Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem
For engineers modeling coupled electromagnetic-circuit systems, this work provides a method to reduce computational cost in uncertainty quantification, though it is an incremental application of existing techniques to a specific problem.
The paper addresses uncertainty quantification in a coupled field-circuit problem by using sparse polynomial chaos expansions and model order reduction to achieve accurate approximations with fewer basis functions.
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.