Multi-objective Optimization of EDM Process with Performance Appraisal of GA based Algorithms in Neural Network Environment

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ScienceDirect Materials Today: Proceedings 18 (2019) 3982–3997

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ICMPC-2019

Multi-objective Optimization of EDM Process with Performance Appraisal of GA based Algorithms in Neural Network Environment Shiba Narayan Sahua,*, Sagar Kumar Murmub, Narayan Chandra Nayakc a b

Department of Production Engineering, Parala Maharaja Engineering College, Brahmapur-761003, Odisha, India Department of Mechanical Engineering, Parala Maharaja Engineering College, Brahmapur-761003, Odisha, India c Department of Mechanical Engineering, Indira Gandhi Institute of Technology, Sarang - 759146, Odisha, India

Abstract This work focuses on the material removal rate and electrode wear rate of A2 steel in the EDM process, which are considered as to be the important governing parameters for higher productivity and accuracy. The purpose of this investigation is to minimize the electrode wear rate and maximize the material removal rate by controlling the machining parameters. In this work, an experimental investigation has been carried out by considering four machining control parameters such as discharge current (Ip), pulse duration (Ton), duty cycle (τ or Tau) and voltage (V) by using the full factorial design methodology. Artificial Neural Network (ANN) model has been developed to correlate the data generated from experimental results. To obtain an efficient ANN model and to achieve minimum prediction error, ANN architectures, learning/training algorithms and numbers of hidden neurons are generally varied. However, so far the variations have been made in a random manner. For this reason a full factorial design integrated Analysis of Variance (ANOVA) has been utilized to investigate the influence of control factors on response. Developed ANN model equation of material removal rate and electrode wear rate were subsequently used as the fitness functions in Genetic Algorithm (GA) based multi-objective algorithms. Three advanced GA based optimization techniques, i.e., Nondominating Sorting Genetic Algorithm-II (NSGA-II), controlled NSGA-II and Strength Pareto Evolutionary Algorithm 2 (SPEA2) were attempted for the considered EDM process. Furthermore, a non-dominated set of solution was obtained to have diversity in the solutions for the EDM process. The result obtained using the ANN method and optimization techniques were confirmed using confirmation experiments. © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019 Keywords: Electro-discharge machining; A2 Steel; Artificial neural network; GA; Multi-objective optimization; NSGA-II; CNSGA-II; SPEA2

* Corresponding author. E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019

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1. Introduction Electro Discharge Machining (EDM) is the process of machining electrically conductive materials by using precisely controlled sparks that occur between the electrode and work piece, submerged in a dielectric fluid. Among the thermal modes of machining, EDM is one of the most widely used non-traditional machining processes. This process plays a significant role in modern machining processes, especially in the case of machining of hard and high strength but electrically conductive parts. EDM provides an economic advantage for making majority of the tools, dies and moulds dealing with materials having a higher hardness. Artificial Neural Networks (ANNs) are massively parallel adaptive networks of simple nonlinear computing elements called neurons, which are intended to abstract and model some of the functionality of the human nervous system in an attempt to partially capture some of its computational strengths. Neural networks perform like a blackbox, aiming at solving the problems using their universal approximation capability. This negates the necessity of analyzing the structure or looking for knowledge of the problems. Only the inputs and outputs have physical meaning [1]. In recent years, ANNs have demonstrated great potential in adaptability and nonlinear universal function approximations in high-dimensional spaces of the complex and non-linear systems. The ANN can approximate well to any continuous multivariate functions with high accuracy and can easily handle imprecise, fuzzy, noisy and probabilistic information. Multi-Objective Evolutionary Algorithms (MOEAs) is an interdisciplinary research field having a relationship with biology, artificial intelligence, numerical optimization and decision support in almost any engineering discipline. In the recent past, evolutionary algorithms have been used with an increased degree of success to solve multi objective optimization problems. The evolutionary optimization algorithms rely on finding the globally optimal solutions by chance and incorporate methods (heuristics) to reduce the possibility of being trapped inside a locally optimal basin [2]. Some of the notable efforts in designing MOEAs are the SPEA2 [3], Controlled NSGA-II [4], NSGA-II [5], etc. A2 steel is an air hardening, cold work, tool steel. The presence of 5% chromium in the steel provides high hardness after heat treatment with dimensional stability. It is heat treatable and offers hardness in the range of 57-64 HRC. A2 delivers good toughness with medium wear resistance. In many cases, tools made from this steel have given better tooling economy than high-carbon, high-chromium steels of the D3/ W.-Nr. 2080 type. Typical applications of this steel are blanking tools, punch dies, stamping dies, trim dies, forming dies, gauges, shear blades etc. EDM is a suitable machining process for machining hardened steels in concern with the economy and accuracy prospective. Productivity is constantly a matter of concern with a high level of accuracy for any machining process. Therefore, it is always desirable to have machining with maximum material removal rate and minimal electrode wear rate [6]. 2. Review of Literature In recent research trend, the artificial intelligent processes are being implemented for controlling the machining parameters to achieve the desired responses [7-9]. To obtain the optimum parameter setting for machining process is utmost important. Machining in EDM is characterized by nonlinear, stochastic and randomness between process parameters and response parameters. Predicting the output of such a process with reasonable accuracy is rather difficult [10]. In EDM, a quantitative relationship between the process parameters and controllable input variables is often required to achieve desired quality. Several attempts have been made to model and control the EDM process parameters [11-13]. To establish the relation between different significant input parameters and output parameters of the EDM process, various approaches like empirical relation, non-linear regression, Taguchi Approach, full factorial design methodology, Response Surface Methodology(RSM), Analysis of Variance (ANOVA), neural network modeling, fuzzy modelling, support vector machine regression, Neuro-fuzzy etc., have been implemented. However, modern learning based methodologies, being capable of reading the underlying unseen effect of control factors on responses, appears to be effective in this regard. For multi-objective optimization of EDM process various conventional techniques like Grey Relational Analysis (GRA), Principal Component Analysis (PCA), TOPSIS

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method, desirability approach and hybrid or combined methodology of them like Fuzzy-TOPSIS, GRA-PCA approach, Taguchi-grey etc. have been implemented [14-19]. Development of MOEA has been started since last few decades and still it is in the exploring stage [20]. In recent years, many researchers have shown their keen interest in the implementation of MOEA, but until now, it has not achieved the wide applicability [21-23]. Panda and Bhoi [24] have attempted to develop an artificial feed forward neural network based on the LevenbergMarquardt back propagation technique of appropriate architecture of the logistic sigmoid activation function to predict the Material Removal Rate (MRR). Kuriakose and Shunmugam [25] have used Non-dominating Sorting Genetic Algorithm (NSGA) to optimize the Wire-EDM process. A Multiple linear regression model was used to represent the relation between machine setting parameters and output variables. Mandal et al. [26] have used NSGAII integrated with an ANN model equation to optimize the MRR and Electrode Wear Rate (EWR). Kodali et al. [27] have used NSGA-II for two conflicting objectives, minimizing the total production cost (CT) and maximizing the workpiece removal parameter (WRP) for the optimal grinding conditions. MahdaviNejad [28] has used NSGA-II to optimize the EDM process. He used ANN with back propagation algorithm to model the process. Sahu and Nayak [29] used NSGA-II algorithm to find out the best trade-ups between the two conflicting response parameters MRR and TWR. Golshan et al. [30] presented the effect of EDM on SR and MRR of Al/SiC metal matrix composite. They studied the correlation between four input variables that are pulse-on time, pulse peak current, average gap voltage, percent volume fraction of SiC and the process outputs. In addition, they found the optimal conditions for outputs from NSGA-II. Experimental models were developed for the SR and MRR with machining parameters like pulse-on time, pulse-off time, and discharge current. Padhee et al. [31] used multi-objective optimization method of NSGA-II to obtain the Pareto-optimal set of solutions. NSGA-II has been implemented to optimize the responses of EDM technology using a powder-mixed dielectric. They used mathematical models for prediction of MRR and SR through the knowledge of four process variables such as discharge current, concentration of powder (silicon) in the dielectric fluid, pulse-on time and duty cycle with EN-31 tool steel as a workpiece material. The RSM was adopted to study the effect of control variable on responses and to develop the predictive models. Nayak et al. [32] have investigated on machining of D2 steel in EDM. They modeled MRR, surface roughness, crack density and residual stress with the help of regression equation and GA was used to perform multi-objective optimization. 2.1. Research Background A comprehensive knowledge on controlling the process parameters of EDM on A2 steel is lacking. Literature review reveals that modern learning based methodology; ANN is efficient and sufficient to predict the output of stochastic, random and non-linear processes like EDM. It was also concluded that the efficiency or performance of ANN could be improvised by appropriate selection of learning algorithm, number of hidden neurons and neural architecture. Investigators have varied only one or two of these parameters simultaneously to develop a robust model for implementing onto a particular purpose [21, 24, 33, and 34]. Thorough study of literature reveals that different MOEAs have been implemented for MOO of EDM process, but GA based optimization algorithms are found to be more efficient in finding out the optimal process parameter setting [26 and 35-39]. For multi-objective optimization methods, some modifications to the simple GAs are necessary. When the objective functions become discontinuous, discrete and non-convex, GA possesses advantages that it does not call for any gradient information and has inherent parallelism in searching the design space, thus making it a robust adaptive optimization technique [33]. Another advantage of GA algorithms over the other conventional type of optimization techniques is that, it can search for the optimal process parameter settings in a bounded range, provided that the fitness function has higher accuracy of prediction. In the manufacturing sector productivity and dimension accuracy has an essential importance. In EDM process, to achieve higher productivity and dimensional accuracy, attention is required for simultaneous optimization of MRR and EWR. A2 tool steel is having a wide applicability in manufacturing industry, but less research work has been reported on the selection of machining parameters and multi-objective optimization in EDM process. Thus, the main objective of this investigation is to formulate and execute a multi attribute decision-making framework to select the optimal process parameter settings in die sinking EDM of A2 tool steel. The main objectives of this work on machining of A2 steel in the EDM process with different process parameters are as follows:

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1. 2. 3. 4. 5.

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To conduct a set of experiments with the help of full factorial design methodology, To develop an efficient ANN model equation by considering the experimental data sets, To perform the multi-objective optimization by NSGA-II, Controlled NSGA-II and SPEA2 algorithms, using the ANN model equation as fitness function, To obtain the optimal process parameter settings for the MOO optimization A2 steel in EDM process and To perform the qualitative and quantitative performance appraisals for the various optimal process parameter settings obtained from the three GA based algorithms.

3. Experimental Setup and Materials The experimental setup and materials is the same as that of Shiba and Nayak [40]. 4. Research Methodology 4.1. ANN Modelling Several attempts have been made to model the performance parameters of EDM process using ANN. So far, the ANN architectures, learning/training algorithms, a number of hidden neurons etc. have been varied in a random manner for development of an efficient ANN model equation. For this reason, an attempt has been made here to implement the full factorial design and ANOVA to obtain the optimal ANN process parameter settings. The model equation of an ANN model (for a single hidden layer model) can be expressed with the help of weight and bias matrix and can be represented as:





a 2  f 2 (W 2 f 1 W1p  b1  b 2 )

(1)

where a2 is the output vector of the second layer, f1 represents the transfer function, W1 and W2 are the weight matrices of hidden layer and output layer, respectively, p is the input vector, b1 and b2 are the bias vectors of first layer and second layer respectively. The ANN modelling of EDM process has been performed in this research investigation through the following steps: Step1: Selection of values/types of un-established parameters of ANN using full factorial methodology and ANOVA Step 2: Selection of training, validation, testing datasets and their ratio Step 3: Selection of well-established parameters of ANN, its value/types Step 4: ANN modelling of the EDM process by using the process parameters, selected from step1 to step 3 Step 5: The weight and bias matrix of the trained model in step 4 were expressed in the form of equation 3 using MATLAB coding. This representation will be further used as a fitness function in multi-objective optimization phase. Variation in ANN parameter settings: The process parameters ANN architectures, learning/training algorithms and number of hidden neurons have been varied in various investigations to obtain an efficient ANN model. However, the significance and the contribution of these process parameters to ANN model have not been demonstrated properly. To appraise the performance and significance of ANN architectures, learning/training algorithms and number of hidden neurons on ANN model, these have been selected as the process parameters to a full factorial design methodology. The process parameters; ANN architecture, learning/training algorithm and numbers of hidden neuron have been considered at two levels, three levels and four levels respectively and have been shown in Table 1. The two neural architectures are Multi-Layer Perceptron (MLP) and Cascade forward (CF) neural architecture. CF networks are a generalization of the MLP such that connections can jump over one or more layers. In theory, an MLP can solve any problem that a

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CF network can solve. In practice, however, CF networks often solve the problem much more efficiently (Beale et al. 2010). Levenberg-Marquardt (LM), Scale Conjugate Gradient Algorithm (SCGA) and Conjugate Gradient with Powell-Beale restarts (CGB) are the list of the training algorithms that are available in the Neural Network Toolbox software, which uses gradients or Jacobian-based methods. The fastest training algorithm is the LevenbergMarquardt, and it is the default-training algorithm for feed-forward neural network. The best architecture has been selected by varying the number of neurons in the hidden layer at the levels of 8, 16, 24 and 32. The performance parameters, testing Mean Squared Error (MSE) and testing correlation coefficient (R) have been considered here as the performance measures of the developed ANN model. These two parameters are the default performances evaluating parameters considered by MATLAB in evaluating the ANN models. The testing data set is the unseen data and hence the robustness of an ANN model can be decided more accurately by these two parameters. Table 1. Parameters and their levels Process parameter

Levels 1

2

3

4

Neural Architecture

MLP

CF

-

-

Learning Algorithm

LM

SCGA

CGB

-

Numbers of hidden neuron

8

16

24

32

Training, validation and testing Data: A total number of 150 experimental runs was carried out using the full factorial design methodology. The 150 sets of experimental data were divided into training, validation and test dataset, each consisting of 120, 15 and 15 data respectively. The data proportion between training, validation and test data set were taken as 80, 10 and10 respectively. The training data set is used for the function approximation between input and output parameters. The early stopping criteria decided by a validation data set were used to stop the ANN training. The test data set is the unseen data to the trained model and was used to appraise the performance and generalization error of the fully trained model. Generalization means how well the trained model approximates to the unseen data set and early stopping criteria is very much essential for reducing the generalization error. Fixed parameter settings in ANN modelling: Table 2. Important fixed parameter settings in ANN modelling S. No.

Parameter Numbers of input neuron

Data/ Data range 4

1

Technique used or Type of Parameter used -

2

Numbers of output neuron

2

-

3

Total number of experimental runs

150

-

4

Proportion of training, validation and testing data

80:10:10

-

5

Data normalization Technique

0.05 to 0.95

Min-max data normalization technique

6

Weight initialization Technique

-0.5 to 0.5

Random weight initialization technique

7

Activation function

0 and 1

8

Error function

-

Log-sigmoid function (for both hidden & output layer) Mean squared error function

9

Mode of training

-

Batch mode

10

Type of Learning rule

-

Supervised learning rule

11

Stopping criteria

-

Early stopping

ANN modelling involves settings of many parameters, well-established parameters are kept constant and others are varied to achieve a robust ANN model. Consideration of four input parameters and two output parameters reflect in ANN as four input neurons and two output neurons. According to Fausett [41], the back propagation architecture

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with one hidden layer is sufficient for the majority of applications. Hence, the effect of variation of hidden layer has not been considered here and only one hidden layer has been taken. The Random weight initialization technique has been employed here for initializing the weights. Here the weights were initialized as random function values between -0.5 to 0.5. The choice of initial weights influences the goal of achieving global minimum error and convergence rate. If the initial values of weights are too large, then the inputs to the sigmoid activation functions are also likely to be larger and so the output of the sigmoid transfer functions/neurons will be either 0 or 1 (reached the so-called saturation region, reached its maximum or minimum value). Several important features of the transfer function are to be followed while selecting a transfer function. The significant characteristics are; it should be continuous, nonlinear, differentiable and monotonically non-decreasing. If the transfer function is discontinuous, then it is not possible to compute the gradient, Jacobian matrix and Hessian matrix required in many gradients based optimization methods used in the backward pass. Here the sigmoid function has been used in both hidden and output layers. The other important fixed parameters, their types and data range as used in the ANN modelling have been exemplified in Table 2. 4.2. Multi-objective optimization (MOO) Most of the real world problems as well as the modern-day engineering problems involve more than one objective. The presence of multiple conflicting objectives is natural in many problems and it takes in the optimization problem challenging. The same can likewise be noted in the case of optimization of EDM process. Higher MRR and lower EWR are always preferred but these two performance parameters are highly conflicting in nature and are un-correlated. Due to population approach, Evolutionary Algorithms (EAs) can find multiple solutions in one complete execution and have become very popular because of their ease of implementation and high effectiveness. Strength Pareto Evolutionary Algorithm 2 (SPEA 2) is actually a revised version of SPEA and was introduced in 2001. NSGA-II is an elitism algorithm and was introduced in 2002 as an upgrade of NSGA. In the last few years, many populations- approaches based MOEAs have been developed. However, among them the most popular from these algorithms are NSGA-II, controlled NSGA-II and SPEA2 algorithms etc. In this research work, an attempt has been made to find out the optimal process parameter settings for the two conflicting responses MRR and EWR of EDM process. For finding out the optimal process parameters, NSGA-II, controlled NSGA-II and SPEA2 algorithms have been implemented. The multi-objective optimization of EDM process has been performed in this research investigation through the following steps: Step 1: Formulation of multi-objective optimization problem Step 2: Selection of process parameters for MOO Step 3: Performing the multi-objective optimization using NSGA-II, CNSAGA-II an SPEA2 algorithm Step 4: Performing comparative analysis between the solutions of the three multi-objective analysis Formulation of multi-objective optimization problem: In this case, multi-objective optimization is concerned with the minimization of two vectors of objectives f (x) = [EWR, 1/ (1+MRR)]. The objective function is subjected to a number of constraints or bounds i.e., 4≤Ip≤16, 100 ≤Ton≤500, 45≤Tau≤65 and 40≤V≤60. For implementing the three GA based algorithms, a multi-objective minimization problem with four decision variables and two objectives were formulated as follows: Minimize

y f

 x



 f  x  , f  x  1

2

subjected to boundary conditions 4≤Ip≤16 100≤Ton≤500 45≤Tau≤65 40≤V≤60 where x= (Ip, Ton, Tau, V) and y= (y1, y2).

(2)

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During this investigation the objective is to minimize the multi-objective function or fitness function y= f(x), which was obtained from the fully trained ANN model. As the real objective is to minimize the EWR and maximize the MRR of EDM process, a suitable modification was introduced in the individual objective of MRR and EWR and has represented as below: f1  x   1/ 1  MRR  (3)

f 2  x   EWR

(4)

Selection of process parameters of MOO techniques: NSGA-II, controlled NSGA-II and SPEA2 are GA based multi-objective algorithms. For a fair comparison between the results of these algorithms, uniformity have been maintained in all possible process parameter settings. The fixed process parameter settings for NSGA-II, controlled NSGA-II and SPEA2 have been tabulated in Table 3. Table 3. Fixed process parameter settings Types of operation/ parameter Population a. size b. creation function Selection Reproduction a. crossover fraction Cross over a. crossover function b. crossover ratio Mutation Distance measure function Stopping criteria a. b. c.

generation stall generation functional tolerance

Parameter’s value/type 60 Feasible population Tournament 0.8 Intermediate 1.0 Adaptive feasible Distance crowding 800 100 1x10-4

All the parameters settings in Controlled NSGA-II are same as NSGA-II, except Pareto-front population fraction (which defines the distribution of fit population down to the specified fraction in order to maintain the diversity) and population size, which were set to 0.35 and 171 respectively. In SPEA2 algorithm, for every generation an external set (or external archive) is used to store the newly formed parent population and the size of the external archive may be different from the initial population size. The raw fitness assignment of an individual in SPEA2 is decided by strength of its dominators (in both archive and population) and density (based on kth nearest neighbour method).The diversity among the solutions is maintained in this algorithm by density estimation (based on kth nearest neighbour method). 5. Result and discussion 5.1. Performance evaluation of ANN From the literature review it was found that, the selection of ANN modelling process parameters is being performed in a random manner, which introduces errors in the subsequent phase of multi-objective optimization. This problem generally occurs in the cases where an EA based MOO algorithm is being used for finding out optimal process parameter setting. The training data set is used to fit the model and a test data set is used to evaluate the model. Hence, the main effect plots and ANOVA of testing data set were considered for evaluation of the ANN models. Two performance evaluation parameters, i.e., Mean Square Error (MSE) and value of regression coefficient (R) have been used here for an appraisal of the performance of an ANN model.

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R-value indicates the relationship between the experimental data and ANN predicted data. The value of R lies between 0 and 1. If R =1, this indicates that there is an exact relationship between experimental data and ANN predicted data. If R is close to zero, then there is no linear relationship between experimental data and ANN predicted data. The correlation coefficient between a network output (a) and a desired output (d) can be mathematically expressed as:        a a d d  n1  n   n  N N

R



   dn  d    N 

N n 1

2



N n 1

   an  a    N 

2

(5)

where n is the exemplar or run number, an and dn are the network output and desired output respectively at a particular exemplary, and are the data mean of network output and desired output respectively. The MSE error function that has been implemented here for supervised training can be mathematically represented as:

  d MSE  N

n 1

K

k 1

nk

 a nk 

2

KN

(6)

where dnk is the experimental value of an experimental run n at the neuron k of output layer and ank is the ANN predicted value of an experimental run n at neuron k of output layer; K is the number of neurons in the output layer and N is the total number of experimental runs. Influence on test MSE: A qualitative idea about the influence of ANN architectures, training algorithms and number of hidden neurons on test MSE can be studied from Fig.1. Neural architectures are having minute or insignificant effect on test MSE. Among the three training algorithms, Levenberg-Marquardt algorithm is having minimum test MSE. The maximum test MSE can be observed with the SCGA. The difference of test MSE between CGB and LM is minimal, but LM is responsible for lowest test MSE. Sixteen numbers of neuron in the hidden layer are generating minimum test MSE whereas maximum test MSE is observed at thirty numbers of neurons. No substantial difference has been observed between the test MSE of 8 and 24 numbers of hidden neurons.

Fig.1. Main effect plots for test MSE

Fig.2. Main effect plots for test R

At a confidence level of 95%, if the P value is less than the significance (i.e., 0.05), then only the hypothesis test is called to be statistically significant. The ANOVA of test MSE has been depicted in Table 4. Except the neural architecture, all the individual parameters were found to be significant. All the two levels and three level interaction of the parameters presented in the Table 4 also significantly contribute towards test MSE. A maximum of 28.03% of the contribution for test MSE is from the number of hidden neurons. The lowest and insignificant contribution of

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0.67% is from the neural architecture. The two level interaction of the Neural architecture*Learning algorithm, Neural architecture*Number of hidden neurons and Learning algorithm* Number of hidden neurons are having a considerable contribution of 10.47%, 10.52% and 12.36% respectively towards the test MSE. Table 4. Analysis of Variance for test MSE Source

DF

Neural architecture

1

Seq SS 0.019

Learning algorithm

2

0.223

Number of hidden neurons

3

Neural architecture* Learning algorithm Neural architecture* Number of hidden neurons Learning algorithm* Number of hidden neurons Neural architecture* Learning algorithm* Number of hidden neurons Error Total

Adj MS 0.019

F

P

2.85

0.096*

% of contribution 0.67

0.111

16.64

0.000

7.80

0.804

0.268

39.88

0.000

28.03

2

0.300

0.150

22.33

0.000

10.47

3

0.302

0.100

14.97

0.000

10.52

6

0.354

0.059

8.79

0.000

12.36

6

0.381

0.063

9.45

0.000

13.28

72 95

0.484 2.871

0.006

16.87 100

* insignificant

Influence on test R: Correlation coefficient can be used to determine how well the network output fits the desired output. The R-value of an ANN modelling approaching 1 is considered as the most efficient ANN model. The testing data set is the unseen data and the robustness of an ANN model is decided by the value of the correlation co-efficient of the test data set. Main effect plot for test R has been shown in Fig.2. Neural architecture seems to have some insignificance towards the contribution of test MSE. Maximum value of test R was obtained through Levenberg-Marquardt algorithm and lowest test R-value was obtained by SCGA training algorithm. With the increase of the number of hidden neurons at the levels of 16, 24 and 32, the test R-value was found to be decreasing. However, the minimum value of test R was found at eight numbers of hidden neurons. Table 5. Analysis of Variance for Test R Source

DF

Seq SS

Adj MS

F

P

Neural architecture

1

0.0000000

0.0000000

0.03

0.872*

% of contribution 0.00

Learning algorithm

2

0.0000003

0.0000002

21.18

0.000

8.82

Number of hidden neurons

3

0.0000011

0.0000004

47.74

0.000

32.35

Neural architecture* Learning algorithm Neural architecture* Number of hidden neurons Learning algorithm* Number of hidden neurons

2

0.0000001

0.0000001

9.13

0.000

2.94

3

0.0000003

0.0000001

13.70

0.000

8.82

6

0.0000004

0.0000001

9.08

0.000

11.76

Neural architecture* Learning algorithm* Number of hidden neurons

6

0.0000005

0.0000001

9.99

0.000

14.70

Error

72

0.0000006

0.0000000

Total

95

0.0000034

*insignificant

17.64 100

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The analysis of variance for test R has been shown in Table 5. The P-value of neural architecture has been found to be 0.872, which is greater than 0.05 due to which the parameter becomes insignificant. The other two individual parameters, learning algorithm and the number of hidden neurons are found to be significant towards test MSE. The two levels and three level interaction of all the considered parameters were found to be significant. The maximum contribution of 32.35% towards the test R is from number of hidden neurons. Neural architecture is not at all contributing towards test R. 5.2. Modelling of MRR and EWR using ANN MRR

MRR Output

MRR

80 Output

Output

60 40 20

80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113

0

MRR Output

Exemplar

Exemplar

Fig.3. Variation of experimental MRR and ANN predicted MRR (Training data set)

TWR

Fig.4. Variation of experimental MRR and ANN predicted MRR (Testing data set) TWR

TWR Output

2 Output

Output

1.5 1 0.5 -0.5

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113

0

(Training data set)

2 1.5 1 0.5 0 -0.5 1

3

Exemplar

Fig.5. Variation of experimental EWR and ANN predicted EWR

TWR Output

5

7

9

Exemplar

11

13

15

Fig.6. Variation of experimental EWR and ANN predicted EWR (Testing data set)

The ANOVA and main effect plots of test MSE and test R reveals that the number of hidden neurons is the most significant parameter for accurate function approximation of EDM process. The total number of 16 neurons in the hidden layer is resulting the minimum test MSE and maximum test R-value. Succeeding to the number of hidden neurons, learning algorithm is the next parameter, which holds a considerable effect on the ANN output. Among the three learning algorithms used, Levenberg-Marquardt algorithm was found to be the most appropriate algorithm for training an ANN model with an advantage of faster training rate. Levenberg-Marquardt training algorithm has achieved the maximum value of test R and minimum value of test MSE. The variances of neural architectures CF and MLP were found to be insignificant towards test MSE and test R. MLP has been implemented in many recent investigations, so it was decided to give weightage to MLP, on the selection of the process parameters of ANN [4244] Finally, an ANN model was trained with the selected 16 number of hidden neurons, Levenberg-Marquardt training algorithm and MLP neural architecture. The weights and biases matrices of the fully trained model were saved and further utilized in the development of ANN model equations. Variation in experimental MRR and ANN predicted MRR for training data set has been depicted in Fig.3. For test data set, comparison of experimental MRR

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and ANN predicted MRR have been shown in Fig.4. For both the training and testing data set, it can be observed that the network output fits the desired output in an excellent manner. The comparison of experimental EWR and ANN predicted EWR of training data sets have been shown in Fig.5. For test data set, the fitting of experimental EWR vs. ANN predicted EWR have been shown in Fig.6. From the qualitative point of view, if a comparison between the fittings of MRR and EWR will be analyzed, the fitting of experimental MRR and ANN predicted MRR would seem to have more accuracy. This may be due to the reason that the domains of values of EWR are very small, and the normalization of the data will take care of this. 5.3. Multi-objective optimization Three separate MATLAB codes (version: MATLAB 8.1) were written to integrate the ANN model equation (equation 1) with the optimization techniques and to perform the multi-objective optimization processes such as NSGA-II, CNSGA-II, and SPEA2. The codes were run on an Intel® core i5TM machine with 1792 MB dynamic video memory and 12GB DDR3 L memory. MOEAs are stochastic in nature, to ensure that the solutions have not stuck up in the local optimal values; each algorithm was run for five times. The results of the each run indicating the respective level of terminated iteration and total computation time have been tabulated in Table 6(a) and 6(b) . As mentioned in the Table 5, three types of stopping criteria were set to stop the optimization run. But in this investigation, it was found that all the optimization attempts were terminated at the iteration, where the average change in the spread of Pareto solutions becomes less than the function tolerance (=1x 10-4). The average change in the spread of Pareto solutions between two consecutive iterations in an optimization attempt has been calculated using the following equation: Average change in the spread of Pareto solutions

  p 1770    p 1770      dij k 1  /1770       dij k  p 1   p 1     where

d ij 

 y  y  x  x  2

i

j

i

j

2

   /1770   

(7)

,

k = current iteration number i =1, 2, 3... n (=60) and j = 1,2, 3, 4,…, m( =60 ); for i ≠ j and i < j, p= number of non-repetitive and non-zero distances between any two solution dij = span length between any two solutions, and (xi, yi) and (xj, yj) are the any two solutions along the Pareto-optimal front. From the results of five experimental runs of the different algorithms (Table 6(a) and 6(b)), it can be concluded that NSGA-II, CNSGA-II and SPEA 2 were terminated at the average iterations of 72, 114 and 152 respectively. The average computation time of NSGA-II, CNSGA-II and SPEA 2 were found to be 12.57 minutes, 20.55 minutes and 28.09 minutes respectively. In this investigation, the Pareto optimal solutions of each algorithm at the highest terminating iteration among the five experimental runs have been considered. Pareto-optimal decision vectors of NSGA-II algorithm at the experimental run number 4 and iteration number 92 has been presented in the Fig.7. CNSGA-II algorithm was terminated at the maximum iterations of 127 in the fifth experimental run; the Pareto optimal solution of the same has been shown in Fig.8. Similarly, Pareto optimal solutions of SPEA 2 algorithm at run number 3 and iteration number 163 has been presented in the Fig.9. Table 6(a). Iteration and total computation time at different runs Algorithm

NSGA-II CNSGA-II SPEA 2

Terminated at iteration

01 Total computation time (minute)

Run number 02 Terminated Total computation time at iteration (minute)

Terminated at iteration

03 Total computation time (minute)

65 111 146

11.56 20.56 27.22

71 109 157

63 106 163

11.37 19.37 30.34

13.06 20.13 29.35

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Table 6(b). Iteration and total computation time at different runs Algorithm

05 Total computation time (minute)

92 116 149

16.57 21.27 27.58

12.21 23.29 26.28

67 127 141

Electrode Wear Rate (EWR) (mm3/min)

NSGA-II CNSGA-II SPEA 2

Terminated at iteration

Run number 04 Total computation time Terminated (minute) at iteration

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 A -0.4 0

E

B

D

C 20

40

60

80

Material Removal Rate (MRR) (mm3/min) Fig.7. Pareto-optimal front obtained from NSGA-II algorithm (At experimental run 4 and terminated iteration number 92)

Fig.8. Pareto-optimal front obtained from CNSGA-II algorithm (At experimental run 5 and terminated iteration number 127)

In the region AB and CD of Fig.7, the values of EWR were found to be negative. The values of MRR in the region AB ranges from 5.15 mm3/min to 11.19 mm3/min while the values of EWR in the same region ranges from 0.140 mm3/min to -0.126 mm3/min. In the region AB and CD, the corresponding EWR increase proportionately with MRR in a balanced manner. The minimum value of MRR and EWR in the region CD were found to be 33.69 mm3/min and -0.126 mm3/min respectively. The maximum values of MRR and EWR obtained in the region CD were 56.47 mm3/min and -0.040 mm3/min respectively. In the region EF, EWR ranges from a minimum value of 0.004 mm3/min to a maximum value of 0.241 mm3/min. Similarly, the values of MRR for the same region were found to be in the range 57.01 mm3/min to 59.15 mm3/min. High proportionate variation of EWR as compared to corresponding MRR was observed in the region EF. A minimum value of 6.05 mm3/min of MRR and -0.138 mm3/min of EWR was observed in the region AB of the Pareto optimal front of CNSGA-II algorithm shown in Fig.8. The maximum values of MRR and EWR in the region DE were found to be 61.33 mm3/min and 1.343 mm3/min respectively. This indicates that controlled NSGA-II algorithm has an expanded band of optimal process parameter setting in comparison to NSGA-II algorithm. The solutions in the different regions of the Pareto optimal front of CNSGA-II algorithm seems to be more uniformly distributed as compared to that of the Pareto optimal front of NSGA-II algorithm. The non-dominated decision vectors in the region AB and CD of the Pareto-optimal front of CNSGA-II algorithm were found to generate higher values of MRR as compared to the values of respective EWR. In the region DE, minor increment in the values of MRR was found to be responsible for higher values of corresponding EWR.

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Electrode Wear Rate (EWR) (mm3/min)

3994

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4

E

A

B C

0

D

20 40 60 80 3 Material Removal Rate (MRR) (mm /min)

Fig.9. Pareto-optimal front obtained from SPEA2 algorithm (At experimental run 3 and terminated iteration number 163)

The maximum values of MRR and EWR were observed in the DE region of the Pareto optimal front obtained from SPEA2 algorithm and were found to be 60.90 mm3/min and 0.911 mm3/min respectively. A very few number of optimal solutions were found in the region DE of the Pareto optimal front. In the same region, reduction in density of the solution was observed with the increased value of MRR. The solution with minimum values of MRR and corresponding EWR was found in the region AB with the values of 5.98 mm3/min and -0.141mm3/min respectively. Maximum number of solutions were observed in the region CD of the Pareto optimal front. The minimum-maximum range of MRR for the same region was found to be 35.46 mm3/min and 57.30 mm3/min while the corresponding values of EWR were recoded as -0.127mm3/min and -0.0158mm3/min. Selection of optimal solution: Dealing with the case of multiple conflicting objectives, no single solution can be termed as an optimum solution. Conventional optimization techniques at best can find out one solution in one epoch, thereby making those methods inconvenient to solve the multi-objective optimization problems. Each of the sixty sets of optimal process parameter settings were found out from the three GA based multi-objective algorithms. The sixty sets of optimal solutions (= 15 x number of input variables) were decided as per the MATLAB Global Optimization Toolbox, User’s Guide. The sixty sets of optimal solutions of each algorithm have been presented as the Pareto-optimal front in Fig.10. The abscissa of the Pareto-optimal front represents the MRR as volumetric loss. EWR in mm3/min has been represented in the ordinate of the Pareto-optimal front. The Red, blue and green colour squares represent the solution of CNSGA-II, NSGA-II and SPEA2 respectively. None of the solutions in the non-dominated set is absolutely better than any other, any one of them is an acceptable solution [35, 45]. Hence, the choice of one solution over the other depends on the requirement of the process engineer. Suitability of one solution depends on a number of factors, including user’s choice and problem environment, and hence finding the entire set of optimal solutions may be desired [25,33]. Based on a specific requirement say a high MRR with moderate EWR or a moderate MRR with lower EWR, a suitable combination of variables can be selected from the sixty sets of Pareto optimal solutions. In this investigation, the objective is to select the optimal process parameter setting with high MRR and lower EWR (approximately zero EWR). The Pareto optimal fronts of the three algorithms can be broadly divided into three parts. The first one is the solution region where the values of EWRs are negative (will be referred as AB), second one is the region where values of EWRs approximately tend to zero (will be referred as BC) and the third one, where EWRs are about positive values (will be referred CD). EWR is negative means, some material is being re-deposited on the tool, and this may be due to the deposition of carbon particle from the decomposition of dielectric fluid in such a high temperature of EDM process.

Electrode Wear Rate(mm3/min)

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1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4

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CNSGA-II NSGA-II SPEA2

0

20

40

Material Removal

60

80

Rate(mm3/min)

Fig.10. Pareto-optimal fronts of different Algorithms

In the Pareto optimal front of NSGA-II algorithm, the lowest value of MRR has been observed in process parameter setting of Ip=4A, Ton=309.7 µs, Tau =57.8 % and V=40. 2volts, where the value of MRR is 5.1463 mm3/min and EWR is -0.1395 mm3/min. This is an optimal process parameter setting from a mathematical point of view, but cannot be the optimal process parameter setting from the machining point of view. This data represents a very low MRR, and the negative value of the electrode wear rate is indicating the deposition of some material on the tool, which will lead to poor dimensional accuracy and higher machining time. The highest electrode wear rate has been found to be 0.2469 mm3/min with an MRR of 59.1664 mm3/min in the process parameter setting of Ip=16 A, Ton=348.8 µs, Tau =65% and V=40.3volts. This data represents very high MRR and the highest value of tool wear, which will lead to poor dimensional accuracy. From the qualitative degree of thought, keeping an eye on the dimensional accuracy and maximum material removal rate, the best optimal process parameter setting among the sixty set of optimal solutions must be lying around the region BC. The most suitable and acceptable optimal process parameter setting from the sixty sets of the optimal solution is Ip=16A, Ton= 463 µs, Tau =65% and V=40 volts. For this optimal set of process parameters, the MRR will be high and EWR will be low, leading to high productivity and high dimensional accuracy. The value of MRR and EWR for this setup of process parameters are 57.35 mm3/min and -0.0040 mm3/min. In the Pareto optimal front of CNSGA-II algorithm, the lowest value of MRR has been observed in process parameter setting of Ip=4A, Ton=303 µs, Tau =59% and V=40volts, where the value of MRR is 6.05 mm3/min and EWR is -0.1386 mm3/min. The highest electrode wear rate has been found to be 1.3435 mm3/min with an MRR of 61.34 mm3/min in the process parameter setting of Ip=16 A, Ton=113µs, Tau =65% and V=40volts. However, the only feasible and acceptable optimal process parameter setting from the sixty sets of the optimal solution of CNSGA-II is Ip=16A, Ton= 450 µs, Tau =65% and V=40 volts. The value of MRR and EWR for this setup of process parameters are 57.36 mm3/min and 0.0137 mm3/min. From the Pareto optimal front of SPEA2 algorithm, the lowest value of MRR has been observed in process parameter setting of Ip=4A, Ton=289µs, Tau =58% and V=40volts, where the value of MRR is 5.38 mm3/min and EWR is -0.1428 mm3/min. The highest electrode wear rate has been found to be 1.4232 mm3/min with an MRR of 61.4 mm3/min in the process parameter setting of Ip=16 A, Ton=100 µs, Tau =65% and V=40volts. The most suitable and acceptable optimal process parameter setting from the sixty sets of the optimal solution of SPEA2 is Ip=16A, Ton= 472 µs, Tau =65% and V=40 volts. The value of MRR and EWR for this setup of process parameters are 57.3 mm3/min and -0.0159mm3/min.

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Confirmatory test: A total each of sixty solutions were predicted by each ANN integrated GAs, but none of these solutions can be better than another. The best solution depends upon the requirement of product, dimensional accuracy and productivity. Confirmatory experiments were performed on Ip=16A, Ton=463µs, Tau=65% and V=40volts for NSGA-II, Ip=16A, Ton=450µs, Tau=65% and V=40 volts for CNSGA-II and Ip=16 A, Ton=472 µs, Tau=65% and V= 40 volts for SPEA2. These process parameter settings obtained from the Pareto optimal front of the respective algorithm, are pursuing the goal of high MRR and lower EWR (approximately zero EWR). Table 7 represents the predicted values of fitness functions and experimental values. Confirmatory experiments represent excellent results and good agreement with the ANN predicted values. Table 7. Results of confirmatory test S.No

Algorithm

Optimal process parameter settings ANN predicted

Results Experimental

EWR MRR (mm3/min) (mm3/min) 01

NSGA-II

02

CNSGA-II

03

SPEA2

Ip=16A, Ton=463µs, Tau=65% and V=40 volts Ip=16A, Ton=450µs, Tau=65% and V=40 volts Ip=16A, Ton=472µs, Tau=65% and V= 40 volts

MRR EWR (mm3/min) (mm3/min)

57.35

-0.0040

56.98

0.0711

57.36

0.0137

57.13

0.075

57.3

-0.0159

56.88

0.0684

6. Conclusions The fitness function to the three GA based algorithm was successfully developed from the ANN modelling. Based on results of test R and test MSE, the three process parameters of ANN i.e., MLP neural architecture, Levenberg-Marquardt training algorithm and 16 numbers of hidden neurons were selected for ANN modelling. The significance of these parameters were checked using ANOVA and it was revealed that the number of hidden layer neurons have the most influence on both the considered performance parameters test MSE and test R. The percentage contribution of a number of hidden neurons in test MSE and test R were found to be 28.03% and 32.35% respectively. The correlation coefficient values in the training data set, validation data set and testing data set were found to be 0.99995, 0.99977 and 0.9998 respectively, which indicates the robustness of function approximation capability of the developed ANN model equation. In this paper, the EDM process parameters for A2 tool steel material (hardened, 62 HRC) have been successfully optimized by using three EA based optimization techniques and ANN. The main objective was to obtain the optimum performance parameters (i.e., MRR and EWR) and domains of the process parameters such as discharge current, spark on time, duty cycle and discharge voltage. The optimal process parameter setting of Ip=16A, Tau=65% and V= 40 volts were found to be same in the three algorithms. The only variation observed was with the value of Ton. The value of Ton was found to be 463µs, 450µs and 472µs from NSGA-II, CNSGA-II and SPEA2 respectively. The best solutions obtained for MRR and EWR were 56.98mm3/min 0.0711mm3/min from NSGA-II, 57.13 mm3/min and 0.075 mm3/min from CNSGA-II and 56.88 mm3/min, 0.0684 mm3/min from SPEA2 respectively. Confirmatory tests were performed and they validated the predicted values and experimental values with a good accuracy. The confirmatory tests also validate the superiority of the ANN integrated optimization techniques. Thus, the three optimization techniques NSGA-II, CNSGA-II and SPEA2 are very effective and beneficial for attaining high performance in terms of MRR and EWR for machining hardened A2 tool steel in the considered EDM process. References [1] K.L. Du, M.N. Swamy, Neural networks in a softcomputing framework, Springer Science & Business Media, 2006. [2] S. Tiwari, G. Fadel, K. Deb, Engineering Optimization, 43(4) (2011) 377-401. [3] E. Zitzler, M. Laumanns, L. Thiele, Technical report 103, Swiss Federal Institute of Technology (ETH), Zürich, 2001.

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