RT Journal Article
ID 5f8d70fa26e5d34a
A1 Jakeman, John D.
A1 Pulch, Roland
T1 TIME AND FREQUENCY DOMAIN METHODS FOR BASIS SELECTION IN RANDOM LINEAR DYNAMICAL SYSTEMS
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2018
FD 2018-10-24
VO 8
IS 6
SP 495
OP 510
K1 linear dynamical system
K1 random variable
K1 orthogonal basis
K1 polynomial chaos
K1 stochastic Galerkin method
K1 least squares problem
K1 orthogonal matching pursuit
K1 uncertainty quantification
AB Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore,
several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of
interest in a model, where just a few orthogonal basis polynomials are required. We consider linear dynamical systems consisting of ordinary differential equations with random variables. The aim of this paper is to explore methods for producing low-dimensional approximations of the quantity of interest further. We investigate two numerical techniques to compute a low-dimensional representation, which both fit the approximation to a set of samples in the time domain. On the one hand, a frequency domain analysis of a stochastic Galerkin system yields the selection of the basis polynomials. It follows a linear least squares problem. On the other hand, a sparse minimization yields the choice of the basis polynomials by information from the time domain only. An orthogonal matching pursuit produces an approximate solution of the minimization problem. We compare the two approaches using a test example from a mechanical application.

PB Begell House
LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,23dc16a4645b89c9,5f8d70fa26e5d34a.html