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Computing derivative-based global sensitivity measures using polynomial chaos expansions

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  • Sudret, B.
  • Mai, C.V.

Abstract

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol׳ indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol׳ indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSMs) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis.

Suggested Citation

  • Sudret, B. & Mai, C.V., 2015. "Computing derivative-based global sensitivity measures using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 241-250.
    • Handle: RePEc:eee:reensy:v:134:y:2015:i:c:p:241-250
    DOI: 10.1016/j.ress.2014.07.009
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    References listed on IDEAS

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