Uncertainty Quantification of Crosstalk Using Stochastic Reduced Order Models

Abstract

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 non-intrusive, accurate, efficient, and stable, thus could be a promising alternative to some well-established methods such as the stochastic Galerkin (SG) 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 are first accurately approximated by SROMs, 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 (MC) 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.

Towards a common vocabulary for describing the accuracy of computational electromagnetics models and comparisons with measurements

“…Providing probability distributions for such inputs can enable simulation results to be similarly expressed in terms of probability distributions rather than single values (e.g. [26]), but these should not be confused with the probability distributions that represent the precision or uncertainty (combining precision and estimated bias) of measurements.…”

Machine-Learning-Based Hybrid Random-Fuzzy Uncertainty Quantification for EMC and SI Assessment

“…Even in relatively simple test setups several parameters are inherently unknown and/or hard to control. For these reasons, advanced statistical techniques have recently been applied to EMC and SI problems [1], [2], [3], [4], [5], [6], [7] with the objective to outperform the standard brute-force approach, based on Monte Carlo (MC) repeated simulations, in terms of computational efficiency, while retaining comparable accuracy in predicting the variability of the output variables.…”

Stochastic reduced-order models for stable nonlinear ordinary differential equations

“…It has been shown that for static problems the SROM-based method can be improved significantly [37], and an adaptive method to further refine SROMs used in solving stochastic equations was proposed in [38]. Recently, SROMs have already been used successfully in applications for the quantification of the uncertainty in electromagnetic-signals interference in cables [39], or in the inter-granular corrosion rates [40]. SROMs have also been used in solving inverse problems, with applications in the identification of material properties in elastodynamics [41], traditionally solved using Bayesian inferences or stochastic-optimisation approaches.…”