Uncertainty Quantification of Crosstalk Using Stochastic Reduced Order Models

This paper introduces a novel statistical method, referred to as the stochastic reduced order model (SROM) method, to predict the variability of cable crosstalk subject to a range of parametric uncertainties. The SROM method is a new member of the family of stochastic approaches to quantify propagated uncertainty in the presence of multiple uncertainty sources. It is nonintrusive, accurate, efficient, and stable, thus could be a promising alternative to some well-established methods, such as the Stochastic Galerkin and stochastic collocation (SC) methods. In this paper, the SROM method is successfully applied to obtain the statistics of cable crosstalk subject to single and multiple uncertainty sources. The statistics of uncertain cable parameters is first accurately approximated by SROM, i.e., pairs of very few samples with known probabilities, such that the uncertain input space is well represented. Then, a deterministic solver is used to produce the samples of cable crosstalk with the corresponding probabilities, and finally the uncertainty propagated to the crosstalk is quantified with good accuracy. Compared to the conventional Monte-Carlo simulation, the statistics of crosstalk obtained by the SROM method converge much faster by orders of magnitude. Also, the computational cost of the SROM method is shown to be small and can be tuned flexibly depending on the accuracy requirement. The SC method based on tensor product sampling strategy is also implemented to validate the efficacy of the SROM method.