Numerical Calculation of Polynomial Chaos Coefficients for Stochastic Per-Unit-Length Parameters of Circular Conductors

This paper presents a numerical procedure for the calculation of the polynomial chaos (PC)-expansion coefficients for the per-unit-length capacitance and inductance matrices of wire structures affected by random parameter variability. According to the recent literature results, these coefficients in turn allow the generation of electrical circuit models for stochastic cables. The procedure is based on the twofold expansion of the nonuniform and stochastic charge distributions on the wire boundaries in terms of both Fourier and PC expansions. A stochastic Galerkin method allows to cast the problem in terms of a deterministic system of equations, whose solution provides the unknown coefficients. The proposed methodology is validated via the generation of statistical models for wire structures with random parameters, whose probabilistic responses are compared against the results of Monte Carlo simulations.