期刊
RELIABILITY ENGINEERING & SYSTEM SAFETY
卷 93, 期 7, 页码 964-979出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.ress.2007.04.002
关键词
global sensitivity analysis; Sobol' indices; analysis of variance; polynomial chaos; generalized chaos; regression; stochastic finite elements
Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol' indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression- based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2-3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol' indices. (C) 2007 Elsevier Ltd. All rights reserved.
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