Confidence intervals for RLCG cell influenced by coloured noise

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering - Tập 36 Số 4 - Trang 838-849 - 2017
Edita Kolářová1, Lubomír Brančík2
1Department of Mathematics, Brno University of Technology, Brno, Czech Republic
2Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic

Tóm tắt

Purpose The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise. Design/methodology/approach The deterministic model of the basic RLCG cell leads to an ordinary differential equation. In this paper, a stochastic model is formulated and the corresponding stochastic differential equation is analysed using the Itô stochastic calculus. Findings Equations for the first and the second moment of the stochastic solution of the coloured noise-affected RLCG cell are obtained, and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by an implicit Euler scheme, which turns out to be very effective. For comparison, the confidence intervals are computed statistically by an implementation of the Euler scheme using stochastic differential equations. Practical implications/implications The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab. A possible generalization for transmission line models is indicated. Originality/value The Itô-type stochastic differential equation describing the coloured noise RLCG cell is formulated, and equations for the respective moments are derived. Owing to this original approach, the confidence intervals can be found more effectively by solving a system of ordinary differential equations rather than by using statistical methods.

Từ khóa


Tài liệu tham khảo

1974, Stochastic Differential Equations: Theory and Applications

2012, Stochastic differential equations approach in the analysis of MTLs with randomly varied parameters, 725

2013, Simulation of higher-order electrical circuits with stochastic parameters via SDEs, Advances in Electrical and Computer Engineering, 13, 17, 10.4316/AECE.2013.01003

2014, Application of stochastic differential-algebraic equations in hybrid MTL systems analysis, Elektronika ir Elektrotechnika, 20, 41

2015, Variance assesment at transmission lines with randomly varying parameters via SDE theory, 287

2016, Simulation of multiconductor transmission lines with random parameters via stochastic differential equations approach, Transactions of the Society for Modeling and Simulation International, 92, 521, 10.1177/0037549716645198

1998, Time-domain analysis of transmission lines with stochastic input and general load, 968

1996, Matrix Computations

2000, Complete noise analysis for CMOS switching mixers via stochastic differential equations, 439

2016, Stochastic EMC/EMI experiments optimization using resampling techniques, IEEE Transactions on Electromagnetic Compatibility, 58, 1143, 10.1109/TEMC.2016.2557847

1997, Numerical Solution of SDE Through Computer Experiments

2015, Applications of second order stochastic integral equations to electrical networks, Tatra Mountains Mathematical Publications, 63, 163, 10.1515/tmmp-2015-0028

2012, Application of stochastic differential equations in second-order electrical circuits analysis, Przeglad Elektrotechniczny, 88, 103

2016, Reliability and sensitivity analysis of transmission lines in a probabilistic EMC context, IEEE Transactions on Electromagnetic Compatibility, 58, 561, 10.1109/TEMC.2016.2520205

2016, The adaptive controlled stratification method applied to the determination of extreme interference levels in EMC modeling with uncertain input variables, IEEE Transactions on Electromagnetic Compatibility, 58, 543, 10.1109/TEMC.2015.2510666

2012, Closed-form formulas for the stochastic electromagnetic field coupling to a transmission line with arbitrary loads, IEEE Transactions on Electromagnetic Compatibility, 54, 1147, 10.1109/TEMC.2012.2193130

2013, Crosstalk in stochastic cables via numerical multiseries expansions, 1527

2014, Impact on signal integrity of interconnect variabilities, 673

2000, Stochastic Differential Equations, An Introduction with Applications

2011, A stochastic perspective of RL electrical circuit using different noise terms, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 30, 812, 10.1108/03321641111101221

2010, Electrical Solitons: Theory, Design, and Applications

2004, Monte Carlo Statistical Methods

2012, Variability analysis of multiport systems via polynomial-chaos expansion, IEEE Transactions on Microwave Theory and Techniques, 60, 2329, 10.1109/TMTT.2012.2202685

2008, Experimental validation of the stochastic model of a randomly fluctuating transmission-line, 833

2009, Analysis of stochastic resonances in electromagnetic couplings to transmission lines, 33

1988, Iterative solution of the Lyapunov matrix equation, Applied Mathematics Letters, 1, 87, 10.1016/0893-9659(88)90183-8

2015, Analysis of RLC elements under stochastic conditions using the first and the second moments, Advances in Electrical and Computer Engineering, 15, 75, 10.4316/AECE.2015.04010

Thông tin
Thông tin xuất bản

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

Tập 36 Số 4

838-849

Thông tin tác giả