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17th CIRP Conference on Modelling of Machining Operations
17th CIRP Conference on Modelling of Machining Operations An Intelligent Metrology Informatics System based on Neural Networks for Multistage Manufacturing Processes An Intelligent Metrology Informatics System based onFrance Neural Networks for 28th CIRP Design Conference, May 2018, Nantes, b a a Manufacturing Processes Moschos PapananiasaMultistage *, to Thomas E McLeay , Mahdi Mahfouf Visakan Kadirkamanathan A new methodology analyze the functional and ,physical architecture of a Control and Systems Engineering,b The University of Sheffield, aMappin Street, Sheffield S1 3JD, UK a Department of Automatic Moschos Papananias *,with Thomas E McLeayoriented , Mahdi Mahfouf , Visakan Kadirkamanathan existing products for an assembly family identification Advanced Manufacturing Research Centre Boeing, The University of Sheffield, Advancedproduct Manufacturing Park, Wallis Way, Catcliffe, Rotherham S60 5TZ, a
b
a Department of Automatic Control and Systems Engineering, UK The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK Advanced Manufacturing Research Centre with Boeing, The University of Sheffield, Advanced Manufacturing Park, Wallis Way, Catcliffe, Rotherham S60 5TZ, * Corresponding author. E-mail address: m.papananias@sheffield.ac.uk UK École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France * Corresponding author. E-mail address: m.papananias@sheffield.ac.uk b
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
*Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: paul.stief@ensam.eu
The ability to gather manufacturing data from various workstations has been explored for several decades and the advances in sensory and data Abstract acquisition techniques have led to the increasing availability of high-dimensional data. This paper presents an intelligent metrology informatics system to extract useful informationdata from Multistage Manufacturing (MMP) for dataseveral and predict part quality characteristics suchand as data true Abstract The ability to gather manufacturing from various workstations hasProcess been explored decades and the advances in sensory position andtechniques circularityhave usingled neural The input dataofinclude the tempering temperature, force and vibration while acquisition to thenetworks. increasing availability high-dimensional data. This papermaterial presentsconditions, an intelligent metrology informatics output data include comparative coordinate measurements. effectiveness of the proposed method isquality demonstrated using experimental Inthe today’s environment, the trend more productThe variety and customization is unbroken. Due to thischaracteristics development, the need of system to business extract useful information from towards Multistage Manufacturing Process (MMP) data and predict part such as true data fromand a MMP. agile and reconfigurable production emerged to cope with various products temperature, and product material families.conditions, To design force and optimize production position circularity using neural systems networks. The input data include the tempering and vibration while systems as well to choose the optimal productmeasurements. matches, product methods areproposed needed. Indeed, of the known methods aim to the output data as include comparative coordinate The analysis effectiveness of the method most is demonstrated using experimental © 2019 Authors. Published by Elsevier B.V. analyze aThe product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and data from a MMP. Peer-review under responsibility of the scientific committee of The and 17thchoice CIRP Conference on Modelling of Machining Operations, nature ofThe components. This fact by impedes anB.V. efficient comparison of appropriate product family combinations for the production © 2019 Authors. Published Elsevier in the person ofmethodology the Conference Chair Drto Erdem and products Co-chairs Tom and Dr Rachid Msaoubi. system. AThe new is proposed analyze existing view ofMcleay their functional physical architecture. aim is to cluster © 2019 Authors. Published by of Elsevier B.V.Ozturk Peer-review under responsibility the scientific committee of TheinDr 17th CIRP Conference onand Modelling of MachiningThe Operations these productsunder in new assembly oriented product families for the optimization existing assembly lines and creationOperations, of future reconfigurable Peer-review responsibility of the scientific committee of The 17th CIRPofConference on Modelling of the Machining Keywords: Multistage Manufacturing; Intelligent/Smart Manufacturing Informatics; Artificial Neural Networks assembly systems. on Datum Flow Chain, Ozturk theManufacturing; physical structure of the products analyzed. Functional subassemblies are identified, and in the person of theBased Conference Chair Dr Erdem and Co-chairs Dr Tom Mcleayisand Dr Rachid Msaoubi. a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the Keywords:between Multistage Manufacturing; Informatics; Artificial Neuraland Networks similarity product familiesIntelligent/Smart by providing Manufacturing; design supportManufacturing to both, production system planners product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of 1. Introduction geometric human errors, and environmental effects, that thyssenkrupp Presta France is then carried out to give a first industrial evaluation of theerrors, proposed approach. affect the machining process and thus the quality of machined © 2017 The Authors. Published by Elsevier B.V. 1. Introduction geometric errors, human and environmental effects, that Manufacturing is the process alteringcommittee the geometry parts [1, 2]. In addition, in multistage manufacturing, where Peer-review under responsibility of theofscientific of the and 28th CIRP Design Conference 2018.errors,
affect the machining process multiple and thus the quality of machined each product goes through processing stages, part parts [1, 2]. In addition, in multistage manufacturing, where quality is also affected by the accumulated errors transmitted properties of a given starting inspection, material to assembly produce parts. Metal each through stages. multipleTherefore, processingthestages, such as forming, machining, and testing from product previousgoes processing final part manufacturing processes usually involve multiple operations quality is also affected by the accumulated errors transmitted to produce a high-quality part or product that performs variation is subject to the accumulation of variations from all such as forming, machining, inspection, assembly testing from previous according to its design specifications. Forming is anand important operations [3]. processing stages. Therefore, the final part 1. Introduction of the product range and characteristics manufactured and/or to produce a high-quality part or product that performs variation is the accumulation variations from all step in manufacturing metallic products to obtain the desired To ensuresubject producttoquality and process of safety, each operation assembled in this system. In this context, the main challenge in according to its design specifications. Forming is an important operations [3]. shape and dimensions of the workpiece through mechanical in a manufacturing system is often monitored using various Due to the fast development in the domain of modelling and analysis is now not only to cope with single step in manufacturing metallic to obtain the desired To ensure productsystems quality and process safety, each operation deformation. In addition, once products the desired geometry of the sensors and software [4, 5]. For example, in machining, communication and an ongoing trend of digitization and products, a limited product range or existing product families, shape and dimensions of the workpiece through mechanical in a manufacturing system is often monitored using various workpiece is obtained, it is often necessary to modify the key process performance indicators such as force, vibration, digitalization, manufacturing enterprises are facing important but also to be able to analyze and to compare products to define deformation. In addition, once the desired geometry of the sensors and software systems [4, 5]. For example, in machining, microstructure and mechanical properties of the workpiece, temperature and Acoustic Emission (AE) data can be obtained challenges in today’s market environments: a continuing new product families. It can be observed that classical existing workpiece is obtained, it is often necessary to modify the key process performance indicatorsmanufacturing such as force,data vibration, without changing its geometry, using heat treatment techniques. during part production. Therefore, belong tendency towards reduction of product development times and product families are regrouped in function of clients or features. microstructure and mechanical properties of the workpiece, temperature and Acoustic Emission (AE) data can be Machining typically includes a series of metal-removing to the typical family of big data characterized by high obtained volume, shortened product lifecycles. In addition, there is an increasing However, assembly oriented product families are hardly to find. without changing its geometry, heat treatment techniques. during part production. Therefore, operations to achieve parts withusing the desired shape, dimensions velocity, variety and veracity [6, 7].manufacturing data belong demand of customization, being at the same time in a global On the product family level, products differ mainly in two Machining typically includes a series of metal-removing to the typical family of big data characterized by high volume, and surface finish. However, there are many factors, such as Statistical Process Control (SPC) is a necessary process to competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the operations to achieve parts with the desired shape, dimensions velocity, variety and veracity [6, 7]. cutting parameters, tool wear, cutting forces, vibration, detect early abnormal operating conditions during the which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). and surface finish. However, there are many factors, such as Statistical Process Control (SPC) is a necessary process to markets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products cutting parameters, tool wear, cutting forces, vibration, detect early abnormal operating conditions during the 2212-8271 © 2019 The Authors. Published by Elsevier B.V. product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the Peer-review under responsibility of the scientific of The 17th CIRP on Modelling Machininglevel Operations, in the person of the To cope with this augmenting variety as committee well as to be able to Conference product structure on of a physical (components level) which Conference Chair Dr Erdem Ozturk and Co-chairs Dr Tom Mcleay and Dr Rachid Msaoubi. 2212-8271 possible © 2019 The optimization Authors. Publishedpotentials by Elsevier B.V. identify in the existing causes difficulties regarding an efficient definition and Peer-review under responsibility of the scientific The 17th CIRP Conference on Modelling of Machining Operations, in theAddressing person of the this production system, it is important to havecommittee a preciseofknowledge comparison of different product families. properties of a given starting material to produce parts. Metal
Keywords: Assembly; Design Family identification Manufacturing is themethod; process ofinvolve altering the geometry and manufacturing processes usually multiple operations
Conference Chair Dr Erdem Ozturk and Co-chairs Dr Tom Mcleay and Dr Rachid Msaoubi. 2212-8271 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the by scientific of The 17th CIRP Conference on Modelling of Machining Operations 2212-8271 © 2017 The Authors. Published Elseviercommittee B.V. 10.1016/j.procir.2019.04.148 Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
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Moschos Papananias et al. / Procedia CIRP 82 (2019) 444–449 Author name / Procedia CIRP 00 (2019) 000–000
manufacturing process and diagnose their sources. A major advantage of SPC over post-process inspection is that compensating adjustments can be made in the manufacturing process as the product is manufactured in order to reduce variability and scrap levels. A review of the development of Statistical Process Monitoring (SPM) technology can be found in [7]. Traditional SPC is based on univariate statistical methods. One of the main disadvantages of this approach is the complexity in monitoring the control charts as the number of variables increases. Control charts are SPC tools that have been traditionally used in the manufacturing industry to monitor variability. Multivariate Statistical Process Control (MSPC) approaches treat the variables simultaneously and often use latent variable methods to exploit the correlation of measured variables and deal with missing and noisy data [7, 8]. In order to cope with dimensionality reduction, multivariate statistical techniques such as Principal Component Analysis (PCA) are generally used. PCA projects the information in the process variables into a low-dimensional space defined by a few latent variables. Ferrer [9] illustrated the practical benefits of PCAbased MSPC over conventional SPC in an autobody assembly process. The fourth industrial revolution (Industry 4.0) moves from automated to autonomous intelligent/smart manufacturing. Therefore, efficient big data and predictive analytics tools are required to extract useful information from a manufacturing process and improve manufacturing efficiency for a wide range of manufacturing conditions using Artificial Intelligence (AI) models. Artificial Neural Networks (ANNs) are one of the most commonly used AI tools in SPC applications due to their ability to learn and model complex and nonlinear relationships [1012]. Over the years, many research efforts have been made to develop intelligent monitoring systems for machining processes using sensor measurements of the process and machine learning models. Most publications are focused on tool wear and machined surface roughness monitoring systems. Ă–zel and Karpat [13] developed models based on feedforward neural networks to predict both surface roughness and tool flank wear in finish hard turning using workpiece hardness, cutting speed, feed rate, axial cutting length and the mean values of cutting forces. Salgado et al. [14] presented a method based on Least Squares Support Vector Machines (LS-SVMs) to predict surface roughness for turning processes using cutting parameters, tool geometry parameters and features extracted from vibration signals by utilizing Singular Spectrum Analysis (SSA). Huang [15] developed an intelligent neural-fuzzy inprocess surface roughness monitoring system for an end milling operation using cutting parameters (spindle speed, feed rate and depth of cut) and cutting force signals (the average resultant peak force and the absolute average force). This paper presents a new system for intelligent manufacturing that learns from in-process metrology data and predicts the final condition of a product. Compared to most previous research focusing on monitoring the machining processes to identify the finish-machined part condition, this system, based on neural networks, is novel given it uses data from multiple different processes to predict the end product quality. A case study is presented where metrology data comes
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available as each product goes through the steps of heat treatment and machining. The measured variables used as model inputs include the tempering temperature, material conditions, force and vibration. Comparative coordinate measurements are used as output variables to train the models. The performance of the proposed method is demonstrated by predicting the true position and circularity of a circular feature. The remainder of the paper is organized as follows. Section 2 describes ANNs. Section 3 presents the experimental work performed to produce the parts and obtain the multistage manufacturing data required to validate the proposed method. Section 4 develops the intelligent metrology informatics system based on ANNs to predict the accuracy of the manufactured parts from the measured variables obtained during production. Finally, concluding remarks are given in Section 5. 2. Artificial neural networks ANNs are human brain-inspired computing systems intended to replicate the human learning process. The most popular neural networks are considered to be the Multi-Layer Perceptron (MLP) networks. An MLP network is a feedforward neural network model consisting of one input layer, one or more hidden layers, and one output layer. Each layer includes one or more nodes. Apart from the input nodes, each node is an artificial neuron. The first model of an artificial neuron was proposed by McCulloch and Pitts [16]. Fig. 1 shows an architectural graph of an MLP network consisting of a number of inputs, one hidden layer with a number of hidden neuros, and one output. Each node in one layer connects (with a certain weight) to every node in the following layer. Each node in the hidden and output layer (artificial neurons) includes: i) a summation unit, which computes a weighted sum over its inputs and adds a bias or threshold term to the sum, and, ii) a nonlinear activation function that is differentiable [17]. However, linear output layer activations are also common [18]. The output of a neuron can be described by: ��
đ?‘Śđ?‘Ś = đ?‘“đ?‘“ (∑ đ?‘¤đ?‘¤đ?‘–đ?‘– đ?“?đ?“?đ?‘–đ?‘– + đ?‘?đ?‘?) đ?‘–đ?‘–=1
(1)
where đ?‘“đ?‘“(¡) is a nonlinear activation function, đ?‘¤đ?‘¤đ?‘–đ?‘– denotes the synaptic weight coefficient associated with the đ?‘–đ?‘– -th neuron input, đ?“?đ?“?đ?‘–đ?‘– , and đ?‘?đ?‘? is the bias input. The MLP network is a supervised network because a desired output is required for learning. A critical step in developing a neural network model involves the selection of the number of neurons in the hidden layer since in most cases a single hidden layer is sufficient. The number of hidden neurons can be determined easily by trial and error. The number of inputs and outputs of the network is determined by the dimensions of the input and output data. The supervised learning technique utilized by an MLP network for training is a particular BackPropagation (BP) learning algorithm. The BP is an optimization procedure based on gradient descent that adjusts the network’s weights in order to minimise the system error computed by the difference between the network output and the desired output.
Moschos Papananias et al. / Procedia CIRP 82 (2019) 444–449 Author name / Procedia CIRP 00 (2019) 000–000
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Fig. 1. Architectural graph of an MLP network with one hidden layer and one output.
In this work, two different MATLAB network training functions are used to train the predictive models: i) the Variable Learning Rate Back-Propagation (VLRBP) that updates weight and bias values according to gradient descent momentum and an adaptive learning rate, and, ii) the Conjugate Gradient with Powell/Beale restarts (CGB) that updates weight and bias values according to the conjugate gradient BP with PowellBeale restarts. The data required to train the MLP network are the đ?‘ƒđ?‘ƒ pattern đ?‘ƒđ?‘ƒ
(đ?‘?đ?‘?)
(đ?‘?đ?‘?) T
pairs {(đ?’™đ?’™(đ?‘?đ?‘?) , đ?’…đ?’…(đ?‘?đ?‘?) )}đ?‘?đ?‘?=1 , where đ?’™đ?’™(đ?‘?đ?‘?) = [đ?‘Ľđ?‘Ľ1 , ‌ , đ?‘Ľđ?‘Ľđ?‘›đ?‘› ] is the (đ?‘?đ?‘?)
(đ?‘?đ?‘?) T
input vector for the đ?‘?đ?‘?-th pattern and đ?’…đ?’…(đ?‘?đ?‘?) = [đ?‘‘đ?‘‘1 , ‌ , đ?‘‘đ?‘‘đ?‘šđ?‘š ] is the desired or target vector for the đ?‘?đ?‘?-th pattern. The Mean Squared Error (MSE) is given by: đ?‘ƒđ?‘ƒ
1 2 đ??˝đ??˝ = ∑‖đ?’…đ?’…(đ?‘?đ?‘?) − đ?”‚đ?”‚(đ?‘?đ?‘?) ‖ đ?‘ƒđ?‘ƒ đ?‘?đ?‘?=1 đ?‘ƒđ?‘ƒ
đ?‘šđ?‘š
1 (đ?‘?đ?‘?) (đ?‘?đ?‘?) 2 = ∑ ∑[đ?‘‘đ?‘‘đ?‘–đ?‘– − đ?“Žđ?“Žđ?‘–đ?‘– ] đ?‘ƒđ?‘ƒ đ?‘?đ?‘?=1 đ?‘–đ?‘–=1
(đ?‘?đ?‘?)
(2)
(đ?‘?đ?‘?) T
where đ?”‚đ?”‚(đ?‘?đ?‘?) = [đ?“Žđ?“Ž1 , ‌ , đ?“Žđ?“Žđ?‘šđ?‘š ] is the output vector for the đ?‘?đ?‘?-th pattern. Although the method employed in this work uses MLP networks, Elman networks are also developed for comparison with other types of neural networks. Elman networks use positive feedback from the hidden layer to construct some form of memory in the network. 3. Experimental work This section describes the experimental work performed to produce the parts and obtain metrology data from heat treatment, machining and dimensional inspection. Fig. 2 shows the Computer-Aided-Design (CAD) model of the part. Experimental work was performed using a VECSTAR furnace, a DMG MORI NVX 5080 3-axis machine and a Renishaw Equator 300 Extended Height System, supplied with the SP25 3-axis analogue scanning probe. The material (steel EN24) was
3
heat treated before machining (see Fig. 3). In particular, the material blocks were heated up to 845°C and then quenched in oil for hardening. After hardening, the material blocks were tempered at different temperatures, including 450°C, 550°C and 650°C, to obtain workpieces with different mechanical properties such as material surface hardness. High temperature thermocouples were placed in the furnace to measure temperature gradient and temperature variation during hardening and tempering. Surface hardness measurements were performed on the heat treated blocks using a Rockwell device. For machining, a full factorial design with four factors at two levels and one center point each was conducted. The factors considered were: material surface hardness, feed rate, spindle speed, and datum error (when the part is flipped around the Y axis for the machining of the second orientation). All the cutting tools used for the machining operations were inspected for wear using a Leica microscope after machining each workpiece. The tool wear was measured on each flute. Each cutting tool was used until it reached a given flank wear width to reduce the influence of tool wear on product variation and measured variables. Coolant was used for all the machining operations. During machining, cutting force data were obtained at 10 kHz using a Kistler dynamometer (9255B), located between the vice holding the workpiece and the machine table, and DynoWare software (see Fig. 4). The dynamometer contains four sensors. The system was configured to output: the sum combination of force signal in the X direction from the first and second sensor; the sum combination of force signal in the X direction from the third and fourth sensor; the sum combination of force signal in the Y direction from the first and fourth sensor; the sum combination of force signal in the Y direction from the second and third sensor; a single force signal in the Z direction from each sensor; and the sum combination of force signals for each direction from all the sensors. In addition, vibration data were obtained at 10 kHz using an accelerometer placed on the spindle and NI LabVIEW SignalExpress software. The product quality characteristics of interest in this work are the true position and circularity of the large circular feature (see Fig. 2), which were evaluated using the Equator gauge in scanning mode under workshop conditions. The Equator is a Coordinate Measuring System (CMS) operating in comparator mode. Comparative coordinate measurement benefits from the fact that constant systematic effects associated with the measurement system cancel out through the principle of mastering [19-23]. This system provides two main comparison methods: the “Golden Compare� method and the “Coordinate Measuring Machine (CMM) Compare� method. The Golden Compare method requires a reference master part to calibrate the comparator system and assumes that the master part is produced to drawing nominals. Therefore, any deviation of the master part from drawing nominals will be included in the measurements. The most accurate method of using an Equator gauge is the CMM Compare. This method does not require a reference master part to calibrate the comparator system. However, it requires to calibrate a production part, produced close to drawing nominals, on an accurate CMS such as a CMM in order to generate a calibration file for the comparator system.
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Moschos Papananias et al. / Procedia CIRP 82 (2019) 444–449 Author name / Procedia CIRP 00 (2019) 000–000
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The calibration file is read by the comparator system during mastering to enable the individual points of a master dataset to be compared with that of test datasets. The CMM Compare method was employed to calibrate the comparator system. The stylus used was a typical 30 mm long stylus with tungsten carbide stem and a 2 mm diameter ruby ball. The calibration file, required for this Compare method, was generated using a Mitutoyo CMM with a Renishaw REVO RSP3 3D scanning probe (see Fig. 5). The CMM Compare procedure consists of the following steps: a) Obtain a master part from the production parts. b) Generate the required part program on the Equator. c) Edit the part program on the CMM. The part program at this stage should include the commands COMPARE/ON, CAL and COMPARE/OFF. d) Measure the master part on the CMM to produce a calibration file for the Equator. e) Transfer the calibration file to the Equator and edit the part program on the Equator to add the commands COMPARE/ON, CAL and COMPARE/OFF. f) Place the master part on the Equator and run the part program in master mode to produce a master file with reference to the calibration file. g) Run the part program using the master part in measure mode (verification step). h) Remove the master part and replace with the production parts to be measured. CMM accuracy is dependent upon the ambient thermal environment in which it operates because thermal effects degrade CMM accuracy. Therefore, the production of the calibration file required for CMM Compare was performed using a CMM located in a temperature controlled room. According to manufacturer’s instructions, it is required to generate more point data from the CMM for CMM Compare using scanning measurements. The required minimum ratio of points measured on the CMM is ten for every single point measured on the Equator. Also, good measurement practice to maintain accuracy on the CMM is to reduce the part program speeds, accelerations and scan velocity according to the CMM’s specification. It is worth mentioning that this inspection approach requires repeatable part fixturing because the comparison process involves a point-to-point comparison between the master part data and the test part data. The same fixturing arrangement was used for both the CMM and the Equator gauge. Fig. 6 shows the experimental setup on Equator gauge.
Fig. 3. Heat treatment.
Fig. 4. Machining.
Fig. 5. CMM measurement.
Note that eighteen parts were produced in total; seventeen parts were produced to complete the experimental design (sixteen parts for the base design and one part for the center point) and train and test the predictive models and one part was produced in order to be used as a master part in comparator measurement. Fig. 2. CAD model of the part.
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Fig. 6. Comparative coordinate measurement.
4. Metrology informatics system development To predict the end product quality, an MLP network with eight inputs, one hidden layer consisting of ten neurons, and one output was developed. Tan-sigmoid transfer functions were used for both the hidden and the output layers to provide the nonlinear characteristic to the network. The first three inputs to the MLP network are the Root Mean Square (RMS) values of the sum combination of force signal in the X, Y and Z direction, respectively, from all the four sensors of the dynamometer. The next three inputs to the network are the RMS values of vibration signal in the X, Y and Z direction, respectively. The seventh input is a coded vector corresponding to the surface hardness of the material. The eighth input is the maximum tempering temperature obtained from the five thermocouples during the heat treatment process of the material blocks. The output is the vector of measurand of interest (true position and circularity). To study the linear dependence of the measured data, the correlation coefficients of the network inputs and the desired outputs for the training dataset are shown in Table 1. The correlation between two random variables đ?‘Ľđ?‘Ľ and đ?‘‘đ?‘‘ can be defined in terms of the covariance of the two variables and the product of the standard deviations of the two variables: đ?œŒđ?œŒ =
đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?(đ?‘Ľđ?‘Ľ, đ?‘‘đ?‘‘) , − 1 ≤ đ?œŒđ?œŒ ≤ 1 đ?œŽđ?œŽđ?‘Ľđ?‘Ľ đ?œŽđ?œŽđ?‘‘đ?‘‘
(3)
Table 1. Correlation coefficients for true position and circularity for the training dataset. Network inputs
đ?œŒđ?œŒ for true position
đ?œŒđ?œŒ for circularity
0.5119
0.3786
1
RMS-FX
2
RMS-FY
0.6134
3
RMS-FZ
0.5080
0.5834
4
RMS-VX
0.0843
0.4092
5
RMS-VY
-0.0334
0.4441
6
RMS-VZ
-0.1106
0.4084
7
Surface hardness
0.7472
0.3452
8
Tempering temperature
-0.4139
-0.0066
0.3717
5
The results in Table 1 indicate the degree of linear dependence between the network inputs and the desired outputs. If the variables are independent, then đ?œŒđ?œŒ = 0, and the closer the coefficient đ?œŒđ?œŒ is to either 1 or -1, the stronger the correlation between the variables. Data from the manufacture of nine parts were used for training and data from the manufacture of eight parts were used for testing. By varying the simulations in MATLAB with different training algorithms, two models were trained for each measurand. The first model was trained using VLRBP while the second model was trained using CGB. For comparison with other types of neural networks such as recurrent, Elman networks, with one hidden layer consisting of ten neurons, were also developed for each measurand. As with the MLP networks, the VLRBP and the CGB algorithms were used to train the Elman networks. All the models were trained for a different number of epochs to let the errors converge to zero. The MSE performance function was used to measure each network’s performance. Tables 2 and 3 show the results obtained from all the developed models on non-training data for true position and circularity, respectively. Training multiple times generates different prediction results due to different initial conditions and sampling. Based on Tables 2 and 3, it can be concluded that both the feedforward and recurrent predictive models can provide accurate predictions for both measurands and the differences in the MSE values are very small especially for true position. Also, the models trained using CGB needed much less training epochs to achieve a low MSE value than the models trained using VLRBP. Table 2. Performance of neural network models for true position. ANN Models
Epochs
Training algorithm
MSE (mm)
1
MLP-1
1000
VLRBP
7.37 Ă— 10-7
2
MLP-2
162
CGB
8.81 Ă— 10-7
3
Elman-1
1000
VLRBP
8.51 Ă— 10-7
4
Elman-2
70
CGB
6.95 Ă— 10-7
Table 3. Performance of neural network models for circularity. ANN Models
Epochs
Training algorithm
MSE (mm)
1
MLP-1
1000
VLRBP
4.46 Ă— 10-6
2
MLP-2
106
CGB
7.60 Ă— 10-7
3
Elman-1
1000
VLRBP
4.13 Ă— 10-6
4
Elman-2
118
CGB
4.56 Ă— 10-6
Tables 4 and 5 show the residual values, calculated by the difference between the Equator measured values and the model predictions, for true position and circularity, respectively. As can be seen from Tables 4 and 5, the residual values for true position are less than 1.5 Îźm for all the models while the residual values for circularity range in total from 0.2 to 5.6 Îźm for the first, third and fourth model and from 0.4 to 1.1 Îźm for the second model. It can be concluded that the proposed system provides a high degree of accuracy in predicting the end product quality and thus determining whether or not a product is within the allowable tolerances. However, in order to determine conformance or nonconformance to a tolerance, it is
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Moschos Papananias et al. / Procedia CIRP 82 (2019) 444–449 Author name / Procedia CIRP 00 (2019) 000–000
necessary to evaluate the uncertainty of predictions so that the risks involved in the product acceptance/rejection or reengineering decision can be accurately assessed. Table 4. Residuals for true position. Parts 1 2 3 4 5 6 7 8
Model 1
Model 2
Model 3
Model 4
(μm)
(μm)
(μm)
(μm)
1.4
1.4
1.4
1.4
0.1
0.1
0.1
0.1
0.9
1.3
1.2
0.9
1.0
1.2
1.1
0.2
1.2
1.1
1.2
1.4
0.6
0.6
0.6
0.6
0.1
0.6
0.7
0.4
0.4
0.1
0.0
0.3
Table 5. Residuals for circularity. Parts 1 2 3 4 5 6 7 8
Model 1
Model 2
Model 3
Model 4
(μm)
(μm)
(μm)
(μm)
0.9
0.9
0.9
1.2
0.9
1.1
0.6
0.2
0.9
1.1
0.9
1.1
0.7
0.4
0.7
0.4
1.0
1.0
1.0
0.8
0.3
0.8
0.9
0.9
1.1
0.7
1.0
0.9
5.5
0.7
5.3
5.6
5. Conclusions and future work This paper has presented an intelligent metrology informatics system based on neural networks to transform the Multistage Manufacturing Process (MMP) data into knowledge of the process and part state and thus, supporting time-effective decision-making while minimising non-added value processes during part production. The MMP considered in this work included heat treatment, subtractive machining and postprocess inspection. MLP and Elman networks were developed to predict the true position and circularity of the large bore of machined parts. The predicted results compared well with the experimental comparator measurements obtained from the Equator gauge. However, a limitation of this approach is the ability to only finding a single estimate for a feature characteristic without quantifying the associated uncertainty on the prediction. Therefore, future work will focus on developing learning algorithms that take into account the uncertainty in the metrology data. Acknowledgements The authors gratefully acknowledge funding for this research from the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant Reference: EP/P006930/1.
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References [1] Schmitz TL, Ziegert JC, Canning JS, Zapata R. Case study: A comparison of error sources in high-speed milling. Prec Eng 2008;32:126-33. [2] Papananias M, McLeay TE, Mahfouf M, Kadirkamanathan V. A Bayesian framework to estimate part quality and associated uncertainties in multistage manufacturing. Comput Ind 2019;105:35-47. [3] Shi J. Stream of variation modeling and analysis for multistage manufacturing processes. CRC press; 2006. [4] Karandikar J, McLeay TE, Turner S, Schmitz T. Tool wear monitoring using naïve Bayes classifiers. Int J Adv Manuf Technol 2015;77:1613-26. [5] McLeay TE. Unsupervised monitoring of machining processes. PhD Thesis. University of Sheffield; 2016. [6] Gandomi A, Haider M. Beyond the hype: Big data concepts, methods, and analytics. Int J Inf Manag 2015;35:137-44. [7] He QP, Wang J. Statistical process monitoring as a big data analytics tool for smart manufacturing. J Proc Contr 2018;67:35-43. [8] Kourti T. Application of latent variable methods to process control and multivariate statistical process control in industry. Int J Adapt Contr Sign Proc 2005;19:213-46. [9] Ferrer A. Multivariate statistical process control based on principal component analysis (MSPC-PCA): Some reflections and a case study in an autobody assembly process. Qual Eng 2007;19:311-25. [10] Chen Z, Lu S, Lam S. A hybrid system for SPC concurrent pattern recognition. Adv Eng Informat 2007;21:303-10. [11] El-Midany TT, El-Baz MA, Abd-Elwahed MS. A proposed framework for control chart pattern recognition in multivariate process using artificial neural networks. Exp Sys Appl 2010;37:1035-42. [12] Addeh A, Khormali A, Golilarz NA. Control chart pattern recognition using RBF neural network with new training algorithm and practical features. ISA Trans 2018;79:202-16. [13] Özel T, Karpat Y. Predictive modeling of surface roughness and tool wear in hard turning using regression and neural networks. Int J Mach T Manuf 2005;45:467-79. [14] Salgado DR, Alonso FJ, Cambero I, Marcelo A. In-process surface roughness prediction system using cutting vibrations in turning. Int J Adv Manuf Technol 2009;43:40-51. [15] Huang PB. An intelligent neural-fuzzy model for an in-process surface roughness monitoring system in end milling operations. J Intell Manuf 2016;27:689-700. [16] McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biol 1943;5:115-33. [17] Haykin S. Neural networks and learning machines. 3rd ed. New Jersey: Pearson; 2009. [18] Manry MT, Chandrasekaran H, Hsieh CH. Signal processing using the multilayer perceptron. In: Hu YH, Hwang JN, editors. Handbook of neural network signal processing. CRC Press LLC; 2002. [19] Forbes AB, Mengot A, Jonas K. Uncertainty associated with coordinate measurement in comparator mode. In: Laser Metrology and Machine Performance XI, LAMDAMAP. Huddersfield, UK; 2015. [20] Papananias M, Fletcher S, Longstaff AP, Forbes AB. Uncertainty evaluation associated with versatile automated gauging influenced by process variations through design of experiments approach. Prec Eng 2017;49:440-55. [21] Forbes AB, Papananias M, Longstaff AP, Fletcher S, Mengot A, Jonas K. Developments in automated flexible gauging and the uncertainty associated with comparative coordinate measurement. In: Euspen's 16th International Conference. Nottingham, UK; 2016. [22] Papananias M, Fletcher S, Longstaff AP, Mengot A, Jonas K, Forbes AB. Modelling uncertainty associated with comparative coordinate measurement through analysis of variance techniques. In: Euspen's 17th International Conference. Hannover, Germany; 2017. [23] Papananias M, Fletcher S, Longstaff AP, Mengot A, Jonas K, Forbes AB. Evaluation of automated flexible gauge performance using experimental designs. In: Laser Metrology and Machine Performance XII, LAMDAMAP. Wotton-under-Edge, UK; 2017.
Applied Soft Computing Journal 97 (2020) 106787
Contents lists available at ScienceDirect
Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc
Inspection by exception: A new machine learning-based approach for multistage manufacturing ∗
Moschos Papananias a , , Thomas E. McLeay b , Olusayo Obajemu a , Mahdi Mahfouf a , Visakan Kadirkamanathan a a b
Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK Sandvik Coromant, Mossvägen 10, Sandviken 811 34, Sweden
article
info
Article history: Received 5 December 2019 Received in revised form 19 August 2020 Accepted 9 October 2020 Available online 14 October 2020 Keywords: Artificial Neural Network (ANN) Fuzzy C-Means (FCM) Intelligent/smart manufacturing Machine learning Multistage Manufacturing Process (MMP) Principal Component Analysis (PCA)
a b s t r a c t Manufacturing processes usually consist of multiple different stages, each of which is influenced by a multitude of factors. Therefore, variations in product quality at a certain stage are contributed to by the errors generated at the current, as well as preceding, stages. The high cost of each production stage in the manufacture of high-quality products has stimulated a drive towards decreasing the volume of non-added value processes such as inspection. This paper presents a new method for what the authors have referred to as ‘inspection by exception’ – the principle of actively detecting and then inspecting only the parts that cannot be categorized as healthy or unhealthy with a high degree of certainty. The key idea is that by inspecting only those parts that are in the corridor of uncertainty, the volume of inspections are considerably reduced. This possibility is explored using multistage manufacturing data and both unsupervised and supervised learning algorithms. A case study is presented whereby material conditions and time domain features for force, vibration and tempering temperature are used as input data. Fuzzy C-Means (FCM) clustering is implemented to achieve inspection by exception in an unsupervised manner based on the normalized Euclidean distances between the principal components and cluster centres. Also, deviation vectors for product health are obtained using a comparator system to train neural networks for supervised learning-based inspection by exception. It is shown that the volume of inspections can be reduced by as much as 82% and 93% using the unsupervised and supervised learning approaches, respectively. © 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
1. Introduction Metal manufacturing processes usually involve a series of processing stages to achieve the desired geometry and properties of parts. There are various manufacturing methods including casting, forming and machining [1]. Each manufacturing method has its own advantages and disadvantages and the selection of the appropriate technology depends largely on the specific application. Forming and casting processes are mostly followed by machining operations to obtain the final geometry and surface finish of parts. Also, in many manufacturing applications, heat treatment techniques such as quenching, tempering and annealing are employed to modify the physical and mechanical properties of the workpiece. Thus, due to the multistage nature of a typical manufacturing process for metallic parts, the part quality deviations from the nominal geometry at a certain processing stage are contributed by multiple error sources introduced by the current, as well as previous, processing stages [2]. ∗ Corresponding author. E-mail address: m.papananias@sheffield.ac.uk (M. Papananias).
In traditional manufacturing, machining operations are usually followed by dimensional inspection to evaluate part tolerances. There is a variety of dimensional inspection methods including dedicated gauging, On-Machine Probing (OMP) and Coordinate Measuring Machine (CMM) measurement. Dedicated gauging can enable fast feedback to the production loop but it requires an operator to perform the measurements usually with multiple different gauges in order to evaluate all the specified part tolerances and thus, leading to additional high costs for calibrating each hard gauge. OMP refers to the use of Computer Numerically Controlled (CNC) machine tool as a CMM by using a machine tool probe. OMP possesses the advantage of in-situ inspection and thus, allowing machining and inspection with a single workholding setup as well as immediate re-work of the part when required. However, OMP suffers from significant measurement uncertainties due to the large range of complex influence factors and fails to detect machine tool error-induced deviations [3]. Therefore, supplementing with independent measurements, such as CMM measurement, is usually required. CMMs are accurate measurement systems but most require thermally controlled environments to guarantee their measuring capability. In addition,
https://doi.org/10.1016/j.asoc.2020.106787 1568-4946/© 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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the heavyweight structure of these machines gives rise to hysteresis error and results in conservative scanning speeds being selected in order to reduce the dynamic effects [4]. To deal with the machine’s dynamic and thermal errors, software technology for error compensation has been proposed and applied to CMMs but software error compensation solutions increase the already high cost of these measurement systems. This research work employs a shop floor Coordinate Measuring System (CMS) based on the parallel kinematic configuration. Parallel Kinematic Machines (PKMs) possess many advantages over Cartesian ones such as better dynamic performance and speed capability but they have a limited operational workspace and nonlinear behaviour across it. In recent years, manufacturers have faced many challenges to remain competitive with respect to costs, quality, delivery, flexibility, adaptability and sustainability. The trend towards autonomous and intelligent manufacturing systems, relies upon efficient data analytics tools such as those that enable process and product health monitoring and control. The fourth industrial revolution, known as Industry 4.0, concerns the digital transformation of manufacturing processes by integrating manufacturing equipment and systems with data analytics to enable production machines to take decisions based on available data and machine learning algorithms. In particular, modern manufacturing processes are supported by numerous data sources from models and monitored processes. However, the efficient use of these datasets requires statistical techniques such as Principal Component Analysis (PCA) to extract the useful information. PCA is a matrix factorization technique used to reduce the dimensionality of a dataset and reveal hidden informative underlying variables. Over the years, many monitoring systems for machining have been proposed to detect early abnormal process behaviour and reduce product quality variations. Two of the most studied areas of machining process monitoring are the cutting-tool and part condition monitoring based on sensor signals such as force and vibration [5]. Continuous tool monitoring is of high importance especially for difficult-to-machine materials where significant variation in tool life is observed. Most proposed methods are based on supervised learning algorithms though unsupervised learning has also been applied [6]. In particular, machine learning algorithms are largely classified into supervised and unsupervised, based on the mechanism by which the learning process is achieved. Unsupervised learning is a class of machine learning techniques that learn from unlabelled data; only input samples are available. Unsupervised learning techniques can be used in various applications such as dimensionality reduction, clustering and anomaly detection. Supervised learning requires labelled data (input–output samples) for training an algorithm. With the continuously growing amount of data collected from all the production process stages at which each product goes through, there exists a gap in the literature for intelligent product condition monitoring considering the dimensional accuracy of the product and the multistage manufacturing scenario. In addition, while many intelligent condition monitoring systems have been developed for manufacturing processes, most are based on supervised machine learning algorithms. Supervised monitoring systems for fault detection suffer from higher training costs since labelled training data (e.g. post-process inspection results) are required. The present work focuses on reducing the volume of dimensional inspections using multistage manufacturing data and machine learning techniques including both unsupervised and supervised; PCA, Fuzzy C-Means (FCM), and Artificial Neural Networks (ANNs). Section 2 presents a detailed review of literature relating to monitoring and control methods for manufacturing processes. Section 3 describes the proposed method for inspection by exception. Section 4 presents the basic theory for the algorithms
employed in the present work. Section 5 presents the experimental work. Section 6 implements and validates the proposed method for inspection by exception based on both unsupervised and supervised learning. Section 7 presents the concluding remarks. 2. Related literature Manufacturing enterprises are currently confronted with many challenges as a consequence of growing demands for higher quality of finished products, shorter manufacturing times, greater product complexity and variety, and reduced manufacturing costs, energy consumption and material waste in production. To meet these needs, the refinement of existing monitoring and control systems is becoming increasingly important for intelligent, autonomous manufacturing processes. Manufacturing includes a variety of processes and systems. In CNC machining processes, errors can be broadly classified into two main categories: static or quasi-static and dynamic [2]. Quasi-static errors refer to the static or slow-varying errors and include geometric and kinematic errors, thermal errors, cutting force induced errors, fixturing errors, starting material and tooling inaccuracies, etc. Dynamic errors are much larger and more dependent on the particular process conditions than static errors and are typically caused by sources such as controller error and machine structure vibration. A production process for metallic parts or products usually involves multiple stations or operations such as forming and heat treatment, subtractive machining, in-process and post-process inspection, assembly, and testing. Therefore, in a Multistage Manufacturing Process (MMP), workpiece geometric deviations at a certain production stage are caused by the variation sources introduced by the current stage, as well as the variation propagated from preceding stages [7]. In this paper, we focus on MMPs consisting of heat treatment operations, metal-removing operations, including milling and drilling, conducted on CNC machine tools, and post post-process inspection using automated comparator gauges calibrated through CMM measurements on a master part. Manufacturing operations can be divided into two types: value adding operations and non-value adding operations. For example, machining operations are value adding because they add value to the workpiece by changing its shape, dimensions and surface finish, while inspection operations such as OMP are non-value adding, though they can provide significant advantages to the manufacturing industry in terms of productivity and scrap levels. With the increasing complexity of manufacturing processes employed to change the geometry and certain properties of a workpiece, conventional CNC approaches may not be able to achieve the desired results in terms of dimension, form and geometry. Dimensional product variation management and reduction for MMPs have been studied extensively and several modelling techniques have been proposed over the years, particularly linearized Stream of Variation (SoV) modelling methods based on differential motion vectors, equivalent fixture error, and kinematic analysis [8]. SoV is a model-based method that utilizes mathematical models such as state-space models to describe the dimensional variation and propagation in multistage assembly processes and multistage machining processes. The derivation of such models is based upon physical knowledge and/or process monitoring data [9]. Loose et al. [10] developed a state-space variation propagation model to describe the product dimensional variation propagation among multiple machining operations with different setups. Their modelling approach can handle general fixture layouts, but they limited the scope of the model only to setup errors. Bazdar et al. [11] focused on diagnosing faults within multistage machining processes using state-space variation propagation modelling and discriminant analysis of setup 2
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Applied Soft Computing Journal 97 (2020) 106787
stages. In addition, although the subject of manufacturing process monitoring and control is a well-developed field of intelligent manufacturing, the manufacturing industry has adopted few monitoring and control systems to replace decision making of a human with a machine. The robustness issues when operating under different conditions and the high costs of training supervised monitoring systems remain two of the major issues faced when extending academic research solutions to industrial exploitation. There is therefore a need for intelligent monitoring and control systems that are able to function under various process conditions and conditions of uncertainty. This paper presents a new method, referred to as ‘inspection by exception’. The proposed method is based on the idea of predicting the end product quality using machine learning and multistage, inprocess monitoring data in order to capture sufficient knowledge about the production process and then inspecting the product only if it cannot be classified as conforming or non-conforming with a high degree of certainty. The proposed methodology is tested on a MMP consisting of different processing stages including heat treatment and machining, and on different dimensional metrology characteristics including diameter, true position, and circularity. This modelling problem can be considered to be representative of many manufacturing processes, particularly small batch manufacturing sectors such as aerospace manufacturing applications due to the nonlinearity, high dimensionality, sparsity and uncertainty of the manufacturing process and workpiece data. In addition, in order to achieve inspection by exception with the minimal cost of implementation, clustering-based inspection by exception is also proposed and validated.
errors. Du et al. [12] presented a generic framework for variation propagation modelling for multistage turning processes of rotary workpieces based on differential motion vectors. Wang et al. [13] described a generic variation propagation framework incorporating the elastic deformation variations into state-space modelling for multistage machining processes and Variable Stiffness Structure (VSS) workpieces as most existing SoV methodologies assume that the workpiece is a rigid body. The validation results obtained from a case study concerned with a four-cylinder engine block indicated that the prediction errors are significantly lower than those obtained from conventional SoV modelling methodologies. Although a large amount of research works have showed the reliability of SoV modelling methods for multistage machining processes to predict the dimensional product quality, the applicability of this approach is limited due to the challenges and difficulties associated with constructing and utilizing the SoV model for many MMPs. In recent years, manufacturing systems have reaped considerable benefit from advances in sensor and information technologies. Therefore, advanced process and product health monitoring and control techniques based on machine learning models and sensor signals such as temperature, force and vibration have attracted a lot of interest. The use of product health monitoring systems can allow us to identify issues associated with the product being manufactured before post-process inspection and thus can greatly help reduce the need for screening inspection without sacrificing the quality of the manufactured product. Wang et al. [14] proposed Multilayer Feedforward Neural Networks (MFNNs), based on an autoencoder for dimensionality reduction, to detect defective products from a powder metallurgy process. An ANN is a collection of interconnected neurons that are able to learn incrementally from their experience to solve complex problems such as nonlinear function approximation. Li et al. [15] proposed a deep learning-based classification model to detect defective products using the concept of fog computing in order to deal with large amounts of data. Papananias et al. [16] presented a Bayesian approach to estimate the results of postprocess inspection given in-process inspection data. For turning processes, Salgado et al. [17] proposed an in-process surface roughness prediction system, based on Least Squares Support Vector Machines (LS-SVMs), that uses as inputs feed rate, cutting speed, depth of cut, tool geometry parameters and information extracted from vibrations signals using Singular Spectrum Analysis (SSA). Özel and Karpat [18] used MFNNs to predict both surface roughness and tool flank wear in finish dry hard turning using as inputs material hardness in Rockwell-C scale, cutting speed, feed rate, axial cutting length and the mean values of three force components. For milling processes, Huang [19] presented an intelligent neural-fuzzy in-process surface roughness monitoring system for an end-milling operation using five inputs including spindle speed, feed rate, depth of cut, the average resultant peak force and the absolute average force. Kovac et al. [20] applied fuzzy logic and regression to predict surface roughness in dry face milling using as inputs cutting speed, feed rate, depth of cut and flank wear land width. Han et al. [21] presented a varyingparameter drilling method to improve manufacturing efficiency in successive drilling operations and hole surface quality for multi-hole components. They developed Radial Basis Function (RBF) neural networks to predict surface roughness using spindle speed, feed rate, crater wear, flank wear, outer corner wear, thrust force and torque. Published research on dimensional product health monitoring is limited and much of it focuses on monitoring only the machining process to identify the end product quality, though manufacturing processes typically involve multiple production
3. Inspection by exception method This section describes the proposed method for inspection by exception. The key idea of the method is that inspection is not required for parts that can be categorized as healthy or unhealthy with a high degree of certainty but only for those parts that are in the corridor of uncertainty so that the volume of inspections can be reduced without making a wrong decision, e.g. rejecting a part that conforms to design specifications (Type I error) or accepting a part that does not conform to design specifications (Type II error). The part quality characteristics considered in this paper are the diameter deviation, true position and circularity of a bore. Table 1 shows the deviations from nominal values for the three quality characteristics of interest obtained from the Equator gauge in scanning mode using the CMM Compare method. The columns of Table 1 are as follows: the first column includes the part label/number; the second column includes the diameter deviation; the third column includes the true position; the fourth column includes the circularity; and the fifth column indicates which parts conform to the specified tolerances. The deviations from (drawing) nominal values have been obtained by calculating the absolute difference between the actual/measured value and⏐ the ⏐ nominal value for each measurand and thus, hj = ⏐ yj − ỹj ⏐, for j = 1, 2, . . . , n, where yj denotes an observation of the measured quantity Yj and ỹj denotes the (drawing) nominal value of the same quantity, Yj . Suppose the tolerances are ±0.0700 mm for diameter, 0.0100 mm for true position (47.5 ± 0.075 in X axis from datum B and 40 ± 0.075 in Y axis from datum A), and 0.0500 mm for circularity. The parts that do not conform to the specified tolerances are the parts labelled as: 1, 10, and 23. The diameter deviations for these three parts are: 0.0771 mm, 0.0705 mm, and 0.0802 mm, respectively. The fourth largest diameter deviation is 0.0623 mm for part 19. The decision rule of the proposed method is given by:
If ĥjp
⎧ ⎪ ⎨ ⎪ ⎩
3
< τj
Healthy parts − No inspection
Other w ise
Inspect parts
> τj
Unhealthy parts − No inspection
(1)
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Applied Soft Computing Journal 97 (2020) 106787
be obtained by finding the weight vector a1 of N constants that maximizes the variance of aT1 x, given that ∥a1 ∥ = 1. The technique of Lagrange multipliers can be used to maximize V (y1 ) = aT1 Σa1 subject to aT1 a1 = 1. The second principal component can be obtained by finding the weight vector a2 of N constants that maximizes the variance of aT2 x, given that aT2 a2 = 1 and aT2 Σa1 = 0. Hence, the K th principal component is given by yK = aTK x where aK is an eigenvector of Σ corresponding to its K th largest eigenvalue λK = V (yK ). The proportion of the total variability explained by the first K principal components can be calculated as:
Table 1 Product quality deviations obtained from the Equator gauge. Parts
Diameter deviation (mm)
True position (mm)
Circularity (mm)
Conforming parts
1 2 6 7 9 10 12 13 14 15 16 18 19 21 22 23 24
0.0771 0.0573 0.0604 0.0550 0.0502 0.0705 0.0509 0.0574 0.0579 0.0564 0.0500 0.0525 0.0623 0.0598 0.0509 0.0802 0.0542
0.0075 0.0036 0.0032 0.0045 0.0039 0.0061 0.0016 0.0046 0.0019 0.0029 0.0060 0.0046 0.0061 0.0029 0.0042 0.0055 0.0028
0.0429 0.0364 0.0370 0.0355 0.0354 0.0420 0.0379 0.0406 0.0389 0.0365 0.0368 0.0363 0.0398 0.0364 0.0367 0.0411 0.0410
No Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes
ĥj1 , ĥj2 , . . . , ĥjP̃
)T
λj
∑N
λj
j=1 j=1
.
(2)
4.2. Fuzzy C-means clustering Clustering algorithms find natural groupings in data. Clustering methods utilize distance functions to measure the similarity of data points. The FCM algorithm is a soft clustering method in which each data point can belong to multiple clusters with varying degrees of membership [24]. The distance between data points and cluster centres can be computed by the Euclidean distance:
Two implementations are presented in this paper, both using machine learning but other modelling techniques may be applicable and may also be possibly advantageous to implement the method. In particular, a neural network-based approach is developed to predict the product health metric deviation vector, ĥj =
(
∑K
dij = xi − cj ,
, for p = 1, 2, . . . , P̃, and assess the require-
(3)
where xi ∈ R , for i = 1, 2, . . . , M, is the ith data point of Mobservations in N-dimensional Euclidean space and cj ∈ RN , for j = 1, 2, . . . , C , is the centre of the jth cluster. FCM is based on the minimization of the following objective function: N
ment for inspection, where P̃ denotes the number of parts used to test the model. The proposed method allows users freedom to choose their preferred bounds τ j and τ j . However, if the bounds τ j and τ j are not selected appropriately, then the gap between τ j and τ j may be too large, resulting in unnecessary inspections or the gap may be too small, which may result in healthy parts being rejected (Type I error) and unhealthy parts being accepted (Type II error). The gap between the bounds depends on the accuracy of the model and the uncertainty associated with the directly measured product health metric deviation vector, hjp . Also, a clustering-based approach is developed to achieve inspection by exception based on the normalized Euclidean distances between the principal components and cluster centres. This approach is based on the FCM algorithm, which allows each data point to belong to more than one cluster. The unsupervised approach will be presented first in this work.
Jw =
M C ∑ ∑
µijw d2ij ,
1 < w < ∞,
(4)
i=1 j=1
subject to the constraints µij ∈ [0, 1] and ∀i: j=1 µij = 1, where µij is the degree of membership of xi in the jth cluster and w is the weighting exponent which controls the degree of fuzziness. Note that the cluster centres are calculated by:
∑C
∑M
i=1
cj = ∑M
µijw xi
i=1
µijw
.
(5)
The FCM algorithm in MATLAB performs the following steps during clustering:
4. Basic theory
i The cluster membership values, µij , are randomly initialized. ii The cluster centres, cj , are calculated by Eq. (5): iii The cluster membership values, µij , are updated according to: 1
4.1. Principal component analysis The main purpose of PCA is to extract the useful information from a dataset consisting of a set of correlated variables and to represent this information as a new set of uncorrelated variables [22,23]. These uncorrelated variables are principal components and are the directions in which the data have the largest variances. Suppose that we have observations on N variables x1 , x2 , . . . , xN . The first principal component, y1 , is defined ∑N to be the linear combination a11 x1 + a12 x2 + · · · + a1N xN = j=1 a1j xj , ∥a1 ∥ = 1, with maximum variance. The second principal component, y2 , is a linear combination a21 x1 + a22 x2 + · · · + a2N xN = ∑ N j=1 a2j xj , ∥a2 ∥ = 1, which is uncorrelated with the first derived variable and has maximum variance. The K th principal component, yK , for K = 1, 2, . . . , N, can be as a linear ∑defined N combination aK 1 x1 + aK 2 x2 + · · · + aKN xN = j=1 aKj xj , ∥aK ∥ = 1, which is uncorrelated with the first K − 1 derived variables and which has maximum variance. Let Σ be the covariance matrix of the vector of variables x = (x1 , x2 , . . . , xN )T , which we assume to be positive definite. Then, the first principal component can
µij =
∑C
k=1
(
∥ x i − cj ∥
) w2−1
∥xi −ck ∥
iv The objective function, J w , is calculated by Eq. (4). Steps ii–iv are repeated until J w improves by less than a predefined threshold value between two consecutive iterations or until a predefined number of iterations has been reached. 4.3. Artificial neural networks ANNs are computational models that emulate the learning process of biological neural networks. Over the years, many different types of ANNs have been proposed, one of the most popular being the MFNNs also known as Multi-Layer Perceptron (MLP) networks. Let L be the number of layers of the network. Each layer 4
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Applied Soft Computing Journal 97 (2020) 106787
Table 2 Chemical composition of starting material. Carbon C (%)
Silicon Si (%)
Manganese Mn (%)
Phosphorus P (%)
Sulphur S (%)
Chromium Cr (%)
Nickel Ni (%)
Molybdenum Mo (%)
Copper Cu (%)
0.37
0.23
0.55
0.007
0.001
1.34
1.53
0.22
0.11
is denoted by l, l = 0, 1, . . . , L, with l = 0 denoting the input layer, l = L the output layer, and l = 1, . . . , L − 1 the hidden layers. The neurons in any layer l = 1, . . . , L operate as follows:
Table 3 Mechanical properties of starting material.
N(l−1)
netj (l) =
∑
Size (mm)
Rp02 N/mm2 (MPa)
Rm N/mm2 (MPa)
A5 (%)
Z (%)
Hardness (HB)
10
766
941
18.5
63
272-296
) ( wij (l − 1, l) Oi (l − 1)+θj (l) , Oj (l) = f netj (l) ,
i=1
(6)
during heat treatment. Following the heat treatment process, the blocks were grinded to improve the quality of material surface and measure the material surface hardness. A Rockwell device was used to measure the surface hardness of the heat treated blocks. A full factorial design (see Table 5) was performed for machining using a DMG MORI NVX 5080 3-axis machine. The factors included material surface hardness, feed rate, spindle speed and datum error in both X and Y axes when handing over to the second orientation of the workpiece (flipped around the Y axis) for machining the features of its bottom side. All the factors included two levels and one centre point. Each workpiece was machined with coolant. Six cutting tools were employed to manufacture the steel bearing housing parts and changed when reached a certain flank wear width. The wear was evaluated on each flute using a Leica microscope after obtaining each product. A Kistler quartz multicomponent dynamometer (9255B), consisting of four 3-component force sensors, and DynoWare software were used to measure force. The dynamometer was located between the vice holding the workpiece and the machine table. An accelerometer sensor, placed on the spindle, and NI LabVIEW SignalExpress software were used to obtain vibration data. The sampling rate for both force and vibration data was 10 kHz. In total, eighteen parts were machined (seventeen parts for the experimental design and one part to be used as a master part in CMM Compare measurement). A Renishaw Equator gauge (300 Extended Height) equipped with the SP25 3-axis analogue scanning probe was used for post-process inspection under workshop conditions [26,27]. The Equator was employed in CMM Compare and in scanning measuring mode. The CMM Compare method requires a production part to be labelled as a ‘master’ part and measured on a calibrated CMM to produce a calibration file for the comparator measurement system [28]. A Mitutoyo CMM located in a temperature controlled room was used to produce the calibration file. The master part had been thermally stabilized before generating the calibration file. The CMM was equipped with a Renishaw REVO RSP3 3D scanning probe. The stylus used for both the Equator and the CMM was a typical 30 mm long stylus with tungsten carbide stem and a 2 mm diameter ruby ball. The same part fixturing setup was also used for both the Equator and the CMM.
where Oj (l) is the output of neuron j in layer l, f is an activation function, N(l − 1) is the number of nodes in layer l − 1, wij (l − 1, l) is the synaptic weight coefficient associated with the connection from node i in layer l−1 to node j in layer l, Oi (l − 1) is the output of node i in layer l−1, and θj (l) is the bias of neuron j in layer l. The dataset required to train the network consists{ of P input-desired } output patterns x(1) , h(1) , x(2) , h(2) , . . . , x(P ) , h(P ) , where
{
x(p) =
[
(p)
} {
(p)
x1 , . . . , xN(0)
[
(p)
]T
is the input vector for the pth pattern
(p)
and h(p) = h1 , . . . , hN(L) (p)
pth pattern. Let ĥ
[
}
]T
(p)
is the desired output vector for the
= ĥ1 , . . . , ĥ(Np)(L)
]T
denote the output vector
for the pth pattern. The Mean Squared Error (MSE) is given by: Jw =
P 1∑
P
e(p),
(7)
p=1
(p) 2
∑N(L) [
(p)
(p)
]2
. Minimizahj − ĥj where e (p) = h(p) − ĥ = j=1 tion of Jw is attempted by using a particular Back-Propagation (BP) algorithm to adjust the network’s weights [25]. 5. Experimental work Experimental work was performed, involving multiple stages of manufacturing, to produce steel bearing housing parts. The MMP consists of heat treatment, grinding, hardness testing, machining and post-process inspection on the shop floor (see Fig. 1). The drawing and Computer-Aided Design (CAD) model of the part is shown in Fig. 2. The part has several critical features that should be sensitive to manufacturing process conditions and errors. For example, any tool/spindle runout can be indicated in the diameter measurement and variation in material hardness can cause differing levels of deflection. The starting material was EN24T steel. The chemical composition of this material is shown is Table 2. Table 3 shows the mechanical properties of the starting material. The EN24T material, is readily machinable because it is heat treated (hardened and tempered and stressfree annealed) by the supplier. However, the starting material was further hardened and tempered at different temperatures. A VECSTAR furnace was used for heat treatment. In particular, the starting material bar was sawn and machined to a nominal size, 25 off blocks. The twenty-five material blocks were divided into five batches and heated up to 845 ◦ C, separately (five batches of five blocks each), and then quenched in oil for hardening. After the hardening operation, tempering was performed at different temperatures (450 ◦ C, 550 ◦ C and 650 ◦ C) to add variability in the properties of the material such as surface hardness (see Table 4). Five K-type thermocouples with protection sheath were used to measure variation in temperature gradient within the furnace
6. Implementation and validation of the proposed method 6.1. Clustering-based inspection by exception method This section presents an unsupervised learning approach to achieve inspection by exception. The machined parts were clustered into two groups using the FCM clustering algorithm in MATLAB. The dataset includes: the Root-Mean-Square (RMS), sample kurtosis, sample skewness, sample variance and mean features of three vibration components (Vx, Vy, Vz); the same five features (RMS, sample kurtosis, sample skewness, sample variance and 5
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Fig. 1. Multistage manufacturing process.
Fig. 2. Drawing and CAD model of the part.
sample mean) of average values of three force components (Fx, Fy, Fz) obtained from all the four sensors of the dynamometer; the maximum temperature obtained from the five K-type thermocouples during tempering; and a coded vector corresponding to the material surface hardness. All the extracted features were normalized by the Euclidean norm (2-norm). One major difficulty in multivariate analysis is the problem of visualizing high-dimensional data. To reduce the number of variables to a few (≪N) variables that represent most of the
information in the original variables, PCA was performed in MATLAB using a Singular Value Decomposition (SVD) of the input data matrix X = U ΣVT ∈ RM ×N , where both U ∈ RM ×M and V ∈ RN ×N are orthogonal matrices and Σ ∈ RM ×N is a diagonal matrix with diagonal elements, σj , such that σ1 ≥ σ2 ≥ · · · ≥ σmin(M ,N) ≥ 0. Therefore, mean-centring the columns of the normalized input data matrix X was an essential pre-processing step in the process of dimensionality reduction. A 2-fold cross-validation approach was employed to test the PCA-based clustering approach using 6
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Table 4 Heat treatment. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Block number
Hardening (◦ C)
Tempering (◦ C)
13 14 10 12 22 15 9 19 16 24 21 7 2 18 6 23 1
845 845 845 845 845 845 845 845 845 845 845 845 835 845 845 845 835
450 550 450 650 450 650 650 450 450 650 650 450 650 650 650 450 450
Table 5 Full factorial design.
Fig. 3. PCA-based FCM clustering results for fold 1 (training).
Block number
Surface hardness
Feed rate
Spindle speed
Datum error in both X and Y (mm)
13 14 10 12 22 15 9 19 16 24 21 7 2 18 6 23 1
Hard Middle Hard Soft Hard Soft Soft Hard Hard Soft Soft Hard Soft Soft Soft Hard Hard
Programmed +10% +20% Programmed Programmed +20% Programmed Programmed Programmed Programmed +20% +20% +20% Programmed +20% +20% +20%
+20% +10%
0 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0 0 0.02 0.02 0 0 0 0 0
Programmed Programmed Programmed +20% +20% +20% Programmed Programmed Programmed +20% +20% +20% Programmed +20% Programmed
the minimum improvement in objective function between two consecutive iterations was set to 0.00001. The clustering algorithm was trained using the first two principal components of the training dataset. Then, new data/test dataset were assigned to the existing clusters and the normalized Euclidean distances between the first two principal components and cluster centres were computed. The computed distances are used to assess whether or not a product meets its specifications and identify the parts that require inspection for conformance assessment. Figs. 3–6 show the clustering results. Figs. 3 and 5 show the clustering results obtained from training the clustering algorithm for fold 1 and 2, respectively, using the first two principal components. Fold 1 uses sub-dataset 1 for training and sub-dataset 2 for testing. Fold 2 uses sub-dataset 2 for training and sub-dataset 1 for testing. Figs. 4 and 6 show the assignment of the test dataset (the first two principal components obtained from the trained PCA model) to the existing clusters shown in Figs. 3 and 5, respectively. Figs. 7 and 8 show the normalized Euclidean distances between the first two principal components and cluster centres for fold 1 and 2, respectively. Based on the results shown in Figs. 7 and 8, it can be concluded that the PCA-based FCM clustering approach can reduce the volume of inspections from seventeen parts to one part for fold 1 and to three parts for fold 2, since only part 19 for fold 1 and parts 10, 13 and 7 for fold 2 require inspection to determine successfully whether or not they conform to specifications.
data from the whole experimental design (seventeen manufactured parts). In particular, the dataset of seventeen parts was partitioned into two sub-datasets: one sub-dataset was used for training the clustering algorithm and one sub-dataset was used for testing it. The cross-validation process was repeated two times so that both sub-datasets were used as the validation dataset once. Sub-dataset 1 includes the parts: 1, 2, 6, 7, 9, 10, 12, 13, 14. Sub-dataset 2 includes the parts: 15, 16, 18, 19, 21, 22, 23, 24. The percent variability explained by the first two components are: 81.23% for sub-dataset 1 and 89.61% for sub-dataset 2. For sub-dataset 2 used as test dataset, the mean squared reconstruction error for the training data considering the first two principal components was 0.00071 and for the test data considering the first two principal components obtained from the trained PCA model was 0.00430. Similarly, for sub-dataset 1 used as test dataset, they were 0.00075 and 0.00180, respectively. Given the first two principal components, the FCM algorithm was employed to partition the data into two clusters. The FCM algorithm initially generates a random membership matrix. In each clustering iteration, the FCM algorithm calculates the cluster centres and updates the membership matrix using the calculated cluster centre locations. The algorithm then computes the objective function value. The clustering process stops when the objective function improvement falls below a predefined threshold value or when the maximum number of iterations has been reached. The amount of fuzzy overlap during clustering was set to 15, the maximum number of iterations was set to 100, and
6.2. Neural network-based inspection by exception method This section implements a supervised learning approach using PCA-based MLP networks to provide deviation vectors for product health and achieve inspection by exception. 6.2.1. Product health metric vectors A CMS operating in comparator mode (Equator) was used to obtain m measurements on a quantity Y , regarded as a random variable and called the measurand, e.g. the diameter of a bore. Let y1 , y2 , . . . , ym denote the corresponding measured values obtained from the comparator system in reproducibility conditions. The measurements y1 , y2 , . . . , ym involve comparator measurements and thus, random effects are dominant [29]. Given the measurand Y and its attached Probability Density ∫ ∞ Function (PDF) g ( y), with g ( y) ≥ 0 for all values of y and −∞ g ( y) d y = 1, the 7
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Fig. 7. Normalized Euclidean distances between the first two principal components and cluster centres for fold 1.
Fig. 4. PCA-based FCM clustering results for fold 1 (testing).
Fig. 5. PCA-based FCM clustering results for fold 2 (training).
Fig. 8. Normalized Euclidean distances between the first two principal components and cluster centres for fold 2.
expectation E(Y ) and the variance V (Y ) are defined, respectively, as: E (Y ) =
∫
∞
yg ( y) d y,
(8)
−∞
V (Y ) = E (Y − E (Y ))2 =
[
]
∞
∫
[ y − E (Y )]2 g ( y) d y,
(9)
−∞
Note that if Y ∼ N µ, σ 2 then E (Y ) = µ and V (Y ) = σ 2 , where µ is the expectation or mean and σ is the standard deviation, the positive square root of the variance σ 2 . For n geometric tolerances applied to one or more features, let Y denote the product health matrix:
(
)
y11
y12
···
y1n
( ) ⎢ y21 Y = yij = ⎢ ⎢ ..
y22
.. .
... .. .
y2n ⎥
ym1
ym2
...
ymn
⎡ ⎢
⎣ .
Fig. 6. PCA-based FCM clustering results for fold 2 (testing). 8
⎤
⎥ m×n .. ⎥ ⎥∈R , . ⎦
(10)
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The standard uncertainty, u(cal), was estimated by the exper√ imental standard deviation of the mean, s ( ycal ) = s/ mcal , using the CMM measurements on the master part. The uncertainty components, u(p) and u(b), were calculated by the experimental standard deviation of the mean using the comparative coordinate measurements on the test part and master part, respectively. The systematic error component, b, was calculated by | y − ycal |, where y denotes the mean value of the Equator measurements on the master part and ycal is the CMM calibrated (mean) value of the same part and measurand. The expanded measurement uncertainties, U, of the master part, used to validate the CMM Compare method, are: 0.54 µm, 0.76 µm and 1.08 µm for diameter, true position and circularity, respectively, for a coverage factor k = 2 and a confidence level of 95.45%. For example, for the test part 24, the expanded measurement uncertainties are similarly: 0.63 µm, 0.91 µm and 2.66 µm, respectively. If a random sample of size m is drawn from a population which forms a normal ( distribution, √ ) then, the appropriate test statistic is t = ( y − µ) / s/ m , which has a student’s t-distribution with ν = m − 1 degrees of freedom. The mean of the t-distribution is zero and its variance is ν/(ν − 2) for ν > 2. As ν → ∞, the t-distribution approaches a normal distribution with µ = 0 and σ = 1 [30].
where yij denotes the element located in the ith row and the jth column of the product health matrix Y. Given that the product is measured m times independently, under repeatability conditions, estimates for µ1 , µ2 , . . . , µn and σ1 , σ2 , . . . , σn can be obtained by the sample means y1 , y2 , . . . , yn and the sample standard deviations s1 , s2 , . . . , sn , respectively:
yj =
m 1 ∑
m
yij , sj = √
i=1
m ∑ (
1 m−1
yij − yj
)2
, j = 1, 2, . . . , n,
i=1
(11) 2
Note that while the sample variance s is an unbiased estimator of the population variance σ 2 , the sample standard deviation s is a biased estimator of the population standard deviation σ [30]. A measure of linear association between the observations of jth and lth product quality characteristics can be provided by the sample covariance: sjl =
m ∑ (
1 m−1
yij − yj ( yil − yl ) ,
j = 1, 2, . . . , n,
)
i=1
l = 1, 2, . . . , n.
(12)
6.2.3. Prediction of product health metric deviation vectors To predict the product health metric deviation vectors, an MLP network with 3 inputs, one hidden layer consisting of five neurons, and one output was developed for each product quality characteristic in MATLAB. For all the models, tan-sigmoid transfer functions were used in the hidden layer and a linear activation function was used for the output neuron. The inputs to the network are the first three principal components of the normalized dataset used for the clustering approach presented in Section 6.1. The output is the product health metric deviation vector for each quality characteristic (diameter, true position and circularity of the bore), obtained by the absolute difference between the (drawing) nominal value and the measured value obtained from the Equator gauge in scanning mode using the CMM Compare method. All the models were trained by Resilient BP, which converges faster than the traditional BP algorithm [33]. A 4-fold cross-validation approach was employed to test the neural network models using data from the manufacture of sixteen parts (block 14 was excluded). In particular, the dataset of sixteen parts was randomly partitioned into four sub-datasets and three sub-datasets were used to train the models and a single sub-dataset was used to test the models. The cross-validation process was repeated four times so that each of the sub-datasets was used as the validation dataset once. The performance of each model was evaluated using the MSE. The training process was stopped when reaching the specified maximum number of epochs (1000) or the validation error began to rise. Sub-dataset 1 includes the parts: 2, 23, 22, 21. Sub-dataset 2 includes the parts: 12, 13, 24, 7. Sub-dataset 3 includes the parts: 19, 6, 9, 10. Subdataset 4 includes the parts: 1, 16, 15, 18. Each neural network model was trained using the first three components obtained from the PCA transformation of the training dataset. The percent variability explained by the first three components are: 89.17% for sub-datasets 2,3,4; 90.76% for sub-datasets 1,3,4; 90.88% for sub-datasets 1,2,4; and 93.27% for sub-datasets 1,2,3. Each trained neural network model was tested using the first three components obtained from the trained PCA model on the test dataset. The mean squared reconstruction error for the training dataset using the first three components was 0.00044 for sub-dataset 1 used as test dataset; 0.00063 for sub-dataset 2; 0.00061 for sub-dataset 3; and 0.00037 for sub-dataset 4. The mean squared reconstruction error obtained from the trained PCA model on the
The sample covariance of the standardized observations can be given by the sample correlation coefficient:
∑m (
sjl
i=1
rjl = √ √ = √ ∑m ( sjj sll i=1
yij − yj ( yil − yl )
yij − yj
)
)2 √∑m
− 1 ≤ rjl ≤ 1.
i=1
( yil − yl )2
, (13)
Two random variables ) ( ( Yj)and Yl are statistically independent = yj , yl can be factored as gjl yj , yl if (their joint PDF g jl ) gj yj gl ( yl ). Independent random variables are also uncorrelated but the converse does not necessarily hold [31]. The product correlation matrix given by: 1
r12
···
r1 n
⎢ r21 R=⎢ ⎢ .. .
1
.. .
... .. .
r2 n ⎥
r n2
...
⎡ ⎢ ⎣
r n1
⎤
⎥ .. ⎥ ⎥, . ⎦
(14)
1
can be computed to exploit the correlation between the same characteristics for identical features. 6.2.2. Experimental evaluation of uncertainty associated with equator CMM compare measurement This section presents an experimental method to evaluate the measurement uncertainty associated with an estimate of a product quality characteristic in order to provide confidence in the comparator measurement results and allow the calculation of conformance and non-conformance probabilities. The measurement uncertainties associated with Equator CMM Compare method were calculated experimentally considering: (i) the standard uncertainty, u(cal), associated with the uncertainty of the calibration of the master part; ii) the standard uncertainty, u(p), associated with the comparative coordinate measurement procedure; and iii) the standard uncertainty, u(b), associated with the systematic error component, b, of the comparative coordinate measurement [32]. The effect of the uncertainty in the Coefficient of Thermal Expansion (CTE) will not be considered in this evaluation procedure. The combined standard uncertainty, uc ( y), of any measurand was calculated as follows: uc ( y) =
√
u2 (cal) + u2 (p) + u2 (b) + b.
(15) 9
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Applied Soft Computing Journal 97 (2020) 106787 Table 6 4-fold cross-validation for neural network model.
test dataset using the first three components was 0.00440 for subdataset 1 used as test dataset; 0.00082 for sub-dataset 2; 0.00099 for sub-dataset 3; and 0.00240 for sub-dataset 4. The MSE results obtained from all the models on non-training data are shown in Table 6. Based on Table 6, it can be concluded that the MLP network provides accurate predictions for all the measurands and the differences in the MSE values between each sub-dataset are very small. Also, the residual values were calculated by the absolute difference between the measured deviations obtained from the comparator system and the predicted deviations. The residual values range from 0.4 µm to 6.3 µm for diameter, from 0.0 µm to 1.3 µm for true position, and from 0.0 µm to 2.7 µm for circularity. The average residual values for diameter, true position and circularity are 3.0 µm, 0.6 µm and 1.3 µm, respectively. Therefore, it can be concluded that feedforward neural networks perform well in predicting the end product quality deviations especially for true position and circularity. The proposed method for inspection by exception is based on the following scheme to identify the parts that require inspection in order to assess whether or not they conform to design specifications. Given the predicted product health metric deviation vector ĥj : the parts with ĥjp < τ j , for p = 1, 2, . . . , P̃, are conforming parts and do not require inspection because their predicted deviations are far from the specified tolerances; in order to account for the uncertainty associated with the model predictions, the parts with τ j ≤ ĥjp ≤ τ j require inspection because their predicted deviations are close to the specified tolerances; and the parts with ĥjp > τ j are non-conforming parts with no requirements for inspection because their predicted deviations have greatly exceeded the tolerance specifications. Given the model predictions, ĥj , and part tolerances (±0.0700 mm for diameter, 0.0100 mm for true position and 0.0500 mm for circularity), the non-conforming parts are the parts: 1, 10, and 23. The predicted diameter deviations for these three parts are: 0.0766 mm, 0.0713 mm, and 0.0794 mm, respectively. Accounting for ±6 µm, ±2 µm and ±3 µm uncertainty associated with the model predictions, for diameter deviation, true position, and circularity, respectively, and thus, given that τ j = 0.0640 mm, where j = 1 for diameter deviation, τ j = 0.0080 mm, where j = 2 for true position, and τ j = 0.0470 mm, where j = 3 for circularity, and, τ j = 0.0760 mm, where j = 1 for diameter deviation, τ j = 0.0120 mm, where j = 2 for true position, and τ j = 0.0530 mm, where j = 3 for circularity, only the part 10 requires inspection because its predicted diameter deviation is within τ 1 and τ 1 . Given these bounds, the proposed method based on PCA-based neural networks can reduce inspection volume from sixteen parts to just one part. For comparison, linear regression models were also developed. Figs. 9–11 show the normal probability plots of the residuals of the fitted linear regression models. The MSE results on nontraining data are shown in Table 7. Figs. 12–14 are the bar graphs of residuals calculated by the absolute difference between the measured deviations obtained from the comparator measurement system and the predicted deviations obtained from the neural network and the linear model. Linear regression models are among the most fundamental and widely used tools for many modelling problems due to their simplicity, interpretability and performance in low-data regimes. However, they may be inadequate as models for nonlinear problems and, as a result, they may not fit the data as well as neural networks. Many advanced regression modelling methods including neural networks can be considered as extensions of linear regression modelling [34]. Compared to linear regression, the neural network model provides more accurate predictions. For the linear regression model, the residual values range from 0.2 µm to 12.9 µm for diameter, from 0.1 µm to 1.8 µm for true position, and from 0.2 µm
Sub-dataset
Diameter deviation MSE (mm2 )
1 2 3 4
1.21 1.25 2.26 5.93
× × × ×
10−5 10−5 10−5 10−6
True position MSE (mm2 ) 5.48 7.80 3.99 3.55
× × × ×
10−7 10−7 10−7 10−7
Circularity MSE (mm2 ) 1.16 4.54 3.24 5.10
× × × ×
10−6 10−6 10−6 10−7
Table 7 4-fold cross-validation for linear regression model. Sub-dataset
Diameter deviation MSE (mm2 )
1 2 3 4
2.68 1.18 4.87 5.58
× × × ×
10−5 10−5 10−5 10−5
True position MSE (mm2 ) 4.90 1.22 1.00 7.76
× × × ×
10−7 10−6 10−6 10−7
Circularity MSE (mm2 ) 8.92 1.10 5.39 5.47
× × × ×
10−6 10−5 10−6 10−6
Table 8 Predicted deviations from neural network model. Parts
Diameter deviation (mm)
True position (mm)
Circularity(mm)
2 23 22 21 12 13 24 7 19 6 9 10 1 16 15 18
0.0533 0.0794 0.0523 0.0543 0.0517 0.0570 0.0494 0.0499 0.0575 0.0541 0.0554 0.0713 0.0766 0.0457 0.0545 0.0537
0.0043 0.0056 0.0038 0.0017 0.0029 0.0054 0.0029 0.0053 0.0061 0.0021 0.0035 0.0057 0.0073 0.0058 0.0036 0.0037
0.0364 0.0400 0.0355 0.0378 0.0382 0.0383 0.0383 0.0378 0.0382 0.0367 0.0372 0.0447 0.0416 0.0370 0.0368 0.0357
Table 9 Predicted deviations from linear regression model. Parts
Diameter deviation (mm)
True position (mm)
Circularity (mm)
2 23 22 21 12 13 24 7 19 6 9 10 1 16 15 18
0.0571 0.0857 0.0580 0.0547 0.0553 0.0605 0.0540 0.0593 0.0573 0.0577 0.0539 0.0583 0.0642 0.0545 0.0518 0.0566
0.0038 0.0064 0.0052 0.0026 0.0031 0.0057 0.0031 0.0056 0.0055 0.0031 0.0033 0.0043 0.0067 0.0049 0.0032 0.0036
0.0378 0.0462 0.0390 0.0380 0.0360 0.0392 0.0358 0.0388 0.0383 0.0378 0.0373 0.0381 0.0385 0.0380 0.0367 0.0372
to 5.2 µm for circularity. The average residual values for the regression model for diameter, true position and circularity are 5.0 µm, 0.8 µm, and 2.3 µm, respectively. The predicted diameter deviations from the regression model for parts 1, 10 and 23 are: 0.0642 mm, 0.0583 mm, and 0.0857 mm, respectively, and thus, the linear regression model fails to achieve inspection by exception. Tables 8 and 9 show the predicted deviations from the neural network model and linear regression model, respectively. 6.2.4. Conformance and non-conformance probabilities The probability that a random variable H is no greater than a specified value T is given by the integral of the PDF between −∞ 10
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Applied Soft Computing Journal 97 (2020) 106787
Fig. 9. Normal probability plots of residuals for diameter deviation.
Fig. 10. Normal probability plots of residuals for true position.
and T and represented by the Cumulative Distribution Function
with limT →−∞ G (T ) = 0 and limT →∞ G (T ) = 1. Therefore, the
(CDF):
CDF can be used to compute the conformance probability:
G (T ) = P (H ≤ T ) =
∫
T
g (h) dh,
T ∈ R,
pc = P (TL ≤ H ≤ TU ) = G (TU ) − G (TL ) =
(16)
∫
TU TL
−∞
11
g (h) dh.
(17)
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Fig. 11. Normal probability plots of residuals for circularity.
Fig. 12. Residual magnitude for diameter deviation for all parts evaluated by cross validation.
is 1 µm. The non-conformance probability is pc
Given the tolerance limits TL and TU for diameter, the best estimate h1p , and associated standard ( uncertainty ) (u(h1p ), )the conformance probability is pc (h1p ) = Φ
TU −h1p u(h1p )
−Φ
TL −h1p u(h1p )
= 1 − pc .
Similarly, the conformance and non-conformance probabilities can be obtained from the prediction results ĥjp by calculating an
, where
Φ is the CDF of the standard normal random variable with zero mean and unit variance. For example, pc (h1p ) = 0.3 for p = 10 (part 10) given that the tolerance limits are −0.07 mm and
estimate of the variance from the residuals. However, for true po-
0.07 mm, the mean is 0.0705 mm, and the standard uncertainty
j = 2 and j = 3. Note that, although the (diameter) deviations
sition and circularity, one-sided tolerance intervals with ( a single ) upper tolerance limit are used and thus, pc (hjp ) = Φ 12
TU −hjp u(hjp )
for
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Fig. 13. Residual magnitude for true position for all parts evaluated by cross validation.
Fig. 14. Residual magnitude for circularity for all parts evaluated by cross validation.
have been obtained as absolute values, two-sided tolerance intervals with lower and upper tolerance limits are still required to obtain the conformance and non-conformance probabilities for diameter deviations. Finally, signed deviations must be used for non-symmetrical two-sided tolerance intervals.
strategies for intelligent/smart manufacturing. The choice of data analytics and machine learning algorithms used to discover automatically useful patterns and trends in collected data or perform accurate predictions depends on many factors such as the cost and practicality in collecting the class labels. This paper presented a new method for what the authors have called â&#x20AC;&#x2DC;inspection by exceptionâ&#x20AC;&#x2122;. The proposed method is based on multistage manufacturing data and machine learning techniques, including both unsupervised and supervised learning algorithms. The input data samples included material conditions, tempering temperature,
7. Summary and concluding remarks With the proliferation of in-process metrology data over the years, there has been an increase of interest in machine learning techniques to develop more efficient monitoring and control 13
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and vibration and force signals of the metal cutting process. PCA was used for dimensionality reduction. An unsupervised learning approach was developed to partition the manufactured products into two groups using the first two principal components of the normalized dataset and the FCM clustering algorithm. The normalized Euclidean distances between the principal components and cluster centres were then computed to identify the conforming parts, the non-conforming parts, and the parts that require inspection in order to determine whether or not they conform to specifications. The unsupervised learning approach reduced significantly the requirement for inspection, and, in particular, based on the 2-fold cross validation results, it was demonstrated that the volume of inspections were reduced from seventeen parts to only three parts. A supervised learning approach based on neural networks was also developed to provide deviation vectors for product health using the first three principal components of the normalized dataset. The output data used for training the supervised model were obtained from an automated comparator system. An experimental methodology to evaluate the uncertainty associated with comparator measurement was presented to provide confidence in the measurement results and enable the calculation of conformance and non-conformance probabilities. The predicted product health metric deviation vectors compared well with the measured ones especially for true position and circularity. Regression models were also developed and compared with the neural network models. The results showed that the neural network models outperform the regression models. Based on the 4-fold cross validation results from the supervised learning approach, the volume of inspections were reduced from sixteen parts to just one part. The proposed method for inspection by exception accounts for model uncertainties and therefore, it can comply with applications that suffer from tight part tolerances. Determining the parts that require inspection for conformance assessment in an unsupervised manner has the advantage of lower cost since class labels are not required for training the machine learning algorithm. However, obtaining the health condition of the parts require supervised models.
[3] R.J. Hocken, P.H. Pereira, Coordinate Measuring Machines and Systems, CRC Press, 2016. [4] P. Pereira, R. Hocken, Characterization and compensation of dynamic errors of a scanning coordinate measuring machine, Precis. Eng. 31 (1) (2007) 22–32. [5] J.V. Abellan-Nebot, F.R. Subirón, A review of machining monitoring systems based on artificial intelligence process models, Int. J. Adv. Manuf. Technol. 47 (1–4) (2010) 237–257. [6] T.E. McLeay, Unsupervised Monitoring of Machining Processes, University of Sheffield, 2016. [7] D. Ceglarek, et al., Time-based competition in multistage manufacturing: Stream-of-variation analysis (SOVA) methodology, Int. J. Flexible Manuf. Syst. 16 (1) (2004) 11–44. [8] F. Yang, S. Jin, Z. Li, A comprehensive study of linear variation propagation modeling methods for multistage machining processes, Int. J. Adv. Manuf. Technol. 90 (5–8) (2017) 2139–2151. [9] J. Shi, in: J. Baillieul, T. Samad (Eds.), Stream of Variations Analysis, in Encyclopedia of Systems and Control, Springer London, London, 2014, pp. 1–6. [10] J.-P. Loose, S. Zhou, D. Ceglarek, Kinematic analysis of dimensional variation propagation for multistage machining processes with general fixture layouts, IEEE Trans. Autom. Sci. Eng. 4 (2) (2007) 141–152. [11] A. Bazdar, R.B. Kazemzadeh, S.T.A. Niaki, Fault diagnosis within multistage machining processes using linear discriminant analysis: a case study in automotive industry, Qual. Technol. Quant. Manage. 14 (2) (2017) 129–141. [12] S. Du, et al., Three-dimensional variation propagation modeling for multistage turning process of rotary workpieces, Comput. Ind. Eng. 82 (2015) 41–53. [13] K. Wang, et al., State space modelling of variation propagation in multistage machining processes for variable stiffness structure workpieces, Int. J. Prod. Res. (2020) 1–20. [14] G. Wang, et al., A generative neural network model for the quality prediction of work in progress products, Appl. Soft Comput. 85 (2019) 105683. [15] L. Li, K. Ota, M. Dong, Deep learning for smart industry: Efficient manufacture inspection system with fog computing, IEEE Trans. Ind. Inf. 14 (10) (2018) 4665–4673. [16] M. Papananias, et al., A Bayesian framework to estimate part quality and associated uncertainties in multistage manufacturing, Comput. Ind. 105 (2019) 35–47. [17] D.R. Salgado, et al., In-process surface roughness prediction system using cutting vibrations in turning, Int. J. Adv. Manuf. Technol. 43 (1–2) (2009) 40–51. [18] T. Özel, Y. Karpat, Predictive modeling of surface roughness and tool wear in hard turning using regression and neural networks, Int. J. Mach. Tools Manuf. 45 (4–5) (2005) 467–479. [19] P.B. Huang, An intelligent neural-fuzzy model for an in-process surface roughness monitoring system in end milling operations, J. Intell. Manuf. 27 (3) (2016) 689–700. [20] P. Kovac, et al., Application of fuzzy logic and regression analysis for modeling surface roughness in face milliing, J. Intell. Manuf. 24 (4) (2013) 755–762. [21] C. Han, M. Luo, D. Zhang, Optimization of varying-parameter drilling for multi-hole parts using metaheuristic algorithm coupled with self-adaptive penalty method, Appl. Soft Comput. (2020) 106489. [22] I. Jolliffe, Principal component analysis, in: International Encyclopedia of Statistical Science, Springer, 2011, pp. 1094–1096. [23] R.B. Bapat, Linear Algebra and Linear Models, Springer Science & Business Media, 2012. [24] J.C. Bezdek, R. Ehrlich, W. Full, FCM: The fuzzy c-means clustering algorithm, Comput. Geosci. 10 (2–3) (1984) 191–203. [25] S.S. Haykin, Neural Networks and Learning Machines, Vol. 3, Pearson Upper Saddle River, NJ, USA, 2009. [26] M. Papananias, et al., Uncertainty evaluation associated with versatile automated gauging influenced by process variations through design of experiments approach, Precis. Eng. 49 (2017) 440–455. [27] M. Papananias, et al., Evaluation of automated flexible gauge performance using experimental designs, in: Laser Metrology and Machine Performance XII, LAMDAMAP, euspen, Wotton-under-Edge, UK, 2017. [28] M. Papananias, et al., An intelligent metrology informatics system based on neural networks for multistage manufacturing processes, Procedia CIRP 82 (2019) 444–449. [29] A. Forbes, A. Mengot, K. Jonas, Uncertainty associated with coordinate measurement in comparator mode, in: Laser Metrology and Machine Performance XI, LAMDAMAP, euspen, Huddersfield, UK, 2015. [30] BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, Evaluation of measurement data — Guide to the expression of uncertainty in measurement, Joint Committee for Guides in Metrology, JCGM 100: 2008, GUM 1995 with minor corrections. [31] I. Lira, Evaluating the Measurement Uncertainty: Fundamentals and Practical Guidance, IOP, 2002.
CRediT authorship contribution statement Moschos Papananias: Implemented the proposed approach and prepared the manuscript. Thomas E. McLeay: Conceived the proposed approach and reviewed the manuscript. Olusayo Obajemu: Reviewed the manuscript. Mahdi Mahfouf: Reviewed the manuscript. Visakan Kadirkamanathan: Supervised the implementation and reviewed the manuscript. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors gratefully acknowledge funding for this research from the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant Reference: EP/P006930/1. References [1] M.P. Groover, Fundamentals of Modern Manufacturing: Materials Processes, and Systems, John Wiley & Sons, 2007. [2] J. Shi, Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes, CRC press, 2006. 14
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[32] BS EN ISO 15530-3: 2011: Geometrical product specifications (GPS). Coordinate measuring machines (CMM). Technique for determining the uncertainty of measurement. Use of calibrated workpieces or measurement standards. British Standards Institute.
[33] M. Riedmiller, H. Braun, A direct adaptive method for faster backpropagation learning: The RPROP algorithm, IEEE International Conference on Neural Networks, San Francisco, CA, USA, 1993. [34] S. Weisberg, Applied Linear Regression, Vol. 528, John Wiley & Sons, 2005.
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Towards a Digital Twin with Generative Adversarial Network Modelling of Machining Vibration Chapter · May 2020 DOI: 10.1007/978-3-030-48791-1_14
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Towards a digital twin with generative adversarial network modelling of machining vibration Evgeny Zotov1[0000−0002−5135−1543] , Ashutosh Tiwari1 , and Visakan Kadirkamanathan1[0000−0002−4243−2501] Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK ezotov1@sheffield.ac.uk, a.tiwari@sheffield.ac.uk, visakan@sheffield.ac.uk
Abstract. Transition towards Industry 4.0 relies heavily on manufacturing digitalisation. Digital twin plays a significant role among the pool of relevant technologies as a powerful tool that is expected provide digital access to detailed real-time monitoring of the physical processes and enable significant optimisation due to utilisation of big data acquired from them. Over the past years a significant number of works produced conceptual frameworks of digital twins and discussed their requirements and benefits. The research literature demonstrates application examples and proofs of concepts, although the content is less rich. This paper presents a generative model based on generative adversarial networks (GAN) for machining vibration data, discusses its performance and analyses the drawbacks. The proposed model includes process parameter inputs used to condition the features of generated signals. The control over the generator and a neural network architecture utilising techniques from styletransfer research provide the means to analyse the signal building blocks learned by the model and explore their relationship. The quality of the learned process representation is demonstrated using a dataset obtained from a machining time-domain simulation. The novel results constitute a critical component of a machining digital twin and open new research directions towards development of comprehensive manufacturing digital twins. Keywords: Generative adversarial network · Digital twin · Machining
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Introduction
The 4th industrial revolution, i.e. the strategic vision of transition to Industry 4.0, draws a path to a totally customisable production with viable single-item batch production, just-in-time execution and high resource-efficiency. Advances along this path are believed to be feasible as a result of pervasive digitalisation throughout the industry, spanning from the shop-floor to the whole supply chain and to the users of the end-products [7]. Total factory digitalisation is being
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made possible by the technologies emerging from the research fields of big data, cyber-physical systems (CPS) and industrial internet of things (IIoT). Digital twin is a precise representation of a physical object or process in the digital realm. Development of digital twins is an important step of the digitalisation process, as the unification of digital and physical data within a single virtual object enables significant efficiency improvements across multiple stages of the objectâ&#x20AC;&#x2122;s life cycle [17]. Expert-based analytics models tend to achieve high accuracy rates, but have several drawbacks that can become blocking factors for implementation of a digital twin. On one hand, in an interconnected CPS environment interactions between the components introduce very high complexity of the modelled phenomena. On the other hand, the incremental character of module development and the fluid module composition cause an almost constant stream of changes in the system [12]. Data-driven modelling addresses these issues by making use of big data produced by the various manufacturerâ&#x20AC;&#x2122;s CPS and automating the modelling process, thus aligning the digital twin state with the evolutionary changes in the modelled systems. Development of efficient and flexible generative data-driven models of physical manufacturing processes is an important step towards CPS digitalisation in general, and particularly to wide adoption of digital twins throughout the industry. Artificial neural networks (ANN) have shown increasingly impressive state-of-art results on many data-driven problems during the past decades. Generative adversarial network (GAN) is a type of ANN architecture based on a minimax game between two ANN: the generator that learns to produce artificial data samples and the discriminator that learns to identify fake data samples [5]. Recently GANs found various uses, most notable in generation of realistic images of human faces [10]. GAN is a suitable candidate for digital twin development due to its efficiency at inference time and the generative nature of the model, in addition to the flexibility of a data-driven method. This paper proposes a GAN-based digital twin model that captures the conditional distribution of a signal, conditioned on the controlled parameters of the underlying process. Vibration is selected as the analysed signal type based on the low expected cost of its acquisition and potential usefulness in analysis of the process.
2 2.1
Methodology Dataset: Machining Tool Vibration
The proposed model is tested on a simulated dataset representing the displacement (vibration) of a cutting tool along the x direction originating from the interactions between the tool and a workpiece. The operation considered is a linear non-slotting milling cut performed with a straight-teeth cutting tool on a metal workpiece. The dataset is produced using a physics-based time domain simulation model described in [15]. The model tracks the position of each cutting tooth and the workpiece geometry produced by previous cuts and derives
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the tool displacement from the forces produced by the interaction of the cutting teeth and the workpiece at each simulation time step. The simulation parameters used are detailed in Table 1. The parameter values are constant throughout each cutting operation, and the parameters varied across the samples in the produced dataset are chip width and spindle speed in ranges from 4e-3 to 5e-3 and 3000 to 4000 respectively. The generated signals represent the displacement of the cutting tool during the third revolution of the cutting tool, sampled at a rate proportional to the spindle speed so that all signals are of the same length. Table 1. Milling time domain simulation parameters Parameter feed rate f spindle speed ω number of teeth Nt chip width b steps per revolution start angle of cut φs exit angle of cut φe process dependent coefficient Ks force angle β x direction dynamics parameter kx x direction dynamics parameter ζx y direction dynamics parameter ky y direction dynamics parameter ζy number of revolutions (data recorded for third revolution only)
2.2
Value 10.2 3000 to 4000 3 4e-3 to 5e-3 256 126.9 180 2250e6 75 9e6 0.02 1e7 0.01 3
Model Architecture
The proposed digital twin is based on the generative adversarial network (GAN) model conceived in 2014 [5]. The authors combined two neural networks within a zero-sum game. One network, the discriminator is rewarded for high accuracy of classification of data samples as either real or fake. The other network, the generator, is rewarded for generation of fake samples that are classified by the discriminator as real. Therefore, the generator approximates the true data distribution through the training process. The approach was extended in multiple directions, including but not limited to research on various neural network architectures for the generator and the discriminator (e.g., Deep Convolutional GAN [13], BigGAN [2], StackGAN [19], WaveGAN [4], SeqGAN [18], Bayesian GAN [14]) reviews of the GAN training approaches and the networks’ loss functions (notably, the application of Earth Mover distance as the loss metric in
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Wasserstein GAN [1], its extension with gradient penalty in WGAN-GP [6] and progressive GAN growing [9]),experiments with conditioning the GAN by additional inputs or outputs, as proposed in Conditional GAN [11], InfoGAN [3] and ss-InfoGAN [16]. The developed neural network architecture is inspired by StyleGAN [10], an image generation model based on two-dimensional deep convolutional discriminator and generator networks. Elements of the StyleGAN are repurposed for the 1D case of a time domain signal, excluding the noise inputs, as the variation of outputs of the target model is deterministic with respect to the input process parameters. The architecture is enhanced with the substitution of the random input latent vector for continuous labels C: the machining process parameters, chip width and spindle speed. The process parameters are used as inputs to the generator and as outputs of the discriminator, i.e. the discriminator learns to not only identify synthetic data samples, but also to estimate the labels associated with a given time-series. The architecture includes a non-linear mapping network M that projects latent inputs into disentangled latent space, approximated by a multi-layer feedforward neural network. The styles S = M (C) produced from the input labels C by the mapping network subsequently control the modulation of outputs of the convolutional layers within the synthesis network F of the generator (see Figure 1). The GAN loss function is based on Wasserstein GAN with gradient penalty (WGAN-GP) [6]. WGAN-GP losses for the generator and the discriminator are Lwgan-gp = − E [D(x̃)], G x̃∼Pg
Lwgan-gp D
= E [D(x̃)] − E [D(x)] + λgp Lgp x̃∼Pg
(1)
x∼Pr
respectively, where Lgp = E [(||∇x̃ D(x̃)||2 − 1)2 ] x̃∼Px̃
(2)
is the gradient penalty and λgp is its scaling hyperparameter. The loss functions are adjusted to accommodate the inclusion of machining process parameters in the networks architecture by addition of terms that penalise inaccurate label predictions. This is similar to the approach followed by the authors of InfoGAN [3], with the following difference. The accuracy of label predictions for training o data Linf impacts only the discriminator, while the accuracy of the predictions D o for fake data samples Linf is taken into account only by the generator. The loss G terms are sP n 2 j=1 (cf,j − ct,j ) inf o , LG = n (3) sP n 2 (c − c ) t,j j=1 r,j o Linf = , D n where cf,j is a value of parameter j predicted by the discriminator based on a fake signal, cr,j is a value predicted from a real signal, and ct,j are the true
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Fig. 1. Architecture of the generator F . ”A” denotes learned affine transformations of style components si ; ”AdaIN” - adaptive instance normalisation [8], outputs of which are modulated by the transformed style components.
parameter values. On one hand, the generator is thus incentivised to encode the label information in an identifiable way within the synthesised samples. On the other hand, the discriminator learns the relationship between labels and samples only on the real data, thus preserving the non-cooperative nature of the minimax game between the generator and the discriminator. The total loss functions for the generator LG and the discriminator LD are therefore: o LG = Lwgan-gp + λinf o Linf , G G o LD = Lwgan-gp + λinf o Linf D D ,
where λinf o is the scaling factor for the label prediction accuracy error loss.
(4)
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Fig. 2. Comparison of generated time-series samples (blue) and validation data samples (yellow). X axis represents time steps, Y axis - displacement magnitude in log scale.
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Experimental Results
The paper shows that the generator successfully learns to capture the relationship between the process parameters and the time domain signal and performs well both on training and validation data. Figure 2 depicts several samples of generated time-series against the signals from training data produced using the same process parameters. 3.1
Visualisation of Generator Performance
The generative performance of the neural network is investigated via analysis of metrics mapped across machining process parameter values, chip width and spindle speed. This is visualised by calculating the inspected metric for a range of process parameter pairs and plotting the values on a two-dimensional figure with spindle speed varied across the X axis and chip width across the Y axis. The
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training data exhibits high variability, especially across the spindle speed parameter values, visible on the plot of standard deviations of the training data signals (Figure 3). Figure 4 depicts the root mean square error (RMSE) of the generated time-series (i.e. the error between synthetics signals and dataset signals) on training and on validation data. RMSE distributions are nearly identical, i.e. the generator performs equivalently during both training and validation.
Fig. 3. Standard deviation of training data samples (log scale).
Fig. 4. RMSE values in log scale for generated time-series across various process parameter values for training data (left) and validation data (right). Equivalence of accuracy on both indicates low over-fitting.
In contrast to the high accuracy of the generator in the areas of the parameter space characterised by low dispersion in the training data, the generative performance is suboptimal in some regions of high training data variance. Closer inspection of a region between 3500 and 3600 spindle speed reveals that the generator experiences local mode collapse (for an example refer to Figure 5). The troughs visible on the RMSE map in this region represent a parameter space where the generator successfully learnt the modes of the target signal, while the three peaks between and to the sides along the X axis from these narrow bands
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Fig. 5. Example of a path in labels space where the transition between the signal modes is smooth in the training data, but abrupt in the signals produced by the generator. The blue dot on the RMSE maps (left) indicates the parameter values used to compare the two signals (right), real signal in yellow and generated signal in blue. The differences between the fake signals along the labels transition paths shown on the two top figures and the two bottom figures are much lower than for the real signal. The opposite is true for the transition captured by the two middle figures.
of high accuracy are indicative of the dropped modes. An inspection of the dynamics of change of the training data signals compared to the change of the synthesised signals reveals that whereas the training data signals change shape linearly with the change in spindle speed, the generated signals remain constant
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for most of the inspected parameter space and sharply switch to the next mode near the peak on the RMSE map. 3.2
Interpolation Analysis
Fig. 6. Interpolated signal x̃3 comparison with a source signals x̃1 (top two figures) and x̃2 (bottom two figures). The blue dashed line on the first figure represents the initial signal x̃1 . Red line, an interpolated signal based on s1..5 from signal 2 style set S2 and s6..16 from S1 , is significantly different from x̃1 in its phase and modes. Green line, an interpolated signal for w1..5 = 0, w6..16 = 1, differs from the source in its local high-frequency features.
The style-based neural network architecture enables inspection of the influence of the disentangled input parameter vectors si at the different layers i of the synthesis network G(S) within GAN, where S = {si } = M (C) is a set of style vectors produced by the mapping network of the generator M () from the input label vectors C. This is performed by analysing the changes in the generated signals arising from alteration of the disentangled inputs. For two different sets
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of styles S1 = {s1,i } and S2 = {s2,i } and the respective generated signals x̃1 = G(S1 ) and x̃2 = G(S2 ), an interpolated styles set S3 is produced as a set of affine combinations of elements of S1 and S2 : S3 = {s3,i } = {s1,i ∗ wi + s2,i ∗ (1 − wi )}. Thus, at each style level i the style component of S3 is the weighted sum of the components of S1 and S2 at this level, with the weight wi = 0 indicating that only the component of the first style set is used and wi = 1 implying that only the second style is applied at this level. The interpolated signal is acquired from the interpolated style set by feeding the styles into the synthesis network, x̃3 = G(S3 ). The variation of the generated signals produced as a result of gradual changes to one or several style components reveals the features that the style components at the respective levels control. By performing a linear interpolation between s1,i and s2,i for each i = k while keeping s3,i = s1,i for each i 6= k, we observe that the generator model style layers can be classified into two groups: low-level styles s1 to s5 and high-level styles s6 to s16 . The low-level styles significantly affect the low-frequency features of the output signal like its phase and general shape. The high-level styles impact the high-frequency detail of the generated output. Figure 6 visualises the end points of this interpolation: an initial signal x̃1 , its interpolation towards x̃2 in low-level styles only and in high-level styles only.
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Conclusion
To the best of authors’ knowledge this work is the first attempt to develop a generative model of a machining process using GANs. The neural network architecture at the base of the proposed model is computationally cheap at inference time. This and the generative nature of GAN enable the development of a machining digital twin component that digitally recreates the underlying physical process in real-time. The architecture described in the paper allows a significant degree of control over the generator via input process parameters, thus enhancing the flexibility of the model and opening the potential for exploratory analysis of the modelled process. The shown success of GAN in recreating the machining vibration is an important step towards widespread implementation of data-driven simulation models in Industry 4.0, which could find important applications in monitoring and predictive analytics within manufacturing. The analysis of the interaction between the inputs and the per-layer style components within the trained GAN model shows the distinct parts of the model that separately control the high- and the low-level features of the generated signal. The accuracy of developed model is analysed, revealing certain conditions under which the generator fails to learn the correct signal mode distribution. Investigation of the conditions under which the proposed model performance is suboptimal would be the likely next research steps. The conditions of suboptimal model behaviour can be investigated via analysis of the activations output by the convolutional layers of the generator. Furthermore, the convolutional kernels learned by the neural network could be analysed to identify possible similarities with filter models used in expert-based signal processing. Both the activations
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and the kernels could be analysed relationship with the style modulation components could be additionally explored via the interpolation analysis described in the paper. As a real world implementation would likely be limited in terms of available data, an investigation of the modelâ&#x20AC;&#x2122;s capability with sparse data or unobservable factors is an important step in its verification. Categorisation of the continuous labels used to condition the model could make the dataset more closely represent data likely to be encountered on a shop-floor. Other next steps in this research direction would include evaluation of alternative neural network architectures and validation of the proposed model on real manufacturing data, as well as broadening the scope of the digital twin with inclusion of multiple data sources and modelled processes.
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Acknowledgements
Professor Ashutosh Tiwari acknowledges the support of the Royal Academy of Engineering under the Research Chairs and Senior Research Fellowships scheme (RCSRF1718\5\41).
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