International Journal of Nonlinear Analysis and Applications

Stochastic approach for noise analysis and parameter estimation for RC and RLC electrical circuits

Document Type : Research Paper

Authors

1 Faculty of Science‎, ‎Urmia University of Technology‎, ‎Urmia‎, ‎Iran

2 Faculty of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Tehran‎, ‎Iran

Abstract

‎The main focus of this paper is to examine the effects of Gaussian white noise and Gaussian colored noise perturbations on the voltage of RC and RLC electrical circuits‎. ‎For this purpose‎, ‎the input voltage is assumed to be corrupted by the white noise and the charge is observed at discrete time points‎. ‎The deterministic models will be transferred to stochastic differential equations and these models will be solved analytically using Ito's lemma‎. ‎Random colored noise excitations‎, ‎more close to real environmental excitations‎, ‎so Gaussian colored noise is considered in these electrical circuits‎. ‎Scince there is not always a closed form analytical solution for stochastic differential equations‎, ‎then these models will be solved numerically based on the Euler‎- ‎maruyama scheme‎. ‎The parameter estimation for these stochastic models is investigated using the least square estimator when the parameters are missing data that it is a concern in electrical engeineering‎. ‎Finally‎, ‎some numerical simulations via Matlab programming are carried out in order to show the efficiency and accuracy of the present work‎.

Keywords

[1] L. Arnold, Stochastic Differential Equations, Theory and Applications, Johan Wiley & Sons, 1974.
[2] R. Farnoosh, P. Nabati, R. Rezaeyan and M. Ebrahimi, A stochastic perspective of RL electrical circuit using different noise terms, Int. J. Comput. Math. Elect. Electr. Engin. 30 (2011) 812–822.
[3] R. Farnoosh, P. Nabati, A. Hajrajabi, Parameter estimation for RL electrical circuits based on least square and Bayesian approach, Int. J. Comput. Math. Elect. Electr. Engin. 31 (2012) 1711–1725.
[4] R.F. Fox, Second order algorithm for the numerical integration of colored noise problems, Phys, Rev. A 43 (1991).
[5] R.F. Fox, I.R. Gatland, R. Roy and G. Vemuri Accurate algorithm for numerical simulation of exponentially correlated colored noise, Phys, Rev. A 38 (1988).
[6] R. Farnoosh and P. Nabati, A stochastic perspective to random ship heave motion based on different noises, Iran.  J. Sci. Technol. Trans. A: Sci. 37 (2013) 211–217.
[7] D. Ham and A. Hajimiri, Complete noise analysis for CMOS switching mixtures via SDEs, IEEE Custom Integrated Circuits Conf., 2000, pp. 439–442.
[8] W. Kampowsky, P. Rentrop and W. Schmidt, Classification and numerical simulation of electric circuits, Surveys Math. Indust. (1992) 23–65.
[9] Y. Kamarianakis and N. Frangos, Deterministic and stochastic differential equations modeling for electrical networks, Hellenic and European Research in Computational Mathematics Conference, Athens University of Economics Business, 2001.
[10] R.A. Kasonga, The consistency of a nonlinear least square estimator for diffusion processes, Stoch. Proces. Appl. 30(2) (1988) 263–275.
[11] C. Kim and E.K. Lee, Numerical method for solving differential equations with dichotomous noise, Phys. Rev. E73 (2006) 026101.
[12] P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1995.
[13] E. Kolarova, Modeling RL electrical circuits by SDEs, Int. Conf. Computer as a Tool, (2005) pp. 1236–1238.
[14] G.N. Milstein and M.V. Tretyakov, Numerical solution of differential equation with colored noise, J. Stat. Phys. 77 (1994) 691.
[15] B. Oksendal, Stochastic Differential Equations an Introduction with Applications, Springer-Verlage, 2000.
[16] C. Penski, A new numerical method for SDEs and its application in circuit simulation, Com. Appl. Math. (2000) 461-470.
[17] B. L.S. Prakasa Rao, Asymptotic theory for nonlinear least square estimator for diffusion processes, Math. Oper. Forsch. Stat. 14(2) (1983) 195–209.
[18] T.K. Rawat and H. Parthasarathy, Modeling of an RC circuit using SDEs, Int. J. SC. Tech. 13(2) (2008).
[19] J.M. Stijnen, A.W. Heemink and K. Pollambalam, Numerical treatment of stochastic river quality models driven by colored noise, Water Resour. Search 39(3) (2003).
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 433-444
  • Receive Date: 19 October 2017
  • Revise Date: 12 January 2018
  • Accept Date: 23 March 2019