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Reseach Article

Solution of Linear Electrical Circuit Problem Using Neural Networks

by J.Abdul Samath, P.Senthil Kumar, Ayisha Begum
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 2 - Number 1
Year of Publication: 2010
Authors: J.Abdul Samath, P.Senthil Kumar, Ayisha Begum
10.5120/618-869

J.Abdul Samath, P.Senthil Kumar, Ayisha Begum . Solution of Linear Electrical Circuit Problem Using Neural Networks. International Journal of Computer Applications. 2, 1 ( May 2010), 6-13. DOI=10.5120/618-869

@article{ 10.5120/618-869,
author = { J.Abdul Samath, P.Senthil Kumar, Ayisha Begum },
title = { Solution of Linear Electrical Circuit Problem Using Neural Networks },
journal = { International Journal of Computer Applications },
issue_date = { May 2010 },
volume = { 2 },
number = { 1 },
month = { May },
year = { 2010 },
issn = { 0975-8887 },
pages = { 6-13 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume2/number1/618-869/ },
doi = { 10.5120/618-869 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T19:49:35.500443+05:30
%A J.Abdul Samath
%A P.Senthil Kumar
%A Ayisha Begum
%T Solution of Linear Electrical Circuit Problem Using Neural Networks
%J International Journal of Computer Applications
%@ 0975-8887
%V 2
%N 1
%P 6-13
%D 2010
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, Neural network algorithm is introduced to study the singular system of a linear electrical circuit for time invariant and time varying cases. The discrete solutions obtained using neural network are compared with Runge-Kutta(RK) method and exact solutions of the electrical circuit problem and are found to be very accurate. Error graphs for inductor currents and capacitor voltages are presented in a graphical form to show the efficiency of neural network algorithm. This neural network algorithm can be easily implemented in a digital computer for any singular system of electrical circuits.

References
  1. R .K. Alexander and J.J. Coyle, “Runge-Kutta Methods for Differential-Algebric Systems,” SIAM J. of Numerical Analysis, vol. 27, no. 3, 1990, pp. 736-752.
  2. S.I.Amari “Mathematical Foundations of neurocomputing" Proc. IEEE, Vol. 78, pp. 1443-1463, Sep. 1990.
  3. J. A. Anderson and E. Rosenfeld, Eds., Neurocomputing: Foundations of Research.Cambridge, MA: MIT Press, 1988.
  4. G.K.Boray and M.D.Srinath, ”Conjugate Gradient Techniques for Adaptive Filtering," IEEE Trans. Circuits Syst.-I, Vol. 39, pp. 1-10, Jan. 1992.
  5. S.L.Campbell, Singular Systems of Differential Equations, Pitman, Marshfield, MA, 1980.
  6. S.L.Campbell, Singular Systems of Differential Equations II, Pitman, Marshfield, MA, 1982.
  7. L.O. Chua and P.M. Lin, Computer-Aided Analysis of Electronic Circuits, Prentice-Hall, New Jersey, USA, 1975.
  8. L.O.Chua, C. A. Desoer and E. S. Kuh, Linear and Nonlinear Circuits. McGraw-Hill, 1987.
  9. L.Dai, Singular Control Systems, Lecture Notes in Control and Information Sciences, Springer Verlag, NewYork, 1989.
  10. D.J. Evans, “A New 4th Order Runge-Kutta Method for Initial Value Problems with Error Control,” Int.lJ. Computer Mathematics, vol. 139, 1991, pp. 217-227.
  11. D.J. Evans and A.R. Yaakub, “A New Fifth Order Weighted Runge-Kutta Formula,” Int.J.Computer Mathematics, vol. 59, 1996, pp. 227-243.
  12. D.J.Evans and A.R.Yaakub, “Weighted Fifth Order Runge-Kutta Formulas for Second Order Differential Equations,” Int. J.Computer Mathematics, vol. 70, 1998, pp. 233-239.
  13. P. Friedel and D.Zwierski, Introduction to Neural networks. (Introduction aux Reseaux de Neurones.) LEP Technical Report C 91 503, December 1991.
  14. D.Hammerstrom, “Neural networks at work," IEEE Spectrum, pp. 26-32, June 1993.
  15. R. Hecht-Nielsen, “Nearest matched filter classification of spatio- temporal patterns ", Applied Optics, Vol. 26, pp. 1892-1899, May 1987.
  16. D. R. Hush and B. G. Horne, “Progress in Supervised Neural Networks," IEEE Sign.Proc. Mag., pp. 8-39, Jan.1993.
  17. J. S. R. Jang, “Self-Learning Fuzzy Controllers Based on Temporal Back Propagation," IEEE Trans. Neural Networks, Vol. 3, pp. 714-723, Sep. 1992.
  18. D.R.Kincaid and E.W.Cheney, Numerical Analysis: Mathematics of Scientific Computing. Books/Cole Publishing Company, 1991.
  19. I.E. Lagaris, A. Likas, D.I.Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans.Neural Networks 9(1998) 987–1000.
  20. J.D. Lambert, Numerical Methods for Ordinary Differential Systems. The Initial Value Problem, John Wiley & Sons, Chichester, UK, 1991.
  21. F.L. Lewis, A Survey of linear singular systems, Circ. Syst. Signal Process. 5 (1986) 3–36.
  22. R.P. Lippmann, “An Introduction to Computing with neural Nets," IEEE ASSP Mag., pp. 4-22, Apr. 1987
  23. C. A. Mead, Analog VLSI and Neural Systems. Reading, MA: Addison-Wesley, 1989.
  24. P. B. L. Meijer, “Fast and Smooth Highly Nonlinear Table Models for Device Modeling," IEEE Trans. Circuits Syst., Vol. 37, pp. 335-346, Mar. 1990.
  25. K.Murugesan, D.Paul Dhayabaran, and D.J. Evans, “Analysis of Different Second Order Systems via Runge- Kutta Method,” Int. J.Computer Mathematics, vol. 70, 1999, pp. 477- 493.
  26. K.Murugesan, D.Paul Dhayabaran, and D.J. Evans,“Analysis of Different Second Order Multivariable Linear System Using Single Term Walsh Series Technique and Runge-Kutta Method,” Int. J. of Computer Mathematics, vol. 72, 1999, pp. 367-374.
  27. K. Murugesan, D. Paul Dhayabaran, and D.J. Evans, “Analysis of Non-Linear Singular System from Fluid Dynamics Using Extended Runge-Kutta Methods,” Int. Journal.Computer Mathematics, vol. 76, 2000, pp. 239- 266.
  28. K. Murugesan, D.Paul Dhayabaran, E.C. Henry Amirtharaj, and D.J. Evans, “A Comparison of Extended Runge-Kutta Formulae Based on Variety of Means to Solve System of IVPs,” International .Journal of Computer Mathematics, vol. 78, 2001, pp. 225-252.
  29. K. Murugesan, D. Paul Dhayabaran, E.C. Henry Amirtharaj and D.J. Evans, “A Fourth Order Embedded Runge-Kutta RKACeM(4,4) Method Based on Arithmetic and Centrodial Means with Error Control,” Int. J. Computer Mathematics, vol. 79, no. 2, 2002, pp. 247- 269.
  30. K. S. Narendra, K. Parthasarathy, “Gradient Methods for the Optimization of Dynamical Systems Containing Neural Networks," IEEE Trans. Neural Networks, Vol. 2, pp. 252- 262, Mar. 1991. 170 BIBLIOGRAPHY
  31. D.E . Rumelhart and J.L. McClelland, Eds.,Parallel Distributed Processing, Explorations in the Microstructure of Cognition. Vols. 1 and 2. Cambridge, MA: MIT Press, 1986.
  32. F. M. A. Salam, Y. Wang and M.-R. Choi, “On the analysis of Dynamic Feedback Neural Nets," IEEE Trans. Circuits Syst., Vol. 38, pp. 196-201, Feb. 1991.
  33. Senjyu, T., Sakihara, H., Tamaki, Y., and Uezato, K. 2000.“Next Day Peak Load Forecasting using Neural Network with Adaptive Learning Algorithm Based on Similarity”. Electric Machines and Power Systems. 28(7):613- 624.
  34. P. De Wilde, Neural Network Models, second ed., Springer Verlag, London, 1997.
Index Terms

Computer Science
Information Sciences

Keywords

Singular systems Runge-Kutta method Neural networks