Abstract
Cable bundles often exhibit random parameter variations due to uncertain or uncontrollable physical properties and wire positioning. Efficient tools, based on the so-called polynomial chaos, exist to rapidly assess the impact of such variations on the per-unit-length capacitance and inductance matrices, and on the pertinent cable response. Nevertheless, the state-of-the-art method for the statistical extraction of the per-unit-length capacitance and inductance matrices of cables suffers from several inefficiencies that hinder its applicability to large problems, in terms of number of random parameters and/or conductors. This paper presents an improved methodology that overcomes the aforementioned limitations by exploiting a recently-published, alternative approach to generate the pertinent polynomial chaos system of equations. A sparse and decoupled system is obtained that provides remarkable benefits in terms of speed, memory consumption and problem size that can be dealt with. The technique is thoroughly validated through the statistical analysis of two canonical structures, i.e. a ribbon cable and a shielded cable with random geometry and position.
Highlights
Cable bundles are commonly employed in a variety of critical applications, including medical, industrial and aerospace equipment
Electromagnetic compatibility (EMC) studies comprise the statistical assessment of the coupling occurring in wire bundles with random parameters [1]–[10]
It allows to obtain stochastic information concerning the cable response, like for example the crosstalk between the wires. This is achieved through the simulation of an equivalent, deterministic cable with augmented p.u.l. matrices, which are constructed from the PCE coefficients of the capacitance and inductance matrices [13]
Summary
Cable bundles are commonly employed in a variety of critical applications, including medical, industrial and aerospace equipment. The calculation of the PC-expansion (PCE) coefficients of the p.u.l. capacitance and inductance matrices for random cables was addressed in [16]. A deterministic system of equations for the PCE coefficients is constructed by applying a stochastic Galerkin method (SGM) [17] to the classical numerical schemes for circular conductors [18]–[20], and solved by standard linear system inversion. The rest of the paper is organized as follows: Section 2 briefly recalls the deterministic numerical scheme for the calculation of the p.u.l. capacitance and inductance matrices for circular wires.
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