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.
Purpose -The main purpose of this paper is to estimate the resistance and inductor in the RL electrical circuit when these are unavailable or missing data that it is a concern in electrical engineering. The input voltage is assumed to be corrupted by the noise and the current is observed at discrete time points. Design/methodology/approach -The authors propose a computationally efficient framework for parameters estimation using least square estimator and Bayesian Monte Carlo scheme. Findings -The explicit formulas for least square estimator are derived and the strong consistency of resistance estimator is verified when inductor is a known parameter, then Bayesian estimation of parameters governed by using Markov chain Monte Carlo methods. The applicability of the results is demonstrated by using numerical examples. Several numerical results and figures are presented via Matlab and R programming to illustrate the performance of the estimators. Practical implications -The paper can be used in various types of electrical engineering real time projects. The projects include electrical circuits, electrical machines theory and drives, especially when the parameters are uncertain that it is a worry in electrical engineering. Originality/value -To the author's best knowledge, least square and Bayesian estimation of resistance and inductor have not been studied before. The proposed model is nonlinear with respect to inductor (L); therefore the present work has fundamental difference in comparison with the similar models.
This paper introduces a novel approach, withen the context of energy market,
by employing a three-factor mean reverting Ornstein-Uhlenbeck process with a
stochastic nonlinear autoregressive drift term having a dependent error.
Initially the unique solvability for the given nonlinear system is
investigated. Then, to estimate the nonlinear regression function, a
semiparametric method, based on the conditional least square estimator for
the parametric approach, and the nonparametric kernel method for
autoregressive modification estimation have been presented . A maximum
likelihood estimator has been used for parameter estimation of the
Ornstein-Uhlenbeck process. Finally, some numerical simulations and real
data studies have been provided to support the main conclusions of the
study.
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