AWERProcedia Information Technology & Computer Science

AWERProcedia Information Technology & Computer Science Vol 04 (2013) 349-355

3rd World Conference on Innovation and Computer Sciences 2013

An Artificial Neural Network Model for The Ampere’s Law Ömer Faruk Alcin *, Dept. of Electronics and Computer Science, Faculty of Technical Education, Firat University, Elazig 23119,Turkey. Deniz Korkmaz, Dept. of Electronics and Computer Science, Faculty of Technical Education, Firat University, Elazig 23119,Turkey. Sami Ekici, Dept. of Energy Systems Engineering, Faculty of Technology, Firat University, Elazig 23119, Turkey. Abdulkadir Şengür, Dept. of Electrical and Electronics Engineering, Faculty of Technology, Firat University, Elazig 23119,Turkey. Suggested Citation: Alcin F., Ö., Korkmaz D., Ekici S. & Şengür A. An article neural network model for the ampere’s law. AWERProcedia Information Technology & Computer Science. [Online]. 2013, 04, pp 349-355. Available from: www.awer-center.org/pitcs Received December 09, 2012; revised January 24, 2013; accepted March 14, 2013. Selection and peer review under responsibility of Prof. Dr. Fahrettin Sadıkoglu, Near East University. ©2013 Academic World Education & Research Center. All rights reserved. Abstract Artificial neural network is biological nervous systems which designed by computer aided programs to simulate processes information of the human brain. The multilayered artificial neural network based on back-propagation algorithm is the most preferred method in many studies. In this study, an artificial neural network model is presented for the Ampere’s Law. The designed model consists of the back-propagation feed-forward neural network. Before training, input and target data sets are normalized in range of -1 to 1. The data sets used in the study are obtained from the Virtual Physics Laboratory. Also, various training algorithms are examined for better performance. Comparison of the simulation results showing the performance of network model are illustrated in the paper. Keywords: Artificial neural network, Back-propagation, Feed-forward, Ampere’s Law;

* ADDRESS FOR CORRESPONDENCE: Ömer Faruk Alçin, Firat University, Dept. of Elect. And Comp. Science, Elazig 23119, Turkey,

E-mail address: [email protected] / Tel.: +90-424-237-0000

Alcin F., Ö., Korkmaz D., Ekici S. & Şengür A. An article neural network model for the ampere’s law. AWERProcedia Information Technology & Computer Science. [Online]. 2013, 04, pp 349-355. Available from: www.awer-center.org/pitcs

1. Introduction Interest in intelligent computing techniques, such as Artificial Neural Network (ANN), is increasingly growing. ANN is a computational structure inspired by biological nervous systems. ANN’s consist of simple processing units called neurons that receive information from each other [1-5]. Communication of the neurons is provided via weighted connections. ANN’s consist of several layers as input layer, hidden layer and output layer. ANN’s have learning ability, training, simulation and prediction of data [6-10]. ANN’s is also known as good tool for modeling of system dynamics. One of the features of modeling based on ANN is that ANN’s can be performed without physical parameters for modeling [11]. At the same time, ANN’s are possessed a learning ability by using experimental data and especially capable to overcome complex systems [9-13]. In this way, there are many different types of neural networks, from relatively simple to very complex. ANN’s can be widely used to utilize in many different fields such as modeling of system dynamics, fault detection, pattern recognition, identification, classification and control systems. The common use of ANN is to predict to actions of system model [5,9-15]. The first use of artificial neural networks can be dated in 1940's [10]. In 1964, Hu initiated the implementation of ANN in weather forecasting [5,14]. After several years, National Aeronautics and Space Administration (NASA) studied to predict lightning using three-level back-propagation ANN [6]. Also, ANN is utilized in many medical applications to detect and categorize specific type of diseases [1]. Over the past decades, the increasing of interest in these systems makes ANN more attractive for modeling the natural life to the fields of engineering. Many researches have increasingly focused on modeling of complex non-linear systems by using ANN due to its computational speed, robustness, learning capabilities and performing in real time ability [1,5-8,10]. Thus, ANN’s in modeling and prediction for nonlinear problems have become a relatively research area for scientists. The aim of this paper is to design and perform of an artificial neural network model for the Ampere’s Law. In the designed model, ANN consists of the back-propagation feed-forward network. In addition, various training algorithms are examined for better performance of the model. The rest of this paper is organized as follows: In Section 2, principle of the Ampere’s Law is given. Section 3 describes the ANN model for Ampere’s Law. Simulation results are given in Section 4. Finally, conclusions are presented in Section 5. 2. Principle of The Ampere’s Law A relationship between the magnetic field around a current carrying conductor and its current source is known as the Ampere’s Law. The Ampere’s Law states that the line integral of the tangential component of magnetic field force (H) at any enclosed path is exactly equal to the net current (I) enclosed by the path, which is given by [16,17]:

 H .dl  I

(1)

c

Figure 1 shows the current carrying straight wire for schematic representation of the Ampere’s Law. Here, r is radius of the enclosed path and P is a point on the closed path.

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Alcin F., Ö., Korkmaz D., Ekici S. & Şengür A. An article neural network model for the ampere’s law. AWERProcedia Information Technology & Computer Science. [Online]. 2013, 04, pp 349-355. Available from: www.awer-center.org/pitcs z

Enclosed path

I

 H

d

x

r

dl P

y

conductor wire

Figure 1. Schematic representation of the Ampere’s Law

To determine magnetic field force H, the following two conditions must be provided [16,17]:  Magnetic field force must be tangential to the path at each point on the enclosed path.  Magnetic field force must be at all points of the path where is tangential to the enclosed path.

The magnetic flux density B is associated with magnetic field force, which is given by;

B  H

(2)

In this equation, µ is permeability, which is expressed by µ = µ0µr. Here, µ0 is permeability of free space and equals to 4π10-7. µr is relative permeability of material and equals to 1 for air [16,17]. 3. The Artificial Neural Network Model The ANN can exhibit complex global behavior determined by the connection between processing units and parameters. Back-propagation feed-forward ANN’s (BP-ANN) adopt error with back propagation algorithm as its learning algorithm. BP-ANN generally performs better than single layer perceptron in cases of nonlinear function approximation, learning, generalization and etc. [7,18]. The Ampere’s Law model based on the experimental work of the Virtual Physics Laboratory [19] is designed and performed by BP-ANN with Matlab/Neural Network toolbox. Experimental setup of the Virtual Physics Laboratory is given in Figure 2. The magnetic flux density is measured with a GMR sensor. The output of the sensor is voltage which is directly proportional to the magnetic flux density and the detailed knowledge about the experimental setup can be found in [19].

Figure 2. Experimental setup of the Virtual Physics Laboratory for the Ampere’s Law [19]

For performing BP-ANN, the weights of the network are randomly initialized firstly. Following, the error at the output layer is calculated by comparison of actual output and then, weights of the output and hidden layers are updated to reach the desired value. Finally, the network error is also propagated backward and used to update the weights of previous layers [7]. By trying different ANN parameters, 351


the best ANN architecture is designed and summarized in Table 1. Flowchart of the ANN is shown in Figure 3. Table 1. The designed ANN architecture

Initiliazation of the Network Parameters

Set Network Parameters

Training Loading Target Output

Simulation

Network Output Data

Determination of Randomly Target Data

Parameters [1, 3, 1] tansig, tansig, purelin mse 0.07 1e-5 Levenberg-Marquardt 1e-5 50/100 500

Denormalization

Normalization

Loading Input Data

ANN Properties Network Configuration Transfer Functions Performance Function Learning Rate Initial Momentum Constant Training Technique Training Goal Training / Testing Patterns Maximum Epochs

Artificial Neural Network

Figure 3. The flowchart of ANN for Ampere’s Law model

Also, various training algorithms are examined to achieve better performance. Comparisons of the simulation results are illustrated as follow. 4. Simulation Results and Discussions For the construction of ANN model, 301 patterns are obtained from [19], as data sets. At the training procedure, 50 patterns are randomly chosen from the data sets. 100 patterns of data sets are used for testing. Input data consist of the distance and target data are the voltage. In order to achieve better performance all of data sets are utilized in form of normalized data, which scale in range of [-1 to 1]. The results of training time, regression (R2), Mean Square Error (MSE) and epochs are illustrated for various well knowing training algorithms in Table 2. Table 2. Comparison results for various training algorithms Training Algorithms Levenberg-Marquardt (Trainlm) Quasi-Newton (Trainbfg) Resilient Backpropagation (Trainrp) Scaled Conjugate Gradient (Trainscg) Conjugate Gradient (Traincgb) Fletcher-Powell Conjugate Gradient (Traincgf) Polak-Ribiére Conjugate Gradient (Traincgp) One Step Secant (Trainoss) Variable Learning Rate Backpropagation (Traingdx)

Training Time (s) 1.109689 6.723634 2.743791 3.916278 1.488256 1.676758 1.661760 6.942028 2.923305

Regression 0.99997 0.99992 0.9962 0.99986 0.99881 0.99855 0.99872 0.99969 0.99616

Epochs 140 500 500 500 61 77 78 500 500

MSE 9.72e-6 2.2e-5 0.00133 4.13e-5 3.48e-4 4.22e-4 3.73e-4 9.20e-5 1.12e-3

Table 2 shows that Levenberg-Marquardt provides the best training time, R2 and MSE in the training process. Figure 4 shows the training performance and comparison of randomly testing results at 100 patterns, respectively, for Levenberg-Marquardt algorithm. 352


Best Training Performance is 9.4172e-06 at epoch 140

Testing Results for Target-ANN Output 10

Train Best Goal

0

Target ANN Output

9 8 7 Voltage (V)

Mean Squared Error (mse)

10

-2

10

-4

6 5 4 3

10

2 1

X: 140 Y: 1e-05

-6

10

0

20

40

60

80

100

120

140

0

0

20

40 60 Random Pattern

140 Epochs

(a)

80

100

(b)

Figure 4. (a) Performance of training (b) Comparison of testing results between target and BP-ANN output

Figure 4.a clearly shows that the best MSE of the BP-ANN occurred at 140 epochs and testing results reach to the good performance for randomly chosen patterns, as seen in Figure 4.b. Comparison of validation results are revealed for all data sets in Figure 5.a and the regression line of BP-ANN output with Levenberg-Marquardt algorithm is shown in Figure 5.b. Figure 5.a indicates that there is a good coherence between all target and BP-ANN output. It can be seen from Figure 5.b that network output is so close to the target value. Target - ANN Output

: R=0.99994 1

Target ANN Output

0.8

Output ~= 1*Target + -0.0015

12

10

Voltage (V)

8

6

4

2

0.6

Data Fit Y=T

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8

0

0

5

10

15 Distance (mm)

(a)

20

25

30

-1 -1

-0.5

0

0.5

1

Target

(b)

Figure 5. (a) Validation results between target and BP-ANN for all data sets (b) Regression line of BP-ANN output

Figure 6.a shows the comparison of target with BP-ANN for magnetic field density that is derived by B=kΔV, where, k is calibration constant (approximately equals to 9.13x10-5) and ΔV is subtraction of the output voltage at current flowing with offset voltage at no current flowing [19]. Figure 6.b shows the comparison of magnetic field force derived from magnetic field density by equation 2. In Figure 6, the distance is defined as r=r0+d, where r0 is the offset measurement distance and d is the adjusting measurement distance [19]. 353


-3

1.2

Magnetic Field Density - Distance

x 10

ro

Magnetic Field Force - Distance ro

Target ANN Output

X: 1.68 Y: 0.001129

900 800 700 Magnetic Field Force (A/mm)

Magnetic Field Density (Tesla)

1

Target ANN Output

X: 1.68 Y: 926.3

0.8

0.6

0.4

600 500 400 300 200

0.2 100

0

0

5

10

15 20 Distance (mm)

(a)

25

30

0 0

5

10

15 20 Distance (mm)

25

30

(b)

Figure 6. (a) Comparison of target with BP-ANN for magnetic field density (b) Comparison of target with BP-ANN for magnetic field force

Conclusion In this paper, an ANN model is presented for the Ampere’s Law. The ANN model is performed by back-propagation feed-forward network for various training algorithms. All data sets are derived based on the experimental work of the Virtual Physics Laboratory. BP-ANN prediction results achieved better training time, MSE and excellent regression around %99.9 with Levenberg-Marquardt algorithm. By using this training model, magnetic field density can be computed and its effect can be estimated. In addition, the principle of Ampere’s Law can be practiced in many educational applications and experimental studies. References Lo, S. C. B., Lou, A., Lin, J. S., Freedman, M. T., Chien, M. V. and Mun S. K. Artificial Convolution Neural Network Techniques and Application for Lung Nodule Detection, IEEE Transaction on Medical Imaging, December 1995, 14 (4), pp 711-718. Wu, A., Zhang, J., Zeng, Z. Dynamic Behaviors of a Class of Memristor-based Hopfield Networks, Physics Letter A, Elsevier B.V., 2011, 375, pp 1661-1665. Venkatesan, R. and Balamurugan, B. A Real-Time Hardware Fault Detector Using an Artificial Neural Network for Distance Protection, IEEE Transaction on Power Delivery, January 2001, 16 (1), pp 75-82. Sun, Y. X., Guo, G. H., Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Application of Artificial Neural Network on Prediction Reservoir Sensitivity, Guangzhou, 18-21 August 2005, pp 4770-4773. Abbishek, K., Kumar, A., Ranjan, R., Kumar S. IEEE Control and System Graduate Research Colloquium, A Rainfall Prediction Model Using Artifical Neural Network, Malaysia, 2012, pp 82-87. th Johari, D., Rahman, T. K. A., Musirin, I. The 5 Student Conference on Research and Development, Artificial Neural Network Based Technique for Lightning Prediction, Malaysia, 11-12 December 2007, pp 1-5. Routh, T. K., Yousuf A. H. B., Hossain, M. N., Asasduzzaman, M. M., Hossain M. L., Husnaeen, U., Mubarek, M. IEEE/OSA/IAPR International Conference on Informatics, Electronics and Vision, Artificial Neural Network Based Temperature Prediction and its Impact on Solar Cell, Dhaka, Bangladesh, 18-19 May 2012, pp 897902.

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