Perturbative Reformulation of the Stochastic Galerkin Method for Statistical Analysis of Wiring Structures with Several Random Parameters

In this paper, a novel approach for statistical analysis of cable harnesses characterized by several random parameters is proposed, which is based on a perturbative reformulation of the well-known stochastic Galerkin method (SGM). With respect to the traditional SGM, the proposed method avoids the solution of an augmented multiconductor transmission line (MTL), whose dimensions may become prohibitive in case of structures characterized by several wires and random parameters. Namely, it resorts to the iterative and repeated solution of a MTL having the same number of wires as the original structure, where the effects of random variations of geometrical parameters are included by means of equivalent sources. The proposed approach is here applied to collect statistical information of voltages and currents at the terminations of a shielded cable. Through such an example, involving a large number of wires (7) and random variables (12), it is proven that the proposed method yields a significant reduction of computational time with respect to the traditional SGM, at the same time providing similar accuracy in the prediction of statistical moments.