A stochastic perspective of RL electrical circuit using different noise terms

Abstract

PurposeThe 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/approachBy 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).FindingsOwing 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 implicationsNumerical 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/valueIt 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.

Parameters estimation for RL electrical circuits based on least square and Bayesian approach

“…For a given positive integer n, let Dt ¼ T/n and consider the partitions: (2), we derive the following stochastic difference equation (Farnoosh et al, 2011):…”

“…For a given positive integer n, let Δ t = T / n and consider the partitions: Equation 4 of the interval [0, T]. With a simple forward Euler discretization of equation (2), we derive the following stochastic difference equation (Farnoosh et al , 2011): Equation 5 where B t +Δ t is iid with the standard normal distribution. Denote I i Δ t by I i .…”

“…Among other disturbing signals, electronic noise in electrical devices is not avoidable. Farnoosh et al (2011) have been presented a stochastic perspective for RL electrical circuits using different noise terms. The accurate parameter estimation of both the drift and diffusion terms of the aforementioned model is a concern.…”

Noise analysis of band pass filters using stochastic differential equations

“…Rawat and Parthasarathy (2008) modeled the RC electrical circuits with white noise. Farnoosh et al (2011) studied the effects of different noise terms in RL electrical circuits. Parameter estimation for RL electrical circuits based on least squares and Bayesian approach were studied by Farnoosh et al (2012).…”

Simulation of multiconductor transmission lines with random parameters via stochastic differential equations approach

“…1–3 As for electrical engineering, the SDE approach has been mostly used to solve noisy issues in electronic circuits with lumped parameters, including monolithic integrated circuits. 4–11 The present paper applies SDE theory to networks with distributed parameters, and transmission lines (TL) in particular, which are very often utilized for high-speed data transmission. 12–14 To catch effects of random variations of system parameters, standard methods like Monte Carlo are commonly utilized.…”