Stochastic Analysis of Multitwisted Cables With Random Parameters Excited by Random Plane-Wave Fields

Abstract

A generalized multiconductor transmission line (MTL) model is integrated with the polynomial chaos stochastic Galerkin method (PC-SGM) in order to predict the stochastic response of a nonuniform multitwisted bundle of twisted-wire pairs (MTB-TWP) with random parameters, which is excited by random plane waves. The twist pitches of such nonuniform MTB-TWP are considered to be spatial stochastic functions, where its parametric equations are derived in their general form. Moreover, by taking the geometry deformation of the MTB-TWP cable into account, some of its parameters are represented by random variables, and the incident plane-wave fields can also be changed in some ran- dom ways. After that, the PC-SGM is applied to the stochastic telegrapher’s equations in order to obtain deterministic ones that can be solved by using the MTL model. Therefore, the effects of the uncertainties of the parameters on the common mode and the differential mode currents are investigated in details, where, in each case, the probability density function is given. The results are validated in comparison with Monte Carlo (MC) method, where a very good agreement is obtained. It is shown that the PC-SGM simulation time is much smaller than that of the MC method as the number of random variables is relatively small.