Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- University of Greifswald (Germany)
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 Lab. (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, Vol. 8, Issue 6; ISSN 2152-5080
- Publisher:
- Begell HouseCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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