Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem

TL;DR

This paper explores sparse polynomial chaos expansions and model order reduction techniques to efficiently quantify uncertainty in a coupled electric circuit and electromagnetic field model.

Contribution

It introduces methods for sparse polynomial chaos representations and applies proper orthogonal decomposition for model reduction in coupled field-circuit problems.

Findings

Sparse polynomial chaos can accurately approximate uncertain quantities with few basis polynomials.

Model order reduction via proper orthogonal decomposition reduces computational complexity.

The combined approach enhances efficiency in uncertainty quantification for coupled systems.

Abstract

We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing physical parameters into random variables. A random quantity of interest is expanded into the (generalised) polynomial chaos using orthogonal basis polynomials. We investigate the determination of sparse representations, where just a few basis polynomials are required for a sufficiently accurate approximation. Furthermore, we apply model order reduction with proper orthogonal decomposition to obtain a low-dimensional representation in an alternative basis.