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Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems

Journal Article · · International Journal for Uncertainty Quantification
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. University of Greifswald (Germany)
+ Show Author Affiliations
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. In this work, 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. Finally, we compare the two approaches using a test example from a mechanical application.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1496998
Report Number(s):
SAND--2018-10420J; 672091
Journal Information:
International Journal for Uncertainty Quantification, Journal Name: International Journal for Uncertainty Quantification Journal Issue: 6 Vol. 8; ISSN 2152-5080
Publisher:
Begell HouseCopyright Statement
Country of Publication:
United States
Language:
English

Figures / Tables (8)

FIG. 1(p. 13)figure FIG. 1
FIG. 2(p. 14)figure FIG. 2
FIG. 3(p. 15)figure FIG. 3
FIG. 4(p. 15)figure FIG. 4
FIG. 5(p. 16)figure FIG. 5
FIG. 6(p. 16)figure FIG. 6
FIG. 7(p. 17)figure FIG. 7
FIG. 8(p. 18)figure FIG. 8

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Related Subjects

97 MATHEMATICS AND COMPUTING
least squares problem
linear dynamical system
orthogonal basis
orthogonal matching pursuit
polynomial chaos
random variable
stochastic Galerkin method
uncertainty quantification