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A stochastic perspective of RL electrical circuit using different noise terms

Rahman Farnoosh (Applied Mathematics Department, Iran University of Science and Technology, Tehran, Islamic Republic of Iran)
Parisa Nabati (Applied Mathematics Department, Iran University of Science and Technology, Tehran, Islamic Republic of Iran)
Ramazan Rezaeyan (Department of Mathematics, Sciences and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran)
Morteza Ebrahimi (Applied Mathematics Department, Iran University of Science and Technology, Tehran, Islamic Republic of Iran)

Abstract

Purpose

The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit including potential source and resistance.

Design/methodology/approach

By adding different noise terms in the voltage and resistance parameters of an RL electrical circuit, the deterministic model is replaced by a stochastic differential equation (SDE).

Findings

Owing to the application of multiple Ito's formula the analytical solutions of resulted SDEs have been obtained. Furthermore, based on a numerical method involving Euler‐Maruyama scheme, the solution of the problem at the point of interest as a continuous time stochastic process has been obtained. Also shown is that the confidence interval for mean of solutions with colored and mixture noises is better than white noise.

Practical implications

Numerical tests via Matlab programming are performed in order to show the efficiency and accuracy of the present work. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes time at Pentium IV‐2.4 GHz PC.

Originality/value

It is believed that the stochastic model of an RL circuit with colored and mixture noises in potential source has not been studied before. Furthermore, according to latest information from the research works, two stochastic parameters in voltage and resistance of RL circuit including colored and mixture noise processes have been investigated for the first time in this paper.

Keywords

Citation

Farnoosh, R., Nabati, P., Rezaeyan, R. and Ebrahimi, M. (2011), "A stochastic perspective of RL electrical circuit using different noise terms", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 2, pp. 812-822. https://doi.org/10.1108/03321641111101221

Publisher

:

Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited

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