Stochastic differential equations for MTL simulation

What is it about?

This article addresses a method for the simulation of multiconductor transmission lines (MTLs) with fluctuating parameters based on the theory of stochastic differential equations (SDEs). Specifically, confidence intervals of MTL model’s stochastic responses are effectively evaluated. First, the MTL’s deterministic model with lumped parameters, based on generalized PI sections connected in cascade, is formulated and described through a state variable method, which results in a vector ordinary differential equation (ODE) in the time domain. A vector SDE is then developed by incorporating the respective stochastic processes into its deterministic counterpart. Next, the first two moments of the stochastic processes are calculated via the solution of respective Lyapunov-like ODEs, to assess expectations and the variances of stochastic responses, and also to determine relevant confidence intervals. A statistical processing of individual stochastic trajectories is used to validate the results.

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Why is it important?

The SDE approach can markedly speed up determination of confidence intervals at the systems with ramdomly varied parameters in comparison to standard statistical techniques.