artificial neural network approach to predict the electrical

8/3/2019 Artificial Neural Network Approach to Predict the Electrical

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Fig. 1 The structure of three-layered neural network in the

present study.

layers, the geometry and functionality of which have been

likened to that of the human brain. ANNs learn by experience,

generalize from previous experiences to new ones, and can

make decisions (Kohonen, 1980). Neural elements of a human

brain have a computing speed of a few milliseconds, whereas

the computing speed of electronic circuits is in the order of

microseconds.

The network has one input layer, one hidden layer and

one output layer. The input layer consists of all the input fac-

tors. Information from the input layer is then processed in the

course of one hidden layer, following output vector is com-puted in the final (output) layer. A schematic description of

the layers is given in Fig. 1. In developing an ANN model, the

available data set is divided into two sets, one to be used for

training of the network, and the remaining is to be used to

verify the generalization capability of the network (Haykin,

1999; Rojas, 1996; Bernhaut and Pfalzgraf, 2002). Inputoutput

pairs are presented to the network and weights are adjusted

to minimize the error between the network output and actual

value.

Among the various kinds of ANN approaches that exist,

the multi-layer perceptron (MLP) architecture with back-

propagation learning algorithm has become the most popular

in engineering applications (Mandal et al., 2007; Mandal and

Roy, 2006). Back-propagation is based on minimization of the

quadratic cost function by tuning the network parameters.The mean square error is considered as a measurement cri-

terion for a training set. Parameters which minimize this cost

function are determined. The averaged square error is given

by Eqs. (1) and (2) (Zurada, 1992):

ej(n) = dj(n) yj(n) (1)

(n) =1

2P

jC

Pn=1

e2j (n) (2)

In these equationse

,n

,d

,y

,P

andC

indicate error signal at theoutput, iteration number, desired output, generated output

by network, total number of patterns contained in the train-

ing set and number of neurons at output layer, respectively.

The adjustment of synaptic weights between hidden layer and

output layer is given by Eqs. (3) and (4) (Zurada, 1992):

wji(n) = j(n)yi(n) (3)

j(n) = ej(n)

mi=0

wji(n)yi(n)

(4)

indicates learning rate parameters and has different valuesin different problems. The adjustment of synapticweightcoef-

ficients between input layer and hidden layer are given by Eq.

(5) (Zurada, 1992):

j(n) =

mi=0

wji(n)yi(n)

k

k(n)wkj(n) (5)

Fig. 2 General architecture of the learning and predicting system.


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472 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 8 ( 2 0 0 8 ) 470476

In case of the network does notconverge, theformula, whichis

used to determine weight coefficients including momentum

parameter has been generalized and given in Eq. (6) (Zurada,

1992):

wji(n) = wji(n 1) + j(n)yi(n) (6)

The general architecture of learning and predicting themechanical properties system is given in Fig. 2.

3. Experimental data and working platform

The chemical compositions, electrical conductivity and den-

sity of AgNi binary alloys were collected from related

standards and ASM Hand Books (Watson, 2000) and given in

Table 1. At this study, ANN model wasemployed to predict the

electrical conductivity and density of AgNi binary alloys. The

network has two input parameters: Ag (wt%), Ni (wt%) con-

tents and three output parameters: calculated density, typical

density andelectrical conductivity. So,the architectureof ANNbecomes 2-10-3, 2 corresponding to the input values, 10 to the

number of hidden layer neurons and 3 to the outputs.

MATLAB platform was used to train and test the ANN. In

the training, increased number of neurons (812)in the hidden

layer has been used in order to define the output accurately.

After training the network successfully, it has been tested by

using the known data. Statistical methods were used to com-

pare the results produced by the network. Errors occurring

at the learning and testing stages are called the root-mean

squared (RMS), absolute fraction of variance (R2), and mean

percentage error (MPE) values. They are defined as follows,

respectively (Zurada, 1992):

RMS =

1p

j

|tj oj|2

1/2

(7)

R2 = 1

j(tj oj)

2j(oj)

2

(8)

Fig. 3 Performance changing of neural network in training

stage.

MPE =1

pj

tj ojtj 100

(9)

4. Evaluation of results and discussions

Typical densities of AgNi binary alloy were recorded between

8 and 10g/cm3. The density of Ag99.7Ni0.3 binary alloy was

recorded 10 g/cm3 while Ag20Ni80 binary alloy was recorded

8g/cm3. It has been observed that, Ni additions decrease the

typical densities of AgNi binary alloys.

The electrical conductivity of Ag99.7Ni0.3 binary alloy was

recorded as 100 (%IACS) while Ag20Ni80 binary alloy wasrecorded 21 (%IACS). It has been observed that, Ni additions

to AgNi binary alloy significantly affect the electrical conduc-

tivity (Findik and Uzun, 2003).

The experimental data set includes 17 patterns, of which

11 patterns were used for training the network and 6 pat-

terns were selected randomly to test the performance of the

trained network. All the input and output values were nor-

Table 1 Experimental data (Watson, 2000)

Ag (wt%) Ni (wt%) Calculated density (g/cm3) Typical density (g/cm3) Electrical conductivity (%IACS)

99.7 0.3 10.49 10.12 100

95 5 10.41 10.105 87.590 10 10.31 10.01 82.5

85 15 10.22 9.76 73

80 20 10.13 9.4 69

75 25 10.05 9.2 59

70 30 9.96 9.465 55.5

65 35 9.88 9 49

60 40 9.8 9.25 45.5

55 45 9.71 8.8 41

50 50 9.63 9 38

45 55 9.56 8.5 35

40 60 9.48 8.8 32

35 65 9.4 8.6 30

30 70 9.32 8.5 27

25 75 9.25 8.2 24

20 80 9.17 8 21


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Table 2 MLP architecture and training parameters

The number of layers 3

The number of neuron on the

layers

Input: 2, hidden: 10, output: 3

The initial weights and biases Randomly between 1 and +1

Activation functions for

hidden and output layers

Log-sigmoid

Training parameters learningrule

Back-propagation

Adaptive learning rate for

hidden layer

From 0.9 to 0.890893

Adaptive learning rate for

output layer

From 0.7 to 0.692917

Number of iteration 10170

Momentum constant 0.95

Duration of learning time 1min 25s

Acceptable mean-squared

error

0.001

malized between 0.1 and 0.9 by using linear scaling. The

log-sigmoid transferfunction wasused in thehidden andout-

put layer. During the trainingperiod, the averaged square errordecreased with increasing number of iteration. After 10,000

training cycles, significant effect on error reduction has not

been traced. The performance changing of ANN in training

stage is given in Fig. 3.

The amount of reliable input data improves the results

of training session and target outputs. The MLP architec-

ture and training parameters used in learning stage for ANN

Table 3 Weights between input layer and hidden layer

i Ei =G1Ag+G2Ni+G3

G1 G2 G3

1 1.9708 1.3389 0.39475

2 0.78788 0.014128 0.66146

3 0.018137 1.5157 0.76732

4 8.7658 4.6679 4.9214

5 5.6298 9.3214 4.9394

6 1.5432 1.3847 2.1631

7 0.043249 2.187 0.08912

8 0.61724 1.3799 0.90053

9 1.0528 1.0077 1.0008

10 2.2492 0.44481 0.93207

structure are presented in Table 2. A comparison of the

measured and predicted calculated density, typical density

and electrical conductivity, at training stage, is presented

in Figs. 4a, 5a, and 6a, respectively. From these comparison

charts, it can be clearly seen that the ANN is properly trained

and shows a consistency among the properties. A comparisonof the measured and predicted calculated density, typical den-

sity and electrical conductivity, at testing stage, is presented

in Figs. 7a, 8a, and 9a, respectively. Comparison of measured

and predicted mechanical properties at testing stage indicated

that there is a high correlation between them.

The results of verifying by the ANN are shown in

Figs.4b,5b,6b,7b,8b,and9b as scatterplots.It canbe seenfrom

Fig. 4 For the training stage of calculated density. (a) Comparison, (b) scatter plot.

Fig. 5 For the training stage of typical density. (a) Comparison, (b) scatter plot.


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Fig. 6 For the training stage of electrical conductivity. (a) Comparison, (b) scatter plot.

Fig. 7 For the testing stage of calculated density. (a) Comparison, (b) scatter plot.

Fig. 8 For the testing stage of typical density. (a) Comparison, (b) scatter plot.

Fig. 9 For the testing stage of electrical conductivity. (a) Comparison, (b) scatter plot.


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Table 4 Statistical values of calculated density, typical density and electrical conductivity

RMS train R2 train MPE train RMS test R2 test MPE test

Calculated density (g/cm3) 0.0145 1.0000 0.2186 0.0219 1.0000 0.0408

Typical density (g/cm3) 0.1289 0.9998 2.1757 0.1645 0.9997 0.7881

Electrical conductivity (%IACS) 2.5007 0.9983 3.0262 1.8609 0.9987 0.5321

the scatter diagramsthat theslope andintercept of theregres-

sion equations for the outputs are significantly near to 1 and

0, respectively. The scatterplots reveal that the well-trained

network model has great accuracy in predicting calculated

density, typical density and electrical conductivity.

The decision as to the number of neurons used in the hid-

den layer usually depends on the arithmetical mean of the

number of inputs and outputs. In this application 812 hidden

layers were employed to test. The algorithm with 10 hidden

layer neurons is suggested to be used in present application

since minimum meansquare errorwas obtained.Weight coef-

ficients between input layer andhidden layer were used at the

trainingtesting stages of the network and are presented inTable 3.

The activation function used in this study is given as fol-

lows:

Mi =1

1 + eEi(10)

where Ei is the weighted sum of the input depending on per-

centage of Ag and Ni. The constants for the calculation of Miwere taken from Table 3.

The outputs are calculated as follows:

Calculated density =1

1 + e(1.31M10.56M2+1.54M34.12M4+2.61M51.56M6+0.96M7+1.11M8+1.90M91.40M100.22) (11)

Typical density =1

1 + e(1.14M1+0.06M2+0.66M34.50M4+7.32M51.16M6+0.44M7+0.63M8+0.71M90.77M10+0.20)(12)

Electrical conductivity =1

1 + e(1.97M10.85M20.17M32.66M4+2.68M51.40M6+1.94M7+1.26M8+0.87M90.81M100.25)(13)

Statistical values of electrical conductivity and density of

AgNi binary alloys were presented in Table 4. As a result the

statistical values namely, RMS, R2 and MPE, are within accept-

able ranges which meet the integrity of the ANN learning and

testing stages.

5. Conclusion

The addition of nickel to AgNi binary alloys decreases the

density and the electrical conductivity while increasing the

other mechanical properties, namely strength of the compo-

nent. The effect of nickel additions on densities and electrical

conductivity was presented in Table 1.

The main quality indicator of a neural network is its gen-

eralization ability, its ability to predict accurately the output

of unseen test data. In this study, we have utilized fea-

tures of ANN. It has been observed that MLP architecture

with back-propagation learning algorithm can be used as a

tool for predicting of physical properties (namely, calculated

density, typical density and electrical conductivity) of AgNi

binary alloy. In this study, the ANN architecture, 2-10-3, was

employed. The algorithm with 10 hidden layer neurons is sug-

gestedto be used in present application since minimum mean

square error was obtained.

Regarding to thescatterplots(Figs. 4b, 5b, 6b, 7b, 8b, and 9b)

at training and testing stages, the electrical conductivity and

density of AgNi binary alloys were predicted with a high suc-

cess rate since the slopes of the functions are very close to

1. With the increasing number of input patterns, the success

rateof capturing those patternswas beingimproved gradually.

This method(ANN)couldbe also employed in predictingother

physical properties of metal alloys if reliable process parame-ters and test results are given as ANN input and output data,

respectively (Vasudevan et al., 2005; Ohdar and Pasha, 2003;

Miaoquan et al., 2002).

Acknowledgements

Theauthor would like to thank DicleUniversity Research Com-

mittee since a part of this study is supported through grant

DUAPK 03-MF-86. Special thanks to TUBITAK (The Scientific

and Technological Research Council of Turkey) for their unfail-

ing support to the researchers.

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artificial neural network approach to predict the electrical

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