IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v121y2014icp263-275.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832013002688
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2013.09.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matieyendou Lamboni, 2020. "Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices," Statistical Papers, Springer, vol. 61(5), pages 1939-1970, October.
    2. Deman, G. & Konakli, K. & Sudret, B. & Kerrou, J. & Perrochet, P. & Benabderrahmane, H., 2016. "Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 156-169.
    3. Touzani, Samir & Busby, Daniel, 2013. "Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 67-81.
    4. Zhang, Xufang & Pandey, Mahesh D., 2014. "An effective approximation for variance-based global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 164-174.
    5. Matieyendou Lamboni, 2018. "Global sensitivity analysis: a generalized, unbiased and optimal estimator of total-effect variance," Statistical Papers, Springer, vol. 59(1), pages 361-386, March.
    6. Oladyshkin, S. & Nowak, W., 2012. "Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 179-190.
    7. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    8. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    9. Haro Sandoval, Eduardo & Anstett-Collin, Floriane & Basset, Michel, 2012. "Sensitivity study of dynamic systems using polynomial chaos," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 15-26.
    10. Becker, William, 2020. "Metafunctions for benchmarking in sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    11. Hu, Zhen & Mahadevan, Sankaran, 2019. "Probability models for data-Driven global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 40-57.
    12. Barry Anderson & Emanuele Borgonovo & Marzio Galeotti & Roberto Roson, 2014. "Uncertainty in Climate Change Modeling: Can Global Sensitivity Analysis Be of Help?," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 271-293, February.
    13. Konakli, Katerina & Sudret, Bruno, 2016. "Global sensitivity analysis using low-rank tensor approximations," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 64-83.
    14. Miftakhova, Alena, 2021. "Global sensitivity analysis for optimal climate policies: Finding what truly matters," Economic Modelling, Elsevier, vol. 105(C).
    15. Elmar Plischke & Emanuele Borgonovo, 2020. "Fighting the Curse of Sparsity: Probabilistic Sensitivity Measures From Cumulative Distribution Functions," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2639-2660, December.
    16. Garcia-Cabrejo, Oscar & Valocchi, Albert, 2014. "Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 25-36.
    17. S. Cucurachi & E. Borgonovo & R. Heijungs, 2016. "A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 357-377, February.
    18. Cheng, Kai & Lu, Zhenzhou, 2018. "Sparse polynomial chaos expansion based on D-MORPH regression," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 17-30.
    19. Zhai, Qingqing & Yang, Jun & Zhao, Yu, 2014. "Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 66-82.
    20. Lambert, Romain S.C. & Lemke, Frank & Kucherenko, Sergei S. & Song, Shufang & Shah, Nilay, 2016. "Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 42-54.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:121:y:2014:i:c:p:263-275. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.