution level j can be expressed either as a linear combination of its resolution level subspace, or using any rougher resolution level scaling function subspace as a basis, and adding wavelets to it as a re‑ �inement, i.e., as f [j] (x) =

3.1. Multiresolution Analysis

34 34

The discrete wavelet transform is mathematically de�ined by a so called multiresolution analysis of the function space, mostly the square integrable functi‑ ons’ Hilbert space. It consists of subspaces embedded into each other, each subspace belonging to a resolu‑ tion level, hence the name. The �inest resolution level subspace is dense in the original function space (i.e., to any function of the original function space to any li‑ mit there can bee found a function in the in�initely �ine resolution subspace that is closer than the limit). The lowest (in�initely low) resolution level consists of only constant functions. The most interesting part of this approach of the function space is that each subspace is expanded by a set of basis functions, which have the same shape, just shifted over a regular grid. The shape of the basis functions change from subspace to subspace, i.e., from resolution level to resolution level only by shrinking or dilation: the �ine resolution level subspaces have higher and narrower basis function distributed over Articles

(3)

∞ ∑

cjk ϕjk (x),

−∞

or by decreasing the basic resolution level by 1 as f [j] (x) =

∞ ∑

cj−1 k ϕj−1 k (x) +

−∞

∞ ∑

(5)

dj−1 k ψj−1 k (x),

−∞

(6) or by decreasing the rougher resolution level to zero, as f [j] (x) =

∞ ∑

c0k ϕ0k (x) +

j−1 ∑ ∞ ∑

dik ϕik (x),

i=0 −∞

−∞

(7)

Practically, measurement results can be treated as a very �ine resolution level coef�icient set of the sam‑ pled function, their wavelet transform results in the rougher resolution level scaling function and wavelet coef�icients by using the so called re�inement equation ϕ(x) = 21/2

Ns ∑ i=0

hi ϕ(2x − i),

(8)

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VOLUME 2020 VOLUME 14,14, N°N° 2 2 2020

the probabilities were equal. This approximation is still used if nothing is known about the probability dis‑ tributions, only the number of the possible outcomes. For α = 2 the formula turns into

c’i ci d’i

Fig. 4. One step of the wavelet transform as two branches of convolutional filter signal processing and downsampling steps. The low‐pass filter results in the scaling function expansion coefficients c′i , while the high‐pass filters give the fine details, i.e., the wavelet expansion coefficients d′i and its wavelet counterpart ψ(x) = 21/2

1 ∑

i=−Ns +1

(−1)i h−i+1 ϕ(2x − i).

(9)

For the simplest wavelet family, the so called Haar wa‑ velets [12], the coef�icients h0 = h1 , these mother ba‑ sis functions have a support length 1 unit; the other wavelets have more coef�icients, thus longer support. 3.2. Wavelet Analysis in Signal Processing

This mathematical de�inition can be translated to signal processing devices: practically the usage of (8) and (9) can be translated directly to digital signal pro‑ cessors as convolutional �iltering and downsampling, as it can be seen in Fig. 4. The coef�icients in the con‑ volutional �ilters are proportional to the coef�icients at the re�inement equations. In multiple dimension data sets either multiple dimension wavelets, or more often separate wavelet analysis steps in the separate dimensions has to be carried out.

4. Entropies as Compact Descriptions of Two‐ Dimensional Datasets

The entropy in information theory was introduced by Shannon [13] as the expectation value of the infor‑ mation for a complete set of events, i.e., for such sets, where all the events have probabilities between 0 and 1, and the sum of all the probabilities is 1. If the pro‑ babilities are {p1 , p2 , . . . , pN }, then the entropy can be written as N ∑ pi log2 pi . (10) S=− i=1

4.1. Rényi Entropies

Shannon’s entropy de�inition was generalised for many purposes, Ré nyi’s [14] series of entropies, i.e., Sα =

N ∑ 1 log pα i , 1−α i=1

(11)

gives the Shannon entropy as a limit at α = 1. For α = 0 this entropy is the entropy of the uni‑ form distribution. This is sometimes called Hartley en‑ tropy, as Hartley has introduced the concept of infor‑ mation and its expectation value using such set, where

S2 = − log

N ∑

p2i .

i=1

(12)

4.2. Structural Entropies of Probability Distributions In the beginning of the 1990s Pipek and Varga [15], [16] found out, that the difference of Ré nyi entropies can characterize the structure of the probability dis‑ tribution {p1 , p2 , . . . , pN } in a very peculiar way. They introduced structural entropy as the difference of two Ré nyi entropies Sstr = S1 − S2 ,

(13)

and similarly, the they proved that the so called �il‑ ling factor q, which was used in solid state physics and quantum mechanics, is also related to a Ré nyi entropy difference the following way log(q) = S0 − S2 .

(14)

Later these quantities were applied in characterisa‑ tion of the localisation of pixel intensities in scanning microscopy images [17], [18]. Bonyá r developed a lo‑ calization factor for describing the roughness of gold electrodes based on these entropy differences [19], [20]

5. Telecommunication Lines

5.1. Measurements In telecommunication line performance prediction the goal is to develop a method that approximates the real‑life performance of the line suf�iciently well, without actually building the connection, as it is cos‑ tly and time consuming. For SHDSL lines, which are mainly for business use, errors in the prediction lead to �inancial loss to the telecommunications provider. Lilik measured over 170 lines [21], and developed a fuzzy method for performance prediction [22], [23]. During the measurements the SHDSL links were built, and their performances were measured. Also many physical parameters were determined using ge‑ neral measuring devices available at telecommunicati‑ ons service providers. Sorting out the noise, the return loss and many other parameters, it was proved that based on solely the insertion loss values of an area’s te‑ lecommunications lines their performance can be eva‑ luated with rather high reliability. The measured in‑ sertion loss values over the 0 to 2 MHz frequency ban can be seen in Fig. 5. 5.2. Characterisation Scheme In order to be able to build a classi�ication met‑ hod, the measured data was separated to a training set and a test set. In the original characterisation scheme simple, triangular rules were built from the measured data of the training set according to Fig. 3. As the inser‑ tion loss values have rather large �luctuations around Articles

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2020 2020

Measured insertion loss and its wavelet transform

140 120

IL [dB]

100 80 60 40 20 0 0

0.5

1 Frequency [Hz]

1.5

2 ×10 6

Fig. 5. Measured insertion loss as a function of frequency for the lines of the 5 performance groups. The darker shades of colours mean the measured lines properties, while the brighter counterparts denote the wavelet transforms

a quite smooth trend, �ive characteristic frequencies were chosen, and the insertion loss values at those fre‑ quencies served as antecedents. Selecting fewer fre‑ quency points makes the calculations unstable, more points make it unnecessarily complicated. Still, there were a lot of lines that were not evaluable, and there were very few cases, when the �luctuations were so bad, that the evaluation was not successful, i.e., instead of sorting the line into its real performance group, or one group below it (which is still acceptable for the provider), it sorted it to better performing group or predicted much worse data rate than the real one. For overcoming these problems, as a �irst step, we introduced fuzzy rule interpolation to out classi�ica‑ tion scheme, thus making practically all the lines eva‑ luable. Instead of selecting �ive representative samples from the complete insertion loss‑frequency function, we also applied wavelet analysis to �ilter out the large‑ scale trends from the function. The �irst wavelet trans‑ form we use can also be seen in Fig. 5. It can be seen, that the distribution of the transformed points is not equidistant: in the lower frequency domain we in‑ cluded one step �iner resolution level results than in the higher frequencies, because the communication’s spectral power density is much larger at lower fre‑ quencies. 65 lines were used for testing, in the case of the characteristic frequencies, 12 lines were put to one class lower than their real group, while in the case of the wavelet transformed antecedent selection 8 lines went to the acceptable group and the remaining 57 ones to their true classes. In both cases all the lines were classi�ied well, moreover, if the wavelet trans‑ form was carried out until 2 or 4 points remained, the classi�ication was still as correct as the 5‑point ver‑ sion [23].

36 36

With these results we demonstrated that wavelets can be used for stabilising calculations, if the measu‑ red data �luctuates and lowering the antecedent di‑ mension as well. Articles

Fig. 6. A measured surface segment before wavelet analysis

6. Wear If the number of the antecedent dimensions is al‑ ready too low, like in the case of classi�ication based on the Sstr and ln q values calculated for an image, wavelets can provide 4 more pictures to be analysed, as it can be seen in Fig. 6 and Fig. 7. In 2D data sets the wavelet analysis is carried out in both dimensi‑ ons. This results in 4 output pictures of approxima‑ tely quarter of the size of the original data set (half in each direction), one output for the case of using low‑pass �ilters in both dimensions, which is a kind of average of the original image, two outputs where one of the directions have low‑pass, the other high‑pass �il‑ ter, and one output where both �ilters are high‑pass. In the followings the latest picture will be called dia‑ gonal, the �irst averaging, and the two between will be mentioned as vertical and horizontal results, depen‑ ding on which direction has the �ine details, i.e., which direction used high‑pass �ilter. 6.1. Measurements

In [24] Solecki and Dreyer measured a combustion engine using silicone replica and surface scanners. Si‑ licone replicas are often used in geometrical measu‑ rements as the shape of many instruments does not allow to access certain interesting points of an object. In the case of a combustion engine the inner surface of the cylinders can be accessed only by specially desig‑ ned devices that are not available in general laborato‑ ries, but they are developed exquisitely for one type of automated measurement in the industry. These highly specialized tools are expensive thus if hardly accessi‑ ble surfaces are to be measured, either the object has to be cut, or replicas are to be taken from the surface. If the object under test is needed for further tests, clearly only the second option is possible. The measurements of the 4 cylinders of the engine under test were carried out using Struers RepliSet F5 which is able to reproduce patterns of size down to 0.1 microns. Replicas were taken of the new engine before building it and after 500 hours of polycyclic endurance test (later the engine was cut so that the worn surface could be studied directly, as well). The resulting sam‑ ples were measured by a TalysurfCLI2000 white‑light surface scanner at 5 points for each of the cylinders. These points were selected so that one point would

Journal Automation, Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation,

VOLUME 14,14, N°N° 2 2 2020 VOLUME 2020

Fig. 8. A measured surface segment before and after the polycyclic endurance run

Fig. 7. A measured surface segment after wavelet analysis be between the topmost and the second ring’s turning point, another point would be between the next two piston rings’s turning points, and three along the path where all 3 piston rings had worn the surface. An ex‑ ample of the 1 mm by 1 mm surface parts of a new and worn engine can be seen in Fig. 8. Slight vertical scra‑ tches can be seen on the worn surface. Such a verti‑ cal scratch can be seen in the previous worn image of Fig. 6, too, and slightly visible in the vertical transfor‑ med picture of Fig. 7. 6.2. Characterisation Scheme

The classi�ication scheme was very similar to the one in the previous section. The antecedents consis‑

ted of solely the structural entropy and the logarithm of the �illing factor, i.e., the two �e� nyi entropy diffe‑ rences. The Sstr (ln q) plot of 128 measured surface sub‑domains are plotted in Fig. 9. It can be seen, that though the points corresponding to worn and new sur‑ faces occupy overlapping domains, there are clearly such parts of the plot which belong to only one type of surface. However, these two characterising quantities are not suf�icient for building fu��y classi�ication scheme: from the 128 surface subdomains 64 were used for building the rulebase, and of the 64 test data, only 33 could be classi�ied correctly, which is worse than a random guess. In the case of two‑dimensional data, such as the above surface scans, wavelet transformation has to be carried out in both dimensions, thus resulting in 4 out‑ put data matrices: one for the transformation, where both directions had low‑pass �ilters, one for the high‑ pass‑high‑pass case, and two mixed �ilter pairs. The structural entropy and the �illing factor can be calcu‑ lated for all 4 of the resulting matrices, thus the an‑ tecedent dimension can be increased from 2 to up to 10. We tested [25] the method with all 4 wavelet transformed surface types as well as with only the low‑pass–low‑pass and high‑pass–high‑pass matrices, and the results were not different from each other. The number of incorrectly classi�ied surface elements went down to 13, which indicates, that the structural entropies are not suitable for being antecedents wit‑ hout other quantities. The second wavelet transform usually does not improve the results in this example. However we could demonstrate that wavelet ana‑ lysis is able to introduce independent information to the overly simpli�ied antecedents. Articles

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VOLUME 2020 VOLUME 14,14, N°N°22 2020

0.1 limit exponential Gaussian power law new worn

0.09 0.08 0.07

str

0.06 0.05 0.04 0.03 0.02 0.01 0 −0.2

−0.15

−0.1

−0.05

ln q

Fig. 9. Structural entropy map of 64 new and 64 worn surface segments. This is a typical way of plotting structural entropy, and determining the localization type of the studied distribution. The teal thick solid line denotes the theoretical limiting curve, above which no points should appear. The dashed, dotted and dash‐dotted lines shows three typical distributions, i.e., if a point is near the line corresponding to the 2nd order power law distribution (dash‐dotted), then the average localization type in the distribution is similar to the second order power law function. The green squares give the points generated from the new surfaces’s scans, while the red circles the worn ones

7. Colorectal Polyps Colorectal polyps are wart‑like objects inside the last parts of the bowel system. Some of these polyps can develop into colorectal cancer, which is a really dangerous type of cancer, as it can be detected usu‑ ally quite lately. If these polyps, that have the possibi‑ lity to develop into cancer could be detected and re‑ moved early, then they would not develop into malign objects, thus detecting and classifying colorectal po‑ lyps is a really important task. Having a visual aid for the medical experts based on automatic image proces‑ sing can help the diagnosis. There are several groups trying to �ind polyps on colonoscopy images, some of them even have their own database built. In the fol‑ lowing considerations, we apply our method founded in [26] on the pictures of [27]. An example can be seen in Fig. 10, while the wavelet transform of the picture is given in Fig. 11.

Fig. 10. A colonoscopy picture of [27] turned into grayscale image, before wavelet analysis 38 38

Articles

Fig. 11. Colonoscopy picture after wavelet analysis. Note that the upper left corner of the picture in Fig. 10, i.e., the pixel of index (1,1) moved to the lower left part of the coordinate system (the picture is upside down)

The classi�ication scheme consists of the following steps. First, the images are cut into tiles of size N × N , where N is generally between tenth and �ifth of the original image size, in our case 200 compared to the image size of magnitude 1000. Next, using the masks provided by the database, for each tile the polyp con‑ tent, i.e., the percentage of the area with masked pixels is calculated� based on this value the tiles are classi�ied as ”with polyp” and ”without polyp”. For each of the ti‑ les, for all 3 colour channels the antecedents were cal‑ culated. The antecedents are the mean, standard de‑ viation, edge density, structural entropy and ln q and

Journal Mobile Robotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation, Mobile

ACKNOWLEDGEMENTS

The authors would like to thank the �inancial sup‑ port of the projects GINOP‑2.3.4‑15‑2016‑00003 and the �� N�P‑1�‑4 New National Excellence Programme of the Ministry of Human Capacities of Hungary. This work was supported by National Research, Develop‑ ment and Innovation Of�ice (N�FIH) �124055. The authors would like to thank to EFOP‑3.6.1‑16‑2016‑ 00017 1 “˜Internationalisation, initiatives to establish a new source of researchers and graduates, and de‑ velopment of knowledge and technological transfer as

0.8

True positive rate

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0.05

0.1

0.15

0.2

0.25

0.3

False positive rate ROC, without wavelets 1

0.6

0.4

0.2

20 0 0

0.05

0.1

0.15

False positive rate

0.2

0.25

0.3

Picture group

True positive rate

0.8

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Picture group ROC with wavelets

1 0.95

True positive rate

0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55

0.005

0.01

0.015

0.02

0.025

0.03

0.035

False positive rate ROC with wavelets 1

0.8

0.7

0.6

20 0.5 0

0.01

0.02

0.03

False positive rate

0.04

Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Rule 10 Rule 11 Rule 12 Rule 13 Rule 14 Rule 15 Rule 16 Rule 17 Rule 18 Rule 19 Rule 20 Rule 21 Rule 22 Rule 23 Rule 24 Rule 25 Rule 26 Rule 27 Rule 28 Rule 29 Rule 30 Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Rule 10 Rule 11 Rule 12 Rule 13 Rule 14 Rule 15 Rule 16 Rule 17 Rule 18 Rule 19 Rule 20 Rule 21 Rule 22 Rule 23 Rule 24 Rule 25 Rule 26 Rule 27 Rule 28 Rule 29 Rule 30

ROC with wavelets

1 0.95 0.9

True positive rate

Picture group

True positive rate

0.9

0.85 0.8 0.75 0.7 0.65 0.6 0.55

ROC, without wavelets

1 0.9

8. Conclusion

In this articles the usage of wavelet transform in fuzzy antecedent selection was studied. Two comple‑ tely different strategies were mentioned. First, the simpli�ication of the decision and decrease of the number of antecedents by using wavelet transform instead of samples form a measured data vector, which scheme’s effectiveness was demonstrated on insertion loss‑based performance prediction of tele‑ communication lines. Second, the introduction of new, independent information by using wavelet transfor‑ med data beside the original one for classi�ication schemes with overly simplifying antecedent selection such as selecting structural entropies. Combustion en‑ gine cylinder surface scan classi�ication was used as a demonstrating example, where the performance of the classi�ication could be improved signi�icantly by introducing two of the wavelet transforms of the sur‑ face matrix. the other example was colonoscopy pic‑ ture segment classi�ication, where the improvement due to wavelet analysis was more visible, and to al‑ most all the image types the classi�ication error rate became acceptable.

ROC, without wavelets

1 0.9

True positive rate

the gradients. The edge density is calculated the follo‑ wing way: the tile is transformed to a black and white edge image by Canny �iltering, then the rate of the ed‑ ges (white points) compared to the tile‑size. Next, every second image is used for determining the fuzzy rules according to Fig. 3. As out previous ex‑ periences show, that for different types of images the classi�ication success rates are different, we sorted the pictures into groups of the same patient of the same take, and generated rules from each of the groups. The thus arising rules are applied for classi�ication using the same method as in the case of the cylinder surfa‑ ces, only the antecedent dimension increased to 21, or 99 in the case of using wavelet analysed pictures, too. The results for both cases can be seen as ROC plots in Fig. 12. The Classical ROC plots are not that much visible due to the large number of points, however, if a 3rd axis, i.e., the image group number is also given, we can conclude the followings. The false positive rate is rather low in all cases, especially in the case of using wavelet analysed images, too. The true positive rate is for some pictures extremely low, so this method wit‑ hout wavelet analysis is not usable, however, wavelets improve the results up to a more acceptable level in all cases.

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Picture group

Fig. 12. True positive vs false positive rate for the various picture groups for the various rulebases. First plot is the ROC, the second is a 3D view, and 3rd plot focuses n true positive rate. First row: without wavelet analysis, 21 antecedents, second row: with wavelet analysis, 99 antecedents

Articles

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Journal of of Automation, Automation,Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems

instruments of intelligent specialisations at Szé chenyi Istvá n University” for the support of the research.

AUTHORS

Ferenc Lilik∗ – Szé chenyi Istvá n University, H‑9026 Győ r, Egyetem té r 1, e‑mail: lilikf@sze.hu. Levente Solecki – Szé chenyi Istvá n University, H‑ 9026 Győ r, Egyetem té r 1. Brigita Sziová – Szé chenyi Istvá n University, H‑9026 Győ r, Egyetem té r 1. László T. Kóczy – Szé chenyi Istvá n University, H‑9026 Győ r, Egyetem té r 1. Szilvia Nagy – Szé chenyi Istvá n University, H‑9026 Győ r, Egyetem té r 1. ∗

Corresponding author

REFERENCES

[1] L. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, no. 3, 1965, 338–353, 10.1016/S0019‑ 9958(65)90241‑X.

[2] E. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic control‑ ler”, International Journal of Man‑Machine Stu‑ dies, vol. 7, no. 1, 1975, 1–13, 10.1016/S0020‑ 7373(75)80002‑2. [3] L. A. Zadeh, “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes”, IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC‑3, no. 1, 1973, 28–44, 10.1109/TSMC.1973.5408575. [4] L. Kó czy and K. Hirota, “Approximate reaso‑ ning by linear rule interpolation and general ap‑ proximation”, International Journal of Approxi‑ mate Reasoning, vol. 9, no. 3, 1993, 197–225, 10.1016/0888‑613X(93)90010‑B.

[5] L. Kó czy and K. Hirota, “Interpolative rea‑ soning with insuf�icient evidence in sparse fuzzy rule bases”, Information Sciences, vol. 71, no. 1‑2, 1993, 169–201, 10.1016/0020‑ 0255(93)90070‑3.

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[8] A. Kiely and M. Klimesh. “The ICER progressive wavelet image compressor”. https://ipnpr.jpl.nasa.gov/progress_ report/42-155/155J.pdf, 2003, Accessed on: 2020‑09‑18.

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[13] C. E. Shannon, “A mathematical theory of com‑ munication”, The Bell System Technical Journal, vol. 27, no. 3, 1948, 379–423, 10.1002/j.1538‑ 7305.1948.tb01338.x. [14] A. Ré nyi, “On Measures of Entropy and Informa‑ tion”. In: Proceedings of the fourth Berkeley Sym‑ posium on Mathematics, Statistics and Probabi‑ lity, 1961, 547–561.

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networks’ wire pairs”. In: AFRICON 2015, Ad‑ dis Ababa, Ethiopia, 2015, 1–5, 10.1109/AFR‑ CON.2015.7332034.

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CATEGORIZATION OF PERSONS BASED ON THEIR MENTIONS IN POLISH NEWS TEXTS Submitted: 20th October 2018; accepted: 2nd June 2020

Maciej Pachocki, Anna Wróblewska DOI: 10.14313/JAMRIS/2‐2020/19 Abstract: Our goal described in this paper was to design, imple‐ ment and test a method of categorization of mentions of persons in Polish news texts. We gathered and classified the input data in order to measure the accuracy of the method. Train and test data were constructed by using lists of persons collected from YAGO knowledge base and Polish Wikipedia. During tests the efficiency of categori‐ zation depending on different representations of a per‐ son was studied. Experiments were executed on our and a chosen solution from literature. The results are shown and discussed in the paper. Keywords: fined‐grained named entity classification, text classification, categorization of persons

1. Introduction

The problem of categorizing persons considered in this article concerns �inding additional information about individuals detected in text written in the Po‑ lish language. Apart from the basic knowledge that a given entity in text is a person further classi�ication predominantly lets us obtain the name of the profes‑ sion which is pursued by a given person. It results from the fact that most often in text people are mentioned or described in terms of their work and less often with respect to their beliefs, age or interests. The categorization of persons enables the creation of a taxonomy of people sharing the same profession. This can be applied in different domains. In informa‑ tion retrieval task persons following the same profes‑ sion can be suggested (e.g. in Web search engines). Furthermore a taxonomy of individuals may be em‑ ployed in a question answering system. In comparison to the recognition of general enti‑ ties (persons, places, organisations, etc.) the catego‑ rization of people is a narrower area of study and at the same time more dif�icult due to higher number of possible categories and fewer semantic differences appearing between them. Mistakes made by a compu‑ ter classi�ier or even by a human will more often be an assignment of an unsuitable profession for an in‑ dividual rather than the recognition of a person as a place or organisation or other named entity. Words occurring on the left and right side of the given en‑ tity very often indicate her general category (person, place or organisation). However after detecting a per‑ son in text these words may be not suf�icient to de�ine her/his occupation.

Most of the analyzed methods applied to cate‑ gorizing persons used supervised machine learning ([1], [2], [3], [4], [5]). The authors of mentioned pa‑ pers focused on feature selection and data set gene‑ ration. Other considered methods employed an algo‑ rithm which measured similarity between an entity’s representation and possible categories ([6], [7]). Sub‑ sequently the considered entity was categorized to the most similar category in a taxonomy. The objective of this work was to design and im‑ plement an application which would categorize per‑ sons previously recognized in texts written in Polish language. The program takes as input a text contai‑ ning tags which indicate occurrences of persons. Re‑ sult of the application is assigning each occurring per‑ son to one of the possible categories. The number of used categories was restricted to ten. These catego‑ ries were: ”clergymen”, ”painters”, ”musicians”, ”jour‑ nalists”, ”sportsmen”, ”politicians”, ”lawyers”, ”actors”, ”doctors” and ”poets”. In the next section we describe our method. Subse‑ quently we show the results (section 3), discuss them (section 4) and draw conclusions (section 5).

2. The Categorization Method

Subsection 2.1 describes a procedure used to de‑ termine possible categories of persons. The developed categorization method uses supervised machine lear‑ ning. The next subsections present the realization of the fundamental stages that must be followed accor‑ ding to this approach. 2.1. Set of Possible Categories

In order to determine the main possible categories of persons an algorithm has been developed which ta‑ kes as input lists of persons from YAGO knowledge base ([8]) and a corpus and automatically detects most often appearing classes of persons. The devised algo‑ rithm consists of the following steps: 1) Download lists of persons from YAGO knowledge base which has more than k persons (k = 10 000).

2) Search the set of documents in order to �ind the number of occurrences of persons belonging to each list.

3) Select categories in which the number of occurren‑ ces of persons is bigger than l (l = 200). Subse‑ quently delete categories which are not leafs in the created hierarchy and do not concern certain pro‑ fession.

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YAGO knowledge base makes available a very large hierarchy of persons consisting of categories down‑ loaded from taxonomy of WordNet and category sy‑ stem of English Wikipedia. To cut it down in the �irst step of the algorithm the taxonomy was restricted to categories which has more than 10,000 persons. Con‑ sequently 105 categories were obtained. The second step of the algorithm was conducted on a subcorpus of National Corpus of Polish1 which has approxima‑ tely 1 million of words. In the third step the minimum number of occurrences of persons was set to 200. Af‑ ter deleting categories which are not leafs in the cre‑ ated hierarchy and do not concern a certain profes‑ sion 10 categories were left. Six categories from YAGO are consistent with the �inal set of categories. Cate‑ gory ”football player” was replaced with more general ”sportsman”. Classes ”minister”, ”president” and ”ar‑ tist” were deleted. The �irst two were removed be‑ cause they were very similar to ”politician” category and the third one was too general. Newly added clas‑ ses were: ”doctor”, ”musician” and ”painter”. 2.2. Input Data set

A set of documents was constructed from texts pu‑ blished on popular Polish news portals. Ten thousand documents were gathered. The method of creating a data set used in categorization is shown in Figure 1. The depicted process consists of: • acquiring lists of persons grouped according to their profession ‑ it is based on gathering list of persons for each possible category; in our method lists were downloaded from the YAGO knowledge base and Po‑ lish Wikipedia; • recognizing persons in text ‑ it is based on applying a program whose task is to process a set of documents and tag places where persons occur in text; this kind of application was made available by Findwise com‑ pany2 ;

• adding to persons tags denoting their category ‑ it is based on comparing entities tagged as persons in texts with individuals appearing in lists of persons grouped by categories. As a result the data set used in categorization is created with marked places of occurring politicians, actors, etc. Figure 1 also shows the processing of an example sentence in the developed method. The sentence in our set of documents may be: ”A Postgame interview was conducted with the captain of Polish team Jakub Błaszczykowski” (number 1 on the illustration). After recognizing the persons in this sentence the place of a person’s occurrence is marked using the appropriate tags (number 2 on the illustration). In the stage of ad‑ ding tags denoting a profession Jakub Błaszczykowski gets the category ”sportsman” because he was found on the list with sportsmen (number 3 on the illustra‑ tion). Thereby he can be included in the data set for categorization. 2.3. Input Data Representation

Considering the number of contexts which can be included in a person’s representation it can be na‑

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med a single‑context or multi‑context representation. A single‑context representation consists of a single context‑sentence in which a given person appeared. Multi‑context representation of a given person com‑ prises several contexts (sentences) in which the indi‑ vidual appeared. The connection of several contexts of a given person can be restricted to a single document or the whole set of documents. In the �irst case such a representation was named a document multi‑context representation while in the second case the name is a corpus multi‑context representation. Three repre‑ sentations of a person mentioned above are shown in �ig. 2. The possibility of categorization according to an accepted person’s representation requires an ade‑ quate procedure of splitting persons’ occurrences from data set used in classi�ication. For a single‑ context representation single sentences are processed independently. Obtaining all of the contexts in which a given person appeared (whether in any document or the whole corpus) involves the creation of lists whose entries are groups of occurrences. Subsequently trai‑ ning and test set are constructed from these groups. Feature extraction and classi�ication depend on a selected person’s representation. For a single‑context representation feature extraction and classi�ication is realized for each person’s occurrence separately. On the other hand for a multi‑context representation the construction of a feature vector and categorization task is performed simultaneously for all occurrences of a given person. Polish language is an in�lected language. There‑ fore the main part of the preprocessing of text was obtaining base forms of words which were retrieved using WCRFT ‑ morpho‑syntactic tagger for Polish lan‑ guage [9]. At the end of processing stop words were removed. List of stop words for Polish language was acquired from Wikipedia3 . 2.4. Implemented Features

Features from the literature. The approach presen‑ ted in [5] was implemented in order to compare it with our solution. In the paper the categorization task was carried out for English texts. The used features were context, cluster‑based, entity‑related and class‑ speci�ic ones. The similarity between these features and ours will be de�ined in the next sections of the article. Measures connected with micro‑averaging and macro‑averaging achieved for our input data set which contained Polish news texts were much smaller. The results obtained for different input data sets presen‑ ted in [5] are shown in tab. 1.

Tab. 1. Results of method [5] obtained for different input data sets Input data set English texts Polish texts

Micro‑F1 79.60 48.05

Macro‑F1 76.50 48.52 Articles

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Fig. 1. The method of creating a data set used in the categorization procedure

Fig. 2. Representations of a person that are considered during tests In the following subsections features used in our categorization method will be described.

Context features. Context features use words sur‑ rounding person’s occurrence from left and right side together with their parts of speech. Our features are created only from content words which in Polish lan‑ guage are verbs, nouns, adjectives, numerals, adverbs and pronouns. Context features from [5] solution did not �ilter words in terms of their part of speech.

Features of words co‐occurring with a category. Next features are features of words co‑occurring with a ca‑ tegory. To determine them a training set was used to create sets of words which appear only with persons’ occurrences from one category. For the surroundings of a given person’s occurrence the number of words that belong to each word set is counted. A feature ta‑ kes the value 1 for a category whose word set contai‑ ned the highest number of surrounding words. Similar features were class‑speci�ic features from [5] but they also included in word sets words that appeared often enough with persons from one category more than the others (threshold 0.8).

Synonym features. The third type of features are syn‑ onym features. Words creating context features in dif‑ ferent occurrences of persons may be more or less semantically similar. For two synonyms it is not visi‑ ble while comparing text strings. Therefore identi�iers of sets of synonyms were collected for context words Articles

using Polish Wordnet([10]). These features are similar to cluster‑based features from [5] which in contrast to our implementation used groups of synonyms created using Brown algorithm and TDT5 corpora [11].

Category synonyms features. The last type of devi‑ sed features are category synonyms features. For each possible category a separate �ile with her synonyms was created. Synonyms were downloaded from an on‑ line dictionary of Polish synonyms4 . Queries concer‑ ned the masculine forms of professions. From these words feminine forms were created and added manu‑ ally. A feature takes the value 1 for a category when any of the words surrounding a person’s occurrence belonged to her/his synonym set. The number of words taken into consideration from left and right side of person’s occurrence was determined separately for features of words co‑ occurring with a category and category synonyms fea‑ tures. On the other hand the width of the context win‑ dow for context and synonym features was the same.

An example. Figure 3 presents an example sentence with a person’s occurrence and our extracted features. On the top of the illustration the original sentence in Polish language and translated into English are pre‑ sented. The rectangles on the right side of �igure show extracted features translated into English. For the example presented in �ig. 3 the context fe‑ atures are the words surrounding the person’s occur‑ rence together with their parts of speech. In this case

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Fig. 3. Our features extracted from an example sentence with a person’s occurrence the words ”Polish” (adjective) and ”team” (noun) are included. For features of words co‑occurring with a ca‑ tegory only the feature connected with sportsmen ca‑ tegory took the value 1 (sportsmen�1 in �igure 3) be‑ cause the biggest number of words surrounding the considered person was found in a word set connected with sportsmen. Some of the words creating a word set for sportsmen are presented in �ig. 3 (these are team, ball and goalkeeper). Synonym features consist of identi�iers returned by Polish Wordnet for words ”Polish” and ”team”. Thus the words belonging to the same synonym set were given common feature values. All of the category synonyms features took the value 0 because in the surroundings of person’s occurrence did not appear a synonym from any category. The sam‑ ple words creating a synonyms set for the sportsmen category were: athlete, runner or player.

results obtained for each category. In this case sin‑ gle classi�ications have smaller in�luence on measures being calculated while precision and recall computed for the whole categories have bigger importance. For each category basing on her confusion table precision (P), recall (R) and F1 score is computed. Subsequently the following measures are calculated:

Building and testing a classi�ier was based on a 2‑ fold cross‑validation in which every person’s occur‑ rence was used for building a model and testing it. As quality measures of the whole classi�ication task micro‑averaging and macro‑averaging techni‑ ques were adopted. Micro‑averaging is based on sum‑ ming the correct classi�ications of persons from each category and gives us an idea about the overall perfor‑ mance. After computing a confusion table Ti for each from k possible categories the following measures are calculated:

3.1. Experiments With Different Persons Lists

2.5. Building a Classifier

M icro ‑P = ∑k

∑k

i=1

T P Ti

i=1 (T P Ti

+ F P Ti )

∑k

+ F N Ti )

M icro ‑R = ∑k

i=1

T P Ti

i=1 (T P Ti

M icro ‑F1 =

2 M icro ‑P M icro ‑R M icro ‑P + M icro ‑R

(1)

(2) (3)

A complementary technique to micro‑averaging is macro‑averaging which calculates an average from the

M acro ‑P =

3. Results

i=1

∑k

(4)

(5)

2 M acro ‑P M acro ‑R M acro ‑P + M acro ‑R

(6)

M acro ‑R = M acro ‑F1 =

∑k

i=1

In our method of creating a data set used in the categorization procedure (Fig. 1) different persons’ lists were used. Before merging lists downloaded from YAGO knowledge base with lists from Polish Wikipedia certain tests were executed. Fig. 4 presents a compari‑ son of number of found persons in a set of documents using different persons’ lists. The merged lists in each category let us acquire more unique persons than using both types of lists se‑ parately. A signi�icant part of found persons in YAGO lists and merged lists were politicians. Figure 5 presents a comparison of number of found persons’ occurrences in a set of documents using dif‑ ferent persons’ lists. The number of persons’ occur‑ rences varies greatly for the studied lists and sim‑ ple growth trend is not visible like for found unique persons. in �ig. 5 politicians were not mentioned be‑ cause the number of found persons’ occurrences from this category is much bigger than in other categories. For politicians the following numbers were achieved: 16,336 persons’ occurence (lists from YAGO), 4,627 Articles

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500 460

Number of unique persons

421

Lists from YAGO Lists from Wikipedia Lists from YAGO and Wikipedia

400

300

200

183 149 124

145 111

100 51

113

48 56

65 59

89 55

67 70

36 40

53 54 26

po et s

do ct or s

ac to rs

la w ye rs

pa in te rs m us ic ia ns jo ur na lis ts sp or ts m en po lit ic ia ns

cl er gy m en

Highcharts.com

Fig. 4. The number of unique persons found in a set of documents using different persons’ lists (lists from Wikipedia), 16,161 (merged lists). All per‑ sons and their occurrences in Figures 4 and 5 were counted only if they were found exactly in one list. After merging the lists from YAGO and Wikipedia the number of persons in every list raised but in the same overlapping of persons in categories increased. The ef‑ fect of this phenomenon is visible in �ig. 5 where in some categories the number of persons’ occurrences decreased after merging lists. 3.2. Categorization Results

Tests were carried out with different classi�iers. A maximum Entropy classi�ier available in OpenN�P Maxent library5 was used and 5 classi�iers from Weka machine learning software ([12]). These were Naive‑ Bayes, C4.5, SMO (sequential minimal optimization), RandomTree and BayesNet. The Maxent classi�ier was used in order to have the same setup as in [5]. The �ive algorithms from Weka library were chosen basing on the achieved results gathered from initial tests. Most of the applicable classi�iers in Weka library6 were exami‑ ned. Algorithms with the top �ive results with using the default parameters were selected. Experiments were performed with all person’s representations presen‑ ted in section 2.3. Tests were conducted on our and chosen solution from literature [5] with default para‑ meters of classi�iers. Table 2 presents results for diffe‑ rent settings whereas table 3 shows the best outcomes achieved according to tested method and representa‑ tion of a person. In both tested solutions the best results were achieved for the multi‑context document represen‑ tation. The highest values of measures for both im‑ plementations were about 5‑7% bigger than in the tests with single‑context representation. The worst re‑ sults were computed for the corpus multi‑context re‑ presentation. The best outcome for our method was about 3% better than for the solution implemented from the literature and it was attained with a Maxi‑ mum Entropy classi�ier. The differences in Micro‑F1 and Macro‑F1 for the single‑context and document multi‑context representation were small for all used classi�iers. �owever the spread of these measures for corpus multi‑context representation was very large which means that the classi�ication in the categories Articles

was very unequal. Table 4 shows the results in each category for best classi�ication outcome (Micro‑F1 =51.36%, Macro‑F1 =51.34%).

4. Discussion

Tests were carried out according to the devised person’s representations described in section 2.3. Alt‑ hough all sentences of a given person (whether in a document or a corpus) were taken into consideration it did not ensure high categorization results. In the �i‑ nal stage of the study one hundred of misclassi�ication cases were examined and 42% of them were subjecti‑ vely assessed by ourselves as not possible to classify by a human. In the analyzed cases all sentences with a given person in the document were took into account in assigning a category (multi‑context document re‑ presentation). Further improvement of our categori‑ zation method seems viable with information about the topic of the document. Additional features indica‑ ting a topic could be determined based on all senten‑ ces in a given text. Assuming that the content of a docu‑ ment is often related with profession of persons men‑ tioned in it, it can be employed to classify individuals who are not surrounded with words that indicate their profession.

5. Conclusion

�uring experiments we studied the ef�iciency of categorization depending on the adopted representa‑ tion of person. The use of grouped persons’ occurren‑ ces brought different results. For a document multi‑ context representation a signi�icant growth of the cal‑ culated measures can be noticed in comparison with a single‑context representation. On the other hand the use of corpus multi‑context representation did not im‑ prove the classi�ication measures. Tests were conducted on our and a chosen so‑ lution from the literature with use of six classi�iers (Maxent, NaiveBayes, C4.5, SMO, RandomTree i Bayes‑ Net). Better results were achieved using our categori‑ zation method in comparison with a solution from the literature that was redesigned and adopted to the Po‑

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Lists from YAGO Lists from Wikipedia Lists from YAGO and Wikipedia

2,057

2k 1,447

1,142

1,036 930 779

762

707 478 324 302

752 584

538

414

581 555 393 350

309

250

110 114 161

107

159

po et s

do ct or s

ac to rs

la w ye rs

s sp or ts m en

jo ur na lis t

pa in te rs m us ic ia ns

cl er gy m en

Number of persons' occurrences

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Highcharts.com

Fig. 5. The number of persons’ occurrences found in a set of documents using different persons’ lists Tab. 2. Results achieved for different settings Method literature

Representation single‑context

our

single‑context

literature

multi‑context document

our

multi‑context document

literature

multi‑context corpus

our

multi‑context corpus

lish language. The best outcomes were attained with a Maximum �ntropy classi�ier.

Classi�ier Maxent NaiveBayes C4.5 SMO RandomTree BayesNet Maxent NaiveBayes C4.5 SMO RandomTree BayesNet Maxent NaiveBayes C4.5 SMO RandomTree BayesNet Maxent NaiveBayes C4.5 SMO RandomTree BayesNet Maxent NaiveBayes C4.5 SMO RandomTree BayesNet Maxent NaiveBayes C4.5 SMO RandomTree BayesNet

Micro‑F1 42.39 36.95 29.75 34.13 24.33 36.91 43.88 42.09 41.00 43.36 34.22 39.65 48.05 41.77 36.86 31.19 21.28 39.94 51.36 45.64 42.71 46.14 29.81 44.15 18.77 48.33 39.79 48.34 27.56 15.22 17.02 45.27 47.64 29.34 15.25 48.13

Macro‑F1 42.88 34.84 27.31 33.50 22.72 35.64 43.74 42.39 40.35 42.61 32.77 41.31 48.52 39.23 33.54 28.56 20.07 37.86 51.34 43.04 42.09 45.56 28.29 43.37 31.41 34.07 23.08 35.30 14.01 6.99 27.96 32.00 34.91 30.25 17.24 36.30

Notes

1 http://nkjp.pl/

2 http://findwise.com

3 http://pl.wikipedia.org/wiki/Wikipedia:Stopwords

4 Online dictionary of Polish synonyms, http://synonim.net 5 OpenN�P

Maxent classi�ier, http://maxent.sourceforge.

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Tab. 3. Best results achieved for different methods and representations of a person Method

Representation

Classi�ier

our single‑context Maxent literature single‑context Maxent our multi‑context document Maxent literature multi‑context document Maxent our multi‑context corpus BayesNet literature multi‑context corpus SMO Tab. 4. Precision, recall and F1 measure for each category in both iterations of 2‐fold cross‐validation Category Precision Recall

clergymen painters musicians journalists sportsmen politicians lawyers actors doctors poets

67.35 70.27 41.67 53.17 50.24 37.7 44.43 41.87 77.57 67.5

84.77 32.1 36.23 51.69 36.3 42.6 57.4 37.05 48.82 33.75

75.06 44.07 38.76 52.42 42.15 40 50.09 39.31 59.93 45

clergymen painters musicians journalists sportsmen politicians lawyers actors doctors poets

68.64 93.33 61.07 66.22 68.09 43.79 50.57 62.03 59.87 55.32

74.37 17.5 38.65 68.04 54.79 64.2 52.15 53.07 52.22 32.91

71.39 29.47 47.34 67.12 60.72 52.07 51.35 57.2 55.79 41.27

Category Precision Recall

net/about.html 6 Weka classi�iers, http://wiki.pentaho.com/display/ DATAMINING/Classifiers

AUTHORS

Maciej Pachocki – Warsaw University of Technology, Faculty of Mathematics and Information Science, ul. Koszykowa 75, Warsaw, Poland. Anna Wróblewska∗ – Warsaw University of Technology, Faculty of Mathematics and Infor‑ mation Science, ul. Koszykowa 75, Warsaw, Po‑ land, e‑mail: a.wroblewska@mini.pw.edu.pl, www: www.ii.pw.edu.pl/~awroblew. ∗

Corresponding author

REFERENCES

[1] M. Fleischman and E. Hovy, “Fine Grained Clas‑ si�ication of Named Entities”. In: COLING 2002: Articles

Micro‑F1 (%) Macro‑F1 (%) 43.88 42.39 51.36 48.05 49.78 48.34

43.74 42.88 51.34 48.52 37.55 35.30

The 19th International Conference on Computati‑ onal Linguistics, 2002.

[2] V. Ganti, A. C. Kö nig, and R. Vernica, “Entity ca‑ tegorization over large document collections”. In: Proceedings of the 14th ACM SIGKDD inter‑ national conference on Knowledge discovery and data mining, New York, NY, USA, 2008, 274–282, 10.1145/1401890.1401927.

[3] C. Giuliano, “Fine‑Grained Classi�ication of Na‑ med Entities Exploiting Latent Semantic Ker‑ nels”. In: Proceedings of the Thirteenth Confe‑ rence on Computational Natural Language Le‑ arning (CoNLL‑2009), Boulder, Colorado, 2009, 201–209.

[4] A. Ekbal, E. Sourjikova, A. Frank, and S. P. Pon‑ zetto, “Assessing the Challenge of Fine‑Grained Named Entity Recognition and Classi�ication”. In: Proceedings of the 2010 Named Entities Works‑ hop, Uppsala, Sweden, 2010, 93–101. [5] W. Li, J. Li, Y. Tian, and Z. Sui, “Fine‑Grained Classi�ication of Named Entities by Fusing Multi‑ Features”. In: Proceedings of COLING 2012: Pos‑ ters, Mumbai, India, 2012, 693–702.

[6] E. Alfonseca and S. Manandhar, “An Unsupervi‑ sed Method for General Named Entity Recogni‑ tion and Automated Concept Discovery”. In: Pro‑ ceedings of the 1 st International Conference on General WordNet, Mysore, India, 2002, 34–43. [7] P. Cimiano and J. Vö lker, “Towards large‑scale, open‑domain and ontology‑based named entity classi�ication”. In: Proceedings of the Internati‑ onal Conference on Recent Advances in Natural Language Processing RANLP’05, 2005, 166–172.

[8] F. M. Suchanek, G. Kasneci, and G. Weikum, “YAGO: a core of semantic knowledge”. In: Pro‑ ceedings of the 16th international conference on World Wide Web, New York, NY, USA, 2007, 697– 706, 10.1145/1242572.1242667.

[9] A. Radziszewski. “A Tiered CRF Tagger for Po‑ lish”. In: R. Bembenik, L. Skonieczny, H. Rybinski, M. Kryszkiewicz, and M. Niezgodka, eds., Intel‑ ligent Tools for �uilding a Scienti�ic Information Platform: Advanced Architectures and Solutions, Studies in Computational Intelligence, 215–230. Springer, Berlin, Heidelberg, 2013.

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[10] M. Maziarz, M. Piasecki, and S. Szpakowicz, “Ap‑ proaching plWordNet 2.0”. In: C. Fellbaum and P. Vossen, eds., Proceedings of 6th International Global Wordnet Conference, Matsue, Japan, 2012, 189–196, Book: http://www.globalwordnet. org/gwa/proceedings/gwc2012.pdf.

[11] P. F. Brown, V. J. Della Pietra, P. V. deSouza, J. C. Lai, and R. L. Mercer, “Class‑Based n‑gram Mo‑ dels of Natural Language”, Computational Lin‑ guistics, vol. 18, no. 4, 1992, 467–480.

[12] M. Hall, E. Frank, G. Holmes, B. Pfahringer, P. Reu‑ temann, and I. H. Witten, “The WEKA data mi‑ ning software: an update”, ACM SIGKDD Explo‑ rations Newsletter, vol. 11, no. 1, 2009, 10–18, 10.1145/1656274.1656278.

Articles

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VOLUME 2020 VOLUME 14,14, N°N°2 2 2020

SUPPORTING DECISIONS ON THE FOREX MARKET USING FUZZY APPROACH Submitted: 20th October 2018; accepted: 2nd June 2020

Przemysław Juszczuk, Lech Kruś DOI: 10.14313/JAMRIS/2‐2020/20 Abstract: A new concept of the multicriteria fuzzy trading system using the technical analysis is proposed. The existing tra‐ ding systems use different indicators of the technical ana‐ lysis and generate buy or sell signal only when assumed conditions for a given indicator are satisfied. The informa‐ tion presented to the trader – decision maker is binary. The decision maker obtains a signal or no. In compari‐ son to the existing traditional systems called as crisp, the proposed system treats all considered indicators jointly using the multicriteria approach and the binary informa‐ tion is extended with the use of the fuzzy approach. Cur‐ rency pairs are considered as variants in the multicriteria space in which criteria refer to different technical indica‐ tors. The introduced domination relation allows genera‐ ting the most efficient, non‐dominated (Pareto optimal) variants in the space. An algorithm generated these non‐ dominated variants is proposed. It is implemented in a computer‐based system assuring the sovereignty of the decision maker. We compare the proposed system with the traditional crisp trading system. It is made experimentally on diffe‐ rent sets of real‐world data for three different types of trading: short‐term, medium and long‐term trading. The achieved results show the computational efficiency of the proposed system. The proposed approach is more robust and flexible than the traditional crisp approach. The set of variants derived for the decision maker in the case of the proposed approach includes only non‐dominated va‐ riants, what is not possible in the case of the traditional crisp approach. The reservation point and its impact on the overall results are measured with the use of the sen‐ sitivity analysis. Keywords: Trading system, Forex, fuzzy membership function, multicriteria analysis

1. Introduction

50 50

In this paper, we propose an extension of the tra‑ ditional trading systems based on the technical ana‑ lysis using the concept of fuzziness. This concept can be implemented in a decision support system aiding the trader in making his decisions. As a �ield for expe‑ riments, we selected the Forex market, which is a glo‑ bal, decentralized market with currency pairs as basic instruments. According to the Bank for International Settlements, its average daily turnover reached $5.3 trillion in January 2014 [28]. Unlike other markets, the Forex is completely decentralized and housed electro‑ nically. It is considered one of the largest markets in

the world, where about 90% of its turnover is genera‑ ted by currency speculators. Still growing number of instruments available for the trader – decision maker in the last few years makes it very dif�icult to manually manage even the single transaction. Three main approaches of �inancial data analysis are used to forecast prices on the Forex market: the technical analysis, the fundamental analysis, and the sentiment analysis. The fundamental analysis inclu‑ ding the text‑mining techniques was adapted to the stock market in [20], [34], as well as for the Forex mar‑ ket in [32]. The sentiment analysis called also the opi‑ nion mining was presented in [10]. The technical ana‑ lysis is based on the assumption, that there it is pos‑ sible to predict future prices on the basis of the histo‑ rical prices, in other words, that past behavior of the price has an effect on the future prices. The process of construction of such indicator can be considered as a dimension reduction [38]. In such an approach, the initial data is transformed to another domain which may be simpler than the original data. Such action le‑ ads to a situation, where price and technical indica‑ tor values become an independent example of the pro‑ blem. One of the main directions of development of the trading systems based on the technical analysis con‑ sists in using various indicators which are mostly some complex formulas used for historical data to ex‑ tract hidden information from price time series or to reduce some irrelevant noise. Such an approach is used to identify moments to open the positions on the market. The technical analysis is the most popular tool used in the trading. Moreover, its importance is incre‑ asing over years [17]. By the trading system, we understand any system (manual or automatic), which with the use of data ana‑ lyzed from the market calculates values of the market indicators. Such values are further used to generate a signal and open the position related to the selected currency pair. �owever, there exists a signi�icant dra‑ wback, where all selected indicators must give the sig‑ nal at the same time, thus increasing the number of market indicators leads to more seldom signals. What is obvious, even in the case, where all necessary con‑ ditions all ful�illed, there is no guarantee, that derived signal will be pro�itable. Newer works like [4] suggest, that especially very volatile markets like Forex may be very dif�icult to ana‑ lyze. That leads to various works which limit the ap‑ plication of the fully automatic concept of trading sy‑ stems for the decision support. There are also ma‑

Journal of Automation, Mobile Robotics and Intelligent Systems Journal of Automation, Mobile Robotics and Intelligent Systems

nual trading systems which generate signals for opeâ&#x20AC;&#x2018; ning and closing positions on the market, where the ďż˝inal decision is made by the decision maker. One of the most signiďż˝icant advantages of such manual traâ&#x20AC;&#x2018; ding systems is that the decision maker may additioâ&#x20AC;&#x2018; nally apply other types of analysis on the market situâ&#x20AC;&#x2018; ations. Examples of such systems can be found in [13], [18], [8]. Thus one of the most important advantages of such systems is that they assure sovereignty of the decision maker.

The paper discusses decision support problems in the case of the manual trading systems. A typical syâ&#x20AC;&#x2018; stem analyses data from the market, calculate techniâ&#x20AC;&#x2018; cal indicators, generates buy or sell signals when a giâ&#x20AC;&#x2018; ven set of rules is satisďż˝ied for a given indicator. The decision maker observing the signals can make the ďż˝inal decision. Still growing number of instruments available for the decision makers results in a dynaâ&#x20AC;&#x2018; mic growth of the decision space. Therefore a new apâ&#x20AC;&#x2018; proach capable to handle such difďż˝iculties is required. In this article, we investigate problems arising in the case of the traditional crisp trading systems, where the decision is made on the basis of a simple binary function. The ďż˝irst limitation of such systems is enâ&#x20AC;&#x2018; countered, where all initially deďż˝ined rules should reâ&#x20AC;&#x2018; turn the â&#x20AC;?trueâ&#x20AC;? value to open the position at the same time. By increasing the number of rules included in the system results in a reduction of the number of possiâ&#x20AC;&#x2018; bilities for the decision maker and often none of the variants are considered as a promising. The traditioâ&#x20AC;&#x2018; nal system disregard situations when all the indicators are very close to satisfying the assumed rules. Such siâ&#x20AC;&#x2018; tuations can be in general much more promising than in the case of the signal when the rules are satisďż˝ied for only one indicator.

To cover this gap we propose to apply a multicriâ&#x20AC;&#x2018; teria fuzzy approach. In this approach, all considered indicators are considered jointly. Each indicator is reâ&#x20AC;&#x2018; presented by a criterion in a multicriteria space of variants. The traditional strict rules are replaced by fuzzy rules. Values of the criteria are calculated by inâ&#x20AC;&#x2018; troduced membership functions. The decision maker can control the introduced fuzziness using concepts of aspiration and reservation points adopted from the reference point approach of the multicriteria analyâ&#x20AC;&#x2018; sis (see [42]). An algorithm generating nonâ&#x20AC;&#x2018;dominated variants in the criteria space is proposed. Concepts of the domination cons applied in the algorithm ensure the high computational efďż˝iciency of the algorithm apâ&#x20AC;&#x2018; proved in experiments made on real data from the Foâ&#x20AC;&#x2018; rex market.

We introduce the risk proďż˝ile of the decision maâ&#x20AC;&#x2018; ker in the form of a single point in the criteria space. It seems to be consistent with the regulations imposed by the European Union according to the directive Miâ&#x20AC;&#x2018; FID II [1]. This law forces every entity present on the market to estimate the soâ&#x20AC;&#x2018;called risk proďż˝ile of the sinâ&#x20AC;&#x2018; gle decision maker. The risk proďż˝ile is built on the basis of a questionnaire, which is further used to estimate the risk aversion of the decision maker. In our work, we propose to use the soâ&#x20AC;&#x2018;called reservation point reâ&#x20AC;&#x2018;

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presenting the minimal acceptable risk taken by the decision maker during the trading session. We present the proposed multicriteria approach for đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; technical indicators. The introduced fuzzy conâ&#x20AC;&#x2018; cepts are shown on the example of three indicators: the moving averages (MA), Relative Strength Index (RSI) and Commodity Channel Index (CCI). For the three indicators, the results of computation experiâ&#x20AC;&#x2018; ments on real data from the Forex market are preâ&#x20AC;&#x2018; sented and analyzed. Examples of the technical indiâ&#x20AC;&#x2018; cators are presented in Section 2. Section 3 introduces the concept of the traditional (crisp) trading system. Section 4 includes a detailed description of the propoâ&#x20AC;&#x2018; sed fuzzy approach along with deďż˝initions of all fuzzy membership functions included in the system. The alâ&#x20AC;&#x2018; gorithm which generates the nonâ&#x20AC;&#x2018;dominated variants for the decision maker is proposed. Section 5 contains the results of various experiments with different realâ&#x20AC;&#x2018; world data sets. The discussion presented along with experiments results points out the weakness of exisâ&#x20AC;&#x2018; ting crisp systems and emphasizes the advantages of the proposed fuzzy system.

2. Related Works

The existing trading system can be divided into two main groups. The ďż˝irst group includes systems related to the High Frequency Trading (HFT), where strategies are mostly based on the complex algorithms capable to effectively analyze multiple markets. One of their main features is a very short transaction time which leads to small proďż˝its. Duration of the single transaction rarely exceeds a few seconds. Despite the efďż˝iciency of such systems, their applicability for sinâ&#x20AC;&#x2018; gle decision makers is debatable. Issues related to the mentioned HFT are focused on examining factors like market liquidity and its impact on the system efďż˝iâ&#x20AC;&#x2018; ciency [23], [21]. There are also articles measuring the impact of the unexpected events on the proďż˝its geneâ&#x20AC;&#x2018; rated by the transaction system. Despite the fact of general high interest in the HFT, there are authors [35] pointed out, that possible outcomes offered by the HFT approach are decreasing. At the same time, the group of trading systems deaâ&#x20AC;&#x2018; ling with the Low Frequency Trading (LFT) gains more attention. Opposite to the HFT approach, in the LFT concept, reaction time pays less important role and duration of the single transaction may last longer than in case of HFT approach. In the following, we discuss the traiding systems applying the LFT approach. We propose to use in the trading systems the ideas of fuzzy sets theory as were originally introduced by [44]. There are multiple publications related to the use of fuzzy concepts with stock data (rarely with Foâ&#x20AC;&#x2018; rex data) such as [39, 19, 40]. In this article, the fuzzy sets view is combined with the multicriteria analysis. One of the crucial concepts in the analysis relates to soâ&#x20AC;&#x2018;called aspiration levels introduced by Wierzbicki in [41], who provided a mathematical background for satisfying the decision making. In the papers [11, 33] and in the newer one [2] ideas of multicriteria decision making in the case of fuzzy sets are developed. Articles

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Systems based on new trading rules generated on the basis of existing technical analysis indicators often rely on approximate mechanisms such as metaheuâ&#x20AC;&#x2018; ristics. Examples of such papers include genetic proâ&#x20AC;&#x2018; gramming [26], grammar evolution [9], and evolutioâ&#x20AC;&#x2018; nary algorithms [6]. Such approaches are based on the concept of setting optimal values of the technical indiâ&#x20AC;&#x2018; cators. More recent papers in this ďż˝ield rely on the conâ&#x20AC;&#x2018; cept of evolutionary multicriteria algorithms [7] and particle swarm optimization [5]. Approximate approâ&#x20AC;&#x2018; aches in this ďż˝ield are presented in [31] and [30]. It is worth noting new combined technical analysis indicators used for decision support, however, there is only a small group of articles in this ďż˝ield. An examâ&#x20AC;&#x2018; ple of such work may be found in [16], in which a new indicator correlated with the risk factor was presenâ&#x20AC;&#x2018; ted. An extension of this concept based on the matheâ&#x20AC;&#x2018; matical evidence of trends in ďż˝inancial data was preâ&#x20AC;&#x2018; sented in [15]. Another example is a new moving minâ&#x20AC;&#x2018; max indicator described in [36]. This indicator was used as a chart smoothing tool allowing to ignore small price corrections. It is worth noting that there are very few approaches in which decision support systems are preferred over automated trading. In most of the apâ&#x20AC;&#x2018; proaches, the complete trading system is treated like a black box, where the set of input data is transformed into the output data signal; however, in article [25] the authors proposed an approach in which it is possible to set parameters representing the risk aversion. The ruleâ&#x20AC;&#x2018;based trading systems are not the unique class of systems used on the Forex market. There are also trading systems based on neural networks. Publiâ&#x20AC;&#x2018; cations related to this subject emerged already in 1995 when a neural network was used to generate a preliâ&#x20AC;&#x2018; minary signal [12]. To the best of the authorsâ&#x20AC;&#x2122; knowâ&#x20AC;&#x2018; ledge, using the neural networks on the market was described in [29] as in one of the ďż˝irst articles dedicaâ&#x20AC;&#x2018; ted to this area. Newer approaches include the use of neural networks for data prediction [43] or applying technical indicators as neural network entry points [37]. A selfâ&#x20AC;&#x2018;organizing map is used as a mechanism of detecting correlations between Japanese candlesâ&#x20AC;&#x2018; ticks. A similar concept was proposed in [14], where the kâ&#x20AC;&#x2018;means algorithm was used to detect some Japaâ&#x20AC;&#x2018; nese candlestick patterns. The authors of [27] propoâ&#x20AC;&#x2018; sed to use different volatility measures as an input for the support vector machines. The ARIMA model was compared with the artiďż˝icial neural network for the prediction on the Forex market in [24]. More complex systems involving the use of modern metaheuristics like Cuckoo Search Algorithm [3] or heuristicâ&#x20AC;&#x2018;based trading systems combining different trading rules [31] were also proposed.

3. Background

ďż˝e deďż˝ine a trading system as a pair: đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018; đ?&#x2018; = {đ??śđ??śđ??ś đ??śđ??śđ??śđ??śđ??śđ??ś

52 52

(1)

where đ??śđ??ś is the set including the single, or multiple curâ&#x20AC;&#x2018; rency pairs analyzed by the trading system, while đ??´đ??´đ??´đ??´ Articles

includes all rules generated on the basis of market inâ&#x20AC;&#x2018; dicators used in the trading system. In its trivial form, đ??´đ??´đ??´đ??´ may include one up to many different rules, while more complex approach involves using subsets of đ??´đ??´đ??´đ??´, where each subset relates to đ??śđ??ś. Thus different sets of rules are applied at the same time to the same set of currency pairs. Below we introduce a simple division of the traâ&#x20AC;&#x2018; ding systems. The division is made on the basis of number of currency pairs and transaction concepts inâ&#x20AC;&#x2018; volved in the decision process: â&#x20AC;&#x2018; one currency pair â&#x20AC;&#x201C; one set of rules â&#x20AC;&#x201C; the simplest concept used on the Forex market. In this approach, there is only one set of rules used with the single currency pair. Often some additional elements corâ&#x20AC;&#x2018; related directly with the currency pair characterisâ&#x20AC;&#x2018; tics are used in such a system.

â&#x20AC;&#x2018; one currency pair â&#x20AC;&#x201C; n sets of rules â&#x20AC;&#x201C; a signal may be generated on a basis of a few different sets of rules. This mechanism is used for example in the social traâ&#x20AC;&#x2018; ding, where there is a possibility to copy orders from different transaction systems. â&#x20AC;&#x2018; n currency pairs â&#x20AC;&#x201C; one set of rules â&#x20AC;&#x201C; this holds the assumption, that the same set of rules is capable to give proper signals to more than one currency pair. In such a situation, the system is active for any conâ&#x20AC;&#x2018; sidered set of currency pairs.

â&#x20AC;&#x2018; n currency pairs and m sets of rules â&#x20AC;&#x201C; the most comâ&#x20AC;&#x2018; plex mechanism which involves parallel using of difâ&#x20AC;&#x2018; ferent sets of rules. Even in the case of shortâ&#x20AC;&#x2018;term trading it may lead to the concept of portfolio builâ&#x20AC;&#x2018; ding, where elements of such portfolio are currency pairs. 3.1. Decision Process on the Forex Market

ďż˝e deďż˝ine three independent phases, where each phase has a crucial impact on the trading process efâ&#x20AC;&#x2018; fectiveness. There are different issues referring to the effectiveness. They include not only proďż˝it maximizaâ&#x20AC;&#x2018; tion but also minimizing the maximum drawdown, duâ&#x20AC;&#x2018; ration of the open position, risk diversiďż˝ication and the time which is devoted to the currency pair analysis. The general schema of opening and managing the poâ&#x20AC;&#x2018; sition on the Forex market is presented in ďż˝ig. 1. In this ďż˝igure we present three different phases reâ&#x20AC;&#x2018; ferring to the process of making the decision on the market. Each phase includes different mechanisms caâ&#x20AC;&#x2018; pable to effectively manage the position. Below we inâ&#x20AC;&#x2018; troduce and shortly describe each of the three phases: â&#x20AC;&#x2018; opening position â&#x20AC;&#x201C; a crucial phase which includes concepts related with opening the single or multiâ&#x20AC;&#x2018; ple positions. At this phase, there is a need to conâ&#x20AC;&#x2018; sider a set of conditions, which must be fulďż˝illed to open the position and move to the next phase. In the most cases, such conditions include the constant set of crisp rules related with different market indicaâ&#x20AC;&#x2018; tors. Fulďż˝illment of these rules leads to generating the signals. Depending on the type of trading system, this phase ends with opening a set of positions (in the case of the automatic trading system) or deriving

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of oscillators is the Relative Strength Index (RSI): đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą

1â&#x2C6;&#x2019;

100

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;

(3)

where đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą is the value of the RSI indicator calculaâ&#x20AC;&#x2018; ted on the basis of the last đ?&#x2018;?đ?&#x2018;? periods in time đ?&#x2018;Ąđ?&#x2018;Ą, đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; is the sum of gains over the past đ?&#x2018;?đ?&#x2018;? periods and đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122; is the sum of losses over the past đ?&#x2018;?đ?&#x2018;? periods. The second oscillator to be used is the Commodity Channel Index (CCI): đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą

Fig. 1. Managing position phases the set of signals to the decision maker (in the deciâ&#x20AC;&#x2018; sion support trading system).

â&#x20AC;&#x2018; managing the position phase â&#x20AC;&#x201C; the phase focused on managing all opened positions, which, depending on the risk proďż˝ile of the decision maker may include realizing small proďż˝its, opening additional positions, adďż˝usting the taking proďż˝it or cutting loses levels and more.

â&#x20AC;&#x2018; closing the position phase â&#x20AC;&#x201C; in the trivial case, this phase may correspond to closing the position by hitâ&#x20AC;&#x2018; ting some price levels deďż˝ined in the previous phase. Other possibilities may include closing the position on the basis of different market indicator, closing the position as the effect of opening an opposite posiâ&#x20AC;&#x2018; tion, or applying more complex rules related to the concept of portfolio management. We purport, that crucial phase, which has the greâ&#x20AC;&#x2018; atest impact on the effectiveness of the trading system is the ďż˝irst phase, in which the most preferred currency pair is selected from the set of all possible variants. Thus the ďż˝irst phase will be our main interest in this article.

4. Examples of Technical Indicators

In the following three equally important market indicators frequently used in the transaction systems are presented: the moving average and two oscillaâ&#x20AC;&#x2018; tors. The proposed approach can, however, include any number of indicators. The moving average equation is given as follows: đ?&#x2018;?đ?&#x2018;?

â&#x2C6;&#x2018; đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; , đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;?đ?&#x2018;?

(2)

where đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą is the value of the moving average for period đ?&#x2018;?đ?&#x2018;? in time đ?&#x2018;Ąđ?&#x2018;Ą, đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; is a currency pair value for a given time đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;, and đ?&#x2018;?đ?&#x2018;? is the number of included values. An example concept based on moving averages may be found in [22]. The ďż˝irst technical indicator belonging to the group

1 đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą Âˇ , đ?&#x2018;?đ?&#x2018;? đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x153;&#x17D;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą )

(4)

where đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą is the value of the CCI indicator calcuâ&#x20AC;&#x2018; lated on the basis of đ?&#x2018;?đ?&#x2018;? periods in time đ?&#x2018;Ąđ?&#x2018;Ą, đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą is the typical price calculated as the average value of the Close, Low and High price from a given period, đ?&#x153;&#x17D;đ?&#x153;&#x17D; is the mean absolute deviation and đ?&#x2018;?đ?&#x2018;? is the constant vaâ&#x20AC;&#x2018; lue used for scaling the mean absolute deviation value; for đ??śđ??śđ??śđ??śđ??śđ??ś20 (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą this value is equal to 0.015.

5. Crisp Trading System

Actions of the typical crisp system can be descriâ&#x20AC;&#x2018; bed with the use of a binary activation function. The function takes the value one when a respective condiâ&#x20AC;&#x2018; tion for a technical indicator is true and takes the value zero otherwise. The signal to open a position on the market is generated only in the ďż˝irst case. Let us denote these conditions for the considered indicators as đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC; , đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; and đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ??śđ??śđ??śđ??śđ??śđ??ś . A potenâ&#x20AC;&#x2018; tial BUY signal may be generated for a given currency pair when at least one of the conditions is fulďż˝illed: đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą if (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą

đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ??śđ??śđ??śđ??śđ??śđ??śđ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

(5)

where conditions đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ , đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ , đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ??śđ??śđ??śđ??śđ??śđ??śđ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ refer to the moving averages, RSI and CCI indicators respectively. If neither of the conditions is fulďż˝illed the currency pair is removed from further analysis: đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? = đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; if ÂŹ(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

â&#x2C6;¨đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ??śđ??śđ??śđ??śđ??śđ??śđ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

(6)

The typical conditions used in the existing trading syâ&#x20AC;&#x2018; stems for the considered technical indicators are preâ&#x20AC;&#x2018; sented below. The condition for the moving averages takes the form: đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą if (đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;§(đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

(7)

where đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ą is the value of the moving average from the lower period in time đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą, đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 1) is the value of the moving average from the higher period in time đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ą. An example signal is generated if two moving averages cross each other. In the case of the oscillators RSI and CCI, the binary activation functions are built on the basis of crossing the indicator with some predeďż˝ined levels. ďż˝or RSI this Articles

53 53

of Automation, Automation,Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of

VOLUME 14,14, NÂ° VOLUME NÂ°22 2020 2020

level will be 30. In the case of CCI it is â&#x2C6;&#x2019;100. The conâ&#x20AC;&#x2018; ditions take the form: đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą if (đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

â&#x2C6;§(đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

and

đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ??śđ??śđ??śđ??śđ??śđ??śđ??ľđ??ľđ??ľđ??ľđ??ľđ??ľ = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą if (đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;§(đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

(8)

(9)

where đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą and đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą denote respectively the values of đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; and đ??śđ??śđ??śđ??śđ??śđ??ś in time đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ą.

6. Proposed Fuzzy Trading System

In the proposed system the different indicators are considered jointly and the activation conditions are fuzzy. Each currency pair is treated as a variâ&#x20AC;&#x2018; ant in a multicriteria decision space. Criteria in this space refer to particular indicators. Values of the criâ&#x20AC;&#x2018; teria are deďż˝ined by membership functions referring to particular indicators. It is assumed that the memâ&#x20AC;&#x2018; bership function for each indicator takes values in the range â&#x;¨0, 1â&#x;Š. The membership function takes the value 1 when the value 1 is achieved by the binary activation function in the crisp approach. In the fuzzy approach, the original signal generaâ&#x20AC;&#x2018; ted in the case of crisp approach is still included. Hoâ&#x20AC;&#x2018; wever, the situation when the conditions for a given indicator are almost satisďż˝ied, omitted in the crisp apâ&#x20AC;&#x2018; proach, can be included in the fuzzy approach with the use of the membership function. Let each currency pair đ?&#x2018;?đ?&#x2018;? will be treated as a variant đ?&#x2018;Śđ?&#x2018;Ś in the decision space â&#x201E;?đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ; thus every variant đ?&#x2018;Śđ?&#x2018;Ś will be denoted as the vector of criteria đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś1 , đ?&#x2018;Śđ?&#x2018;Ś2 , ..., đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ), đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; â&#x2C6;&#x2C6; â&#x;¨0, 1â&#x;Š, đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;, where đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; is the number of conâ&#x20AC;&#x2018; sidered indicators. The criteria are deďż˝ined by values of the membership function calculated for particular indicators. Due to limited space, we introduce only membersâ&#x20AC;&#x2018; hip functions related to the BUY signals. The memâ&#x20AC;&#x2018; bership functions for the ďż˝ELL signals can be deďż˝ined in a similar way. The membership function for the MMA indicator is proposed in the form: đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;

54 54

đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122; if (đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;§ đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x2C6;§(đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; < đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x17D;Ş đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122; â&#x17D;Ş â&#x2C6;§(đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş 1 if (đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x153;&#x2021;đ?&#x153;&#x2021;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC; (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? â&#x2C6;§(đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;¨ đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;â&#x201E;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; if (đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x2C6;§(đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; â&#x201E;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; < đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x17D;Ş â&#x2C6;§(đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC; â&#x17D;Ş đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x201C; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 0 in other case â&#x17D;Š (10) where đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; is the maximal number of readings used in the calculations, đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;â&#x201E;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; is a function used to count reaâ&#x20AC;&#x2018; dings above the moving average with a higher period and đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x2122; is a function used to count readings below the moving average with a higher period. It is assumed in

Articles

the above calculations that in the case of reading witâ&#x20AC;&#x2018; hout the crossover of moving averages the possibility of a trend change would rise while the present trend would continue. The membership function deďż˝ined for the Rďż˝I indiâ&#x20AC;&#x2018; cator is given as follows: đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą

đ?&#x2018;?đ?&#x2018;? â&#x17D;§ 30 if (đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş 1 if ((đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş â&#x2C6;§(đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş â&#x2C6;¨(đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x153;&#x2021;đ?&#x153;&#x2021;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? 0.9 â&#x17D;¨ đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą Âˇ đ?&#x203A;źđ?&#x203A;ź if (đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş â&#x2C6;§(đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;?đ?&#x2018;? â&#x17D;Ş â&#x17D;Ş â&#x2C6;§(đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Š 0 if (đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (11) In the case of the CCI indicator the membership function takes the form:

0 if (đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ) â&#x17D;§ đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x17D;Ş â&#x2C6;&#x2019;đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x2C6;&#x2019;100 if â&#x17D;Ş (đ??śđ??śđ??śđ??śđ??śđ??ś (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą ) đ?&#x2018;?đ?&#x2018;? đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; â&#x17D;Ş â&#x17D;Ş â&#x2C6;§(đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 1 if (đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x153;&#x2021;đ?&#x153;&#x2021;đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??ś (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? â&#x2C6;§(đ??śđ??śđ??śđ??śđ??śđ??ś đ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;¨ â&#x17D;Ş đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą if (đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;50 â&#x17D;Ş â&#x17D;Ş â&#x2C6;§(đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Ş â&#x2C6;§(đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x17D;Š 0 if (đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (12) where đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;?đ?&#x2018;? (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą is a value of the đ??śđ??śđ??śđ??śđ??śđ??ś indicator in the present time, đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; is the maximal considered CCI value and đ??śđ??śđ??śđ??śđ??śđ??śđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; is the minimal considered CCI vaâ&#x20AC;&#x2018; lue. A vector of scalar values in the range of â&#x;¨0; 1â&#x;Š is generated in a given time đ?&#x2018;Ąđ?&#x2018;Ą for all of the given indicaâ&#x20AC;&#x2018; tors and represents each currency pair as a variant in the multicriteria space. In this space, we made multiâ&#x20AC;&#x2018; criteria analysis and look for the Pareto optimal (nonâ&#x20AC;&#x2018; dominated) variants. Respective domination relations have to be introduced. The following relations between variants are introâ&#x20AC;&#x2018; duced in â&#x201E;?đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; space: Â&#x2021;Ď?Â&#x2039;Â?Â&#x2039;Â&#x2013;Â&#x2039;Â&#x2018;Â? Íł A variant đ?&#x2018;Śđ?&#x2018;Ś is at least as preferred as a vaâ&#x20AC;&#x2018; riant đ?&#x2018;§đ?&#x2018;§ if each criterion of đ?&#x2018;Śđ?&#x2018;Ś is not worse than the reâ&#x20AC;&#x2018; spective criterion of đ?&#x2018;§đ?&#x2018;§. đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś1 â&#x2030;Ľ đ?&#x2018;§đ?&#x2018;§1 ) â&#x2C6;§ (đ?&#x2018;Śđ?&#x2018;Ś2 â&#x2030;Ľ đ?&#x2018;§đ?&#x2018;§2 ) â&#x2C6;§ ... â&#x2C6;§ (đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2030;Ľ đ?&#x2018;§đ?&#x2018;§đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ). (13)

Â&#x2021;Ď?Â&#x2039;Â?Â&#x2039;Â&#x2013;Â&#x2039;Â&#x2018;Â? Í´ A variant đ?&#x2018;Śđ?&#x2018;Ś is more preferred (better) than a variant đ?&#x2018;§đ?&#x2018;§ according to the logical formulae: đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś

(14)

An algorithm deriving nonâ&#x20AC;&#x2018;dominated variants is proposed. The following notions are used in the algoâ&#x20AC;&#x2018; rithm: the ideal â&#x20AC;&#x201C; aspiration point đ?&#x2018;˘đ?&#x2018;˘, the reservation point đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ1 ,đ?&#x2018;Ľđ?&#x2018;Ľ2 , ...,đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;&#x203A;đ?&#x2018;&#x203A; )_đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; â&#x2C6;&#x2C6; [0, 1], the set of all variants đ?&#x2018;&#x152;đ?&#x2018;&#x152;, the set of points removed from the anaâ&#x20AC;&#x2018; lysis in the algorithm đ?&#x2018;&#x152;đ?&#x2018;&#x152;â&#x2C6;&#x2019; , the set of points accepted for further analysis in the algorithm đ?&#x2018;&#x152;đ?&#x2018;&#x152;+ = đ?&#x2018;&#x152;đ?&#x2018;&#x152; đ?&#x2018;&#x152; đ?&#x2018;&#x152;đ?&#x2018;&#x152;â&#x2C6;&#x2019; , the set of nonâ&#x20AC;&#x2018;dominated variants đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; . The aspiration point đ?&#x2018;˘đ?&#x2018;˘ refers to the case when BUY signals are generated for

Journal of Automation, Automation,Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems

all indicators, i.e. when all the membership functions take the value 1. The reservation point đ?&#x2018;Ľđ?&#x2018;Ľ is deďż˝ined by the minimum values of membership functions accepâ&#x20AC;&#x2018; ted by the decision maker. The simpliďż˝ied idea of the algorithm is given below: â&#x20AC;&#x2018; Step 0. In this initial step, the sets đ?&#x2018;&#x152;đ?&#x2018;&#x152; and đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; are created. The aspiration point đ?&#x2018;˘đ?&#x2018;˘ đ?&#x2018;˘ đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ đ?&#x2018;˘ đ?&#x2018;˘ đ?&#x2018;˘đ?&#x2018;˘ and the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ assumed by the decision maker are ďż˝ixed.

â&#x20AC;&#x2018; Step 1. The set đ?&#x2018;&#x152;đ?&#x2018;&#x152;â&#x2C6;&#x2019; is generated as the set of points dominated by the reservation point and removed from further analysis. All other points belong to the set đ?&#x2018;&#x152;đ?&#x2018;&#x152;+ . â&#x20AC;&#x2018; Step 2. If there exists variant đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Ś+ , đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś, then đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; . End of the algorithm.

â&#x20AC;&#x2018; Step 3. Each variant đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Ś+ is checked: if đ?&#x2018;Śđ?&#x2018;Ś đ?&#x2018;Ś đ?&#x2018;Śđ?&#x2018;Śâ&#x2C6;&#x2019; then it is removed from further analysis, else it is compared with the points in the set đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; (it is added to đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; if đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; is empty). For each point đ?&#x2018;§đ?&#x2018;§ đ?&#x2018;§đ?&#x2018;§đ?&#x2018;§đ?&#x2018;§đ?&#x2018;§, if đ?&#x2018;Śđ?&#x2018;Ś dominates đ?&#x2018;§đ?&#x2018;§, then đ?&#x2018;§đ?&#x2018;§ is removed from đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; , đ?&#x2018;Śđ?&#x2018;Ś is added to đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; and the set đ?&#x2018;&#x152;đ?&#x2018;&#x152;â&#x2C6;&#x2019; is extended by the set of point dominated by đ?&#x2018;Śđ?&#x2018;Ś; if đ?&#x2018;Śđ?&#x2018;Ś is dominated by đ?&#x2018;§đ?&#x2018;§ then đ?&#x2018;Śđ?&#x2018;Ś is reâ&#x20AC;&#x2018; moved from analysis, i.e. removed from the set đ?&#x2018;&#x152;đ?&#x2018;&#x152;+ . The algorithm ends, when all variants from the set đ?&#x2018;&#x152;đ?&#x2018;&#x152;+ are checked. In the algorithm, the concept of domination cons is used. For each point đ?&#x2018;&#x152;đ?&#x2018;&#x152; added to the set đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; , the set đ?&#x2018;&#x152;đ?&#x2018;&#x152;â&#x2C6;&#x2019; is extended using the domination cone. The successive extensions of this set of points removed from analysis assure the high computational efďż˝iciency of the algoâ&#x20AC;&#x2018; rithm.

Fig. 2. An illustrative example It has been proved that the algorithm derives all nonâ&#x20AC;&#x2018;dominated variants in the set of variants nonâ&#x20AC;&#x2018; dominated by the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ. All other variâ&#x20AC;&#x2018; ants are eliminated from the analysis. The algorithm has been implemented in a computerâ&#x20AC;&#x2018;based trading system to make expeâ&#x20AC;&#x2018; riments using real data from the Forex market. The fuzzy approach introduces additional uncerâ&#x20AC;&#x2018; tainty which is not present in the case of the crisp apâ&#x20AC;&#x2018; proach. The decision maker selecting one of the variâ&#x20AC;&#x2018; ants derived by the fuzzy trading system takes a risk

VOLUME 2020 VOLUME 14,14, NÂ°NÂ° 2 2 2020

that the variant can be not effective. The uncertainty and risk depend on the distance of the reservation point from the aspiration point đ?&#x2018;˘đ?&#x2018;˘. In the case of the reâ&#x20AC;&#x2018; servation point which is close to the aspiration point, the risk is lower but only a few or even not any variant can be derived by the system. The risk is greater when the distance increases but the system can derive and propose a greater number of nonâ&#x20AC;&#x2018;dominated variants. The decision maker is aware of this decides on the poâ&#x20AC;&#x2018; sitioning of the reservation point. Figure 2 presents variants analyzed by the algoâ&#x20AC;&#x2018; rithm in a twoâ&#x20AC;&#x2018;dimensional criteria space. The aspiâ&#x20AC;&#x2018; ration point đ?&#x2018;˘đ?&#x2018;˘ and the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ are shown. The algorithm, from the set of all variants, selects the nonâ&#x20AC;&#x2018;dominated variants đ?&#x2018;Śđ?&#x2018;Ś 3 , đ?&#x2018;Śđ?&#x2018;Ś 5 and đ?&#x2018;Śđ?&#x2018;Ś 6 . The shadowed area represents the set of points dominated by the vaâ&#x20AC;&#x2018; riants above. The classical crisp system generates 5 signals for variants đ?&#x2018;Śđ?&#x2018;Ś 1 , đ?&#x2018;Śđ?&#x2018;Ś 2 , đ?&#x2018;Śđ?&#x2018;Ś 3 , đ?&#x2018;Śđ?&#x2018;Ś 4 , đ?&#x2018;Śđ?&#x2018;Ś 5 not informing, which of them are more or less promising. Let us note, that variants đ?&#x2018;Śđ?&#x2018;Ś 1 , đ?&#x2018;Śđ?&#x2018;Ś 2 , đ?&#x2018;Śđ?&#x2018;Ś 4 are eliminated and removed from analysis by the proposed fuzzy system.

7. Numerical Experiments In this section, we present the results of numerical experiments with real data from the Forex market. In the experiments, the proposed fuzzy trading system is compared with the existing crisp trading systems for the three indicators considered above. Our main moâ&#x20AC;&#x2018; tivation was to estimate the number of variants poâ&#x20AC;&#x2018; tentially interesting for the decision maker, indicated by the different trading systems. We tested 30 succesâ&#x20AC;&#x2018; sive readings. By a reading, we mean a single situation on the price chart which is observed in a speciďż˝ic time window. The systems derived variants interested for the decision maker in every reading. We selected three different time windows (frames) corresponding to the scalping system with aggressive trading (the length of a single time window was equal to 5 minutes), to the intraday system (the length of a single time window was equal to 1 hour) and ďż˝inally to the longâ&#x20AC;&#x2018;term traâ&#x20AC;&#x2018; ding with the length of a single time window equal to 1 day. The overall length of the experiments in the case of the scalping system was equal to 30 Âˇ 5 = 100 miâ&#x20AC;&#x2018; nutes, for the intraday system the overall length of the experiments was equal to 30 hours, and 30 days for the longâ&#x20AC;&#x2018;term trading. Information about the selected time windows can be found in Table 1. The number of variants (currency pairs) available and analyzed in every reading was always equal to 68. Systems with two and three indicators were analyzed separately. Tab. 1. Data sets summary 5 Minutes 1 Hour 1 Day

Starting Date 2017 IV 03 8.00 2017 I 02 7.00 2017 II 03 00.00

Ending Date 2017 IV 03 10.25 2017 I 03 12.00 2017 III 15 00.00 Articles

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7.1. Data Example With Two Indicators We selected an approach with two criteria based on the CCI and RSI indicators and the most popular 1â&#x20AC;&#x2018;hour time window and the date of January 3, 2017, which was connected with the opening of the New York trading session. All generated variants are preâ&#x20AC;&#x2018; sented in the twoâ&#x20AC;&#x2018;dimensional criteria space shown in Fig. 3a. In the analysis, we focused only on the buy signals. A similar analysis can be performed for short sells.

Fig. 3. Twoâ&#x20AC;?criteria example with đ?&#x2018;Śđ?&#x2018;Ś1 = đ?&#x153;&#x2021;đ?&#x153;&#x2021;đ??śđ??śđ??śđ??śđ??śđ??ś , đ?&#x2018;Śđ?&#x2018;Ś2 = đ?&#x153;&#x2021;đ?&#x153;&#x2021;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; . a) all 68 variants generated; b) set of considered variants along with the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ; c) set of nonâ&#x20AC;?dominated variants derived for the decision maker A characteristic arrangement of variants in the criâ&#x20AC;&#x2018; teria space can be observed in the case of the system based only on two criteria. In a large number of variâ&#x20AC;&#x2018; ants only one criterion has a very high value (close to 1), while the other criterion is often below the accepâ&#x20AC;&#x2018; table value. The results of the fuzzy approach are preâ&#x20AC;&#x2018; sented in Fig. 3b. The dot lines in Fig. 3b and Fig. 3c denote the position of the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľ (0.75, 0.75). First, all variants dominated by the reserâ&#x20AC;&#x2018; vation point đ?&#x2018;Ľđ?&#x2018;Ľ are excluded from further analysis. This situation can be observed in Fig. 3b. After obtaining a set of variants that are potentially acceptable to the decision maker, the proposed algorithm is used to geâ&#x20AC;&#x2018; nerate a set of nonâ&#x20AC;&#x2018;dominated solutions đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; . These vaâ&#x20AC;&#x2018; riants can be seen in Fig. 3c. Finally, 5 nonâ&#x20AC;&#x2018;dominated, different variants were derived for the decision maker. In the case of the crisp approach, the number of variants derived for the decision maker is relatively small, while the fuzzy approach can be used to extend the set of nonâ&#x20AC;&#x2018;dominated variants derived for the deâ&#x20AC;&#x2018; cision maker. 7.2. Number of Variants Derived to the Decision Maker

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Selected results of the experiments are presented in Table 2 for the 5â&#x20AC;&#x2018;minute time window, in Table 3 for the 1â&#x20AC;&#x2018;hour time window and in Table 4 for the largest 1â&#x20AC;&#x2018;day time window. The tables present the numbers Articles

VOLUME 14,14, NÂ° VOLUME NÂ°22 2020 2020

of the nonâ&#x20AC;&#x2018;dominated variants derived by the propoâ&#x20AC;&#x2018; sed fuzzy system for four different values of the reâ&#x20AC;&#x2018; servation point: đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ1 , đ?&#x2018;Ľđ?&#x2018;Ľ2 , đ?&#x2018;Ľđ?&#x2018;Ľ3 ), â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = 0.7, đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = 0.8, đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = 0.9, đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; = 0.95 (the columns are marked by đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ respectively). Theses results are compared to the numbers of sigâ&#x20AC;&#x2018; nals generated by three versions of the crisp approach: Crispâ&#x2C6;&#x2014; , Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014; and Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014;â&#x2C6;&#x2014; , wherein the Crispâ&#x2C6;&#x2014; approâ&#x20AC;&#x2018; ach a signal is generated and presented to the deciâ&#x20AC;&#x2018; sion maker when at least one of the conditions deďż˝iâ&#x20AC;&#x2018; ned by the binary activation function is satisďż˝ied, in the second considered approach â&#x20AC;&#x201C; Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014; at least 2 conâ&#x20AC;&#x2018; ditions must be fulďż˝illed, while in the last considered Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014;â&#x2C6;&#x2014; approach all the 3 conditions have to be satisâ&#x20AC;&#x2018; ďż˝ied. In the last case, the generated signal corresponds to the variants equal to the aspiration point đ?&#x2018;˘đ?&#x2018;˘. The Crispâ&#x2C6;&#x2014; approach overproduces the number of variants proposed to the decision maker, thus seâ&#x20AC;&#x2018; lection of a single variant by the decision maker to make the trading decision may be extremely difďż˝icult. A decreasing number of criteria is observed in the case of Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014; so that it leads to an empty set of variants derived for the decision maker. In the case of Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014;â&#x2C6;&#x2014; , which corresponds to the situation, in which a variant equal to the aspiration point đ?&#x2018;˘đ?&#x2018;˘ should be found, even a single solution was not observed. The fuzzy approach generates relatively small sets of nonâ&#x20AC;&#x2018;dominated variants which are far easier to anaâ&#x20AC;&#x2018; lyze by the decision maker. We use bold font to indicate in the tables the desiâ&#x20AC;&#x2018; rable market situations when the number of variants derived by the fuzzy system for the decision maker is 4, 3 or 2. We use the italic font to indicate situations when the empty set of variants derived for the deciâ&#x20AC;&#x2018; sion maker by the Crispâ&#x2C6;&#x2014;â&#x2C6;&#x2014; method is observed, e.g. in readings 6, 7, 9, 10, 12, 13 in Table 2; see also readings 1, 3â&#x2C6;&#x2019;6, 8 in Table 3 and readings 1, 3â&#x2C6;&#x2019;7, 9, 13 in Table 4. There were also situations when the proposed fuzzy approach derives a relatively large set of variâ&#x20AC;&#x2018; ants, which may be difďż˝icult to analyze by the deciâ&#x20AC;&#x2018; sion maker. In the case of the 1â&#x20AC;&#x2018;hour and 1â&#x20AC;&#x2018;day time window, such a situation is undesirable, but the deâ&#x20AC;&#x2018; cision maker has additional time to perform the anaâ&#x20AC;&#x2018; lysis. While for the smaller time windows such situâ&#x20AC;&#x2018; ations need some additional extension of the propoâ&#x20AC;&#x2018; sed approach. Such an extension is planned in further works with the use of respective ranking methods. It is crucial to understand that all variants derived for the decision maker in the case of the fuzzy approâ&#x20AC;&#x2018; ach are nonâ&#x20AC;&#x2018;dominated, while in the case of the Crispâ&#x2C6;&#x2014; approach (due to the binary activation function) many variants indicated by the system can be dominated. In the case of the crisp system, the decision maker has no information which of the generated variants is betâ&#x20AC;&#x2018; ter or worse. This leads to an important observation that in the case of the crisp approach a single variant is treated as acceptable if any criterion is equal to 1. Thus, in the case of two variants, đ?&#x2018;Śđ?&#x2018;Ś 1 = (0, 0.05, 1) and đ?&#x2018;Śđ?&#x2018;Ś 2 = (0, 0.95, 1), both of them are treated as equally good as (0, 0, 1), while in the fuzzy approach it is posâ&#x20AC;&#x2018;

Journal of Automation, Automation,Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems

sible to distinguish these two variants in favor of đ?&#x2018;Śđ?&#x2018;Ś 2 which strictly dominates the ďż˝irst variant. Similar experiments were conducted for two reâ&#x20AC;&#x2018; maining time windows observed in Table 3 and Table 4. In the case of the reservation point being far from the aspiration point đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ the sets of geneâ&#x20AC;&#x2018; rated variants often exceeded the assumed limits. The fuzzy system generates only a few variants, which can be easily analyzed. In the 1â&#x20AC;&#x2018;day tie window, an inteâ&#x20AC;&#x2018; resting situation could be observed in readings 4, 18 and 20, where the đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014; could not deliver even a sinâ&#x20AC;&#x2018; gle variant while đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014; generated a number of variâ&#x20AC;&#x2018; ants that greatly exceeded the analytical capabilities of the decision maker. The fuzzy approach, in turn, once again allowed to obtain a reasonable number of nonâ&#x20AC;&#x2018; dominated variants in successive readings. The obtained results are also presented in the graphical form for the fuzzy approach with đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ, and compared to the đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014; and đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014; approaches. The results from Table 3 are presented in Fig. 4, reâ&#x20AC;&#x2018; maining results from Table 4 and 5 are presented reâ&#x20AC;&#x2018; spectively in Fig. 5 and Fig. 6. One can easily observe disproportions in the number of variants generated by both crisp methods and a reasonable number of nonâ&#x20AC;&#x2018; dominated variants derive from the proposed fuzzy system.

Fig. 4. 5â&#x20AC;?minute time window linear chart for the fuzzy approach with đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ, đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014; and đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014;

Fig. 5. 1â&#x20AC;?hour time window linear chart for the fuzzy approach with đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ, đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014; and đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014;

The number of solutions generated in the case of đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014; fairly exceeds analytical capabilities of the deâ&#x20AC;&#x2018; cision maker, while đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014; often generates no soluâ&#x20AC;&#x2018; tions at all, and the most restrictive crisp approach

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Fig. 6. 1â&#x20AC;?day time window linear chart for the fuzzy approach with đ?&#x2018;Ľđ?&#x2018;Ľ đ?&#x2018;Ľ đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ, đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014; and đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014;

đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śâ&#x2C6;&#x2014;â&#x2C6;&#x2014;â&#x2C6;&#x2014; not delivered any variants at all. The proâ&#x20AC;&#x2018; posed fuzzy approach gives the possibility to control the number of generated variants on the basis of the risk aversion adjusted with the use of the reservation point. It may be easily extended on the trading systems with four and more indicators represented by criteria in a multicriteria space of possible decisions. 7.3. Sensitivity Analysis for the Reservation Point

To investigate the impact of the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ on the results achieved by the fuzzy approach, we additionally performed the sensitivity analysis for this particular parameter. Expected results should lead to the conclusion, that equivalent decreasing the đ?&#x2018;Ľđ?&#x2018;Ľ value for all criteria increases the number of variants deriâ&#x20AC;&#x2018; ved for the decision maker. At the same time the risk related to these variants will be higher than in the case of the crisp approach. However, decreasing only one component đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;&#x2013;đ?&#x2018;&#x2013; relates to the respective criterion and the risk is increasing only in the case of this criterion. This should also lead to increasing number of variants derived for the decision maker without excessive risk. The performed sensitivity analysis referring to the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ allows to estimate the impact of đ?&#x2018;Ľđ?&#x2018;Ľ on the overall number of variants generated for the deâ&#x20AC;&#x2018; cision maker. It is obvious, that the number of variants will be decreasing, while đ?&#x2018;Ľđ?&#x2018;Ľ is moved towards the aspiâ&#x20AC;&#x2018; ration point đ?&#x2018;˘đ?&#x2018;˘. Thus two important questions emerge. First of all, we investigate, whether the selected data set (to be more precise, the length of the time window) has an impact on the overall number of variants in the set đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; . The shape of the chart indicates, that the average number of variants derived to the decision maker graâ&#x20AC;&#x2018; dually rises without any sudden changes, while the reâ&#x20AC;&#x2018; servation point is moved out of the aspiration point (see Fig. 7). It would indicate the positive correlation between the position of the đ?&#x2018;Ľđ?&#x2018;Ľ and the number of vaâ&#x20AC;&#x2018; riants available for the decision maker without any observable anomalies. Such anomalies would include large leap for some boundary values of the point đ?&#x2018;Ľđ?&#x2018;Ľ. Results for two out of three analyzed time winâ&#x20AC;&#x2018; dows are presented in Fig. 7. While the position of the reservation point đ?&#x2018;Ľđ?&#x2018;Ľ is moved away from the aspiration point đ?&#x2018;˘đ?&#x2018;˘, the average number of variants interesting for the decision maker is increased. Moreover, no visible Articles

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Tab. 2. Number of variants available to the decision maker for the 5‐minute time window Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Reading 6 Reading 7 Reading 8 Reading 9 Reading 10 Reading 11 Reading 12 Reading 13 Reading 14 Reading 15 Reading 16 Reading 17 Reading 18 Reading 19 Reading 20 Reading 21 Reading 22 Reading 23 Reading 24 Reading 25 Reading 26 Reading 27 Reading 28 Reading 29 Reading 30

large leaps are observed.

x = 0.7 7 6 10 9 6 12 7 8 7 9 4 6 8 6 9 10 11 6 9 8 12 4 8 3 7 5 5 4 9 8

x = 0.8 6 6 10 8 4 12 7 8 7 8 4 5 7 5 9 8 8 6 8 7 11 4 8 3 7 4 5 3 9 7

x = 0.9 5 6 6 7 3 11 6 8 7 8 3 4 6 5 5 6 7 4 5 6 10 3 6 3 7 4 5 3 9 7

8. Conclusion

58 58

Existing trading systems based on the crisp appro‑ ach have a number of disadvantages. In this article, we proposed the multicriteria fuzzy trading system inclu‑ ding three different technical indicators. Trading ru‑ les for both: the classical crisp and the proposed fuzzy trading system were de�ined. A new concept of the fuzzy trading system including the possibility to gene‑ rate sets of non‑dominated variants derived to the de‑ cision maker was introduced as well. All concepts of trading systems were experimentally veri�ied and tes‑ ted on the limited set of technical indicators. We experimentally veri�ied, that proposed fuzzy trading system is capable to effectively derive Pareto‑ optimal variants for the decision maker. The proposed system was compared in the experiments to three ver‑ sions of the crisp system: Crisp∗ , Crisp∗∗ , Crisp∗∗∗ . In contrary to the fuzzy approach, the crisp system de‑ rives very small (or even none) variants in the case of the Crisp∗∗ or number of variants is too large to be effectively handled by the decision maker – what was observed in the case of the Crisp∗ . The third ver‑ sion of the classical trading system Crisp∗∗∗ was not Articles

x = 0.95 5 6 6 5 3 10 5 7 4 8 2 3 5 5 4 5 6 4 4 6 8 3 4 3 7 4 5 3 8 5

Crisp* 8 16 11 9 12 9 3 15 10 5 7 13 7 12 11 9 4 10 6 5 8 13 10 5 5 7 11 8 10 9

Crisp** 1 1 2 1 1 0 0 5 0 0 1 0 0 2 0 2 0 3 0 0 0 1 0 2 0 1 3 1 0 0

Crisp*** 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

capable to derive even single variant. One of the most important advantages of the proposed approach is that the fuzzy system is capable to derive sets of non‑ dominated solutions, which could be further used to develop a system for generating portfolios of variants.

Further works should include the application of methods allowing ranking of the derived variants ac‑ cording to preferences of the decision maker. Besi‑ des the further development of the fuzzy concept, a more robust and less computationally expensive al‑ gorithm capable to derive a set of non‑dominated va‑ riants should be developed as well.

AUTHORS Przemysław Juszczuk∗ – University of Econo‑ mics, Faculty of Informatics and Communica‑ tion, Department of Knowledge Engineering, 1 Maja 50, 40‑287 Katowice, Poland, e‑mail: przem‑ yslaw.juszczuk@ue.katowice.pl.

Lech Kruś∗ – Systems Research Institute, Polish Aca‑ demy of Sciences, Newelska 6, 01‑447 Warsaw, Po‑ land, e‑mail: krus@ibspan.waw.pl. ∗

Corresponding author

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Tab. 3. Number of variants available to the decision maker for the 1‐hour time window

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Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Reading 6 Reading 7 Reading 8 Reading 9 Reading 10 Reading 11 Reading 12 Reading 13 Reading 14 Reading 15 Reading 16 Reading 17 Reading 18 Reading 19 Reading 20 Reading 21 Reading 22 Reading 23 Reading 24 Reading 25 Reading 26 Reading 27 Reading 28 Reading 29 Reading 30

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x = 0.9 7 5 6 5 5 4 9 5 7 4 3 5 5 5 3 3 3 4 5 3 3 4 3 4 4 5 4 3 4 3

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Articles

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Non-Contact Video-Based Remote Photoplethysmography for Human Stress Detection Submitted: 20th October 2018; accepted: 2nd June 2020

Sergii Nikolaiev, Sergii Telenyk, Yury Tymoshenko

DOI: 10.14313/JAMRIS/2-2020/21 Abstract: This paper presents the experimental results for stress index calculation using developed by the authors information technology for non-contact remote human heart rate variability (HRV) retrieval in various conditions from video stream using common wide spread web cameras with minimal frame resolution of 640x480 pixels at average frame rate of 25 frames per second. The developed system architecture based on remote photoplethysmography (rPPG) technology is overviewed including description of all its main components and processes involved in converting video stream of frames into valuable rPPG signal. Also, algorithm of RR-peaks detection and RR-intervals retrieval is described. It is capable to detect 99.3% of heart contractions from raw rPPG signal. The usecases of measuring stress index in a wide variety of situations starting with car and tractor drivers at work research and finishing with students passing exams are presented and analyzed in detail. The results of the experiments have shown that the rPPG system is capable of retrieving stress level that is in accordance with the feelings of experiments’ participants. Keywords: video processing; web cameras; stress index; remote photoplethysmography; rPPG; heart rate; heart rate variability; Predictive, Preventive, Personalized and Participatory Medicine.

1. Introduction At present, the formation of the XXI century medicine requires a new philosophy and the platforms for more effective person’s treatments to advance current healthcare systems. There are several needs that the modern and innovative healthcare systems across the planet should respond to and among them are: the rising costs of medical care and the emerging need to reduce such costs; the grand challenges facing the healthcare and biomedical industry in order to utilize many of the novel technologies; the necessity of radical improvement in wellness and disease prevention; the developing shortage of healthcare professionals; the strong desire of the individual persons to participate more in every aspects of their healthcare.

These tasks to be solved need a new paradigm of advanced healthcare in terms of predictive, preventive, personalized, and participatory (P4) medicine [1]. The core elements of that vision are widely accepted now providing physicians and patients with personalized information about everyone’s health on different system levels. During the development of P4 medicine, many rapidly developing technologies such as artificial intelligence, telemedicine, smart clothes with wearable sensors, mobile apps and beyond will result in treating the causes rather than the symptoms of disease, more efficient patient management and hence a better quality of life. The healthcare industry is on the cusp of substantial changes in the coming decade as new technologies are being developed. In this paper, the authors follow the paradigm of P4 Medicine, which is a global trend in the 21st century and it involves continuous monitoring of the humans’ condition even before any signs of negative changes [2]. The authors have developed robust contactless remote photoplethysmography information technology that uses video stream processing in real time. The developed system is able to obtain biological indicators like HRV through the use of widely distributed web and other video cameras. Mass adoption of such information technology (IT) will allow people to provide an appropriate level of heart health through continuous contactless monitoring of HRV without changing their life styles and could make our medicine preventive. Considering that the relationship between stress, heart disease and sudden death has been recognized since antiquity the main focus of this paper will be dedicated to stress. The choice of studying stress is dictated by the following facts: According to statistics, annual costs to employers because of stress related health care issues and missed work are estimated in $300 Billion [3]. Moreover 77 % of respondents of the research marked that they regularly experience physical symptoms caused by stress. And 73 % of people experience psychological symptoms because of stress. 33% feel that they are living with extreme stress. So, detecting and measuring stress may not only help to make lives better, but also to reduce heart and other diseases. In this paper the results of measuring stress index of humans in different conditions with the help of developed system are presented.

Journal of Automation, Mobile Robotics and Intelligent Systems

2. Heart Rate Variability “Heart Rate Variability” (HRV) has become the conventionally accepted term to describe variations of both instantaneous heart rate and the series of times between consequential pairs of heart contractions (so called RR-intervals). The analysis of HRV has been widely used as a non-invasive and reliable tool to evaluate cardiovascular autonomic control in health and disease. To describe oscillation in consecutive cardiac cycles, other terms have also been used in the literature: for e.g. cycle length/ heart period variability or RR interval sequences (tachograms), and they more appropriately emphasize the fact that it is the interval between consecutive beats that is being analyzed rather than the heart rate per se [4]. In this work the term HRV will be used throughout the article. Usually for the accurate diagnosis of cardiovascular diseases the Holter device is used as the medical standard for heart activity measuring. It requires a patient to visit a doctor, install the device for couple of days, and then follow doctor’s examining of obtained electrocardiograms (ECGs) manually. But many heart diseases do not require the entire ECG to be examined, and for diagnostics it is enough to have only beat-to-beat time intervals, so-called RR intervals. The phenomenon to focus on is the oscillation in the intervals between consecutive heart beats as well as the oscillations between consecutive instantaneous heart rates. Patterns in these oscillations contain enough information for unveiling not only heart pathologies but also dysfunctions of the whole organism. The modern IT development infinitely extends the possibility of tracking various biological signals of a person with further computer processing of digital data. In recent years, there have been various alternatives to the Holter device, namely: personal pulse meters, “smart” clocks, fitness trackers that allow you to record HR, continuous monitoring of the cardiovascular system and reduce the risk of cardiovascular diseases (CVD. Modern markets of mobile soft- and hardware are filled with a different kind of applications for health monitoring and pulsometer-like gadgets that may read, store and process our biological signals. But the only problem remains that all these approaches are contact and in some types of applications it is impossible to make contact measurement and remote technology is needed to estimate HR and heart rate variability.

3. Contactless Remote Photoplethysmography

In recent years, the possibility to extract the heart rate (HR) with the help of a remote photo detector has been established. The approach is called remote photoplethysmography (rPPG) [5–9]. The new technique offers a heart rate (HR) measurement that does not need to have contact with the studied object, which is a valuable feature for both medical and surveillance purposes [8]. rPPG contactless monitors of human Articles

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heart activity detect subtle human skin color variations from reflected light observed by the camera which are induced by heart contractions and blood flow [10]. Lately, several new rPPG algorithms have been developed for pulse-signal extraction from the face with RGB-cameras as photo detectors [6, 7]. These include: (a) Blind Source Separation (e.g., PCA-based [11] and ICA-based [12]), which use different criteria to separate temporal RGB traces into uncorrelated or independent signal sources to retrieve the pulse; (b) CHROM [13], which linearly combines the chrominance signals by assuming a standardized skincolor to white-balance the camera; (c) PBV [14], which uses the signature of blood volume changes in different wavelengths to explicitly distinguish the pulse-induced color changes from motion noise in RGB measurements; and (d) 2SR [15], which measures the temporal rotation between spatial subspaces of skin-pixels for pulse extraction. The essential difference between these rPPG algorithms is in the way of combining RGB-signals into a pulse-signal. The use of three color channels with multiple wavelengths gives the methods the possibility to be robust to motion of the subject. A better understanding of the core rPPG algorithms could benefit many systems/applications for video health monitoring, such as the monitoring of heart-rate [16–20], respiration [17], SpO2 [21], blood pressure [22], neonates [23–24], and the detection of atrial fibrillation [25] and mental stress [26].

4. Remote PPG System’s Architecture Description The developed by the authors of this work rPPG technology is based on the one-pixel camera mathematical model. This means that we in theory can replace our camera with theoretical camera that has only one single pixel. This pixel measures with infinite precision the amount of lite that falls into photosensitive sensor for all three color-channels and do not generate any noise. Thus, the mathematical model expects noise-free real valued luminance signal in three different spectral channels (red, green and blue). To be able to use such abstraction with real multi-pixel cameras that produce many types of noise and have finite precision of measurement the following modules structure is proposed: 1) Face detection module; 2) Images spatial filtering module; 3) Module for skin tints time series frequencies filtration; 4) Heart beats’ time detection module Video processing begins with sequential analysis of each video frame applying face detector, and spatial filters like: skin-detector to find binary mask of skin pixels on the frames; transformations of color tint signal spaces to compensate energy of skin luminance;

Journal of Automation, Mobile Robotics and Intelligent Systems

aggregating skin pixel colors to reduce camera’s sensor’s pixel noise. At this stage the more pixels are aggregated the higher precision is achieved and the lower noise levels are present so the processed signal satisfies criteria of one-pixel camera model. On the next stage temporal filters including frequency finite impulse response pass-band filter with frequencies of heart rate to remove all temporal noises except heart signal. Heart beats’ time detection module returns sequence of heart con-traction moments in time that allow to calculate time deltas between each pair of R-peaks resulting in series of RR-intervals. In the following sections each processing stage will be described in more details.

4.1. Face Detection

The problem of finding faces in the images and video frames can be defined as follows: in a given picture with dimensions K*M pixels, it is necessary to find the coordinates of rectangles that correspond to the bounding boxes of minimal size that fully contain faces of the image. Different approaches are known that solve this task [27]. As a front face detector, in this work Haar cascade classifier was used because of its high speed and accuracy in real-time video processing applications. In order to train the classifier, it is necessary to have labeled images dataset, which consists of a set of images with faces (positive samples) and a set of background images (negative samples). The resulting detector was trained on a dataset containing 35,200 frontal faces and 60,000 background images. Each image in the dataset has dimension of 20x20 pixels. The face detector was trained using the Viola and Jones algorithm (ADAboost). For the Haar cascade quality improvement, bootstrapping procedure has been sequentially applied to modify the training set of negative samples before each training iteration. The depth of the resulting cascade is 25 stages. The sequence of stages with increasing number of features (only two features are checked at the first stage and 218 features – at the last stage) causes low level of false detections and small average calculation time for the whole cascade. Such cascade structure allows to process 17 frames/second in resolution 640x480 pixels on AMD dual core 1.8GHz laptop and more that 30 frames/second in resolution 320x240 which is enough for our purposes. On i7-7700 HQ CPU processing more than 30 frames per second was achieved on frames with resolution 1280x720 pixels. The quality of the trained classifier was checked on a test sample of 7000 faces and 3400 background images. The following metrics of the classifier quality were obtained: tp=6953 – true positives – the number of correctly classified images with faces, fp=47 – false positives – the number of images with faces classified as background, tn=3372 – true negatives – the number of correctly classified images with background,

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– false negatives – the number of images with background classified as faces. precision recall = accuracy =

tp = 0.9932 tp + fp

tp = 0.9959 tp + fn

tp + tn = 0.9927 tp + fp + tn+ fn

(1) (2) (3)

To speed up the process of finding faces in live stream video and to lower CPU load, the refinement search principle is being used during detection phase. This principle allows reducing the amount of computation when processing the next frames of video stream after frame with already found faces. The essence of the refinement search is that after a successful detection of a face in one frame, the search for this face on the next frame is performed only in the vicinity of the already found bounding box rectangle of this given face and not throughout the whole frame. The task of finding pulse and separate heartbeats from video stream requires low noise levels from all components of the system. In the described above algorithm detected bounding box coordinates may change on couple of pixels frame to frame and this effect add additional noise on the next levels of signal processing. So, to avoid this noise the algorithm of stabilizing the position and size of the face bounding box on the frame is used. Its main purpose is cuts off accidental changes in the position and size of the found face rectangle. Thus, the face detection module output consists of the video stream with stabilized human face images.

4.2. Frames Spatial Filtering

In this paper one-pixel camera model is used so the purpose of this module is to create mapping S ( I ) → R of each video frame I ∈ R N ×N ×3 into a one-dimensional real number s * ∈ R, which encodes face skin tint from the input image. At this stage the analysis takes place within the same frame over spatial coordinates excluding temporal factors. This operation of spatial filtration aggregates pixels colors of skin and thus excludes pixel noise with zero mean and captures mean of skin tint which can be tracked later in temporal context. In order for the pixels of the background not to add additional noise, the first step of spatial filter module is to apply a skin detector to the input image and obtain the skin mask. The most skin detectors are based on the comparison of pixel colors with the database of known skin colors, and if the examined color is in the database – then in the resulting mask corresponding pixel is set to 1, and 0 otherwise. Another approach is to have a model (for example based on RBF neural network) that approximates skin colors probability distribution and returns for each given input pixel or region of pixels a probability that the input is part of skin. Articles

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Applying threshold for resulting probabilities the skin bitmask is obtained. Finding a skin binary pixel mask is done with the following algorithm: • blur input image to reduce pixel noise artifacts; • convert the color space of the input image into HSV (Hue-Saturation-Value) space; • select skin mask M of pixels where model probability for each pixel of being skin pixel is higher than 80%; • apply “dilation” and “erosion” operations to reduce noise between frames in time; • calculate the weighted average of the pixel intensities ix,y,z under the mask M : ( x, y )∈ M for each of the channels z ∈ {R,G,B}. Thus, after applying this algorithm, three real values of the average intensities of the skin pixels are obtained for each input image: I z = E ( x, y )∈M i x, y,z one intensity value for each of the color channel z ∈ {R,G,B}. From the mathematical point of view the intensity of one single pixel can be represented as

çi x, y,z = i z + s x, y,z + x, y,z , where iz is the average illumination of the observed object from external light source; ηx,y,z component is the pixels noise induced by light sensing element of the camera; sx,y,z component is the skin tint change we want to measure. Usually η x, y,z  s x, y,z , but given the fact that the noise has zero mean (E x, yη x, y,z = η z = 0), the average of a sufficient number of pixels over the mask allows to reduce the noise level ηx,y,z to values where the amplitude of the useful skin tint signal sz becomes larger than the amplitude of the pixels noise s z  η z . The larger the number of pixels is used for averaging is the better. Therefore, after applying the transform: E ( x, y )∈M ( i x, y,z −= i z ) E x, y s x, y,z + E x, yη= x, y,z

E x, y s x, y,z = s z the desired signal sz is obtained. But at this stage, the component iz remains unknown. Let’s consider the following fact that oxyhemoglobin and hemoglobin absorb and reflect light in different parts of the spectrum differently. So, between channels z ∈ {R,G,B} the values of sR, sG, and sB are non-constant quantities that are nonlinearly dependent on the ratio of levels oxyhemoglobin and hemoglobin in the capillaries of the skin. Thus, the time series sR(t), sG(t) and sB(t), where t is timestamp of received frame from the camera, also show nonlinear dependence. At the same time, when the illumination of the object changes, components iR(t), iG(t) and iB(t) change proportionally or remain unchanged with constant illumination. By selecting the constants Tz ,z ∈ {R,G,B} so that TR ∗ iR ( t ) +TG ∗ iG ( t ) +TB ∗ iB ( t ) = 0 the variation of the useful signal can be preserved while the intensity component of the object’s illumination in time is removed from the equation. Articles

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Introducing the following designation of the vectors s ( t ) =  sR ( t ) ,sG ( t ) ,sB ( t )  and TRGB = [TR ,TG ,TB ], the final equation becomes:

∑

z∈{R,G,B}

∑

z∈{R,G,B}

E ( x, y )∈M Tz ∗ i x, y,z =

Tz ∗ E x, y s x, y,z +Tz ∗ i z +Tz ∗ E x, yη x, y,z =

∑

z∈{R,G,B}

Tz ∗ E x, y s x, y,z = TRGB ∗ s = s *

(4)

where s * – is the desired signal. To calculate the TRGB value let’s use the fact that the variances of the object illumination level time series and the signal differ by several orders of magnitude Dt ( i z ( t ) )  Dt ( s z )  Dt (η z ) . This allows us to apply the methods of blind source separation, which rotate and distort the space {I z ( t ) ,z ∈ {R,G,B}} in the way so that the useful signal s * becomes one of the components, and everything else is distributed among other components. The bests results were obtained by applying Independent Component Analysis (ICA) as blind source separation method that changes the joint distribution of the components and separates the desired signal s * . The following coefficients were obtained as a result of ICA algorithm application: TRGB = [ −0.25,0.764 , −0.285]

(5) After this transformation, a time series of skin tints s ∗ ( t ) are obtained that may also contain other noise in addition to the heartbeats signal. So filtering in frequency domain should be applied to s ∗ ( t ) to leave only the frequency band that contains the heart signal, and throw away other bands as noise.

4.3. Skin Tints Time Series Frequencies Filtration

This module is needed to separate the useful heartbeat signal from the noise. Considering that frames from the video camera are obtained at different time intervals, it is necessary to process the resulting unevenly sampled series applying the following steps: • Evenly resample the output series s ∗ ( t ) . • Perform frequency filtering of the uniformly re sampled series with sampling rate of 30Hz by applying bandpass filter in the range of heartbeat frequencies – from 30/60 Hz to 180/60 Hz. For non-uniformly sampled time series it is necessary to use only those resampling methods that can work in real time applications and that do not distort the shape of the signal. Therefore, three methods were considered: linear interpolation, interpolation with cubic splines and optimal sinc interpolation. Researching the specifics of the residual noise and the form of the signal s ∗ ( t ) , it was found that the linear interpolation has the smallest impact on the signal distortion, which is why it was chosen as resampling method in this work. The raw input signal sampling rate varies in the range from 5 Hz to 30 Hz. After the

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resampling process the signal with a constant sampling rate equal to 30Hz is obtained. The frequency filters can be applied to the uniformly sampled time series, leaving only heart frequencies band in the range from 30 beats per minute to 180 beats /min. Finite impulse response (FIR) filter has shown the best performance. The filters of the moving average, Bessel, Butterworth and Chebyshev were also considered. The authors did not manage to construct Bessel, or Butterworth filters that would satisfy the quality requirements, so the choice was stopped on the family of bandpass finite impulse response filters of the order greater than 60. Optimal quality/execution time tradeoff was achieved with 61 order of the filter. Such a high filter order is caused by the necessity to obtain the width of the signal bandwidth in diapason 1.5–2 hertz with very sharp transition between passing and blocking filter mode and this requires the amplitude-frequency characteristic (AFC) of the filter to have very similar form with the ideal filter. The higher the order of the filter, the better is the quality of the filtered signal but on the other hand, the greater time delay in the data processing pipeline is observed. Time delays are undesirable effect for real-time systems but at lower orders of the filter the signal remained too much noise because of too smooth AFC form.

4.4. Heart Beats’ Time Detection

The next step after frequency filtering is to get markup of signal peaks corresponding to heart beats. The filtered signal has the form of a quasiperiodic sinusoid ( E  s ( t )  = 0 ), where local maxima correspond to the moments of the heart ventricles contraction. Therefore, it is necessary to determine the moments in time of the appearance of these maxima in the filtered signal, which uses the following algorithm: 1. Find the time intervals Ti, where s(t) > 0, 2. For each interval from 1, the global maximum i smax = max s ( t ) should be computed, t ∈Ti

3. Determine the time moment ti when this global i maximum simax: t i = argmaxt∈Ti ( smax = s ( t ) ) , has appeared,

4. For two consecutive maxima, calculate the RRinterval values as rrk = t 2k+1 − t 2k, 60 60 5. If rrk < or rrk > , where 30 and 180 are 30 180 responsible for the minimum and maximum heart rate, then mark the RR interval as false, Thus, in this section, the structure and algorithms used to retrieve human rPPG by processing facial image from the video were described. The system using wide-spread web camera with minimal frame resolution of 640x480 pixels and average speed of 25 frames per second, detects 99.3% of heart contractions. The experiments have shown that standard deviation of delta time between heart beat

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contractions’ time detected by the system and Holter monitor is 0.046 seconds. As the output – the system returns time series of RR intervals and as result HRV can be calculated, same as spectrograms of retrieved cardiointervalograms [27–29]. HRV and RR intervals are very useful indicators for estimating user’s body regulatory abilities and reactions to external factors. For example, stress represents a wide range of physical responses that occur as a direct effect of a stressor causing an upset in the homeostasis of the body, and the corresponding state of the nervous system of the body (or the body as a whole). In medicine, physiology, psychology positive (eustress) and negative (distress) forms of stress are distinguished.

5. Stress Index Calculation Having series of RR-intervals, it is possible to apply variational pulsometry that is used for stress calculation. The essence of variational pulsometry consists in learning the distribution law of cardio intervals. The distributions of cardio intervals are also called histograms. A traditional manner of grouping cardio intervals in the range from 400 to 1300 ms with the buckets’ intervals of 50 ms was constituted in perennial practice. Thus, 20 fixed ranges of cardio-intervals' length are considered that allow to compare pulsograms received by different researchers. The timing capacity of pulsograms is set to 5-minute standard. Cardio interval histogram is a bar plot with buckets' width of 50 ms. Cardio RR-intervals are distributed among these buckets and form columns. The higher the column, the more cardio intervals it includes with duration within the beginning and end time of the bucket. A healthy person with a normal energy potential has symmetrical histogram of pyramidal shape with its central column containing between 30%–50% of all cardio intervals. According to [30] variational pulsometry is widely practiced in Russia and post-soviet countries and is called "index of regulatory systems tension" or stress index (SI). Prof. R. Baevskiy has proposed [30] to capture the factors that are caused by stress into one single formula, namely:

SI =

AMo ∗ 2 ∗ îM MxDMn

(6)

where: Mo (the mode) – is the most frequently occurring value of cardio intervals in milliseconds. Mo differs a little from mathematic expectation (M) in the case of normal allocation and high stationarity; Amo (the mode amplitude) – is the proportion of the most common cardio intervals, from which the central column of the histogram was formed, of all cardio intervals. Articles

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MxDMn (the RR-intervals variation range) – the difference between cardio intervals of the minimum and maximum duration. Stress index calculation is only one of approaches in interpretation and estimation of the variational pulsogram. This parameter is very sensitive to amplification of sympathetic tone and in norm SI varies within the limits of 80–150. Small load (physical or emotional) increases SI up to 1,5–2 times and for significant loads it increases up to 5–10 times. SI in rest can be equal to 400–600 units for the patients with constant tension of regulatory systems illness and may reach 1000– 1500 units for people with coronary heart diseases.

6. Stress Index Measurement Using Developed Remote rPPG System With the help of developed rPPG system several experiments were conducted to measure people stress level in different situations.

6.1. Drivers’ Stress

The rPPG system was used to track HRV and driver stress during many hours of operating cars during summer 2017. The camera was mounted in the car's interior on the celling to have clear view on the drivers’ face (see fig. 1). The drivers were around 5-6 hours in the road covering intercity distances and measurement of SI before and immediately after the journey were compared. Also the drivers were asked to fill in small survey with questions about their level of tiredness. The results of comparisons have shown that stress index that was in range 14-32 before the journey was almost twice higher in the end of the route.

Fig. 1. Stress index of the driver after 5-hour intercity journey is twice higher compared to measurement before the journey

The system was also tested on several drivers in the field using various models of tractors. The camera was mounted near the steering wheel (see fig. 2) or on the ceiling depending on the tractor model. It was shown that drivers who were working in more Articles

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comfortable models of tractors and have been fewer hours on their shift by the moment of experiment conduction had less stress index values.

Fig. 2. The system testing also involved several tractordrivers in field conditions on tractors of different models

6.2. Students Stress Another experiment was conducted at IASA NTUU “Igor Sikorsky KPI” involving group of 23 students. The purpose of this experiment was to detect a change in the student's internal state directly before and during the exam at session. The null hypothesis to test was that students would feel calm two days before the exam as they still have two days to prepare. During the exam, everyone will be little worried. Those who fail to pass the exam will be very worried and experience severe stress. The experiment consisted of two phases: on the first phase students’ stress index was measured in calm conditions. At this stage no coming events for the next two days have been planned that could have been treated by students as alert factor. Also, students have not performed any active physical exercises at least for half an hour before the beginning of the experiment that could have affected the measurements. During this stage experimental measurements of SI with the rPPG system have shown average SI to be in the range 12–37 and heart rate to be in range 61–73 bpm. The second phase of the experiment was conducted during exam. It appeared that students were extremely stressed out. SI was in range 75–261 and the lowest average heart rate per student was 83 while the highest was 145 bpm. Each experimental recording lasted from four to seven minutes. The goal was to collect at least 300 heartbeats in a row for each recoding to be able to calculate the stress index by Baevsky's method. After processing the results, it turned out that the null hypothesis was confirmed but not for all students. On average, the stress index level during the exam has been greater than two days before the exam. But there were also students who had normal stress index level during both phases and who were also stressed all the time. For example, let’s look at the obtained data of the student whose heart rate was within the normal range

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during both phases of experiment (approximately 67 beats per minute). The figure 3 shows his RR intervals obtained during the experiment on the exam. They are in range from 630 to 1017 milliseconds. The bar height shows the duration of each of the RR intervals in milliseconds (at the bottom of the bar durations in milliseconds are presented in white). Numbers above the bars indicate the instantaneous pulse (beats per minute). Labels under the abscise axis indicate the time of each RR interval occurrence given in seconds from the beginning of the experiment recording. Judging from the figure 3, one can assert that the student is in normal condition and has little stress. After calculating the SI, we get the figure 4, which shows that the student's stress was in the range of 20 to 40 conventional units. To calculate the stress formula,

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the duration of RR-intervals series was taken equal to 150 seconds. Although most of the students had “poker faces” during this experiment and showed no external signs of their emotions and neither the lecturer nor the stuff conducting the experiment noticed any difference from other students, the rPPG system has detected very high heart rate and big SI values from some of the students. For example, the figure 5 shows RR-intervals of an extremely worried student. Her pulse was in the range of 110 to 140 beats per minute and averaged 127 beats per minute, indicating high level of adrenaline in the blood and, accordingly, a high level of stress. At the same time, two days before the exam, she was calm, and her average pulse rate was 65 beats per minute.

Fig. 3. Example of RR-intervals of the student in time (sec). Signatures over the bars show the instantaneous pulse (beats/minute)

Fig. 4. Stress index from time plot of calm student (conventional units) Articles

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Fig. 5. Example of obtained RR-intervals from experiment during exam) Using the proposed IT the student's photoplethysmogram raw signal (yellow-colored) and after frequency filtration (violet-colored) were obtained (figure 6). Yellow vertical lines represent moments in time of heart contractions. A good noise to signal ratio of raw signal can be noticed because the amplitude of the signal is much bigger than the amplitude of noise. This testifies to the high quality and reliability of the obtained PPG and RR-intervals, respectively. After calculating the stress index, we get the following figure 7, from which it can be seen, that the student's stress was in the range of 125 to 132 conventional units. The obtained students’ levels of stress during the exam were surprising even for professor with many years of experience who was conducting this exam.

Fig. 6. Student’s rPPG heartbeat signal before (yellow) and after filtering (violet) in time (sec)

Fig. 7. Stress index from time plot of the stressed student (conventional units)

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It was shown that the system determined the pulse and stress levels of the students without any problems and the rPPG system measurements results were in accordance with students’ answers from questionnaires about their feelings. Also, after a detailed analysis of the rPPG signals retrieved by the system, their quality was confirmed as high and conclusions about the reliability of the results of the experiments themselves were marked as reliable.

7. Conclusion The need of the new non-contact widely available sensors for human bio-signals constant monitoring was described within the framework of predictive, preventive, personalized, and participatory medicine. It was shown that the heart rate variability can be a good indicator for estimating internal states of the human including heart rate, stress levels and heart diseases that cause decrease in productivity and financial loses for the enterprises and to the whole economy. Overview of recent papers and approached was made to show how using widely spread web cameras it is possible to build remote non-contact information technology that can extract precise timings of heart beats from video stream based on remote photo plethysmography. Also, the architecture and main modules of the developed by the authors contactless rPPG system were presented. Several experiments were described for human stress index calculation in different conditions including car and tractor drivers. It was shown that despite the absence of visual signs perceivable by other humans, the rPPG system was able to differentiate and measure internal states of the people who were participating in the experiments. The obtained measurements were in accordance with the feelings of participants and the quality of the obtained results was confirmed by in-depth examining of all stages of signal processing within the rPPG system. In the summary, it can be stated that the developed personal non-contact automatic remote photoplethysmography system for heart beats time moments’ contraction (so called RR-intervals) retrieval, can be used in different applications like: • person’s functional and emotional states detection; • person’s Identification & Authentication via remote detection of vital signs presence; • contactless remote HRV and stress tracking. Developed rPPG method has shown good performance using ordinary web cameras for online R-peaks detection. The technology misses heart beats at rate 0.69% and detects false positives heart beats at rate 1.16%. Root mean square time deviation between correctly classified heart beats is 0.046 seconds. Using cameras filming at higher frame rates one can greatly decrease these errors.

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AUTHORS Sergii Nikolaiev – Institute for Applied System Analysis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine, email: sergiynicolaev@gmail.com. Sergii Telenyk* – Department of Electrical Engineering and Computer Science, Cracow University of Technology, Krakow, Poland, e-mail: stelenyk@pk.edu.pl.

Yury Tymoshenko – Institute for Applied System Analysis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine, e-mail: yury.alex.tym@gmail.com. * Corresponding author

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trix Completion for Heart Rate Estimation from Face Videos under Realistic Conditions”. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016, 2396– 2404 DOI: 10.1109/CVPR.2016.263. [21] A. R. Guazzi, M. Villarroel, J. Jorge, J. Daly, M. C. Frise, P. A. Robbins and L. Tarassenko, “Non-contact measurement of oxygen saturation with an RGB camera”, Biomedical Optics Express, vol. 6, no. 9, 2015 DOI: 10.1364/BOE.6.003320. [22] I. C. Jeong and J. Finkelstein, “Introducing Contactless Blood Pressure Assessment Using a High Speed Video Camera”, Journal of Medical Systems, vol. 40, no. 4, 2016 DOI: 10.1007/s10916-016-0439-z. [23] L. K. Mestha, S. Kyal, Beilei Xu, L. E. Lewis and V. Kumar, “Towards continuous monitoring of pulse rate in neonatal intensive care unit with a webcam”. In: 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2014, 3817–3820 DOI: 10.1109/EMBC.2014.6944455. [24] S. Fernando, W. Wang, I. Kirenko, G. de Haan, S. Bambang Oetomo, H. Corporaal and J. van Dalfsen, “Feasibility of Contactless Pulse Rate Monitoring of Neonates using Google Glass”. In: Proceedings of the 5th EAI International Conference on Wireless Mobile Communication and Healthcare – “Transforming healthcare through innovations in mobile and wireless technologies”, 2015 DOI: 10.4108/eai.14-10-2015.2261589. [25] J.-P. Couderc, S. Kyal, L. K. Mestha, B. Xu, D. R. Peterson, X. Xia and B. Hall, “Detection of atrial fibrillation using contactless facial video monitoring”, Heart Rhythm, vol. 12, no. 1, 2015, 195–201 DOI: 10.1016/j.hrthm.2014.08.035. [26] B. Kaur, S. Moses, M. Luthra and V. N. Ikonomidou, “Remote stress detection using a visible spectrum camera”. In: H. H. Szu, L. Dai and Y. Zheng (eds.), Proceedings Volume 9496, Independent Component Analyses, Compressive Sampling, Large Data Analyses (LDA), Neural Networks, Biosystems, and Nanoengineering XIII, 2015 DOI: 10.1117/12.2177159. [27] S. S. Nikolaiev, Y. O. Tymoshenko and K. Y. Matviiv, “Haar Cascade Face Detector Quality Dependence on Training Dataset Variablity”, Research Bulletin of the National Technical University of Ukraine “Kyiv Politechnic Institute”, no. 6, 2017, 38–46 DOI: 10.20535/1810-0546.2017.6.115181. [28] S. Nikolaiev and H. Chereda, “Sampling Rate Independent Filtration Approach for Automatic ECG Delineation”, International Scientific Journal “Internauka”, vol. 27, no. 5, 2017. [29] S. Nikolaiev, “Metric and algorithm for similarity between two temporal event sequences cal-

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culation”, System research and information technologies, no. 3, 2017, 127–135 DOI: 10.20535/SRIT.2308-8893.2017.3.12. [30] R. M. Bayevsky and G. G. Ivanov, “Cardiac Rhythm Variability: the Theoretical Aspects and the Opportunities of Clinical Application”, Ultrazvukovaya i funktsionalnaya diagnostika, no. 3, 2001, 108–127 (in Russian).

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VOLUME 2020 VOLUME 14,14, N°N°22 2020

RADON‐WAVELET BASED NOVEL IMAGE DESCRIPTOR FOR MAMMOGRAM MASS CLASSIFICATION Submitted: 20th October 2018; accepted: 2nd June 2020

Sk Md Obaidullah, Sajib Ahmed, Teresa Gonçalves, Luís Rato DOI: 10.14313/JAMRIS/2‐2020/22 Abstract: Mammography based breast cancer screening is very po‐ pular because of its lower costing and readily availability. For automated classification of mammogram images as benign or malignant machine learning techniques are in‐ volved. In this paper, a novel image descriptor which is based on the idea of Radon and Wavelet transform is proposed. This method is quite efficient as it performs well without any clinical information. Performance of the method is evaluated using six different classifiers na‐ mely: Bayesian network (BN), Linear discriminant analy‐ sis (LDA), Logistic, Support vector machine (SVM), Multi‐ layer perceptron (MLP) and Random Forest (RF) to choose the best performer. Considering the present experimen‐ tal framework, we found, in terms of area under the ROC curve (AUC), the proposed image descriptor outperforms, upto some extent, previous reported experiments using histogram based hand‐crafted methods, namely Histo‐ gram of Oriented Gradient (HOG) and Histogram of Gra‐ dient Divergence (HGD) and also Convolution Neural Net‐ work (CNN). Our experimental results show the highest AUC value of 0.986, when using only the carniocaudal (CC) view compared to when using only the mediolateral oblique (MLO) (0.738) or combining both views (0.838). These results thus proves the effectiveness of CC view over MLO for better mammogram mass classification. Keywords: Image descriptor, radon transform, mammo‐ graphy, breast cancer, classification

1. Introduction

Breast Cancer is the most frequent cancer among women, impacting over 1.5 million women each year and is also the cause of the highest number of cancer related death among women. In 2015, 570,000 wo‑ men died from breast cancer – which is approxima‑ tely 15% of all cancer deaths among women [1]. If breast cancer is early detected, it is one of the most treatable types of cancer. The primary imaging moda‑ lity for breast cancer is done by a low cost X‑Ray ba‑ sed technique which is known as mammography. Ba‑ sed on the processing modalities, mammography can be classi�ied into two types: (i) Screen Film Mammo‑ graphy (SFM) and (i) Full Field Digital Mammography (FFDM). For SFM, images are captured on the �ilm, whereas for FFDM, images are directly stored in the digital computer. As per the reported study in litera‑ ture [2, 3], both type of mammography, have almost equal ability to detect suspicious lesions in the breast. The present work deals with the SFM images which

are available through the BCDR‑F03 dataset [4, 5], one of the latest breast imaging �ilm mammography ben‑ chmark datasets. In recent years many computational approaches have been proposed for computer assisted diagnostic of breast cancer; these methods are known as Compu‑ ter Aided Diagnostic methods or, in short, CAD [6]. A double checking procedure by radiologists is normally used to reduce the number of false‑negative cases, but this has an obvious cost associated as the number of radiologists are not in general adequate in our health centres. Alternatively, a CAD system can help one radi‑ ologist to verify her/his observations with the result of the automated system without requiring another radi‑ ologist in the same place. That is why the importance of developing CAD system is in demand. Presently various CAD systems have been propo‑ sed in the literature. The general framework for a tra‑ ditional CAD system consists of three parts: (i) prepro‑ cessing the mammogram images for ROI extraction, (ii) feature extraction and �inally (iii) classi�ication. Re‑ cently, deep learning based approaches are also repor‑ ted in literature which replaces the extraction of hand‑ crafted features by combining step (ii) and (iii) in a single stage. In literature works are reported where image descriptors are combined with clinical informa‑ tion for better classi�ication accuracy [6]. The present work focuses on an image descriptor based classi�ica‑ tion of masses from mammogram images. We have not considered any clinical information. Among the reported image descriptors, Constanti‑ nidis et al. [7] and Belkasim et al. [8] considered the Zernike moment based descriptor to classify masses; texture based classi�ication of calci�ication and mas‑ ses using Haralick features [9] was reported by diffe‑ rent authors [10–14]. Haralick texture features were employed in other areas of medical imaging also [15] and a comparison of texture features and a deep le‑ arning approach is reported in [16]. Wavelet [17, 18] and curvelet [19] analysis based feature descriptors are also used by different authors and combination of intensity and texture descriptors was explored by Ra‑ mos et al. [20]. Histogram of oriented gradient (HOG) based features was employed along with the clinical information for mammogram image classi�ication by Moura and Guevara [6] and Arevalo et al. [5] used a convolution neural network to separate malignant and benign masses without using any clinical information reporting the effectiveness of a deep learning based approach over the traditional hand‑crafted one. In this paper, we propose a novel image descrip‑

Journal Automation, Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation,

tor based on radon transform over multi‑resolution images. The block diagram of the proposed method is shown in Figure 1. First �ilm mammogram dataset is considered and images are categorized based on CC and MLO views; ROI are then extracted and their con‑ trast is enhanced; next step computes a feature vector, followed by classi�ication and performance compari‑ son of multiple classi�iers. The rest of the paper is organized as follows: the contributions are reported in Section 2 where we dis‑ cuss about the proposed image descriptor and the de‑ sign of classi�iers; experimental details are reported in Section 3, which include dataset description, expe‑ rimental setup and results with a comparative study. Finally we conclude the paper in Section 4.

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of a pattern f (x, y) and for a given set of angles may be assumed as the projection of all non‑zero points. The projection output is the sum of the non‑zero points for the image pattern in each direction (angle between 0 to π). Finally it results forming a matrix. The matrix elements are related to the integral of f (x, y) over a line Lin(ρ, θ) de�ined by ρ = x cos θ + y sin θ and can formally be expressed as ∫ ∞∫ ∞ f R(ρ, θ) = f (x, y)δ(x cos θ+y sin θ−ρ)dxdy −∞

where δ(.) is the Dirac delta function, δ(x) = 1, if x = 0 and 0 otherwise. Also, θ ∈ [0, π] and ρ ∈] − ∞, ∞[. For the radon transform, Lini be in normal form (ρi , θi ).

(a)

Fig. 1. Block diagram of the proposed method

2. Contribution Outline As mentioned earlier, we propose a novel feature descriptor for classi�ication of mammogram masses. In particular, our target is to classify malignant and be‑ nign masses from mammogram images using this no‑ vel image descriptor. We describe the image descrip‑ tor in detail in the following sub section. 2.1. Design of the Image Descriptor

The propose image descriptor uses the concepts of radon transform and multi‑resolution analysis. In general, the radon transform is an integral transform computes the projection of an image matrix along a speci�ied angle. This method has wide application in the domain of medical imaging as it is used to re‑ construct images from medical CT scans. The radon transform method was introduced in 1917 by Johann Radon [21] and a formula for the inverse transform was also provided by him. The basic principal of these techniques are described below. Radon transform. Radon transform is an integral transform that consists of a set of projections of a pat‑ tern at different angles [21], as illustrated in Figure 2 where, the part (a) shows the projection principal and part (b) shows different angles considered for the pre‑ sent work. It is a mapping of a function f (x, y) to anot‑ her function f R(x, y) de�ined on the 2D space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line for the gi‑ ven set of angles. In other words, the radon transform

−∞

(b)

Fig. 2. Illustrating the radon transform theory: (a) generation of radon spectrum, (b) different angular directions considered for the present work to compute the line integral Multi‑resolution analysis. The time‑frequency response of a signal (for present work it is an image) is represented through wavelet transform. Daubechies wavelets [22], which belongs to the family of discrete wavelet techniques, are used for the present work. Wavelets are used for multi‑resolution analysis and their advantage includes: computational ease with mi‑ nimum resource and time requirements. These ortho‑ gonal wavelets are characterized by maximum num‑ ber of vanishing moments for some given support. We decompose an image into different frequencies with different resolutions for further analysis. The family of Daubechies wavelet is denoted as ‘dbN’, where the wa‑ velet family is denoted by the term ‘db’ and the number of vanishing moments is represented by ‘N’. An image can be represented by the combination of different components of different coef�icients. For the present work, the wavelet decomposition has been done at le‑ vel 1 for db1, db2 and db3 which capture the constant, linear and quadratic coef�icients of an image compo‑ nent. Four sub‑band images namely, approximation coef�icients (cA), horizontal coef�icients (cH), vertical coef�icients (cV), and diagonal coef�icients (cD) are ge‑ nerated by this process for each of the db1, db2 and db3 part, resulting a total of 12 sub‑band images. Design of the descriptor. The image descriptor is developed by combining the idea of radon transform over multi‑resolution analysis. The texture pattern of benign and malignant masses are different. The malig‑ nant mass region has more irregular in comparison to benign masses whose boundary regions are more re‑ Articles

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gular in shape. Radon transform computes the line in‑ tegral of a set of pixels over a speci�ied direction. So, if we compute radon transform on benign and malignant masses the line integral value will be different for each case. Figure 3 shows the radon spectrum of benign and malignant masses: Figure 3(a) is a benign mass and its radon spectrum is shown in Figure 3(c); Figure 3(b) is a malignant mass and its radon spectrum is shown in Figure 3(d). There are several methods available for image de‑ composition like, divide by “n” and quad‑tree decom‑ position among others. Here, we chose wavelet, as dif‑ ferent directional approximation can be done through wavelet decomposition. From each of the sub‑band images i.e. on cA, cH, cV and cD, we compute the ra‑ don spectrum. Finally, statistical values are computed from those radon‑wavelet spectrum which are used to construct the feature vector.

Fig. 3. ROI extracted from mammogram images and their radon spectrum (a) benign mass, (b) malignant mass, (c) radon spectrum of figure a, (a) radon spectrum of figure b

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Feature vector generation. In what follows, we summarize the generation of feature vector: First, ROIs were extracted from the original mam‑ mogram images and contrast enhancement was done on each ROI. The enhanced ROI was then stored as a gray‑scale image. Wavelet decomposition at level 1 was done using Daubechies method for db1, db2 and db3. This step ge‑ nerates 04 sub band images for each coef�icients re‑ sulting a total of 12 sub‑band images. Radon transform is applied on the original ROI image and each of the 12 sub‑band images generated on the previous step. At this step we generate a total of 13 radon spectrum. From each of the 13 radon spectrum we compute one energy and three statistical features value. Alto‑ gether this step generates 52 features (04 × 13). Then, we compute 04 statistical features namely: entropy, mean, standard deviation and maximum coef�icient of radon spectrum from the original gray‑scale image too, so overall we get a feature vector of dimension 56 Articles

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(52 + 04).

2.2. Classifiers In our study, six different classi�iers were used to train and classify the masses. They are Bayesian net‑ work (BN), Linear discriminant analysis (LDA), Logis‑ tic, Support vector machine (SVM), Multilayer percep‑ tron (MLP) and Random Forest (RF). We compare the performance of these classi�iers to �ind the best one. These classi�iers are brie�ly explained below. Bayesian network. For the Bayesian network (BN) we used K2, a hill‑climbing technique which is a famous score‑based algorithm that recovers the un‑ derlying distribution in the form of directed acyclic graph ef�iciently. Details can be found in [23]. Linear discriminant analysis. In linear discrimi‑ nant analysis [24], we model the data as a set of multi‑ variate normal distributions where a common covari‑ ance matrix exist with different mean vectors for diffe‑ rent classes. LDA partition the feature‑space by using a hyper‑plane (HP), where two sides of the HP repre‑ sent two classes. The class pattern is determined from the test dataset based on which side of the plane the classes lie. Logistic. Logistic regression is used as a classi�ica‑ tion algorithm to assign observations to a discrete set of classes. The logistic classi�ier transforms its output using a logistic function (sigmoid) and returns a pro‑ bability value. This probability value is then mapped into two or more classes [25]. Support vector machine. SVM classi�ies the data by constructing a hyper‑plane (HP)on the high dimen‑ sional feature space. Different linear and non linear kernels can be used. For the present work, we used SVM tuned by a linear kernel since it’s fast and pre‑ sented promising results. Multilayer perceptron. MLP is one of the most wi‑ dely used classi�iers. Here, the chosen con�iguration was 56‑hl‑2, where 56 is the number of feature va‑ lues, hl is the number of nodes in the hidden layer and 2 is the number of classes. hl can be determined empirically, by considering it as a function of the fea‑ ture dimension (�ifty six) and output classes (two). In our experiment the value of hl is considered as 29, i.e (56+2)/2. Random forest. Theoretically, a random forest is de�ined as a collection of unpruned decision trees which are trained on bootstrap samples using random feature selection in the tree generation process. Among a large number of generated trees, each tree votes for a popular class and, by combining all, a deci‑ sion is taken [26].

3. Experiments

3.1. Dataset & Pre‐processing A benchmark �ilm mammography dataset known as BCDR‑F03 [27,5] from the Breast Cancer Digital Re‑ pository, a wide‑ranging public repository composed of Breast Cancer patients’ cases from Portugal [6], was used in our experiment. The BCDR‑F03 is one of the la‑ test benchmarked �ilm mammography dataset which

Journal Automation, Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation,

consists of 668 �ilm mammogram images. Out of these 668 image there are 736 biopsy proven masses con‑ taining 426 benign masses and 310 malignant masses from 344 patients. Thus, in many cases a single image contains more than one masses. For present work, we have considered one mass per image having a total of 668 masses. Out of these 668 masses, 662 images are considered for classi�i‑ cation after removal of few extremely low resolution images. The samples provided are available in two dif‑ ferent views namely carniocaudal (CC) and mediola‑ teral oblique (MLO) view. In our data we have 328 CC views and 334 MLO views (almost equal ratio for fair comparison). Figure 4 shows different mammogram views with the lesions marked.

Fig. 4. Different mammogram views, (a) LCC, (b) LO, (c) RCC, (d) RO. The green boundary is the ROI The pre‑processing step includes (i) ROI extraction and (ii) contrast enhancement. ROI was extracted ba‑ sed on the information provided by the radiologist; an annotated �ile with the ROI coordinate information is provided along with the BCDR‑F03 dataset. Using au‑ tomated techniques ROIs were extracted and stored in separate folders based on different view types. Furt‑ her, they were categorized into two class folders na‑ mely benign and malignant. Next, ROIs contrast en‑ hancement was performed since original �ilm mam‑ mograms are of very low contrast due to several fac‑ tors (poor lighting condition, orientation, etc.); con‑ trast is enhanced by subtracting the mean of the in‑ tensities in the image to each pixel. Figure 5 shows one original ROI and its contrast enhanced version.

Fig. 5. Contrast enhancement, (a) original low contrast ROI, (b) contrast enhanced image 3.2. Evaluation Metrics To measure the performance of the system, we use the Area Under the Curve of the Receiver Operator Characteristic (AUC). The ROC curve is created by plot‑ ting the true positive rate against the false positive rate. The AUC is a measure of discrimination also used

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in previous works on this dataset [6, 5], allowing then to make a comparison with our method. 3.3. Evaluation Strategy and System Configuration

We carried out three different type of tests: (i) mammogram mass classi�ication from CC view, (ii) mammogram mass classi�ication from MLO view and (iii) mammogram mass classi�ication with both views combined. In each case, the dataset was divided into 60:40 ratio (60% data for training and rest 40% for testing), following the split of previous works for fair comparison [6, 4, 5]. Regarding the resources, all experiments were car‑ ried out using MATLAB 2017b software in a system with 2.8 GHz CPU, 8 GB RAM, 4 GB NVIDIA GPU. 3.4. Results and Analysis

In the present work, we not only propose a novel image descriptor for mammogram mass classi�ication but also study the performance of different classi�iers. In addition, the analysis of which image view is bet‑ ter for mass classi�ication is also done. Table 1 shows the performance of six different classi�iers (BN, LDA, Logistic, SVM, MLP and RF) for three different mam‑ mogram views: CC, MLO and both combined (best va‑ lues are presented in bold face). From the �irst column of the table, which shows the output of the CC view, LDA and RF perform best with 0.986 AUC among the six classi�iers. For the MLO view, RF shows the highest AUC of 0.738 and when both the views are combined (i.e. all images of CC and MLO are considered together) RF also shows highest AUC of 0.838. Given these re‑ sults, it is possible conclude that RF is the best perfor‑ mer irrespective of image view. Previous relevant work – analogy. Prior to this study, Moura et. al [6] proposed one histogram based image descriptor known as HGD and tested the met‑ hod on the BCDR‑F01 dataset, which is a subset of the BCDR‑F03. They reported the highest AUC of 0.787 by HDG and 0.770 by traditional HOG. Nonetheless, these results are not solely based on image descriptor as clinical information was also used. Recently, Arevalo et. al [4, 5] proposed a deep learning based approach on BCDR‑F03 dataset. Applying a convolution neural network (CNN) they obtained a AUC of 0.822; then, using CNN combined with the hand‑crafted HGD fea‑ tures, the overall AUC was boosted upto 0.826, sho‑ wing an improvement of 0.40%. Nonetheless, these two works are not comparable in true sense as dif‑ ferent experimental framework were considered, i.e. for [6], a 80:20 data split for training and testing was considered while for [4, 5] the split was 60:40. Table 2 shows the results reported and allows a qualitative comparison to our method (based on the present experimental consideration and framework). The proposed image descriptor performs signi�icantly well without any clinical information as compared to the traditional approaches, thus proving the effective‑ ness of the image descriptor for mass classi�ication. ��oosing t�e �est �lassi�ier. Not only design of the descriptor, in this paper we also compare the per‑ formance of different classi�iers to choose the best Articles

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Tab. 1. Mammogram mass classification results for CC, MLO and combined (CC+MLO) views on test dataset measured in AUC Classi�ier CC MLO Baysian Network (BN) 0.934 0.690 Linear Discriminant Analaysis (LDA) 0.986 0.672 Logistic 0.958 0.674 Support Vector Machine (SVM) 0.977 0.682 Multilayer Perceptron (MLP) 0.985 0.618 Random Forest (RF) 0.986 0.738

CC+MLO 0.816 0.807 0.811 0.783 0.813 0.838

Tab. 2. Performance comparison of proposed technique with baseline results (CC+MLO views combined) Methods

AUC HOG 0.770 Hand‑crafted techniques [6] HGD 0.787 Deep‑learning based approach [4] [5] CNN 0.822 Deep learning + Hand‑crafted techniques [5] CNN + HDG 0.826 Proposed Method Radon‑wavelet based descriptor 0.838

one and a quantitative comparison is provided. Six different classi�iers namely� Bayesian network (BN), Linear discriminant analysis (LDA), Logistic, Support vector machine (SVM), Multilayer perceptron (MLP) and Random Forest (RF) are considered for perfor‑ mance comparison. From Table 1 we can see Random Forest is the best performer among the six classi�iers irrespective of the image view considered. For CC view images both the Random Forest and Linear Discrimi‑ nant Analysis classi�iers show an AUC of 0.986 fol‑ lowed by Multilayer Perceptron, Support Vector Ma‑ chine and Logistic classi�iers. �e found, for CC view images, among the six classi�iers except Baysian Net‑ work rests �ive provides almost neck to neck results. The CC view accuracy provided by Baysian Network is almost 5.27% less compared to the highest perfor‑ mer i.e. Random Forest. For MLO view, Random Forest shows an AUC of 0.738 which is highest among the six. Finally, when we combined both the views and consi‑ dered all the images together then we found an AUC of 0.838 by the Random Forest classi�ier. Other four classi�iers namely Multilayer Perceptron, Baysian Net‑ work, Linear Discriminant Analysis and Logistic also shows comparable performance. In this scenario, only Support vector Machine shows a bit less performance compared to all. Figure 6 shows a graphical repre‑ sentation of the performance comparison of different classi�iers for different views.

4. Conclusion

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This paper provides a novel image descriptor which is based on radon transform and wavelet trans‑ form to seperate malignant and benign masses from �ilm mammogram images. No doubt, automated di‑ agnostics of breast cancer from mammogram images will support the radiologists by double checking their observations. Several methods are proposed in the li‑ terature for mammogram mass classi�ications from Articles

Fig. 6. Performance comparison of different classifiers for different image views

�ilm mammogram images, but most of the time these descriptors show promising performance if combined with clinical information. In the present work, we pro‑ pose a novel image descriptor which performs well without clinical information. The proposed image des‑ criptor along with the random forest classi�ier shows an AUC of 0.986 for CC view, 0.738 for MLO view and 0.838 for the combined view. For mammogram mass classi�ication the CC view is more effective than MLO one. In this experiment, we found that, CC view shows a 33.60% improvement over MLO.

To support the conclusions drawn on this work, na‑ mely the superiority of the image descriptor and the different discriminating powers of the CC and MLO views, our plan for future work includes evaluating the performance of the proposed descriptor on other publicly available �ilm mammogram datasets and per‑ forming a statistical analysis over the results. Perfor‑ mance comparison of different classi�ier has been car‑ ried out in this paper. In future we intend to do per‑ formance analysis of more classi�iers and performing statistical signi�icance test on them is also in our plan.

Journal Automation, Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation,

AUTHORS

Sk Md Obaidullah∗ – Department of Informatics, Uni‑ versity of E� vora, Rua Roma� o Ramalho, 59, 7000‑671 E� vora, Portugal, e‑mail: sk.obaidullah@gmail.com. Sajib Ahmed – Department of Informatics, University of E� vora, Rua Roma� o Ramalho, 59, 7000‑671 E� vora, Portugal, e‑mail: jack6148@gmail.com. Teresa Gonçalves – Department of Informatics, Uni‑ versity of E� vora, Rua Roma� o Ramalho, 59, 7000‑671 E� vora, Portugal, e‑mail: tcg@uevora.pt. Luís Rato – Department of Informatics, University of E� vora, Rua Roma� o Ramalho, 59, 7000‑671 E� vora, Por‑ tugal, e‑mail: lmr@uevora.pt. ∗

Corresponding author

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[20] R. Ramos‑Pollá n, M. A. Guevara‑Ló pez, C. Suá rez‑ Ortega, G. Dı́az‑Herrero, J. M. Franco‑Valiente, M. Rubio‑Del‑Solar, N. Gonzá lez‑de Posada, M. A. P. Vaz, J. Loureiro, and I. Ramos, “Disco‑ vering mammography‑based machine learning classi�iers for breast cancer diagnosis”, Journal of Medical Systems, vol. 36, no. 4, 2012, 2259–2269, 10.1007/s10916‑011‑9693‑2. [21] S. R. Deans, The Radon transform and some of its applications, Wiley: New York, 1983.

[22] S. Mallat, “A theory for multiresolution sig‑ nal decomposition: the wavelet representation”, IEEE Transactions on Pattern Analysis and Ma‑ chine Intelligence, vol. 11, no. 7, 1989, 674–693, 10.1109/34.192463, Conference Name: IEEE Transactions on Pattern Analysis and Machine Intelligence. [23] C. Bielza, G. Li, and P. Larrañ aga, “Multi‑ dimensional classi�ication with Bayesian networks”, International Journal of Approxi‑ mate Reasoning, vol. 52, no. 6, 2011, 705–727, 10.1016/j.ijar.2011.01.007. [24] S. Mika, G. Ratsch, J. Weston, B. Scholkopf, and K. Mullers, “Fisher discriminant analysis with kernels”. In: Neural Networks for Signal Pro‑ cessing IX: Proceedings of the 1999 IEEE Sig‑ nal Processing Society Workshop, 1999, 41–48, 10.1109/NNSP.1999.788121. [25] “Logistic Regression ‑ ML Glossary documenta‑ tion”. https://ml-cheatsheet.readthedocs. io/en/latest/logistic_regression.html, 2017. Accessed on: 2020‑09‑20.

[26] K. C. Santosh and S. Antani, “Automated Chest X‑ Ray Screening: Can Lung Region Symmetry Help Detect Pulmonary Abnormalities?”, IEEE tran‑ sactions on medical imaging, vol. 37, no. 5, 2018, 1168–1177, 10.1109/TMI.2017.2775636.

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[27] “Breast Cancer Digital Repository”. https:// bcdr.eu/information/about. Accessed on: 2020‑09‑25. Articles

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Journal of Automation, Journal Automation, Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems

VOLUME 2020 VOLUME 14,14, N°N° 2 2 2020

SEGREGATION OF SONGS AND INSTRUMENTALS ‐ A PRECURSOR TO VOICE/ACCOMPANIMENT SEPARATION FROM SONGS IN NOISY SCENARIO Submitted: 20th October 2018; accepted: 2nd June 2020

Himadri Mukherjee, Sk Md Obaidullah, K.C. Santosh, Teresa Gonçalves, Santanu Phadikar, Kaushik Roy DOI: 10.14313/JAMRIS/2‐2020/23 Abstract: The music industry has come a long way since its in‐ ception. Music producers have also adhered to modern technology to infuse life into their creations. Systems ca‐ pable of separating sounds based on sources especially vocals from songs have always been a necessity which has gained attention from researchers as well. The chal‐ lenge of vocal separation elevates even more in the case of the multi‐instrument environment. It is essential for a system to be first able to detect that whether a piece of music contains vocals or not prior to attempting source separation. It is also very much challenging to perform source separation from audio which is contaminated with noise. In this paper, such a system is proposed being tes‐ ted on a database of more than 99 hours of instrumen‐ tals and songs. Experiments were performed with both noise free as well as noisy audio clips. Using line spectral frequency‐based features, we have obtained the highest accuracies of 99.78% and 99.34% (noise free and noisy scenario respectively) from among six different classi‐ fiers, viz. BayesNet, Support Vector Machine, Multi Layer Perceptron, LibLinear, Simple Logistic and Decision Table. Keywords: Background track, Vocals, Noisy audio, Line spectral frequency, Framing

1. Introduction Technology has had a profound impact in every sp‑ here and the music industry has not been an excep‑ tion to this. Audio engineers now have various advan‑ ced solutions to help them with music production. One of the primary requirements of musicians has always been for such a technology that can enable them to separate background tracks from vocals. This can be extremely helpful for acapella extraction for rearran‑ gements. It can also help musicians in understanding minute technicalities of background tracks who have little audio engineering knowledge. The separation of vocals from music is itself a dif�icult task which eleva‑ tes even more in the case songs due to presence of mul‑ tiple instruments. It is also extremely dif�icult to sepa‑ rate vocals from clips which has been breathed upon by noise. A system of this sort can also help towards voice activity detection in songs as well and aid the se‑ paration of individual instruments in songs for further analysis. It is essential to be able to distinguish instru‑ mentals from songs prior to extracting instrumental portions from the songs and perform any kind of ana‑ lysis. In this paper, such a system is proposed which

tries to segregate instrumentals and songs from noisy clips using line spectral frequency (LSF)‑based featu‑ res. The system has been pictorially illustrated in Fi‑ gure 1. It has been tested with multiple feature dimen‑ sions and various classi�iers whose details are presen‑ ted in the subsequent paragraphs. In the rest of the paper, Sections 2, 3 and 4 des‑ cribe the related works, datasets and proposed metho‑ dology, respectively. Section 5 highlights the details of the results while conclusion and future work are pre‑ sented in Section 6.

Fig. 1. Pictorial view of the System

2. Related Work Leung et al. [1] used a supervised variant of in‑ dependent component analysis namely ICA‑FX for the task of segregating instrumentals and voices. They had also used general likelihood ratio based distance and S�M based classi�ication; using 5 and 25 pop songs for training and testing respectively, they obtained a hig‑ hest individual accuracy of 80.04%. Chanrungutai et al. presented a system for separating vocals from mu‑ sic with the aid of a non negative matrix factorization based technique. They performed pitch extraction on the separated voices; their data consisted of both real backing tracks as well as MIDI ones. A detailed account of the results is presented in [2]. Rocamora et al. [3] studied various audio descrip‑ tors for the task of music and voice segregation and concluded the fact that mel frequency cepstral coef�i‑ cient (MFCC)‑based approach is the most appropriate. They also presented a statistical classi�ication techni‑ que with the help of a reduced descriptor set for de‑ tecting voice in songs and obtained a highest accuracy of 78.5%. Hsu et al. performed separation of music ac‑ companiments and unvoiced singing voice on the MIR‑ 1K dataset. They followed the computational auditory scene analysis framework in their experiments whose details are presented in [4]. Ra�ii et al. [5] adopted a repetitive musical struc‑ ture identi�ication based approach for segregating

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voice and music; they experimented with the MIR‑1K dataset and obtained a highest global normalized sig‑ nal to distortion ratio of 1.11. On another work Ra�ii et al. [6] presented a system named REPET for the task of speech and music separation; they experimented with 1000 song clips and 14 songs and extended the system to aid in the pre‑processing stage for detecting pitch to help in melody extraction. Liutkus et al. [7] further extended REPET to handle background variations as well as long excerpts in order to process full songs.

Ghosal et al. [8] adopted a random sample and consensus based approach for the purpose of separa‑ ting songs and instrumentals; they experimented on a dataset of 300 instrumentals and songs each and obtained an accuracy of 95%. Mauch et al. [9] obtai‑ ned an accuracy of 89.8% for the task of instrumen‑ tal solo detection using a combination of four featu‑ res in the thick of MFCC, pitch �luctuation, MFCC of re‑ synthesised predominant voice and normalised am‑ plitude of harmonic partials. Burute and Mane [10] used a robust principal component analysis based approach for separating background music and voice. They experimented with the MIR‑1K dataset and reported results for different parameters in the thick of source to distortion ratio, source to artefact ratio, source to interference ratio and global normalised source to distortion ratio. A best global normalised source to distortion value of around 5.2 decibels was reported by them as well. Ghosal et al. [11] used MFCC based features for seg‑ menting instrumentals and songs. They experimented on a database consisting of 180 songs and instrumen‑ tals each of length 40‑45 seconds. The clips were mo‑ nophonic in nature sampled at 22050 Hz. The dataset consisted of data from different instruments like �lute, guitar, drums and piano as well as different genres like rock, classical and jazz. Among different machine lear‑ ning algorithms, they obtained a highest accuracy of 93.34% using random sample and consensus classi�i‑ cation.

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Regnier and Peeters [12] attempted to detect the presence of voice in music tracks with the aid of vi‑ brato and tremolo characteristics. They also used har‑ monicity based criteria to assign a clip to either of sin‑ ging or non singing class. The experiment was con‑ ducted on database of 90 songs from different artists, genres, languages and tempos out of which 58 songs were used for training ad the rest for training. In the entire dataset, 50.3% were segments with vocals and the remaining were without vocals or only music. A highest F‑measure value of 76.8% was obtained in their experiment. Ozerov et al. [13] applied a bayesian model adaptation‑based approach for source separa‑ tion over a single channel. They experimented with music and voice separation and concluded reported better results using adaptive models over non adap‑ tive models. Hsu et al. [14] proposed a tandem algo‑ rithm for extraction of music pitch and separation of voice from background music. They also used a trend estimation technique to identify pitch range of singing voice and obtained average accuracy of 90%. Articles

VOLUME 14,14, N° VOLUME N°22 2020 2020

Tab. 1. Number of instrumental and song clips for the different datasets Datatset (clip length) D1 (5s) D2 (10s) D3 (15s) D4 (20s)

Song (49:19:48) 35116 17362 11431 8500

Instrumental (49:50:15) 35718 17771 11798 8805

Zhu et al. [15] proposed a multiple stage non nega‑ tive matrix factorization technique for separating mo‑ noaural singing voice. They �irst applied the factoriza‑ tion technique for decomposition of spectrograms fol‑ lowed by application of a spectral discontinuity thres‑ holding technique. Multitudinous experiments were performed on the MIR‑1K dataset consisting of 1000 short audios and the Beach‑Boys dataset consisting of 14 songs whose results are presented in [15].

3. Dataset Development

Data is an essential entity of any experiment. It is always important to ensure that the dataset contains real life characteristics as far as possible. In our expe‑ riment, audio clips of songs and instrumentals were extracted from various websites like YouTube [16]. The top three languages of India namely English, Hindi and Bangla [17] were considered in the case of songs. Songs of different genres and timelines were chosen in order to ensure that the dataset covered various qua‑ lities of songs in terms of rendering and audio engi‑ neering. The song clips had either background music or sections of instrument only parts. Different artists were chosen for collecting instrumental clips in order to get data of various types like genre, playing style, tonality and technicality. Instrumental covers of vari‑ ous songs, as well as original compositions using dif‑ ferent instruments like guitar, violin and piano, along with background music constituted the instrumental part of the dataset. This data was used to generate 4 datasets (D1 ‑D4 ) having clips of lengths 5, 10, 15 and 20 seconds, re‑ spectively. The details of the generated datasets along with that of the original data is presented in Table 1. In order to test the system’s performance in noisy scenario, each of the datasets were subjected to 3 ty‑ pes of noise sources namely humming noise, highway noise and thunder noise. The signal to noise ratios ran‑ ged from ‑20.65 to 14.90. The amplitude based pre‑ sentation for the different noise clips along with those of the instrument and song clips from the 4 datasets is presented in Figures 2‑ 5.

4. Proposed Method 4.1. Pre‐Processing

The audio clips were split into smaller frames as the spectral characteristics tend to show a lot of devi‑ ation for longer clips. The clips were partitioned into 256 sample point wide frames with a 100 point over‑ lap as presented in [18]. Next, the frames were sub‑

Journal MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems Journal of Automation, Mobile

VOLUME 14,14, N°N° 2 2 2020 VOLUME 2020

output of an all pole �ilter (H(z)). The inverse �ilter of H(z) is represented by Equation 2, where r1 , r2 …rT designate the predictive coef�icients up to the order T Fig. 2. Amplitude based representation for 5 second long (a) Instrumental, (b) Song, (c) Highway noise, (d) Humming noise and (e) Thunder noise clips

R(z) = 1+r1 z −1 +r2 z −2 +r3 z −3 +......+rT z −T . (2)

R(z) is decomposed into polynomials F (z) and G(z) as shown in Equation 3 and Equation 4, respecti‑ vely, whose zeros lie on the unit circle. They are also interlaced with each other, thus helping in computa‑ tion (3) F (z) = R(z) + z −(T +1) R(z −1 )and G(z) = R(z) − z −(T +1) R(z −1 ).

Fig. 3. Amplitude based representation for 10 second long (a) Instrumental, (b) Song, (c) Highway noise, (d) Humming noise and (e) Thunder noise clips

Fig. 4. Amplitude based representation for 15 second long (a) Instrumental, (b) Song, (c) Highway noise, (d) Humming noise and (e) Thunder noise clips

Fig. 5. Amplitude based representation for 20 second long (a) Instrumental, (b) Song, (c) Highway noise, (d) Humming noise and (e) Thunder noise clips

jected to a windowing function (Hamming Window as presented in [19]) in order to get rid of the jit‑ ters which might lead to spectral leakage at the time of frequency based analysis. The mathematical repre‑ sentation of hamming window B(n) is given by Equa‑ tion (1) where the value of r ranges between the frame boundary of size R ) ( 2πr . (1) B(n) = 0.54 − 0.46 cos R−1 4.2. Feature Extraction

Line spectral frequency [20] is a method for repre‑ senting linear predictive coef�icients with better inter‑ polation properties. Here, a signal is considered as the

(4)

Each of the datasets were used for extraction of 5, 10, 15 and 20 dimensional standard line spectral frequency features. Since the clips were of disparate lengths, a disparate number of frames were produ‑ ced for the clips, producing features of disparate di‑ mension. In order to tackle this problem, the band wise sums for the energy values were computed which were then used to compute the ratio of distribution of energy across the bands. Along with this, the band numbers were also added to the feature set graded in descending order based on total energy content. It was experimentally found that a clip of just 2 se‑ conds produced 880 frames; if a 5 dimensional LSF was extracted for the clip then a feature set of 4400 dimension was obtained. However with the help of the proposed technique, this dimension was brought down to just 10 (5 ratio distribution values and 5 band numbers). Thus, LSF values of 5, 10, 15 and 20 dimen‑ sions produced even dimensional feature sets of 10, 20, 30 and 40 dimensions which were independent of the length of the clips. Trends of the feature values for the songs and instrumental clips for the 40 dimensio‑ nal features (best result in noise free scenario) is pre‑ sented in Figure 6.

Fig. 6. 40 dimensional feature values for (a) Song, (b) Instrumental

4.3. Classification Each feature set for each datasets was fed into dif‑ ferent classi�iers popularly used in pattern recognition problemsin the thick of BayesNet (BN) [21], Support Vector Machine (SVM) [22], LibLinear (Lib) [23], Multi Articles

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Journal Journal of of Automation, Automation,Mobile MobileRobotics Roboticsand andIntelligent IntelligentSystems Systems

Layer Perceptron (MLP) [24], Simple Logistic (SL) [25] and Decision Table (DT) [26]. BayesNet: is a bayesian classi�ier that makes use of a Bayes Network for learning with the aid of different quality parameters and search algorithms. The base class provides data structures like conditional proba‑ bility distributions, structure of network, etc. and dif‑ ferent facilities which are similar to that of the Baye‑ sian Network learning algorithm like K2. Support Vector Machine: is a supervised learning algorithm that can be used for classi�ication as well as regression analysis. SVM builds a bi‑class model from a set of training instances and then associates each in‑ stance to either class. LibLinear: is a functional and linear type of clas‑ si�ier which is suitable for either large number of in‑ stances or large feature sets. It is also suitable for re‑ gression problems. Decision Table: is one of the simplest supervi‑ sed learning algorithms; it consists of 2 parts namely, schema which de�ines the features to be included in the table and body which embodies the set of instan‑ ces along with their feature values and class labels. Multi Layer Perceptron: is a feed forward vari‑ ant of an arti�icial neural network which maps an in‑ put and output set; it consists of nodes which are con‑ nected by links having weights associated to it. It is one of the most popular classi�iers in pattern recognition problems. Simple Logistic: is a classi�ier used to build linear logistic regression models. The classi�ier has a base le‑ arner associated with it along with number of iterati‑ ons which aids to automatically select attributes. The extremely popular open source classi�ication tool named Weka [27] was used in the present experi‑ ment. We used 5 fold cross validation for all the classi‑ �iers with default parameters. The details of the obtai‑ ned results are presented in the subsequent section.

5. Result and Discussion 5.1. Noise Free Scenario

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The accuracies obtained for datasets D1 –D4 using different classi�iers are presented in Table 2 to Table 5. From Table 2 it is observed that the highest and lo‑ west accuracies of 99.78% and 50.69% were obtained using MLP and LibLinear, respectively, which are the overall best and worst results among all the classi�iers with default parameters. The same behaviour is found for D2 dataset as can be seen in Table 3; the highest and lowest accuracies being 98.27% and 52.27%. On the other hand, for D3 (Table 4), the highest and lowest accuracies were 99.57% and 52.84%, obtained using BayesNet and LibLinear, respectively. Highest and lo‑ west accuracies of 99.39% and 51.77% were obtained using MLP and LibLinear, respectively for D4 (Table 5). Table 6 shows the highest and lowest accuracies obtained for all experiments based on the feature di‑ mension. It can be seen from the Table that LibLinear Articles

VOLUME N°22 2020 2020 VOLUME 14,14, N°

produced the lowest accuracy for every feature dimen‑ sion. It can also be observed that the top 2 results were obtained using MLP on D1 (shortest clips in ex‑ periment) and D4 (longest clips in experiment) which shows the effectiveness of MLP. It is also observed from Tables 2–5 that highest accuracies of 99.57%, 99.31%, 84.86% were obtained for BayesNet, SVM and LibLinear respectively. The lo‑ west accuracies for the same classi�iers were found to be 67.01%, 59.67% and 50.69% respectively. In the case of MLP, Simple Logistic and Decision Table, hig‑ hest accuracies of 99.78%, 89.91% and 97.47% re‑ spectively were obtained. The lowest accuracies for the same were found to be 69.08%, 60.24%, 71.73% respectively. �oncluding, the classi�iers can be organized in the following manner based on their best performance: MLP, BayesNet, SVM, Decision Table, Simple Logistic and LibLinear. MLP is very suitable for audio signal ba‑ sed applications as demonstrated in [24,19,18] which is depicted in the obtained results as well. The confusion matrix for the best result (D1 , MLP with 40 dimensional features) is presented in Table 7 where it can be observed that 0.19% of the song clips and 0.25% of the instrumental clips were confused with each other. One possible reason for this is that during the generation of the dataset (splitting of clips into shorter clips), some of the instrumental parts from the songs might have got entirely isolated for the 5 second clips (it was observed that various songs had instrumental sections of more than 5 seconds at a stretch) which interfered with the trained model. Since the best result was obtained for MLP, we furt‑ her experimented with it by varying the number of training iterations (ephocs); the obtained accuracies are depicted in Table 8. From the Table it can be observed that the highest accuracy (99.81%) was obtained for 1800 iterations and that value maintained for further iterations. The confusion matrix for this experiment is presented in Table 9 where it can be seen that the number of mis‑ classi�ied samples for both the classes decreased with respect to the default con�iguration of MLP as shown in Table 7. We had further experimented by varying the num‑ ber of folds in cross validation for the same setup (best accuracy with lowest number of training iterations); the details are presented in Table 10. We had varied the number of folds for cross validation from 2‑10 to observe the performance of MLP for test and training sets of different sizes. It can be seen from the Table that the best accuracy was obtained for 5 and 7 folds which further decreased on increasing the number of folds. 5.2. Noisy Scenario

The obtained accuracies for the different feature dimensions for the 4 datasets in the presence of highway noise is presented in Table 11. It can be seen from the Table that highest accu‑ racies of 97.77%, 97.85% and 99.16% for D1‑D3 re‑ spectively were obtained for 40 dimensional features

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Tab. 2. Obtained accuracies for D1 using different classifiers and feature dimensions Dimension 10 20 30 40

BN 83.38 67.01 69.47 95.30

MLP 86.22 72.83 72.36 99.78

DT 86.51 72.92 71.82 94.96

SL 84.86 61.71 61.53 62.36

SVM 84.86 88.15 72.21 73.01

Lib 84.86 57.37 50.69 54.55

Dimension 10 20 30 40

BN 67.38 75.351 89.62 98.27

MLP 69.08 92.51 94.96 98.18

DT 72.06 94.42 96.62 96.76

SL 60.24 64.64 62.16 73.97

SVM 64.57 96.89 94.98 61.21

Lib 60.24 62.47 57.03 52.27

Dimension 10 20 30 40

BN 67.53 78.56 93.27 99.57

MLP 70.26 99.30 97.44 99.52

DT 71.73 99.04 97.36 94.13

SL 60.61 61.97 61.49 89.91

SVM 61.89 99.31 92.55 59.67

Lib 60.62 59.56 52.84 72.56

Dimension 10 20 30 40

BN 85.25 83.55 90.97 90.97

MLP 85.26 96.32 99.39 92.58

DT 85.42 96.51 97.47 90.93

SL 60.77 69.11 62.62 70.43

SVM 84.19 96.16 95.53 64.85

Lib 60.63 66.51 51.77 61.84

Tab. 3. Obtained accuracies for D2 using different classifiers and feature dimensions

Tab. 4. Obtained accuracies for D3 using different classifiers and feature dimensions

Tab. 5. Obtained accuracies for D4 using different classifiers and feature dimensions

Tab. 6. Highest and lowest accuracies obtained for all experiments based on feature dimension along with the classifier and dataset Dimension 10 20 30 40

Highest 86.51 (D1 , DT) 99.31 (D3 , SVM) 99.39 (D4 , MLP) 99.78 (D1 , MLP)

Tab. 7. Confusion matrix for D1 with 40 dimensional features using MLP showing the number of correctly and misclassified instances Song Instrumental

Song 35051 89

Instrumental 65 35629

using MLP. In the case of D4, the best result was obtai‑ ned for 30 dimensional features. The obtained accuracies for the different feature dimensions for the 4 datasets in the presence of hum‑ ming noise is presented in Table 12. It can be seen from the Table that the best results for all 4 datasets was obtained using MLP. The 40 di‑ mensional features produced highest results (96.44% and 98.55%) for D1and D2 respectively while the 30 dimensional features produced the best result for the remaining 2 datasets(98.20% and 98.17% respecti‑

Lowest 60.24 (D2 ,SL; D2 ,Lib) 57.37 (D1 , Lib) 50.69 (D1 , Lib) 52.27 (D2 , Lib)

vely). It can be seen that for D4, the accuracy dropped signi�icantly for 40 dimensional features in compari‑ son to the 30 dimensional features which points to‑ wards over �itting the neural networ�. In the case of D3 it can be seen that an increase of 16.21% in accu‑ racy was obtained for the 30 dimensional features as compared to the 20 dimensional features thereby de‑ monstrating the inability of the 20 dimensional featu‑ res to handle the 15 second long noisy clips.

The obtained accuracies for the different feature dimensions for the 4 datasets in the presence of thun‑ der noise is presented in Table 13.

It can be seen from the Table that in the case of D2, the best result was obtained for decision table with 20 dimensional features. The obtained accuracies for 10 and 30 dimensional features were quite less as com‑ pared to the 20 dimensional features as can be seen in the Table as well. In The remaining datasets produced best results with MLP and 20 dimensional features out Articles

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Tab. 8. Accuracies using MLP for D1 with 40 dimensional features for different training iterations Iterations Accuracy (%) Iterations Accuracy (%) Iterations Accuracy(%)

100 99.66 900 99.79 1700 99.80

200 99.72 1000 99.80 1800 99.81

Tab. 9. Confusion matrix for D1 with 40 dimensional features using MLP at 1800 learning iterations Song Instrumental

Song 35052 74

300 99.72 1100 99.79 1900 99.81

Fig. 7. Amplitude based representation for 10 second long (a) Instrumental, (b) Song, (c) N1, (d) N2, (e) N3 and (f) N4 clips The trend of the feature values for the 2 type of clips in thunder noise scenario as well as N1, N2, N3 and N4 scenario is presented in Figure 8. The obtained accuracies for N1‑N4 is presented in Table 16. It can be seen from the Table that the accuracy dropped slightly for N2 with respect to the original thunder noise scenario. A similar trend is also obser‑ ved for N2 and N3. However, the accuracy dropped Articles

500 99.78 1300 99.80 2100 99.80

600 99.78 1400 99.80 2200 99.81

700 99.78 1500 99.79 2300 99.80

800 99.78 1600 99.80 2400 99.81

Instrumental 64 35644

of which D2 produced the best result (99.19%) among all the noisy scenarios. The confusion matrix for the same is presented in Table 14. Since the best result for noise free scenario using MLP was obtained using MLP with 1800 training ite‑ rations, so the same con�iguration was also used and an accuracy of 99.34% (highest among all noisy scena‑ rios) was obtained whose confusion matrix is presen‑ ted in Table 15. It can be seen from the Table that though the num‑ ber of misclassi�ications for song clips increased slig‑ htly (only 3 more instances) but the number of mis‑ classi�ied instrumental clips reduced by 31% in com‑ parison to the default iteration setup of MLP. We had further experimented with the thunder noise scenario and 20 dimensional feature set of D2 as the best result for noisy scenario was obtained for it. We increased the power of the thunder noise signal by 2 (N1), 5 (N2), 10 (N3) and 20 (N4) dB and added it to the noise free clips of D2 to observe the system’s performance. The amplitude based representation of the noise clips along with that of the original data is presented in Figure 7.

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400 99.79 1200 99.80 2000 99.81

Fig. 8. 40 dimensional feature values for (a), (b) Instrumental

signi�icantly when the noise was increased by 20 dB. The dataset was manually investigated for this scena‑ rio and it was fond that in most of the clips, the propor‑ tion of noise was extremely high in comparison to the original data and in many cases the original data was inaudible. The confusion matrices for the 4 scenarios is presented in Table 17. It can be seen from the Table that in the case of N2 and N3, there is no major difference of the number of misclassi�ied instances though the noise component in N3 is twice to that of N2 which points to the system’s ability to handle noisy clips.

5.3. Statistical Significance Tests Friedman test [28] on the 40 dimensional feature set of D1 (overall highest among all scnarios) was car‑ ried out to check for statistical signi�icance. The data‑ set was divided into 5 parts (N ) and all the 6 classi�iers (k) were involved in the test. The distribution of ranks and accuracies are presented in Table 18. The Friedman statistic (χ2F ) [28] was calculated with the help of Table 18 in accordance with Equa‑ tion 5 where Rj corresponds to the mean rank of the j th classi�ier.   2 ∑ 12N k(k + 1)  . (5) Rj2 − χ2F = k(k + 1) j 4

The critical values of χ2F for the above setup was found to be 11.070 and 9.236 at signi�icance levels of 0.05 and 0.10 respectively; we got a value of 15.54 for χ2F thereby rejecting the null hypothesis.

6. Conclusion

In this paper, a system for segregating instrumen‑ tals and songs from noisy audio is presented using line

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Tab. 10. Accuracies for different number of cross validation folds of cross using MLP for D1 with 40 dimensional features and 1800 training iterations # Folds Accuracy (%)

2 99.36

3 99.75

4 99.69

MLP

5 99.81

6 99.71

7 99.81

8 99.78

SVM

Lib

9 99.75

Tab. 11. Obtained accuracies for D1 ‐D4 and 10‐40 dimensional features in highway noise scenario

10 20 30 40

68.80 67.81 72.06 97.14

68.89 76.15 78.21 97.77

10 20 30 40

80.30 83.77 95.49 97.49

80.89 91.29 97.51 99.16

10 20 30 40

66.91 73.36 87.09 97.02

86.55 80.25 95.62 90.57

69.77 97.40 91.37 97.85

87.05 94.22 98.15 94.02

DT D1 70.28 77.95 78.46 96.61 D2 72.05 92.17 95.33 93.03 D3 80.63 92.66 94.32 96.70 D4 87.30 89.91 97.83 94.73

61.84 63.16 63.36 69.35

61.66 62.70 62.27 56.98

61.51 59.08 55.58 56.96

73.86 70.58 79.96 77.04

74.58 72.13 79.78 83.87

74.09 64.30 71.45 65.77

60.75 64.50 69.73 87.66

86.96 65.29 77.99 67.20

60.52 63.35 63.37 95.12

86.96 64.50 84.95 58.59

10 99.73

60.11 61.05 63.37 77.31

86.96 62.65 69.37 50.70

Tab. 12. Obtained accuracies for D1 ‐D4 and 10‐40 dimensional features in humming noise scenario BN

MLP

10 20 30 40

67.27 62.96 77.66 77.22

68.08 70.07 85.63 96.94

10 20 30 40

87.21 65.22 97.61 91.71

88.00 81.99 98.20 96.92

10 20 30 40

64.95 65.74 97.53 97.78

65.54 72.25 98.02 71.74

66.05 74.12 97.94 98.55

68.23 89.49 98.17 83.32

DT D1 70.07 67.16 92.51 90.56 D2 67.78 72.31 97.80 98.08 D3 87.38 70.70 97.05 93.49 D4 68.86 88.96 98.01 91.10

spectral frequency based features. The clips were sub‑ jected to multifarious noise sources to test the robust‑ ness of the system. We have applied different popular classi�iers on the feature sets and obtained the highest result using MLP algorithm for both noise free as well as noisy scenario.. It was also observed that LibLinear

SVM

Lib

63.10 61.28 65.77 65.28

62.07 59.41 65.13 64.82

62.14 56.20 55.77 53.50

69.83 62.21 87.23 84.38

68.47 60.35 81.01 86.45

69.50 58.68 83.51 74.34

60.53 62.14 97.73 72.75

60.02 62.58 95.03 66.92

61.10 60.59 97.59 82.16

60.53 59.96 98.14 67.50

60.27 58.28 93.62 51.72

60.07 56.98 90.02 52.09

produced most of the accuracies in the lower side. As future work we will experiment with a lar‑ ger and more robust dataset and observe the perfor‑ mance of various other classi�iers. We will also expe‑ riment with other machine learning techniques inclu‑ ding deep learning based approaches and use different Articles

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VOLUME 14, N° N°22 2020 VOLUME 14,

Tab. 13. Obtained accuracies for D1 ‐D4 and 10‐40 dimensional features in thunder noise scenario BN

MLP

10 20 30 40

62.37 68.58 83.86 59.39

63.42 86.47 84.73 73.38

10 20 30 40

62.00 88.20 83.59 69.95

65.99 92.94 84.36 93.93

10 20 30 40

61.15 91.78 68.30 59.14

62.21 95.30 61.87 81.53

62.11 99.19 79.86 87.67

64.66 98.89 63.07 92.92

Tab. 14. Confusion matrix for D2 with 20 dimensional features and thunder noise scenario using MLP with default parameters Song Instrumental

Song 17250 172

Instrumental 112 17599

Song Instrumental

Song 17247 118

Instrumental 115 17653

DT D1 63.34 83.80 81.25 69.64 D2 63.96 99.03 71.23 87.64 D3 65.62 90.54 86.94 98.12 D4 66.22 96.91 65.50 84.36

Tab. 15. Confusion matrix for D2 with 20 dimensional features and thunder noise scenario using MLP with 1800 training iterations

Tab. 16. Obtained accuracies for D2 using MLP when subjected to N1‐N4 sources Noise Scenario Accuracy

N1 98.84

N2 95.23

N3 94.36

N4 68.66

features to further minimize the errors. We also plan to pre‑process the data for noise removal to make the system more robust which is critical for live audio. The system will be further extended to detect instrument sections from songs in real time to separate the vocals and instrument tracks.

AUTHORS

88 88

Himadri Mukherjee – Dept. of Computer Science, West Bengal State University, Kolkata, India, e‑mail: himadrim027@gmail.com. Sk Md Obaidullah – Dept. of Computer Science and Engineering, Aliah University, Kolkata, India, e‑mail: Articles

∗

SVM

Lib

60.99 61.57 77.48 58.99

60.84 58.96 77.08 54.81

61.17 58.76 72.91 50.16

61.15 62.71 84.27 75.68

56.96 63.83 80.89 71.60

57.86 58.25 81.67 54.96

58.97 68.63 78.79 58.94

59.71 84.32 62.34 65.95

58.96 69.43 75.27 52.64

57.51 82.68 54.71 64.27

58.66 66.89 66.90 49.87

58.34 83.52 50.56 55.01

sk.obaidullah@gmail.com. K.C. Santosh – Dept. of Computer Science, The University of South Dakota, SD, USA, e‑mail: san‑ tosh.kc@usd.edu. Teresa Gonçalves – Dept. of Informatics, University of Evora, Evora, Portugal, e‑mail: tcg@uevora.pt. Santanu Phadikar – Dept. of Computer Science and Engineering, Maulana Abul Kalam Azad Univer‑ sity of Technology, Kolkata, India, e‑mail: sphadi‑ kar@yahoo.com. Kaushik Roy – Dept. of Computer Science, West Bengal State University, Kolkata, India, e‑mail: kaus‑ hik.mrg@gmail.com. ∗

Corresponding author

REFERENCES

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Journal Robotics and Intelligent Systems JournalofofAutomation, Automation,Mobile Mobile Robotics and Intelligent Systems

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2020 2020

Tab. 17. Obtained accuracies for D2 using MLP when subjected to N1‐N4 sources Song Instrumental

Song 17001 45 (N1)

Instrumental 361 17726

Song Instrumental

Song 16286 601 (N2)

Instrumental 1076 17170

Song Instrumental

Song 15989 607 (N3)

Instrumental 1373 17164

Song Instrumental

Song 11236 4886 (N4)

Instrumental 6126 12885

Tab. 18. Rank and accuracies for parts of D1 Classi�iers MLP BN SL

SVM Lib

A R A R A R A R A R A R

1 99.64 (3.0) 99.9 (1.5) 99.9 (1.5) 95.4 (4.0) 76.33 (5.0) 55.01 (6.0)

2 99.99 (1.0) 99.72 (2.0) 61.8 (4.0) 92.98 (3.0) 55.12 (5.0) 50.66 (6.0)

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Parts of D1 3 4 99.98 100.0 (2.0) (2.0) 100.0 100.0 (1.0) (2.0) 78.45 99.97 (5.0) (4.0) 99.18 97.72 (3.0) (5.0) 96.05 89.99 (4.0) (6.0) 50.76 100.0 (6.0) (2.0)

5 99.92 (1.0) 99.46 (2.0) 75.81 (5.0) 96.01 (3.0) 76.97 (4.0) 62.36 (6.0)

Mean Rank 1.8 1.7 3.9 3.6 4.8 5.2

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[15] B. Zhu, W. Li, R. Li, and X. Xue, “Multi‑Stage Non‑Negative Matrix Factorization for Mo‑ naural Singing Voice Separation”, IEEE Tran‑ sactions on Audio, Speech, and Language Processing, vol. 21, no. 10, 2013, 2096–2107, 10.1109/TASL.2013.2266773, Conference Name: IEEE Transactions on Audio, Speech, and Language Processing. [16] “Youtube”. https://www.youtube.com/, 2020. Accessed on: 2020‑09‑20.

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The Method of Selecting the Interval of Functional Tests Taking into Account Economic Aspects and Legal Requirements Submitted: 20th October 2018; accepted: 2nd June 2020

Jan Piesik, Emilian Piesik, Marcin Śliwiński

DOI: 10.14313/JAMRIS/2-2020/24 Abstract: The article discusses the problem of choosing the optimal frequency of functional tests, taking into account the reliability and law requirements, but also the impact of business aspects in the company. The subject of functional test interval is well described for purposes of the process industry. Unfortunately, this is not the case for the machinery safety functions with low demand mode. This is followed by a presentation of the current business approach, which, in order to achieve industrial excellence, monitor their performance through the appropriate selection of key performance indicators. In addition, companies are increasingly exploring potential risks in the following areas: new challenges in advanced risk management, including the perception of the company’s facilities as a safe workplace insight of customers and business partners. Eliminating potential hazards is increasingly taking into account, especially the impact of human activity and its interaction with machines. The case study has been presented based on the machines used for the production of tire semi-finished products. In this article, the authors propose a solution for selecting the interval of functional tests of safety functions and additional machine protection measures as a compromise to achieve satisfactory results in terms of safety requirements, performance and legal requirements. Keywords: Functional test, maintenance engineering, parameter, optimisation, safety analysis, time-schedule control, tires

1. Introduction At present, there is a sharp increase in the requirements and scope that every enterprise manages. Year after year, the business requirements set by companies are increasing. Those results in finding further areas which can be better managed to get tangible benefits for the company. One of such areas is planned stoppages for maintenance. Planned maintenance consists of functional test, inspection, cleaning, lubrication, planned replacement of elements, e.g. batteries, condition monitoring. A comprehensive approach to maintenance and effective optimisation is implemented in companies

through the implementation of Total Productive Maintenance (TPM) [1] and the implementation of the Reliability Centered Maintenance (RCM) [18]. In this article, the authors reflect on the testing and optimisation of functional tests. Optimisation of preventive stops is widely described in the literature. Their optimisation is analyzed in terms of incurred costs [21], in short term cost optimisation and long term cost optimisation [3] and time-dependent inspection frequency models [20]. Most of the current articles focus on a narrow range of individual cost optimisations. In industry, in addition to compliance with costs, law, safety standards, workplace requirements, increasingly essential interactions between them and other business risks (e.g. brand strength perceived by customers) are becoming increasingly important. The approach to business management has also changed rapidly in recent years. This can be observed in many changes over the years in standards, e.g. in the quality management standard, which in the latest version of ISO 9001:2015 [8] introduces new, additional requirements of stakeholders. The certification of this standard has now become the basis for company management. However, it still does not cover the entire scope of activities. For this reason, ISO 31000 [12] and ISO 22301 [11], which cover risk management and business continuity management, were created. The reason for this is that the management process is becoming more complicated than at the end of the 20th century and new threats to companies are being identified. The actual methods presented in the literature do not cover these issues. Therefore, a new policy has to be implemented and the approach has to be modified and adapted. The authors in this article present a new integrated approach to this subject, based on well-known methodology presented in international standards [4],[6],[9],and the impact of environment and humans aspects to the functional test interval selection. Due to the new risk areas managed by companies, counting the stoppage connected to the functional test interval has also taken into consideration other factors, in addition to the direct costs of stoppages, or the costs of potential defects. They are taking into account the wide range of risks in accordance with ISO 31000. It can be stated that the brand good image loss, costs a company (e.g. an accident at work) much more than the cost of additional machine stops associated with

Journal of Automation, Mobile Robotics and Intelligent Systems

the proof test or functional test. Direct costs and efficiency of planned maintenance can be evaluated through Key Performance Indicators (KPIs). The KPIs can be defined according to international standard ISO 22400 [10].

2. Background The following tests and fault detection help to detect and remove hidden faults in the safety system. We have three possibilities for failure detection [19]: • failure detection by automatic (diagnostic) selftests (including operator observation), • failure detection by functional test (manual test), e.g. proof test, • failure detection during process requests/shutdowns.

2.1 Relevance of Proof Test

The term proof test is sometimes used interchangeably with the function test, while some authors consider them to be identical, others see them as different and even use other terms such as functional proof test. As was mentioned the elaborate description about the proof test is given in process industry literature and on this basis. The definition of proof test given is a ‘‘periodic test performed to detect failures in safety-related systems so that the system can be restored to an ‘‘as new’’ condition or as close as practical to this condition’’[15]. The need for routine maintenance action to detect unrevealed failures is established by the standard, and the proof test is one of these activities. Those tests should be made in conditions as close as it is possible to normal operating conditions of Safety Requirement Specification (SRS). The test has to include all elements of SRS starting from sensors, by logic controllers up to output devices. The proof test has to be complex what means all elements have to be tested at the same time. The term functional testing as used in IEC-61508 [4] part 7 means to “reveal failures during the specification and design phases to avoid failures during implementation and integration of software and hardware”. This consequently means that proof test and functional tests have different meanings. Sometimes because of production specificity, there are made tests only of few elements, what is called partial tests. However, also with rare frequency entire tests has to be done. Differences between them arrive in three most important aspects: frequency of tests, percent of failure detection and need to stop complete installation or made during standard work. The partial tests (e.g. visual inspections) can detect only some system failures. The full tests done mainly during overhauls granted restore the system to full operating condition. According to IEC61508-2 [4], the frequency of proof test will be dependent upon the target failure measure associated with the Safety Integrity Level (SIL), the archiArticles

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tecture, the automatic diagnostic coverage and the expected demand rate.

2.2 Scope of Functional Tests

In the article, it is assumed that a proof test is one of the functional tests. Functional testing shall include, but not be limited to, verifying the following: • the operation of all input devices including primary sensors and Safety-Related Electrical Control System (SRECS) input modules; • logic associated with each input device; • logic associated with combined inputs; • trip initiating values (set-points) of all inputs; • release of alarms functions; • the speed of response of the SRECS when necessary; • operating sequence of the logic program; • the function of all final control elements and SRECS output modules; • computational functions performed by the SRECS; • timing and speed of output devices; • the function of the manual trip to bring the system to its safe state; • the function of user-initiated diagnostics; • complete system functionality; • the SRECS is operational after testing. For those applications where partial functional testing is applied, the procedure shall also be written to include [15].: • describing the partial testing on the input and logic solver during operation; • testing the final element during unit shut down; • executing the output(s). There are two ways to minimalise the percentage of planned stops. First is a reduction of the time spent on planned stops which means optimisation and increase the efficiency of works done during those stops. The second way is to maximise the frequency of planned stops. Finding the root cause of failure mentioned in the previous point can result in the elimination of some checking and planned jobs. The most critical to optimise is the time spent on actions required by the law and other regulations. The fact which cannot be neglected is a crucial role of maintenance in maintaining the safety at the appropriate level in operation [22], maintenance and repair stage of overall safety lifecycle [4]. After machine commissioning the maintenance department take care of safety aspects [13] as well as cost criteria what has to be done choosing correct maintenance strategy [14].

2.3. Types of Testing Methods

There exist three general types of systems testing methods: • Shutdown testing. Cons of this type of test are that demands stop of the whole installation to perform the test. This inconvenience is much more severe in the process industry, but it also affects in other

Journal of Automation, Mobile Robotics and Intelligent Systems

branches of industry. The second disadvantage is the need to perform the test manually and to record it also manually. • Bypass testing. On the other hand, for this type of testing, the inconvenience lies in need to disable the safety function during the test and manual testing and to record it manually. The manual test also involves the risk of human error. In addition, additional costs related to bypassing elements are linked to the last item. • Partial stroke testing (PST). Pros for this type of test is that it can be done automatically and registered automatically. Cons is that it does not give absolute certainty about the operation of tested elements. In the machinery, the most common type of testing is shutdown testing.

2.4 How to Determine the Test Frequency

At start-up, the operation of the safety function is validated but the safety function must be maintained by periodic proof testing. The full proof test performing a safety function is treated as the undesired stopping of the production process, which reduces production effectiveness. According to the general safety standard 61508 stated that the proof test interval could be determined based on Average Probability of Failure on Demand (PFDavg) value [4]. According to standard PN-EN ISO 12100:2011 product manufacturer should provide information for end-user about the nature and frequency of inspections for safety functions [6]. Unfortunately, in safety manuals frequently can be found no information about proof test frequency or there is a statement that proof test is recommended to be performed at least once per year. The frequently encountered rule is also that Proof Test Interval should not be more than 50% of demand rate. The standards assume that lifetime of the machinery as twenty years. It is based on the assumption that only a few modern systems last more than twenty years without being replaced or rebuilt. It is also assumed that machine controls get at least one proof test during the lifetime. The proof test is performed as a test of a complete subsystem and not some separate components (subsystem elements) unless the subsystem contains only one element. Subsystem could include the following elements: • complex electronic devices, e.g. PLCs, • electronic devices with the predefined behaviour are, e.g. IO modules, • electromechanical elements, e.g. relays, contactors. The obligation for end-user touch three main domain: • follow the law and regulations, • follow the safety manuals of the manufacturer of the machines, • follow the PFDavg and Probability of Failure per hour (PFH) calculations.

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The first obligation can be fulfilled partially by applying the rules contained in the Recommendation of Use CNB / M / 11.050 published by European co-ordination of Notified Bodies for Machinery concerning dual-channel safety-related systems with two channels with electromechanical outputs: • If the safety integrity requirement for safety function is SIL 3 (Hardware Fault Tolerance (HFT) =1) or Performance Level (PL) e (Cat.3 or Cat. 4) then the proof test of this function shall be performed at least every month; • If the safety integrity requirement for safety function is SIL2 (HFT=1) or PL d (Cat.3), then the proof test of this function shall be performed at least every twelve months. The excellent example of this recommendation is contactor relays, safety relays, emergency stop buttons, switches which are typically safety devices with electromechanical outputs. Second obligation to perform periodic inspections is given by Directive 2009/104/EC of the European Parliament and of the Council of 16 September 2009 concerning the minimum safety and health requirements for the use of work equipment by workers at work. It is implementation done by national law regulations. Following the second obligation only in the standard PN-EN ISO 14119 covering interlocks, we can find direct values of test proof interval. For applications using interlocking devices with automatic monitoring, it is stated that for PL e with Category 3 or Category 4 or SIL 3 with HFT equal one functional test should be performed every month. Moreover, for PL d with category 3 or SIL 2 with HFT=1 functional test should be carried out at least every twelve months [7]. In safety manuals of safety equipment, it can often be found that the producer advises or recommend to make a proof test of the device at least once per year or IEC 61511-1:2016 for the process industry states in clause 16.3.1.3:” The schedule for the proof tests shall be according to the SRS. The frequency of proof tests for a SIF shall be determined through PFDavg or PFH calculation in accordance with 11.9 for the SIS as installed in the operating environment.” [5]. Also, in IEC EN 61508, it is stated that the proof test interval should be based on the PFD calculations [4]. IEC/EN 62061 states that a proof test interval of twenty years is preferred (but not mandatory) [10]. Recently in many safety manuals, manufacturers write that maximum proof test interval in a high demand mode of operation is twenty years. The third obligation is assuming those written above, generally consider PL ≤ c or SIL 1. Determination of the optimal frequency of testing poses difficulties in many companies. The mathematical approach is not very common and demands a high level of technical knowledge and familiarity with the standards and safety aspects. Determining the level of safety after the modification of equipment and adapt it to the requirements put technical departments in the face of new requirements and problems [16]. It was assumed that the hardware component with the smallest value Articles

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for the proof test interval determines the proof test time for the subsystem. Simplified calculation of PFD with perfect prooftest can be obtained as shown below. PFD ( t ) ≈ λDt where: λD – dangerous failure rate, t – time.

(1)

Assuming that the system is using non-repairable elements in configuration 1oo1, equation receives following form equal: 1 PFDavg1oo1 ≈ λDU TI 2

where: λDU – dangerous undetected failure rate, TI – proof test interval.

(2)

Values of the failure probability requirements are required for the whole safety function, including different systems or subsystems. The average probability of failure on demand of a safety function is determined by calculation of PFDavg for all subsystems, which as a whole create safety function. The end-user of the safety-related system has to make an analysis of PFDavg based on the data received from the producer of each part of the safety-related system.

2020

companies work on improving management efficiency, which will increase revenues and thus profits. In order to be effective, the aspects of management analysed by the author must represent all the opportunities and threats that arise. This is an essential development in the approach to analysis proposed by ISO 9001: 2015 [8]. As a result of these changes, the management models presented in the past have recently been expanded with the identification of internal and external risks. Risk management can be performed at any level and type of business activity. The process of risk identification consists of searching, identifying, classifying sources of risk and dangerous events, taking into account their causes and effects. The risk identification process may be based on various sources of information, such as historical expert knowledge, theoretical analysis and risks arising from stakeholder needs [2]. The risk management may also include business continuity management described in ISO 22301 [11]. In this article, the solution proposed by the authors takes into account the results of the risk management process analysis. This is due to the fact that many procedural imperatives have their origin in the results of risk analysis. An example can be the instructions that oblige departments to perform a monthly functional test. The frequency of these tests does not result from the risk analysis of the safety function, but rather from minimising the risk of an accident at work.

2.5. Measuring Production Efficiency

3. Proposed Solution

The efficiency of a production plant can be evaluated through KPIs. This method is widely utilized in many companies. Recently definition of KPIs was defined by international standards, e.g. ISO 22400 [10]. KPIs in manufacturing facilities are ranked according to many categories. Indicators are reflected in the objectives of the plant. They play the role of a performance measure of plant operations. Typically, they are different at different levels of business management. Their right choice often determines the success of the company. KPIs can be implemented in all types of industries, including machinery, continuous and batch processes. Proper selection of indicators allows for quick identification of losses. The key maintenance indicators set out in standard ISO 22301 allow for increased dynamics in maintenance operations.

As it was presented in previous chapters, a test of machinery issue is not precisely defined taking into consideration three crucial factors: law and standards requirements, new aspects of risk analysis, the increase in productivity. The proof test objective is to discover critical errors not found by the diagnostics. Definition of proof test frequency is stated as diagnostics of components, sub-systems and whole control systems. Is intended to determine their state in the formulation of the assessment of the willingness to perform safety functions. The proposition consists of two elements: a) The proposition of test interval for machinery; b) Method of estimation additional risk influences into proof test frequency for low demand mode. The first part of the proposition helps to increase the productivity of the machines by standardisation of test frequency. The second part takes into account the risks defined by a broader approach to company risk management [17].

2.6. Impact of Risk Management on Business Operations

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As presented earlier, the role of quality management in improving business performance is growing year by year. This is due to strong market competitiveness and comparable technical solutions used in both machines and processes. In many situations, manufacturers purchase machines from third-party companies, which means that competitors have the same machine park. Therefore, in order to be competitive, Articles

3.1. A Proposal for Estimating Test Intervals for Machinery

The variety of applications in many sectors of industry required periodic proof testing and functional tests. There is a gap in the law and standards in explaining the frequency of functional tests, proof

Journal of Automation, Mobile Robotics and Intelligent Systems

tests and shutdowns used to detect failures. This mainly affects the functions of SIL 1. As is apparent from the literature, the user defining a functional test must rely on the data provided by the machine manufacturer. Tab. 1. Recommendation for test periods for machinery Preconized test interval 1/year

1/month

Source

SIL (EN 62061)

HFT (EN 62061)

CNB / M / 11.050

Authors

CNB / M / 11.050

Frequently proof test interval is estimated by the manufacturer to twenty years. The second source of information can be historical data about the frequency of demands for the safety-related action of the Safety Related Part of the Control System. Based on this data, the frequency may be changed. The first component of the authors’ proposal is presented in Table 1.

3.2 Assessment of the Impact of the Identified Risks on the Frequency of Proof Test in LowDemand Mode

For some machines equipped with safety function and complementary protective measures working in low demand mode because of construction, the specification of production, ergonomics, lack of space happens that safety functions or complementary protective measures can be activated incidentally, e.g. forklift attacked safety mate, product fall and activate safety line. This provokes that machine stops because of function activation. The more dangerous is the situation, where this function was not activated, and only some mechanical parts were defected. That in the future can result in incorrect operation of the safety function. Usually, operators should alert maintenance stuff, and after verification, the machine can be given back for production. This situation has taken place in general but taking into consideration human errors (e.g. incidental impact by a forklift), based on the author’s analysis quarter of such incidents are not reported [17]. To assure that safety function or complementary protective measures are still able to fulfill its function authors propose to made additional estimation shown in Fig. 1 [17]. SIL 1 F1 D1 D2

SIL 2 F2

F1 D2

SIL 3 F2

D2 D1

F2 D1

N/A FTI VI MSIL2 N/A FTI VI FTI N/A FTI

Fig. 1. Graph of additional action estimation for machines working in low demand mode where: • Safety Integrity Level: SIL1, SIL2, SIL3.

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• The frequency of unplanned activation of the function: F1 – seldom to less often; F2 – frequent; • The possibility of detection eventual damages without stopping machines/production line: D1 – possible; D2 – practically impossible; • Action: N/A – No action necessary, VI – Visual inspection, FTI – More Frequent Time interval; MSIL2 – Modification to SIL2; The presented analysis took into account three categories: SIL of the system and dived it into three scopes. First for SIL1, the second one for the SIL2, and the third one for SIL3. The second category is the frequency of such unintended safety function activation. It is divided into seldom and frequent. The third category is the possibility of eventual damages detection without stopping the production line or machine. This category is divided into possible to detect cases and impossible to detect without stop events. As a result, it can be obtained four possible scenarios. First with the lowest risk finish with no actions. The second result is adding into maintenance preventive plan additional visual verification of safety function elements, or complementary protective measures elements state. The term complementary safety measures are used in ISO 12100 standard and are used to avoid or to limit the harm [6]. Example of this can be emergency stop systems. The frequency of that inspection should be not less than twice as often as the period between two proof or functional tests. The third action is requested to modify the elements to fulfill the requirements of SIL2. The last scenario is an increase in the frequency of proof or functional test interval. The frequency of the test should be not less than twice the period between two known accidental activation.

4. Case Study – Tire Cord Treating Line The chosen for case study object is a modern single end impregnation line used to treat yarns made of polyamide, polyester, viscose and other raw materials so they are suitable for applications – use in tires. The pull roll section is a part of a line analysed in this case study. Following a risk analysis (Failure Modes, Effects and Criticality Analysis), one safety function and two complementary protective measures were identified in this section of the production line. The safety function secures by restricting access to the machine’s rotating parts and parts with ingress angles. The first complementary protective measures role is to prevent the hand or forearm from being caught by the thread of textile cord by installing a cable pull safety switch. The second is a typical emergency stop button. The safety function has SIL 2. The other two complementary protective measures have an estimated SIL1. It can be calculated from the manufacturer’s data that each of the given safety functions and supplementary measures has reached the factory SIL level (SIL 2, SIL1, SIL1). Articles

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In the course of the productivity loss analysis, one of the elements of the maintenance work – preventive maintenance time causing downtime – was identified as one of the leading productivity losses. This indicator shows that a company loses three hours of production per month for a given machine (including procedures for stopping and starting machinery). In order to improve this result, it was decided to analyse the indicated machine according to the model presented above. The first supplementary measure, which prevents staff from being caught by the threads of a textile cord, based on the reliability data of the components of this function, has a functional test equal to a service life of twenty years, which means that there is no need for a control test of this function. The analysis proposed by the authors has been carried out taking into account the facts of risk management. During the analysis it was assumed – SIL1. The analysis of entries to the Computerized Maintenance Management System application and conversations with both production operators and maintenance staff shows that an unintentional activation of complementary protective measures by the operator or product takes place on average once every twelve months. Therefore, it can be qualified to group F1. The last analysis criterion, which is the possibility of detecting a defect, was assessed as practically impossible to detect. Based on the estimation of additional actions (Fig. 2), it can be concluded that it is necessary to change the time interval of the functional test. Taking into account the frequency of activation of the function and damage, on average once a year it is proposed to double the frequency of activation – which corresponds to six months. In conclusion, the result of the analysis is to change the functional test interval to six months. The company’s profit can be estimated as an additional 30 hours of machine operation per year and minimisation of the risks identified in the risk analysis. SIL 1 F1

SIL 2 F2

D1 D2

F1 D2

SIL 3 F2

D2 D1

F2 D1

N/A FTI VI MSIL2 N/A FTI VI FTI N/A FTI

Fig. 2. Graph of additional action estimation for a first complementary measure of a section of impregnation line working in low demand mode

SIL 1 F1 D1 D2

SIL 2 F2

F1 D2

N/A FTI VI MSIL2 N/A FTI VI FTI N/A FTI

Fig. 3. Graph of additional action estimation for 96

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Severity (Se) 4 3 2 1

Class (Cl) 8-10 SIL2 SIL1

5-7 SIL2

3-4 SIL2

14-15 SIL3 SIL3 SIL2 SIL1

11-13 SIL3 SIL2 SIL1

Fig. 4. SIL assignment matrix for the analysed safety function Safety function with value SIL2. Analysing available data was assumed that the frequency of unplanned activation is frequent, and the detection of possible damages is possible without stopping the machine. The following proposed method can be estimated that additional action, in this case, is additional visual inspection (Fig. 5). As the average frequency of unplanned activation or damage was estimated to six months, visual inspection of that element was planned for three months. Manufactures data presents the T1 value for proof test interval as 20 years. So, there is no need to plan an additional test for this element. According to authors proposal, functional test is completed with the frequency of twelve months.

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Second complementary measure – emergency stop. The frequency of use is rare, and detection was quantified as possible. For this reason, no additional action is necessary (Fig. 3). Also, in this case, the manufacturer gave T1 value to twenty years. Concluding there is no proof test necessary during the lifetime of this function. According to the authors proposition (every year test for SIL1) time the functional test of that complementary measure is done in the double frequency as the first one. The case study is based on pull roll section with the safety function of door locking and monitoring. The required Safety integrity level is the result of a risk assessment and refers to the amount of the risk reduction to be conducted by the safety-related parts of the control system. Part of the risk reduction process is to determine the safety functions of the machine. Safety function which protects by restricting access to the cabinet has estimated SIL2 based on SIL assignment matrix proposed in the EN 62061 standard. The severity of the injury was estimated as level 3. Frequency and duration with note 3, the probability of hazard event as possible and note 4, avoidance as possible with note 4. Cl=Fr+Pr+Av=3+4+4=11 (Fig. 4).

SIL 1

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a second complementary measure of a section of impregnation line working in low demand mode

SIL 3 F2

D2 D1

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D1 D2

SIL 2 F2

F1 D2

SIL 3 F2

D2 D1

F2 D1

N/A FTI VI MSIL2 N/A FTI VI FTI N/A FTI

Fig. 5. Graph of additional action estimation for defined

Journal of Automation, Mobile Robotics and Intelligent Systems

safety function of the cord twisting machine Summarizing achieved results can be stated that the use of the proposed method was achieved two goals. First, the rules of functional test frequency become clear from a user point of view. Based on risk analysis and manufacturer data, level can be stated required SIL and SIL achieved by the installation. With this information based on Tab. 1 user can stated recommended frequency. This influence into minimalisation of time spends into preventive maintenance. What in consequence increase productivity KPIs. Second, a graph of additional action estimation helps the user to minimalise additional risks not covered before. The tool is easy in use and can be easily utilised by maintenance or responsible for safety personnel. Implementation of actions defined in proposed graph influence on results of risk analysis made at the different level of company management according to ISO 31000 [12].

5. Discussion The proposed solution allows to provide the required SIL, taking into account the aspects of risk management in the company, which are not taken into account when calculating the SIL according to IEC 62061 [9]. This method takes into account EU recommendations and provisions of the standards. Additional verification or a shorter frequency of proof tests allows to minimize the risk of the performance level decreasing over time. The third important thing is to combine the frequency of the different tests in order to minimise machine downtime and consequently minimise production lose. The tools take into account the impact of the environment in the operational stage of life cycle. The tools presented above are a new approach taking into account the experience of the authors. At the same time, it is recommended that an analysis of the causes of unintentional SIF activation be carried out, in order to eliminate the root cause of the increased risk. An in-depth analysis and subsequent action plan can eliminate this cause, which will result in a return to a regular interval.

6. Conclusion The tool presented by the authors serves to improve the productivity KPIs defined above, helps to optimize the functional and proof test intervals taking into account specific aspects of risk management. This tool is the authors’ response to problems encountered in their professional practice and takes into account typically practical aspects. An important point to emphasize is the fact that many safety system manufacturers assume that the mission time of the machines is twenty years. This fact must be taken into account by the user for machines that are already around twenty years old, as they have to prepare for the wear-out phase of the systems. Other conditions,

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which could be included in new versions of the risk management or quality management standards, may necessitate changes to the proposed method. This tool has been used several times so far and further testing is needed to confirm its effectiveness in different cases.

AUTHORS Jan Piesik* – Michelin Polska S.A., Olsztyn, Poland, email: jan.piesik@michelin.com.

Emilian Piesik – Gdansk University of Technology, Gdańsk, Poland, e-mail: emilian.piesik@pg.gda.pl. Marcin Śliwinski – Gdansk University of Technology, Gdańsk, Poland, e-mail: marcin.sliwinski@pg.gda.pl. *Corresponding author

References [1] T. Carannante, “The introduction and implementation of TPM using a conceptual model developed in-house – phase I”, Maintenance & Asset Management, vol. 18, no. 5/6, 2003.

[2] D. Gołębiewski and K. Kosmowski, “Towards a process based management system for oil port infrastructure in context of insurance”, Journal of Polish Safety and Reliability Association, vol. 8, No. 1, 2017.

[3] H. Guo, F. Szidarovszky, A. Gerokostopoulos and P. Niu, “On determining optimal inspection interval for minimizing maintenance cost”. In: 2015 Annual Reliability and Maintainability Symposium (RAMS), 2015, DOI: 10.1109/RAMS.2015.7105163. [4] IEC 61508 1-7:2010: Functional safety of electrical/ electronic/programmable electronic safety-related systems, International Electrotechnical Commission, Geneva, 2010.

[5] IEC 61511 1-3:2016: Functional safety – Safety instrumented systems for the process industry sector, International Electrotechnical Commission, Geneva, 2016. [6] ISO 12100-2:2010: Safety of machinery – Basic concepts, general principles for design – Part 2: Technical principles, International Organization for Standardization, Geneva, 2010.

[7] EN ISO 14119:2013: Safety of machinery – interlocking devices associated with guards – Principles for design and selection, International Organization for Standardization, Geneva, 2013. [8] ISO 9001:2015: Quality Management System – Requirements, International Organization for Standardization, Geneva, 2015. [9] EN 62061:2005: Safety of machinery – Functional safety of safety-related electrical, electronic and Articles

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programmable electronic control system, International Organization for Standardization, Geneva, 2005.

[10] ISO 22400: Automation Systems and integration – Key performance Indicators for Manufacturing Operations Management, International Organization for Standardization, Geneva, 2014.

[11] ISO 22301: Societal security – Business continuity management – Requirements, International Organization for Standardization, Geneva, 2012. [12] ISO 31000: Risk management- Principles and guidelines, International Organization for Standardization, Geneva, 2009.

[13] T. P. Kelly and J. A. McDermid, “A systematic approach to safety case maintenance”, Reliability Engineering & System Safety, vol. 71, no. 3, 2001, 271–284, DOI: 10.1016/S0951-8320(00)00079-X.

[14] L. Lu and J. Jiang, “Analysis of on-line maintenance strategies for k-out-of-n standby safety systems”, Reliability Engineering & System Safety, vol. 92, no. 2, 2007, 144–155, DOI: 10.1016/j.ress.2005.11.012. [15] Application of IEC 61508 and IEC 61511 in the Norwegian Petroleum Industry (Recommended SIL requirements), Norwegian Oil and Gas Association, 2004.

[16] J. Piesik and K. T. Kosmowski, “Aktualne problemy zarządzania niezawodnością i bezpieczeństwem linii produkcyjnej”, Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej, vol. 51, 2016 (in Polish). [17] J. Piesik, E. Piesik and M. Śliwiński, “A method of Functional Test interval selection with regards to Machinery and Economical aspects”, Contemporary Computational Science: 3rd conference on Information Technology, Systems Research and Computational Physics, 2018, 31–44.

[18] M. Rausand, “Reliability centered maintenance”, Reliability Engineering & System Safety, vol. 60, no. 2, 1998, 121–132, DOI: 10.1016/S0951-8320(98)83005-6.

[19] Reliability prediction method for safety instrumented systems: PDS method handbook 2010 edition, SINTEF Technology and Society, 2010.

[20] M. Subhash, “Optimal inspection frequency: A tool for maintenance planning/forecasting”, International Journal of Quality & Reliability Management, vol. 21, no. 7, 2004, 763–771, DOI: 10.1108/02656710410549109.

[21] J. K. Vaurio, “A Note on Optimal Inspection Intervals”, International Journal of Quality & Reliability Management, vol. 11, no. 6, 1994, 65–68, DOI: 10.1108/02656719410064685. [22] E. Zio and M. Compare, “Evaluating maintenance policies by quantitative modeling and analysis”, Reliability Engineering & System Safety, vol. 109, 2013, 53–65, DOI: 10.1016/j.ress.2012.08.002. 98

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Three level fuzzy signature based decision methodology for packaging system design Submitted: 20th October 2018; accepted: 2nd June 2020

Kata Vöröskői, Gergő Fogarasi, Adrienn Buruzs, Péter Földesi, László T. Kóczy

DOI: 10.14313/JAMRIS/2-2020/25 Abstract: In the field of logistics packaging, companies have to take decisions on determining the optimal packaging solutions and expenses. The decisions often involve a choice between one-way (disposable) and reusable (returnable) packaging solutions. Even nowadays, in most cases the decisions are made based on traditions and mainly consider the material and investment costs. Although cost is an important factor, it might not be sufficient for finding the optimal solution. Traditional (two-valued) logic is not suitable for modelling this problem, so here the application of a fuzzy approach, because of the metrical aspects, a fuzzy signature approach is considered. In this paper three different fuzzy signatures connected by fuzzy rules modelling the packaging decision are suggested, based on logistics expert opinions, in order to support the decision making process of choosing the right packaging system. Two real life examples are also given, one in the field of customer packaging and one in industrial packaging.

As a matter of course, the environmental aspects are also part of these important processes, including the reduction of waste during production [11]. Furthermore, improving the efficiency of packaging is an important strategic goal for the organizations considering the aspects of sustainability and economy [7]. Legislation has also forced companies to rethink their packaging operations [6]. The functions of packaging in general can be classified as follows [4]: • Product and environment protection (physical, safety, natural deterioration, waste reduction) • Logistics containment and handling (unit, bulk, pallet, containers) • Information (symbol, logo, description) Packaging systems can have different levels: primary, secondary and tertiary packaging (Figure 1).

Keywords: fuzzy signature, one-way packaging, returnable packaging

1. Introduction Packaging is a significant element in any logistics system [12]. Without proper packaging handling and transportation would be difficult and expensive along the supply chain (SC). Although cost is an important factor, it is not enough to consider only the costs of material and investment while choosing the right pack-aging system, many other aspects should be considered. It has been found that paying limited attention to packaging can cause higher costs in the physical distribution. Furthermore, researchers argue that packaging should not only be considered from the point of view of cost, but focus should be put on its role as a value-added function in the SC [5]. The best packaging solutions are those that, beside the optimal cost levels maximize the use of packaging capacity so that all the products can easily be packed and stacked, and at the same time reduce packaging waste [9].

Fig. 1. Use Packaging system levels [8] Primary packaging is the main package that holds the product that is being processed [8]. The aim of secondary packaging (it is also called transport or distribution packaging) is to preserve the product on its way from the point of manufacture to the customer. It includes the shipping container, the internal protective packaging and any utilizing materials for shipping. It does not include packaging for consumer products (primary packaging) [16]. Tertiary packaging combines all of the secondary packages for example into one pallet [8].

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The functions of transport packaging are: • Containment (basic purpose, supplying use value to products) • Protection (ensuring integrity and safety of the contents and occasionally also protecting the environment from the product) • Performance (transportation, handling, storing, selling and use of the product) • Communication (identification of the contents and informing about package features and requirements) [16]. The most important actors of an industrial packaging supply chain (PSC) are suppliers, assembly factories and packaging collectors (if returnable packaging is used) [13]. Packaging producers are also important, but choosing the right packaging for the product belongs to the competency of the factories, their suppliers, or both together.

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Managing returnable packaging systems requires more than just inverse transportation. The cleaning and maintenance of containers, as well as the storage and the administration are also involved in the process [3]. In most cases distance decides if the packaging comes back, but it also depends on the complexity of the supply chain. Transport modes also can play a noticeable role (for example road, rail or maritime transport). Packaging waste is an important issue in disposable-returnable packaging system design. The management of packaging waste has been an integral part of European waste policies since the 1990s. The European Union formulated new regulations in the Directive 2018/852 on packaging and packaging waste. According to that waste prevention is the most efficient way to improve resource efficiency and to reduce the environmental impact of waste. It is important therefore that Member States take appropriate measures to encourage the increase in the share of reusable packaging placed on the market and the reuse of packaging. Collaboration is crucial to packaging success. Many successful companies work closely with their suppliers to establish consistent shipping specifications before a new production program starts. [17]

2. The Fuzzy Signature Model Fig. 2. Packaging supply chain – open loop system [14]

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In the field of logistic packaging (industrial transportation, or even consumer packaging) the companies take decisions in order to determine the optimal packaging expenses. This decision-making situation practically means a choice between one-way (disposable) and reusable (returnable) packaging systems [1] [2]. The former is only suitable for one use as far as reusable containers and packaging are loaded with products and shipped to the destination, then the empty container is sent back to the supplier, refilled with products and this cycle is repeated over and over again as a closed-loop system. In case of an open-loop system reusable packaging is collected at a centralized return handling center, where it is cleaned, stocked, and distributed for refilling [16]. In the second case the packaging is not necessarily returning back to the initial partner who filled it. The main problem with one-way packaging is the waste created after the usage while relative production cost is lower. On the other hand, transportation and maintaining cost is a relevant issue in case of returnable packaging [2] [10]. Returnable packaging has been frequently used for example in the US automotive industry in order to reduce waste, costs, transport damages and for enabling just in time (JIT) deliveries [15]. Articles

In this section, the structure of three different fuzzy signatures (S1, S2, S3) and the fuzzy rules among them modelling the packaging problem on hand will be proposed including the tree graphs and the aggregation operations in the intermediate nodes. In the FSig in the intermediate nodes the use of weighted arithmetic mean operations is proposed. Based on expert knowledge three main aspects were defined earlier, this in used as the base of the improved model (the first level in the new model) when a decision has to be made about one-way or returnable packaging. Thus the three aspects in the first FSig will be as follows: • characteristics of the product to be packaged • characteristics of the supply chain and • external factors After considering the first three aspects, an additional aspect will be examined at the second level: • characteristics of the packaging material. In the third signature, also cost factors will be added in order to get the final result of the model. The relation among the three signatures is determined by the following rules: If µS1 ≥ 0.5 then check S2 If µS1 ≥ 0.5 & µS2 ≥ 0.5 then check S3 If µS1 ≥ 0.5 & µS2 ≥ 0.5 & µS3 ≥ 0.5 then returnable.

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Fig. 3. Tree structure of the fuzzy signatures

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All leaves of the tree assume their values (µi) from the interval [0,1]. [18] The values belonging to the intermediate nodes are calculated by respective functions specified to each leaf according to the logistics meaning and role. The relations among the individual descendants on the same level are determined with respective aggregations (see in chapter 2.1). The final purpose of the model is to sup-port the decision whether a disposable (one-way) or returnable packaging system should be used. When the final value created by the aggregation in the root (a0) is close to 0, it should rather be one-way, if the result of a7 is close to 1, the packaging should rather be returnable.

2.1. Definition of the Aggregation Operators

Based on the opinion of a panel of logistics experts is was decided that all aggregations are of the weighted arithmetic mean type, because the components of the individual characteristics and features are comparably importance, which may be expressed by weights of the same order of magnitude (given in tables 2-6). The examples based on real life goods packaging technologies used by real companies have confirmed the values and the type of aggregations used in this rather complex fuzzy signature.

2.2. Defining the Main Aspects and the Weights

In the following the parent and child nodes are described in groups: weights (wi) with aggregations of the intermediate nodes are listed in Tables 1-6. Table 1 determines the weights of aggregation operators (weights of the roots of the different sub-trees which are not further defined in the following section, but essential for the calculation). Tab. 1. Weights of the aggregation operators in the model

ID Features 1121 1122 1123 112 111 11 12

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product characteristics supply chain external factors S1 root packaging material S2 root cost

Weig hts 3 9 2 4 8 4 8

Product characteristics. This attribute represents the technical aspects of designing the right packaging for a particular product. Production batch size and turnover are two strong aspects, but also geometrical characteristics like shape, size and weight of the product should be considered. Furthermore, physical, biological, chemical sensitivity and value of the goods also play an important role. Within physical sensitivity the mechanical and climate effects must be differentiated. The rankArticles

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ing and weights in the fuzzy aggregation can be seen in Table 2. ID represents the position of the aspect (as a leaf or aggregation) in the fuzzy signature. Tab. 2. Ranking and aggregation weights of product characteristics and its sub-trees

1 product characteristics

ID Features 11211 batch size 11212 turnover 11213 geometrical 11214 sensitivity 11215 value 1.3 geometrical characteristics ID Features 112131 shape 112132 size 112133 weight 1.4 sensitivity ID Features 112141 physical 112142 biological 112143 chemical 1.4.1 physical ID Features 1121411 mechanical 1121412 climate

Ranking 1-2. 1-2. 3. 4-5. 4-5.

Weights 9 9 7 2 2

Ranking 1. 2-3. 2-3.

Weights 4 1 1

Ranking 1. 2. 3.

Weights 6 3 2

Ranking 1. 2.

Weights 6 4

Supply chain (logistics) characteristics. This attribute represents the logistics aspects of designing the right packaging for the given product. Transportation represents the main part of logistics activities in the supply chain (SC), but material handling and IT support are also essential for an effectively working SC. As it was mentioned earlier, transportation distance is highly important, as well as the volume of goods delivered at the same time. From the packaging point of view environmental circumstances during transportation (temperature, vibration and humidity) evidently influencing the decision. Quality of the infrastructure and the transport modes used (modality) should also not be left out of consideration. Material handling means all operations related to handling of the goods in the supply chain, including warehousing, unloading, uploading and transshipments. The organizational level of truck loads (full truck load – FTL, less than truck load – LTL) is also significant when deciding about returnable packaging because the complexity of the task is growing with the number of participants in the process. The ranking and aggregation weights in the fuzzy sub model can be seen in Table 3. Packaging material. After the results of the first signature show that returnable packaging may be used, an additional aspect should be considered. In the second signature planning aspects and characteristics of the packaging material will be examined. In respect of the used material robustness represents the quality and quantity of the material used in order to make the packaging strong enough. Availability is

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connected to the procurement options of the material while recyclability and reusability play an important role within the supply chain after the material is used. Tare weight, collapsibility and packaging fill rate determine the capacity usage while transport and especially return transport. Number of uses represents here the technical suitability for reuse. The ranking and weights in the second fuzzy signature can be seen in Table 5. Tab. 3. Ranking and aggregation weights of supply chain characteristics and its sub-trees

2 supply chain characteristics

ID Features 11221 transportation 11222 IT support 11223 material handling 2.1 transportation ID Features 112211 distance 112212 volume 112213 impacts 112214 infrastructure 112215 modality 2.3 material handling ID Features 112231 transshipment 112232 FTL/LTL 2.1.3 environmental impacts ID Features 1122131 temperature 1122132 vibration 1122133 humidity

Ranking 1. 2. 3.

Weights 8 7 2

Ranking 1. 2. 3. 4. 5.

Weights 8 7 5 3 1

Ranking 1. 2.

Weights 8 2

Ranking 1. 2. 3.

Weights 4 3 2

Tab. 4. Ranking and aggregation weights of the external factors and its sub-trees

3 external factors

ID Features 11231 cooperation 11232 regulations 11233 legal 11234 environmental effects 3.2 regulations ID Features 112321 environmental 112322 health 112323 benefits 112324 standards 3.4 environmental effects ID Features 112341 production related 112342 CO2 emission 112343 pool size 112345 effective vehicle utilisation 3.4.1 production related ID Features 1123411 raw material 1123412 energy

Ranking 1. 2. 3-4. 3-4.

Weights 8 3 2 2

Ranking 1-4. 1-4. 1-4. 1-4.

Weights 2 2 2 2

Ranking 1 2 3 4

Weights 10 8 7 5

Ranking 1. 2.

Weights 10 8

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Tab. 5. Ranking and aggregation weights of the packaging material and its sub-trees

4 packaging material

ID Features 1111 used material 1112 packaging fill rate 1113 number of uses 1114 collapsibility 4.1 Used material ID Features 11111 robustness 11112 availability 11113 recyclability 11114 reusability 11115 tare weight

Ranking 1. 2-4. 2-4. 2-4.

Weights 9 8 7 7

Ranking 1. 2. 3-4. 3-4. 5.

Weights 8 7 4 4 2

External factors. This attribute represents the external conditions, regulations and legal aspects. The degree of cooperation among the participants is aÂ very important aspect and it fundamentally determines the possibility of using returnable packaging sys-tems. Environmental effects cannot always be clearly expressed and considered enough in corporate practice, but they are necessary to be built in the model. These are the following: quantity of raw materials and energy consumed in pro-duction, CO2 emission while return transportation, effective vehicle utilization and pool size (it means the total quantity of returnable packaging devices circu-lating in the system to ensure the stabile operation). The ranking and weights in the fuzzy model can be seen in Table 4. Cost. Cost aspects in corporate decisions have obviously major importance, still we consider them merely in the third signature. The reason for that is because of the different cost structure of one-way and returnable packaging systems, there are certain cost components that only occur in case of returnable packaging solutions (i.e. cleaning and maintenance or administration). At this point the results already justified the opportunity for returnable packaging, according to the fuzzy rules in the model, cost will be only examined in this case. The ranking and weights in the third fuzzy signature can be seen in Table 6. Tab. 6. Ranking and aggregation weights of the packaging material and its sub-trees

5 cost ID 121 122 123 124 125 126

Features packaging material disposal capital asset cleaning & maintenance storage administration

Ranking 1-6. 1-6. 1-6. 1-6. 1-6. 1-6.

Weights 5 5 5 5 5 5

All membership functions are variants of the triangular or trapezoidal member-ship functions (see e.g. Figure 4). Articles

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Fig. 4. Membership function examples

3. Application of the Model In this chapter two real life examples (an industrial and a customer packaging) will be shown in order to illustrate the applicability of the proposed model.

3.1. Case Study 1

The products considered are automotive engines (CKD) transported from Eu-rope to two different destinations in India and China. The finished engines are sensitive products therefore special (wooden) crates are used mainly to store and transport them in the practice. These ensure safe and reliable transport and stor-age. The columns of the crates are usually collapsible in order to save space while returning back as empty packaging transportation. There are posts inside the crate which are supposed to keep the engine in place, but these can be also collapsed.

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According to the aspects considered in the model, the packaging system should rather be returnable. This is in full accordance with the practice of the automotive engine factory providing data for the case study. Some of the sub sub-models result in µ<0.5 which should induce one way packaging but these values may be compensated by the other two sub-models, so the final result and the aggregated final membership degree all suggest returnable packaging.

3.2. Case Study 2

The packaging problem considered here is a well known customer packaging: the pet bottle. The methodology is the same like in the case of the wooden crates. The result is calculated by the first FSig of the model above described is a112 = 0.519534. In the improved model the result of S2 is a0=0.481103 which means according to the rule the program stops the calculation here. Although reusable plastic bottles existed and they are still used today in some places, according to the aspects considered in the model this packaging system should rather be one way. Reusable pet bottles really had issues in the practice.

4. Conclusion In both case study examples the use of fuzzy signature models led to overall membership degrees, supporting the use of the type of packaging that is in accordance with expert domain knowledge. As a conclusion we may state that the improved model with the additional two signatures is even more suitable for decision support than the previous basic model we proposed earlier. Further research is going on, towards refining the model, especially separating customer and industrial products; and modeling the environmental issues in more detail.

Acknowledgements

Fig. 5. Returnable packaging used for overseas CKD transport

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The program counts every sub-tree according to the fuzzy signature. The values of all leaves (µi) are fuzzy membership degrees calculated from membership functions and all values of the parents are calculated according to an aggregation and the respective weights. The characteristics of the engine crate are described by logistics experts. The result of the first FSig was calculated by all aggregations according to Tables 2-4 is a112 = 0.6089. If we recalculate it with the additional signatures, the result in the improved model is a0=0.6103. Articles

The authors would like to thank to EFOP-3.6.116-2016-00017 1 ‘Internationalisation, initiatives to establish a new source of researchers and graduates, and development of knowledge and technological transfer as instruments of intelligent specialisations at Széchenyi István University’ for the support of the re-search. This work was supported by the National Research, Development and Innovation Office (NKFIH), Hungary; grant number K124055.

AUTHORS Kata Vöröskői* – Department of Logistics and Forwarding, Széchenyi István University, Győr, Hungary, e-mail: voroskoi.kata@sze.hu.

Journal of Automation, Mobile Robotics and Intelligent Systems

Gergő Fogarasi – Department of Information Technology, Széchenyi István University, Győr, Hungary.

Adrienn Buruzs – Department of Environmental Engineering, Széchenyi István University, Győr, Hungary. Péter Földesi – Department of Logistics and Forwarding, Széchenyi István University, Győr, Hungary.

László T. Kóczy – Department of Information Technology, Széchenyi István University, Győr, Hungary, Budapest University of Technology and Economics. *Corresponding author

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