Journal of Automation, Mobile Robotics and Intelligent Systems JAMRIS 04/2018

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VOLUME 12 N°1 2018 www.jamris.org VOLUME 12 N°4(PRINT) 2018 www.jamris.org pISSN 1897-8649 / eISSN 2080-2145 (ONLINE)

Journal of Automation, Mobile Robotics & Intelligent Systems

pISSN 1897-8649

(PRINT)

/ eISSN 2080-2145

(ONLINE)

VOLUME 12, N° 4

2018

pISSN 1897-8649 (PRINT) / eISSN 2080-2145 (ONLINE)

Publisher: Industrial Research Institute for Automation and Measurements PIAP

pISSN 1897-8649 (PRINT) /eISSN 2080-2145 (ONLINE)

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JOURNAL OF AUTOMATION, MOBILE ROBOTICS & INTELLIGENT SYSTEMS

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JOURNAL OF AUTOMATION, MOBILE ROBOTICS & INTELLIGENT SYSTEMS VOLUME 12, N° 4, 2018 DOI: 10.14313/JAMRIS_4-2018

CONTENTS 58

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Modelling and Control of Flexible Manufacturing Systems by Means of Interpreted Petri Nets František Čapkovič DOI: JAMRIS_4-2018/21

Double Block Zero Padding Acquisition Algorithm for GPS Software Receiver S.V.S. Prasad DOI: JAMRIS_4-2018/26

An Analytical Study for the Role of Fuzzy Logic in Improving Metaheuristic Optimization Algorithms Sonakshi Vij, Amita Jain, Devendra Tayal, Oscar Castillo DOI: JAMRIS_4-2018/22

Software Implementation of Exchange Processes in a Distributed Network Environment of Transmission and Processing of Information Nadirbek Yusupbekov, Shukhrat Gulyamov, Sadikdjan Kasymov, Nargiza Usmanova, Dilshod Mirzaev DOI: JAMRIS_4-2018/27

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Identification of Influence of Part Tolerances of 1PWR-SE Pump on its Total Efficiency taking into consideration Multi-Valued Logic Trees Adam Deptuła, Piotr Osiński, Marian A. Partyka DOI: JAMRIS_4-2018/23 42

Systematic and Complete Enumeration of Statically Stable Multipod Gaits Jörg Roth DOI: JAMRIS_4-2018/24 51

Impulse Identification and Discrete P/PD Control of Electro-Hydraulic Servodrive Jakub Możaryn, Arkadiusz Winnicki, Damian Suski DOI: JAMRIS_4-2018/25

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Articles

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Customer Product Review Summarization over time for Competitive Intelligence Kamal Amarouche, Houda Benbrahim, Ismail Kassou DOI: JAMRIS_4-2018/28 83

Algorithms of Sustainable Estimation of Unknown Input Signals in Control Systems Nadirbek Yusupbekov, Husan Igamberdiev, Uktam Mamirov DOI: JAMRIS_4-2018/29

Journal of Journal of Automation, Automation,Mobile MobileRobotics Robotics&&Intelligent IntelligentSystems Systems

VOLUME 2018 VOLUME 12,12, N°N°4 4 2018

M�������� ��� ������� �� �������� M������������ S������ �� M���� �� I���������� ����� ���� ��bm��ed: 10th October 2018; accepted: 12th December 2018

František Čapkovič DOI: 10.14313/JAMRIS_4-2018/21 Abstract: Because flexible manufacturing systems (FMS) are discrete event systems (DES), their modelling and control by means of Petri nets (PN) is widely used. While PN transi�ons are observable and controllable and PN places are measurable, place/transi�on PN (P/T PN) are su�cient for this aim. �owever, when some PN transi�ons are unobservable and/or uncontrollable and some places are non-measurable/unobservable, P/T PN are insufficient for modelling and especially for control. In such a case interpreted Petri nets (IPN) seem to be an appropriate replacement for P/T PN. In this paper a possibility of usage of IPN for FMS modelling and control is pointed out. Illustra�ve examples as well as the case study on a robo��ed assembly cell are introduced. By means of using �med PN (TPN) also the performance evalua�on of the IPN model of controlled plant is accomplished whereby the simula�on in Matlab.

Keywords: control, discrete event systems, flexible manufacturing systems, interpreted Petri nets, modelling, performance evalua�on, place/transi�on Petri nets, �med Petri nets

1. ��trod�c�o� Discrete event systems (DES) are frequently modelled by Petri Nets (PN). As to their structure PN are bipartite directed graphs with two kinds of nodes places pi ∈ P, i = 1, . . . , n, and transitions tj ∈ T, j = 1, . . . , m, and two kinds of edges - �irst ones directed from places to transitions, being expressed by means of the incidence matrix F ∈ Z(n×m) , and second ones directed from transitions to places, being expressed by means of the incidence matrix G ∈ Z(m×n) , where Z represents integers. Places model particular operations of DES, states of which are expressed by the so called marking - i.e. by the number of tokens nt ∈ {0, . . . , ∞} put into them. Transitions model the discrete events in DES. A transition can be disabled (it cannot be �ired) or enabled (it can be �ired). The occurrence of a discrete event is modelled by means of �iring the corresponding transition. As to dynamics (the marking evolution) PN are expressed (see e.g. [10]) by the linear discrete state equation as follows xk+1 = xk + B.uk ,

k = 0, . . . N

restricted in any step k by means of the inequality F.uk ≤ xk

(1)

(2)

Here, xk = (σp1 , . . . , σpn )T is the state vector of places in the step k with σpki ∈ {0, . . . , ∞}, i = 1, . . . , n; uk = (γt1 , . . . , γtm )T is the state vector of transitions in the step k (named as the control vector) with γtj ∈ {0, 1}, where 0 denotes the disabled transitions and 1 denotes the enabled ones; B = GT − F is the structural matrix of PN. Hence, the formulae (1) and (2) represent the PNbased model of a system of the type DES. More details about PN can be found e.g. in [3, 8, 9] which are basic (historical) sources and/or on many other papers.

In [3] the name P/T PN was introduced for such a kind of PN instead of PN. 1.1. Timed Petri Nets

However, P/T PN do not contain explicitly time.

The steps of their evolution depends only on the occurrence of discrete events. Of course, events occur implicitly in real time but time is not incorporated into the P/T PN model. To see time relations explicitly, timed Petri nets (TPN) [10, 12, 13] can be used. Consequently, TPN are suitable also for �inding the performance evaluation and throughput of DES. Namely, TPN directly yield the marking evolution with respect to (wrt.) time. In this paper, time speci�ications are assigned exclusively to the P/T PN transitions as their + duration function D : T → Q+ 0 , where Q0 symbolizes non-negative rational numbers. In such a way P/T PN turn to TPN. The time speci�ications are represented by certain time delays of the transitions (in deterministic cases), or by the probability density of timing the transitions (in non-deterministic cases) - e.g. uniform, exponential, Poisson’s, etc. Most often the uniform probability density { 1/(b − a) if x ∈ (a, b) u fx = (3) 0 otherwise is used in DES models, especially in FMS ones.

Assigning time into a transition, the duration of operations modelled by the input places of the transition is set up in the DES model. Because the transition can be �ired only in the case when all operations modelled by its input places are �inished, assigned time represents the duration of the longest running operation. When in the case of simulation the duration of an operation is supposed to be �ixed, we speak about deterministic case of timing and the corresponding time delay is assigned to the transition. Otherwise, we speak about non-deterministic timing. In such a case we are not able to guess exactly the duArticles

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VOLUME 12, N° 4 2018 VOLUME 12, N° 4 2018

ration of running operations. Therefore, a probability density is assigned to the transition. It yields a probable time in which the longest running operation may be �inished.

1.2. Interpreted Petri Nets

There exist also unobservable and uncontrollable transitions as well as the nonmeasurable/unobservable places in PN models of real DES. P/T PN are not able to deal with such transitions and places. One of the approaches, how to deal with such a non-determinism at DES modelling and control, is usage of interpreted Petri nets (IPN) [11]. IPN are an extension of P/T PN. They allow to represent the output signals of measurable/observable places (occurring when a marking is reached), and the input signals (connected with controllable transitions). IPN are also helpful at avoiding the state explosion problem occurring often in P/T PN models.

Formally, IPN can be represented by the 6-tuple Q = {(N, x0 ), Σ, Φ, λ, Ψ, φ}

4

4

yk = φ.xk , k = 0, . . . , N

(5)

is its output equation.

More details about theory of IPN can be found e.g. in [1, 2, 4–7].

1.�. I���str���e ����p�e �n IPN To illustrate the previous de�inition of IPN let us introduce Figure 1. Suppose that the measured pla-

(4)

where P N = (N, x0 ) is the PN with the structure N and the initial state x0 ; Σ = {α1 , …, αr } is the input alphabet of the IPN with αi , i = 1, . . . , r, being input symbols; Φ = {δ1 , …, δs } is the output alphabet of the IPN with δj , j = 1, . . . , s, being the output symbols; λ : T → Σ ∪ {ε} is a labelling function assigning an input symbol to each PN transition with the following constraints: ∀tj , tk ∈ T, j ̸= k, if ∀pi , F (pi , tj ) = F (pi , tk ) ̸= 0 and λ(tj ) ̸= ε, λ(tk ) ̸= ε, then λ(tj ) ̸= λ(tk ). Here, ε represents a spontaneous system event which cannot be in�luenced from outside - i.e. internal system event. If for a transition ti holds λ(ti ) ̸= ε, then the transition is controllable. Otherwise the transition is uncontrollable. Denote the set of controllable transitions as Tc and the set of uncontrollable transitions as Tu ; Ψ : P → Φ ∪ {ε} is a labeling function of the places assigning an output symbol δ ∈ Φ or the null symbol ε to each place - it means that Ψ(pi ) = δk when pi models an output signal, otherwise Ψ(pi ) = ε. Thus, the set P of all places is divided into two subsets - the set of measurable places Pm = {pi |Ψ(pi ) ̸= ε} and the set of non-measurable places Pnm = {pi |Ψ(pi ) = ε}.

Of course, it holds Pnm = P \Pm . The number of the measurable places is q = |Pm |; φ : R(N, x0 ) → Zq≥0 is an output function, where R(N, x0 ) is a reachability set of (N, x0 ) and Zq≥0 represents non-negative integers including 0. It maps a reachable marking xk to a (q × 1) observation vector yk of non-negative integers. The output function is a (q×n)dimensional matrix φ. Each its row is an elementary (1, n)-dimensional vector φ(i, •) , i = 1, . . . , q, having only one nonzero entry equal to 1, namely φ(i, j) = 1, if the place pj is the i-th measured place. When the i-th place is non-measured, φ(i, j) = 0.

Above introduced description means that IPN distinguish controllable and uncontrollable transitions as Articles

well as the measurable and non-measurable places.

When we consider (in analogy with continuous systems) the equation (1), restricted by (2), to be the state equation of a PN-based model, then

Figure 1. An example of IPN ces are Pm = {p1 , p5 , p6 } and the non-measurable places are Pnm = P \Pm = {p2 , p3 , p4 , p7 , p8 }. Suppose that the controllable transitions are Tc = {t1 , t5 } and the uncontrollable transitions are Tu = T \Tc = {t2 , t3 , t4 }. Consider that the input and output alphabet are, respectively, Σ = {a, b} and Φ = {δ1 , δ2 , δ3 }.

Hence, λ(tk )k=1,...,5 = {a, ε, ε, ε, b}, Ψ(pi )i=1,...,8 = {δ1 , ε, ε, ε, δ2 , δ3 , ε, ε}. Consequently, the IPN output vector in the step k is given by (5) where   1 0 0 0 0 0 0 0 φ= 0 0 0 0 1 0 0 0  (6) 0 0 0 0 0 1 0 0 It means, that for the state xk = (0, 2, 0, 1, 1, 0, 1, 1)T displayed in Figure 1, the output vector can be obtained in the following form yk = φ.xk = (0, 1, 0)T .

As we can see, the output vector represents a crippled state vector free of the non-measurable places.

Hereinafter, the problem of control will be analyzed in Section 2.

1.�. �er�in���e �e��r�s �nd P�per �r��ni����n In this paper the P/T PN are used for modelling FMS (i.e. the plant) to be controlled. In case when all transitions are controllable and all places are measurable, there are different methods for the model based control (e.g. the supervisory control). However, in case of the P/T PN model with uncontrollable transitions and non-measurable places, the speci�ic IPNbased controller (different from a supervisor) has to be added. Thus, the IPN model of the controlled FMS rises. Applying TPN, i.e. assigning time to the transitions of the IPN model of controlled system, the performance evaluation can be �ind by means of simulation.

Simulation was performed in Matlab by means of the

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

VOLUME 12, N° 4 2018 VOLUME 12, N° 4 2018

HYPENS tool. De�initions all of kinds of PN used here were introduced above in this section - Section 1.

It is necessary to emphasize that there is used a speci�ic kind of controller, completely different from a supervisor, in this approach. The principle of its construction is explained in the Section 2 together with a simple illustrative example. The detailed case study on the model of real FMS is introduced in Section 3.

In comparison with the author’s conference paper [11], the aim of this paper is to deeply analyze and describe a situation in a robotized system (often occurring in practice), where uncontrollable transitions and unobservable places occur, by means of IPNbased model of a controlled system. Namely, there are explained and describe in more detail: (i) the principle of control of P/T PN model of FMS containing uncontrollable transitions and non-measurable places by means of the model of the IPN-based controller; (ii) the difference in comparison with deterministic model with controllable transitions and observable places is emphasized with introducing the reachability tree (RT); and (iii) the interconnection of both models - the model of the controlled plant and the controller into the IPN based model of the controlled plant. Moreover, the performance evaluation of the IPN-based model of the controlled system was accomplished by means of simulation in Matlab using the HYPENS tool applying TPN - i.e. by means of assigning time to the transitions of the IPN model of controlled system. The description of the performance evaluation as well as its results are introduced in Section 4.

At the structure displayed in Figure 2 the transition t1 is controllable. Moreover, it is enabled because p1 and p4 (being the state of a sensor) are active (they have the token). The self-loop between p4 and t1 represents the relation between the place of the control speci�ication and the controllable discrete event of the plant. The transition t2 is uncontrollable. The place p2 is non-measurable. The transition t3 is enabled because of the active p4 . It models the event which expresses the situation when the plant and control speci�ication have the same output. The place p3 models the state of another sensor. The self-loop between p3 and t3 expresses the relation between the measured place of the controlled plant and the event representing a control speci�ication. In such a way the uncontrollable transition t2 and non-measurable place p2 are bypassed. In spite of this, after �iring t1 the place p2 can be active and consecutively t2 can be �ired, only the activity of p2 cannot be observed and �iring of t2 cannot be affected from outside.

The corresponding reachability graph (RG) is in Figure 3. Here, x0 = (1, 0, 0, 1)T , x1 = (0, 1, 0, 1)T ,

The principled idea of this control is to create a controller in such a way that the output of the controlled system always be equal to the prescribed control speci�ication output. The speci�ication describes some relevant sequences of states that the system must pass.

Let us introduce the principle how to control DES with P/T PN model containing uncontrollable transitions and non-measurable places by means of adding the IPN model of control speci�ications. Consider a segment of the IPN model of a controlled system in the form given in Figure 2. The upper line (containing

Let us apply the IPN-based approach to modelling and control of a simple FMS. The scheme of the system is displayed in Figure 4. FMS represents a robotized assembly cell consisting of two input conveyers

2. A View on Control of IPN

Figure 2. The segment of the IPN model of controlled FMS the place p4 and transition t3 ) represents the fragment of the IPN model of the control system, while the lower line (containing p1 , p2 , p3 , t1 , t2 ) represents the fragment of the P/T PN model of the controlled object/plant.

Figure 3. The corresponding reachability graph x2 = (0, 0, 1, 1)T , and x3 = (0, 0, 1, 0)T . Because RG has no branching, it shows that the control process is unambiguous.

3. Case Study on FMS

Figure 4. The scheme of the FMS C1 (feeding parts of a kind A) and C2 (feeding parts of a kind B), the robot R, the assembly place AP, and the output conveyer C3 (carrying the assembled parts away). R takes subsequently the parts A, B from the conveyers C1, C2 and inserts them into the AP, where they are assembled (i.e. the assembly A + B is performed). After �inishing the assembly process, R picks the assembled con�iguration from AP and put it on C3.

3.1. P/T PN Based Model of the Plant

The P/T PN model of the robotized assembly workcell is given in Figure 5. The places represent there the following activities: Articles

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VOLUME N°44 2018 2018 VOLUME 12,12, N°

Figure 5. The P/T PN model of the uncontrolled FMS

Figure 6. The RT of the P/T PN model of the uncontrolled FMS when t1 , t4 , and t11 are fired only once

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6

p1 - means that C1 conveys the part A; p2 - means that C1 is available; p3 - means that R takes the part A from C1 and transfers it to AP; p4 - expresses that R inserts A into AP; p5 - models that C2 conveys the part B; p6 - models the availability of C2; p7 - represents the situation when R takes B from C2 and transfers it to AP; p8 - means that R inserts B into AP; Articles

p9 - ensures the mutual exclusion, because R cannot take A from C1 and B from C2 simultaneously; p10 - models the situation that the parts A, B are assembled in AP; p11 - models that R unloads the �inished con�iguration from AP; p12 - expresses that R transfers the �inished con�iguration from AP to C3; p13 - means that R put the �inished con�iguration on C3; p14 - represents that a free place on C3 is available.

The RT of this model corresponds to the initial state x0 depicted in Figure 5. Unlimited inputs ensured by t1 and t4 and unlimited output ensured by t11 in the model displayed in Figure 5 cause that the RT is too large and loops occur in some nodes. Owing to these reasons it can be introduced here neither in a N graphical form nor in the form of matrix XP reach of reachable states.

However, when t1 , t4 , and t11 are �ired only once, the RT of the P/T PN model of the uncontrolled plant has the form displayed in Figure 6 with the nodes represented by the columns of the matrix (7).   01001000100100000000  10110111011011111111     00010001000001000000     00000010001010100000     00101001001000000000     11010110110111111111     00000100100010000000  N   = XP reach  0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0  (7)    11101010011100111111     00000000000000010000     00000000000000001000     00000000000000000100     00000000000000000010  11111111111111111101 Note that the �irst column and the last column are the same - i.e. the system comes back into the initial state.

It is necessary to say that the RT corresponds to this model only when all transitions are controllable and all places are measurable.

Till now we have considered that all places are observable/measurable and all transitions are controllable and observable. However, in fact it is not true.

In the model of a real plant several transitions could be considered to be uncontrollable and several pla-

Journal of Journal of Automation, Automation,Mobile MobileRobotics Robotics&&Intelligent IntelligentSystems Systems

ces could be non-measurable. Consider, for example, that only the assembly process cannot be in�luenced from outside. Essentially, it is true, of course, because the process run autonomously and cannot be affected from outside.

Moreover, faults can occur in real systems - e.g. a part can fall down from the robot gripper, etc. Here, in this paper, we will not study any non-determinism concerning faults. The simple application of IPN will be presented only to illustrate how to avoid problems with unobservable/non-measurable places and uncontrollable and/or unobservable transitions at control synthesis of real FMS. 3.2. IPN Based Control of the Plant

Building the controller in the sense of the procedure described in Section 2, the IPN model of the controlled FMS is given as it is displayed in Figure 7. Here, in this model, it is supposed that the transition t8 is uncontrollable and the place p10 is non-measurable. It corresponds to reality. Namely, the automatically running assembly process inside AP (being an automatic workstation) represented by p10 cannot be in�luenced from outside during its activity. It is fully autonomous.

Thus, the current state of the assembly process cannot be measured in any way. Only two states of the assembly process - the start and the end - are observable.

While meaning of the plant places is the same as in the P/T PN model, meaning of the places in the control speci�ication module is clear from the analogy with Figure 2. Namely, the control speci�ication place p17 makes possible to �ire t7 representing the controllable discrete event. Thus, the assembly process can be started when the parts A and B are inserted into AP (see meaning of p4 and p8 ). When uncontrollable event represented by t8 occurs (i.e. when the assembly process in AP was �inished) the measurable/observable place p11 becomes active. Because of active p17 and p11 the transition t14 is enabled and can be �ired. Consequently, the control process can continue.

Starting from the P/T PN model in Figure 5, parameters of the IPN model are as follows ) ) ( T ( Gp GTpc Fp Fpc T ; G = (8) F= Fcp Fc GTcp GTc

Here, the parameters of the PN model of the plant to be controlled are   0 1 0 0 0 0 0 0 0 0 0  1 0 0 0 0 0 0 0 0 0 0     0 0 1 0 0 0 0 0 0 0 0     0 0 0 0 0 0 1 0 0 0 0     0 0 0 0 1 0 0 0 0 0 0     0 0 0 1 0 0 0 0 0 0 0     0 0 0 0 0 1 0 0 0 0 0   Fp =   0 0 0 0 0 0 1 0 0 0 0  (9)    0 1 0 0 1 0 0 0 0 0 0     0 0 0 0 0 0 0 1 0 0 0     0 0 0 0 0 0 0 0 1 0 0     0 0 0 0 0 0 0 0 0 1 0     0 0 0 0 0 0 0 0 0 0 1  0 0 0 0 0 0 0 0 0 0 1

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

           GTp =            

1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 1 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 1



            (10)           

being, respectively, the incidence matrices of directed arcs from the plant places to its transitions and from the plant transitions to its places.

The cross parameters between the plant and control system are 

Fpc

           =           

1 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 0





                      T  ; Gpc =                       

1 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 0



            (11)           

being, respectively, the incidence matrices of directed arcs from the plant places to the control system transitions and from the control system transitions to the plant places.

The cross parameters between the control system and plant are Fcp



  =   

  GTcp =   

1 0 0 0 0

0 1 0 0 0

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 0 0 0

0 0 1 0 0

0 0 0 0 0

0 1 0 1 0

0 0 0 0 1

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 0 0 0

0 0 1 0 0

0 0 0 0 0

0 0 0 1 0

0 0 0 0 0

1 0 0 0 0



   (12)   

   (13)  

being, respectively, the incidence matrices of directed arcs from the control system places to the plant transitions and from the plant transitions to the control system places.

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Finally, the parameters of the control system are 

  Fc =   

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0





   T   ; Gc =     

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1



   (14)  

being, respectively, the incidence matrices of directed arcs from the control system places to its transitions and from the control system transitions to its places.

The RG corresponding to the model in Figure 7 is given in Figure 8. Its nodes are state vectors (the initial state x0 and all states reachable from it) represented by the columns of the following reachability matrix (15) 

                Xr =                 

0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0

1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0

0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0

1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0

1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0

0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0

1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0

0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0

1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0

0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0

0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0

0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0

0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0

0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0

0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0

0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0

0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0

0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1

0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

                                 

(15) The matrix φ in the output equation (5) is (18 × 19)dimensional, because p10 is not observable. It has the following form 

               φ=               

88

                               

(16) The 10-th column is the zero vector. Thus, the output vector yk is the (18 × 1)-dimensional vector.

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�. ����o���nc� ���lu��on Let us view on the operation of the controlled plant in time. Consider the non-deterministic timing of the uncontrollable transition t8 . Treat other transitions as deterministic. In deterministic timing the duration of technological operations can be guessed and the transition delays represent the �ixed duration of technological operations. In the uncontrollable transition t8 the duration of the operation modelled by p10 cannot be guessed exactly. Therefore, the uniform probability density (3) will be applied in order to obtain probable time in which the running operation may be �inished.

To accomplish the performance evaluation of the controlled plant by means of simulation, let us apply TPN-based approach on the controlled IPN model of the controlled plant. Consider uniform probability density for t8 with parameters a = 5.5, b = 8.5. For other transitions consider the following time delays in a time unit. Namely, for t1 , t2 , t4 , t5 , t10 , t11 the delay ∆1 = 1, for t3 , t6 , t9 the delay ∆2 = 2, for t7 ∆3 = 5 and for t12 , t13 , t14 , t15 ∆4 = 0.1. All of the numerical values concerning the parameters are still multiplied by the constant 50. Simulation was performed on the time interval ⟨0, 4000⟩ of time units using the simulation tool HYPENS in Matlab. �.�. �i�ul��on ��sul�s

During the simulation process the graphical results expressing the performance evaluation of the controlled plant were found. Although the course of marking wrt. time can be displayed for any place of Figure 8, only courses of marking wrt. time of some places are introduced here. It has two reasons. Namely, on the one hand these places are most important as to understanding the system behaviour, and on the other hand the courses of marking all of 18 places wrt. time occupy much space. While the courses of markings of the places p1 - p8 (M (p1 ) - M (p8 )) wrt. time are not so interesting (they correspond with those being standard like in P/T PN model), the courses of markings of the places p9 - p12 (M (p9 ) - M (p12 )) wrt. time are given in Figure 9. The courses of markings of the places p13 - p21 (M (p13 ) - M (p21 )) wrt. time are also not so important like the previous ones because of reasons mentioned at p1 - p8 (M (p1 ) - M (p8 )). From the point of view of the IPN model application the most interesting is the course of marking in the places p10 and p11 . Namely, the length of the assembly process represented by p10 cannot be exactly measurable. Consequently, the robot which activity is modelled by p11 , does not know exactly when it can unload the assembly place. Just on that account timing the transition t8 , situated among these places, was modelled as nondeterministic one.

5. Conclusion

This paper presents a possibility how to model and control FMS by means of PN in case when some PN transitions are unobservable and/or uncontrollable and some places are non-measurable/unobservable.

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Figure 7. The IPN model of the controlled FMS

Figure 8. The corresponding RG of the IPN model of the controlled FMS

Figure �. The simul��on results - perform�nce e��lu��on of the pl�ces p9 - p12 Namely, in such a case P/T PN are not able to describe such a non-determinism. Therefore, IPN were

applied here. They yield the appropriate replacement for P/T PN as well as the effective tool how to deal Articles

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with the non-determinism. IPN are an extension of P/T PN. Main difference between P/T PN and IPN consists in the fact that IPN allow to represent both (i) the output signals which are generated when a marking is reached; (ii) and the input signals being associated with the controllable transitions. Moreover, IPN make possible to express the symbiosis of both the model of controlled plant and the controller expressing directly the control speci�ications. These facts make possible to deal with the non-determinism caused by uncontrollable/unobservable transitions and non-measurable/unobservable places.

The mathematical description of IPN and their usage for FMS modelling and control were introduced.

For illustration the explanation example was introduced in Subsection 1.3. The principle of the IPN-based control was explained and illustrated by example in Section 2. The main part of the paper - Section 3 - presents the simple case study on a robotized assembly cell. The non-determinism arises when an operation of FMS represented by a PN place cannot be observable/measurable - like the automatically performed assembly process cannot be affected from outside. The operation of assembly does not take (because of different reasons) the same time in each working cycle of the plant. This fact causes that the �inal assembled part cannot be unloaded from the assembly device before �inishing the assembly process. A suitable bypass of the uncontrollable transitions and unobservable places of the plant by means of the controller leads to the successful control of the non-deterministic plant.

The simulation results concerning the performance evaluation of the controlled plant in the case study introduced in Section 4 corroborate the applicability of IPN-based models of DES and show that the usage of IPN for modelling and control of FMS can be effective and applicable in practice.

AUTHOR František Čapkovič∗ – Institute of Informatics, Slovak Academy of Sciences, Dú bravská cesta 9, 845 07 Bratislava, Slovak Republic, e-mail: Frantisek.Capkovic@savba.sk, www: www.ui.sav.sk/home/capkovic. ∗

Corresponding author

ACKNOWLEDGEMENTS This work was supported by the Slovak Scienti�ic Grant Agency VEGA under grant No. 2/0029/17. The author thanks VEGA for the support.

References

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[1] C. D. J.-V. A. Santoyo-Sanchez, A. Ramirez-Trevino and L. I. Aguirre-Salas, “Step state-feedback supervisory control of discrete event systems using interpreted petri nets”. In: Proceedings of IEEE International Conference on Emerging Technologies and Factory Automation - ETFA 2008, Hamburg, Germany, 2008, 926–933.

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[2] M. P. Cabasino, A. Giua, and C. Seatzu, “Fault diagnosis using labeled petri nets where faults may either be silent or undistinguishable events”, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems, vol. 43, no. 2, 2013, 345–555, DOI: 10.1109/COASE.2010.5583995.

[3] J. Desel and W. Reisig, “Place/transition petri nets”. In: W. Reisig and G. Rozenberg, eds., Advances in Petri Nets, vol. LNCS, no. 1491, Springer, 1998, 122–173, DOI: 10.1007/3-54065306-6_15.

[4] M. Dotoli, M. P. Fanti, and A. M. Mangini, “On-line identi�ication of discrete event systems by interpreted petri nets”. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics - SMC’06, vol. 4, Taipei, Taiwan, 2006, 3040–3045, DOI: 10.1109/ICSMC.2006.384582.

[5] K. Hernandez-Rueda, M. E. Meda-Campana, and J. Aramburo-Lizarraga, “Enforcing diagnosability in interpreted petri nets”, IFACPapersOnLine, vol. 48, no. 7, 2008, 58–63, DOI: 10.1016/j.ifacol.2015.06.473.

[6] A. Lutz-Ley and E. Ló pez-Mellado, “Stability based characterization of fault tolerance in petri net models of discrete event systems”. In: Proceedings of IEEE Conference on Computational Engineering in Systems Applications - CESA 2012, Santiago, Chile, 2012, 19–24.

[7] A. Lutz-Ley and E. Ló pez-Mellado, “Synthesis of fault recovery sequences in a class of controlled discrete event systems modelled with petri nets”. In: Proceedings of 2013 Iberoamerican Conference on Electronics Engineering and Computer Science, vol. 7, San Luis Potosi, Mexico, 2013, 257–264, DOI: 10.1016/j.protcy.2013.04.032.

[8] T. Murata, “Petri nets: Properties, analysis and applications”, Proceedings of the IEEE, vol. 77, no.

4, 1989, 541–580, DOI: 10.1109/5.24143.

[9] J. L. Peterson, Petri Net Theory and the Modeling of Systems, Prentice-Hall Inc., Englewood Cliffs, N.J.: New Yersey, 1981.

[10] F. C� apkovic� , “Timed and hybrid petri nets at solving problems of computational intelligence”, Computing and Informatics, vol. 34, no. 4, 2015, 746–778.

[11] F. C� apkovic� , “Interpreted petri nets in des control synthesis”. In: N.-T. Nguyen, B. Trawinski, H. Fujita, and T.-P. Hong, eds., Intelligent Information and Database Systems, Part I, vol. LNAI, no. 9621, Springer, 2016, 377–387, DOI: 10.1007/978-3662-49381-6_36.

[12] F. C� apkovic� , “Petri nets in discrete-event and hybrid systems modelling, analysing, performance evaluation and control”. In: Automation 2017, Springer, 2016, 3–21, DOI: 10.1007/978-3-31954042-9_1.

[13] J. Wang, Timed Petri Nets, Kluwer Academic Publishers: Boston, MA, USA, 1998, DOI: 10.1007/978-1-4615-5537-7.

Journal of Automation, Mobile Robotics & Intelligent Systems

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An Analytical Study For The Role Of Fuzzy Logic In Improving Metaheuristic Optimization Algorithms Submitted: 21st November 2018; accepted: 07th December 2018

Sonakshi Vij, Amita Jain, Devendra Tayal, Oscar Castillo

DOI: 10.14313/JAMRIS_4-2018/22 Abstract: The research applications of fuzzy logic have always been multidisciplinary in nature due to its ability in handling vagueness and imprecision. This paper presents an analytical study in the role of fuzzy logic in the area of metaheuristics using Web of Science (WoS) as the data source.

In this case, 178 research papers are extracted from it in the time span of 1989-2016. This paper analyzes various aspects of a research publication in a scientometric manner. The top cited research papers, country wise contribution, topmost organizations, top research areas, top source titles, control terms and WoS categories are analyzed. Also, the top 3 fuzzy evolutionary algorithms are extracted and their top research papers are mentioned along with their topmost research domain. Since neuro fuzzy logic poses feasible options for solving numerous research problems, hence a section is also included by the authors to present an analytical study regarding research in it. Overall, this study helps in evaluating the recent research patterns in the field of fuzzy metaheuristics along with envisioning the future trends for the same.

While on one hand this helps in providing a new path to the researchers who are beginners in this field as they can start exploring it through the analysis mentioned here, on the other hand it provides an insight to professional researchers too who can dig a little deeper in this field using knowledge from this study.

Keywords: Fuzzy Logic, Metaheuristics, Evolutionary Computing, Genetic Algorithm, Particle Swarm Optimization, Ant Colony Optimization, Fuzzy Evolutionary Algorithms, Fuzzy Cuckoo, Fuzzy Simulated Annealing, Fuzzy Swarm Intelligence, Fuzzy Differential Evolution, Tabu, Fuzzy Mutation, Fuzzy Natural Selection, Fuzzy Fitness Function, Big Bang Big Crunch, Fuzzy Bacterial, Neuro Fuzzy Logic

1. Introduction While dealing with mathematical and computer science application based optimizations, metaheuristics are considered to be among the best computing solutions [1]. Evolutionary computing is a subset of metaheuristics that are motivated by the concept of biological evolution. Instances include genetic algorithm, differential evolution and genetic program-

ming. Swarm intelligence includes methods like, particle swarm optimization, artificial bee colony algorithm etc. Genetic algorithm is one of the most popular metaheuristic algorithms that is based on the notions of “natural selection” [2]. It follows the concept of the “survival of the fittest” and utilizes a fitness function for optimization. It finds its applications in various domains ranging from control engineering to natural language processing.

Another category of metaheuristic algorithms is particle swarm optimization (PSO) which uses an iterative method of evaluation for optimization [3]. A particular population of candidate solutions is moved in the search space till an optimum solution is achieved.

Various other algorithms also exist that help in optimization using nature inspired computing such as the artificial bee colony (ABC) algorithm which replicates the behavior of the “honey bee swarm” for practical engineering applications [4].

Fuzzy logic has also been closely associated to optimization, mainly because of its ability to handle uncertainty, vagueness and imprecision. Due to this it is applied in amalgamation with existing metaheuristic algorithms to give better results. This gives rise to the fuzzy genetic algorithm, fuzzy particle swarm optimization and fuzzy artificial bee colony algorithm. These algorithms have been applied on various applications mainly in the field of computer science. Fuzzy evolutionary computing also provides a way to implement real life natural language processing applications like text summarization. Hence one can say that fuzzy logic and metaheuristics go hand in hand.

In this paper, an analytical study has been performed to highlight the role of fuzzy logic in metaheuristics, evolutionary computing and neuro fuzzy logic. The source of research papers is taken to be Web of Science (WoS). 178 research papers are extracted from it from the time span 1989-2016 [5-182]. The top cited research papers, top research areas, top WoS core categories, fuzzy evolutionary based algorithms, topmost organizations, country wise contribution, top source titles and various control terms are analyzed.

The control terms help in identifying the most commonly discussed research concepts in this field. The top 3 fuzzy evolutionary algorithms obtained are highlighted along with their top research papers and topmost research domain. This study helps in evaluating the recent research patterns in the field of fuzzy metaheuristics and fuzzy evolutionary computing. Also, it assists in predicting the future trends that might occur.

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The rest of the paper is organized as follows: Section 2 describes the data and methodology; Section 3 highlights the results of the study with corresponding visualizations; Section 4 concludes the work.

2. Data and Methodology

The data for this study is collected using Web of Science as the data source, which is a huge database of research papers indexed in Science Citation Index-Expanded (SCI-E), SSCIA&HCI and ESCI. A total of 178 research papers are extracted for the concerned search query [5-182]. The details of the data collected are shown in Table 1.

3. Analytical Study

The research patterns using WoS as the data source during the time span of 1989-2016, in the field of fuzzy metaheuristics and fuzzy evolutionary computing are evaluated in the following sub-sections.

Table 1. Details of the collected data

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3.1. Top Cited Research Papers The top 5 research papers in the field of fuzzy metaheuristics and fuzzy evolutionary computing are evaluated for their respective citation and average citation score per year. The details for the same are shown as in Figure 1. Any researcher who is new to this field can have a look at this study and can start exploring with the help of these top cited research papers.

3.2. Research Areas

Fuzzy logic has found its application for optimization in various disciplines and research areas ranging from computer science to energy fuels. The record count for the top 10 research areas are recorded as shown in Table 2 and can be visualized as illustrated in Figure 2.

3.3. WoS Core Categories

WoS defines various research categories that can be used to define the domain of the various research papers. These categories and the record count of their respective research papers are tabulated as presented in Table 3. The radar chart for the same is shown as illustrated in Figure 3.

Source of research papers

Query entered

Time Span

Total number of research papers

Indexing

WOS (web of science)

TI=(„fuzzy metaheuristics” OR „fuzzy bat” OR „fuzzy genetic” OR „fuzzy PSO” OR „fuzzy particle swarm optimization” OR „fuzzy ACO” OR „fuzzy ant colony optimization” OR „fuzzy ant colony” OR „fuzzy evolutionary” OR „fuzzy cuckoo” OR „fuzzy simulated annealing” OR „fuzzy swarm intelligence” OR „fuzzy differential evolution” OR „fuzzy tabu” OR „fuzzy memetic” OR „fuzzy ABC” OR „fuzzy artificial bee colony” OR „fuzzy harmony” OR „fuzzy mutation” OR „fuzzy natural selection” OR „fuzzy fitness function” OR „fuzzy big bang big crunch” or „fuzzy bacterial”)

1989-2016

178 [5-182]

Science Citation IndexExpanded (SCI-E), SSCIA&HCI and ESCI.

Fig. 1. Citation and average citation per year of the top 5 research papers 12

N° 4

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RESEARCH AREAS

1 2

Computer Science Engineering Operations Research Management Science Mathematics Automation Control Systems Water Resources Energy Fuels Telecommunications Mechanics Science Technology Other Topics

3

4 5 6 7 8 9 10

2018

Table 3. Record count for top 10 WoS core categories

Table 2. Record count for top 10 research areas S.NO.

N° 4

RECORD COUNT 99 96

S.NO.

WOS CATEGORIES

1 2

Computer Science Artificial Intelligence Engineering Electrical Electronic Computer Science Interdisciplinary Applications Operations Research Management Science Engineering Multidisciplinary Computer Science Theory Methods Automation Control Systems Computer Science Information Systems Engineering Civil Mathematics Applied

20 16 15 8 5 5 4 4

3

4 5 6 7 8 9 10

RECORD COUNT 63 47 22 20 18 16 15 15 13 9

Fig. 2. Record count for top 10 research areas

Fig. 3. Radar chart for record count of top 10 WoS core categories Articles

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3.4. Fuzzy Evolutionary Algorithm Based Analysis

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are being currently applied. The top cited research paper for each fuzzy evolutionary algorithm is also mentioned for reference of the researchers. All these credentials are recorded as shown in Table 4 and visualized in the form of a cluster dendrogram as illustrated in Figure 4.

The popularity of various fuzzy evolutionary algorithms among researchers was analyzed using their record count. The top 3 fuzzy evolutionary algorithms were found to be fuzzy genetic, fuzzy PSO and fuzzy ACO. Their corresponding topmost research areas were extracted so as to analyze in which domains they

Table 4. Record analysis of various fuzzy evolutionary algorithms S.NO.

1

2

3

FUZZY EVOLUTIONARY ALGORITHMS

QUERY

RECORD COUNT

TOP CITED PAPER

TOP RESEARCH AREA

Fuzzy Genetic Algorithm

TI= ( “fuzzy genetic” OR „fuzzy mutation” OR „fuzzy natural selection” OR „fuzzy fitness function”)

114

A fuzzygenetic approach to breast cancer diagnosis

Engineering

Fuzzy PSO

TI= ( “fuzzy PSO” OR „fuzzy particle swarm optimization” OR „fuzzy swarm intelligence”)

25

Scheduling jobs on computational grids using a fuzzy particle swarm optimization algorithm

Computer Science

Fuzzy ACO

TI= („fuzzy ACO” OR „fuzzy ant colony optimization” OR „fuzzy ant colony” )

10

Developing a diagnostic system through integration of fuzzy case-based reasoning and fuzzy ant colony system

Fig. 4. Cluster Dendrogram for fuzzy evolutionary algorithms record details 14

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Fig. 5. Scatter plot graph for the top organizations The cluster dendrogram shown in Figure 4 is a representation of the data summarized in Table 4.

The attributes of the cluster dendrogram are all inter related and they are seen as a way of performing hierarchical clustering. The three aspects of this cluster dendrogram illustrated in Figure 4 show that: a) PSO (fuzzy) has 25 research publications associated with it and the corresponding research area that the papers belong the most is computer science. b) Genetic algorithm (fuzzy) has 114 research publications associated with it and the corresponding research area that the papers belong the most is engineering. c) ACO (fuzzy) has 10 research publications associated with it and the corresponding research area that the papers belong the most is computer science.

3.5. Top Organizations

The top organizations that have made significant contributions in terms of research papers in the field of fuzzy metaheuristics and fuzzy evolutionary computing are analyzed. These are listed as indicated in Table 5. The credentials are visualized in the form of a scatter plot graph as highlighted in Figure 5. Organizations working in this field may take motivation from the top contributing research organizations to promote research and provide more resources to increase their research contribution, giving rise to a healthy and constructive research competition in this area.

3.6. Countrywise Contribution

The country wise contribution in terms of research paper publications can be seen in terms of record count in WoS. The summary for the same are recorded as in Table 6.

Table 5. Top organizations in terms of research papers S.NO.

ORGANIZATION NAME

RECORD COUNT

1

ISLAMIC AZAD UNIV

11

3

ERCIYES UNIV

5

2

CANIK BASARI UNIV

4

AMIRKABIR UNIV TECHNO

6

KING FAHD UNIV PETR MINERALS

5 7

HEBEI UNIV SCI TECHNOL UNIV GRANADA

Table 6. Country wise record count

5 4 4 4 4

S.NO.

COUNTRY

RECORD COUNT

1

IRAN

28

INDIA

24

2

PEOPLES R CHINA

4

TURKEY

6

USA

3 5 7

TAIWAN

ENGLAND

8

MALAYSIA

10

SAUDI ARABIA

9

SPAIN

26 17 14 13 11 7 7 5

The topmost countries according to research paper publication count, as listed above are mapped (highlighted in purple color) as illustrated in Figure 6.

The country wise contribution can change with time as upcoming publications are lined up for the year 2017.

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Fig. 6. Mapping the top countries

Fig. 7. Area graph for the top source titles

3.7. Top Source Titles The topmost journals publishing research work in the area of fuzzy metaheuristics and fuzzy evolutionary algorithms were extracted. The data for the same is visualized as shown in Figure 7. It can be observed that expert system with applications has been associated with the maximum record count in this field, followed by the journal of intelligent fuzzy systems and applied soft computing.

3.8. Analysis of the Control Terms

16

Control terms are the ones that help in determining the most commonly studied concepts in a particular field and therefore are the ones that are the most frequently mentioned in the corresponding research papers. In this study, several control terms are identified manually (using VOSviewer) in the field of fuzzy metaheuristics and fuzzy evolutionary computing.

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These control terms are shown as in figure 8, in the form of cluster density visualization.

The terms in the same cluster are shown in the same color. The fact that these terms lie in the same cluster show that these terms have a higher probability of occurring in the same research paper. The density plot of these control terms is as shown in Figure 9. The research community can benefit from these control terms in the sense that if they want to study fuzzy metaheuristics or fuzzy evolutionary computing then they can begin by studying these concepts first.

Figure 10 shows the keyword co-occurrence network visualization for the identified control terms.

These are the top ranked keywords according to the frequency of occurrence. The larger is the size of the bubbles in this bubble plot, greater is its significance in the given context.

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Fig. 8. Cluster density visualization for the control terms

Fig. 9. Density plot for control terms

Fig. 10. Keyword co-occurrence network visualization Articles

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Fig. 11. Tree Map for top 15 WoS categories of research areas for neuro fuzzy research publications

3.9. Neuro Fuzzy Logic

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It is worth mentioning that neuro fuzzy logic plays an integral role in the research related to the domain of fuzzy metaheuristics. In the web of science, the total record count for research publications catering to neuro fuzzy logic is 2568. If the past 5 years data from web of science is to be analyzed then one can notice that a total of 918 papers are extracted in this field. This proves the progress in research in neuro fuzzy logic. These 918 papers are cited to a total of 4461 times, which is huge. Figure 11 has been taken as a screenshot from Web of Science for depicting the tree Map for top 15 categories of research areas for neuro fuzzy research publications. This data was visualized for research papers in this field in the last 5 years i.e. 2013-2018. It could be well observed that neuro fuzzy finds application in areas ranging from computer science to energy fuels.

The top 5 research domains catering to neuro fuzzy research are: i. Engineering ii. Computer science iii. Energy fuels

iv. Science technology and other topics, Water resources v. Environmental science ecology The top 5 research publications in this field, ranked according to the times they are cited are as follows: a) Neuro-fuzzy modeling and control, with a citation score of 1105 b) Neuro-fuzzy rule generation: Survey in soft computing framework, with a citation score of 415 c) A neuro-fuzzy computing technique for modeling hydrological time series, with a citation score of 321 d) Adaptive neuro-fuzzy inference system for prediction of water level in reservoir, with a citation score of 260 Articles

e) A comparative study on the predictive ability of the decision tree, support vector machine and neurofuzzy models in landslide susceptibility mapping using GIS, with a citation score of 258 The number of research papers for fuzzy metaheuristics, evolutionary computing and neuro fuzzy logic is expected to further grow in the coming years which would open new doors of research for scientists and academicians across the globe.

4. Conclusion This paper presents an analytical study in the field of fuzzy metaheuristics and fuzzy evolutionary computing. The study is performed on 178 research papers extracted from the Web of Science, in the time span of 1989-2016. The top cited research papers, country wise contribution, top source titles, topmost organizations, control terms, top research areas and WoS core categories are analyzed. Also, the top 3 fuzzy evolutionary algorithms are obtained and their top research papers are highlighted along with their topmost research domain. This type of an analytical study is expected to assist the researchers working in this domain in exploring the discipline.

Researchers can study in depth the practical applications of these algorithms and then apply it according to its relevance in their corresponding research domains. Any researcher who is new to this field can also have a look at this study and start exploring with the help of the top cited research papers that are mentioned here. The country wise contribution can change with time as upcoming publications are lined up for the year 2017 and 2018. Other organizations working in this field may take motivation from the top contributing research organizations mentioned here to promote research and provide more resources to

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increase their research contribution, giving rise to a healthy and constructive research competition.

Various control terms that are identified during this study, will help in guiding the researchers to explore the individual research topics in detail. The top 3 fuzzy evolutionary algorithms are identified which shall assist the research community in exploring their counterparts as well so that research is done in varied fields. A section presents analytical study regarding research in neuro fuzzy as well since it poses feasible options for solving numerous research problems. As a part of the future work, this study can be performed using other databases as well.

Acknowledgments

We thank the Division of Graduate Studies and Research of Tijuana Institute of Technology and the financial support provided by CONACYT contract grant 122.

AUTHORS

Sonakshi Vij – Department of Computer Science Engineering, Indira Gandhi Delhi Technical University for Women, Delhi, India, 110006, sonakshi.vij92@gmail.com.

Amita Jain – Department of Computer Science Engineering, Ambedkar Institute of advanced communication technologies and research, Delhi, India, 110031, amita_jain_17@yahoo.com.

Devendra Tayal – Department of Computer Science Engineering, Indira Gandhi Delhi Technical University for Women, Delhi, India, 110006, dev_tayal2001@yahoo.com.

Oscar Castillo* – Division of Graduate Studies and Research, Tijuana Institute of Technology, Mexico, ocastillo@tectijuana.mx. *Corresponding author

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Identification of Influence of Part Tolerances of 1PWR-SE Pump on its Total Efficiency Taking into Consideration Multi-Valued Logic Trees Submitted: 3rd June 2018; accepted: 27th December 2018

Adam Deptuła, Piotr Osiński, Marian A. Partyka

DOI: 10.14313/JAMRIS_4-2018/23 Abstract: This paper presents a methodology for identifying the influence of the tolerances used in model pump (TYPE 1PWR – SE) construction on the total efficiency.

The identification of the sensitive control dimensions (Value/Tolerance) of examined pumps has been made by means of multi-valued logic and inductive decision trees.

The innovation of the prototype unit is based on oblique gears with involute teeth, modified in the lower and upper part of the profile. The modification in the lower part was made using the so-called tooth root undercutting technique. Through the use of multivalent logic trees, the designated rank of importance of both structural and operational parameters is identified, taking into account the effect of tolerances on construction. The area is increased by cutting the oblique teeth.

Keywords: multiple-valued logic function, optimization, gear pump after tooth root undercutting, degree of parameters importance

1. Introduction

28

Hydraulic systems are often used because of their high power transmission capabilities and relatively high efficiency. One of the main elements of hydraulic systems are the energy generators in the liquid stream, also known as pumps. Industrial gear pumps with external gearing are the most widespread pumps used in the industry. Their share is estimated at around 50%. Such common use results from a simple and compact design, operational reliability, high resistance to contamination of the working medium, high efficiency, small dimensions (compared to other pumping units), and low production costs [3]. The basic element of each hydrostatic system is a positive displacement pump that performs the function of a liquid stream energy generator. The history of pump development has its origins in antiquity. In the mid-third century, a Greek constructor Ktesibios (285 BC–228 BC) invented a piston pump used to extinguish fires. The first industrial application of pumps dates back to the 15th century, when they were used to drain mines. One of the first documented description of a positive displacement pump took place in 1604, by German astronomer and mathematician Johannes Kepler (1571–1630), in one of the first pump patents. The original appli-

cation of the described solution at the time was to pump water out of mines [31, 29].

Currently, a variety of different construction methods are used. In the group of positive displacement pumps, the largest application was found by gear pumps with external gearing. Pumps of this type are characterized by relatively high working pressures of up to 32MPa. In addition, recently there have been solutions proposed with reduced pulsation obtained from the so-called zero lateral play [22]. The axles of the gears are mounted with a predetermined clearance, and loaded with radial force acting on divided bearing bodies. Examples of this design include the Silence construction by Rexroth or the Caspar type Whisper pump constructed according to US Patent No. 5564225 or European Patent No. EP0692633. The production of gears with zero lateral play requires a highly accurate technological intervention. The gears are paired with each other and additionally selected for size based on the clearances in the plain bearings. Such Labor-intensive manufacturing technology generates significant costs [14, 30, 35]. Currently, pumps are among the most widespread working machines and are used in all fields of technology. Gear pumps are the most widespread among the positive displacement pumps used in hydraulic propulsion systems as energy generators. Their participation is estimated at more than half of all pumps manufactured. Such common use results from a simple and compact design, operational reliability, high efficiency factor and low production cost. The development of modern pumping units is currently associated with two trends: minimization of mass, vibrations, and efficiency of pulsation and the reduction of noise emission into the environment. The reduction of internal tolerances is connected with the minimization of energy losses, increasing the transferred power, and improved energy efficiency of the generator [12, 13].

The use of pumps in hydraulic systems is of particular importance, especially as a source of mechanical vibrations. An important source of vibrations are propulsion systems, for example, a combustion engine performing a periodic work cycle with variable characteristics. The working hydraulic system is also a significant source of mechanical vibrations, caused mainly by shock pressure changes, and the periodic nature of displacement pump operation.

Vibrations generated in this way are characteristic at different frequencies, so there are different ways

Journal of Automation, Mobile Robotics & Intelligent Systems

in which they propagate through hydraulic and mechanical systems [11, 28]. This problem also applies to micropumps. The total efficiency of gear pumps which are produced currently is about 80–90% (for nominal pressures reaching 28 MPa). Such a large span is mainly connected with the adopted manufacturing tolerance. Due to the significant difficulty of establishing a precise relationship, the influence of the manufacturing tolerance of particular elements on the energy efficiency of the created pump, this paper tries to identify critical deviations using a method based on multiple-valued logic trees. The improvement of internal tightness is connected with the minimization of energy losses, increasing the transferred power, and energy efficiency of the generator.

The article presents only the results of part of the research concerning the identification of the impact of tolerances on the pump design model (1PWR-SE) on the overall efficiency. A performed identification of sensitive control dimensions of pumps surveyed by various heuristic methods suggests that it is reliable – then subsequently the multi-valued and inductive decision trees were used.

2. Construction and Design of the Volumetric Outline of Pumps for Total Efficiency with the Use of Logical Decision Trees – Assembling Technology Optimization

The increase in requirements related to accuracy results in higher and higher cost requirements for machine tools. The main attention is paid to increasing the efficiency while increasing the accuracy of manufacturing. In order to obtain sufficient accuracy at the level of micrometers, a whole range of errors should be constantly checked and compensated for, that is, kinematic errors, geometrical errors due to cutting forces, and accepted machining parameters.

The errors mentioned can be significantly reduced, but it is not possible to eliminate them completely.

Among the errors arising during the production process, the most important are: 1) thermal errors, 2) geometrical errors, 3) kinematic errors, 4) errors forced during processing, 5) drive system errors, 6) errors of control elements and regulators, 7) errors of measuring systems, 8) and others.

Another type of errors are those that appear during the machine’s operation and result from the operation of individual drives and the inaccuracies of the interpolators. Control circuits operate in a feedback loop, and thus do not react to the error in real time.

Therefore, one should take into account the occurrence of a certain time delay depending on the sampling frequency. The correct selection of the sampling frequency relative to the set machining speed has a significant effect on the kinematic error.

The working environment of machine tools is related to the occurrence of vibrations, which are

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the result of both the machining process on which the process takes place as well as being the result of working machines in the immediate vicinity. The elimination of this type of interference is extremely difficult, and often involves the use of properly selected vibroisolators. The choice of criteria was determined by the main goal of the pumps being constructed, that is, the improvement of selected hydraulic and acoustic parameters. Not achieving the assumed effect was synonymous with a technologically unsuccessful product. The optimization process was carried out by taking into account the following five basic criteria: I. Technical feasibility. Envelope methods are the basic methods of machining gears with involute tooth contours. Unfortunately, it is not possible to machine all tooth contours with enveloping methods. Thus, a formative method is an alternative. The tool in this machining method has a rebate shape. It is important in the context of achieving accuracy of involute outlines when cutting teeth with simple tools. For this reason, the envelope method is used as the basic method of machining gears. The envelope method uses the geometric process of involute formation (see, for example, Fig. 1) [13].

II. Obtaining the minimum compression ratio.

Liquid sealing in the notches of cooperating gears occurs in pumps with external gearing when the number of buttresses is greater than one.

Fig. 1. Envelope method of teeth cutting – course of the boundary positions of the cutting edge [21] In this case, a certain volume of liquid is separated from both the suction and discharge chambers.

Improper unloading leads to an increase in noise and the occurrence of dynamic forces in the meshing that generates additional sound-shaking vibrations.

III. The occurrence of small changes in dynamic forces in meshing. In the literature [13], the influence of modifications to the involute outline on the properties of a dynamic gear pump was demonstrated. The course of the change in stiffness in meshing was determined based on the method of calculation presented in the paper [13]. In the calculations, an even distribution of dynamic loading force (Pd) along the width of the wheels was assumed. In the literature [13], according to the above assumptions, the stiffness of meshing was calculated, which in a further stage was used to determine the stiffness of six gears with different degrees of coverage e = 1.20, 1.15, 1.10, 1.05, 1.01, and 1.00. The results of calculations are shown in Figure 2.

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Journal of Automation, Mobile Robotics & Intelligent Systems

Fig. 2. The course of meshing stiffness at different degrees of undercutting of the tooth’s tooth for z = 10, m0 = 4, á0 = 20°, y = 1.17, x = 0.5 The optimized involute poly contour should provide small changes in dynamic force in meshing as a result of the modifications and corrections used.

IV. Obtaining the minimum pulsation rate of performance. The measure of performance pulsation is the so-called efficiency δ coefficient of performance, defined as the ratio of the difference between the maximum and minimum efficiency and the average efficiency. The value of performance pulsation for typical toothed units with external gearing is on average around 18%. The use of glacial contours, skewed teeth, and zero interdental clearance is an alternative to high-frequency conventional pumps. In addition, such constructions can largely be performed on machines used to manufacture conventional units.

V. Ensure high energy efficiency. An important direction for the development of gear pumps is to minimize energy losses and increase the transferred power, and thus the tendency of changes directed to an even greater increase in the energy efficiency of the generator. The research results presented in the literature indicate the possibility of increasing the efficiency to values ​​well above 90%. Increasing the energy efficiency of prototype units is mainly due to high internal tightness.

2.1 Identification of the impact of construction technology used in the manufacturing of polyinvolute pumps

30

The purpose of the identification of the impact of the technology used in the construction of polyvalent pumps was an attempt to determine the sensitive control dimensions (values ​​and tolerances) of the tested pumps for teeth made using chip technology [17] and grinding [18], [19], and [20]. The control dimensions concerned six details o f t he pump data: the raking gear, the driven gear, the set of bearings, the body, the plate, the cover, and the tightening force of the screws.

Tests carried out for 40 model units and prototype pumps have shown that it is not possible to analyze only the selected details, such as gear wheels, for the overall efficiency of the gear pump. Testing the total efficiency of two units with the same wheels mounted in different bodies gave different results. Therefore, a properly conducted a n al y sis should be extended to control dimensions for all elements. For example, to be able to include in the assessment of the unit in Articles

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which the wheels were correctly made, but the technological criteria of other elements were not met.

The analysis first emp l oy e d a heuristic method based on local searching of the largest deviations between data values [8, 15]. Then an inductive algorithm of decision trees based on the growth of entropy was applied [33, 34]. A neural network was implemented, learning the measurement relationships between the data, and finding the most important control points [9, 10]. An evolutionary (genetic) algorithm was used as the last method [16].

The first publication c ycle concerns the application of the multi-valu e d logical tree method. In the work [5], multi-valued logical trees were used to determine the sensitivity of measurement points for (3PWR-SE) model pumps. The work [4] concerns type 2PWR-SE model pumps. This article presents the results of the use of multi-valued logic trees for the model pump number: 1PWR-SE from the point of view of the criterion of total efficiency. The Quine-McCluskey algorithm of minimizing the partial multivalent logic functions allows th e use of tree structures as the tools of application a n d support for process design, optimization, and decision-making [2, 23]. If the design and/or operating parameters, taking on numeric values ​​from a specific range, were designated by a set of logic variables, we can perform the discretization of such numerical ranges. The set of all number combinations is a tree with the number of levels equal to the number of design and/or operational parameters.

3. The Research Objective

The object of this research was the construction of both m odel and prot o type pumps, the outline of which was optimized using multi-valued logical trees.

The process of optimization has been carried out with respect to the five basic criteria: I. Manufacturability, II. Obtaining a minimum compression ratio, III. The occurrence of small changes in the dynamic forces in the engagement, IV. Obtaining a minimum ratio of pulsation efficiency, V. Ensuring high energy efficiency.

The gear profiles were selected in the optimization algorithm and are characterized by the presence of two involute ordinary and one involute extended profiles. The analysis includes the basic geometrical relationships gear (Fig. 3) [6].

Fig. 3. Elements of design: a) involute summary, b) involute regular, c) involute extended Gear pumps of the prototype series 1PWR – SE belonging to group I [12] were the research object.

Wrocław University of Technology in cooperation

Journal of Automation, Mobile Robotics & Intelligent Systems

with the company HYDROTOR S.A. designed the units. The experimental pump has been designed with taking into consideration the technological capabilities of the company HYDROTOR S.A.. The innovation of the prototype unit is based on using oblique gears with an involute teeth modified in the lower and upper part of the profile. The modification in the lower part was made using the socalled tooth root undercutting. The outline has an elongated shape in the normal plane and its application causes the shortening of a part of the buttress and subsequent reduction of the sealed area [21].

The area has been increased by cutting the oblique teeth. The inclination of the tooth line also favors a decrease in the pressure pulsation [21]. An exemplary outline of teeth for gear wheels is shown in Figure 4a. Before the wheels were made, the kinematics of optimized three-way gearing on wheels printed using 3D printing technology was evaluated. The model wheels shown in Figure 4b were the equivalent of wheels with a unit capacity of q = 8 cm3/rev.

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Table 1. Tested gear pumps #

Serial number

1PWR – SE – 4/28 – 2 – 776

A 150 10001

3.

1PWR – SE – 4/28 – 2 – 776

A 150 10003

2.

4.

5.

6.

9.

10.

Fig. 5. The exploded view of the prototype gear pump type 1PWR-SE

Pump model

1.

8.

The application of a correction in the region of the apex was produced in order to improve the cooperation of gears at the moment of entering the subsequent pair of gears into cooperation. Finally, the gears got apolyevolvent outline. In order to determine the influence of the manufacturing technology on the level of emitted noise [21], it was decided that the gears should be made using classical grinding technology (Fig. 5). The pump prototype was fabricated entirely by the company HYDROTOR S.A.. The research types of gear pumps with serial numbers and performance are summarized in the table 1.

2018

The analyzed pump is characterized with a threepart construction. The consecutive parts are composed of: − a plate with sealing of a roller, flanges fastening the pump to the coupling casing, holes for screws connecting the pump elements, dowel holes, − casing, gears, slide bearing casings, discharge and suction ports, flow holes for screws connecting the casing elements, holes for screws of the flange connections and dowel holes.

7.

Fig. 4. a) Three involute wheels made using 3D printing technology, b) Ground gears

N° 4

1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776 1PWR – SE – 4/28 – 2 – 776

A 150 10002 A 150 10004 A 150 10005 A 150 10006 A 150 10007 A 150 10008 A 150 10009 A 150 10010

The optimization of the analyzed units of model pumps was composed of two parts: The first part concerned the optimization of the pump tooth outline with the use of multi-valued logic trees. The second part was based on the use of logic decision structures in the optimization of processing technology of elements having an influence on the total efficiency of the newly designed unit (the issue has been more deeply analyzed in this article). It resulted in the limitation of dimensions and size tolerance where it is necessary and decreasing the accuracy requirement in places of little importance. The optimization of the technology caused a decrease of the pumps production and an increase in their effectiveness. An advantage of shaved pumps is their higher total efficiency caused by low hydraulic and mechanical losses. Low values of roughness parameters of the tooth profile contribute to the improvement of the lubrication conditions of cooperating teeth. Besides the increase in the volumetric efficiency, the increase in the total efficiency as well as in the hydraulic and mechanical efficiency also took place. It is of particular importance in control distributors in difficult working conditions, designed for marine drilling equipment where there is high flow and small drop in pressure. It is also possible to mention here hydraulic systems used to change the propeller pitch of ships, as well as pump applications in the control and fuel systems of ship engines.

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Fig. 6. Test stand: DC drive motor, feed pump, AC motor [13]

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ed using a METEX microammeter type M-3650B. The pump output torque M is measured by Mt1000 torque sensor 21 with a measuring range of 0-000 Nm and a Beta 2002 recording system. The pump’s number of revolutions n is controlled by the driving motor shaft by a measuring system consisting of a photocell and digital counter 22. For this purpose a disc with internal holes is mounted on the motor shaft. Temperature t of the liquid in the tank was measured by a set of thermistors (sensor PU 391/2 and meter PU 381/1).

Tests were carried out after the trial starting of the rig, that is, after the operation of the pump and the safety valve and the indications of all the measuring instruments had been checked. Measurement began with setting the prescribed shaft rotational speeds to n = 500, 800, 1000, 1500, and 2000 rpm. Pump loading was effected for pt = 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, and 32 MPa [13]. The maximum forcing pressure was limited by the measuring range of the torque meter 21. The static characteristics were tested at a constant working fluid temperature of 50oC.

5. Identification of the Impact of Tolerances on the Pump Design Model (TYPE 1PWR – SE)

Fig. 7. Schematic layout: 1-tested pump, 2-driving DC motor, 3-feed pump, 4-AC motor, 5-suction filter, 6-cut-off valve, 7,8-safety valves, 9,10,11-cutoff valve, 12-drain filter, 13,14-manovacuometer, 15-pressure gauge, 16-flowmeter with microammeter, 17-measuring microphones, 18-sound chamber, 19-tank, 20-electronic rpm adjustment system, 21-torque sensor with recorder, 22-photocell with measuring counter

4. The Measurement Rig

32

The static characteristics of the pump with a multi- evolvental profile were determined using the rig shown in figs. 6-7. In the rig, the tested pump 1 is driven by 100 kW DC motor 2 working in tandem with a SCR control system 20. The Pxob-94a motor and the DSI-0360/MN-503 thyristor control system make it possible for the smooth changing of pump rotational speed from 0 to 2000 rpm [13]. Preliminary pressure pump 3 and tested pump 1 are protected by safety valves 7 and 8. Tested pump 1 is loaded through throttle valve 10. The pump’s actual delivery Qrz is measured by PT-M1 turbine flowmeter 16 with a PT15-100 flow sensor with a measuring range of 0-100 dm3/min. Instantaneous flow rates are recordArticles

The object of the analysis was the control measurements (value and tolerance) for the prototype gear pump series. The aim of the analysis was to identify the sensitive dimensions of the controls (value and tolerance) by testing the pumps. The dimensions of six pieces of data related to pumps: measurement of tightening PDs, active gear KZP , passive gear KZPn, a set of bearings KL and KLa, corps KR, plate PLt , cover PKr. The values ​​and ranges of sensitive dimensions of the audits have not been given due to data protection and tolerance de s ign company producing pumps tested.

The degree o f sensitivity of control dimensions (values and tolerances) implies differences in the values of the analyzed pumps efficiency. The value or tolerance change vulnerability during the measurement of control dimensi o ns of parameters for particular pumps determines their importance rank. The determination of the most important places of particular parameters would make i t possible to create a range of pumps characterized by the best efficiency parameters in the manufacturing process. The following 5 classification and optimization methods were used in the analysis: − heuristic method – based on the local searching of the biggest deviations of given values, − greedy algorithm. In order to determine a solution, a greedy, that is, the most promising at a given moment, choice of a partial solution is made in every step, − application of the neural network. The Neuronix program and the multi-layered unidirectional network with a learning backpropagation algorithm were used in the analysis, − application of the evolutionary algorithm.

A detailed calculation analysis of each of the methods will be presented in subsequent publications. Control measurements, both the most important ones and the less important ones, were determined in the iden-

Journal of Automation, Mobile Robotics & Intelligent Systems

tification of control measurements analysis. Especially important is the correct evaluation of tolerance during the construction of integrated decision-making methods [18]. The most important measurements are those specified by all applied research methods. Less important measurements are control measurements determined by at least one of the applied research methods.

As a result of the calculations, 23 of the most important control measurements and 56 of the less important measurements were obtained. Figures 8-13 show the most important and less important control points for the parameters: measurement of tightening PDs, active gear KZP , passive gear KZPn, a set of bearings KL and KLa, corps KR, plate PLt , cover PKr.

Fig. 8. The most important and less important control points for parameter – measurement of tightening PDs

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Fig. 11.The most important and less important control points for parameters: corps KR

Fig. 12. The most important and less important control points for parameters: plate PLt

Fig. 13. The most important and less important control points for parameters: cover PKr

Fig. 9. The most important and less important control points for parameters: a) active gear KZP, b) passive gear KZPn

Fig. 10. The most important and less important control points for parameters: set of bearings KL

Using a genetic algorithm gave a greater effect, it was used to obtain about 200-300 results for pump designs. Then it would be the proper use of tools, which is reversed correlation matrix. Due to the complexity of computing the exact method, (formal) identification and classification can be used only for a small number of decision variables. Therefore, the sequential determination of the validity rank for the most important parameters can be performed by using multi- valued logic trees methods. It is applied to the algorithm of minimizing the individual logic functions. Additionally, for this purpose, the monotonicity of the value of the most important parameters according to the numbers of pumps is determined. In addition, Hedwig’s algorithm is used for the optimal selection of variables. The Figures 14-18 show a comparison of the efficiency of the ten gear pumps 1PWR – SE for n = 500, 800, 1000, 1500, 2000 [rev / min].

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6. Application of Multi-Valued Logic Trees Using multivalent logic trees the designated rank of importance of structural and operational parameters, taking into account the effect of tolerances construction can be made. The study focused on two parameters selected: discharge pressure Pt and rotation speed n. Determination of the rank of the validity of parameters using multiple-valued trees logic requires the application of appropriate coding. Identification of influence of part tolerances of the 3PWR- SE pump on its total efficiency taking into consideration multi-valued logic trees was presented in [5].

Fig. 16. Total efficiency ηC gear pumps 1PWR-SE for n=1000 [rev /min]

6.1. The Quine–McCluskey Algorithm for the Minimization of Multiple-valued Logic Functions

The Quine-McCluskey algorithm makes it possible to find all prime implicants of a given logic function that is there is a shortened alternative normal form SAPN [7, 24, 25]. The terms of incomplete gluing and elementary absorption have the main role in the search for prime implicants and are used for the APN of a given logic function. The following transformation is called the consensus operation: (1)

where: r = 1, ..., n and A is a partial elementary product, the literals of which possess variables belonging to the set: {x1, ..., xr–i, ..., xr+i, ... xn}.

The following transformation is called the operation of reduction: (2)

where: 0 ≤ u ≤ mr –1, 1 ≤ r ≤ n, and A is a partial elementary product, the literals of which possess variables belonging to the set {x1, ..., xr–1, xr+1, ... xn}.

Fig. 17. Total efficiency ηC gear pumps 1PWR-SE for n=1500 [rev /min]

Fig. 18. Total efficiency ηC gear pumps 1PWR-SE for n=2000 [rev /min] In the case of multi-valued weighting factors, we obtain [1]:

Fig. 14. Total efficiency ηC gear pumps 1PWR-SE for n=500 [rev /min]

(3)

(4)

where: wi is a polyvalent weighting factor.

For example using the formula: where:

Fig. 15. Total efficiency ηC gear pumps 1PWR-SE for n=800 [rev /min] 34

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(5)

,

(6)

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 12,

successive stages of the multi-value logic function minimization: 020, 101, 200, 021, 111, 201, 210, 022, 121, 202, 211, 212, 221 can be presented in the following way (Table 2):

(7)

Table 2. NAPN and MAPN of a given logical function

Fig. 19. A multi-valued decision tree for the parameters x1, x2 , x3 with an appropriate layout of levels Finally, we receive both NAPN and MAPN of a given logical function saved in the form of numbers of a m-position system [23]: {(02-), (20-), (1-1), (21-), (-21)} and {(02-), (20-), (1-1), (21-), (2-1)}.

For example, multiple-valued logical function f(x1, x2, x3), where x1, x2, x3 = 0, 1, 2, written by means of numbers Canonical Alternative Normal Form): 100, 010, 002, 020, 101, 110, 021, 102, 210, 111, 201, 120, 022, 112, 211, 121, 212, 221, 122, there is one MZAPN (Minimal Complex Alternative Normal Form) after the application of the Quine–McCluskey algorithm based on the minimization of individual partial multi-valued logical functions having 13 literals (Fig. 19).

In the isomorphic interpretation of the QuineMcCluskey algorithm, three steps are taken for the graphic matrix formalization [23]: a) putting decision (m1, ..., mn) – valued variables x1, ..., xn in a certain order; creating the n! primary matrices, relative to all combinations of variables,

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2018

b) prioritizing the numbers relative to (m1, ..., mn) the valence in the increasing order from the left side of the matrix, c) combining numbers and removing them (minimization).

6.2. Determination of the Rank of the Validity of the Design Parameters and Operating Pumps Model (TYPE 1PWR-SE), taking into account the Effect of Tolerances Construction

Engineering practice requires correct evaluation of the mathematical model describing a given system with some variables. A proper mathematical model contains a group of functions joining different variables and describing connections between quantities in the system. Decision tables and logical functions [1, 5, 7] can be applied to the simulation of the machine or in data classification and scheduling of measurement points. Besides, there are dependence digraphs of the signal flow. The game structure describes a space of possible solutions in order to find the optimum of objective functions. Determination of the rank of the validity of parameters using multiple-valued trees logic requires the application of appropriate coding. The values of arithmetic discharge pressure Pt and the rotation speed n, taking into account the efficiency of the pumps model were coded logic of the respective periods of the tables 3-4. Tables 5-6 show the specific and general logical coding for ranges of changes Pt and n, in which at least 7 correspond to pump efficiency defined with a tolerance of 5%.

Tables 7-8 show the specific and general logical coding for ranges of changes Pt and n, in which at least 10 correspond to pump efficiency defined with a tolerance of 5%.

The identification of the impact of the manufacturing technology of the model units showed that the important dimensions affecting the efficiency of the pumps are generally repeated in all details, regardless of the analyzed group. The indicated geometrical errors depend mainly on the fastening devices used, deformation of the part in the mounting, the number of fasteners, machining parameters, forces occurring during machining of the element, repeatability of the machine tools. The following is a summary of the most frequently occurring critical dimensions for individual components of the pump.

Figure 24 presents the dimensions and critical deviations: 1) the beating of plugs and the lateral surface of the toothed rim 2) perpendicularity of the side surface of the tooth to the pivots (wheel rotation axis) for the detail of the gears speeding and running.

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0

0 1

1

2

2 3 4 5

0

0 1

1

2

2 3 4 5

Articles

92.7

86.9

86.2

83.3

81.6

87.8

12

14

0

500

16

80.7

83.4

86

83.6

83.9

82.1

86.4

95.1

95.1

84.4

85.1

81.1

83.9

82.8

80.8

82

81.4

85.2

87.4

82.5

85.5

85.5

86

82.1

83.6

87.2

80

82.4

81.3

81.1

80.7

83

83.2

79

81.3

A15010004 81.6

86.9

80.5

82.7

81.7

88.4

82.5

82

83.7

89.3

95.8

88.4

89.3

85.3

80.6

84.7

76.9

81.7

83.7

99.4

96.2

81.8

80.6

83.2

84.8

81.4

86.1

82.5

82

83.2

80.7

88.7

92.3

92.3

88.1

87.9

86

90.3

85.8

85.5

85.4

90.6

85.5

87.8

85.4

86.7

87

83.8

87.6

82.4

80.4

85.6

86.3

87.4

86.4

81.3

88.4

86.7

85.3

85

86

84.9

85.2

83.9

75.2

89

87.6

89.7

87.3

91.2

86.1

86.7

89.4

86.4

86

87.5

91.3

85.7

85.6

87.3

83.1

85.6

86.4

80.9

85.7

87.5

86.9

87.3

87

86.8

89.2

86.9

89.9

86.7

89.9

16

82.2

20

79.9

86.1

86.2

77.6

87.4

86.5

87

86.5

87.3

87.6

83.7

85.1

86.3

84.5

87

85.5

84.7

80.8

88.4

84.1

87.3

91.2

82.3

80.8

90.3

87.7

86.7

82

79

85.7

76.4

86.9

87.3

84.5

83.2

88.7

87.6

86.7

86.7

81.2

88.7

10

86.4

84.5

86.9

78.9

80.3

86.4

90.6

89.2

82.1

90.3

24

84

81.7

85.6

79.3

82.5

84.3

6

22

87.4

81.7

88.7

18

87.8

83.9

88.7

14

95.1

86.1

82.1

85.3

95.5

88.5

95.2

800

%

84

4

1

%

87.8

74.5

12

%

84

24

8

%

91.5

77.6

2

%

90.6

20 22

%

88.7

79.2 79.4

18

91.1

95.5

A150100010

95.5

%

A15010009

88.7

8

10

%

99.9

95.5

6

A15010003

%

4

C*- multivalent logic coding

36

%

A15010008

min-1

A15010007

2

c*

A15010006

MPa

A15010005

 c*

n

A15010002

Pt

A15010001

Table 3. General and specific logical encoding for the full range of change of the pressure Pt and n= 500 and 800 [rev /min]

86.8

80

87.6

83.7

86.2

83.9

84

84.4 83.9

84.7

84

84.1

81.6

83.9

80.6

83.8 83

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Table 4. General and specific logical encoding for the full range of change of the pressure Pt and n= 1000, 1500 and 2000 [rev /min]

0

1

1

2

2 3 4 5

0

0 1

1

2

2 3 4 5

0

0 1

1

2

2 3 4 5

4 8

12 14 16

1000

18

86.9

88.5

91.1

88.3

88

88.9

85.8

87.1

87.2 85.2 84.8 84.5

86.49 86.35 86.32 86.24 87.12 86.66 86.96 86.58

87.4 87.7 87.1 87.4 87.8 87.5 87.4 87

87.45

86.5

86

88.7

77.6

82.5

85.8

85.4

86.1

86.7

87

18

86.4 84.8 84.5 82.5

20

81.6

22

81.3

24

80.3

2

14 16 18 20 22 24

2000

86.1 87.2 87.2 88.1

84.7

87.4 4

86.3

88.9

8

12

86.9

72.7

88.9

10

85.5

90

4 6

A150100010

88.49

88.9

87.2

16

A15010009

93.4

88.72

10 14

A15010008

88.5

84.8

1500

A15010004

88.7

90.9

3

%

83.2

6

12

%

88.7

92

8

%

88.9

99.4

4

%

95.8

80.1

2

%

89.2

80.8

24

%

88.7

81.5

22

%

88.94

82.6

20

%

99.9

88.7 2

A15010003

%

99.9

6 10

%

A15010007

min-1

A15010006

2

c*

A15010005

0

MPa

A15010002

 c*

n A15010001

Pt

86.5 85.8 85.3 84.4 84.3 83.1 82.2 81.1

C*- multivalent logic coding

82.8 84.1

84.8

87.1 88.1

85.5 87.3 87.6 87.2 87.6 86.4

87.1 86.7 87.9 86.4 85.8 82.5

87.9 86.4 85.8

91.8

86

86.5

85.7

87.4

87.1

85.4

90.4

86.7

90.5 89.6 89.3

86.7 87.1 86.1 85.6 89

86.1

88.9

89

85.5

87.8

87.7

89

89

86.7 84.9

88.9

86

89.2

78

77.6

77.6

85.2

86.9

86.7

84.9

86.5 88

86.4

89.2

87.2

88.8

86.8 86.9 86.7 86.4

88.5 89 88

87.9

82.8

82.9

87.4

84.1

86.2 86.8

88

86.7

88.8 85.5 84.9 86.4 85.1 85.7 86.1 86

85.8 85.6

86.5 86.2

87.2 87

88.1

84.2 82.1 85.4

83.6 83.2 83.6 83.5

77.6

87.3

80.4

84.5 85.3 85.9 86.2 86.5

86.4 85.7 85.3

79.8 82.1 81.7 83

88

84.6

86.5

87.8

86.3

87.3

85.6

81.2

82.8

88.2

86.3

83.3

87

86.8

87

84

83.9

73.2 83.3

85.4

83.2

82.8

72.9 85.4

83.8

84.5

88.4 87.6

84

81.8

86.4 85.1

84

77.6 86.4

87

84

82.2

84.1

85.7 85.4

83.1

82.8

83.3

87.2

84.5

81.8

83.6

88

88.2

85.8 82.8

84.5

84.9

82.9

86.4

87

86.9

85.3

86.8

85.8

84.8

83.6

87.6

86.8

87.4

87.4

88.3

87.8

86.7

89

85.9

87.4

87.2

85.8

86.1

87.8 87.2

87.6

86

87.2

89.2 89.5

87.6

87.2

86.5

87.9 87.6

89.2

87.8

85.6

91.2

88.3

86.5

90.3

87.3

86.1

86.7

89.1

87

86

87.1

88.5

89

89.2

86.3

87.1

88.5

82.9

88.7 84.8

92.5

83.2

87.5

86.7

87.2

86.8

87.1

85.5 86.9

86.8

87.2

85.4

86.6

86.5

86

83.6 84.3

88.9

83.6 83.3 83.8 83.6 83.5 82.9 81.8 77.7 82.6 80.6 83.5 82.8 83.6 84

84.2

84.4

84.3

84.8

84.1 83.1

85.7 84 83 Articles

37

Journal of Automation, Mobile Robotics & Intelligent Systems

Table 5. Specific logical coding for ranges of changes Pt and n, in which at least 7 correspond to pump efficiency defined with a tolerance of 5%

N° 4

n

Pt

n

Pt

n

Pt

n

0

0

0

0

1

2

1

2

2

0

2

0

2 3 4 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4

1 2 1 3 2 1 4 3 2 1 4 3 2 5 4 3 5 4 5

0 1 2

3

0

1

2

0

2

1 2 3 4 2 3 4 2 3 4 3 4 4

n

0

0

0

0

1

1

1

1

0 1 2 0 1 2 0 1 2 Articles

1 2 2 2 3 3 3 4 4 4

0 2 1 0 2 1 0 2 1 2

Table 8. General logical coding for ranges of changes Pt and n, in which at least 10 pumps meet prescribed performance with a tolerance of 5% n

Pt

2

4

Pt

n

1

3

n

Pt

0

4

Pt

Table 6. General logical coding for ranges of changes Pt and n, in which at least 7 pumps meet prescribed performance with a tolerance of 5%

1

3

1 2

0

4

1

The complexity of logic tables or truth tables grows exponentially in relation to the number of variables. In case of a larger number of decision variables, there are practical geometric problems which need to be solved in order to extract the least and the most important data. What is more, the graphic matrix formalization can be a computer record of parametric game trees as an adjacency matrix.

In the case of 3-value coding {0, 1, 2} decision discharge pressure Pt {2, 4, 6, 8}, {10, 12, 14, 16}, {18, 20, 22, 24}, for 5- value coding for valuable rotational speed n {500, 800, 1000, 1500, 2000} obtained a higher rank of importance for n compared to Pt. The difference is approximately 20-25%, according to the contractual scale accuracy calculated for the number of branches in the relevant decision trees. Then a minimum of 7 pumps meet certain performance criteria with a tolerance of 5%. If the increase decisiveness discharge pressure Pt to 6-value for encoding {0, 1, 2, 3, 4, 5} respectively, for the values {2, 4}, {6, 8}, {10, 12}, {14, 16}, {18, 20}, {22,24}, at the same speed ranges n, it receives a higher rank of importance for Pt compared to n.

Figures 20-23 show the corresponding multiple-valued logic trees for the tables 5, 6, 7 and 8.

1 2 3 2 3 4 3 4

4

7. Conclusions

2

4

2018

Table 7. Specific logical coding for ranges of changes Pt and n, in which at least 10 pumps meet prescribed performance with a tolerance of 5%

Pt

1

38

VOLUME 12,

Fig. 20. Multi-valued logic trees for the Table 5

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 12,

N° 4

2018

Fig. 21. Multi-valued logic trees for the Table 6 Fig. 25. The perpendicularity of the sump to the pump head for detail: pump corpus

Fig. 22. Multi -valued logic trees for the table 7

Fig. 23. Multi-valued logic trees for the table 8

the above various decision-making valence trading discharge pressure Pt and identical decision valence rotational speed n, assuming that the 10 pumps meet certain performance criteria with a tolerance of 5%.

Then we receive always the same range of validity for n and Pt. The minimization of geometrical and kinematic errors takes place through the appropriate selection of the geometrical-motor structure of the machine tool.

Geometric inaccuracies include surface misalignment errors and shape errors. However, kinematic errors are related to the relative movements of individual machine tool components. In particular, they become important in the case of complex traffic. Properly designed and operated machine tools are characterized by a significant repeatability of kinematic errors, so it is relatively simple to compensate for such errors.

The temperature instability of the machine components is related to their nature of work and the impact of the environment. Often this type of error can be critical and decisive for the accuracy of the workpiece. It is generally assumed that the thermal error is directly proportional to the change in temperature and the coefficient of thermal expansion of the material being heated.

AUTHORS

Fig. 24. The dimensions and critical deviations: 1) the beating of plugs and the lateral surface of the toothed rim 2) perpendicularity of the side surface of the tooth to the pivots (wheel rotation axis) for the detail of the gears speeding and running Figure 25 shows the perpendicularity of the sump to the pump head for detail: pump corpus.

The difference is approximately 25%, according to the contractual scale accuracy calculated for the number of branches in the relevant decision trees. Then a minimum of 7 pumps meet certain performance criteria with a tolerance of 5%. It is also possible for

Adam Deptuła* – Opole University of Technology, Faculty of Production Engineering and Logistic, 75 Ozimska Street, 45-370 Opole, Poland, e-mail: a.deptula@po.opole.pl, www.a.deptula.po.opole.pl

Marian A. Partyka – Opole University of Technology, Faculty of Production Engineering and Logistic, 75 Ozimska Street, 45-370 Opole, Poland, e-mail: m.partyka@po.opole.pl Piotr Osiński – Wrocław University of Technology, Faculty of Mechanical Engineering, 5 Łukasiewicza Street, 50-370 Wrocław, Poland, e-mail: piotr. osinski@pwr.edu.pl *Corresponding author

Articles

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Journal of Automation, Mobile Robotics & Intelligent Systems

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40

A. Deptuła, “Application of game graphs to describe the inverse problem in the designing of mechatronic vibrating systems”. In: Zawiślak S., Rysiński J. (eds.) Graph-Based Modelling in Engineering. Mechanisms and Machine Science, vol. 42, Springer, Cham, 2017, 189–199.

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Systematic and Complete Enumeration of Statically Stable Multipod Gaits Submitted: 10th October 2018; accepted: 20th December 2018

Jörg Roth

DOI: 10.14313/JAMRIS_4-2018/24 Abstract: Insect-like robots have many advantages concerning mobility and stability. The specific sequence of legs going through different phases, the gait, is important when planning and executing a complex motion. The notion of gaits was originally introduced by biologists but gaits also influenced robot development. Typical multipod ro­bots are able to execute much more gaits than occur in wildlife. In this paper we present a formalism to express certain rules for reasonable gaits. We show an algorithm that enumerates all statically stable gaits according to our formalism. We then provide a gait classification by the example of six-legged robots. Finally, we introduce properties to evaluate gaits.

Keywords: Legged Robot, Multipod, Hexapod, Statically Stable Gait

1. Introduction

42

Natural arthropods such as insects or spiders are able to quickly and stably walk over rough terrain.

The re­spective multipod robots have many advantag­ es over wheeled robots or humanoid, biped robots.

On the one hand, they do not have to rely on drivable ground and can go over small obstacles; on the oth­ er hand, they are able to walk statically stable. This means, we can stop a motion at any time and the ro­ bot keeps its upright position. In contrast, dynami­ cally stable mo­tion requires mechanisms to actively maintain the balance.

Apart from the leg’s geometry and moving trajec­ tory, the gait (i.e. the time sequence of moving legs) significantly influences the overall movement charac­ teristic. It defines the timing pattern of lifted and ground legs and affects properties such as the stabil­ ity and speed. In this paper, we abstract from the ac­ tual robot geometry and define general rules that rea­ sonable gaits must fulfill. These can be summa­rized to: fix clock for phase changes, uniformity and stabil­ ity. We discovered that the set of gaits which fulfill our rules is a countably infinite set. Moreover, for a certain number of legs and a limited phase length, the set of gaits is finite. We present an algorithm that finds all gaits for certain parameters.

For the example of six legs we then classify gaits.

Our classification includes well-established gaits such as Tripod, Ripple and Wave, but we also found a new

one, the Split gait. We can assign certain properties to gait classes such as the amount of support, propul­ sion and smoothness. We end with a brief discussion about odd numbers of legs.

2. Related Work

Early research about multipod gaits was con­ ducted in the area of zoology, in particular, about gaits of insects with six legs. Insects are able to sta­ bilize their gait with adhesion effects, thus can exe­ cute gaits that are not possible for statically stable robots. E.g. the Tetrapod gait [3, 22] has four legs on the ground, but their ground polygon (called the support area) does not always cover the center of gravity. If we look at statically stable gaits, most hexapod insects use the Tripod gait. As the actual number of gait variations is low, research often is focused on timing questions.

Research also identified dynamically stable fast gaits, e.g. for escape situations [15, 18]. These were only stable if the multipod is able to balance. We could e.g., classify a Gallop gait for hexapods.

Spiders (officially no insects) and crabs have eight legs, thus allow a larger amount of gait variations.

However, looking at real animals, the gaits only seem to have a large variation in timing and rhythm, not in the actual sequence pattern. Some papers measured the gait timing, energy and support area for differ­ent spiders [2, 19]. A formal classification is difficult. In [8] the authors thus defined a Ran­dom gait that oc­ curs, when a regular pattern is not obvious.

Even though more legs would allow more gaits (from the mathematical view), animals with more than eight legs such as decapods (e.g. crustacean) or centi­pedes tend to use a single pattern where legs are lifted one after the other, the Metachronal gait [4].

A more system-oriented, bio-inspired view on gaits provided [3, 5, 12]. They model gait execution by a network of neurons between legs that trigger leg movement dependent on former leg actions. This view is close to gait execution of real insects. E.g., the Metachronal gait of centipedes can be modeled with­out a central controlling instance that is aware of each leg.

An animal that is able to switch between a larger number of gaits is the horse, in particular in the area of dressage. Here we find a strong classification of dif­ ferent gaits, e.g. the Gallop or Amble gait. Most of them are not statically stable. [14] provided a formal defi­

Journal of Automation, Mobile Robotics & Intelligent Systems

In this section we introduce a formal model to de­ scribe gaits. The gait formalism is two-fold: a geomet­ ric facet describes leg geometries and trajectories.

A rhythmic pattern facet describes the sequence of

2018

legs going through phases. We strongly believe both facets are independent. As a result, we can execute any walking trajectory with any gait rhythm.

The formalism is required to precisely describe a certain gait with parameters and to formulate condi­tions for reasonable gaits. We start with some consid­erations according to the geometric facet. We then ab­stract from the specific multipod geometry to in­tro­duce certain requirements concerning the leg phases. A further section examines static stability.

3.1. Kinematics and Gait Patterns

Mobile multipod robots usually have an even num­ ber of legs with identical geometry. A common model is the hexapod, such as the Bugbot ([13], Fig. 1 top).

Mul­tipod legs must have at last 3 degrees of freedom to freely place and move the foot during gait execu­ tion. The leg segments usually are called Coxa, Femur and Tibia based on insect anatomy naming (Fig. 1 bot­tom). Robot legs with more degrees may provide re­dun­dancy in leg positioning, but are not generally ca­pable to execute more gaits. In this paper, we ab­ stract from inverse kinematics questions and assume, the con­trolling mechanism is capable to place the feet as re­quired by a movement.

αCoxa

r

mu

Fe

αFemur

αTibia

a

3. The Gait Model

N° 4

bi Ti

nition for Walk, Tolt, Trot and Pace gaits and ana­lyzed their timing.

A discussion of gaits and their properties for leg­ ged robots has a long tradition [17]. As a funda­mental structure: each leg periodically goes through two phases. During the stance phase (also called sup­port phase), the foot remains on the ground and car­ries the robot. During the swing phase (also called transfer phase, or ‘in flight’), the foot is moved in the ro­ bot’s movement direction. The time of one stance and one swing phase is called the cycle time. The rela­tion of stance to cycle time is called the duty factor. Orig­ inally, the duty factor is defined per leg and may be different. So-called regular gaits have the same value for each leg.

[16] introduced further properties for gaits: first they distinguish periodic from non-periodic gaits. Pe­ riodic gaits are additionally divided into singular gaits (placing one leg and lifting the next occur at the same time) and symmetric (right and left legs alternate their phase changes). They also identified certain stability measures (sta­bility margin, longitudinal stability mar­ gin) and pro­vided criteria for periodic, regular gaits, foremost the Wave gait.

Most natural multipods have an even number of legs. One exception is the starfish. [9] analyzed their gaits and possible application for robots.

Further papers focus on hexapods. [10] tried to classify hexa­ pod gaits, but mainly discovered the Tri­pod and varia­tions of Wave gaits. Trajectory geome­tries and gait rhythms are mixed. E.g., a class Forward Wave gait is identified that is applied for for­ ward movement only. Also [20] mixed geometry and rhythm and iden­tified a sideways Tripod gait as Mam­ mal gait. [5] analyzed Ripple gaits for hexa­pods and formalized these gaits with nonlinear oscil­lators. [7] also studied some hexapod gait variations for ro­bots and identified new gaits, but without a sys­tem­atic way to enumerate all new variations.

[6] considered a gait as a function that maps a cy­ cle (represented as unit circle –π…π) to leg’s configu­ rations. This view enabled the notion of gait transition, i.e. patterns that connect two gaits. The stance move­ment affects the robot’s trajectory, thus must not be changed between gaits. The approach thus used the legs in swing phase to change to a new gait.

Swings can be slower or faster without affecting the move­ment direction.

Besides classifying gaits and their properties, fur­ ther research tried to generate gaits. [11] presented a genetic algorithm to generate Wave gaits. [21] de­ scribed a constraint-based approach to generate a gait for a specific motion task based on rules that describe kinematics, leg collisions, terrain and stabil­ ity. [1] presented a machine learning approach based on an evolutionary algorithm.

VOLUME 12,

Coxa

Fig. 1. Hexapod robot (top), typical leg geometry (bottom) Multipods can walk in different ways. First, we can distinguish the actual trajectory, e.g. straight forward, sideways (i.e. crab gait), arc or turn in place. Second, we can distinguish the change of legs that are on the ground in stance phase or swing in moving direction.

We call the time sequence of changing phase the gait pattern, or simply, the gait.

Figure 2 shows the two phases for a specific leg.

The stance phase can be described by a move­ment  among the stance vector vi in local robot coordinates.

In world co­ordinates, the foot remains on the ground at the same position (in the absence of slippage). In the swing phase, the leg is lifted and moved in walk­ ing di­rection. In local coordinates, the two phases de­ Articles

43

Journal of Automation, Mobile Robotics & Intelligent Systems

scribe a round trip, i.e. the corresponding vectors can be connected to a polygon.  The set of vi specifies the multipod’s trajectory.

Fig. 2 (bottom right) shows exemplary how these  vec­tors cause an arc movement. For arcs, the vi must re­side on arc tangents and their lengths must be the same multiple of the distance to the arc center.

Fig 2 with alternative colors

vi

x Stance Phase Swing Phase

vi

z vi

x

 Fig. 2. Structure of a multipod gait (top and left), vi and arc trajectory (bottom right) Fig 4 with alternative colors

The gait pattern defines the cooperation of legs w=2 in thew=1 respective phases. Fig. 3 shows the example of the Ripple gait for hexapods. For this gait, always four legs are in the stance phase, whereas a swing phase starts in the middle of another leg’s swing w=4 are known. They differ in phase.w=3 Many fur­ther gaits the amount of legs in stance phase, the amount of time in stance phase and the times of phase changes (see sec­tion 4.2).

LEFT FRONT LEFT MIDDLE LEFT REAR RIGHT FRONT RIGHT MIDDLE RIGHT REAR

Stance Phase

Swing Phase

Fig. 3. Gait pattern for the Ripple gait of hexapods

44

An important observation: the trajectory defini­  tion based on the leg’s vi and the gait patterns are in­dependent. This means, we can walk in any di­ rection (even sideways) with any gait pattern. In reverse this means, the gait pattern mainly defines movement qualities such as stability, propul­sion or smoothness.

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3.2. The Formal Gait Model and Gait Proper­ties Let l ³ 6 denote the number of legs – we first as­ sume an even number. We further assume, all time intervals are multiples of a fixed time interval t. In particular, we have a fix clock for phase changes. This may be considered as limitation, however, it reflects the typi­cal mechanism for motion control: In a loop with con­stant iteration time, the controller computes Figcommands 2 with alternative colors new mo­tion that simultaneously are sent to all legs (e.g. its servos). The legs then independent­ ly move until the next loop iteration computes new r y mu Fe od com­mands.

B Coxa z y Gaits periodically repeat a leg pattern. We call the time before the same leg configuration occurs vi the cy­ cle. The cycle time contains a single stance and a sin­ x gle swing phase. Stance As a basic Phasegait definition we speci­ Swing Phase fy the multiples of t for stance phasevi s, swing phase w and cycle time c with c = s + w.

The phases between legs may be interleaved, i.e. z may start in the middle of another leg’s a swing phase swing phase. In this case, the swing phase must last vi multiple steps t (Fig. 4).

This also affects the granu­ x larity of the swing phase shape. E.g., with w = 3, we can define the swing phase more detailed com­pared to w = 2. The case w = 1 executes a swing phase in a single step.

We require this case later.

Fig 4 with alternative colors ia Tib

y

r mu Fe

ia Tib

z

dy Bo Coxa

VOLUME 12,

w=1

w=3

w=2

w=4

Fig. 4. Swing phases with different phase lengths Even though the number of swing steps affects the geometric definition of the swing phase, the benefit of more steps should not be overestimated. Typical mo­tion systems inherently smooth the paced polygon due to controlling effects. From the geometric view, it usually is not required to go beyond w = 4.

Besides the phase lengths, the timing when a spe­ cific leg changes its phase is important. Let wi Î {0, …, c – 1} for i Î {1, ..., l} be the step number when leg i en­ters the swing phase. As the length of phases is equal for all legs, these numbers fully de­ scribe the change of all phases. If we shift all wi by the same offset, we get a different assignment, but actual­ ly the same gait. We thus assume w1 = 0.

We now are able to fully define a gait G by

G = ( ( l , w , c ) , (ω1 , ω2 , ..., ωl ) )

(1)

In order to define a reasonable gait, c, s and w have to fulfill some rules. Obviously,

s ≥ 1, w ≥ 1, c ≥ 2, (2)

because we require a non-zero time in each phase. We further look at the average number of legs in the re­

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 12,

spective phase. Let nw denote the average num­ber of legs in the swing phase: w c

(3)

where 1 ≤ nw < l. (4) nw = l ⋅

(4) is true, because a smaller nw than 1 is not reason­ able as this means, there is a time where all legs are in stance phase. But at this time, at least one leg could al­ready have started the swing phase what would safe time. It must be less than l, because not all legs can be in swing phase. We can rewrite it as w < c ≤ l ⋅w (5)

Let ns denote the average number of legs in the stance phase. We get

where

s ns =l ⋅ =l − nw c

(6)

3 ≤ ns < l (7)

This is because at least three legs must be in stance phase (see below), but not all.

To formalize further properties, we need to intro­ duce a gait matrix M(G)

 m11  M(G ) =  ... m  l1

... m1c   ...  ... mlc 

1 if ( j − wi − 1 ) mod c < w where mij =  (8) 0 otherwise

This matrix shows the legs (rows) in swing phase over time steps (columns). As an example (Ripple gait with 6 legs): T   0  1      T  3  0 6 1  0   M   2  ,   =     4  0 6     2 0        5 1     

1 0 1 0

0 0 1 0

0 1 0 0

0 1 0 1

0  0 0  1 0 1 1 0 0  0 0 0 0 1 

(9)

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Clw = {c ∈ {w + 1, …, l ⋅ w} | c is integer divider of l ⋅ w} (11) Table 1 shows Clw for 6 to 12 legs, up to 4 swing steps.

Table 1. Clw for certain cases w = 1

w = 2

w = 3

w = 4

2, 3, 6

3, 4, 6, 12

6, 9, 18

6, 8, 12, 24

l = 10

2, 5, 10

4, 5, 10, 20

l = 12

2, 3, 4, 6, 12

3, 4, 6, 8, 12, 24

5, 6, 10, 15, 30

5, 8, 10, 20, 40

l = 6 l = 8

2, 4, 8

4, 8, 16

4, 6, 8, 12, 24 4, 6, 9, 12, 18, 36

8, 16, 32

6, 8, 12, 16, 24, 48

3.3. Static Gait Stability An important demand for a reasonable gait is to be statically stable. This means, the multipod must not drop on legs that are currently in swing phase as a re­sult of gravity. This would have two negative ef­ fects. First, the body would not be horizontal any more, which could, e.g., affect sensor measurements. Second, legs in swing phase would perform movement in op­ posite direction compared to the stance vector. Thus, the current trajectory would not be followed any more.

The topic of stability is usually very complex and also covers dynamic effects, if we e.g., think of bipeds.

For less than three feet on the ground, robots achieve stability with the help of active balancing control or certain mechanical facilities such as larger legs’ soles.

In the area of mul­tipods we usually ignore dynamic effects and request static stability. I.e. balancing is achieved without ac­tive control and we consider feet as single points that touch the ground.

For detailed analysis we would have to take into account the multipod’s geometry in particular of its legs. In addition, we have to consider the overall mass distribution that changes over time because of mov­ ing legs. The feet of legs in stance phase must form a polygon, called support polygon with at least 3 verti­ ces. If the center of mass, projected to the ground is inside this polygon, the multipod is stable (Fig. 5).

We require M to hold two properties: uniformity and stability. Uniformity means: The number of legs in swing phase is equal for all steps in a cycle, i.e.

 l  nw  (10) ∀  ∑ mij = j∈{1,...,c } i =1  

As consequence, nw is not only the average num­ ber of legs in swing phase over all cycle steps, but the identi­cal number for each step. We require this prop­ erty, because this number is distinctive for a specific gait as no other number. Changing this number over time means changing a gait. From this follows that nw and ns are integers. From (3) further follows that c must be an integer divider of l ⋅ w. We thus can define the set of possible c for given l, w as

Fig. 5. Stability condition Such detailed analysis can be done for a certain ro­ bot, but is not suitable for checking, if a gait gen­er­ally is stable. We thus use a condition that only takes into account the set of legs in stance phase.

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Journal of Automation, Mobile Robotics & Intelligent Systems

l=6

l=8

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l=10

Stable

Center of Gravity Stance Swing Support Polygon

Unstable

Footprint Polygon

Marginally Stable (considered

as unstable)

Fig. 6. Stability considerations Fig. 6 illustrates the considerations. Usual mul­ tipod robots are symmetric according the two main axes. Moreover, each connection between opposite legs ap­proximately cuts the center of gravity. We get three cases for support polygons: – The center of gravity is fully enclosed: this is a sta­ ble situation.

– The center of gravity is not enclosed: this is an un­ stable situation.

– The center of gravity resides on the polygon’s bor­ der: this is a marginally stable situation. We count this to ‘unstable’ as the slightest movement during gait execution shifts the center of gravity outside the support polygon.

If the enumeration of legs reflects neighborhood (e.g. leg numbers go counter-clockwise), opposite leg numbers have a distance of l/2. Whenever opposite legs are in stance and the l/2-2 legs between them are in swing phase, we have the marginally stable case. Thus, of l/2-1 legs in a sequence, at least one leg has to be in stance phase; for a specific leg number i: at least one leg in {i, …, i + l/2-2} (if we subtract l from leg num­bers larger than l). We can formalize these con­sidera­tions: a gait matrix M(G) represents a stable gait iff   k +l/2−2  ∀  ∀  ∑ (1 − mij ) > 0   j∈{1,...,c} k∈{1,...,l}  i =k  

(12)

(if we map mij to m(i–l)j for i > l). Note that from (7) and (12) follows l > 4. This is because (7) requires to have at least one leg in swing phase, but l = 4 and (12) re­ quires to have all legs in stance phase.

4. Enumerating Multipod Gaits

4.1. Algorithm to Iterate Through Gaits

46

We start with a first observation: for certain (l, w), only a finite set of (c, w1, w2, …, wl) is possible, thus only a finite set of gaits. As all variations of (l, w) are a countably infinite set, all gaits that fulfill our rules are a countably infinite set as well.

Before we put all together, a last consideration: if G = ( ( l , w , c ) , (ω1 ,ω2 ,...,ωl ) ) is a gait, then for any inte­ger n, G’ = ( ( l , n ⋅ w , n ⋅ c ) , ( n ⋅ ω1 , n ⋅ ω2 ,..., n ⋅ ωl ) ) is Articles

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obvi­ously also a gait. G’ models the swing phase more de­tailed, but is equivalent to G regarding the gait pat­ tern. We call G’ a replica gait of G. Replica gaits do not carry important information. We can produce an infi­ nite number of replica gaits for an original gait. We thus skip these when iterating through all gaits. This how­ever is the reason to consider the case w = 1, even though real systems may not execute swing phases in one step. The case w = 1 summarizes all gaits that do not start a swing phase within another leg’s swing phase.

If nw = 1, i.e. c = l ⋅ w we have the special case of only a single leg in swing phase. In the next section we will classify these gaits as Wave gaits. These gaits only differ in the ordering of lifted legs. As a result, all gaits with nw = 1 produce the same set of (Wave) gaits which are for w > 1 only replica gaits. Examples for Wave gait replica are (l, w, c) = (6, 2, 12), (6, 3, 18), (6, 4, 24), (8, 2, 16). Such combination can be skipped with­out any further investigation.

We now are able to present an algorithm that prints all gaits that fulfill our conditions (Algorithm 1).

For a certain (l, w, c) the second loop iterates through cl–1 iterations. This number can get very high.

Thus, an efficient implementation would not exactly follow the pseudo code. An approach to speed up the exe­cution: if λ

∑m

(13) ij > nw i =1

for a l < l, then (10) cannot be fulfilled, even if we iter­ate through all combinations of wl+1, …, wl. Thus, the entire block of combinations can be skipped.

A similar idea: if k +l/2−2

∑

(14) (1 − mij ) = 0

for a k, and k + l/2-2 < l, then we can skip all combina­ tions of wk+l/2-1, …, wl. With these and some further speed up-techniques not presented here, we are able to execute up to 10 billion checks per seconds on cur­ rent PCs, thus a total of 1015 variations are within range. i =k

Algorithm 1. Print all gaits

Algorithm PrintAllGaits(l, w) for each c ∈ Clw { // (11) if w > 1 and c = l ⋅ w continue // Wave gait replica for each (ω1 ,ω2 ,...,ωl ) ∈ {0} × {0,..., c − 1}l−1 { compute M(G) // (8) if

}

}

∀

j∈{1,...,c }

l

∑m i =1

ij

= nw and

// (10)

 k +l/2−2  ∀  ∑ (1 − mij ) > 0  // (12) k∈{1,...,l}  i =k  and the common divider of c, w and wi is 1 // no replica gaits then print gait ( ( l , w , c ) , (ω1 ,ω2 ,...,ωl ) )

w = 1

w = 2

w = 3

w = 4

l = 6

c = 2: 1 c = 3: 8 c = 6: 120

c = 6: 6

c = 9: 12

c = 12: 12

l = 8

c = 2: 15 c = 4: 630 c = 8: 5 k

c = 4: 210 c = 8: 5 k

c = 6: 820 c = 8: 1870 c = 12: 10 k

c = 8: 1830 c = 16: 10 k

c = 5: 1648 c = 2: 91 c = 4: 82 k c = 8: 356 k c = 6: 82 k c = 5: 18 k c = 10: 265 k l = 10 c = 5: 23 k c = 10: 363 k c = 10: 363 k c = 10: 363 k c = 20: 726 k c = 15: 726 k c = 2: 408 c = 3: 12 k l = 12 c = 4: 92 k c = 6: 1.2 m c = 12: 39 m

c = 3: 2254 c = 4: 166 k c = 6: 2.0 m c = 8: 7.5 m c = 12: 40 m

c = 4: 372 c = 6: 89 k c = 6: 3.8 m c = 8: 30 m c = 9: 24 m c = 12: 104 m c = 12: 55 m c = 16: 135 m c = 18: 80 m c = 24: 80 m

4.2. Classifying Gaits and Further Gait Proper­ties Many of the million gaits in Table 2 only differ in the or­dering of legs. We thus want to identify classes where each gait of a class has the same ba­ sic appear­ance. As minimum requirement, we want to find the named gaits known from literature for hexapods. For l > 6 we can also try to identify class­ es that correspond to hexapod gaits. However, it turned out that we had to invent many subclasses to reflect the huge number of possi­ble gait varia­ tions for more than 6 legs. We thus limit our classi­ fication to l = 6. We also limit w to 4. Ta­ble 3 shows all classified gaits.

1

Amble (org)

6

Amble (irregular)

2

Ripple (org)

2

Ripple (irregular)

4

Example Definition

Varia­tions

Tripod

3 legs alternating in swing

(6, 1, 2), (0, 1, 0, 1, 0, 1)

like Amble (org), but not always one left, one right in swing

(6, 1, 3), (0, 1, 0, 2, 1, 2)

like Ripple (org) but shifted legs do not alter­ nate between left/right

(6, 2, 6), (0, 3, 1, 5, 2, 4)

over 3 steps 2 legs in swing (one left, one right)

left and right iterates through all 3 legs, left/ right shifted among 1/2 ⋅ c swing

Wave (org)

2

Wave (irregular)

118

Split (1/3)

12

Split (1/4)

12

2018

Example Definition

N° 4

one leg after another in swing, iterating front to rear or reverse

(6, 1, 6), (0, 1, 2, 5, 4, 3)

two sequences of 3 legs in swing, each one after another, both sequences are shifted among 1/3 ⋅ c or 2/3 ⋅ c swing

(6, 3, 9), (0, 4, 1, 7, 3, 6)

one leg after another in swing, arbitrary ordering

(6, 1, 6), (0, 2, 1, 3, 4, 5)

…shifted among 1/4 ⋅ c or 3/4 ⋅ c swing

(6, 4, 12), (0, 5, 1, 9, 4, 8)

From the 159 gaits, we could easily find the estab­ lished gaits Tripod, Amble, Ripple and Wave. For all apart from Tripod we have more than one combina­ tion. In addition, we can identify gaits that are similar to the established, but violate a single condition. We add ‘org’ or ‘irregular’ for differentiation. E.g. Wave (irregular) denotes a gait with one leg lifted at a time, but there is no simple pattern, how the lifted legs are al­ternated.

We found 24 gaits that were not classified before, to the best knowledge of the author. We used the name Split gait for these. They have a certain charac­teristic: the set of legs is split into two sets of same size. Legs of one set are put into swing one after an­other, but swing phases between the two sets are shifted by multiplier of the clock rate t. Fig. 7 shows the gait pat­ tern for a Split gait.

LEFT FRONT

LEFT MIDDLE LEFT REAR

Description

Name

Table 3. Classified gaits

Description

Table 2. Number of gaits for certain cases (k = thousand, m = million)

Varia­tions

Table 2 shows the number of gaits for 6 to 12 legs, up to 4 swing steps.

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Name

Journal of Automation, Mobile Robotics & Intelligent Systems

(6, 1, 3), (0, 2, 1, 0, 1, 2)

(6, 2, 6), (0, 4, 2, 5, 1, 3)

RIGHT FRONT RIGHT MIDDLE RIGHT REAR

Stance Phase

Swing Phase

Fig. 7. Pattern of the Split gait (1/3·c) If we want to extend the classes to more than 6 legs, we have to think about some points: – The Tripod gait must be extended to any half num­ ber of legs. For, e.g., l = 8 we call it Tetrapod gait (note that Tetrapod gait also describes a dynami­ cally stable hexapod gait). However, we get a huge number of variations, how to divide the legs in two halves, e.g. front/rear vs. middle legs or odd vs. even numbered legs.

– The patterns of Ripple, Amble, Wave and Split gaits could be transferred to more legs; however, we find more ‘irregular’ variations.

– A new pattern, the Metachronal gait, can be identi­ fied that iterates through all legs, but not one after Articles

47

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 12,

the other as in the original Wave. Instead, the swing phases already started when the last leg still is in swing, i.e. the swing phases start after e.g. 1/3 or 1/4 swing length. As a result, we have always more than one leg in swing (e.g. 3 or 4). We could consider the Metachronal gait either as a variation of Ripple or Wave.

– The more legs we have, the more we can mix multi­ ple gaits to a new gait. E.g. one subset of legs walks in Amble gait, the other subset in Wave gait.

Due to the huge variety, it is difficult to present a com­ plete classification that covers all gaits for more than 6 legs.

As a next step, we want to evaluate the qualities of gaits. We introduce three measures: – propulsion: the amount of movement in the de­ sired direction per time, – support: the amount of legs at the ground, – smoothness: the amount of time without phase changes (swing to stance and vice versa).

We could think about many more measures, but these cover the most important properties. To as­ sign num­bers, we developed some formulas. As a ba­ sic prop­erty of these formulas: they should produce same numbers for replica gaits.

The following considerations lead to the propul­ sion: a certain leg moves the robot’s body in stance  phase among the length of the stance vector vi to­ wards movement direction; this means a move­ment  of vi / s per step. As different legs usually have differ­ent stance vectors, we define the propulsion p as  the multiple of vi per cycle, i.e. c (15) s

This value is the reciprocal of the duty factor.

For the measure of support we use the number of legs in stance phase as provided by ns (6). For smooth­ ness we want to measure the changes between swing and stance phase as they usually cause notice­able jerking of the body. As in a cycle, each leg changes twice and thus is constant for certain l, the sum in a cycle does not indicate a reasonable number. The av­erage changes per step, on the other hand, would pro­duce different numbers for replica gaits. We thus de­cided to measure the maximum number of chang­ es over a cycle. Because we want to produce higher number for higher smoothness, we ended up using the inverse: the minimum number of legs that keep the phase, i.e. p=

 l  m = min=  ∑ χ (mij , mi , j +1 )  j∈{1,...,c}  i =1 

48

(16)

where c= is the indicator function that returns 1 for equal parameters and 0 otherwise. We further map mi,c+1 to mi1.

Table 4 shows the result for our hexapod gaits. Not surprisingly, no single gait has only benefits. Looking at p and ns this is obvious. From (6) and (15) follows, p · ns = 2l, thus is constant for a certain number of legs. As a consequence, propulsion and support are recip­rocal measures.

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Table 4. Gait properties Name

Propulsion p

Support ns

Smoothness m

2

3

0

4

4

Tripod

Amble

1.5

4

1.2

5

Ripple

1.5

Split

1.5

Wave

4.3. Odd Leg Numbers

2

4

4

4

Even though artificial as well as natural multipods usually have an even number of legs, we could briefly think about the influence of an odd number. We may think of circular attached leg configurations of star­ fishes. l=5

l=7

Center of Gravity

Stable

Stance Swing Support Polygon

Unstable

Footprint Polygon

Fig. 8. Stability considerations for odd leg numbers From the formulas above only the condition for stability (12) is affected by odd leg numbers. Look­ ing at the examples in Fig. 8, we do not see a marginal stability case anymore, as no connection be­tween legs touches the center. Thus, of (l + 1)/2-1 legs in a se­ quence, at least one leg has to be in stance phase. This means, we can modify formula (12) to   k +l/2−2  ∀  ∀  ∑ (1 − mij ) > 0    j∈{1,...,c}  k∈{1,...,l}   i =k  

(17)

We thus actually have the minimum number of legs as stated in section 3.3 of 5.

Looking at the gait variations we see two effects: first, odd leg numbers such as 5, 7 and 9 either are primes or have a small number of dividers. According to (11) we thus have a smaller number of variations for Clw (Table 5).

Table 5. Clw for odd l l = 5 l = 7 l = 9

w = 1

w = 2

w = 3

w = 4

5

5, 10

5, 15

5, 10, 20

3, 9

3, 6, 9, 18

9, 27

6, 9, 12, 18, 36

7

7, 14

7, 21

7, 14, 28

Second: classes such as Tripod (or Tetrapod etc.), Split and Amble are only applicable for even leg num­ bers as they require to have two sets of legs with same size (Tripod, Split) or require sequences of pairs of legs (Amble). Not surprisingly, odd leg configura­tions thus

Journal of Automation, Mobile Robotics & Intelligent Systems

mainly enable Ripple, Wave and Metachro­nal gaits.

However, for l = 9 we observe interesting new varia­ tions of Tripod and Split with three alter­nating sets in­ stead of only two. For Tripod this means: we have three steps, each of it has three other legs in swing phase.

Table 6 shows the respective number of gait varia­ tions for odd l up to 9 and up to 4 swing steps.

Table 6. Number of gaits for odd l (k=thousand) w = 1

w = 2

l = 5

c = 5: 24

c = 5: 2

l = 7

c = 7: 720

c = 7: 720

l = 9

c = 3: 560 c = 9: 40 k

c = 3: 44 c = 6: 15 k c = 9: 40 k

w = 3

w = 4 c = 10: 2

c = 7: 242

c = 7: 4 c = 14: 720

c = 9: 71 k

c = 6: 104 c = 9: 25 k c = 12: 151 k c = 18: 40 k

5. Conclusions This paper presents a formalism to systematically enumerate statically stable multipod gaits. For all gaits, we have a countably infinite set, but for fixed leg num­ bers and a limited phase length, the set of gaits is finite.

We assume, the sequence of legs is inde­pendent from the movement trajectory (e.g. forward, side­ ways or arcs). Thus, we can formulate the gait pattern without to know the movement direction. For our gaits we further assume a fix clock for phase changes.

This is a reasonable assumption, if we use a software controller that sends new motion commands for all legs simultaneously in an infinite loop. We identi­ fied reasonable gaits by further rules that model the crite­ria uniformity and stability. Stability criteria are for­mulated without the need to know the actual mul­ tipod’s geometry and mass distribution.

As a result, we can specify each gait by leg number, phase lengths and start step numbers for swing phase that can be mapped to a so-called gait matrix. To filter out gaits that are a result of multiplying each of these numbers by a constant and thus not actual new gaits, we introduced the notion of replica gaits. We finally present an algorithm that lists all gaits for a certain leg number and cycle length. For hexapods this algo­ rithm discovered a new gait, we called Split gait.

We finally evaluated gaits by properties support, pro­pulsion and smoothness and discussed the case of odd leg numbers.

We implemented the approach in our Bugbot hexapod. The runtime code accepts gaits according to our formalism, including stability and uniformity checks. It could easily be integrated on an Arduino platform and enables the robot developer to change the gait at runtime.

AUTHOR

Jörg Roth – Faculty of Computer Science, Nurem­berg Institute of Technology, Nuremberg, Germany, Email: joerg.roth@th-nuernberg.de.

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[15] P. Ramdya, R. Thandiackal, R. Cherney, T. As­ selborn, R. Benton, A.J. Ijspeert, D. Floreano, “Climbing favours the tripod gait over alter­ native faster in­sect gaits”, Nature Communications, 8:14494. DOI: 10.1038/ncomms14494.

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Impulse Identification and Discrete P/PD Control of Electro-Hydraulic Servodrive Submitted: 6th July 2018; accepted: 14th November 2018

Jakub Możaryn, Arkadiusz Winnicki, Damian Suski

DOI: 10.14313/JAMRIS_4-2018/25 Abstract: This article presents the systematic design methodology of a discrete Proportional and Proportional-Derivative (PD) controller for the electro-hydraulic servodrive position control. The controller is based on the identified linear model of the system, with P/PD parameters adjusted with the help of different methods given in the literature. There are compared experimental results of the proposed control system with different controller parameters.

Keywords: PD controller, Identification for control, Analytic design, Identification and control methods.

1. Introduction Nowadays electro-hydraulic servodrive systems are very important components of machines and technological lines because of their high power to weight ratio, high stiffness, and high payload capability. Their unrivaled high energy efficiency, exceeding the efficiency of devices using other media, ease of control, the possibility of obtaining large gear ratios and low inertia make them perfect elements of high precision mechanical systems [1]. They can perform fast and precise mold feed in injection molding machine [2], moving and stacking products on the production line or drilling and tightening screws with a specific torque [3]. In aircraft technology, the operation of landing gear, flaps, flight control surfaces, and brakes is largely accomplished with hydraulic power systems [5]. In automotive industry electro-hydraulic actuators are used in active suspension systems [6].

Recently, they become popular due to the development of walking robotics, where it is necessary to use the low-power input signal and its conversion to high power output [7].

However, the control of electro-hydraulic systems can be a difficult task since their dynamics is highly nonlinear [6]. Therefore, the research is conducted on the position control or the force control for electro-hydraulic actuators using more advanced control techniques i.e. feedback linearization [8], adaptive control [9] or sliding mode control [10].

Despite all the progress in the advanced control, the Proportional-Integral-Derivative (PID) algorithm

remains the most popular. Its gains are often chosen based on experience and through some simple selection methods such as Ziegler-Nichols [11] or Cohen-Coon [12]. However, regardless of the type of controlled process, there is usually requirement of the exact response of the system to set-point changes and disturbances. Without a proper methodology of controller parameters tuning the quality of the control system may be unacceptable. Therefore many researchers in academia and industry develop tuning rules for different processes, with different objectives.

The survey presented in [13] gives the total of 1134 separate rules for PI and PID controllers, and one can expect that until now this number has increased. Recently there are developed methodologies to choose proper tuning rules and improve the performance of the control system [14], [15].

This paper presents the systematic design methodology of a discrete P/PD controller for the electro-hydraulic servodrive position control, based on the identified linear model of the system, and controller parameters tuned using different methods.

The article is organized as follows. Section 2 describes the laboratory test stand as an electro-hydraulic system. Section 3 describes the step identification of the electro-hydraulic servodrive and presents an obtained model of the control object in the form of the transfer function. Section 4 gives a brief introduction to the discrete P/PD controller design procedure and methods of tuning its parameters. Section 5 describes experiments carried out on the laboratory test stand and there is also given a discussion on the performance of the control system. In the last Section the conclusions from the design and experiments are presented, and a proposal for a further investigation is given.

2. Laboratory Test Stand

The operation of the PD controller was tested on a hydraulic test stand, whose structure is shown in the Fig. 1.

The laboratory test stand system consists of a few main parts: hydraulic pump, pressure relief valve, manometer, filter, servo valve, piston, linear position encoder, and PC computer with MATLAB/Simulink1 software and control-card dSpace DS11042. The lab1 2

https://www.mathworks.com/ https:/www.dspace.com/

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oratory test stand consists of electro-hydraulic servo system shown in the Fig. 2 and hydraulic power station shown in the Fig. 3.

Fig. 1. Schematic diagram of the electro-hydraulic system with PD controller

Fig. 2. View of the electro-hydraulic servo system: 1) servo-valve, 2) piston, 3) position encoder, 4) load platform, 5) mass, 6) support

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The controller algorithm and the data acquisition are done using the PC computer and Matlab/Simulink software.

A feedback in the system is obtained by means of a position transmitter whose signal is compared with a set-point signal. This way, the information about the current position error is received and it goes to the controller. On this basis, the controller algorithm generates a control signal that changes the position of the servo valve, which in turn affects the position and velocity of the piston rod of the actuator. Changing the position of the piston rod causes a change in the position signal from the transducer.

The direction and the speed of the actuator was controlled by the two-stage electro-hydraulic servo valve Dowty 4553. The first stage of the valve uses a flapper nozzle and the torque motor. The input current from the DS1104 control card controls the torque motors and this same the flapper position. The flapper position controls the pressure in both chambers of the second stage of the valve – spool valve. The change of input current changes the flapper position and the pressure in chambers on both sides of the spoon in the valve, which cause the servo to move in one direction or the other.

The main advantage of this system is that a low power electrical signal can be used to accurately position an actuator, and the speed of the actuator is almost proportional to the electrical input control signal.

3. Procedure of the Controller Parameters Tuning

The methodology used in the presented research divides the controller tuning process into three main steps [15]: 1) Process identification.

2) Calculation of the controller parameters.

3) Verification of the control system performance in time and frequency domains.

Thorough procedure divided into different sub-stages is presented in Fig. 4.

4. Impulse Response Identification Fig. 3. View of the hydraulic power station: 1) pump Hydral PT02, 2) electric motor, 3) variable frequency drive, 4) oil tank, 5) pressure relief valve, 6) filter, 7) manometer

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In the system there is used a double-acting actuator. In order to stabilize the movement of the actuator, the platform is positioned on slideways. The position of the piston rod is changed by the servo-valve, controlled by the voltage signal in the range [–10 V, 10 V].

The position of the actuator’s piston rod is obtained by means of a magnetostrictive transducer.

The data transfer between the position transmitter, the regulator and the servo-valve is carried out using the 1104 dSPACE controller card with 16-bit analog-to-digital converters (ADCs).

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4.1. Theory The simplified model of the electro-hydraulic servodrive is usually presented in the form of a serial coupling of the proportional gain, the oscillating component and the integrating element [16], with parameters approximation based on the physical properties of the system.

Another method is the ARMAX model identification based on experimental data [17]. This method is popular because of its high reproducibility of the electro-hydraulic servodrive model and the ability to describe it in the state-space form.

During the research, there was used a simple, practical method for the calculation of the 2nd order inertial model for astatic systems based on the system pulse response [18].

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Fig. 4. Procedure of PD controller tuning process [15]

The transfer function of the identified model is described as follows G(s) =

1 1 e −T02 s TI s Ts + 1

(1)

Model (1) is the First Order Lag Plus Integral Plus Time Delay (FOLIPD) model, from the class of non-self-regulating process models.

The identification procedure should be performed in the open loop, by providing a pulse input signal u (= t ) u0 1 ( t ) − 1 ( t − Tu ) 

(2)

where: Tu – the known pulse period.

Then, the object’s response described as p(t) should be analyzed as it is presented in Fig. 5.

It can be seen, that p(t) for t > Tu can be described as follows

p ( t ) u0 = Therefore

1 TI

Tu t   −  T  → u0 u (3) Tu − Te T  e T − 1    t →∞ TI    

 Tu  Tu = = TI lim  u0  u0 t →∞  p∞  p (t ) 

(4)

where p∞ is the impulse response in the steady state.

Fig. 5. Impulse response of an astatic object [18] Determination of missing parameters of the searched model (T and T02) requires analysis of the obtained impulse response p(t) (see Fig. 5). It was shown in [18] that they can be calculated using the tangent the same way as for inertial model, in the following steps Determination of the FOLIPD parameters. ( t 0 ) = 0.

1) Find an inflection point, i.e. point where p 2) Calculate slope coefficient of the tangent line at the inflection point as a = p ( t 0 ) .

3) Calculate the bias of the tangent as b = p(t0 – at0)

(5)

4) Calculate T defined as the time difference between the moment when the tangent reaches asymptote p∞, and time of the inflection point (t0).

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5) Calculate T02 defined as determined as the time difference between the moment when the tangent has value 0 and the moment of impulse excitation.

Then, the values of T and T02, together with the previously calculated value TI can be finally substituted into the transfer function (1).

4.2. Experiment

The identification was carried out on a laboratory stand, giving to the servo valve the impulse signal with an amplitude u0 = 5 V and a pulse period Tu = 0.1 s.

The obtained response allowed to determine the position of the actuator piston rod in a steady state p∞ = 4.3986 mm and the local point of inflection at the time t_s = 0.601 s. On this basis, a tangent was designated at the point t0 described by the formula = y ( t ) 0.0395t − 20.9918

1 e −0.0318 s 0.0144s ( 0.0422s + 1)

(7)

5. Controller Design To implement the PD controller on a microprocessor system, it should be determined in a discrete time form. Such implementation was crucial in the electro-hydraulic servodrive control system with dSPACE controller-card used during research.

5.1. Discrete PD controller algorithm

In digital implementations, an incremental form is often used, i.e. the equation calculating not the absolute value of the control signal but its increase. This is due to the fact that it allows impactless switching of operating modes (manual work/ automatic work) and easier implementation of anti‑windup algorithm [19].

The discrete time form of the PD controller can be described as u= (k ) P (k ) + D(k )

with the proportional term described as P ( k ) = kpe ( k )

the filtered derivative term described as

= D(k )

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(11)

u ( k= ) u ( k − 1) + ∆u ( k )

(12)

the following incremental PD controller algorithm can be stated

 ∆u ( k ) = ∆P ( k ) + ∆D ( k )  ) P ( k ) − P ( k − 1=) kp e ( k ) − e ( k − 1)  ∆P ( k=  Td ∆ ∆D ( k − 1 ) + ) D ( k ) − D ( k − 1=)  D ( k= Tp kd + Td   k pTd kd  e ( k ) − 2e ( k − 1 ) + e ( k − 2)  Tp kd + Td   

(13)

with the following initialization values

5.2. Tuning rules

∆D ( k − 1 ) = 0  0  e ( k − 1) =  e ( k − 2) = 0 

(14)

From the set of PD tuning methods for FOLIPD process described in [13], there were chosen 4 different methods, namely: Coon method (CM, [20], [21]), Haalman method (HM,[22]), Van der Grinten method (VG, [25]) and Viteckova method (V, [23], [24]).

The tuning rules for abovementioned methods are presented in Tab. 13.

Table 1. P and PD controller tuning rules for FOLIPD process Method Coon Haalman Van der Grinten

(9)

Viteckova

kP x1C K m (τ m + Tm ) 0.6667 K mτ m 1 K mτ m x1V K mτ m

Td 0 Tm

Tm + 0.5tm Tm

Parameter x1C for the Coon method is chosen on the basis of the value ratio r = tm/Tm according to Tab. 2.

k pTd kd

e ( k ) − e ( k − 1 )  Tp kd + Td 

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where ySP(k) – set point value, k– discrete time, t = kTp, Tp – sampling time, kp – coefficient of the proportional term, Td – coefficient of the derivative term, kd – dynamic gain.

Assuming that

(8)

Td D ( k − 1) Tp kd + Td +

e= ( k ) y ( k ) − ySP ( k )

(6)

On this basis, the intersection points of the tangent line with 0 and p∞ have been determined using relations from Section 4.1, the model of the control object is obtained as the transfer function G(s) =

and the error signal calculated as

N° 4

(10)

For FOLIPD model (1) the following conversion of the coefficients is required Km = 1/TI, Tm = T, tm = T02 3

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Table 2. Values of the parameter x1C depending on the ratio r values r

x1C

r

x1C

r

x1C

0.020

5.0

0.25

2.2

4.0

1.1

0.110

3.0

1.0

1.3

0.53

4.0

0.43

1.7

Parameter x1V for the Viteckova method is chosen according to expected overshoot k as it is stated in Tab. 3.

The parameters of P and PD controllers for the identified model (7) and calculated using 4 different tuning methods are presented in Tab. 44.

Table 3. Values of the parameter x1V depending on the expected overshoot κ x1V

k

x1V

k

x1V

k

x1V

k

0.368

0

0.641

15

0.801

30

0.957

45

0.581

10

0.748

25

0.906

40

0.514

5

0.696

20

0.853

35

1.008

50

Table 4. Controller setting values according to different methods Method

kP

Td

Coon

0.1997

–

Van der Grinten

0.3575

Haalamn

Viteckova

0.2383

0.0101

0.1315

0.0056

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of position after transient response as the zero level (baseline).

Transient response time tr – which is the time between the beginning of input change (t0) and the moment after which the error signal remains inside a boundary d = 5%emax.

Integral Time Absolute Error quality index tr

ITAE = ∫t e ( t ) dt t0

Integral Time Absolute Control quality index

(16)

tr

6.2. Results

ITAC = ∫t u ( t ) dt t0

(17)

The step responses of control loops for different controller tuning methods of the electro-hydraulic system described in Section 2 are shown in Fig. 6-7.

The control signal from the different controllers for the step response input are shown in Fig. 8-11. The quality parameters for different tuning methods are gathered in Tab. 5.

0.0207

6. Experiments Effectiveness of different tuning methods and controllers has been confirmed experimentally. Within proposed experimental setup, there was possible to change input signal u(t) from P/PD controller in automatic or manual mode. Therefore theoperator could perform identification procedure or examine thecontrol system by changing set-point value ySP(t).

Fig. 6. Step response of electro-hydraulic servodrive with different controller settings

6.1. Quality criteria of the control system

The quality of PD control system was analyzed in the time domain using the following criteria [14] Steady state error of the pistons’ linear position – ex stat

Fig. 7. Zoom of step response of electro-hydraulic servodrive with different controller settings

Overshoot = κ

e2 ⋅ 100% e1

(15)

where e1, e2 – the first 2 consecutive biggest errors with opposite signs, assuming the steady-state value 4

For all PD controllers dynamic gain was chosen as kd = 8.

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Fig. 9. Control signals for Haalman method – PD controller

Fig. 10. Control signals for van der Grintenmethod – PD controller

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though they reached the set point in a slightly longer time, did not have the overshoot. In addition, the advantage of PD controller is a larger band of the gain margin. Quality parameters of all evaluated PD controllers tuned with different methods (Haalman method, Van der Grinten method or Viteckova method) are similar to each other, despite the fact that every method gave different controller parameters.

Unfortunately, the disadvantage of PD controllers is the visible noise in the control signal – in this terms, the Viteckova method is the best one, because of the smallest noise to signal ratio. On the other hand, in electro-hydraulic servodrive systems, a high frequency signal (called dither signal) is often added to control signal. It is used to reduce the hysteresis of the electromechanical transducer and keeps the servo valve spool in constant motion, thus reducing the static friction value.

In the future, it is planned to compare the frequency characteristics of the presented control system with different settings of P and PD controller, and perform more elaborated quality analysis of the control signal with filtering and the dither signal shaping.

AUTHORS

Jakub Możaryn* – Institute of Automatic Control and Robotics, Warsaw University of Technology, ul.

Sw. A. Boboli 8, 02-525, Warsaw, Poland, e-mail: j.mozaryn@mchtr.pw.edu.pl.

Fig. 11. Control signals for Viteckova method – PD controller Table 5. Table of quality control indicators for different control systems Method

ex stat

k[%]

tr

ITAE

ITAC

Coon

0.05

0.31

0.50

2012

113

Van der Grinten

0.07

0

0.89

2760

201

Haalman

Viteckova

0.06 0.10

0 0

0.84 0.90

2664 2694

149 133

7. Conclusions

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This paper discuss the control system design methodology and quality analysis of the electro-hydraulic servodrive position control system with a discrete P/PD controller. It is based on the identified linear model of the system (First Order Lag Plus Integral Plus Time Delay – FOLIPD) model, and the performance is compared for controller parameters tuned using4 different methods. It should be emphasized that PID-type controllers are not recommended for servo control by hydraulic drives because the plant already have integral properties.

Experimental results show that in terms of the steady state error and the transient response time, the proportional (P) controller (with settings determined by the Coon method)managed best, but it was characterized with a small overshoot. In contrary, proportional-derivative (PD) controllers, alArticles

Arkadiusz Winnicki – Institute of Automatic Control and Robotics, Warsaw University of Technology, ul. Sw. A. Boboli 8, 02-525, Warsaw, Poland, e-mail: a.winnicki@mchtr.pw.edu.pl.

Damian Suski – Institute of Automatic Control and Robotics, Warsaw University of Technology, ul. Sw. A. Boboli 8, 02-525, Warsaw, Poland, e-mail: d.suski@mchtr.pw.edu.pl. *Corresponding author

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[25] P.M.E.M. van der Grinten, “Finding optimum controller settings,” Control Engineering, 1963, 51–56.

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Double Block Zero Padding Acquisition Algorithm for GPS Software Receiver Submitted: 21st October 2018; accepted: 20th December 2018

S.V.S. Prasad

DOI: 10.14313/JAMRIS_4-2018/26 Abstract: Several methods of acquisition have been developed so far which aim at accelerating the acquisition process and detection of weak GPS signals. In many of these the search is parallelized in code or frequency space.

However, sometimes the number of samples in code periods based on sampling frequency is not equal to required number of Radix-2 FFT algorithm. So it is again computing the DFT normal method without FFT. The main purpose and objective of this project is to implement a fast and robust for weak signal acquisition algorithm “Double Block Zero Padding Acquisition” (DBZP) for GPS L1 civilian signal. Technique is developed even for the signals where number of samples in the code period taken for correlation is not satisfying the required number for Radix-2 algorithm. It is also suitable for weak GPS signals acquisition, which require Pre-detection, or integration (correlation) Time (PIT) to be long.

Keywords: GPS, Acquisition, Weak Signal, Multi-Constellation, DBZP, FMDBZP.

1. Introduction

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The Global Satellite Navigation technology has been playing a key role in the positioning and navigation applications. GNSS at present is more useful to the military, safety of life applications and for civilian user applications. There is a need at present to design and development of such system with more accuracy and reliability than ever before. To use GPS receivers in these challenging conditions and environments, high sensitivity algorithms has to be used. Software GPS receivers are more flexible and suitable for research and development and also useful for integration with sensors.

All the conventional acquisition algorithms work well on strong GPS signals with minimum dwell time but for weak signals to detect by these algorithms [1], [2] the dwell time needs to be increased which leads to increase of computational load and hence gets slower. For detecting weak GPS signals (for example, C/N0 < 30 dBHz)[14], a GPS receiver has to perform either a coherent accumulation with long integration time T (≫1 ms) or a non-coherent

integration of multiple (Nnc≫1) coherent accumulation outputs with a less coherent integration interval Tco. [4], [5] In practice, however, both these methods are expensive in computation, the longer the coherent integration interval the more the Doppler frequency bins which leads to the smaller step size in Doppler frequency search. Therefore there will be an increase of computational cost in the weak GPS signal detection and which is inevitable.

The goal or principle of acquisition is to get the rough estimates of code phase and carrier frequency [11] which are initial values or parameters given to tracking module.

2. Literature Survey

There are many acquisition methods available so far traditionally. The serial search in time domain is the most basic of the search strategies in terms of algorithm complexity, but because of this simplicity is also the slowest of all the acquisition strategies. In the parallel search all bins of one dimension (frequency or code delay) are searched at the same time. In parallel code phase search acquisition scheme if the input vector to the Fourier Transform is not a power (radix 2) then DFT is performed [13].

There are several acquisition methods which exploit the circular correlation, to name a few like coherent integration, half sized circular correlation.

The goal of these techniques is always to reduce the computation time and enhance sensitivity. The acquisition step requiring a lot of time and operations, there are many developed techniques, some of them are not based on circular correlation. This GNSS [3] receiver is meant for educational and research purposes, then the software technology is well adopted due to its reconfigurable nature and important flexibility.

The efficient and fast acquisition of GPS L1 [2] signal is still a challenge. An acquisition technique which seems adapted to these purpose due to its efficiency and computational speed is the Double Block Zero Padding (DBZP) [14], [15]. By comparing 8 of the previously cited acquisition methods, it was concluded that the DBZP seems to be one of the best for the acquisition of weak signals due to the reduced number of operations. DBZP is found as a relevant method to be used as a base for developing a new Galileo E1 OS [14] acquisition technique.

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3. Double Block Zero Padding

4. Implementation of DBZP

Double Block Zero Padding is a method more suitable for acquisition of weak signals. This method was also referred to as Circular Correlation by Partition and Zero Padding. This method performs long coherent integration with fewer operations and higher sensitivity than other FFT based techniques. The concept of this technique relies on the use of partial correlations on duration equivalent to a few tens of chips.

The computation time gain of this method is the FFT processing on small size vectors instead of large size vectors.

In total, there are five steps involved in this algorithm. Before defining and explaining step by step, we first define two parameters namely – Coherent Integration Time (TC), – Maximum and Minimum Doppler Frequency (fD,Max, fD,Min).

The coherent integration time is defined as correlation time. The minimum integration time is 1 ms and is limited by the spreading sequence period. The minimum and the maximum Doppler frequency parameters represent the minimum and maximum variations from center carrier frequency as there is a relative motion between receiver and the satellites.

Step 1: Incoming signal Preprocessing. Figure 2 shows the preprocessing of incoming signal which is first step of this algorithm. The incoming complex data from the front end is converted into base band just by multiplying with the complex exponential function exp(j*2*p*f*n*T).

The resulting TC ms long baseband samples are split into equal length of M blocks as shown in figure 2.

Fig. 1. Block diagram of DBZP Figure 1 shows the block diagram of DBZP scheme, where the search is parallel in both code and frequency simultaneously and with partial correlations, where partial correlation length is generally taken as a fraction of spreading code period.

This property enables this algorithm faster as well as highly computationally efficient.

The Doppler bins in double block-zero padding and their step value are fixed = Nb

f D ,Max − f D ,Min = 2 f D ,Max × TC 1 TC

(1)

As given below, the number of Doppler bins is always equal to the number of code delay blocks – one block duration tb is: =

= Nb

f D Max

= N spb N s /Nb = t b × f s

– the Doppler frequency resolution Df is:

= ∆f

2 f D. Max 1 = Nb TC

Step 2: Local PRN spreading code. Figure 3 shows the generating local PRN spreading code. Second step in this method consists of generating local PRN spreading code, which is further split into same number of blocks as in step 1. After that each block is appended with same number of zeros to make it 2Nb Samples as shown in figure 3. The second box represents appended zeros of Nb samples, thus by adding those two blocks it makes 2Nb samples per each block.

(2)

– the number of samples per block Nb is equal to:

Fig. 2. Pre-processing of the incoming signal

(3) (4)

Fig. 3. Pre-processing of the local code Articles

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Step 3: Split signals and Partial correlations. The third step is to take the correlation output using FFT. The first two blocks of the incoming signal samples (2Nb samples) and the first block of local PRN code along with the combined appended zeros block Nb samples of code and Nb samples of zeros are to be correlated using FFT method.

Zero-Padding is used in the DBZP acquisition method; when the padding of zeros is not used, the autocorrelation which is normalized function has a peak which suffers a degradation due to attenuation. When it is padded with zeros we can easily observe that there will be no degradation and the peak is isolated without any attenuation.

T0 + ( k â&#x2C6;&#x2019; 1 )TC + lt b ,T0 + ( k â&#x2C6;&#x2019; 1 )Tc + ( l + 1 ) t b  (5)

Furthermore, the phase at

t = To + ( k â&#x20AC;&#x201C;1 )TC + lt b

(6)

The partial in-phase correlator output is iď&#x20AC;Ľ ( k ) = â&#x2C6;Ť

To+( k â&#x2C6;&#x2019;1)Tc +( l +1)tb

To+( k â&#x2C6;&#x2019;1)Tc +ltb

Finally

Blc+1 ( t ) * Bls+1dt

(7)

Iď&#x20AC;Ľl ( k ) =

A d ( k ) Rc1 ( ÎľĎ&#x201E; ( k , l ) ) cos (Ď&#x20AC; f Dt b + Îľ â&#x2C6;&#x2026;o ( k , l ) ) sinc (Ď&#x20AC; f Dt b ) + 2 Ρ Iď&#x20AC;Ľl ( k ) (8) No No N b = 4t b 4TC

2 Ď&#x192; = nď&#x20AC;Ľ

(9)

The partial correlator outputs for all permutations of the C/A code blocks are placed in a matrix form (M Ă&#x2014; Nb).

Step 4: FFT application. FFT is applied to the partial correlation matrix output of size M Ă&#x2014; Nb. An M point FFT is applied to each column corresponding to each delay and stored in another matrix column wise. The mathematical expression (A/2) Rc1 (đ?&#x153;&#x20AC;đ?&#x153;?) sinc(ďż˝fDtb) is constant for all đ?&#x2018;&#x2122; and can be approximated by (A/2) Rc1 (đ?&#x153;&#x20AC;đ?&#x153;?) sinc(ďż˝fDtb) in the neighborhood of đ?&#x153;&#x20AC;đ?&#x153;? = 0. Thus, the Fast Fourier Transform (FFT) of the partial correlator outputs will give the DBZP outputs.

)

where:

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)

5. Experimental Results

The DBZP and Parallel search in code and frequency algorithm is implemented in MATLAB. AÂ Parallel search in code phase (1Â ms integration time) + Parallel search in Frequency (10Â ms integration time) Acquisition Algorithm using DFT.

GPS IF Data_1 specifications: Filename=GPSdata-DiscreteComponents-fs4_774 if1_1935_2MHz1.bin.

IF (Intermediate Frequency) = 1.19352MHz; Sampling Frequency = 4.774MHz; Data Type = int8; Data contains strong satellite signals with PRNs 15, 18, 21, 22 along with weak signals 3, 6, 26.

Table 1. PRNs that are having a threshold 2.5 and above PRN

Peak Metric

Code phase

Doppler

15

7.20

4606

1937.72

21

5.26

1741

-557.24

22 18

7.09 4.35

852

2656

â&#x20AC;&#x201C; m = 0â&#x20AC;ŚM â&#x20AC;&#x201C; are the points FFT is taken which corresponds to a Doppler frequency bin.

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1710.08 253.17

In Table 1, the peak metric is the ratio of first peak to second peak ratio. The figure 4 gives the peak for PRN 15.

The peaks for the PRNs 22, 21 and 18 are in the Figure 4, Figure 5 and Figure 6 respectively. The above same results may not be acquired for the weak signals. For the weak satellite vehicles like PRN 3, 6, 26 double block zero padding method is used, which suffers degradation due to attenuation. When it is padded with zeros we can easily observe that there will be no degradation and the peak is isolated without any attenuation

(10)

( k ) Ď&#x20AC; f Dt b + ( ( Nb â&#x2C6;&#x2019; 1) / Nb ) (Ď&#x20AC; f Dt c â&#x2C6;&#x2019; m ) + â&#x2C6;&#x2C6;â&#x2C6;&#x2026; ( k ,0) 0

2018

Step 5: code block permutations. So far we tested for only one code delay time slice between [0, tb]. C/AÂ code blocks are permutated circularly in order to test for all code delays. On first permutation of local spreading block the last block appears to be the first block and the first block appears to be the second block.

L ( k , m) = A d ( k ) Rc1 (â&#x2C6;&#x2C6;r ) sinc (Ď&#x20AC; f Dt b ) F ( cos (Ď&#x20AC; f Dt b + 2Ď&#x20AC; f D lt b + 2 + â&#x2C6;&#x2C6;â&#x2C6;&#x2026;0 ( k ,0 ) ) + Ρl ( m )

N° 4

Fig. 4. Acquisition Result for PRN 15

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The Figure 8 shows the graph between acquisition metric and PRN number which in turn gives the information between acquired and not acquired signals.

Double block zero padding (DBZP) acquisition Algorithm for 10 ms Integration time The DBZP method for 10 ms Integration time results the phase of the code and Doppler frequency as shown in Table 2.

Table 2. PRNs that are having a threshold 2.5 and above (DBZP) PRN

Peak Metric

Code phase

Doppler

22

6.25

852

1800

21

5.17

1741

-600

Fig. 5. Acquisition Result for PRN 22 18 15 26 6 3

Fig. 6. Acquisition Result for PRN 21

Fig. 7. Acquisition Result for PRN 18

Fig. 8. Acquisition Results PRN vs Acquisition Metric

5.27

2656

4.70

4606

4.22 3.56 2.83

400

2000

3419

-3000

4342

2000

3591

-3700

The acquisition results for weak signals by using DBZP acquisition algorithm is shown in the Figure 9, Figure 10 and Figure 11 respectively. The peak gives the PRNs 22, 18, 21 respectively.

Fig. 9. Acquisition Result for PRN 22 (DBZP)

Fig. 10. Acquisition Result for PRN 18 (DBZP) Articles

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PRN

Parallel Code Phase Search using DFT (10 ms) Doppler X

DBZP Doppler (10 ms PIT) Y

% absolute error |(X-Y)/X*100|

% accuracy (100-% absolute error)

Table 3. Comparison results (DBZP vs DFT method)

15

1937.72

1900

1.946

98.053

21

-557.24

-600

7.67

92.326

22

Fig. 11. Acquisition Result for PRN 21 (DBZP)

18

1710.08

1700

253.17

0.589

300

18.49

99.410 81.50

Table 4. Comparison of Weak satellite peak metrics

PRN

Parallel Code Phase Search using DFT (10ms) Peak Metric

DBZP (10ms PIT) Peak Metric

Increase in Peak metric

26 6 3

2.48 2.12 1.82

4.22 3.56 2.83

1.701 1.67 1.55

Table 5. PRNs that are having a threshold 2.5 and above Fig. 12. Acquisition Result for PRN 15 (DBZP) Figure 12 gives the acquisition result for PRN=15 using double block zero padding acquisition algorithm.

Comparison of Two Acquisition Schemes Comparison of the above two methods is presented below and calculated absolute error and accuracy taking A Parallel search code phase (1 ms integration time) + Parallel search in Frequency (10 ms integration time) as reference acquisition scheme.

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In DBZP scheme PRNs 3, 6, 26 which are low sensitive satellite vehicles present in the data are detected by DBZP method of acquisition. DBZP acquisition method enhances peak metric of these PRNs approximately by 1.6 times. The table gives the comparison of peak metric with both the methods and corresponding increase in the peak metric value in decibels.

The Table 4 gives the comparison between peak metrics of weak satellites for 10 ms PIT by implementing double block zero padding acquisition algorithm.

The PRNs with the threshold value of 2.5 and above with code phase and Doppler is given in Table 5.

The absolute error and accuracy for the PRNs 15, 22, 21, 2, 10, 6, 3, 26 by taking parallel code phase search using FTT as 10 ms Doppler and 10 ms PIT is shown in Table 6.

Articles

PRN

Peak Metric

Code phase

Doppler

15 22 21 2 10 6 3 26

10.69 6.88 4.66 3.08 2.95 2.84 2.81 2.67

4606 852 1741 3714 203 3592 4342 3419

1937.72 1710.08 -557.24 81412.12 5243.08 -3671.38 1919.51 -2970.24

Table 6. Comparison results (DBZP vs FFT method)

PRN

15 22 21 2 10 6 3 26

Parallel Code Phase Search using FFT (10 ms) Doppler 1937.72 1710.08 -557.24 81412.12 5243.08 3671.38 1919.51 2970.24

DBZP Doppler (10 ms PIT)

% absolute error

% accuracy

1900 1700 -600 9900 7900 -3700 1900 -3000

1.946 0.589 7.67 87.83 50.67 0.77 1.01 1.00

98.053 99.410 92.326 12.160 49.32 99.23 98.98 99

By using double block zero padding acquisition method, the PRNs 3, 6, 26 being low sensitive satellite vehicles present in the data enhances peak metric by 1.6 times when compared with other traditional acquisition methods by using double block zero padding acquisition algorithm which is shown in Table 6.

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[3]

[4] [5] Fig. 13. Acquisition Results PRN vs Acquisition Metric The graph between acquisition results and acquisition metric of PRNs using double block zero padding acquisition method by showing acquired signals in green color and non acquired signals in blue color is shown in Figure 13.

6. Conclusion

DBZP method is used in this work, where both code phase and Doppler search take place in parallel and the FFT vector is small compared to Parallel code phase search. This makes the algorithm execution very fast compared to 1+1 ms acquisition method which is mentioned in the literature. The DBZP scheme is implemented and tested in Matlab. It detects weak signals that are present in the IF data. The comparison of results both in absolute error and accuracy is presented. The results are shown in section 5 which shows that it can detect weak signals as compared to the other existing schemes of acquisition and the execution time is also faster due to the partial correlations. Since the FFT length is smaller, the correlations time is also lesser. So we can conclude that by replacing the traditional acquisition schemes in the software receiver with this new method makes the receiver work effectively even for weak signals. Hence it may enable the receiver to give the services indoor or in heavy canopy or in a high vegetation environments.

AUTHOR

S.V.S Prasad – Department of Electronics and Communication Engineering, MLR Institute of Technology, Hyderabad, India, prasad.sista@gmail.com.

[6]

[7]

[8]

[9] [10] [11]

[12]

[13] [14]

REFERENCES [1]

[2]

K. Borre, D.M. Akos, N. Bertelsen, P. Rinder, S.H. Jensen, “A software-defined GPS and Galileo receiver. A single frequency approach,” Birkhäuser Basel, 2007, DOI: 10.1007/978-0-8176-4540-3.

D. Akos, P-L. Normark, A. Hansson, A. Rosenlind, Ch. Stahlberg, F. Svesson, “Global positio-

[15]

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ning system software receiver (gpSrx) implementation in low cost/power programmable processors.” In: Proc. of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001), Salt Lake City, UT, USA, September 2001, 2851– 2858.

R.E. Best, “Phase Locked Loops: Design, Simulation, and Applications,” 4th ed., Mc-Graw Hill, 1999.

J.B. Bullock, M. Foss, G.J. Geier, M. King, “Integration of GPS with Other Sensors and Network Assistance.” In: E. Kaplan, Ch. Hegarty (eds.)

Understanding GPS: principles and applications, Artech House, London, 2005.

V.M. Jovanovic, “Analysis of strategies for serial-search spread-spectrum code acquisition-direct approach.” In: IEEE Transactions on Communications, vol. 36, no. 11, 1988, 1208–1220, DOI: 10.1109/26.8927.

K. Krumvieda, P. Madhani, Ch. Cloman, E. Olson, J. Thomas, P. Axelrad, W. Kober, “A Complete IF Software GPS Receiver: A Tutorial about the Details.” In: Proc. of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001), 2001, 789–829.

M. S. Braasch, A. J. van Dierendonck, “GPS receiver architectures and measurements.” In: Proc. of the IEEE, vol. 87, no. 1, 1999, 48–64, DOI: 10.1109 /5.736341.

P. Misra, P. Enge, “Global Positioning System: Signals, Measurements and Performance,” Ganga-Jamuna Press, 2001.

B.W. Parkinson, J.J. Spilker, “Global Positioning System: Theory and Applications. Vol. I.,” Washington, DC: American Institute of Aeronautics and Astronautics, Inc., 1996.

J.B.-Y. Tsui, “Fundamentals of Global Positioning System Receivers: A Software Approach,” John Wiley & Sons, Inc., 2000.

D.M. Lin, J.B.-Y. Tsui, “Comparison of acquisition methods for software gps receiver,” Proc. of the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000), Salt Lake City, UT, USA, September 2000, 2385–2390.

D.M. Lin, J.B.-Y. Tsui, D. Howell, “Direct p(y)-code acquisition algorithm for software gps receivers,” Proc. of the 12th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1999), Nashville, TN, USA, September 1999, 363–368.

N.I. Ziedan, “GNSS receivers for weak signals,” Artech House, London, 2006.

M. Foucras, O. Julien, Ch. Macabiau, B. Ekambi, “A novel computationally efficient Galileo E 1 OS acquisition method for GNSS software receiver.” In: Proc. of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, TN, USA, September 2012, 365–383.

K. Mollaiyan, R. Santerre, R. Landry, “Acquisition of Weak Signals in Multi-Constellation Frequency Domain Receivers,” Positioning, vol. 4, no. 2, 2013, 144–152, DOI: 10.4236/pos.2013.42014.

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Software Implementation of Exchange Processes in a Distributed Network Environment of Transmission and Processing of Information Submitted: 10th July 2018, accepted 11th December 2018

Nadirbek Yusupbekov, Shukhrat Gulyamov, Sadikdjan Kasymov, Nargiza Usmanova, Dilshod Mirzaev DOI: 10.14313/JAMRIS_4-2018/27 Abstract: The work is devoted to the development of scientific and methodological basis for increasing the functioning efficiency of distributed computer networks and systems through the organization of an info communication network environment for the transmission and processing of information on the basis of implementation of models and mechanisms of associative interaction in a computing environment.

Keywords: Information exchange process, data transfer and processing, distributed network environment, decision support

1. Introduction

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The development, implementation and use of information and communication technologies (ICT) are an essential feature of modern society and are important for its economic growth and development. The emerging ubiquitous information society is based on ICT, enabling new technological opportunities and increasing the efficiency of economic activity, preserving the role of the most important factor of economic growth and social development. In 2003–2009 ICT have created about 5 percent of the global gross product, in 2008, 5.4 percent, Mackenzie experts expect to grow to 8.7 percent by 2020 [1]. According to Gartner, in 2010 the volume of the world ICT market on expenses made 3.4 trillion USD in growth by 5.3% compared to 2009, the cost of IT services by users amounted to 821 billion. On computers – 353 billion (5.7% growth), software, 232 billion (5% growth), on telecommunications, 1.9 trillion dollars [2]. In general, the turnover of foreign trade in ICT and information services increased 2.5 times in the period 1990–2010.

As technically interconnected innovation industries, ICTs are being integrated into different areas, shaping the global information services market and generating information flows that reflect the global economy development trends. It is worth noting that for Big Data, as one of the fastest growing areas of ICT, the total amount of data received and stored is doubled every 1.2 years. For example, for the period from 2012 to 2014 the amount of data transmitted monthly by mobile networks increased by 81%. According to Cisco estimates, in 2014 the volume of mobile

traffic was 2.5 Exabyte per month and in 2019 it will be equal to 24.3 Exabyte. In February 2016, Synergy Research Group published the results of the global cloud services market, which is growing at a steady pace: the Cloud infrastructure services market (including IaaS, PaaS, and also private and hybrid cloud solutions) grew by 52% in 2015, reaching 23 billion dollars. As Gartner predicts, the volume of the global market of public cloud services in 2016 will reach 204 billion USD, which is 16.5% more than in 2015 [3-5].

In this regard, systems of distributed information processing and management, which are of fundamental importance in various fields and fields of ICT, are currently being subjected to research by many groups of the world community. These studies are stimulated by the growing role and increasing development of various networks and technologies (such as semantic Web, Grid-computing, cloud computing, the Internet of things, etc.) each of which has its own principles and peculiarities implementation, but in general, behind all these technologies lies the idea of creating a single environment that allows the user to receive services anywhere and anytime. However, in many areas the possibilities of computing are limited due to the nature of information processing and management of the computational system (for example, in the field of image recognition, solving problems with incomplete information, forecasting the results of proposed action and the development of control, the dynamics of processes in real time, etc.). Current opportunities of information technologies imply realization of new approaches to processing of the information, combined by common properties of associative or intuitive processing the information, giving the possibility to process knowledge, to carry out logical conclusion and, thus, allowing intellectualization of computational systems [6,7].

Today, despite the existence of a sufficiently strong theoretical and practical basis for study distributed systems, the tools of describing evolution in time both of distributed systems and populations are still not developed programme structures. This is due to a number of reasons, among which, first of all, heterogeneity of composition and dynamics of behavior of components, including the presence of changing unpredictable structures. Existing methods of description and research of distributed systems, as the analysis of modern domestic and foreign works shows, is mostly unable to answer many questions in this direction, in particular, how the

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functioning in distributed systems and networks software structures can be formed to effectively interact with components and create a single distributed environment. In this connection, it is necessary to solve problems of efficient organization of distributed computations, to expand corresponding functionality and to improve interaction mechanisms of many elements (components), taking into account functional internal and intersystem processes, as well as complex infrastructure linkages caused by network and system architectures [8].

2. The Task of Software Implementation of Exchange Processes in a Distributed Network Environment of Data Transmission and Processing Scientific and technical publications in the field of distributed systems and networks cover a wide range of research of information interaction processes, peculiarities of intersystem and inside system data interchange, including taking into account the rapidly growing information flow involved in transmission and processing, when the multitude of streams generated as a whole in the network, forms a kind of space that has the structure and principles of the organization.

Many scientists aspire to solve this problem by means of development of different models, ways of interaction of information, at various levels of the network, research of quantitative changes of information, representation of a network as a large information store etc. That can become self-governing in the future, depending on the change in information. These models are largely developed from the point of view of information exchange, allowing to trace formal procedures, whereas for detailed research of information technologies tasks, including their analysis, it is required to study the space specifications (in terms of information technology specifications, standards, profiles, scenarios), as well as technology implementation space (in terms of systems, products and services), which requires a different approach to research.

Principles of organization of distributed systems, realization of interaction of system components and modeling of distributed computations are devoted to works of domestic and foreign scientists, as E. Tanenbaum, J. Foster, K. Kesselman, V.V. Toporkov, A.G. Tormasov et al. Research of questions of mathematical maintenance of computational machines and management of computational processes is the basis of works of R. Kalman, A. Shiryaev, R. Bellman, L. Pontryagin, V.K. Kabulova, F.B. Abutalieva, F.Th. Adylovoj, etc. Some questions of organization of effective information processing and information exchange in computational systems and networks are considered in works of K. Petri, S. Hoare, J. Neumann, V.A. Mizina, Y. Zlotnikov, D. Cobackgammon, D. Melnikov, E. Nelson, and also T.F. Bekmuradova, S.S. Kasimov, M.M. Musayeva, etc. In works V.V. Lipaeva, M. Lipova, E. Nelson, D. Nessera, T. Tejera, and also M.M. Kamilov, D.A. Abdullayev, etc., the issues of increase a functionality of means and systems

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of information exchange are addressed. Interlevel interaction in protocols of information exchange means for services is considered in works N. Anisimov, S. Proteins, V.N. Turchenko, A.D. Ivannikova, etc. The tasks of artificial intelligence in the field of development of components of intellectual environments and application of fuzzy sets in control models and the use of unclear set are important in the field of research of artificial intelligence, which are reflected in the works of L. Zadeh, E. Mamdani, D.A. Paspelava, R.A. Aliyev, as well as R.N. Usmanov, D.F. Muhamedievoj and others. At the same time, the issues of efficient organization of distributed computations in the task of expansion of corresponding functionality and improvement of mechanisms of interaction of many elements (components) are not sufficiently investigated, taking into account functional processes of internal and intersystem character, the presence of a wide variety of environments, platforms, technologies, as well as complex infrastructure links, caused by network and system architectures.

3. Research of Information Interaction and Distributed Network Structures The analysis of information transformations is made on the basis of distributed network calculations: it is shown that there are special rules, algorithms, protocols, etc., used in the functioning and development of different areas and technologies of distributed calculations, and for each of them the tasks of analysis of interrelations, relations and mutual coordination of components and resources are actual, which, in turn, are determined by the principles of management of information processes, realizing each of the concrete destinations [9]. The main form of representation of distributed network computing is the representation on the basis of (distributed) objects of software engineering: it is caused by an important property of the object to hide the internal structure from the outside world through a strictly defined interface. This approach makes it easy to replace or modify objects, leaving the interface unchanged. In addition, the key feature of an object is that it encapsulates data called state and operations on that data, called methods, while access to methods can be obtained through an interface. In this way, access or object state manipulation is the use of methods that are accessed through the interface of the object (in turn, the object can implement many interfaces) accessing. This partitioning on the interfaces and the objects that implement them is accepted by the main element of the distributed associative interaction.

By using an object-oriented approach when creating distributed systems, you can consider system components at different levels of abstraction as objects, each of which would have a certain line of behavior. It is shown that the middleware software provides the functional completeness of the requirements for distributed systems when performing calculations. It can be implemented on the basis of Articles

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Fig. 1. The elements of distributed object model

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different architectures (models) of networks; In this case, the exchange of information between components of the distributed system can be organized using different technologies. The choice of a specific technology depends on requirements of the distributed system.

In general, at the intermediate level is the most appropriate option for the interaction of components of the distributed system and in this chapter postulated that the principles of the organization at the intermediate level can be used to develop models of info communication network environment of transmission and information processing.

Development and integration of distributed applications provides that the main part of the intermediate software is based on a certain model defining the distribution and communication, i.e. on the model of distributed objects (Figure 1). The idea of which is that each object implements an interface that hides all the internal details of the draft from its user, i.e. the interface contains the methods implemented by the object.

In the concepts of object-oriented programming, this model represents the basis of modeling in a distributed environment and correlates with the work methodology when considering the functioning of distributed components in a view staging environment. The interoperability processes of distributed components can be categorized according to the functions performed and the affiliation to different object classes [10].

Interaction of application modules and reflection of service relations with corresponding application processes in many cases there are difficulties connected with peculiarities of application implementation and work of mechanisms themselves in distributed environment. The paper offers a distributed application model and a system model for the software compoArticles

nent, which can be used by formal procedures to record relationships for different requests on the part of certain processes. Based on the procedures of building a system model of software components it is expedient to formalize the processes of information exchange in a distributed network environment that allows investigating and developing specific solutions for distributed systems and networks of varying complexity.

Distributed applications use a number of computers and processes that manage shared information (databases, files, objects). In this case, user programs, depending on the needs of the user, necessary information or modification of the stored (Fig. 2) [11].

The system consisting of the finite set of successive nodes (processes) р1, р2, ..., рn, is considered that interact through the finite number of objects x ∈ X. It is accepted that each object x can be accessed through a write/read operation (the write operation defines a new value for x; the read operation allows the node to get the value of the object). The z value is assigned to the x object as: w(x)z – for writing and r(x)z – for reading. The turn to these computers and processes to obtain the implementation of a pi process can be represented by a sequence of operations: opi1, opi2, …, opik where k is the index that defines the k-th operation of the pi process. The sequence of operations (events) defines the ši events for pi.

If you take ši as a set of operations implemented for pi, and a dependency vector as the directional ratio of the operations implemented by pi (for example, ši as a set (Si, Vi)), you can accept the sequence Š = (S, Vs), and Vs to name the relationship “process-Request”, that is,

S =  si i

(1)

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Fig. 2. The Distributed Application Model  op1 v s op2 (Request op1 before execution of op2), if:  1. ∃pi : op1 v s op2, (2) 2.

op1 = w(x)z, (3)

op2 = r(x)z, i.e. op2 uses the information entered op1,   3. ∃p3: op1 v s op3 and оp3 v s op2. (4)

These formal procedures can be used to record relationships for different requests from different processes.

A distributed network structure is represented by a collection of interconnected nodes that sharing messages over the network; each node functions on its own algorithms of exchange, imposing certain restrictions on the general process of information exchange. Regardless of what kind of exchange, for a separate object (one service), when in exchange involved servers – direct and/or potential participants of exchange and clients – initiators of requests of objects at servers, or for many objects (Services), when servers can act as clients themselves for some objects, its implementation requires appropriate coordination between different services, the functional purpose of which is to fulfill certain requests of the client [12].

In the work on the basis of concepts of object-oriented programming the corresponding positions are substantiated and the possibilities of the object as element of the relationship implementing the program properties are demonstrated. The object has a single name, its own data and procedures. It can consist of several objects and, in turn, be part of a larger object.

All actions in object-oriented programming are performed through messages, etc. In general, the concept of an object is defined by key features such as encapsulation, class-example relationship, inheritance

property, passing messages. Thus, information exchange procedures may be characterized as follows: (a) data and procedures are merged into program objects, (b) messages are used to ensure interconnection between objects, (c) similar objects are grouped into classes, (d) data and procedures are inherited by the class hierarchy. These characteristics have been considered in terms of analyzing information transformations in a distributed environment and showing how the object-class-message model is used for object-oriented software development. Language interface and built-in set of classes as a tool to implement the principles of object-oriented programming.

The mechanisms and procedures of the information exchange, realized by means of the developed software, demonstrate possibilities of use of associative interaction at exchange of the information of the distributed objects and are very convenient means for display processes. The corresponding software implements algorithms of information exchange at intermediate level of distributed environment, has convenient user interface, allows to display information processes on the basis of modules work (as for Client and Server software). In particular, the algorithm of information exchange in distributed systems based on client-server architecture is implemented by developed software, which allows tracing functional relationships of system components in the basic architecture.

For the detailed study of the principles of organization of links in the system and research of interaction of components of distributed system with the purpose of definition of effective mechanisms of information exchange, the tasks of analysis of functional interaction of components in a network on the basis of peer (peer-to) links. These capabilities are justified by developed software that implements the Articles

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User Request

Application

Application

API Interface

API Interface

Security Services

Read Locking File/ Folders

Write

File & Fragment Namespace

Atomic Operations Authentification

System Configuration Mechanism

File Fragments

Response of Server

Connection Mechanism

Access Control Request Handler

Replication of Fragments

Logging Mechanism

Crypto System

MetaData Security Services

Backup

Replication Request Handler

Fragment Attributes

Fragment Attributes

Naming for file/ folders

Naming for file/ folders

Searching Mechanism

Searching Mechanism

Virtual File System

Virtual File System

Connection Mechanism System Health Garbage Collector Load Balancing Data Store Mechanism

Synchronization

OS API Interface

Scanning System OS API Interface

OS API Interface

Client Side

Server Side

Fig. 3. Software modules and their interaction when implementing a query in the file system

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functions of the kernel Task Manager in the distributed system.

The capabilities of developed software that implement the features inherent in the distributed file system are reflected in Figure 3 (logical representation of shared resources for easy administration and load balancing; creating multiple alternative shared resources, which enables the organization of fault-tolerant data storage schemes; maintain the availability of data when you move network shares, which provides high network performance when a user accesses a specific logical name).

The algorithms of interaction between the components of distributed network, realized by means of developed modules of the software, can be used for creation of high-performance systems of distributed data processing in various fields of science and technology.

On the basis of generalization of problems of information interaction and possibilities analysis, realized on the basis of associative processes in mechanisms of information exchange, systematized and categorized aspects of interaction concerning executed in them processes and components that are based on distributed computing or applications.

The work justifies the need for special mechanisms of resource management in heterogeneous distributed environments with the purpose of their coordination and integration. The schemes of organization of the distributed computations are studied, from which Articles

it is obvious, that for management the new principles of planning of computational works and allocation of resources are necessary with definition of classes of tasks of analysis of processes of information exchange in distributed network structures. In addition, the analysis of the distribution of functions by levels and layers, as part of a possible decomposition of the distributed media and information processing, has shown that they can be grouped (by criterion of affiliation to level or layer and use in functional architecture of network structures) [13,14].

4. Conclusion The set of public defense scientific provisions of reviewed work ensured the development of concepts, principles and scientific and methodological bases of the decision of theoretical and applied aspects of the implementation of associative interaction in modern communication network structures of computational systems.

The methodology proposed and substantiated by the authors of the study of communication network structures allows to describe complex functional and informational relations of inter and inside system character on the basis of the unified framework concept and confirms the competence of the initial hypothesis of the executed research: mechanisms of

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associative by the nature of interaction of composite components of computational networks and systems, realized on the basis of principles, methods and algorithms of software engineering at implementation of the postulate of separation and sharing of the potential of distributed information and computational resources in the area of their harmonization and coordination, allow effective interaction of nodes and components of communication network structures and optimal management of real-time computing resources, significantly expanding the potential of automated management and functionality of computing systems.

AUTHORS

Nadirbek Yusupbekov – Department of Automation of Production Processes, Tashkent State Technical University, Tashkent, Republic of Uzbekistan, e-mail: app.tgtu@mail.ru.

Shukhrat Gulyamov – Department of Automation of Production Processes, Tashkent State Technical University, Tashkent, Republic of Uzbekistan, e-mail: app.tgtu@mail.ru.

Sadikdjan Kasymov – Tashkent University of Information Technologies.

Nargiza Usmanova – Department of Networks and Systems of Data Transmission, Tashkent University of Information Technologies, Tashkent, Republic of Uzbekistan, e-mail: nargizausm@mail.ru.

Dilshod Mirzayev – Tashkent University of Information Technologies, Tashkent, Republic of Uzbekistan, e-mail: mdilshod@mail.ru.

REFERENCES

[1] S. Dutta, B. Bilbao-Osorio, The Global Information Technology Report 2012: Living in a Hyperconnected World, World Economic Forum, 2012.

[2] www.gartner.com.

[3] N.B. Usmanova, “Definition of optimal structure of telecommunication networks in conditions of introduction of new technologies,” Uzbek Journal Problems of Informatics and Energy, no. 3–4, 2001, 26–32.

[4] N.B. Usmanova, “The functioning of the transport network and issues of traffic integration,” Uzbek Journal Problems of Informatics and Energy, no. 5, 2002, 37–43.

[5] N.B. Usmanova, “Approach to the description of the processes of transformation and information exchange in the Infocommunication Network,” Uzbek Journal Problems of Informatics and Energy, no. 1, 2006, 38–42.

[6] N.B. Usmanova, N. Kushakova, “The formation of the functional model of the Infocommunication Network,” The World of Communication, Tashkent, no. 4, 2007, 38–42.

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N.B. Usmanova, N. Kushakova, “This is a way to reduce the delay time of packets of fractal traffic on the basis of multi coordinate associative environment,” Uzbek Journal Problems of Informatics and Energy, no. 3, 2009, 65–70.

N. Usmanova, J. Schiller, Distributed Architecture of New Generation Networks: Exploring the Information Interconnections Issues, Technical Report, Institute of Computer Science, Freie Universität Berlin, 2009.

S.S. Kasymov, N.B. Usmanova, “Architectural and System Components of Distributed Infocommunication Network: Properties of information exchange mechanisms,” Naukovi zapysky UNDIZ, Kiev, vol. 14, no. 2, 2010, 99–104.

N.B. Usmanova, Coordination of Distributed Services in Infocommunication Network Environment, Scientific and Technical Journal TUIT Bulletin, Tashkent, no. 2, 2010, 7–10.

N.B. Usmanova, R. Sultanov, “Background of the investigation of ways of interaction of functional blocks in NGN architecture,” Scientific and Technical Journal TUIT Bulletin, Tashkent, no. 4, 2010, 46–50.

N. Usmanova, “Resource Management Issues in Distributed Environment, International Journal of Ubiquitous Computing and Internationalization, South Korea, vol.3., no. 2, 2011, 25–28.

N.R. Yusupbekov, Sh.M. Gulyamov, S.S. Kasymov, N.B. Usmanova, D.A. Mirzaev, “Problems of Development of Multiagent Systems in Tasks of Control of Technological Processes and Production, Industrial ACS and Controllers, Moscow, no. 3, 2018, 3–8.

Sh.M. Gulyamov, N.B. Usmanova, D.A. Mirzaev, “Modern tendencies of development and perfection of systems of control and control of technological processes and manufactures,” Chemical Technology. Control and Management, no. 4, 2017, 55–58.

Articles

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�������� ������� R����� S������������ ���� ���� ��� ����������� I����������� ��bm��ed: 1�th December 2018; accepted: 28th December 2018

Kamal Amarouche, Houda Benbrahim, Ismail Kassou DOI: 10.14313/JAMRIS_4-2018/28 Abstract: Nowadays, Customer’s product reviews can be widely found on the Web, be it in personal blogs, forums, or ecommerce websites. They contain important products’ informa�on and therefore became a new data source for compe��ve intelligence. �n that account, these reviews need to be analyzed and summarized in order to help the leader of an en�ty (company, brand, etc.) to make appropriate decisions in an e�ec�ve way. �owever, most previous review summariza�on studies focus on summarizing sen�ment distribu�on toward di�erent product features without taking into account that the real advantages and disadvantages of a product clarify over �me.

For this reason, in this work we aim to propose a new system for product opinion summariza�on which depends on the �me when reviews are e�pressed and that covers the sen�ments change about product features. The proposed system firstly, generates a summary based on product features in order to give more accurate and efficient informa�on about di�erent features. �econdly, classify the product based on its features in its appropriate class (good, medium or bad product) using a fuzzy logic system. The e�perimental results demonstrate the e�ec�veness of the proposed system to generate the real image of a product and its features in reviews.

Keywords: Feature e�trac�on, Fuzzy logic, Compe��ve intelligence, �pinion mining, �pinion �ummariza�on, �en�ment analysis, �en�WordNet

�� ��trod�c�o� Competitive Intelligence (CI) is a monitoring process of the competitive environment through which information is gathered, analysed and distributed in order to obtain results that will be carried out gradually for ef�icient support to business activity and help to make quali�ied decisions in relation to its competitors (S� tefá niková and Masa� rova� , 2014 [25]). Traditionally, the capability of CI was greatly restricted to the lack of suf�icient and reliable information sources about competitors (Xu et al., 2011 [28]). But nowadays, many people share opinions on a variety of topics and precisely on products/services on the Internet (e.g. Ecommerce websites, social media..). These opinions present a new information source for CI (Amarouche et al., 2015 [3]). Summarizing these opinions automatically in some concise form could bring enormous bene�its to business. �arious research works (Hu and Liu, 2004 [13]; Zhuang et al., 2006 [32]; Wang et al., 2013 [26]; Kansal and Toshniwal, 2014 [15]; Asgarian 70

Articles

and Kahani, 2014 [5]; Chen et al., 2015 [9]; Kangale et al., 2015 [14]; Zhou et al., 2016 [31]; Yang et al., 2016 [29]; Cho and Kim, 2017 [10]) have been conducted on opinion summarization systems that classify them into those that require a set of features (feature-basedsummarization) and those that do not rely on the presence of features (non-feature-based summarization).

Feature-based-Summarization approaches concentrate on the features (called also aspects) of a speci�ic product to produce a summary. They consist of three distinct steps such as, i) Identifying the important features of the product; ii) Identifying the opinion words and predict their polarities; iii) Generating the actual summary. Contrariwise, systems based on Non-feature-based Summarization produce a generalized summary without considering the features. This kind of summarization is useless in CI because it loses some detailed information, which is important to inform the decision maker of an organization regarding the development and marketing of a product/service. However, summaries based on features provide information about different features and show what customers usually try to search while referring to opinions that rend these types of summaries of great demand in many application domains like: recommender system (Ładyż yń ski and Grzegorzewski, 2014 [17]) and trust reputation (Rahimi and Bakkali, 2015 [23]) with different languages such as English (Kansal and Toshniwal, 2014 [15]), Chinese (Zhou et al., 2016 [31]), Arabic (Abd-Elhamid et al., 2016 [1]) and Italian (Maisto and Pelosi, 2014 [21]).

However, the large availability of reviews shared in English allows researchers to focus on this language in their works. Fig. 1 shows an example of a featurebased summary about a cellphone. The ’battery life’ and ’camera’ are two product features among other features of this product. The positive count opinions of the battery life is 200, and 230 negative ones. While in the case of the ’camera’, there are 200 positive and 30 negative opinions. For each product feature, the number of positive and negative opinions is also provided. With such a summary, we can see how many users have liked or disliked a speci�ic feature.

After usage of the product by customers, their opinion may change on the same features. As indicated in reviews 1 and 2 about ’Samsung note 7’ phone on gsmarena.com. In Review 1, the commentator shows a positive sentiment about feature ’battery’. In contrast to Review 2, we can notice that the sentiment about the same feature has changed over time. To put differently, the advantages and disadvantages of the

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presented in Section 4. Section 5 discusses the experimental results. Finally, the conclusion and proposed future works are given in Section 6 of this paper.

2. Related Works

&ŝŐ͘ ϭ͘ &ĞĂƚƵƌĞͲďĂƐĞĚ ƐƵŵŵĂƌLJ ƵƐŝŶŐ ƉŽƐŝƟǀĞ ĂŶĚ ŶĞŐĂƟǀĞ ƐĐŽƌĞƐ ŽĨ ƐŵĂƌƚƉŚŽŶĞ product around its features will be clari�ied in the reviews according to time and its use. Another factor that has an in�luence on the effectiveness of featurebased summary systems is when the product has been improved on one of its features, the results provided using these systems do not re�lect the real image of the product after its improvement. All this shows the importance of the time axis to express opinions in order to generate useful summaries. However, the most current efforts produced a summary without taking into account the changes of sentiments about features over time. For this reason, an opinion summarization system that depends on time to express reviews is needed to cover these features changes if they exist.

Review 1 ”Slim phone with bigger battery” date: 02 May 2016.

Review 2 ”The phone is not problem the important problem is battery, he needs to create a brand new battery for Samsung galaxy note 7” date: 21 Oct 2016.

The objective of this paper is to propose a product review summary system which takes into considiration the time when reviews were expressed in order to produce an effective output re�lecting the real image of the product in reviews. All in all, we summarize our contributions of this research as:

– We have introduced a new feature-basedsummarization method which generates a summary that depends on time where sentiments are expressed around features.

– We have proposed in this system, a Fuzzy Logic process to assign the product to its corresponding class (good, medium or bad) that is important to being able to compare it with its competitors.

– We have conducted experiments using real data concerning mobile phones and hotels to show that our system does not refer to any domain information.

2

The rest of this paper is structured in the following sections. Section 2 discusses the related works.

Section 3 formally de�ines the problems that will be solved in this work. The proposed system in detail is

This section presents a review of some important previous works performed in the feature-based summarization �ield. Their contributions usually focus on the three major tasks which were mentioned above that are (1) feature identi�ication, (2) featureassociated opinion classi�ication, (3) feature-based summaries generation. As such, the different approaches proposed in these previous works are presented.

One of the earliest works was done by Hu and Liu (2004) [13] that proposed a system to generate feature-based summaries of products’ customer reviews. First, nouns and noun phrases that frequently appeared in reviews were identi�ied as candidate product features. Next, two types of pruning methods were used to remove unlikely features. Then, they extracted the adjectives as opinion words from the sentences that contained one or more features. Based on the orientation of these opinion words and negation words, the orientations of opinion sentences were generated. Finally, a statistical summary that shows features with their corresponding review sentences and their positive and negative numbers is produced.

Liu et al. (2005) [20] proposed a framework called Opinion Observer for analyzing and comparing consumer opinions of competing products which gives the strength and weakness of each product in terms of various product features. The product features were extracted by the association miner. They used adjectives as opinion words and assign prior polarity to these by WordNet exploring method. Zhuang et al. (2006) [32] proposed an approach based on multi-knowledge to summarize movie reviews. First, a keyword list was built to �ind features and opinions. Then, they mined the relations between features and associate opinion words using dependency grammar graph and the building list. Next, the valid feature-opinion pairs were identi�ied by applying these mined relations. Finally, a summary was generated based on the sentences that contained opinions or extracted features. Abulaish et al. (2009) [2] proposed a system that produced a graphical summary about a product features.

Frist, they extracted features and opinion words using a semantic and linguistics analysis of reviews. Then, the polarity of opinions was detected using a lexical resource. Finally, they provided a feature-based summary of reviews in a graphical way.

But during the last few years, this problem has been an attractive research topic. In practice, much work has been devoted to perform this problem as a system.

Wang et al. (2013) [26] proposed a Web-based review summarization system called SumView. They extracted product features and grouped the sentences into feature relevant clusters using a Featurebased weighted Non-Negative Matrix Factorization algorithm. Then, a summary was generated by selecting Articles

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the sentence that had the highest probability in each cluster.

Bafna and Toshniwal (2013) [6] proposed a dynamic system called FBS for feature-based opinion summarization. The product features were identi�ied using a combination of association mining and probabilistic approaches. Next, they extracted the opinions associated to each feature and their polarities were detected based on lexicon dictionaries. Finally, the system generated a feature-based summary by extracting the relevant excerpts according to each feature-opinions pair and placing it into their respective feature-based cluster.

Kansal and Toshniwal (2014) [15] proposed a system called ASAS (Aspect Based Sentiment Analysis and Summarization) that took into account the context dependent opinion words. The product features were extracted using an approach like the one proposed by Bafna and Toshniwal (2013) [6]. They mapped each opinion word to its closest products features, then, applied some natural linguistic rules to �ind the polarity of context dependent words.

Asgarian and Kahani (2014) [5] designed a semantic framework for structured summarization. They extracted the features, analysed the sentiment and then integrated and summarized the opinions using a developed ontology. The framework of their proposed ontology shows the output results of the structured summarization as semantic data.

Chen et al. (2015) [9] proposed a system to handle Cantonese opinion mining. They built an opinion orientation dictionary to identify the orientation of opinion words, then explored some syntax rules to predict the opinion sentences orientation. Finally, they �inished by a summarization which categorized all the related opinion sentences into positive or negative categories, they counted the respective numbers.

Kangale et al. (2015) [14] proposed a featurebased review-summary system. �n the �irst step, the data were passed through opinion spam �ilter, which could detect fake reviews. After that, the features would be identi�ied using association rule mining.

Then, feature trimming was used to trim some of the unwanted features using the kinds of pruning that was described in Hu and Liu (2004) and added others called miscellaneous pruning which improved this task.

They used database-based algorithm to predict the orientation of every opinion word near to a feature. Finally, this system produced a graphical summary.

A system called SSPA (Sentiment Summarization on Product Aspect) was proposed by Li et al. (2015) [19]. SSPA used bootstrapping dependency patterns to extract features and opinion words, then, the system clustered these features into aspects based on word semantic similarities. Next, it disambiguated sentiment orientations of opinion collocations for each aspect. Finally, the system extracted aspect opinion clauses and analysed their sentiment strengths for each aspect.

Zhou et al. (2016) [31] built a feature-based opinion summarization system for Chinese microblogs Articles

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called CMiner. They extracted opinion targets using an unsupervised label propagation algorithm and built a lexicon-based sentiment classi�ier to classify a message into positive, negative or neutral class.

Yang et al. (2016) [29] proposed an approach helpful to the prediction by leveraging aspect analysis of reviews. They extracted features using a proposed model that exploited product category information. Then, a two-layer regression model was built to predict helpfulness scores on all aspects and then ensembled them into �inal helpfulness score.

Cho and Kim (2017) [10] proposed a feature network-driven quadrant mapping to extract the most representative opinions from customer reviews. They found all product features and usersâ&#x20AC;&#x2122; opinion scores for each product reviews using a feature-based summary method as in Hu and Liu (2004). Then, feature relationships within the reviews are discovered from the perspective of co-occurrence and semantic similarity. A paired feature-dictionary feature network was proposed to investigate feature relationship between features that were used to construct a feature network. Finally, a graph was generated by mapping the results of the feature network into a quadrant to summarize customer reviews.

Note that, the contributions of the related works usually focus on the standard sub-tasks, such as features extraction, sentiments identiďż˝ication around these features, polarity detection of these sentiments and summarization styles (Yuan et al., 2015 [30]). However, the effectiveness of summaries also focuses on the good exploitation of reviews to produce an effective summary that describes the real image of the product in the market. For this reason, in this paper, a system which summarizes products customersâ&#x20AC;&#x2122; reviews has been proposed. This system takes into account the time when reviews were expressed to cover the changes of sentiments over time in order to generate a feature-based summarization, and based on it, a product classiďż˝ication will be performed to assign the product to its corresponding class (good, medium or bad).

ĎŻÍ&#x2DC; WĆ&#x152;Ĺ˝Ä?ĹŻÄ&#x17E;Ĺľ &Ĺ˝Ć&#x152;žƾůÄ&#x201A;Ć&#x;ŽŜ

Denote đ?&#x2018;&#x192;đ?&#x2018;&#x192; đ?&#x2018;&#x192; đ?&#x2018;&#x192;đ?&#x2018;&#x192;đ?&#x2018;&#x192;ďż˝ , đ?&#x2018;?đ?&#x2018;?ďż˝ , .., đ?&#x2018;?đ?&#x2018;?ďż˝ } a set of comparative products (e.g. a cellphone), where đ?&#x2018;?đ?&#x2018;?ďż˝ (đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x2013; đ?&#x2018;&#x2013; to đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;) denotes the đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; �� product. đ??šđ??š đ??šđ??šđ??šđ??šďż˝ , đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ , .., đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ } is the set of product features that can be determined by the consumers according to their preferences concerning the product đ?&#x2018;?đ?&#x2018;?ďż˝ , where đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ (đ?&#x2018;&#x2014;đ?&#x2018;&#x2014; đ?&#x2018;&#x2014;đ?&#x2018;&#x2014; to đ?&#x2018;&#x161;đ?&#x2018;&#x161;) denotes the đ?&#x2018;&#x2014;đ?&#x2018;&#x2014;�� product feature. đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; {đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; ďż˝ , đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; ďż˝ , .., đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; ďż˝ } is a vector of number of online reviews about products, where đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; ďż˝ denotes the number of the online reviews concerning product đ?&#x2018;?đ?&#x2018;?ďż˝ . For each product đ?&#x2018;?đ?&#x2018;?ďż˝ â&#x2C6;&#x2C6; đ?&#x2018;&#x192;đ?&#x2018;&#x192;, đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;ďż˝ = {đ?&#x2018;&#x;đ?&#x2018;&#x;�� , đ?&#x2018;&#x;đ?&#x2018;&#x;�� , .., đ?&#x2018;&#x;đ?&#x2018;&#x;�������� } a set of online reviews and a set đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ ={đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ , đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ , .., đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ďż˝ďż˝ďż˝ďż˝ďż˝ďż˝ } of times when these reviews are expressed is deďż˝ined.

After de�ining the set notations that will be used throughout this paper, the problems are de�ined as follows:

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Journal JournalofofAutomation, Automation,Mobile MobileRobotics Robotics&&Intelligent Intelligent Systems Systems

Problem 1 (feature-based summary) Given the sets of online Reviews đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;ďż˝ and time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ concerning a product đ?&#x2018;?đ?&#x2018;?ďż˝ â&#x2C6;&#x2C6; đ?&#x2018;&#x192;đ?&#x2018;&#x192; described by a set of features đ??šđ??š, our goal is to generate a summary that includes two representative values concerning the positive and negative sentiments, about each feature by taking into account the time (identiďż˝ied from đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ ) when they were expressed.

We provide more perspectives of Problem 1 using the reviews 1 and 2 that are expressed about the feature â&#x20AC;&#x2122;batteryâ&#x20AC;&#x2122; of Samsung note 7 cellphone. Note that in Review 1, a positive sentiment was expressed about this feature in â&#x20AC;&#x2122;02 May 2016â&#x20AC;&#x2122;. Contrariwise to Review 2 which contains a negative sentiment for the same feature in â&#x20AC;&#x2122;21 Oct 2016â&#x20AC;&#x2122;. Since this product has experienced a problem in the battery, it is obvious that the large number of positive sentiments generated before detecting that problem by the consumer, inďż˝luences this featureâ&#x20AC;&#x2122;s values. Another example is a product that has experienced improvements in some features will still be inďż˝luenced by the negative sentiments which are expressed before their improvement. To capture the changing of sentiments concerning a speciďż˝ic feature over time, our proposed method to solve Problem 1 is to take into account the polarity of sentiments which are associated to the feature, and the time when they are expressed, to generate a feature-based-summary vector of product đ?&#x2018;?đ?&#x2018;?ďż˝ . The proposed method at this stage produces a feature-based-value at each đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ (such that đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ â&#x2C6;&#x2C6; đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ ) for product đ?&#x2018;?đ?&#x2018;?ďż˝ :It can also show all the changing sentiments about a given feature that helps the manufacturer to have an idea about the quality of this product and compare it with his competitors.

Problem 2 (aggregation of feature-based-summary) Consider the output produced by feature-basedsummary step, for each product đ?&#x2018;?đ?&#x2018;?ďż˝ of đ?&#x2018;&#x192;đ?&#x2018;&#x192;, the main goal here is to summarize the values generated in a single value to take a decision about this product (good, medium or bad product) and compare it with competitors (the other products of the set đ?&#x2018;&#x192;đ?&#x2018;&#x192;). This summarization will be realized via an aggregation of the values generated around the features to get a global score value of polarities (positive and negative) about product đ?&#x2018;?đ?&#x2018;?ďż˝ . The proposed process at this stage, solves the problem of assigning a decision to products that have score values of polarities close together using a fuzzy logic technique.

4. The Proposed System

4

This section discusses the design of the proposed system (Fig. 2) that takes as input a set of crawled reviews for a particular product đ?&#x2018;?đ?&#x2018;?ďż˝ and competing products (đ?&#x2018;?đ?&#x2018;?ďż˝ ,..,đ?&#x2018;?đ?&#x2018;?ďż˝ ). These competing products are selected by a supervisor who takes into account those belonging to the same familly of đ?&#x2018;?đ?&#x2018;?ďż˝ . After preprocessing these reviews, the system extracts automatically product features in the ďż˝irst step, then, identiďż˝ied their associated sentiments of them, and generates a polarity (positive, negative) to each one in the second step.

Afterwards, we produce a summary for each product

VOLUME 12, 12, N° 4N° 4 2018 VOLUME 2018

based on the features. Finally, we classify each product in its appropriate class (bad, medium or good).

&Ĺ?Ĺ?Í&#x2DC; ĎŽÍ&#x2DC; WĆ&#x152;Ĺ˝Ć&#x2030;Ĺ˝Ć?Ä&#x17E;Ä&#x161; Ć?ƾžžÄ&#x201A;Ć&#x152;Ĺ?Ç&#x152;Ä&#x201A;Ć&#x;ŽŜ Ć?Ç&#x2021;Ć?Ć&#x161;Ä&#x17E;Ĺľ 4.1. Preprocessing After collecting reviews from different sources, they must be pre-processed. Frequently, these reviews contain several syntactic features that might not be useful, thatâ&#x20AC;&#x2122;s why, we will clean them from the data (delete @, username, digits....). After that, the reviews written in English will be selected after detecting the language (Shuyo, 2014 [24]) for each one, because our system performs only on English opinions. Then, a web service1 will be used to detect and correct the spelling errors in these reviews. Finally, Part-OfSpeech Tagger (POS tagger2 ) will be applied in order to associate each word with its grammatical function.

The main goal of using this tagger is to extract nouns and convert plural to singular nouns that are important to increase their weight in order to facilitate the product feature identi�ication step (e.g. batteries to battery in phone reviews), also to produce a useful summary about products.

4.2. Prod�ct �e�t�re iden��c��on After the preprocessing of reviews, we, then, extract candidate product features from reviews using an algorithm proposed by (Amarouche et al., 2016 [4]) which builds a list that contains nouns composed of one or multiple words extracted from reviews.

The main goal of this step is to identify product features from this list. This identi�ication is based on Time Weighting Term Frequency Inverse Document Frequency (TW-TFIDF) method (Amarouche et al., 2016 [4]). This method combines Time Weighting (TW) that is based on the time when opinions are expressed and Articles

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

VOLUME VOLUME 12,

N°44 2018 2018 N°

Term Frequency Inverse Document Frequency (TFIDF) that exploits the frequency of candidate features appearing in reviews. Then, we will select the top n of these features in order to generate a list constituting them. Finally, a supervisor veriďż˝ies the product features list in order to validate them. Ď°Í&#x2DC;ĎŻÍ&#x2DC; Ć?Ć?Ĺ˝Ä?Ĺ?Ä&#x201A;Ć&#x;ĹśĹ? Ć&#x2030;Ć&#x152;Ĺ˝Ä&#x161;ĆľÄ?Ć&#x161; ĨÄ&#x17E;Ä&#x201A;Ć&#x161;ĆľĆ&#x152;Ä&#x17E;Í&#x2022; Ć?Ä&#x17E;ĹśĆ&#x;ĹľÄ&#x17E;ĹśĆ&#x161; Ä&#x201A;ĹśÄ&#x161; Ć&#x;ĹľÄ&#x17E;

To identify feature-sentiment-time triple for each product, reviews are collected from data sources and product features are used as input in this step. Then, we will select features and their associated sentiment terms that appear in reviews. Finally, we will build feature-sentiment-time triple where time is when a review is expressed.

Finding out how sentiments are expressed about these features is an important task in this step, we will analyze dependency relations in reviews using the Stanford CoreNLP3 that identi�ies a term�s role and dependency relations in a review. We may �ind many different dependency relations in reviews, but only some of them are helpful to this task. We will consider four major typed dependencies as in Wu et al. study (2009) [27]. It includes nsubj (nominal subject), amod (adjectival modi�ier), rcmod (relative clause modi�ier), dobj (direct object) in the feature-sentimenttime extraction step. The four dependencies (mentioned above) are used to identify the feature-sentiment pairs and we will add neg (negation) to the list of dependencies which is important to check because the meaning will change if a negation is associated to a sentiment.

To associate sentiments to features in sentences that contain just one feature, we have simply to respect these four dependency relations. But in reality, we may ďż˝ind some sentences that contain more than one feature. For instance, the following review contains two features: â&#x20AC;?Signal strength will affect the battery lifeâ&#x20AC;?. After applying the parsing to this sentence, we can identify two important types of dependence nsubj (Signal strength, affect) and dobj (battery life, affect) which rely on two features with one sentiment.

This poses a problem for associating sentiments to features in this case. For this reason, we will use some rules (Chatterji et al., 2017 [8]) to associate sentiment with its corresponding feature in a sentence. Then, we will extract a negation that associates to the sentiment if it exists that is identi�ied with neg (negation) type.

Algorithm 1 summarizes the main steps of extracting feature-polarity-time triplet. It takes as input the set of features and reviews about product đ?&#x2018;?đ?&#x2018;?ďż˝ , then, returns a set of polarity-time pair corresponding to each feature đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ . When each review đ?&#x2018;&#x;đ?&#x2018;&#x;�� has been split to a set of sentences and parsed thereafter, we will be extracting sentiments associated to each feature đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ using the rules (Chatterji et al., 2017 [8]). Then, the polarity is generated based on this sentiment and negation if it exists.

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Articles

To generate the polarity for each sentiment, a SentiWordNet4 (SWN) is used to assign sentiment scores for English synsets (Hassan Khan et al., 2016 [16]).

Three sentiment scores (positivity, negativity and objectivity) are assigned to each synset in SWN. These scores are assigned by a committee of classi�iers (Esuli and Sebastiani, 2006 [12]) for classi�ication of each sysnet that has a range from 0.0 to 1.0 and they always sum up to 1. The following tab. 1 describes SWN structure and sentiment scores associated to their entries.

Headers of the table columns have the following meanings: â&#x20AC;&#x201C; POS: This can take four possible values: a â&#x2020;Ś adjective; v â&#x2020;Ś verb; r â&#x2020;Ś adverb; n â&#x2020;Ś noun. â&#x20AC;&#x201C; Offset: Numerical ID which is associated with part of speech uniquely identiďż˝ies a synset in the database. â&#x20AC;&#x201C; PosScore: Positive score.

â&#x20AC;&#x201C; NegScore: Negative score.

â&#x20AC;&#x201C; SysnsetTerms: List of all terms included in the synset.

The polarity classiďż˝ication of the sentiment is based on the difference value between its PosScore and NegScore. So, if this value is greater than zero, it will be classiďż˝ied as positive, whereas if it will be less than zero, it is classiďż˝ied as negative. Ď°Í&#x2DC;Ď°Í&#x2DC; &Ä&#x17E;Ä&#x201A;Ć&#x161;ĆľĆ&#x152;Ä&#x17E;ͲÄ?Ä&#x201A;Ć?Ä&#x17E;Ä&#x161; Ć?ƾžžÄ&#x201A;Ć&#x152;Ĺ?Ç&#x152;Ä&#x201A;Ć&#x;ŽŜ

After generating the set of polarity and associated time {(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;?đ?&#x2018;?�� ), (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;?đ?&#x2018;?�� ) ,..., (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;?đ?&#x2018;?�������� )} for each product feature đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ (where the couple đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;? đ?&#x2018;?đ?&#x2018;?�� is composed of polarity which is positive or negative, and time đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ when this polarity is identiďż˝ied) on a product đ?&#x2018;?đ?&#x2018;?ďż˝ , the main goal of this step is to generate a percentage for each polarity (positive and negative) around each feature đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ .

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Journal JournalofofAutomation, Automation,Mobile MobileRobotics Robotics&&Intelligent Intelligent Systems Systems

VOLUME 12, 12, N° 4N° 4 2018 VOLUME 2018

Ta�le �. �en��ord�et frag�ent POS

Offset

PosScore

NegScore

a

01150475

0

0.625

a n

00005839 03931044

0.5 0

0.125 0

v

01824736

0.125

0

living#3 picture#1 image#3 ikon#1 icon#2

Formula 1 calculates this percentage for the set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ which depends, at the same time, on the number of polarities and time đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ when they are identiďż˝ied.

On the other hand, it produces two values that are: ďż˝ ďż˝ đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?��� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) and đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?��� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;) which represent percentage values that summarize respectively the positive and negative polarities expressed around feature đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ for the set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ on a product đ?&#x2018;?đ?&#x2018;?ďż˝ . This percentage introduces a weighting function đ?&#x153;&#x152;đ?&#x153;&#x152;��� (formula 2) to give the importance to the polarities that are identiďż˝ied at đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ compared to others that are expressed before this time. To put differently, the latest polarities that are identiďż˝ied around each đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ have a great importance compared to the oldest.

Knowing that the set đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ is in order from the oldest đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ to the latest đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ďż˝ďż˝ďż˝ďż˝ďż˝ďż˝ (some elements of đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ are repeated because we can ďż˝ind several reviews that are expressed at the same time), so before calculating this function for each element of đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ , the ďż˝irst step is to quantify each one from it to give it as input to this function. This quantiďż˝ication is based on a chosen step (đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;, đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤đ?&#x2018;¤, 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;đ?&#x2018;&#x161;đ?&#x2018;&#x161;) which depends on the đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? type. Otherwise, the sentiments expressed around the features can change daily for a speciďż˝ic type of products unlike for others that might change weekly or monthly.

An advantage which can be seen from Fig. 3 of this function is the đ?&#x203A;žđ?&#x203A;ž value that is affected by the speed convergence of this function. In other words, its speed increases when the value of đ?&#x203A;žđ?&#x203A;ž gets closer to 0 therefore it is important to assign good weights to sentiments polarities. ďż˝

đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?��� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) =

â&#x2C6;&#x2018;��� ��� đ?&#x153;&#x152;đ?&#x153;&#x152;��� Ă&#x2014; đ?&#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;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? â&#x2C6;&#x2018;��� ��� đ?&#x153;&#x152;đ?&#x153;&#x152;��� Ă&#x2014; đ?&#x2018; đ?&#x2018; ��� ďż˝

đ?&#x153;&#x152;đ?&#x153;&#x152;��� = đ?&#x203A;žđ?&#x203A;žďż˝ďż˝ďż˝ďż˝

where: ďż˝ : is the quantiďż˝ied value of the time đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ . â&#x20AC;&#x201C; đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝

â&#x20AC;&#x201C; đ?&#x203A;žđ?&#x203A;ž: is a number in the range 0< đ?&#x203A;žđ?&#x203A;ž đ?&#x203A;ž1.

6

SynsetTerms#rank sorry#1 regretful#1 bad#5

wish#2 care#3

like#1

Gloss feeling or expressing regret or sorrow or a sense of loss over something done or undone (informal) absolute a visual representation (of an object or scene or person or abstraction) produced on a surface prefer or wish to do something

â&#x20AC;&#x201C; đ?&#x2018; đ?&#x2018; ��� : is the total number of polarities identiďż˝ied around đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ at đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ .

Fig. 3. The inďŹ&#x201A;uence of đ?&#x203A;žđ?&#x203A;ž value on speed convergence of the ďż˝eighďż˝ng funcďż˝on đ?&#x153;&#x152;đ?&#x153;&#x152;���

Note that, the set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ will be divided into ranges of times đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ so that we can have in each range (đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;đ?&#x2018;&#x;), a set of đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ (Fig. 4). The set of đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ can be deďż˝ined based on a step duration. For example, if we choose the 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; as a step, automatically each đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ that belongs to the same month will be grouped into the same range.

However, to show the impact of time in the variation results, we must calculate the percentage from the start to each range, For example, to calculate the percentage in the range l, we need to use in the calculation process all đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ of the previous ranges including (ďż˝) the range l as a new deďż˝ined set mentioned as đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ (Fig. 4).

(1) (2)

â&#x20AC;&#x201C; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;��� : is the total number of polarities identiďż˝ied around đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ that has same polarity (positive or negative) at đ?&#x2018;Ąđ?&#x2018;Ąďż˝ďż˝ .

Fig. 4. The division of the set into ranges 4.5. Classifying product After obtaining the positive and negative percentage scores for each product feature đ?&#x2018;&#x201C;đ?&#x2018;&#x201C;ďż˝ on a product Articles

75

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

VOLUME VOLUME 12, 12,

(ďż˝)

đ?&#x2018;?đ?&#x2018;?ďż˝ over time (for each set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ ) as demonstrated in the above section, the main goal of this step is to take a decision that the product đ?&#x2018;?đ?&#x2018;?ďż˝ is bad, medium or good. To put differently, we assign the product to its appropriate class (good, medium or bad) for each set (ďż˝) of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ to show its variation over time and compare it with competitors (the other products of the set P).

For this reason, the ďż˝irst step is to aggregate the percentage scores of the features selected by a supervisor of the system from the set of feature F using formula 3. In the normal case, we give the same weight to all product features (đ?&#x2018;¤đ?&#x2018;¤ďż˝ = 1/đ?&#x2018;&#x161;đ?&#x2018;&#x161; ) to calculate this aggregation. Also, the proposed system allows the supervisor to modify these weights in order to give more priority to some features compared to others. Then, we calculate the difference between the positive and negative values of this aggre(ďż˝)

ďż˝ gation (đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;���

(ďż˝)

ďż˝ (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) and đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;)) (ďż˝) time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ using formula 4 to clas-

for each set of sify the product đ?&#x2018;?đ?&#x2018;?ďż˝ (good, medium or bad). let us explain this with an example. When calculating this aggregation for both positive and negative polarities. If ďż˝

(ďż˝)

ďż˝

(ďż˝)

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) = 0.9 and đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;) = 0.1, the product đ?&#x2018;?đ?&#x2018;?ďż˝ can be classiďż˝ied in good product (ďż˝) class for the set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ ). ďż˝

(ďż˝)

ďż˝

(ďż˝)

ďż˝

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) = ďż˝ đ?&#x2018;¤đ?&#x2018;¤ďż˝ Ă&#x2014; đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?��� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) ���

(ďż˝)

(ďż˝)

ďż˝

(3)

(ďż˝)

ďż˝

ďż˝

ďż˝ ďż˝ (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) â&#x2C6;&#x2019; đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;) đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� = đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;�� (4)

However, a problem will arise when the values ďż˝

(ďż˝)

ďż˝

(ďż˝)

of đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) and đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;��� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;) are close together,in this case, it is not always right to assign the product to the medium product class (e.g. the (���) product đ?&#x2018;?đ?&#x2018;?ďż˝ was bad for the set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ ). To put differently, the difference between the aggregation of (ďż˝) (���) the same polarity for both sets đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ and đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ (formula 5) is important to classify each product that have this problem. So, we need a system that takes into account these parameters as input, consequently a â&#x20AC;&#x2122;badâ&#x20AC;&#x2122;, â&#x20AC;&#x2DC;mediumâ&#x20AC;&#x2122; or â&#x20AC;&#x2122;goodâ&#x20AC;&#x2122; product will be generated as output. (ďż˝)

(���)

�� ��� đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� (ďż˝) �� ��

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) =

ďż˝

(���)

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) â&#x2C6;&#x2019; đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;���

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?)

(5)

In reality, we generally do not use crisp numeric values to assign a product to its appropriate class for (ďż˝) the set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ , but we use linguistic terms like good or bad. Therefore, we convert the numeric values ďż˝

76

(ďż˝)

ďż˝

(ďż˝)

��

(���)

ďż˝ ďż˝ ďż˝ which are đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� , and đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;������

Articles

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?)

ďż˝

(ďż˝)

��

N°44 2018 2018 N°

(���)

ďż˝ ďż˝ (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;))to linguistic terms and (or đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� use them in this classiďż˝ication.

The proposed process employs fuzzy logic to do these conversions and calculate a comprehensive classifying product score for every product đ?&#x2018;?đ?&#x2018;?ďż˝ . This process illustrated in Fig. 5 consists of several parts that will be explained in the following subsections:

���� �� ����� �o��c �rocess �se� �or c��c������ �ro��c� scores

����i�c���n In a fuzzy inference system, we have a set of crisp input variables which should be proces�

(ďż˝)

ďż˝

(ďż˝)

��

(���)

ďż˝ ďż˝ ďż˝ (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) sed that are đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� , and đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;������ in our system. Corresponding to each input value, we usually deďż˝ine a linguistic variable with the same name as input variables. Each linguistic variable, that is represented by a function called membership function (denoted by đ?&#x153;&#x2021;đ?&#x153;&#x2021;), contains a set of linguistic values corresponding to each input variable. The output of a membership function is a real number in the range [0, 1] which reďż˝lects the level of membership of an input variable to a linguistic variable. The fuzziďż˝ier uses these membership functions to convert crisp input variables to fuzzy linguistic variables. In the proposed process, we use a trapezoidal fuzzy set that demonstrates its effectiveness in many works in the literature like (Boltzheim et al., 2001 [7]; Daneshvar, 2011 [11]).

In our process, two variables have been

used

as

(ďż˝)

input

(���)

�� ��� đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� ��

which

are

ďż˝

(ďż˝)

ďż˝ đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� ,

and

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) , and one output variable which is classifying product that should be (ďż˝) calculated for each set of time đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;ďż˝ . The membership functions for both input variables (normalized between 0 and 1) is depicted in Fig. 6 and 7, and the membership function of classifying product as the output function is deďż˝ined in Fig. ďż˝.

Inference engine The main goal of the inference engine is to convert fuzzy inputs to fuzzy output. This conversion is done using a set of IF-THEN type rules called fuzzy rules. A fuzzy rule speci�ies the condition in which a set of fuzzy inputs can be mapped to an output fuzzy variable. Since we have 2 input variables and each of which can have 3 different values. Each combination can potentially represent a particular level of product ranking.

In order to arrive to classifying a product, an inference engine should evaluate all fuzzy rules and then

7

Journal JournalofofAutomation, Automation,Mobile MobileRobotics Robotics&&Intelligent Intelligent Systems Systems

VOLUME 12, 12, N° 4N° 4 2018 VOLUME 2018

Medium;

ďż˝

�efu��i��a�on Based on different values of input fuzzy variables, several fuzzy rules might be activated in the same time and the result is a set of linguistic output values which are included in output with different levels of membership. In this step, we employ the Center-of-Gravity (CoG) method that is the most popular method and is also quick and accurate in computations (Leekwijck et al., 1999 [18]). The �inal value of classifying product is calculated using this COG approach that produces a real number between 0 and 1.

The values close to 1 represent a good product based on our designed model. Low values for classifying product show that it is a bad product.

(ďż˝)

ďż˝ Fig. 6. đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� ��������iďż˝ �������

5. Experiment

ďż˝

(ďż˝)

��

(���)

ďż˝ ďż˝ Fig. 7. đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� ��

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) ��������iďż˝ �������

This section evaluates the proposed system which generates summaries from a data set that contains reviews about the same type of products. The procedure for our implementation is as follows: After crawling reviews from the source, they must be pre-processed by selecting only the reviews written in English, then, the system detects and corrects the spelling errors. After that, POS tagger tags all the words in each review to their appropriate part of speech tag in order to identify word nouns that are important to the next step.

After that, a list containing candidate features is being built, then, potential product features will be identiďż˝ied from this list using TW-TFIďż˝F (Amarouche et al., 2016 [4]). Lastly, in this step, a list of product features is built which is validated by a supervisor. Next step is, the sentiment classiďż˝ication that contains two substeps: 1) associate product features with their corresponding sentiments and time when each one is expressed, 2) determinate the polarity for each sentiment using sentiWordNet. Finally, our system produces a summary based on the features for each product đ?&#x2018;?đ?&#x2018;?ďż˝ , then, assign each one to its corresponding class (bad, medium or good product) over time.

5.�. �ata sets des�rip�on

Fig. �. �����i��i�g ������� ������ ��������i� ������� compose the results of these evaluations to de�ine output zones for the output variable. An example of some rules used in this step: - RULE

ďż˝

1:

(ďż˝)

��

IF

(���)

ďż˝

(ďż˝)

ďż˝

(ďż˝)

ďż˝

(ďż˝)

ďż˝ đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� ��

IS

Low

AND

ďż˝ ďż˝ (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) is Decreased THEN đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� �� Product IS Bad;

- RULE

2:

- RULE

3:

IF

(�) (���) �� ��� ������

ďż˝ đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� ��

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018; Product IS Good;

8

(ďż˝)

(���)

�� ��� đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� ��

IF

is

ďż˝ đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;���� ��

IS

Low

AND

Increased

THEN

IS

Low

AND

(đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?) is Low THEN Product IS

The proposed system is experimented with user reviews on two data sets. The �irst is about four cellphone products that were collected from gsmarena5 .

The second data set contains four hotels reviews that were crawled from Tripadvisor6 . The details of these data sets are shown in Tab. 2 and 3.

5.2. Experiments on feature-based opinion summaries

In the literature, all proposed works ignore the evolution of feature-based summary over time, however, to compare our method with the others we donâ&#x20AC;&#x2122;t have a direct comparison criterion. So, to show the performance of the proposed method, we need to show the impact of taking into account time axis when reviews are expressed compared with the standards methods.

Fig. 9 (a and b) shows the experimental results of feature-based summaries using the proposed approach on the four cellphones. For each cellphone, �ive Articles

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

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ďż˝able ďż˝. ďż˝ata descripďż˝on of cellphone reďż˝iews Product Product (P) Description đ?&#x2018;?đ?&#x2018;?ďż˝ Sony Xperia XA Ultra đ?&#x2018;?đ?&#x2018;?ďż˝ OnePlus 3

Number of reviews

Interval of extraction

1210

17 May 2016 to 4 Jan 2017

đ?&#x2018;?đ?&#x2018;?ďż˝

904

đ?&#x2018;?đ?&#x2018;?ďż˝

Samsung Galaxy Note7 Apple iPhone 7

1681 1679

ďż˝able ďż˝. ďż˝ata descripďż˝on of hotel reďż˝iews Hotel (H) â&#x201E;&#x17D;ďż˝ â&#x201E;&#x17D;ďż˝ â&#x201E;&#x17D;ďż˝ â&#x201E;&#x17D;ďż˝

78

Location San Francisco, California Barcelona, Catalonia Hong Kong New York

Number of reviews 324 244 249 263

25 Mar 2016 to 5 Jan 2017 2 May 2016 to 15 Dec 2016 26 Apr 2016 to 5 Jan 2017 Interval of extraction 21 Nov 2006 to 7 Jan 2009 4 Nov 2004 to 5 Jan 2009 5 Jun 2005 to 7 Jan 2009 16 Feb 2006 to 6 Jan 2009

product features are used as important ďż˝ields to describe the products (such as đ?&#x203A;žđ?&#x203A;ž đ?&#x203A;ž đ?&#x203A;žđ?&#x203A;žđ?&#x203A;ž).

The comparison between the proposed method in Fig. 9 (a and b) shows that the results generated by the one where the chosen step is 1 week gives the real image of product features in the reviews compared to the other (Fig. 9 (b)) that exploits the step (1 month). To illustrate this, we take the example of galaxy note 7 cellphone which is produced by Samsung that encounters a big problem in the feature â&#x20AC;&#x2122;batteryâ&#x20AC;&#x2122;. So, this problem was easy detected in the proposed approach where the step chosen is 1 week ( đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?������� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? and đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?������� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;), contrariwise, it is not detected by the proposed method using the step 1 month ( đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?������� (đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? and đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?������� (đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;), which makes that the choice of the step (day, week, month ..) is very important to produce an effective summary depending on the domain.

Using the same steps of the proposed method to generate feature-based summaries and without implementing the times where reviews are expressed, Fig. 10 shows the results obtained about the same �ive product features. The way to generate this summary showed in Fig. 10 is like the approaches used in several works such as (Hu and Liu, 2004 [13]), (Liu et al., 2005 [20]) and (Abulaish et al., 2009 [2]) after its normalization between -1 and 1 in order to compare it with the proposed method. From Fig. 10, we can �ind that the results generated by the standard method Articles

(a) step chosen is 1 week

(b) step chosen is 1 month

Fig. 9. Bar chart showing the proposed feature-based summaries corresponds to the cellphone corpus about feature â&#x20AC;&#x2122;batteryâ&#x20AC;&#x2122; of Samsung galaxy note 7 is still a good feature (the positive score is 0.6408.. and negative score is 0.3591..) even if the product has experienced a problem in this feature. However, the large number of positive sentiments about it which were shared at the beginning inďż˝luence on the results generated by the standard approach after the detection of the problem by consumers about this feature.

To demonstrate the effectiveness of the proposed approach to detect this problem in the feature â&#x20AC;&#x2122;batteryâ&#x20AC;&#x2122; of Samsung galaxy note 7, Fig. 11 shows a comparison of positive scores between the proposed approach

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does not exploit times axis produces a summary close to reality just for features that do not experience changes in sentiments over time. On the other hand, the other features which have experienced changes after detecting a problem or improvement, it is dif�icult for this type of summaries to produce one which re�lects the real state of these features after changing the sentiments. However, the proposed approach generates a summary that takes into account the change of sentiments about features over time if it exists.

Fig. 10. Bar chart showing the feature-based summaries approach without integraďż˝ng ďż˝me when reviews are expressed, corresponds to the cellphone corpus and standard approach over time. By choosing week as a step in the weighting function of the proposed approach, we can detect the problem of feature â&#x20AC;&#x2122;batteryâ&#x20AC;&#x2122; effectively (after October 2016) due to this function which gives the importance to the reviews week after the other. On the other hand, the curve of the proposed method such as the chosen step is 1 month is close to the standard method which always makes the choice of a step as an important role for the product domain where we are operating.

Fig. 11. � comparison between the varia�on of posi�ve score of the proposed and standard methods about feature �ba�er�� of ��amsung galax� note �� over �me

10

Fig. 12 shows an example of feature-based summaries about ďż˝ive features of hotels data set using the proposed approach (such as step=1 month and đ?&#x203A;žđ?&#x203A;ž đ?&#x203A;ž đ?&#x203A;žđ?&#x203A;žđ?&#x203A;ž), which shows that the proposed system is domain independent. By comparing the experimental results in Fig. 12 and 1ďż˝, we ďż˝ind that the standard summary that

Fig. 12. Bar chart showing the proposed feature-based summaries corresponds to the hotel corpus

Fig. 13. Bar chart showing the feature-based summaries approach without integraďż˝ng ďż˝me when reviews are expressed, corresponds to the hotel corpu By comparing this variation of the feature â&#x20AC;&#x2122;serviceâ&#x20AC;&#x2122; which has experienced a change over time using both approaches, we can notice, the proposed one takes Articles

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

into consideration this change to produce its positive score ((1) an increase between June 2007 and January 2008 and between June 2008 and January 2009; and (2) a decrease between January and June 2008).

Contrariwise, this change is not taken into account in the standard approach. For the feature ’room’ that has an output (negative or positive score) close together using both methods as indicated in Fig. 12 and 13, we �ind that the proposed method detects a change of sentiments in its time interval (Fig. 14) that focuses on an increase of positive sentiment between June 2006 and January 2008, by cons in the �irst six months of 2008 and the beginning of the year 2009, this proposed method knows an increase of negative scores that the standard approach do not do it. This means that, even if the output of both methods is close, the proposed method detects all the changes over time by exploiting this time axis to produce feature-based summary. However, the sentiments expressed about the features always have an in�luence on the standard approach output with the same way which does not allow detecting a change of feelings if exist.

�i�� �4� � comparison between the varia�on of posi�ve score of the proposed and standard method about two features ’room’ and ’service’ of hotel 4 reviews over �me 5.3. Experiments on classifying product

80

Fig. 15 and 16 show the variation of classifying cellphones and hotels data sets over time using the fuzzy logic system. This variation is to know the position of these data sets (good, medium or bad) over time. For example, Eig 15 shows that, the position of product ’note 7’ which faces a problem in its feature ’battery’ will be positioned in the ’bad’ and ’medium’ class over time. Based on its variation, we can take a decision that it is a ’bad’ product. Also, the score produced by the system allows to compare a speci�ic product with its competitors that is an important step in CI. Fig. 16, shows the variation of each hotel position over time that allows to know the performance of each one based on several competitor attributes which are aggregated including room, service, breakfast, bar and location. According to the �indings of �ohammed et al. (2014) [22], several competitor attributes are conArticles

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sidered by hotel managers, including proximity of location, room rate similarity, product and service offerings, service quality delivery, and sales channels. For this reason, our system gives to the supervisor the permission to modify the list of these attributes in order to classify the hotel according to its vision of the attributes that in�luence the performance of the hotel.

�i�� ��� �he varia�on of classif�in� cellphone over �me

�i�� ��� �he varia�on of classif�in� hotels over �me

6. Conclusion In this study, we proposed a product opinion summarization framework, comprising two main components: feature-based opinion summary, and product classi�ication. These components have an important role to product manufacturers according to their need like improving their product or launching a new one.

After extracting product features in a list and select the top m from it that is validated by a supervisor, the proposed feature-based summary approach produces a summary based on the times where the reviews are expressed. Existing related methods, such as (Hu and Liu, 2004 [13]), (Liu et al., 2005 [20]) and (Abulaish et al., 2009 [2]), generate summaries without introducing the time axis in their methods. However, the experimental part demonstrates the robustness of the proposed approach to take into account the change of

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Journal JournalofofAutomation, Automation,Mobile MobileRobotics Robotics&&Intelligent Intelligent Systems Systems

sentiments about features over time if it exists. For the product classi�ication, we employ the fuzzy logic technique to rank each product to its appropriate class (bad, medium or good). Then, we compare the products with their competitors based on this classi�ication.

For future work, the stage of selecting the competing products in the proposed system that belongs to the same range of a particular product is performed by a supervisor (manually). For this reason, a study will be conducted to detect these competing products automatically. On the other hand, we have seen that our data sets contain an important number of sentences that have no opinions. These sentences need to be �iltered since they introduce noise to the proposed system process.

Notes

1 http://wsf.cdyne.com/SpellChecker/check.asmx 2 http://nlp.stanford.edu/software/tagger.shtml

3 http://nlp.stanford.edu/software/corenlp.shtml 4 http://sentiwordnet.isti.cnr.it/ 5 www.gsmarena.com

6 www.tripadvisor.com

AUTHORS

Kamal Amarouche∗ – ALBIRONI Research Team, ENSIAS, Mohammed 5 University, Rabat, Morocco, e-mail: amarouchekamal@gmail.com.

Houda Benbrahim – ALBIRONI Research Team, ENSIAS, Mohammed 5 University, Rabat, Morocco, e-mail: houda.benbrahim@um5.ac.ma.

Ismail Kassou – ALBIRONI Research Team, ENSIAS, Mohammed 5 University, Rabat, Morocco, e-mail: ismail.kassou@um5.ac.ma. ∗

Corresponding author

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Algorithms of Sustainable Estimation of Unknown Input Signals in Control Systems Submitted: 10th July 2018; accepted 29th November 2018

Nadirbek Yusupbekov, Husan Igamberdiev, Uktam Mamirov

DOI: 10.14313/JAMRIS_4-2018/29 Abstract: The problem of estimating unknown input effects in control systems based on the methods of the theory of optimal dynamic filtering and the principle of expansion of mathematical models is considered. Equations of dynamics and observations of an extended dynamical system are obtained. Algorithms for estimating input signals based on regularization and singular expansion methods are given. The above estimation algorithms provide a certain roughness of the filter parameters to various violations of the conditions of model problems, i.e. are not very sensitive to changes in the a priori data.

Keywords: control system, state, signal reconstruction, regularization, regularization parameter

1. Introduction When constructing and implementing automatic control systems, the problem of statistical signal reconstruction is extremely important, since at these stages of system development reliable statistical characteristics of disturbances are usually absent.

The main requirement for signal restoration is the requirement to obtain qualitative estimates of uncontrolled signals in accordance with the chosen optimality criterion. The processing of measurement results of experimental data under real operating conditions of automatic systems can be performed on the basis of statistical signal reconstruction, and signal recovery algorithms can conveniently be synthesized on the basis of optimal filtering methods [1–7].

In the theory of optimal Kalman filtration, a Gaussian Markov random process is generated, as is well known, at the output of a dynamical system whose input receives an independent Gaussian random process of white noise type. In this case, the measurement interference is also a Gaussian random process of white noise type, the influence of which is taken into account in the mathematical model of the measuring system [1, 2].

Descriptions of object noise and interference measurements by time-correlated random Gaussian Markov processes violate the conditions for the general formulation of the classical optimal Kalman filtering problem.

However, in these cases, the Kalman filtration method can also be used, since there are methods for generalizing the filtration method to the cases under consider-

ation [1–3]. This is achieved by using the principle of expanding the mathematical models of the original dynamical system [3]. In [7], a general formalized scheme for constructing regularized algorithms for restoring input effects in control systems based on the principle of model expansion is presented.

2. Formulation of the Problem

Consider a linear dynamical system xi+1 = Axi + fi, x i0 = x0, i = 0, 1, ...,

(1)

the input effect fi of which is the output of the shaping filter, the input of which receives white noise wi fi = D1ξi ,

(2)

ξi +1 =+ D2ξi D3wi , ξi0 = ξ0 , (3)

where the xi – n1-dimensional state vector of the initial system, the fi – q-dimensional vector of statistical input actions, A – the matrix of the corresponding dimension, the ξi – n2-dimensional state vector of the additional linear dynamical system; wi – µ-dimensional noise vector of a white noise type with characteristics E [wi ] = 0 , E wi wkT  = Qi δ ik ; D1 , D2 , D3 – matrices of corresponding dimensions.

We assume that observations of the state of system (1) are carried out in accordance with equations

= z1,i H1 x i + v1,i ,

ξi +1 =+ D2ξi D3wi , ξi = ξ0 , 0

(4)

where z1,i and z2,i – are respectively m1- and m2-dimensional observation vectors characterizing the behavior of the initial dynamical system, v1,i and v2,i – are the m1- and m2-dimensional noise interference vectors of Gaussian white noise type with the characteristics E[v1,i] = 0, E[v1,i v1,T k ] = R1,i δ ik , E[v1,i] = 0, E[v2,i v2,T k ] = R2,i δ ik , k = 0, 1, ..., δ ik – symbol of Kronecker, H1 and H2 – matrix of measurements corresponding to dimensions.

We assume that the covariance matrices Qi, R1,i, R2,i are unknown, but they are functions of time. In the conditions formulated above, the equations of dynamics and observation of the extended dynamical system can be written in the following form:

 x i +1  = ξ   i +1 

 A D1   x i   0   0 D  ξ  +  D  w i , 2    i   3 

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Journal of Automation, Mobile Robotics & Intelligent Systems

 z1,i   H1 = z   0  2,i  

0   x i  v1,i  + , H2  ξi  v2,i 

or in a more compact form:

where:

VOLUME 12,

= x i*+1 A* x i* + D* wi* , (5)

= zi* H * x i* + vi* , (6)

 A D1  *

= A* = , H  0 D2   x i +1  * = x i*+1  =  , vi ξi +1 

 H1 0  * ,D  0= H2  

v1,i  * =  , zi v2,i 

0 D  ,  3 

 z1,i  *  z  , wi = wi .  2,i 

To estimate the extended state vector on the basis of equations (5), (6), one can use the traditional Kalman filter [1,4]: x

=Ax ,

* i +1|i

*

* i|i

= Pi * 1|i A* Pi|*i A*T + D*Qˆ i D*T

x i*+= x i*+1|i + K i*+1 yi*+1 , 1|i +1

yi*= zi*+1 − H * x i*+1|i , +1|i

K i*+1 = Pi +* 1|i H *T [Ci*+1 ]−1 ,

= C H P * i +1

*

* i +1|i

H

*T

+ Ri +1 ,

(7) (8) (9)

(10)

Pi +* 1|i +1= ( I − K i*+1 H * )Pi +* 1|i .

(11) (12)

(13)

On the basis of the values of ξi +1 computed at each step, expression (2) gives the value of the unknown input action fi. Based on the Kalman filter form (7)–(13), it is easy to see that the amplification factor of the Kalman filter algorithm K i*+1 depends on the matrices Qi and Ri+1. Thus, in the case where the noise covariance matrices Qi and Ri+1 are unknown, the coefficient K i*+1 , which must be found to determine the state vector estimate, is also unknown.

Analyzing the expressions (7)–(13), we can conclude that the relations (8), (11)–(13) should be excluded from the extrapolation and filtering algorithms, because the estimates Qi and Ri+1 are used in their calculation. In [1, 2] we show that in this case the gain K i*+1 can be calculated from a sample of measure+l ments Z ii+1 based on the following two-stage computational procedure:

SL = M, (14)

and

where:

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K i*+1Φ * = L,

 H  y y   * *    H A  * y y    S= A , M= ,      * * l −2   * *T   H A   yi +l|i yi +1|i  *

* i +2|i * i +3|i

*T i +1|i *T i +1|i

L = Pi +* 1|i H *T , Ô * = [ yi*+1|i yi*+T1|i ].

(15)

N° 4

2018

Such an approach allows the use of real measurement information, which is of significant importance when a priori information is given inaccurately. In other words, the above algorithm is robust to changing a priori data.

The system of equations (14) for determining the matrix L can be poorly conditioned, which contributes to a decrease in the accuracy of the calculation of the sought solution. This circumstance in the solution of this equation leads to the necessity of applying regularization methods. Among them we should mention a group of methods based on the general regularization principle of A.N. Tikhonov [8–13], and methods of effective pseudoinversion, based on the singular matrix decomposition [14–17].

3. Solution of the Task

In the real situation, the initial data of system (14) are known only approximately. Almost in place of system (14) another system is used

S h L = Mδ , (16)

such that S h − S ≤ h, Mδ − M ≤ δ . Thus, approximate data are characterized by a set of S h , Mδ , η , where η = {δ , h} – is the error vector.

We write down the expression for the smoothing functional of A.N. Tikhonov Gα [Lαη ] = S h Lαη − M δ + α Lαη ,

where a > 0 – regularization parameter.

We introduce the following functions [10,11]:

γ η (α ) = Lαη ,

α h η

βη= (α )

(

S L − Mδ ,

)

2

ρη (α= ) βη (α ) − δ + h γ η (α ) − µη2 .

where: Lαη – is the extremal of the functional A.N. Tikhonov Gα [L] for fixed a > 0, the functions gη(a), bη(a), rη(a) are monotonic and continuous as functions of a in the domain a > 0, = µη inf S h L − Mδ – a measure L∈D

of incompatibility of equation (16) with approximate data on the set D ∈Θ.

The solution of equation (16) on the basis of the regularization method of A.N. Tikhonov is given by the formula [9, 10] Lα = (α I + S hT S h )−1 S hT Mδ = gα ( S hT S h )S hT Mδ ,

where: ga(l) = (a + l)–1, a > 0, 0 ≤ l > ∞ – generating system of functions for the method of A.N. Tikhonov.

We assume that the natural condition Mδ

2

> δ 2 + µη2 . (17)

The function of the generalized residual rη(a) has the following limit values at the ends of the segment [11]

lim ρη (α )=

Mδ − δ 2 − µη2 , lim ρη (α ) = −δ 2 .

α →0+0

Thus, if condition (17) is satisfied, equation rη(a) = 0 has in root a > 0 a root a′(η), and element Lαη ′(η ) is uniquely defined. α →+∞

Journal of Automation, Mobile Robotics & Intelligent Systems

If, however, the numbers h and d are unknown or their computation is associated with considerable difficulties, then the regularization parameter a is expedient to be determined on the basis of the quasioptimality or relations [13] Lαi +1 = − Lαi min, = α i +1 ζα i ,

rrel (α ) = r1 (α ) r(α ),

where:

0 < ζ <,

= i 0,1,2,...,

(

r1 (α ) = S hγ α − S h Lα − Mδ

),

γ α = α ( dLα dα ) .

When solving the system of equations (16), it is expedient to use regularization on the basis of extended systems [15, 17, 18]. It is known [17] that the normal pseudosolution L* = S h+ Mδ is a normal solution of the normal system of equations S hT S h L = S hT Mδ (18)

T or S h ς = 0, where= ς Mδ − S h L. Thus, the normal system of equations (18) is equivalent to an extended system of equations Rhq = bd , (19)

where:

 Il( m−1) S h  ς  Rh  T = = ; z =   ; bδ 0   S h  L 

(

)

T

 Mδ     0  ,

= and q ςT , LT ∈ R l( m−1)+n.

Since the normal system of equations (18) is always consistent [15, 17], it follows immediately from this that the extended system (19) for any initial data d = { S h , Mδ } is also consistent, and the normal solution of the extended system is deT + fined as= q* R= ς*T , LT* , where L* = S h+ Mδ and h bδ = ς* Mδ − S h L* .

Using the regularization method of A.N. Tikhonov, regularized solution qα of the system (19) is defined as the unique solution of the Euler equation

(

)

(Rh2 + α Il( m−1)+n )q = Rh bδ .

(20)

2 T T where: Rh = Rh Rh (Rh = Rh ), Rh − R = S h − S ≤ h, bδ − b = Mδ − M ≤ δ .

It was shown in [18] that if we put a = h in equation (20), then the deviation error has the form

qα − q* = O(h + δ ),

 M − SL  + where qα – decision (20),= q* R= b   , L = S+M.  L  The last estimate shows that in the case under consideration it is sufficient to match the regularization parameter a only with the value h, i.e. with a measure of the error of the matrix S, in other words, in essence, the problem of choosing the regularization parameter is removed.

The method of effective pseudoinversion, as is known [14, 16], is based on the singular expansion of the matrix Sh, i.e. on its presentation in the form

S h = UTV T ,

VOLUME 12,

N° 4

2018

where U – orthogonal ((l – 1)m × 2p)–matrix; V – orthogonal (2p × n)–matrix; T – diagonal (2p × 2p)–matrix.

The columns ui and vi of the matrices U and V are the eigenvectors of the matrices S h S hT and S hT S h, and the diagonal elements µi of the matrix T – are the positive roots of the eigenvalues λi of the matrix S hT S h (or S h S hT ).

The pseudoinverse Moore-Penrose matrix S h+ makes it possible to obtain the estimate [14, 16] + T = L* VT = U Mδ

r

1

∑µ

vi uiT , (21)

i =1 i

+ + + where T = diag(t1 ,..., t i ) – pseudo-inverse matrix for the matrix T; n – rank of the matrix Sh, i.e. the number of non-zero singular numbers µi (i = 1,..., p); t i+ = 1 / µi , if µi ≠ 0, and t i+ = 0, if µi = 0.

In the case where the rank of the matrix Sh n = p, the pseudoinverse estimate (21) coincides with the estimate (16) for the least squares and, correspondingly, is characterized by low accuracy. In connection with this, the so-called effective pseudoinverse matrices and the estimates

= L*τ VTτ= U T Mδ

r'

1

∑µ

vi ⋅ uiT ,

i =1 i

+ T where τ – effective pseudo-matrix T = diag(t1+τ ,..., t n+τ ); n' < n, t i+τ = 1 / µi , if µi > τ , and t i+τ = 0, if µi = 0.

Taking into account the symmetry and the positive definiteness of the matrix Ô * in (15) for the stable calculation of the matrix gain factor K i*+1, it is expedient to use the M.M. Lavrentev computational scheme

= K i*+1 L* (Φ * + α I )−1 ,

where the regularization parameter a is expedient to be determined on the basis of the quasioptimality method.

4. Conclusion

The above algorithms of stable recovery of unknown input signals in control systems allow to raise the level of a priori information about the control object, the reliability of statistical characteristics of external influences, and thus the quality of control processes in statistically indeterminate situations.

AUTHORS

Nadirbek Yusupbekov – Department of Automation of Production Processes, Tashkent State Technical University, Tashkent, Republic of Uzbekistan, e-mail: app.tgtu@mail.ru.

Husan Igamberdiev – Department Information processing and control systems, Tashkent State Technical University, Tashkent, Republic of Uzbekistan, e-mail: uz3121@rambler.ru.

Uktam Mamirov – Department of Information processing and management system, Tashkent State Technical University, Tashkent, Republic of Uzbekistan, e-mail: uktammamirov@gmail.com.

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Journal of Automation, Mobile Robotics & Intelligent Systems

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N° 4

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VOLUME 12 N°1 2018 www.jamris.org VOLUME 12 N°4(PRINT) 2018 www.jamris.org pISSN 1897-8649 / eISSN 2080-2145 (ONLINE)

Journal of Automation, Mobile Robotics & Intelligent Systems

pISSN 1897-8649

(PRINT)

/ eISSN 2080-2145

(ONLINE)

VOLUME 12, N° 4

2018

pISSN 1897-8649 (PRINT) / eISSN 2080-2145 (ONLINE)

Publisher: Industrial Research Institute for Automation and Measurements PIAP

pISSN 1897-8649 (PRINT) /eISSN 2080-2145 (ONLINE)

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