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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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
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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
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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
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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
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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
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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
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symmetric similar behavior of material removal rate and
surface roughness against variation in process inputs.
References
1. Ramani V, Cassidenti ML (1985) Inert-gas electrical dischargemachining. NASA Technical Brief Number NPO 15660
2. Kunieda M, Furuoya S, Taniguchi N (1991) Improvement of
EDM efficiency by supplying oxygen gas into gap. CIRP Ann
Manuf Technol 40:215–218
3. Kunieda M, Yoshida M, Taniguchi N (1997) Electrical discharge
machining in gas. CIRP Ann Manuf Technol 46:143–146
4. Saha SK, Choudhury SK (2009) Experimental investigation and
empirical modeling of the dry electric discharge machining pro-
cess. Int J Mach Tools Manuf 49(3–4):297–308
5. Govindan P, Joshi SS (2010) Experimental characterization of
material removal in dry electrical discharge drilling. Int J Mach
Tools Manuf 50:431–443
6. Kuneida M, Miyoshi Y, Takaya T, Nakajima N, Bo YZ, Yoshida
M (2003) High speed 3D milling by dry EDM. CIRP Ann Manuf
Technol 52:147–1507. Yu Z, Jun T, Masanori K (2004) Dry electrical discharge
machining of cemented carbide. In: 14th international symposium
on electromachining (ISEM XIV), J Mater Process Technol 149
(1–3):353–357
8. Zhanbo Y, Takahashi J, Nakajima N, Sano S, Karato K, Kuneida
M (2005) Feasibility of 3-D surface machining by dry EDM. Int J
Electr Mach 10:15–20
9. Soni JS, Chakraverti G (1994) Machining characteristics of tita-
nium alloy with rotary electro-discharge machining. Wear
171:51–58
10. Chattophaday KD, Veram S, Satsangi PS, Sharma PC (2009)
Development of empirical model for different process parameters
during rotary electrical discharge machining of copper-steel
(EN-8) system. J Mater Process Technol 209:1454–1465
11. Mohan B, Rajadurai A, Satyanarayana KG (2002) Effect of SiCand rotation of tool electrode on electric discharge machining of
Al–SiC composite. J Mater Process Technol 124:297–304
12. Kuppan P, Rajadurai A, Narayanan S (2008) Influence of EDM
process parameters in deep hole drilling of Inconel 718. Int J Adv
Manuf Technol 38:74–84
13. Sohani MS, Gaitonde VN, Siddeswarappa B, Deshpande AS
(2009) Investigations into the effect of tool shapes with size
factor consideration in sink electrical discharge machining
(EDM) process. Int J Adv Manuf Tech 45:1131–1145
14. Tsai KM, Wang PJ (2001) Comparisons of neural network
models on material removal rate in electrical discharge machin-
ing. J Mater Process Technol 117:111–124
15. Kumar S, Chodhury SK (2007) Prediction of wear and surface
roughness in electro-discharge diamond grinding. J Mater Process
Technol 191:206–209
16. Mandal D, Pal SK, Saha P (2007) Modeling of electrical dis-
charge machining process using back propagation neural network
and multi-objective optimization using non-dominating sorting
genetic algorithm-II. J Mater Process Technol 186:154–162
17. Yang SH, Srinivas J, Mohan S, Lee DM, Blajee S (2009) Opti-
mization of electric discharge machining using simulated
annealing. J Mater Process Technol 209:4471–4475
18. Akay B, Karaboga D Artificial bee colony algorithm for large-
scale problems and engineering design optimization. J Intell
Manuf. doi:10.1007/s10845-010-0393-4
19. Basturk B, Karaboga D (2006) An artificial bee colony (ABC)
algorithm for numeric function optimization. In: Proceedings of
the IEEE swarm intelligence symposium, Indianapolis, IN, USA,
May 12–14
20. Rao RV, Pawar PJ (2009) Modelling and optimization of process
parameters of wire electrical discharge machining. Proc IMechE,
Part B J Eng Manuf 223(11):1431–1440
21. Samanta S, Chakraborty S (2011) Parametric optimization of
some non-traditional machining processes using artificial bee
colony algorithm. Eng Appl Artif Intell 24:946–957
22. Chen HC, Lin JC, Yang YK, Tsai CH (2010) Optimization of
wire electrical discharge machining for pure tungsten using a
neural network integrated simulated annealing approach. Expert
Syst Appl 37:7147–7153
23. Joshi SN, Pande SS (2011) Intelligent process modeling and
optimization of die-sinking electric discharge machining. Appl
Soft Comput 11:2743–2755
24. Singh PN, Raghukandan N, Pai BC (2004) Optimization by Grey
relational analysis of EDM parameters on machining Al–10 % SiCP
composites. J Mater Process Technol 155–156:1658–1661
25. Hagan MT, Demuth HB, Beale M (1996) Neural network design.
PWS Publishing Company, Boston, MA
26. Rao SS (2009) Engineering optimization: theory and practice.
Wiley, Hoboken, NJ
504 Prod. Eng. Res. Devel. (2012) 6:493–504
1 3
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