Applied Soft Computing 11 (2011) 2743–2755

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Applied Soft Computing

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ntelligent process modeling and optimization of die-sinking electric dischargeachining

.N. Joshia, S.S. Pandeb,∗

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, IndiaDepartment of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India

r t i c l e i n f o

rticle history:eceived 31 January 2009eceived in revised form 11 June 2010ccepted 17 November 2010vailable online 24 November 2010

eywords:lectric discharge machining (EDM)rocess modeling and optimizationinite element method (FEM)rtificial neural networks (ANN)caled conjugate gradient algorithm (SCG)on-dominated sorting genetic algorithm

NSGA)

a b s t r a c t

This paper reports an intelligent approach for process modeling and optimization of electric dischargemachining (EDM). Physics based process modeling using finite element method (FEM) has been inte-grated with the soft computing techniques like artificial neural networks (ANN) and genetic algorithm(GA) to improve prediction accuracy of the model with less dependency on the experimental data. Atwo-dimensional axi-symmetric numerical (FEM) model of single spark EDM process has been devel-oped based on more realistic assumptions such as Gaussian distribution of heat flux, time and energydependent spark radius, etc. to predict the shape of crater, material removal rate (MRR) and tool wear rate(TWR). The model is validated using the reported analytical and experimental results. A comprehensiveANN based process model is proposed to establish relation between input process conditions (current,discharge voltage, duty cycle and discharge duration) and the process responses (crater size, MRR andTWR) .The ANN model was trained, tested and tuned by using the data generated from the numerical(FEM) model. It was found to accurately predict EDM process responses for chosen process conditions. Thedeveloped ANN process model was used in conjunction with the evolutionary non-dominated sortinggenetic algorithm II (NSGA-II) to select optimal process parameters for roughing and finishing opera-tions of EDM. Experimental studies were carried out to verify the process performance for the optimummachining conditions suggested by our approach. The proposed integrated (FEM–ANN–GA) approachwas found efficient and robust as the suggested optimum process parameters were found to give theexpected optimum performance of the EDM process.

© 2010 Elsevier B.V. All rights reserved.

. Introduction

Electric discharge machining (EDM) is a widely used uncon-entional manufacturing process that uses thermal energy of thepark to machine electrically conductive as well as non-conductivearts regardless of the hardness of the work material. EDM can cut

The process has however, some limitations such as high spe-cific energy consumption, longer lead times and lower productivitywhich limit its applications. Researchers worldwide are thus, focus-ing on process modeling and optimization of EDM to improve theproductivity and finishing capability of the process.

Literature reports several attempts to develop analytical pro-

ntricate contours or cavities in pre-hardened steel or metal alloyTitanium, Hastelloy, Inconel) without the need for heat treatmento soften and re-harden the materials. The process has also beenpplied to shape the polycrystalline diamond tools and machine of

cess models to predict process responses such as material removalrate (MRR) and surface roughness from the process parameterslike current, discharge duration, discharge voltage, duty cycle, etc.Simplifying assumptions like constant spark radius, disc or uni-

icro holes and 3-D micro cavities [1,2]. During the EDM operation,ool does not make direct contact with the work piece eliminat-ng mechanical stresses, chatter and vibration problems. EDM hashus, become an indispensable machining option in the meso and

icro manufacturing of difficult to machine complex shaped diesnd molds and the critical components of automobile, aerospace,edical and other industrial applications.

∗ Corresponding author. Tel.: +91 22 2576 7545; fax: +91 22 2572 6875/3480.E-mail address: s.s.pande@iitb.ac.in (S.S. Pande).

568-4946/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2010.11.005

form shaped heat flux, constant thermal properties of work andtool material severely restrict their prediction accuracy [2]. Fewattempts have also been directed to developing models from exper-imental results using statistical techniques [1]. These are specific towork–tool material pairs, shop conditions and thus, lack generality.

Due to the complex and non-linear relationship between theinput process parameters and output performance parameters, itis quite difficult to develop an accurate process model and use itto select the optimum process parameters for EDM process. In therecent years, the soft computing techniques viz. artificial neuralnetworks (ANN), genetic algorithm (GA) have shown great promisein solving complex non-linear real life problems in such diverse

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744 S.N. Joshi, S.S. Pande / Applied S

elds of manufacturing process modeling, multi-objective opti-ization, pattern recognition, signal processing and control [1,3].

he ANN based process modeling offers several advantages such ashe ability to capture non-linear and complex relationship betweennput process parameters and output performance parameters; toearn and generalize the input data patterns; to tolerate noise in annput pattern (data set) and relatively faster speed in learning [3].A provides better optimal solution in the global search space due

ts robustness [4].The focus of the present work is thus, on developing an intel-

igent approach for process modeling and optimization of EDMrocess. Physics based process modeling using FEM has been inte-rated with the soft computing techniques like ANN and GA tomprove prediction accuracy of the model with less dependencyn the experimental data. This approach will help a process engi-eer to improve the process productivity, finishing capability andconomical operation of die-sinking EDM process.

Rest of the paper is organized as under. Section 2 presents reviewf relevant papers on the use of ANN and GA for process modelingnd optimization. Overview of the developed intelligent processodel for EDM using FEM and ANN is presented in Section 3. Sec-

ion 4 presents the overview of the thermo-physical (FEM) modelf EDM process developed and its validation. Section 5 describes, inetail, the development of ANN based process model of EDM whileection 6 reports the approach for the selection optimal processarameters for roughing and finishing operations using NSGA-

I. Section 7 presents the results of the verification experiments.onclusions and contributions from this work are summarized inection 8.

. Literature review

Literature reports extensive experimental and analytical stud-es on process modeling and optimization of EDM process tomprove its accuracy and productivity. Experimental research works focused on obtaining process parameters to achieve optimalDM performance by using various statistical techniques such asesponse surface methodology (RSM), factorial analysis, regressionnalysis, analysis of variance (ANOVA) technique, and Taguchi anal-sis [1,2]. The recommendations based on these models are specifico tool, work materials, experimental conditions and thus, lack gen-rality.

On the analytical front, since the early seventies, researchersave attempted to model the electric discharge phenomenaplasma channel) and the mechanism of cathode and anode erosionn the EDM process [1,5]. Different thermal models have been pro-osed by taking a microscopic view of the process considering thepark and its surrounding area [6]. The reported thermo-physicalodels of the EDM process however, significantly over predict the

rocess responses such as material removal rate (MRR) and surfaceoughness. This is primarily due to various simplifying assump-ions such as uniform (disc) heat source [5], point heat source [7],onstant heat source radius [8,9] for all discharge conditions andonstant thermo-physical properties over the temperature range5,7]. These simplifying assumptions do not simulate the real lifeonditions and thus, severely limit the applicability of the results.ery scant literature has been reported on the study of shape of

he crater produced at the cathode/anode surface after the spark.need thus, exists to develop a numerical model based on the

hermal analysis of EDM spark to predict accurately the crater

nd associated material removal by modifying the above statedssumptions.

Researchers, of late, are focusing upon employment of arti-cial intelligence (AI) techniques viz. ANN, GA, fuzzy logic, etc.

or the process modeling and optimization of manufacturing pro-

mputing 11 (2011) 2743–2755

cesses which are expected to overcome some of the limitationsof conventional process modeling techniques. Initially, Tsei andWang [10,11] compared various ANN training algorithms for pre-diction of MRR and surface roughness separately. They reportedthat adaptive-network-based fuzzy inference system (ANFIS) withbell shape membership function was best suited for MRR prediction[10] whereas ANFIS, radial basis function neural network (RBFN)and tangent multi layered perceptrons (TANMLP) were found moreconsistent in the prediction of surface roughness [11]. Wang et al.[12] developed hybrid model of EDM process using ANN and GA forprediction of MRR and surface roughness. GA was used to optimizethe synaptic weightages. Fenggou and Dayong [13] have proposedanother GA based ANN modeling approach for the prediction ofthe processing depth. The number of nodes in the hidden layer wasoptimized by using GA. Panda and Bhoi [14] have used back prop-agation neural network (BPNN) with Levenberg–Marquardt (LM)algorithm for the prediction of MRR.

Su et al. [15] developed an ANN model of the EDM processand further used it to optimize the input process parameters byusing GA. Later Sen and Shan [16], Mandal et al. [17], Gao et al.[18], Rao et al. [19,20] followed the similar methodology for themodeling and optimization of EDM process for different work–toolmaterial pairs. Recently, Yanga et al. [21] used simulated anneal-ing (SA) technique with ANN for optimization of MRR and surfaceroughness. Tzeng and Chen [22] have used the fuzzy logic anal-ysis coupled with the Taguchi dynamic approach to optimize themachining precision and accuracy.

The above referred process modeling and optimizationapproaches using AI techniques are based on the experimental datato predict work material removal or surface roughness under stan-dard experimental machining conditions for specific tool–workmaterials. Scant research work is reported on a comprehensivemodel to predict all output performance parameters viz. MRR, TWRand surface roughness in an integrated fashion.

In conclusion, it can be seen that no efficient, generalizedapproach to model the EDM process so far has been reported tostudy and predict the accurate crater shapes, MRR, TWR duringEDM and use it further to derive the optimal process parameters.

In the present work, an attempt has been made to developa comprehensive intelligent and integrated (FEM–ANN–GA)approach to model and optimize the die-sinking EDM process.

3. Overview of process model development

Fig. 1 shows the proposed approach for the development ofintelligent process model for EDM using FEM, ANN and GA. It pri-marily comprises of three stages:

• Numerical (FEM) modeling of the EDM process considering thethermo-physical characteristics of the process.

• Development of ANN based process model based on the datagenerated using the simulation of the numerical (FEM) model.

• Optimum selection of process parameters using GA based opti-mization of ANN process model.

This integrated approach of model development(FEM–ANN–GA) has a peculiar merit that it is based on accu-rate FEM analysis and not on experimental data collection, whichcould be costly, time consuming and error prone. Important stagesin the model development are discussed in the sections to follow.

4. Thermo-physical modeling of EDM process using FEM

In this work, a two-dimensional axi-symmetric non-linear tran-sient thermo-physical (FEM) model of single spark EDM process

S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755 2745

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Fig. 1. EDM process model deve

as been developed. Compared to the reported thermal models,ore realistic assumptions were employed such as consideration

f current–discharge duration dependent spark radius, Gaussianistribution of heat source, temperature dependent thermal prop-rties and consideration of latent heat of melting. Details regardinghe thermo-physical (FEM) model development are discussed atength in our earlier paper [6]. Salient features of the model areresented here.

Fig. 2 shows the schematic diagram of the process continuumnd associated boundary conditions used.

Material removal in EDM process is primarily due to the meltingnd evaporation caused by intense heat generated by the sparklasma. As a result transient, Fourier heat conduction equation (Eq.1)) with necessary boundary conditions was used.

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here r and z are the coordinates of cylindrical work domain, T ishe temperature, Kt is the thermal conductivity, � is the densitynd Cp is the specific heat capacity of work piece or tool mate-ial. The heat entering into the workpiece due to EDM spark, qas derived (Eq. (2)) considering the spark radius as a function

f current–discharge duration and Gaussian distribution of heatource [6].

(t) = 3.4878 × 105FVI0.14

ton0.88

exp

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(t

ton

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(2)

Fig. 2. Process continuum and boundary conditions.

ent and optimization approach.

where q(t) is the heat flux to be appied at boundary 1 (Fig. 2),F is the fraction of total EDM spark power going to the cathode oranode, V is the voltage, I is the discharge current, ton is the discahrgeduration and t is the time variable.

The governing equation with boundary conditions was solvedby using finite element method (FEM) solver ANSYS 10.0 [23].A 2-D continuum was considered for the analysis. Four-nodeaxi-symmetric thermal solid element ‘Plane 55’ was used for dis-cretization of the continuum. Material properties viz. temperaturedependent thermal conductivity, specific heat, density and latentheat of melting were employed. The transient heat transfer problemwas solved using the discharge duration as the time step for anal-ysis. Nodes showing temperature more than melting point wereselected and later eliminated from the work domain. A typicalcrater generated is shown in Fig. 3. Crater size (depth and radius)and associated material removal were computed. Following thismethodology, comprehensive thermal analysis of both the cathode(work) and anode (tool) erosion was carried out.

The results obtained from our numerical model (with and with-out considering latent heat of melting) were compared with thosefrom earlier analytical models and the published experimentaldata. Recently, Yeo et al. [5] critically compared the predictionaccuracies of five well referred thermal models and concluded thatthe MRR results predicted by DiBitonto’s model [7] are closer tothe experimental data compared to all the other models. Fig. 4shows the comparison of MRR predicted by our model, Yeo’s recom-mended model (DiBitonto et al. [7]) and the AGIE SIT experimental

data. It is seen that, the values of MRR predicted by our model arefurther closer to the experimental results compared to those byDiBitonto et al. [7] for a wide range of discharge energy levels upto 650 mJ. Our numerical model would thus, give better predictionof MRR compared to the reported models. This may be due to the

Fig. 3. Predicted bowl shaped crater using FEM analysis. (crater depth: 30.2 �m,crater radius: 70.3 �m, work material – AISI P20 mold steel, discharge current 10 A,spark on-time 100 �s and discharge voltage 40 V).

2746 S.N. Joshi, S.S. Pande / Applied Soft Co

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Fig. 4. Comparison of computed and experimental results: cathode erosion.

ncorporation of more accurate and realistic equivalent spark radiusquation, which is a function of current and discharge duration.n addition, our model considers the transient analysis of singlepark with the expanding radius, which may also add more accu-acy to our results. In comparison, DiBitonto’s model approximatedhe spark as point on cathode with created hemispherical crater,hich is quite simplified, compared to reality.

For higher values of discharge power and discharge durationdischarge energy > 650 mJ), our model under predicts the MRRompared to the experimental results. This may be due to the facthat longer pulses with higher values of current provide more sur-ace area to heat conduction, which might lead to reduction in heatensity. Constant value of duty factor may also result in compara-ively less MRR [6]. This could possibly be the reason for the modelrediction deviating from the experimental results. The shape ofrater (bowl) predicted by our numerical (FEM) model (Fig. 3) wasound to have a shape similar to the reported experimental results.

The complete problem solving procedure for the thermal analy-is was automated by using ANSYS Parametric Design LanguageAPDL) [23]. Important process parameters were identified andxtensive parametric studies were carried out to study the effectf different process parameters on the performance parametersor a work–tool pair as AISI P20 mold steel and copper. From theesults, it was concluded that, the performance measures of EDMrocess such as MRR, TWR and crater dimensions are influencedy four interacting process parameters viz. discharge current, dis-harge duration, discharge voltage and duty cycle. It has noted thathere exists a complex and non-linear relationship between inputrocess parameters and output performance parameters [6].

The FEM based numerical model developed in this work wasound to be accurate but computationally expensive due to the non-inear and complex nature of the governing equation and boundaryonditions, particularly to carry out exhaustive parametric analy-is for suggesting the optimum process parameters. This providedotivation to develop an ANN based process model based on the

ata generated on the FEM model that can be used to predict theerformance parameters of the EDM process reasonably accuratelynd quickly for a set of chosen input process conditions.

. Intelligent process modeling using ANN

With the primary objective of the present work outlinedbove, various modeling techniques such as Statistical techniquesRegression analysis, Taguchi’s method, etc.) and soft comput-

mputing 11 (2011) 2743–2755

ing techniques (ANN, fuzzy logic, etc.) were studied. Statisticaltechniques offer advantages such as, reduced numbers of trials,optimum selection of parameters, assessment of experimentalerror, and qualitative estimation of parameters effect. While suchtechniques are useful for identifying general trends in processinputs and outputs, they are beset with many limitations. Fittingcurves to non-linear and noisy data needs the selection of trans-forms, which, inevitably, is subjective and often becomes difficultwhen multiple inputs and multiple outputs are involved. The largevariations in the factors may give misleading results and quite oftenguidelines on selection of optimum ranges of variables are not avail-able [24]. These considerations have led to the identification of theneural network approach, which overcomes some of these difficul-ties.

In recent times, neural networks (NN) and fuzzy logic (FL)techniques are commonly used in the modeling of manufacturingprocesses [25,26]. FL based strategies depend on the rule base for-mulated which often varies from developer to developer [27]. Asthe number of input and output parameters increase, the develop-ment of rule base becomes quite tedious. FL provides the explicitinformation about the process to be modeled. However, largeamount of real life data is needed for automatic rule generation.Requirement of human expertise, process knowledge and skill fur-ther limits the applicability of FL based strategies. On the otherhand, ANNs are well proven techniques when reasonable amountof training data is available [26].

ANNs are well known due to their ability to approximatenon-linear and complex relationship between process parametersand performance measures. Relatively faster learning, generaliza-tion capabilities from imprecise and noisy data make them moresuitable option in modeling of complex manufacturing processesthough they do not provide explicit information about the processto be modeled [14–21,24–26].

It was, therefore, thought appropriate and convenient todevelop a comprehensive (4 inputs – 4 outputs) EDM processmodel using ANN for quicker and accurate prediction of processperformance results. A comprehensive process model of EDM wasdeveloped using ANN to accurately predict the process responsesviz. MRR, TWR and crater dimensions in an integrated manner. Totrain the ANN based process model, exhaustive data was gener-ated by using numerical (FEM) simulations of the process modeldeveloped. The following ranges of the input process parametersidentified from the published research [1,2] and machining hand-book [28] were chosen for our study.

• Discharge current: 5–10–20–30–40 A• Discharge duration: 25–50–100–300–500–700 �s• Duty cycle: 50–65–80%• Break down voltage: 30–40–50 V• Work material: AISI P20 mold steel• Tool material: Copper

Various ANN configurations viz. radial basis function neural net-work (RBFN) (4-N-4) and feed forward back propagation neuralnetwork (BPNN) (4-N-4, 4-N1-N2-4) were extensively tried out fortheir prediction performance. The primary objective was to developa single comprehensive process model of the 4 inputs – 4 outputstype. The overview of the development of RBFN and BPNN basedprocess model and their prediction performances are discussed indetails as under.

5.1. Development of RBFN based process model

RBFN is alternative supervised learning network architectureto the multilayered perceptrons (MLP). The topology of the RBFNis similar to the MLP but the characteristics of the hidden neu-

S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755 2747

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Fig. 5. Network topology of RBFN.

ons are quite different (Fig. 5). It consists of an input layer, oneidden layer and an output layer. The input layer is made up ofource neurons with a linear function that simply feeds the inputignals to the hidden layer. The neurons calculate the Euclidean dis-ance between the center and the network input vector, and thenasses the result through a non-linear function (Gaussian func-ion/multiquadric/thin plate spline, etc.). It produces a localizedesponse to determine the positions of centers of the radial hid-en elements in the input space. The output layer, which supplieshe response of the network, is a set of linear combiners, which isiven by [29],

(x) =N∑

i=1

wijG (||x − ci|| · b) (3)

here N is the number of data points available for training, wij is theeight associated with each hidden neuron, x is the input variable,

i is the center points and b is the bias. The localized response fromhe hidden element using Gaussian function [29] is given by,

(||x − ci|| · b) = exp

(− 1

2�2i

(||x − ci|| · b)2

)(4)

here �i is the spread of Gaussian function. It represents the rangef ||x − ci|| in the input space to which the RBF neuron shouldespond. Usually, the spread should not be more than the possi-le maximum distance between input vector and the center of theBF. It is determined based on number of hit and trials [26]. Theransformation from input layer to the hidden layer is non-linearut the transformation from the hidden layer to the output layer

s linear. Determination of number of hidden neurons, centers ci ofhe RBF neurons and the weights wij of the output layer based onhe given training samples are the key tasks in RBFN design. Thesearameters were optimized using Orthogonal Least Square (OLS)pproach [29].

Using the thermo-physical (FEM) model [6], a dataset of total78 input–target pairs for the chosen work–tool pair was prepared.ataset was divided into a training set (262 input–target pairs)nd a testing set (16 input–target pairs). Performance of each can-idate network (RBFN and BPNN) was tested by studying threeypes of errors viz. prediction error of each performance param-ter (MRR/TWR/crater size) of each input–target pair of the testing

ataset, mean error of each performance parameter for the com-lete testing dataset and the average mean error (AME) of all theerformance parameters for the whole testing dataset. To choosehe optimal network configuration, number of simulations has beenarried out by varying the spread factor from 0.15 to 0.4. RBFN net-

Fig. 6. Variation of testing error: 4-250-4 RBFN network with spread factor 0.12.

work 4-250-4 with spread factor of 0.12 gave AME of about 19%.It was found to be the best possible configuration. Fig. 6 showsthe variation of the testing errors of all performance parameterswith the testing datasets for the 4-250-4 RBFN network with spreadfactor of 0.12.

From Fig. 6, it can be observed that the 4-250-4 RBFN networkpredicts the MRR, crater depth and crater radius with reasonablemean prediction error (ME) of about 10% and about 80% of the totaltesting datasets lie within an error bound of ±15%. The networkshows poor prediction capability for the TWR with mean predictionerror (ME) of about 46% and only 25% of the total datasets lie withinthe error bound of ±15%. Overall, this best possible trained network(4-250-4) gave very poor prediction performance (prediction errorof TWR of the order of 50–150%). In spite of simplicity in design andfaster learning, 4-N-4 RBFN configuration was not found suitable forthe EDM process model development due to its poor generalizationcapability. This might be due to insufficient training data and localnature of fitting.

In comparison with RBFN configuration, BPNN configurationwith a fast learning algorithm viz. scaled conjugate gradient (SCG)[30] gave much superior results for our problem. The details regard-ing the development of BPNN based process model viz. networkarchitecture, training, testing and the selection of suitable ANNarchitecture for our problem are presented at length elsewhere [6].The overview of the development of BPNN based process model ispresented in the next section.

5.2. Development of BPNN based process model

Fig. 7 shows the schematic diagram of a BPNN configurationwith two hidden layers, one input layer and output layer each.BPNN configuration with SCG algorithm was tried out. Exhaustivenumerical experimentation was carried out to choose the optimalBPNN architecture by varying the number of hidden layers (sin-gle and two layered) and number of neurons in each hidden layer(from 4 to 30). The 4-5-28-4 BPNN architecture was found to bemore accurate and generalized with very good prediction accuracy(of about 7%) in comparison with the 4-250-4 RBFN configuration.Fig. 8 shows the error in prediction of process responses viz. MRR,TWR, crater depth and crater radius for various testing data sets.It was seen that, about 90% of the testing dataset lie within 15% of

error bound (Fig. 8). This might be due to its global nature of learn-ing, ability to optimize the learning rate and momentum constant.As a result, the process model based on 4-5-28-4 BPNN architecturewas chosen as the final process model developed.

2748 S.N. Joshi, S.S. Pande / Applied Soft Co

Fig. 7. Schematic of BPNN architecture.

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Fig. 8. Prediction accuracy of 4-5-28-4 BPNN network.

Compared to the earlier reported works based on experimen-al results, our ANN model was found to be more accurate andeneralized as it predicted the intermediate data points with goodrediction accuracy. This approach of process model development

s unique as the ANN model predicts EDM process responses (MRR,WR, and crater size) quickly and accurately from the input processonditions without the need to go for a rigorous FEM analysis. Thentelligent ANN based process model developed was further inte-rated with an optimization algorithm to obtain process conditionsor optimum performance of the EDM process.

. Optimum selection of EDM process parameters usingenetic algorithm

Selection of the most favorable (optimum) EDM process param-ters is based on shop experience or handbook values, which oftenesults in inconsistent machining performance [1,2]. Due to theomplex and non-linear relationship between the input process

Fig. 9. Integrated ANN–NSGA appro

mputing 11 (2011) 2743–2755

parameters and output performance parameters, it is quite difficultto select the optimum process parameters for specific applicationof EDM process i.e. roughing or finishing operation.

Literature reports, GA as a better optimization methodologyover the traditional optimization techniques due to its advantagesviz. robustness, independency of gradient information and use ofinherent parallelism in searching the design space [4,15–20]. In thepresent work, the following ANN–NSGA-II approach (Fig. 9) wasdeveloped for the selection of optimum EDM process parametersfor roughing and finishing operations.

• ANN based process model developed earlier is used to predictthe values of the output performance parameters on the basis ofinput process parameters.

• Multiple objectives are defined for the GA based optimization forroughing and finishing applications.

• Non-dominated sorting genetic algorithm II (NSGA-II) based opti-mization strategy [32] is applied to obtain a set of optimal inputprocess parameters.

6.1. Selection of suitable optimization strategy

Owing to the complex nature of EDM process and conflictingrelationship exists between input process parameters and outputperformance parameters making it very difficult to determine opti-mal process parameters for improving the process performance.There is no single optimal combination of process parameters, asthe influences of the parameters on the MRR, TWR and crater depthare often opposite in nature. It is thus, difficult to find a single opti-mal combination of parameters for higher MRR, lower TWR andlower crater depth as the case may be. Hence, there is a need for amulti-objective optimization method to arrive at the solutions tothis problem. Various classical methods of obtaining the solutionsto multi-objective problems such as Min–Max, Weighted Sum andDistance Function methods [4] change the multi-objective probleminto a single objective, with the corresponding weights based ontheir relative importance. These methods suffer from a drawbackthat the decision maker must have a thorough knowledge ofranking of objective functions. Also, these methods fail when theobjective functions become discontinuous. In such situations,GA possesses advantages that it does not require any gradientinformation and has inherent parallelism in searching the designspace, thus making it a robust adaptive optimization technique.For multi-objective optimization methods, some modificationto simple GA is necessary. In this present work non-dominatedsorting genetic algorithm II (NSGA-II) [31,32] in conjunction withANN based process model is used to obtain the optimal processconditions for EDM process.

The non-dominated sorting genetic algorithm is an evolution-ary, fast and elitist genetic algorithm which provides multiplePareto-optimal solutions to the multi-objective optimization prob-

lems. NSGA-II is essentially a modified form of conventional GA. Thecrossover and mutation operators remain as usual, but selectionoperator works differently from simple GA. Selection is done withthe help of crowded-distance comparison operator, based on rank-ing (according to non-domination level) and crowding distance.

ach for process optimization.

S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755 2749

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ig. 10. Flow chart of ANN–NSGA approach for optimization of EDM process param-ters.

.2. Objective functions and variables

In the present work, following objective functions were definedor the optimization of roughing and finishing EDM operations.

For roughing operation◦ Obj. 1 = Maximize MRR (for fast roughing operation).◦ Obj. 2 = Maximize 1/(1 + TWR) (for moderate tool wear, eco-

nomical roughing operation).For finishing operation◦ Obj. 1 = Maximize 1/(1 + Crater depth) (for superior quality sur-

face finish).◦ Obj. 2 = Maximize 1/(1 + TWR) (for accurate and economical

operation).◦ Obj. 3 = Maximize MRR (for faster finishing operation).

The ranges of the process variables taken for this study are pre-ented in Section 5.

.3. The integrated ANN–NSGA-II approach

Fig. 10 shows the various steps of the integrated ANN–NSGA-IIpproach developed. Initially a real-parameter random population

of size N is created by using the results of the 4-5-28-4 BPNN

ased EDM process model (Section 5). It is sorted into differenton-domination levels by checking whether the solution underonsideration satisfies the rules given below:

Fig. 11. A Typical chromosome.

For roughing operation

Obj. 1[i] > Obj. 1[j] and Obj. 2[i] ≥ Obj. 2[j] (5)

or

Obj. 1[i] ≥ Obj. 1[j] and Obj. 2[i] > Obj. 2[j], i /= j (6)

where i and j are the solution numbers.If above rules are satisfied then the selected solution is marked

as non-dominated. Otherwise the selected solution is marked asdominated. In the first sorting, all non-dominated solutions (N1) areassigned rank 1. From the remaining (N–N1) dominated solutions,candidate solutions are again sorted. The non-dominated solutionsafter the second sorting are ranked 2. Each solution is assigned afitness equal to its non-domination level (1 is the best level). Theprocedure shown in Fig. 10 will be repeated till the Pareto optimalfront is obtained. The steps are described as follows:

Step 1: Parents are selected from the population by using the Tour-nament selection based method and then sorted using crowdingdistance algorithm [31,32] (from previous generation). The algo-rithm is presented at length in the step 4.Step 2: The selected population generates offspring usingcrossover and mutation operators. Simulated Binary Crossover(SBX) operator for crossover and polynomial mutation are usedin this study. Fig. 11 shows a typical chromosome made up of 4genes viz. duty cycle, current, discharge duration and dischargevoltage.Step 3: Combine parent and offspring populations and performa non-dominated sorting. If a solution is strictly better than anyother solutions in all objectives then it is called non-dominantsolution i.e. it is not dominated by any other solution and a setof such solutions is called non-dominated set. The first front beingcompletely non-dominant set in such sorted population and thesecond front being dominated by the individuals in the first frontonly and the front goes so on. Each individual in each front areassigned rank (fitness) values based on the front in which theybelong to. Individuals in first front are given a fitness value of 1and individuals in second are assigned fitness value as 2 and so on.Step 4: Once the non-dominated sort is complete, the crowdingdistance is assigned. The crowing distance of a solution is a mea-sure of the search space around the solution which is not occupiedby any other solution in the population. It expresses the Euclid-ian distance between each individual in a front based on their mobjectives in the m dimensional hyper space. Crowding distanceis assigned frontwise [31,32]. Comparing the crowding distancebetween two individuals in different fronts is meaningless. Largeaverage crowding distance will result in better diversity in thepopulation. The individuals in the boundary are always selectedsince they have infinite distance assignment. The stepwise crowd-ing distance (CD) assignment procedure is as under.Step 4.1: Say the number of elements in a Front is equal to p.Step 4.2: For each objective function (m = 1, 2, . . ., M), sort the ele-

ments in the ascending order of objective function value (fm) i.e.find sorted indices vector (Im).Step 4.3: Assign the large CD values to boundary elements insorted elements in step 4.2 or dIm

1= dIm

p= ∞, and for other solu-

2 oft Computing 11 (2011) 2743–2755

ASpctrEP

pofb

6

oTioiIMcwvctBtrbc

fp((sit

ls

750 S.N. Joshi, S.S. Pande / Applied S

tions j = 2 to (p − 1), the CD is calculated using,

dImj

= dIm−1j

+ fImj+1

m − fImj−1

m

f maxm − f min

m

(7)

where Imj

denotes the solution index of jth member in the sortedlist based on mth objective function. d

Im−1j

is the CD value from

previous objective function. f maxm and f min

m are the maximum and

minimum values of mth objective function. fImj+1

m and fImj−1

m arethe objective function values of the neighboring elements in thesorted list from step 4.2.

Step 5: The new generation is filled by each front subsequentlyuntil the population size exceeds the current population size fromnon-dominated sorted population from step 3. If by adding all theindividuals in a front, the population exceeds maximum popula-tion size, then individuals in the front are selected based on theircrowding distance in the descending order until the populationsize reached its maximum size.

A computer code was written in MATLAB 7.0 to integrate theNN based process model and the NSGA-II tool box developed byastry [33]. In the first iteration of the GA, the developed coderovides the initial population of probable solutions (Parents) byalling the ANN based process model. In the subsequent iterations,he ANN based process model was used to compute the processesponses viz. MRR, TWR and crater depth for the new offspring.ach NSGA-II run with 50 iterations took about 15–20 min on aentium IV machine with 2 GB RAM.

Using the above discussed NSGA-II algorithm and the ANN basedrocess model developed earlier, analysis was carried out to selectptimum process parameters for roughing and finishing operationsor AISI P20–copper (work–tool) pair. The results are presentedelow.

.4. Optimum process parameters for roughing operation

During the present study the objective set for the optimizationf roughing application was to maximize the MRR and minimize theWR. Extensive studies using the NSGA-II have been carried out todentify the range of process parameters for optimal performancef EDM process. An initial random real valued population of 100ndividuals was taken and fed it into the ANN based process model.n each generation of the NSGA-II, the process responses such as

RR, TWR and crater depth were predicted by the ANN based pro-ess model for the new individuals of the population. The fitnessas evaluated through the objective criteria and NSGA-II to sur-

ey the probability. A new population for next the generation wasreated based on the old population using different operator func-ions viz. selection (Tournament with size 4), Crossover (Simulatedinary Crossover with probability 0.5) and Mutation (polynomial ofhe order of 20 with probability 0.1). The generation was executedecursively to search for the Pareto-optimal front until the num-er of generations exceeds the limiting value. For attaining betteronvergence, 50 generations were taken in this study.

Table A.1 (Appendix A) presents the typical results of NSGA-IIor the roughing optimization problem. About 100 optimal processarameters (decision variables) of the non-dominated solution setoptimal Pareto front) and the corresponding process responsesobjective function values) were obtained. The non-dominatedolution set obtained over the entire optimization process is shown

n Fig. 12. This shows the formation of the Pareto front leading tohe final set of solutions.

Since none of the solutions in the non-dominated set is abso-utely better than any other, any one of them is an acceptableolution. The choice of one solution over the other depends on the

Fig. 12. Pareto optimal front for roughing.

requirement of the process engineer. Based on a specific require-ment say a high MRR with moderate TWR or a moderate MRR withlower TWR, a suitable combination of variables can be selected fromTable A.1 (presented in Appendix A). For example with a require-ment of a high MRR with wear ratio less than 20% a process engineercan look for the possible combinations of input process param-eters. It is seen that a process parameters set with duty cycle of80%, discharge current of 40 A, discharge duration of 415.7 �s anddischarge voltage of 50 V gives high MRR of 654.6 mm3/min andlow TWR of 124.5 mm3/min with acceptable wear ratio of 19%.It can thus, be seen that the integrated ANN–GA based approachdeveloped in this work can give the process engineer an efficienttool to choose a range of optimal process parameters for fast andeconomical roughing.

6.5. Optimum process parameters for finishing operation

For finishing operation of the EDM process, three objective cri-teria were thought of viz. low crater depth (surface roughness),low TWR and moderate MRR. Methodology similar to the rough-ing application (outlined in the previous Section 6.4) was used toderive the Pareto optimal set.

Table A.2 (Appendix A) shows the typical results predicted bythe NSGA-II for the finishing operation of EDM process. Fig. 13shows the surface generated by all the optimal solutions givenby the NSGA-II. It is observed that NSGA-II provided all the pos-sible combinations of input process parameters for best possiblefitness values of the objective functions viz. minimize crater depthand TWR, and maximize MRR. The solutions encircled in red colorsuggested the best optimal solutions for finishing operation. Theyprovide minimum crater depth, low TWR and moderate MRR.The other solutions also provide process conditions but they arenot suitable for finishing operation. For example solution no. 2,Table A.2 which gives lower crater depth but has very high TWR.In a similar manner, solution no. 3, Table A.2 suggested low TWR,high MRR but gives very high crater depth, which is also not suit-able. After studying the Table A.2 and Fig. 13, it can be noted that aprocess parameter set with duty cycle of 56%, discharge current of5 A, discharge duration of 25 �s and discharge voltage of 33 V gives

high quality surface finish (crater depth of 11.8 �m) with minimumtool wear of 3.7 mm3/min and significant MRR of 24.2 mm3/min.The integrated ANN–GA approach with NSGA-II algorithm can thusprovide a very effective tool for the process engineers to select therange of optimum machining conditions for the finishing operation.

S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755 2751

es

cfrcppoc8edmdd

ocp

7

tbvbtCtws

TS

N

Fig. 13. Optimal solutions for finishing operation.

From the above study, the range of optimum process param-ters for roughing and finishing operations of EDM have beenuggested (Table 1).

The optimum results suggested by our approach (Table 1) wereompared with the optimum process conditions recommendedrom experimental studies for the same work and tool mate-ial combinations by Amorim and Weingaertner [34,35]. Theyarried out exhaustive experiments for the selection of optimalrocess parameters for roughing and finishing operation of EDMrocess using AISI P20–copper (work–tool material) pair. The rec-mmended optimal values of process conditions are: dischargeurrent of about 32 A, discharge duration 400 �s and duty cycle0% for roughing operation. Our results closely match with theirxperimental ranges particularly for the discharge duration anduty cycle. Our recommended current value is also in good agree-ent with their experimental results. The optimum value of the

ischarge voltage was not available as the experiments were con-ucted with constant value of open circuit voltage of 180 V.

To gain further confidence, it was thought appropriate to carryut a set of our own experiments to verify the optimal processonditions suggested by our FEM–ANN–GA approach. Details areresented in the next section.

. Verification experiments

The aim of these experimental studies was to assess the effec-iveness and robustness of the proposed FEM-ANN-GA approachy verifying the process performance corresponding to the optimalalues of input process conditions suggested. Experiments haveeen conducted on the die-sinking EDM machine PS-50 ZNC, Elec-

ronica (Pune, India) available at Godrej and Boyce Manufacturingo. Ltd., Mumbai. AISI P20 mold steel and copper were chosen ashe work material and tool material, respectively. Fig. 14 shows theorkpiece and tool electrode specimens used in the experimental

tudies.

able 1uggested parametric ranges.

Process parameters Roughing

Our study Expt. stud

Current 38–40 A 32 ADischarge voltage 45–50 V NADischarge duration 400–420 �s 400 �sDuty cycle 75–80% 80%

A – not available.

Fig. 14. Tool and workpiece specimen.

7.1. Verification of optimum process conditions for roughing

Table 1 shows that for roughing operation, the suggested opti-mal values for current, discharge voltage and duty cycle are themaximum values of the input parameter range used in this work.For the discharge duration, the optimal value is 400–420 �s, whichis an intermediate value in the respective parametric range. It was,thus, decided to verify the optimality of discharge duration by vary-ing its value within a range of 200–750 �s. Table 2 lists the differentmachining conditions set up during the experimentation. The dis-charge voltage of 50 V, current 40 A and duty cycle of 80% were

kept constant throughout. Special EDM oil with 20–40 kPa pressurewas used as the dielectric medium. Table 2 shows the experimen-tal results observed during the optima verification experiments forroughing operation. Fig. 15 shows the variation of material removalrate with various values of discharge duration.

Finishing

ies [34] Our study Expt. studies [35]

5–7 A 3–5 A30–35 V NA25–30 �s 12.5 �s50–55% 50%

2752 S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755

Tab

le2

Ver

ifica

tion

exp

erim

ents

for

rou

ghin

g.

Exp

t.n

o.C

urr

ent

(A)

Spar

k-on

tim

e(�

s)W

ork

mat

eria

lw

eigh

tbe

fore

mac

hin

ing

(gm

)

Wor

km

ater

ial

wei

ght

afte

rm

ach

inin

g(g

m)

Tool

mat

eria

lw

eigh

tbe

fore

mac

hin

ing

(gm

)

Tool

mat

eria

lw

eigh

taf

ter

mac

hin

ing

(gm

)

Mac

hin

ing

tim

e(m

in)

MR

R(m

m3/m

in)

Avg

.MR

R(m

m3/m

in)

TWR

(mm

3/m

in)

Avg

.TW

R(m

m3/m

in)

1A

4020

073

.528

968

.811

866

.145

65.2

341

320

1.59

212.

6734

.12

34.3

8B

73.2

995

68.0

636

66.3

646

65.4

394

322

3.76

34.6

52

A40

300

71.2

182

66.1

198

66.1

474

65.6

112

321

7.88

222.

2720

.08

21.0

6B

72.7

328

67.4

2966

.514

265

.925

93

226.

6622

.03

3A

4040

072

.405

766

.203

766

.435

965

.797

73

265.

0426

3.34

23.9

019

.35

B73

.487

365

.364

866

.348

365

.953

326

1.65

14.8

14

A40

500

73.6

524

67.8

703

66.4

966

.239

73

247.

1024

4.25

9.37

8.64

B71

.233

965

.584

966

.607

766

.396

43

241.

417.

915

A40

750

73.4

994

67.7

613

66.3

607

66.2

215

324

5.22

227.

475.

215.

16B

73.1

859

68.2

784

66.3

863

66.2

502

320

9.72

5.10

Cu

rren

t40

A,d

isch

arge

volt

age

50V

,du

tycy

cle

80%

.W

ork

mat

eria

l:A

ISIP

20m

old

stee

l,to

olm

ater

ial:

cop

per

.

Fig. 15. Variation of MRR with discharge duration.

It can be noted that the MRR initially increases with the dis-charge duration, attains a peak at 400 �s and then decreasesfurther. The maximum MRR is obtained at the value of dischargeduration (400 �s) which closely matches with the optimum rangesuggested by our integrated FEM–ANN–GA approach (Table 1).

Fig. 16 shows that the TWR continuously decreases with thedischarge duration. For the suggested optimal value of dischargeduration viz. 400 �s, it shows acceptable tool wear of about20 mm3/min.

In conclusion it can be stated that the process performance atthe optimal values suggested by our FEM–ANN–GA approach forproducing maximum possible MRR with acceptable tool wear isrealized in the experimental domain also. The optimum processconditions suggested by our approach can thus, be applied withconfidence in practice.

7.2. Verification of optimum process conditions for finishing

For finishing operation, our approach (FEM–ANN–GA) sug-gested minimum values of the process parameters viz. dischargecurrent 5 A, discharge duration 30 �s and discharge voltage 30 V(Table 1). From the parametric study of the EDM process [6], it was

Fig. 16. Variation of TWR with discharge duration.

S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755 2753

Table 3Verification experiments for finishing.

Sr. no. Current Surface roughness,Ra (�m)

Avg. surfaceroughness, Ra (�m)

1 5 2.426 2.582.5782.736

2 10 3.449 3.223.023.177

3 15 4.581 4.404.2084.425

4 20 5.074 4.794.8984.386

5 25 4.721 4.804.728

Wd

swatu

l

c

TT

4.942

ork material: AISI P20 mold steel; tool material copper; discharge duration 30 �s;ischarge voltage 30 V; duty cycle 50%.

een that discharge current was the main input process parameterhich affects the crater depth. Therefore, it was thought appropri-

te to vary the discharge current within a range of 5–25 A to studyhe effect of the same. Total five experiments were carried out by

sing the machining conditions listed in Table 3.

Table 3 shows the surface roughness measured at three differentocations and their average values.

Fig. 17 shows the variation of surface roughness with dischargeurrent. The surface roughness initially increases with discharge

able A.1ypical results of ANN–NSGA (roughing operation).

Set no. Pareto optimal set – roughing operation

Process parameters (input)

Duty cycle (%) Current (A) Discharge duration (�s) V

1 46 35.3 417.2 32 80 40 108.6 53 80 31.2 416.3 34 80 36.3 699.9 55 80 40 207.2 56 80 35.3 698 57 79.9 40 415.7 5...34 80 40 275.2 535 80 38.5 699.5 436 80 40 527 537 80 40 245.6 538 80 40 253.7 5...55 80 40 221.6 556 80 40 323.9 557 80 40 327.2 558 80 40 280.2 559 80 39.6 699.9 4...80 80 40 226.7 581 80 40 262.1 582 80 40 267 583 80 38.7 700 4...96 80 40 560.6 597 80 40 605.7 598 80 40 232.3 599 80 40 307 5100 46 37.6 417.2 3

a Insignificant crater.

Fig. 17. Variation of surface roughness with discharge current.

current and then tapers off. Similar trend of variation of crater depth

with discharge current was observed [6].

It is seen that fine surface finish (minimum surface rough-ness of about 2.6 �m) can be obtained at discharge current 5 A.This matches with the recommended value by our FEM–ANN–GAapproach.

Performance parameters (output)

oltage (V) MRR (mm3/min) TWR (mm3/min) Wear ratio (%)

3.7 189 a a

0 702.1 501.2 71.44.6 293.4 a a

0 563.1 7.9 1.40 685.9 364.3 53.10 545.4 4.7 0.90 654.6 124.5 19

0 670.7 245.4 36.68.6 577.8 13.7 2.40 643.5 76.6 11.90 676.9 296.6 43.80 675.1 282.1 41.8

0 682.1 339.3 49.70 663.2 182.8 27.60 662.7 179.7 27.10 669.7 237.6 35.59.2 610 22.1 3.6

0 681.2 330.8 48.60 673.3 267.3 39.70 672.3 259 38.59.2 593.6 16.8 2.8

0 640.1 64.3 10.10 636.2 50.2 7.90 679.9 320.7 47.20 665.4 201.1 30.23.7 201.4 a a

2754 S.N. Joshi, S.S. Pande / Applied Soft Computing 11 (2011) 2743–2755

Table A.2Typical results of ANN–NSGA (finishing operation).

Set no. Pareto optimal set – finishing operation

Process parameters (input) Performance parameters (output)

Duty cycle (%) Current (A) Discharge duration (�s) Voltage (V) Crater depth (�m) TWR (mm3/min) MRR (mm3/min)

1 56.1 5.1 25.2 33.4 11.8 3.7 24.22 79.9 39.7 25.6 49.9 27.0 779.7 613.53 80.0 40.0 692.9 50.0 78.2 29.5 631.04 61.6 31.5 332.7 31.9 50.1 a 222.65 79.9 29.1 96.5 30.6 34.1 49.3 317.16 79.9 38.2 659.5 50 77 23.4 599.57 80 40 645.2 45.7 73.3 17.5 549.8...34 79.1 35.1 530 42.8 66 5.6 438.335 79.3 7.7 47.2 34.9 19.5 2.5 72.136 79.1 32.8 532.4 31.1 52.3 a 244.637 79.3 38.2 337.2 41.6 59.2 58.7 502.838 79.4 35.3 613.5 50 74.7 13.7 543.9...61 79.1 39.1 356.7 48.3 67.9 123.3 608.462 79.1 7.6 36.9 48.4 24.1 26.2 110.963 79.8 39.6 74.4 33.6 37.2 230.3 503.164 79.9 7.2 25.6 34.9 14.9 14.7 65.6...95 79.9 7.2 25.6 34.9 14.9 14.7 65.696 76.8 38 317.3 43.5 58.4 85.6 515.297 57.2 39.1 385 33.7 54.5 0 268.398 57.2 39.1 385 33.7 54.5 0 268.3

5048.5

vsdc

8

oawtbdbeiBrmwauirwriewpp

[

99 79.4 35.3 641.3100 79.1 39.4 330.1

a Insignificant crater.

It is concluded that the process performance for the optimalalues suggested by our FEM–ANN–GA approach for producinguperior quality surface finish can be realized in the experimentalomain. Recommended process parameters can thus, be applied inonfidence.

. Conclusions

In this paper, a unique integrated approach for modeling andptimization of EDM process has been developed using FEM, ANNnd GA. Comprehensive thermo-physical analysis of EDM processas carried out using two-dimensional axi-symmetric non-linear

ransient FEM model. Using results from this FEM analysis, ANNased process model was developed and optimized for the pre-iction of material removal, tool wear and crater dimensions. Twoasic ANN configurations viz. RBFN and BPNN were developed andxtensively tested for their prediction performance and general-zation capability. Though the RBFN is fast and easy to configure,PNN network with SCG training algorithm provided more accu-ate process model and has more potential for modeling of complexanufacturing processes such as EDM. Optimal BPNN based net-ork architecture 4-5-28-4 was found to give good prediction

ccuracy (with mean prediction error of about 7%). The model wassed further to select optimum EDM process parameters for rough-

ng and finishing applications using NSGA algorithm. The optimalanges of process parameters for roughing and finishing operationsere identified. Our results matched closely with available optimal

anges reported in literature as well as our own experimental stud-

es. The proposed integrated (FEM–ANN–GA) approach was foundfficient and robust as the optimum process parameters suggestedere found to give the expected optimum performance of the EDMrocess. It also provides flexibility to the user to choose optimumarameters suiting specific shop needs.

[

[

75.3 10.4 54264.6 147.1 619.1

In conclusion, the intelligent process modeling and optimiza-tion approach developed in this work will provide a very effectivetool to a process engineer to choose optimum process parametersfor enhancing the productivity and finishing capability of the EDMprocess.

Appendix A.

See Tables A.1 and A.2.

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