RESEARCH ARTICLE

Reza TEIMOURI, Hamed SOHRABPOOR

Application of adaptive neuro-fuzzy inference system andcuckoo optimization algorithm for analyzing electro chemicalmachining process

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013

Abstract Electrochemical machining process (ECM) isincreasing its importance due to some of the specificadvantages which can be exploited during machiningoperation. The process offers several special privilegessuch as higher machining rate, better accuracy and control,and wider range of materials that can be machined.Contribution of too many predominate parameters in theprocess, makes its prediction and selection of optimalvalues really complex, especially while the process isprogrammized for machining of hard materials. In thepresent work in order to investigate effects of electrolyteconcentration, electrolyte flow rate, applied voltage andfeed rate on material removal rate (MRR) and surfaceroughness (SR) the adaptive neuro-fuzzy inferencesystems (ANFIS) have been used for creation predictivemodels based on experimental observations. Then theANFIS 3D surfaces have been plotted for analyzing effectsof process parameters on MRR and SR. Finally, the cuckoooptimization algorithm (COA) was used for selectionsolutions in which the process reaches maximum materialremoval rate and minimum surface roughness simulta-neously. Results indicated that the ANFIS technique hassuperiority in modeling of MRR and SR with highprediction accuracy. Also, results obtained while applyingof COA have been compared with those derived fromconfirmatory experiments which validate the applicabilityand suitability of the proposed techniques in enhancing theperformance of ECM process.

Keywords electrochemical machining process (ECM),modeling, adaptive neuro-fuzzy inference system (ANFIS),optimization, cuckoo optimization algorithm (COA)

1 Introduction

The cemented tungsten carbide is a hard and toughcomposite with noticeable wear resistance that satisfiesgrowing demands of material with higher mechanicalproperties and lower weight. Due to high wear resistanceand hardness of this material, it cannot be machine withconventional machining process. Among non-conven-tional machining methods electrochemical machining(ECM) is a potential process which is useful for machiningsuch difficult-to-cut electrically conductive materials.ECM has been extensively used in machining of hard-to-cut materials such as titanium, stainless steel, high-strengthtemperature resistant alloys, ceramics, refractories, fiber-reinforced composites, super alloys and etc. which are notsuitable to be machined by the conventional machiningprocesses because of their high hardness, strength,brittleness, toughness and low machinability properties.Moreover, by application of ECM process, any kind ofintricate shape can be generated with high accuracy andprecision with minimum residual stress generation. How-ever, the process is not exactly the substitutes of theconventional machining processes, but can only comple-ment them [1,2]. The ECM has complex nature due tovarious complex physico-chemical and hydrodynamicphenomena that occur in the machining gap [3]. Duringthe course of machining, the machining rate at any instantdepends not only on the end gap, but also on other processparameters [4]. The electrolyte flow velocity plays animportant role in surface formation [5]; moreover, theincrement in gap resistance due to various causes, e.g.,electrolyte heating, gas bubble generation sludge forma-tion, etc., leads to an uneven current flow, causing overcut

Received April 29, 2013; accepted July 20, 2013

Reza TEIMOURI (✉)Mechanical engineering department, Babol University of Technology,Babol, IranE-mail: reza_teimoori@yahoo.com

Hamed SOHRABPOORMechanical engineering department, Islamic Azad University of Dezful,Dezful, Iran

Front. Mech. Eng.DOI 10.1007/s11465-013-0277-3

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phenomena that result in poor dimensional control of theworkpiece [6]. So, optimal quality of workpiece andeconomical aspects of ECM can be achieved throughcombinational control of various process parameters.According to above explanation, generation of a certainphysical model which provides a precise prediction ofECM process is actually difficult especially when theprocess is characterized for machining of hard-to-cutmaterials.According to above explanations, in order to generate a

model which can predict behavior of complex ECMprocess, researchers focused on developing comprehensivepredictive model based on statistical analysis and artificialintelligence. Methods such as response surface methodol-ogy (RSM), artificial neural network (ANN), fuzzyinference system and etc. are most commonly used formodeling of the manufacturing processes. In the case ofECM, Bhattacharyya and Sorkhel [7] applied responsesurface methodology for investigation and modeling ofelectrochemical machining process. They developedmathematical models to correlate relationships betweenelectrolytic concentration, electrolytic flow rate, appliedvoltage and inter-electrode gap as process inputs tomaterial removal rate and overcut as responses. Senthilk-umar et al. [8] used RSM to study effects of ECMparameters on MRR and SR. They showed that increasingin applied voltage and feed rate leads to higher MRR andlower surface roughness. Also, they indicated thatincreasing in electrolytic concentration and flow rateresulted in higher material removal rate and better surfacefinish. Moreover, they optimize the process for achievinghigher MRR and lower Ra based on RSM. In the case ofmodified ECM, Baran Puri and Banerjee [9] studied effectsof voltage and cutting speed on current density, materialremoval rate and surface finish in electrochemical grindingprocess. They applied regression analysis to develop amathematical model for each response. Then, they utilizeddesirability approach and overlapping contour plots tooptimize the process in the form of multiple responsesproblem. Furthermore, Taweel and Gouda [10] proposedwire electrochemical turning process and fulfilled afeasibility study to use wire as tool. They investigatedeffects of applied voltage, wire feed rate, wire diameter,workpiece rotational speed and overlap distance onmaterial removal rate, surface roughness and roughnesserror. The experimental results were statistically analyzedand modeled through response surface methodology.Although there are numbers of publications that usedRSM and statistical techniques in modeling of ECMprocess, there is not a certain work which uses thepredictive methods based artificial intelligence for model-ing the characteristics of ECM process. The superiority ofintelligent method such as neural network rather than RSMhas been verified by researchers [11–14]. However, theneural network is a potential method in modeling ofmanufacturing process rather than statistical models and

mathematical equations, but the main weakness of neuralnetwork is its dependency on large amount of data for aproblem in which many inputs are contributed. Also, in thecase of manufacturing processes with complex behaviorthe neural network cannot predict the process character-istics as well. It means that for a process with complexbehavior some linguistic terms are needed to provide aprecise prediction. Thus, application of fuzzy logic can bebeneficial for modeling of complex behavior. But con-struction of an appropriate fuzzy membership function andfuzzy rules is really difficult and time consuming job.Thus, for modeling of a complex process with smallamount of data in a short time, a method with bothconcepts of neural network and fuzzy logic is needed.Therefore, an adaptive neuro-fuzzy inference system(ANFIS) is proposed as a hybrid predictive approach thatuses both meanings of neural network and fuzzy logic formodeling of complex processes in which many inputs arecontributed and the amount of experimental data are small.According to the surveyed literatures, there is not a certainpublication that uses the ANFIS for modeling of ECMprocess. Hence, application of this method in the presentwork is quite novel. However, there number of publica-tions that used ANFIS for modeling characteristics of non-traditional machining process. In this case, Caydas et al.[15] used ANFIS for modeling white layer thickness inwire EDM process. Gill and Singh [16] applied ANFIS topredict depth of cut in stationary ultrasonic drilling ofsillimanite ceramic. Maji and Pratihar [17] utilized ANFISfor forward and reverse mapping of MRR and SR inelectrical discharge machining process. Pradhan andBiswas [18] applied ANFIS along with neural networkfor modeling various responses in EDM process.Non-traditional optimization algorithms have been

widely used in the case of processes in which too manyparameters affect performances. Genetic algorithm (GA),simulated annealing (SA), particle swarm optimization(PSO), artificial bee colony (ABC), imperialist competitivealgorithm (ICA) and etc. have been utilized mostcommonly by researches for optimization of non-traditional machining process. In this case, Rao et al. [15]applied a particle swarm optimization (PSO)-based algo-rithm to find out the optimal process parameters for anelectrochemical machining (ECM) process and comparedits performance with that obtained by the other optimiza-tion methods. Dimensional accuracy, tool life and materialremoval rate of the ECM process were optimized subject tothe constraints of temperature choking and passivity.Teimouri and Baseri [11] applied SA and PSO alongwith the ANFIS and ANN for generating smoother surfacein magnetic abrasive finishing process. Teimouri et al. [12]used PSO to determine the optimal combination of processparameters for a wire electric discharge machining(WEDM) process. Teimouri and Baseri [13] associatedartificial bee colony algorithm with neural network foroptimization of dry EDM process in both cases of single-

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objective and multi-objectives problem. In another attemptTeimouri et al. [14] used the ICA for minimizing spring-back in bending of CK45 sheets. Cuckoo optimizationalgorithm (COA) is a novel evolutionary algorithm,suitable for continuous nonlinear optimization problems[19]. This algorithm is inspired by the life of a bird family,called Cuckoo. Special lifestyle of these birds and theircharacteristics in egg laying and breeding has been thebasic motivation for development of this new evolutionaryoptimization algorithm. In the present work, the mainreason for choosing the COA to optimize the ECM processis its faster performance rather than other algorithms suchas GA and PSO [19]. Due to existing special elitistmechanism in COA, the executing time is about 5 timeshorter than one by GA or PSO. It means that in a problemwith too many inputs the COA converges to a globaloptimum just after 7 iterations. Hence, it is claimed thatapplication of COA in the present work may lead toreduction of optimization time and the work is quite novel.By searching through conducted researches, it can beinferred that there is not a certain publication which usedCOA in optimization of manufacturing processes. There isonly one publication which associated the cuckoo searchalgorithm with fuzzy logic to solve multi-objectivescheduling problem [20]. Hence, association of thisalgorithm with ANFIS and their applications for analyzingECM process is quite novel and it is innovative approach.The present work can be summarized as follows:1) Designing and conducting experiments based on four

factors-five levels central composite design2) Creating predictive models of material removal rate

and surface roughness using ANFIS technique3) Plotting ANFIS 3D surfaces of MRR and SR for

analyzing effect of process parameters4) Multi-objective optimization of the process using

cuckoo algorithm5) Comparing results obtained through COAwith those

derived by confirmatory experiments6) Analyzing optimal results based on process physical

behavior

2 Methodologies

2.1 Adaptive neuro-fuzzy inference system (ANFIS)

An adaptive neuro-fuzzy inference system is a hybridpredictive model which uses both of neural network andfuzzy logic to generate mapping relationship betweeninputs and outputs [21]. The structure of this modelconsists of five layers which each layer is constructed byseveral nodes. Such as a neural network, in an ANFISstructure the inputs of each layer are gained by the nodesfrom pervious layer. Figure 1 describes an ANFISstructure. It can be inferred from Fig. 1 that the networkincludesm inputs (X1,…,Xm), in which each one consists ofn membership functions (MFs). Moreover, a layer with Rfuzzy rules and also an output layer are contributed toconstruction of this model. Number of nodes in first layercan be calculated by product of m as number of inputs andn as number MFs (N = m.n). Number of nodes in otherlayers (layers 2–4) relates to number of fuzzy rules (R).In the present work this technique is used to correlate

mapping relationship between process inputs (e.g., elec-trolyte concentration, electrolyte flow rate, applied voltageand feed rate) and main outputs (material removal rate and

Fig. 1 Basic structure of an ANFIS model [22]

Reza TEIMOURI et al. Application of adaptive neuro-fuzzy inference system and cuckoo optimization algorithm for analyzing electrochemical machining process 3

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surface roughness). Thus, for each output a separateANFIS structure can be defined. For example for MRR thefirst layer of ANFIS structure is input layer that containsfour nodes (for four inputs). And the last layer (outputlayer) has one node that represents values of MRR. Figure2a and 2b indicates the proposed ANFIS topography forMRR and SR, respectively. Further details about imple-mentation of ANFIS network has been presented inliterature [22].The layers of ANFIS can be summarized as follows:First layer: fuzzification layerIn this layer crisp inputs transforms to linguistic type Aij

(such as bad, middle, good) by using of membershipfunctions. The output of this layer can be expressed as:

O1ij ¼ �ijðXiÞ, i ¼ 1,:::,m, j ¼ 1,:::,n (1)

where mij is the jth membership function for the input Xi.Several types of MFs are used, for example, triangular,trapezoidal and generalized bell function. In this study theTriangular and Gaussian functions has been selected forMRR and SR, respectively. The matematical equations forTriangular and Gaussian type of membership function areexpressed as Eqs. (2) and (3), respectively.For Triangular type of MF, the mathematical equation is:

�ðX ,a,b,cÞ ¼

0, x<a

xjabja a<x<b

cjxcjb b<x<c

0, xjc

8>>>>>>><

>>>>>>>:

(2)

� X ,a,b,cð Þ ¼ exp –x – c

a

� �2� �

(3)

where a and b vary the width of the curve and c locates thecenter of the curve. The parameter b should be positive.These parameters are named as premise parameters.Second layer: product layerThird layer: normalized layerFourth layer: defuzzificationFifth layer: output layerThe root mean square error (RMSE) function is applied

to this network for inspection of trained model perfor-mances. It can be calculated by following equation:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

M

XM

z¼1

ðSz – YzÞ2vuut (4)

Fig. 2 Structure of developed ANFIS model for predicting (a) MRR and (b) SR

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where M is the total number of training sample, Sz is thereal output value, and Yz is the ANFIS output value intraining.For further information about the development of

ANFIS network, it is suggested the interested readersread the literature [19].

2.2 Cuckoo optimization algorithm (COA)

The cuckoo optimization algorithm inspired by the life of abird family called cuckoo [16]. Special lifestyle of thesebirds and their characteristics in egg laying and breedinghas been the basic motivation for development of this newevolutionary optimization algorithm. Similar to otherevolutionary methods, Cuckoo Optimization Algorithm(COA) starts with an initial population. The cuckoopopulation, in different societies, is in two types: maturecuckoos and eggs. The effort to survive among cuckoosconstitutes the basis of Cuckoo Optimization Algorithm.During the survival competition some of the cuckoos ortheir eggs, demise. The survived cuckoo societiesimmigrate to a better environment and start reproducingand laying eggs. Cuckoos’ survival effort hopefullyconverges to a state that there is only one cuckoo society,all with the same profit values.The COA consists of five main phases, each phase is

describing as follow:

2.2.1 First phase: generating initial cuckoo habitat

To solve an optimization problem, it is necessary that thevalues of problem variables be formed as an array. In GAand PSO terminologies, this array is called “Chromosome”and “Particle Position,” respectively. But here in CuckooOptimization Algorithm (COA) it is called “habitat.” In aNvar-dimensional optimization problem, a habitat is anarray of 1 � Nvar, representing current living position ofcuckoo. This array is defined as follows:

habitat ¼ ½x1,x2,:::,xvar� (5)

Where each of the variable values (x1, x2,..., xNvar) isfloating point number.The profit of a habitat is obtained by evaluation of profit

function fp at a habitat of (x1, x2,..., xNvar). So

profit ¼ fpðhabitatÞ ¼ fpðx1,x2,:::,xNvarÞ (6)

As it is seen, COA is an algorithm that maximizes aprofit function. To use COA in cost minimizationproblems, one can easily maximize the following profitfunction:

profit ¼ –CostðhabitatÞ ¼ – fcðx1,x2,:::,xNvarÞ (7)

To start the optimization algorithm, a candidate habitatmatrix of size Npop � Nvar is generated. Then somerandomly produced number of eggs is supposed for each of

these initial cuckoo habitats. In nature, each cuckoo laysfrom 5 to 20 eggs. These values are used as the upper andlower limits of egg dedication to each cuckoo at differentiterations. Another habit of real cuckoos is that they laydifferent iterations. Another habit of real cuckoos is thatthey lay eggs within a maximum distance from theirhabitat. From now on, this maximum range will be called“Egg Laying Radius (ELR).” In an optimization problemwith upper limit of varhi and lower limit of varlow forvariables, each cuckoo has an egg laying radius (ELR)which is proportional to the total number of eggs, numberof current cuckoo’s eggs and also variable limits of varhiand varlow. So ELR is defined as:

ELR ¼ α� Ncurrent

Ntoatal� ðvarhi – varlowÞ (8)

where α is an integer, supposed to handle the maximumvalue of ELR, Ncurrent is number of current cuckoo’s eggand Ntotal is total number of egg.

2.2.2 Second phase: egg laying

Each cuckoo starts laying eggs randomly in some otherhost birds’ nests within her ELR. After all cuckoos’ eggsare laid in host birds’ nests, some of them that are lesssimilar to host birds’ own eggs, are detected by host birdsand though are thrown out of the nest. So after egg layingprocess, p% of all eggs (usually 10%), with less profitvalues, will be killed. These eggs have no chance to grow.Rest of the eggs grow in host nests, hatch and are fed byhost birds. Another interesting point about laid cuckooeggs is that only one egg in a nest has the chance to grow.This is because when cuckoo egg hatches and the chickscome out, she throws the host bird’s own eggs out of thenest. In case that host bird’s eggs hatch earlier and cuckooegg hatches later, cuckoo’s chick eats most of the food hostbird brings to the nest (because of her 3 times bigger body,she pushes other chicks and eats more). After couple ofdays the host bird’s own chicks die from hunger and onlycuckoo chick remains in the nest.

2.2.3 Third phase: immigration of cuckoos

When young cuckoos grow and become mature, they livein their own area and society for some time. But when thetime for egg laying approaches they immigrate to new andbetter habitats with more similarity of eggs to host birdsand also with more food for new youngsters. After thecuckoo groups are formed in different areas, the societywith best profit value is selected as the goal point for othercuckoos to immigrate. When mature cuckoos live in allover the environment, it is difficult to recognize whichcuckoo belongs to which group. To solve this problem, thegrouping of cuckoos is done with K-means clusteringmethod (a k of 3–5 seems to be sufficient in simulations).

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Now that the cuckoo groups are constituted their meanprofit value is calculated. Then the maximum value ofthese mean profits determines the goal group andconsequently that group’s best habitat is the newdestination habitat for immigrant cuckoos.When moving toward goal point, the cuckoos do not fly

all the way to the destination habitat. They only fly a part ofthe way and also have a deviation. According to this fig,each cuckoo only flies g% of all distance toward goalhabitat and also has a deviation of φ radians. These twoparameters, γ and φ, help cuckoos search much morepositions in all environment. For each cuckoo, γ and φ aredefined as follows:

g 2 Uð0,1Þφ 2 ð –ω,ωÞ (9)

where g 2 U(0,1) means that g is a random number(uniformly distributed) between 0 and 1. w is a parameterthat constrains the deviation from goal habitat. Anw ofp/6(rad) seems to be enough for good convergence of thecuckoo population to global maximum profit.When all cuckoos immigrated toward goal point and

new habitats were specified, each mature cuckoo is givensome eggs. Then considering the number of eggs dedicatedto each bird, an ELR is calculated for each cuckoo.Afterward new egg laying process restarts.

2.2.4 Fourth phase: eliminating of cuckoos in worst habitat

Due to the fact that there is always equilibrium in birds’population, so, a number of Nmax controls and limits themaximum number of live cuckoos in the environment.This balance is because of food limitations, being killed bypredators and also inability to find proper nest for eggs. Inthe modeling proposed here in this paper, only those Nmax

number of cuckoos survive that have better profit values,others demise.

2.2.5 Fifth phase: convergence

After some iterations, all the cuckoo population moves toone best habitat with maximum similarity of eggs to thehost birds and also with the maximum food resources. Thishabitat will produce the maximum profit ever. There willbe least egg losses in this best habitat. Convergence ofmore than 95% of all cuckoos to the same habitat puts anend to Cuckoo Optimization Algorithm (COA).Figure 3 shows a flowchart of the proposed algorithm.

3 Experimentations

The KENNAMETAL die-sinking ECM machine withservo motorized vertical up/down movement of tool has

been used for conducting experiments. Figure 4 depicts theECM machine that was used for conducting experiments.The workpiece material is cemented tungsten carbide in theshape of plate with dimensions of 20 mm � 20 mm �10mm. The faces of each specimen were ground to generateaccurate parallel sitting on the machine table. The proper-ties of workpiece have been presented in Table 1. The toolwas made up from copper in the form of cylinders withouter diameter of 12 mm and inner diameter of 6 mm.Electrolyte was axially fed to the cutting zone through thecentral hole of the tool. The electrolyte used for experimentwas fresh NaCl solution, because of the fact that NaClelectrolyte has no passivation effect on the surface of thespecimens.To measure MRR, the WTB RADWAG electronic

weighing machine has been used to measure workpiecemass loss during experiment. In this case the machiningtime were kept constant on 2 h. For evaluating surfaceroughness a MAHR MARSURF PS1 surface profilemeterwith sample length of 10 mm has been used. For eachspecimen, the roughness of side wall was measured fivetimes stochastically and average of them has been reported.The experimental observations were made by varying

predominant process parameters such as applied voltage,electrolyte concentration, electrolyte flow rate, and toolfeed rate. Table 2 presents process factors and their levels.Due to wide range of factors, it was decided to use fourfactors, five levels, central composite design (CCD) matrixto optimize the experimental conditions. For this purpose,the Design Expert V8 statistical software has beenemployed to design experiments. Table 3 shows the 31sets of coded conditions used to form the design matrix.First 16 experimental conditions are derived from fullfactorial experimental design matrix (24 = 16). All thevariables at the intermediate (0) level constitute the centerpoints while the combinations of each process variable ateither their lowest ( – 2) or highest ( + 2) with the otherthree variables of the intermediate levels constitute the starpoints.

4 Results and discussions

4.1 Modeling of MRR and SR by ANFIS

As explained, the adaptive neuro-fuzzy inference systemhas been used for prediction of MRR and SR. For thispurpose, the MATLAB R17 package (ANFIS toolbox) hasbeen utilized.Prediction of material removal rate and surface rough-

ness of the ECM process by ANIFS consists of two mainstages, training and testing. Hence, among 31 data setscited in design matrix, number of 24 data has been selectedstochastically for training of ANFIS network. Then thetrained network has been tested by the other 9 remaining

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Fig. 3 A flow chart of cuckoo optimization algorithm

Fig. 4 The ECM machine that used in this work

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data sets that were not contributed in training.There are some important factors that contributed to

produce an accurate prediction by the ANFIS. They aretype of fuzzy based rule, number of membership functions(MFs) and type of membership functions. In this paper afirst order TSK type fuzzy based rule was used for creationof predictive model. Then the various numbers ofmembership functions have been.By testing various structures of ANFIS model for each

response (MRR and SR), it was obtained that structureswith numbers of 16 membership functions (2MFs for eachinput or 2-2-2-2 topography) has the lowest values ofRMSE. Selection of network with larger number of MFsled to over-fitting and didn’t generate desired value ofRMSE. Another factor which is influential in accuracy ofANFIS model is type of membership functions. In thiswork various types of MFs namely triangular, trapezoid,generalized bell and Gaussian have been practiced. Table 4presents RMSEs of ANFIS models in testing for MRR andSR. It is presented from Table 4 that four types ofmembership functions under 2-2-2-2 structure have beentrained and their RMSEs were calculated. Results indicatedthat for MRR and SR Triangular and Gaussian types ofmembership function leads lowest values of RMSE,respectively. Figure 5a and 5b indicates agreementbetween measured and ANFIS predicted values of testingfor cutting velocity and surface roughness, respectively.According to the figure, it can be inferred the developedANFIS models can model MRR and SR as well. Also,Fig. 6 indicates a very tight agreement between measuredvalues of MRR and SR and predicted values for all data set.The main reason for this accurate prediction is contributionof all data sets in training of the network.

4.2 Effect of process parameters on MRR and SR based onANFIS surfaces

Here, response surface analysis of MRR and SR arepresented using surfaces obtained through ANFIS models.

4.2.1 Response surface analysis of MRR

Figure 7 exhibits ANFIS surfaces of MRR for theinteraction terms. The discussion about this figure isexpressed as follows:Figure 7a indicates response surface of MRR versus

electrolyte concentration and electrolyte flow rate. Fromthis figure it can be seen that high electrolyte concentrationand high electrolyte flow rate combination results in higherMRR. At higher electrolyte concentration the electricalconductivity of the electrolyte increases. Thus themachining current in interior electrolyte gap (IEG)increases accordingly and results in higher MRR [23].Moreover, higher electrolyte concentration leads to gen-eration of higher number of charged ions in IEG thatincrease the current density. Therefore, MRR increases athigh electrolyte concentration. Also, higher MRR isobtainable at high electrolyte flow rate. Increasing inflow rate results in higher mobility of charged ions fromthe workpiece to the solution that lead to increase inchemical reaction. Moreover, the hydrogen bubbles areremoved from cathodic grooves while high flow rate used.Thus, it increases ionic strength and leads to higher MRRon the anodic part. Hence, at high flow rate higher MRR isobtained.Response surface of MRR versus applied voltage and

feed rate is shown in Fig. 7b. It can be seen from this figurethat high applied voltage and high feed rate combinationresults in high MRR. By increasing applied voltage, thecurrent density increases in IEG accordingly and results inremoving more material from workpiece. Also, higher feedrate results in smaller IEG and may lead to increase incurrent density. Hence, the high MRR is obtainable whileusing high feed rate.

4.2.2 Response surface analysis of SR

Figure 8 exhibits ANFIS surfaces of SR for the interactionterms. The discussion about this figure is expressed as

Table 1 main properties of workpiece

Nominal composition Grain size Hardness (HV) Density (Kg$m–3) Transverse strength(MPa)

Compressive strength(MPa)

Modules of elasticity(GPa)

90%WC–10%Co Fine 1300–1800 14600 3100 5170 620

Table 2 process factors and their levels

Parameters Symbol Levels

– 2 – 1 0 1 2

Electrolyte concentration (g$L–1) X1 10 15 20 25 30

Electrolyte flow rate (L$min–1) X2 5 6 7 8 9

Applied Voltage (V) X3 12 13 14 15 16

Feed rate (mm$min–1) X4 0.2 0.4 0.6 0.8 1

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Table 3 design matrix and experimental results

No. Process factors Responses

Electrolyte Concentration Electrolyte flow rate Applied voltage Feed rate

CodedX1

Actual(g$L–1)

CodedX2

Actual(L$min–1)

CodedX3

Actual(V)

CodedX4

Actual(mm$min–1)

MRR(g$min–1)

SR(µm)

1 – 1 15 – 1 6 – 1 13 – 1 0.4 0.301 7.899

2 1 25 – 1 6 – 1 13 – 1 0.4 0.217 6.782

3 – 1 15 1 8 – 1 13 – 1 0.4 0.321 6.781

4 1 25 1 8 – 1 13 – 1 0.4 0.342 5.984

5 – 1 15 – 1 6 1 15 – 1 0.4 0.361 6.889

6 1 25 – 1 6 1 15 – 1 0.4 0.428 6.748

7 – 1 15 1 8 1 15 – 1 0.4 0.317 6.815

8 1 25 1 8 1 15 – 1 0.4 0.561 6.891

9 – 1 15 – 1 6 – 1 13 1 0.8 0.323 6.678

10 1 25 – 1 6 – 1 13 1 0.8 0.501 6.389

11 – 1 15 1 8 – 1 13 1 0.8 0.421 6.364

12 1 25 1 8 – 1 13 1 0.8 0.592 6.214

13 – 1 15 – 1 6 1 15 1 0.8 0.656 6.234

14 1 25 – 1 6 1 15 1 0.8 0.621 6.351

15 – 1 15 1 8 1 15 1 0.8 0.781 6.489

16 1 25 1 8 1 15 1 0.8 0.818 6.342

17 – 2 10 0 7 0 14 0 0.6 0.311 7.982

18 2 30 0 7 0 14 0 0.6 0.644 6.059

19 0 20 – 2 5 0 14 0 0.6 0.362 7.421

20 0 20 2 9 0 14 0 0.6 0.582 6.235

21 0 20 0 7 – 2 12 0 0.6 0.212 6.981

22 0 20 0 7 2 16 0 0.6 0.421 7.981

23 0 20 0 7 0 14 – 2 0.2 0.502 6.578

24 0 20 0 7 0 14 2 1 0.981 5.210

25 0 20 0 7 0 14 0 0.6 0.358 5.021

26 0 20 0 7 0 14 0 0.6 0.218 5.124

27 0 20 0 7 0 14 0 0.6 0.481 5.034

28 0 20 0 7 0 14 0 0.6 0.331 5.482

29 0 20 0 7 0 14 0 0.6 0.356 5.142

30 0 20 0 7 0 14 0 0.6 0.318 5.111

31 0 20 0 7 0 14 0 0.6 0.358 5.214

Table 4 Values of RMSE in testing of MRR and SR for various types of membership function under 2-2-2-2 ANFIS structure

Type of membership functions RMSEs of cutting velocity RSMEs of surface roughness

Triangular 0.0463 0.9873

Trapezoid 0.1321 1.3651

Generalized bell 0.0731 0.4929

Gaussian 0.0827 0.2825

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follows:The response surface of SR versus electrolyte concen-

tration and electrolyte flow rate is shown in Fig. 8a.. It canbe inferred from this figure that the low electrolyteconcentration and high flow rate result in lower SR.Increasing in electrolyte concentration results in accumu-lation of charged ions in interior electrode gap andincreases the current density. Higher current densityleads to formation of deeper pits in workpiece surfaces.Hence, coarser surface is obtained while high electrolyte

concentration is selected. Moreover, high electrolyteconcentration results in higher electrical conductivity thatincreases current density and generates poor surface finish.Hence, for achieving smoother surface low values ofelectrolyte concentration are suggested. On the other hand,higher flow rate values are needed for decreasing surfaceroughness. This is because of the fact that the increase inelectrolyte flow rate leads to higher turbulence. Thus,effects of rotating eddies will be decreased and formationof flow streak will be prevented. Hence, the smoothersurface is obtainable while higher flow rate selected.Figure 8b demonstrates response surface of SR versus

applied voltage and feed rate. It can be seen from the figurethat higher feed rate and lower gap voltage combinationresults in smoother surface. Increasing in applied voltageleads to excessive heat input and causes deterioration of theworkpiece surface and generates poor surface finish. Thus,lower applied voltage is needed for better surface finish.On the other hand, increasing of feed rate results in lowersurface roughness. When the feed rate increases, the IEGbecomes shorter and results in higher electrolyzing currentin the gap. Thus, the grater current yields higher surfacequality.

Fig. 5 Comparison between measured and predicted values oftesting data for (a) MRR and (b) SR

Fig. 6 Comparison between measured and predicted values of alldata for (a) MRR and (b) SR

Fig. 7 Obtained surfaces of MRR through ANFIS model versus(a) electrolyte flow rate and electrolyte concentration and (b) feedrate and voltage

10 Front. Mech. Eng.

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4.3 Optimization of process by cuckoo algorithm

To find solutions in which the process reaches maximumMRR and minimum SR the cuckoo optimization algorithmis used. For this purpose the ANFIS models of MRR andSR are applied as objective function. Better clarificationabout objective functions and is defined as follows:

F ¼ W1^MRR –W2SR (10)

where W1 and W2 are the weighing factor related to each

output according to its importance in the process.^MRR and SR are the normalized values of MRR and SR

which obtained by following equations:

^MRR ¼ MRR –MRRmin

MRRmax –MRRmin

(11)

SR ¼ SR – SRmin

SRmax – SRmin

(12)

Where, MRRmin and MRRmax are the minimum andmaximum values of MRR, respectively. Also SRmin andSRmax are the minimum and maximum values of SR,respectively.In Eq. (10), the minus sign for SR is due to maximizing

nature of COA, while the SR should be minimized.Also the constraints for conducting optimization are

explained as follows:� Electrolyte concentration: 10 to 30 (g$L–1)� Electrolyte flow rate: 5 to 9 (L$min–1)� Applied voltage: 12 to 16 (V)� Feed rate: 0.2 to 2 (mm$min–1)Such as other evolutionary algorithms, the COA needs

its own setup parameters for implementation accurately.Table 5 presents the setup parameters for COA.The optimum results obtained through COA for various

weight factors have been presented in Table 6.According to the results of Table 6 it can be seen that it is

impossible for the process to have high MRR and low SRsimultaneously. It means that selection of parameter settingthat maximizes MRR can increase the SR. Thus based onvarious weight factors various solutions have to beobtained.Among the results of Table 6 some optimal settings are

more desirable than the others. In the case of highermaterial removal rate, the setting of 10.55 g$L–1 electrolyteconcentration, 5 L$min–1 electrolyte flow rate, 12 Vappliedvoltage and 0.2 mm$min–1 feed rate results in MRR about1 g$min–1 and SR about 7 µm. It can be inferred from this

Fig. 8 Obtained surfaces of SR through ANFIS model versus (a)electrolyte flow rate and electrolyte concentration and (b) feed rateand voltage

Table 5 Setup parameters of COA for implementation

Parameter Value/function Definition

X[0] [0 0 0 0] Initial population

NC 50 Number of cuckoos

H(X) H1= MRRH2= – SR

H3=H1+ H2

H1 and H2 are ANFIS models of MRR and Ra respectively and H3 is allocated to multiobjective problem

NEmin 2 Minimum number of eggs

NEmax 5 Maximum number of eggs

NCL 2 Number of clusters

γ 0.9 Motion coefficient

NCmax 200 Maximum number of cuckoos that can live at the same time

RC 50 Radius coefficient (control parameter of egg laying)

PV 1e-13 Stop condition (population variance that cut optimization)

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result that for higher material removal rate the value ofsurface roughness is relatively high.Also, in the case of lower surface roughness the setting

of 21.6 g$L–1 electrolyte concentration, 7.8 L$min–1 elec-trolyte flow rate, 13.5 Vapplied voltage and 0.8 mm$min–1

feed rate results in SR about 1.5 µm and MRR about 0.6 g$min–1. It can be inferred from this result that for lowersurface roughness, the value of material removal rate isrelatively low.Moreover, in the case of middle MRR and middle SR the

setting of 10 g$L–1 electrolyte concentration, 7.6 L$min–1

electrolyte flow rate, 13.1 V applied voltage and 0.2 mm$min–1 feed rate results in MRR about 0.72 g$min–1 and SRabout 2.2 µm. Another setting for middle MRR and middleSR is 12.87 g$L–1 electrolyte concentration, 5.42 L$min–1

electrolyte flow rate, 12.52 V applied voltage and 0.2 mm$min–1 feed rate resulting in MRR about 0.784 g$min–1 andSR about 2.9 µm. From the results of these settings it canbe inferred that for middle values of MRR the values of SRare relatively middle.According to the obtained results, selection of optimal

setting depends on the engineering of the ECM process.For example, for roughing machining regime, the firstsetting is suitable because of its higher value of MRR. Forthe finishing machining regime, the second setting isappropriate due to its lower value of SR. Also,for the semi-roughing-finishing machining regime, the third setting is

recommended due to its middle value of MRR and middlevalue of SR.

5 Conclusions

The present work dealt with both modeling and optimiza-tion approaches for analyzing electro chemical machiningprocess. Here, first, a series of experiments based centralcomposite design was conducted to investigate effects ofelectrolyte concentration, electrolyte flow rate, appliedvoltage and feed rate on material removal rate (MRR) andsurface roughness (SR). Then the adaptive neuro-fuzzyinference system (ANFIS) was applied to generatemapping relationship between process factors andresponses. Afterward the ANFIS surfaces were plotted toanalyze effect of process factors on MRR and SR in thecase of interaction terms. Finally, the novel cuckoooptimization algorithm was used to optimize the ECMprocess for achieving maximum MRR and minimum SRsimultaneously. The obtained results are summarized asfollows:1) In modeling of MRR and SR by ANFIS, the 2-2-2-2

structure was selected as the best topography due to itslowest prediction error and faster performance. Accordingto this structure the Triangular type of membershipfunction was selected for modeling of MRR and Gaussian

Table 6 Obtained optimal results based on various weight factors

Weight factors Optimal setting Responses

Electrolyte concentra-tion (g$L–1)

Electrolyte flow rate(L$min–1)

Applied voltage (V) Feed rate (mm$min–1) MRR (g$min–1) SR (µm)

W1 = 0.1, W2 = 0.9 18.8 7.2 13.3 0.75 0.407 3.212

10 5.6 13.63 0.272 0.65 3.611

W1 = 0.2, W2= 0.8 28.2 5.57 12.45 0.263 0.5 4.02

12.63 0.5 16 0.215 0.7415 5.7

W1 = 0.3, W2= 0.7 11.53 5.5 15.8 0.435 0.54 2.11

11.53 5 16 0.35 0.675 4.447

W1 = 0.4, W2 = 0.6 21.6 7.8 13.5 0.8 0.597 1.47

17.5 7.8 13.5 0.8 0.503 2.85

W1 = 0.5, W2= 0.5 10 7.6 13.1 0.2 0.7161 2.19

19.5 8.81 12 0.215 0.623 3.173

W1 = 0.6, W2 = 0.4 12.87 5.47 12.52 0.2 0.774 2.95

10.55 5 12 0.2 1 7.08

W1 = 0.7, W2= 0.3 18.6 7.27 13.75 0.757 0.4655 2.9

30 5.2 15 0.32 0.55 4.45

W1 = 0.8, W2 = 0.2 27.8 9 15.8 0.2 0.841 7.54

27.8 9 16 0.2 0.865 8

W1 = 0.9, W2= 0.1 30 7.7 15.8 0.3 0.715 2.92

30 7.7 16 0.3 0.733 3.197

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type of membership function was selected for modeling ofSR because of their lowest values of root mean square errorrather than other types.2) According to the ANFIS surfaces, it was obtained that

combination of high electrolyte concentration, highelectrolyte flow rate, high voltage and high feed rateresulted in higher material removal rate.3) The ANFIS surfaces indicated that combination of

low electrolyte concentration, high electrolyte flow rate,low voltage and high feed rate resulted in lower surfaceroughness.4) Results of optimization approach indicated that for

rough machining regime the setting of 10.55 g$L–1

electrolyte concentration, 5 L$min–1 electrolyte flow rate,12 V applied voltage and 0.2 mm$min–1 feed rate resultedin MRR about 1 g$min–1 and SR about 7 µm.5) According to optimal results for finish machining

regime, the setting of 21.6 g$L–1 electrolyte concentration,7.8 L$min–1 electrolyte flow rate, 13.5 V applied voltageand 0.8 mm$min–1 feed rate is recommended due to thevalue of SR about 1.5 µm and MRR about 0.6 g$min–1.6) For achieving middle MRR and middle SR, the

setting of 10 g$L–1 electrolyte concentration, 7.6 L$min–1

electrolyte flow rate, 13.1 V applied voltage and 0.2 mm$min–1 feed rate with MRR about 0.72 g$min–1 and SRabout 2.2 µm and/or setting of 12.87 g$L–1 electrolyteconcentration, 5.42 L$min–1 electrolyte flow rate, 12.52 Vapplied voltage and 0.2 mm$min–1 feed rate with MRRabout 0.784 g$min–1 and SR about 2.9 µm are recom-mended.7) The present work is really applicable for other type of

manufacturing process in which some responses tend to bemaximum and some tend to be minimum. Thus, it isclaimed that the paper has an industrial application. Usingof the present method leads to independency of conductinghuge number of experiments. Therefore, the present workis beneficial in the case of economical aspects ofmanufacturing processes.

References

1. Tipton H. Dynamics of ECM process. Proc. 5th Int. MTDR Conf.

Birmingham, UK, Pergamon, Oxford, 1964, 505–522

2. McGeough J A. Advanced methods of machining. Chapman and

Hall, London, 1988

3. Amalnik M S, McGeough J A. Intelligent concurrent manufactur-

ability evaluation of design for electrochemical machining. Journal

of Materials Processing Technology, 1996, 61(1–2): 130–139

4. Thorpe JF. A mathematical model of electrochemical machining

process, 3rd Int. Sem. on Optimisation of Manufacturing Systems.

CIRP, Pisa, Italy, 1971, CAP–19

5. Chetty O V K, Murthy R, Radhakrishnan V. On some aspects of

surface formation in ECM. Journal of Engineering for Industry,

ASME, 1981, 103(3): 341–348

6. Bhattacharyya B, Sorkhel S K. Computer-aided design of tools in

ECM for accurate job machining, Proc. ISEM—9, Japan, 1989,

240–243

7. Bhattacharyya B, Sorkhel S K. Investigation for controlled

electrochemical machining through response surface methodology

-based approach. Journal of Materials Processing Technology, 1999,

86(1–3): 200–207

8. Senthikumar C, Ganesan G, Karthikeyan R. Study of electroche-

mical machining characteristics of Al/SiCp composites. Interna-

tional Journal of Advanced Manufacturing Technology, 2009, 43(3–

4): 256–263

9. Puri A B, Branjee S. Multiple-response optimisation of electro-

chemical grinding characteristics through response surface metho-

dology. International Journal of Advanced Manufacturing

Technology, 2012,

10. El-Taweel T A, Gouda S A. Performance analysis of wire

electrochemical turning process—RSM approach. International

Journal of Advanced Manufacturing Technology, 2011, 53(1–4):

181–190

11. Temouri R, Baseri H. Artificial evolutionary approaches to produce

smoother surface in magnetic abrasive finishing of hardened AISI

52100 steel. Journal of Mechanical Science and Technology, 2013,

27: 533–539

12. Shayan AV, Azar Afza R, Teimouri R. Parametric study along with

selection of optimal solutions in dry wire cut machining of cemented

tungsten carbide (WC-Co). Journal of Manufacturing Processes,

2013, DOI: 10.1016/j.jmapro.2013.05.001.

13. Teimouri R, Baseri H. Improvement of dry EDM process

characteristics using artificial soft computing methodologies.

Production Engineering Research and Development, 2012,

14. Teimouri R, Baseri H, Rahmani B, Bakhshi-Jooybari M. Modeling

and optimization of spring-back in bending process using multiple

regression analysis and neural computation. International Journal of

Material Forming. 2012.

15. Caydas U, Hascalik A, Ekici S. An adaptive neuro-fuzzy inference

system (ANFIS) model for wire-EDM. Expert Systems with

Applications, 2009, 36(3): 6135–6139

16. Gill S S, Singh J. An Adaptive Neuro-Fuzzy Inference System

modeling for material removal rate in stationary ultrasonic drilling

of sillimanite ceramic. Expert Systems with Applications, 2010, 37

(8): 5590–5598

17. Maji K, Pratihar D K. Forward and reverse mappings of electrical

discharge machining process using adaptive network-based fuzzy

inference system. Expert Systems with Applications, 2010, 37(12):

8566–8574

18. Pradhan M K, Biswas C K. Neuro-fuzzy and neural network-based

prediction of various responses in electrical discharge machining of

AISI D2 steel. International Journal of Advanced Manufacturing

Technology, 2010, 50(5–8): 591–610

19. Rajabioun R. Cuckoo Optimization Algorithm. Applied Soft

Computing, 2011, 11(8): 5508–5518

20. Chandrasekaran K, Sishaj P S. Multi-objective scheduling problem:

hybrid approach using fuzzy assisted cuckoo search algorithm.

Swarm and Evolutionary Computation., 2012, 5: 1–16

21. Jang J S R. ANFIS: Adaptive-Network–Based Fuzzy Inference

System. IEEE Transactions on Systems, Man, and Cybernetics,

1993, 23(3): 665–685

Reza TEIMOURI et al. Application of adaptive neuro-fuzzy inference system and cuckoo optimization algorithm for analyzing electrochemical machining process 13

1

5

10

15

20

25

30

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50

55

1

5

10

15

20

25

30

35

40

45

50

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FME-13030-TR.3d 29/10/013 16:17:38

22. Babajanzade-Roshan S, Behboodi-Jooibari M, Teimouri R,

Asgharzade-Ahmadi G, Falahati-Naghibi M, Sohrabpoor H.

Optimization of friction stir welding process of AA7075 aluminum

alloy to achieve desirable mechanical properties using ANFIS

models and simulated annealing algorithm. International Journal of

Advanced Manufactruign Technology, 2013.

23. Bhattacharya B, Sorkhel S K. Response surface methodology based

analysis for achieving controlled electrochemical machining. In:

Proceedings of the 17th All India Machine Tool Design and

Research Conference, 1997, 307–311

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