Teimouri Improvement DryEDMsoftcomputingmethods PERD 2012

8/9/2019 Teimouri Improvement DryEDMsoftcomputingmethods PERD 2012

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M A C H I N E T O O L

Improvement of dry EDM process characteristics using artificialsoft computing methodologies

Reza Teimouri • Hamid Baseri

Received: 19 March 2012/ Accepted: 4 June 2012 / Published online: 22 June 2012

German Academic Society for Production Engineering (WGP) 2012

Abstract Dry electrical discharge machining (EDM) is

an environmentally-friendly alternative of die-sinkingEDM process, which it uses gaseous medium instead of

liquid as a dielectric. Due to contribution of too many

parameters in this process, selection of optimal parameters

to increase the process performances is a really crucial

concern. In this work, a predictive model based on back-

propagation neural network has been applied to correlate

the inputs and outputs of dry EDM process. Herein, the

inputs were gap voltage, pulse current, pulse on time, duty

factor, air intake pressure and rotational speed of tool, and

also the main outputs were material removal rate (MRR)

and surface roughness (SR). Firstly a back-propagation

(BP) and radial basis function neural network have been

developed based on data generated from literature [Saha

and Choudhary Int J Mach Tools Manuf 49:297–308

(2009)]. Then, the accuracy of proposed models has been

checked by their values of error percent via testing data.

Hereafter, the most accurate model was served as an

objective function to optimize the process using artificial

bee colony (ABC) algorithm. In optimization stage, firstly

a single objective optimization was fulfilled to determine

the optimal factors related to each output separately. Then

a multi-objective optimization was implemented to calcu-

late the best solutions in the case of higher MRR and lower

SR simultaneously. Results indicated that the predictive

model can estimate the dry EDM process precisely, and

also the ABC algorithm could find the optimal solution sets

logically.

Keywords Dry electrical discharge machining

Optimization Back-propagation neural network Radial basis network Artificial bee colony algorithm

Abbreviations

Vg (V) Gap voltage

Id (A) Discharge current

Ton (ls) Pulse on time

D (%) Duty factor

N (rpm) Tool rotational speed

P (kPa) Air intake pressure

MRR (mm3) Material removal rate

SR (lm) Surface roughness

1 Introduction

Electrical discharge machining (EDM) is an electro-ther-

mal non-traditional machining process which removes

material from workpiece by inducing electrical sparks

between tool and workpiece. The space between tool and

workpiece is filled by a liquid namely dielectric medium

which plays important roles in EDM process. Generally,

the materials of dielectric are oil and other hydrocarbons

which they have negative impact on environment andoperator when vaporized in hot by sparks. So, in order to

overcome this problem, dry EDM process is introduced as

a green machining alternative of EDM process. Dry EDM

is modified oil EDM process in which liquid dielectric is

replaced by gaseous medium.

Many researchers published papers in the case of dry

EDM process. In 1985 Ramani and Cassidenti [1] proposed a

first attempt in the case of dry EDM, they uses argon and

helium gas as a dielectric and resulted that this process has

R. Teimouri (&) H. BaseriMechanical Engineering Department,

Babol University of Technology, Babol, Iran

e-mail: [email protected]

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Prod. Eng. Res. Devel. (2012) 6:493–504

DOI 10.1007/s11740-012-0398-2


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lower material removal rate (MRR) rather than oil EDM

process. Later Kuneida et al. [2, 3] injected other gas

medium such as oxygen and air in the gap and they showed

that using oxygen gas improves the MRR rather than air

medium. Saha and Choudhury [4] fulfilled parametric study

on dry EDM process based on response surface method. By

using analysis of variances technique, he could show that

the pulse current and is the most effective factor in the casesof MRR and surface roughness (SR). Then, they developed

regression models to predict the dry EDM process. Govidan

and Joshi [5] designed some experiments to investigate the

effects of process parameters on MRR, tool wear rate and

oversize in EDM process by using oxygen gas. They indi-

cated that pulse current gap voltage and rotational speed of

tool significantly affect on MRR and tool wear rate.

Moreover, there are some benefits associated with dry EDM

process with respect to oil EDM one. They are lower

electrode wear rate, lower heat affected zone, lower residual

stress and thinner recast layer [6–8].

Due to complexity of EDM process, development of amodel which can predict the process precisely is really

obstacle. So, in order approximate the EDM performances,

estimator methods such as regression polynomial models,

and artificial intelligence techniques are used extensively to

forecast the EDM process. There are many publications

which used the statistical polynomial models in the case of

EDM process [9–13]. Also, artificial neural network has

been noticed by the researchers for modeling of the EDM

process. Tsai and Wang [14] illustrated the comparison

models of MRR for various materials considering the

change of polarity among six different neural networks

together with a neuro-fuzzy network. Kumar and Cho-

udhury [15] predicted the wheel wear and SR electro-dis-

charge diamond grinding using two techniques, namely

design of experiments and neural network. Mandal et al.

[16] attempted to model and optimize the complex EDM

process using artificial neural network (ANN) with back

propagation algorithm. Yang et al. [17] developed a

counter propagation neural network for prediction of MRR

and SR in EDM process while pulse current, gap voltage

and pulse time were the process’ main variables. Despite,

application of artificial neural network in EDM is fash-

ionable, it cannot be found any certain research which uses

this method for prediction of dry EDM process.

The artificial bee colony (ABC) algorithm developed by

Karaboga [18, 19] is an evolutionary optimizer method

which has been inspired by foraging behavior of honey

bees in the case of finding food. Due to, novelty of this

algorithm, there are not many researches which used this

technique in optimization of manufacturing process. Rao

and Pawar [20] applied an ABC method to optimize the

wire electrical discharge machining process which too

many inputs contributed on WEDM process. Samanta and

Chakraborty [21] used the ABC algorithm for parametric

optimization of some non-traditional machining process

including electro chemical machining, electrochemical-

discharge machining and electrochemical micro-machin-

ing. Although, there are many researches which used

optimizer algorithms in EDM process [22–24], there is not

a research that utilized the ABC algorithm for optimization

of dry EDM process.

2 Scopes of the present work

As mentioned above, the EDM process has a complex

nature due to contribution of too many parameters in its

performances. In the case of dry EDM process, addition of

rotary motion of tool and replacing of gas instead of liquid

make the process much more intricate. So, development of

an intelligent model which can predict the process pre-

cisely, and selection of optimal setting to improve the

process efficiency are really crucial. In the present work, inorder to develop a predictive model in dry EDM process,

the experimental data from literature [4] have been used.

Then feed forward back-propagation neural network and

radial basis network have been employed as estimator tools.

After selection of most accurate model between existed

ones, the artificial bee colony algorithm is employed to

optimize the process. Both of single objective and multi

objective optimization are fulfilled to find optimal solutions

for achieving to maximum MRR and minimum SR. Then,

the obtained optimal solutions are verified with renewed

experiments and discussion based on process behavior.

In other word, the literature [4] designed and conducted

extensive experiments to investigate the effects of process

parameters on dry EDM performances. Then it developed

statistical models to predict the process characteristics

mathematically. But due to high accuracy of intelligent

models rather than statistical ones, in our work we devel-

oped models based on artificial intelligence techniques

using data generated in [4]. Also, lack of optimization in

literature [4] motivated us to employ artificial bee colony

algorithm in order to find optimal solutions in the case of

maximum material removal rate and minimum surface

roughness. Then in order to verify the obtained optimal

results some renewed experiments were conducted. After-

ward spacious discussions have been fulfilled to prove that

obtained optimal solutions are logical according to process

behavior in literature [4].

3 Experiments

As mentioned above, in this work the experimental infor-

mation of literature [4] have been used for prediction and

494 Prod. Eng. Res. Devel. (2012) 6:493–504

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optimization of dry electrical discharge machining process.

A schematic diagram of the process is visible in Fig. 1a. In

that work, the experiments had been conducted on Znumerically controlled oil die-sinking EDM machine

namely Electra Electronica Machine Tools (R #50) man-

ufactured in India, which was modified by dry EDM

attachment including rotating tool and high velocity gas

flow through tubular tool. Figure 1b demonstrates the

developed tool for conduction of dry EDM experiments.

To enable performing the dry EDM process on existing

EDM machines (which were originally designed for liquid

dielectric only), a dry EDM unit attachment has been

designed and developed. The dry EDM unit including gas

flow container and rotary spindle was mounted on ED

machine.In that work, experiments had been conducted on EN32

mild steel (density 7.8 g/cm3) workpiece using a copper

(density 8.9 g/cm3) tool. The workpiece was in the form of

a thin strip of dimensions 75 mm 9 20 mm 9 5 mm.

Small sized work pieces are used for ease of weight mea-

surement on the balance. Tool electrode is in the form of a

tube such that high velocity gas flows through it. Firstly

exploratory experiments had been carried out to find the

best tool geometry consider to MRR and SR, and finally

the tool with number of two eccentric holes was selected as

the best tool, so it was served as the major tool for con-

ducting all remained experiments. Then, blind holes wasdrilled in EN32 mild steel in constant amount of the time,

and values of MRR were calculated by measuring the mass

loss during machining, and then it converted to volumetric

MRR by knowing the density of workpiece. In order to

measure the SR, a Mitutoyo surface roughness tester was

employed to measure the Ra for end of each machined hole.

Experiments were designed based on central composite

design (CCD) to systematically study the effects of input

parameters such as pulse current, gap voltage, pulse on

time, duty factor, air intake pressure and rotational speed of

tool, on the MRR and SR. Table 1 shows the multiple

levels of each input corresponding to central composite

design.In the current work, after optimization of dry EDM

process it should be verified the optimal parameters.

Therefore some experiments have been done according to

optimal parameters (discussed in Sect. 6.2) to evaluate the

MRR and SR. These new experiment have been done using

the ‘‘Tehran Ekram 304H/60A’’ EDM machine as shown in

Fig. 2. Here, all conditions of experimental procedure are

according to literature [4]. In this setup, tool has been

attached to a rotary head and a belt mechanism transfer the

rotation of motor to the rotary head. Also, level of rota-

tional speed can be controlled by LS600 inverter between 0

and 2,400 rpm. Also, the intake pressure of gas flow wascontrolled by a FESTO gas pressure regulator which can

break and control high pressure air from air compressor to

machining gap.

In order to evaluate the MRR the WTB RADWAG

electronic weigh balance with 1 mg resolution was used.

Also, surface roughness of the workpiece has been mea-

sured using the Mahr Marsurf PS1 surface profilmeter. In

order to decrease the experimental error, three specimens

have been tested for each kind of optimal conditions.

Fig. 1 a Schematic diagram of

experimental setup b rotary tool

with multiple eccentric holes [4]

Table 1 List of parameters values [4]

Parameter Value

Pulse current, IP (A) 9, 16, 29, 42, 49

Gap voltage, Vg (V) 55, 63, 77, 91, 99

Pulse on time, Ton (ls) 50, 200, 500, 750, 1,000

Duty factor, D (%) 8, 24, 48, 72, 88

Air intake pressure, P (kPa) 58.8, 88.2, 147, 205.8, 245

Spindle speed, N (rpm) 300, 650, 1275, 1,900, 2,250

Prod. Eng. Res. Devel. (2012) 6:493–504 495

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4 Definition of intelligent predictive models

4.1 Feed forward back-propagation neural network

(FFBPNN)

Using of neural network is fashionablein telecommunication,

signal processing, pattern recognition, prediction, automated

control and economical analysis. FFBPNN has been adopted

in literatures due to its accuracy and fast response. The BP

structure consists of an input layer, some hiddenlayers andan

output layer. In this structure neurons are connected to each

other by some weighted links. The information from input

layer is mapped to output layer three one or more hidden

layers. The relationship between input and output of a single

node can be written as followed equation [25]:

ak ¼ f ðW ki pi þ bk Þ ð1Þ

where ak is the value of node output, W ki is the weight

connection between inputs and nodes, pi is the output of

pervious nodes in their hidden layer, and bk is the bias

value of current layer and finally f is transfer function.

Generally the transfer functions selected for hidden layers

are log-sigmoid, Eq. 2 or hyperbolic tan-sigmoid, Eq. 3.

And also for the output layer the linear function is

recommended [25].

f ðnÞ ¼ 1

1 þ en ð2Þ

f ðnÞ ¼ en en

en þ en ð3Þ

A feed forward back-Propagation neural network

(FFBPNN) includes two main stage namely feed forward

stage and back-propagation stage. In the first stage (feed

forward stage) the network is trained by using of inputs and

some weighted links, then outputs are calculated. Hereafterthe network’s outputs are compared with real outputs and

the errors are evaluated. The second stage (back-

propagation stage) inspects the value of mean square

error (MSE), Eq. 4. At this stage if the value of MSE is

acceptable, training is stopped and the network reaches to

its desired weight vectors. Otherwise, if the MSE is not

acceptable, the back-propagation algorithm updates

pervious weight matrixes and generates new ones until it

achieves to eligible MSE.

MSE ¼ 1

N X N

k ¼1

ðt k ak Þ2 ð4Þ

where N is whole number of training samples, t k is the real

target value, and ak is the output value of the network. A

learning rate is an important factor which it controls the

training schedule to reach in global minimum of MSE

consider to the lowest training time.

4.2 Radial basis function neural network (RBFNN)

RBFNN is alternative supervised learning network archi-

tecture to the multilayered perceptrons (MLP). The topol-

ogy of the RBFNN is similar to the MLP but the

characteristics of the hidden neurons are quite different. TheRBFNN consists of an input layer, an output layer and a

hidden layer. The input layer is made up of source neurons

with a linear function that simply feeds the input signals to

the hidden layer. The neurons calculate the Euclidean dis-

tance between the center and the network input vector, and

then passes the result through a non-linear function

(Gaussian function/multiquadric/thin plate spline, etc.). It

produces a localized response to determine the positions of

centers of the radial hidden elements in the input space. The

output layer, which supplies the response of the network, is

a set of linear combiners, which is given by [23].

f ð xÞ ¼X N i¼1

wijGð x cik k bÞ ð5Þ

where Nis the number of data points available for training,

wij is the weight associated with each hidden neuron, x is

the input variable, c i is the center points and b is the bias.

The localized response from the hidden element using

Gaussian function [23] is given by,

Fig. 2 Experimental setup for verifying the optimal setting of rotary

dry EDM (prepared by authors)


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Gð x cik k bÞ ¼ exp 1

2r2ið x cik k bÞ

2

ð6Þ

where ri is the spread of Gaussian function. It represents

the range of || x - c i|| in the input space to which the RBF

neuron should respond.

5 Artificial bee colony (ABC) algorithm

ABC algorithm introduced by Karaboga [19] in 2005, for

optimizing numerical problems. It was inspired by the

intelligent foraging behavior of honey bees. The model

consists of three essential components: employed and

unemployed foraging bees, and food sources. The first two

components, employed and unemployed foraging bees,

search for rich food sources, which is the third component,

close to their hive.

In ABC, a colony of artificial forager bees (agents)

search for rich artificial food sources. To apply ABC, theconsidered optimization problem is first converted to the

problem of finding the best parameter vector which mini-

mizes an objective function.

In ABC, the colony of artificial bees contains three

groups of bees: employed bees associated with specific

food sources, onlooker bees watching the dance of

employed bees within the hive to choose a food source, and

scout bees searching for food sources randomly. Both

onlookers and scouts are also called unemployed bees.

Initially, all food source positions are discovered by scout

bees. Thereafter, the nectar of food sources are exploited

by employed bees and onlooker bees, and this continualexploitation will ultimately cause them to become

exhausted. Then, the employed bee which was exploiting

the exhausted food source becomes a scout bee in search of

further food sources once again. In ABC, the position of a

food source represents a possible solution to the problem

and the nectar amount of a food source corresponds to the

quality (fitness) of the associated solution. The number of

employed bees is equal to the number of food sources

(solutions) since each employed bee is associated with one

and only one food source.

As mentioned above, the artificial bee colony algorithm

consists of four main phases, initialize phase, employedbees phase, onlooker bees phase and scout bees phase. The

clarification of each phase is defined as follow.

Initialize phase All the vectors of the population of food

sources, X ms are initialized by scout bees and control

parameters are set. Since each food source X m is a solution

vector to the optimization problem, each X m vector holds

n variables, (X mi , i = 1…n) which are to be optimized so as

to minimize the objective function. After initialization, the

solutions is subjected to repeated cycles C = 1… MCN

(maximum cycle number). This is for the search process of

the employed bees, onlooker bees and scout bees.

Employed bees phase Employed bees search for new

food sources (V m) having more nectar within the neigh-

borhood of the food source ( X m) in their memory. They find

a neighbor food source and then evaluate its profitability(fitness). For example, they can determine a neighbor food

source (V m) using the formula given by:

V mi ¼ X mi þ Umið X mi X kiÞ ð7Þ

where X k is the randomly selected food source, i is ran-

domly chosen parameter index and Umi is a random number

within the range of [-1,1]. After producing the new food

source (V m) its fitness is calculated and a greedy selection

is applied between V m and X m.

The fitness value of the solution fit m( X m) might be cal-

culated for minimization problems using the following

formula:

fit mð X mÞ ¼ f mð X mÞ if f m 0

absð f mð X mÞÞ if f m\0

ð8Þ

where f m(X m) is the objective function value of solution X m.

Onlooker bees phase Unemployed bees consist of two

groups of bees: onlooker bees and scouts. Employed bees

share their food source information with onlooker bees

waiting in the hive and then onlooker bees probabilistically

choose their food sources depending on this information. In

ABC, an onlooker bee chooses a food source depending on

the probability values calculated using the fitness values

provided by employed bees. For this purpose, a fitness

based selection technique can be used, such as the roulette

wheel selection method. The probability value Pm with

which X m is chosen by an onlooker bee can be calculated

by:

Pm ¼ fit mð X mÞPSN

m¼1 fit mð X mÞð9Þ

After a food source X m for an onlooker bee is

probabilistically chosen, a neighborhood source V m is

determined by using Eq. (7), and its fitness value

is computed. As in the employed bees phase, a greedyselection is applied between V m and X m. Hence, more

onlookers are recruited to richer sources and positive

feedback behavior appears.

Scout bees phase The unemployed bees that choose their

food sources randomly are called scouts. Employed bees

whose solutions cannot be improved through a predeter-

mined number of trials, specified by the user of the ABC

algorithm and called ‘‘limit’’ or ‘‘abandonment criteria’’


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herein, become scouts and their solutions are abandoned.

Then, the converted scouts start to search for new solu-

tions, randomly. For instance, if solution X m has been

abandoned, the new solution discovered by the scout that

was the employed bee of X m. Hence those sources which

are initially poor or have been made poor by exploitation

are abandoned and negative feedback behavior arises to

balance the positive feedback.

The flowchart of artificial bee colony algorithm

including main phases is visible in Fig. 3.

6 Results and discussion

6.1 Results of modeling approaches

As mentioned earlier, the modeling of the dry EDM pro-

cess consists of two approaches. At first approach a feed

forward back-propagation network has been hired to cor-relate mapping relationships between inputs and outputs.

The second approach is a model based on radial basis

network which has a hidden layer with variable neurons.

After development of best models based on the lowest

values of mean absolute according to testing data, a com-

parison has been fulfilled between accuracy of each model

based on their error percent. The descriptions about the

results exist as follow.

6.1.1 Development of BPNN model

As mentioned above, in present work, feed forward

back-propagation neural network has been used as an

estimator to forecast dry EDM characteristics. Here,

MATLAB 7.1. Neural Network Toolbox was hired to

develop BPNN model. So in this work a model with six

inputs and two outputs has been considered. In all

86 data obtained in literature [4], numbers of 70 data

were selected stochastically to train the network, and

then the trained network was tested by other remained16 data sets. In order to find the best model mean

absolute error is defined as follow:

MAE ¼ 1

T

XT i¼1

t i aij j ð10Þ

where T is the number of test data, t i is the target value and

ai is FFBPNN modeled value.

Since the size of hidden layer(s) is one of the most

important factors for generation of accurate model, various

architectures based on hidden layers and their neurons have

been practiced. On the other word in order to find a precise

model that gives much more acceptable results, architec-tures based on one and two hidden layers with various

hidden nodes were trained separately, then their accuracy

were checked based on their values of MAE for testing

data. It means that a network with lowest MAE predicts the

process precisely. Also, the various types of transfer

function of log-sigmoid and tan-sigmoid were checked on

the model accuracy. For training of the network, the gra-

dient descent method with variable learning rate has been

trained and the momentum factor was set 0.5 also the error

goal value was 0.01.

By training and testing of various topographies with

different types of transfer functions, finally a model by

(6-8-5-2) topography with ‘‘tansig’’ transfer functions

was selected as the most accurate estimator. It means

that networks with different topographies have been

trained and tested and their MAE value calculated. Then

by comparison of MAE values between existing net-

works, results showed that the (6-8-5-2) network has the

lowest value of MAE. Figure 4 indicates the agreement

between measured and predicted values according to

testing data.

Yes

Yes

Yes

No

Initialize populations

Cycle


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So, due to accuracy of the (6-8-5-2) topography among

all trained/tested topographies, it can be selected as most

accurate topography among other ones.

6.1.2 Development of RBFNN model

As described above, the radial basis network has an input

layer, an output layer, and a hidden layer with various

neurons. Like a BPNN model development of an accurate

RBFNN consists of training and testing. So, between 86

existing experimental data obtained in literature [4], num-

bers of 70 data were used for train the network and then the

performance of the network was checked by the other

remained 16 data. The value of MSE for this network was

set 0.05, and the spread of the Gaussian function was set

equal to 0.6. This value was not selected stochastically;

various values of the spread were selected for training of

RBF network and then the performance of the network was

evaluated by the value of MAE. Results indicated that a

RBF network with numbers of 25 hidden neurons and

spread value of 0.6 can predict the dry EDM process more

accurate than other existing RBFNN models. Figure 5a, b

shows the agreement between measured values and RBF

predicted values according to testing data for material

removal rate and surface roughness respectively.

6.1.3 Comparison of developed models

In order to define accurate models for serving as objective

function in optimization of process, comparisons have been

fulfilled to find the most accurate model between devel-

oped ones (e.g. FFBP model and RBF model). So, com-

parison tools which used for selection of most precise

model are Mean Absolute Error (MAE) Root Mean Square

Error (RMSE) and Prediction Error Percent (PEP). For-

mulation of MAE was expressed in Eq. 10 and definitions

of RMSE and PEP are expressed as follow:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M

X M z¼1

ðS z Y zÞ2

v uut ð11Þ

where M is number of data in testing (in this work M = 16)

S z is the real value of a given output obtained by

experiments and Y z is the value of modeled output by

developed models.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

M R

R ( m m 3 / m i n )

Test No

measured

predicted

(a) MAE=0.2998

2.6

2.8

3

3.2

3.4

3.6

3.8

4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Test No

(b) MAE=0.2773

S R

( µ m )

Fig. 4 Comparison between measured and BPNN predicted values of

a MRR and b SR

S R ( µ

m )

Test No

(b)MAE=0.343

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

M

R R ( m m 3 / m i n )

Test No

measured

predicted

(a) MAE=0.411

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17

Fig. 5 Comparison between measured and RBFNN predicted values

for a MRR and b SR


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PEP ¼ ai yij j

aið12Þ

where ai is the measured values obtained by experiments

and yi is the predicted value by the model.

In order to compare the accuracy of developed models

MAE, RMSE and PEP of each model has been calculated

and model with lowest values of MAE, RMSE and PEP is

introduced as most accurate model, then this model can be

applied as objective function in optimization of process due

to its higher accuracy.

Table 2 demonstrates the measured values, BPNN pre-

dicted values, and RBF predicted values for MRR and SR

for 16 testing data.

Table 3 describes the value of RMSE and MAE for

FFBPNN and RBFNN model. According to this table, it can

be inferred that the back-propagation model had lower value

of MAE and RMSE than the radial basis one in both cases of

MRR and SR. This is due to the fact that the RBF network is

suitable for the problems which number of data is in lower

range. For large variety of data, modeling by use of BPNN is

really proper and it can predict the process precisely.

Also values of PEP for both models have been calcu-

lated and shown in Fig. 6. According to this figure, it is

visible that the developed BPNN model has lower values of

PEP than developed RBFNN for majority of testing data in

both cases of MRR and SR.

According to obtained values of RMSE, MAE and PEP,

it can be inferred that developed 6-8-5-2 BPNN model is

suitable for prediction of process. So this model can be

applied as an objective function for optimization of pro-

cess. In order to optimize the process, all 86 experimental

data are trained with 6-8-5-2 BPNN model to reach to a

model with higher accuracy.

6.2 Optimization of process using ABC

According to results obtained by literature [4] it is evidence

that the MRR and SR have complex behavior in response

to input variations. Also, due to contribution of too many

inputs in the process, selection of optimal sets in which

process riches to desired performances is actually obstacle.

So, in order to find the solutions related to favorable per-

formances, it needs to an optimization technique. Here,

optimization consists of two stages, at first stage number of

two single objective optimizations are carried out to

maximize the MRR and minimize the SR separately. Then,

in second approach multi-objective optimizations will becarried out to maximize the MRR and SR simultaneously.

For ABC optimization algorithm, a MATLAB code was

extracted and it was checked by Rosenbrock optimization

function. Formulation of this function for a problem with

two variables is expressed as follow:

f ð z1; z2Þ ¼ 100ð z2 z21Þ

2 þ ð1 z1Þ2 ð13Þ

Rosenbrock function has a global minimum in

z1 = z2 = 1 and the value of function in this point is

Table 2 Measured and

predicted values of MRR and

SR in 16 testing data

No Measured

MRR [4]

Predicted MRR

using BPNN

Predicted MRR

using RBFNN

Measured

SR [4]

Predicted SR

using BPNN

Predicted SR

using RBFNN

1 2.76 2.63 2.69 3.31 3.43 3.329

2 1.6 1.57 1.68 3.26 3.33 3.236

3 0.99 1.15 0.726 2.96 3.12 3.011

4 5.37 4.51 4.87 3.11 3.22 3.239

5 0.64 0.6 1.118 2.95 3.08 3.1656 0.53 0.513 0.901 3.01 3.26 3.046

7 3.31 3.97 3.08 4.2 3.99 3.839

8 2.69 1.88 1.83 3.13 3.21 3.489

9 0.9 0.88 1.687 3.37 3.4 3.523

10 0.51 0.395 0.152 2.85 3.06 3.078

11 1.59 1.57 1.680 3.79 3.53 3.398

12 1.85 1.57 1.680 3.6 3.46 3.236

13 1.81 1.94 1.709 3.6 3.45 3.211

14 0.51 0.61 1.54 2.75 2.98 3.123

15 1 0.99 1.04 3.49 3.37 3.327

16 1.19 1.55 1.28 2.84 3.04 2.771

Table 3 Values of RMSE and MAE of developed models

Output RMSE MAE

BPNN RBFNN BPNN RBFNN

MRR 0.2411 0.3814 0.2998 0.411

SR 0.2132 0.3376 0.2773 0.343


1 3


9/12

zero [ f ( z1 ,z2) = 0]. Table 4 demonstrates a comparison

between real minima of Rosenbrock function and the

minimum solutions obtained by ABC code. It is evidence that

ABC algorithm can minimize the Rosenbrock function as well.

6.2.1 Single objective optimization

As mentioned earlier, in this stage the ABC algorithm has

been used to maximize the MRR and minimize the SR

separately. So definition of objective function and process

constraints express as follow:

Main object: H 1ð X Þ ¼ MRR; H 2ð X Þ ¼ SR

Subject to:

Gap voltage (Vg): 55–99 V

Discharge current (Id): 9–49 A

Pulse on time (Ton): 50–1,000 ls

Duty factor (D): 8–88 %

Air pressure (P): 58.8–245 kPa

Tool speed (N): 300–2,250 rpm

The ABC algorithm needs to some setup parameters for

implementation. Table 5 defines the main setup parameters

for ABC algorithm.

Table 6 indicates the optimal solutions which minimize

the SR and maximize the MRR separately in the case of

single objective optimization.

6.2.2 Multi objective optimization

In this stage, a multi objective optimization is carried out to

maximize theMRR andminimizethe SR simultaneously. So,

the following optimization function is developed by [26]:

F ¼ W 1 MRR^ þW 2 SR̂ ð14Þ

where W 1 and W 2 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 MRRminð15Þ

SR^

¼ SR SRminSRmax SRmin

ð16Þ

where, MRRmin and MRRmax are the minimum and maxi-

mum values of MRR, respectively. Also SRmin and SRmaxare the minimum and maximum values of SR, respectively.

Since the dry EDM process has lower MRR and high

surface quality with respect to oil EDM process, in this

work improvement of MRR is much more important rather

than minimizing SR. So, the values of W 1 and W 2 are

adjusted according to importance of MRR in dry EDM

process. Thus, values of W 1 are more than 0.5 and values of

W 2 are less than 0.5.

Table 4 Solutions which minimize the Rosenbrock function using

ABC code

z1 z2 f ( z1, z2)

Results of ABC 1.0011 0.9988 0.0012Rosenbrock function minima 1 1 0

P E P f o r M R R ( % )

Test No

P E P f o r S R ( % )

Test No

0

0.2

0.4

0.6

0.8

1

1.2

1.4

BP-NN

RBF-NN

(a)

0 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

BP-NN

RBF-NN

(b)

Fig. 6 Values of prediction error percent of developed models for

a MRR b SR

Table 5 Setup parameters of ABC algorithm

Parameters Value/function Remark

X0 L i ? rand (0,1)

9 (U i - L i)

Equation used for

initialization purpose

Np 20 Number of population

(swarm size)

NEB 50 % of Np Number of employed beesNOB 50 % of Np Number of onlooker bees

NSB 1 Number of scout bees per

cycle

MCN 1000 Maximum cycle number

H(X) y = sim(net,X)

H(X) = y(1),y(2)

Objective function which

uses ‘‘sim’’ to simulate

the BPNN


1 3


10/12

Table 7 demonstrates the optimal solution sets relate to

multi objective optimization with various weight factors.

7 Verification of obtained optimal solutions

In this section, verification of optimal solutions consists of

two stages for both cases of single-objective and multi-objective optimization. In first stage some renewed tests

have been carried out to prove the optimal results. In

second stage logical discussions have been fulfilled based

on experimental results to show that why the ABC algo-

rithm find these points as optimal solution. It means that,

according to dry EDM process behavior conducted by [4],

extensive discussions have been done to prove that optimal

solutions are logical.

7.1 Verification of single-objective optimization

problem

According to obtained optimal results of Table 6 in the

case of single objective optimization, two renewed exper-

iments have been conducted. In order to ensure that the

experiments have low error, each experiment repeated

three times and the average of measured values was

reported. The results of renewed tests to verify the results

of Table 6 are visible in Table 8. By comparison of these

results with results of Table 6, it can be inferred that the

BPNN model and ABC algorithm could model and opti-

mize dry EDM process precisely.

By comparison of Table 6 with Table 8 it can be

inferred that some input parameters in Table 8 are not

exactly the optimal results in Table 6. This is due to the

fact that the ED machine has fixed values of input, so in

verification tests the nearest values to obtained solutionswhich exist on ED machine have been selected.

By comparison of results obtained by single objective

optimization in this work and experimental results of litera-

ture[4], it canbe inferred that theoptimal answers are logical.

Table 6 shows that the optimal voltage is 80.6 V in the

case of maximum MRR and 79.8 V for minimum SR.

These answers seem logical because firstly by increasing in

gap voltage the spark energy increases and leads to

removing more material from workpiece. Also by

increasing in voltage the discharge crater has the form of

lower depth and higher diameter, so increasing in voltage

to 80 V reduces the SR. But when the voltage goes up to80 V due to increasing in gap distances, the injected gas

cannot remove the debris appropriately and leads to lower

MRR and higher SR.

By observation to Table 6, it can be inferred that the

discharge current of 49 A (highest value of current among

existing values) induces maximum MRR and current of

23 A induces minimum SR. Higher discharge current leads

Table 6 Optimal solution for

single objective optimization of

process

State Optimal conditions BPNN output

Vg (V) Id (A) Ton (ls) D (%) P (kPa) N (rpm)

Maximization

of MRR

80.6 49 873.7 88 236.6 2,250 MRR = 5.36 (mm3 /min)

Minimization of SR 79.8 23 50 88 245 2,250 SR = 2.44 (lm)

Table 7 Optimal solution sets

in multi objective optimization

with various weight factors

Weights Optimal conditions BPNN outputs

W1 W2 Vg (V) Id (A) Ton (ls) D (%) P (kPa) N (rpm) MRR (mm3 /min) SR (lm)

0.6 0.4 75.94 49 763 83 245 2,250 5.03 2.95

0.7 0.3 78.347 47.85 786 88 245 2,250 5.21 3.05

0.8 0.2 80.35 49 811 88 245 2,250 5.30 3.16

0.9 0.1 81.2 49 811 88 245 2,250 5.44 3.21

Table 8 Verification of optimal results for single objective optimization

State Vg (V) Id (A) Ton (ls) D (%) P (KPa) N (rpm) BPNN output Measured

value

PEP (%)

Maximization of MRR 80 49 850 88 235 2,250 MRR = 5.36

(mm3 /min)

MRR = 5.19

(mm3 /min)

3.2

Minimization of SR 80 21 50 88 245 2,250 SR = 2.44 (lm) SR = 2.35 (lm) 3.8


1 3


11/12

to increasing in discharge energy and removing more

material from workpiece. Although, by increasing in dis-

charge energy, the volume of discharge crater increases,

but the SR is sensitive to depth of discharge carter, so the

ABC algorithm find the 23 A as the optimal current which

leads to lower SR. By refer to literature [4], it can be

inferred that these values are logical.

According to Table 6, the optimal pulse on times forhighest MRR and lowest SR are 873 and 50 ls respec-

tively. By increasing in pulse on time around 850 ls the

MRR increases due to higher cutting time and higher val-

ues of discharge crater volume. But when the pulse on time

goes beyond around 850 ls the energy density of plasma

channel decreases and induces lower MRR. Also, in 50 ls,

due to lowest value of pulse on time the surface is smoother

and this value is optimum for SR.

Table 6, demonstrates that 88 % of duty factor is opti-

mum for maximum MRR. This is due to the fact that at this

value of duty factor, the pulse off time is about 65 ls.

When the value of pulse of time is lower than 65 ls, due toinappropriate renewal of dielectric, the debris aren’t

removed properly, so leads to lower MRR. Also, when the

pulse off time goes beyond of 65 ls due to increasing in

non-cutting time, MRR decreases dramatically. In the case

of SR the results are same to MRR and the pulse off time of

65 ls is the optimum value of pulse off time, which it

relates to 88 % duty factor.

By observation to Table 6, it is evidence that the opti-

mum air pressure is around 240 kPa for both of MRR and

SR. This is due to the fact that at higher pressure, expulsion

of debris from machining gap improved and leads to

desired MRR and SR.

According to Table 6, optimum value of tool speed is

2,250 rpm and selection of this value is due to better

flushing of debris at higher RPM, which leads to

improvement of MRR and SR.

7.2 Verification of multi-objective optimization

problem

In order to verify the obtained optimal results in the case of

multi-objective optimization problem of this process

(results of Table 7) a confirmation test has been carried out.

By a precise consideration to Table 7, it can be inferred

that by variation of weight factors (e.g. W 1, W 2) there are

not an emphasized differences between optimal solutions

and values of MRR and SR. So number of one confirmation

test seemed adequate for verification of obtained optimal

parameters. Table 9 demonstrates confirmation test to

prove the optimum results of Table 5.

By comparison between confirmation test and optimal

results of Table 7, it can be inferred that the result of

renewed test and results of Table 5 are too close together, it

means that both of BPNN model and ABC algorithm couldfind the optimal results accurately.

By a precise notation to Table 7, it can be inferred that

by changing the weight factors, there are not emphasized

differences between obtained optimal solutions. This is due

to the fact that the MRR and SR have a same behavior

according to changing in process parameters. According to

literature [4], in majority of inputs where MRR reaches to

its maximum value the SR reaches to its minimum. So,

there are not highlight differences between optimal solu-

tions due to similar symmetrical behavior of MRR and SR

against changing in process variables.

8 Conclusions

In current work, prediction of material removal rate and

surface roughness has been carried out for dry EDM pro-

cess. Artificial neural network was developed as an esti-

mator to forecast process characteristic against variation of

input variables. In order to generate the predictive model,

experimental data of literature [4] have been used, in which

gap voltage, discharge current, pulse time, duty factor, air

intake pressure and tool rotary speed were the main process

inputs. Then, by selection of most precise model, it was

served as objective function for optimization by artificial

bee colony algorithm.

By testing of various topographies of back-propagation

neural network a (6-8-5-2) network was selected as the

most accurate estimator due to its lowest value of mean

absolute error. Simulation results by BPNN and compari-

son of predicted values with measured values demonstrated

that the (6-8-5-2) BPNN could generate tight agreements

between them. Then this model was applied as an objective

function for optimization of process. Firstly single objec-

tive optimizations were fulfilled to maximize the material

removal rate and minimize the surface roughness respec-

tively. By comparison of optimal solution with results of

literature [4], it was inferred that the ABC algorithm can

find the optimum points logically and precisely. Afterward,

a multi objective optimization was done to maximize the

material removal rate and minimize the surface roughness

simultaneously. Various weight factors were allocated to

material removal rate and surface roughness, and results

showed that by changing the weight factors, the optimal

solutions were not varied noticeably. This was due to

Table 9 Verification of optimal results for multi-objective

optimization

Vg(V)

Id(A)

Ton(ls)

D

(%)

P

(kPa)

N

(rpm)

Measured

MRR (mm3)

Measured

SR (lm)

80 49 800 88 245 2,250 5.24 3.12


1 3


12/12

symmetric similar behavior of material removal rate and

surface roughness against variation in process inputs.

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