Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

Blatman, Géraud and Bruno Sudret

Reliability Engineering and System Safety, 2010, vol. 95, issue 11, 1216-1229

Abstract: Global sensitivity analysis aims at quantifying the relative importance of uncertain input variables onto the response of a mathematical model of a physical system. ANOVA-based indices such as the Sobol’ indices are well-known in this context. These indices are usually computed by direct Monte Carlo or quasi-Monte Carlo simulation, which may reveal hardly applicable for computationally demanding industrial models. In the present paper, sparse polynomial chaos (PC) expansions are introduced in order to compute sensitivity indices. An adaptive algorithm allows the analyst to build up a PC-based metamodel that only contains the significant terms whereas the PC coefficients are computed by least-square regression using a computer experimental design. The accuracy of the metamodel is assessed by leave-one-out cross validation. Due to the genuine orthogonality properties of the PC basis, ANOVA-based sensitivity indices are post-processed analytically. This paper also develops a bootstrap technique which eventually yields confidence intervals on the results. The approach is illustrated on various application examples up to 21 stochastic dimensions. Accurate results are obtained at a computational cost 2–3 orders of magnitude smaller than that associated with Monte Carlo simulation.

Keywords: Global sensitivity analysis; Sobol’ indices; ANOVA; Sequential experimental design; Sparse polynomial chaos; Stepwise regression (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (48)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0951832010001493
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:95:y:2010:i:11:p:1216-1229

DOI: 10.1016/j.ress.2010.06.015

Access Statistics for this article

Reliability Engineering and System Safety is currently edited by Carlos Guedes Soares

More articles in Reliability Engineering and System Safety from Elsevier
Bibliographic data for series maintained by Catherine Liu ().