ライブラリ登録: Guest
Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集
International Journal for Uncertainty Quantification
インパクトファクター: 4.911 5年インパクトファクター: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 印刷: 2152-5080
ISSN オンライン: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018026902
pages 495-510

TIME AND FREQUENCY DOMAIN METHODS FOR BASIS SELECTION IN RANDOM LINEAR DYNAMICAL SYSTEMS

John D. Jakeman
Sandia National Laboratories, Albuquerque, NM, USA
Roland Pulch
Institute for Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Str. 47, D-17489 Greifswald, Germany

要約

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.


Articles with similar content:

A GRADIENT-BASED SAMPLING APPROACH FOR DIMENSION REDUCTION OF PARTIAL DIFFERENTIAL EQUATIONS WITH STOCHASTIC COEFFICIENTS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 1
Miroslav Stoyanov, Clayton G. Webster
EFFECTIVE SAMPLING SCHEMES FOR BEHAVIOR DISCRIMINATION IN NONLINEAR SYSTEMS
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 6
Gregery T. Buzzard, Vu Dinh, Ann E. Rundell
MACHINE LEARNING FOR TRAJECTORIES OF PARAMETRIC NONLINEAR DYNAMICAL SYSTEMS
Journal of Machine Learning for Modeling and Computing, Vol.1, 2020, issue 1
Maha Youssef, Roland Pulch
STOCHASTIC DESIGN AND CONTROL IN RANDOM HETEROGENEOUS MATERIALS
International Journal for Multiscale Computational Engineering, Vol.9, 2011, issue 4
Phaedon-Stelios Koutsourelakis, Raphael Sternfels
HOMOGENIZATION OF FIBER-REINFORCED COMPOSITES WITH RANDOM PROPERTIES USING THE LEAST-SQUARES RESPONSE FUNCTION APPROACH
International Journal for Multiscale Computational Engineering, Vol.9, 2011, issue 3
Marcin Kaminski