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Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion

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  • Dubreuil, S.
  • Berveiller, M.
  • Petitjean, F.
  • Salaün, M.

Abstract

Sensitivity analysis aims at quantifying influence of input parameters dispersion on the output dispersion of a numerical model. When the model evaluation is time consuming, the computation of Sobol' indices based on Monte Carlo method is not applicable and a surrogate model has to be used. Among all approximation methods, polynomial chaos expansion is one of the most efficient to calculate variance-based sensitivity indices. Indeed, their computation is analytically derived from the expansion coefficients but without error estimators of the meta-model approximation. In order to evaluate the reliability of these indices, we propose to build confidence intervals by bootstrap re-sampling on the experimental design used to estimate the polynomial chaos approximation. Since the evaluation of the sensitivity indices is obtained with confidence intervals, it is possible to find a design of experiments allowing the computation of sensitivity indices with a given accuracy.

Suggested Citation

  • Dubreuil, S. & Berveiller, M. & Petitjean, F. & Salaün, M., 2014. "Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 263-275.
    • Handle: RePEc:eee:reensy:v:121:y:2014:i:c:p:263-275
    DOI: 10.1016/j.ress.2013.09.011
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    References listed on IDEAS

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    1. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    2. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    3. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    4. Rahman, Sharif, 2011. "Global sensitivity analysis by polynomial dimensional decomposition," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 825-837.
    5. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
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    Cited by:

    1. El Moçayd, Nabil & Seaid, Mohammed, 2021. "Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. El Moçayd, Nabil & Shadi Mohamed, M. & Ouazar, Driss & Seaid, Mohammed, 2020. "Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    3. Sun, Zhili & Wang, Jian & Li, Rui & Tong, Cao, 2017. "LIF: A new Kriging based learning function and its application to structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 152-165.
    4. Liu, Zicheng & Lesselier, Dominique & Sudret, Bruno & Wiart, Joe, 2020. "Surrogate modeling based on resampled polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    5. Oladyshkin, Sergey & Nowak, Wolfgang, 2018. "Incomplete statistical information limits the utility of high-order polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 137-148.

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