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Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design

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  • Pronzato, Luc

Abstract

We use the Karhunen–Loève expansion of a random-field model to construct a tensorised Bayesian linear model from which Sobol’ sensitivity indices can be estimated straightforwardly. The method combines the advantages of models built from families of orthonormal functions, which facilitate computations, and Gaussian-process models, which offer a lot of flexibility. The posterior distribution of the indices can be derived, and its normal approximation can be used to design experiments especially adapted to their estimation. Implementation details are provided, and values of tuning parameters are indicated that yield precise estimation from a small number of function evaluations. Several illustrative examples are included that show the good performance of the method, in particular in comparison with estimation based on polynomial chaos expansion.

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  • Pronzato, Luc, 2019. "Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 93-109.
    • Handle: RePEc:eee:reensy:v:187:y:2019:i:c:p:93-109
    DOI: 10.1016/j.ress.2018.01.010
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    1. Marrel, Amandine & Iooss, Bertrand & Laurent, Béatrice & Roustant, Olivier, 2009. "Calculations of Sobol indices for the Gaussian process metamodel," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 742-751.
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    6. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    7. Durrande, N. & Ginsbourger, D. & Roustant, O. & Carraro, L., 2013. "ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 57-67.
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    Cited by:

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    2. Zhao, Yunjie & Cheng, Xi & Zhang, Taihong & Wang, Lei & Shao, Wei & Wiart, Joe, 2023. "A global–local attention network for uncertainty analysis of ground penetrating radar modeling," Reliability Engineering and System Safety, Elsevier, vol. 234(C).

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