IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v94y2009i7p1161-1172.html
   My bibliography  Save this article

Polynomial chaos expansion for sensitivity analysis

Author

Listed:
  • Crestaux, Thierry
  • Le Maıˆtre, Olivier
  • Martinez, Jean-Marc

Abstract

In this paper, the computation of Sobol's sensitivity indices from the polynomial chaos expansion of a model output involving uncertain inputs is investigated. It is shown that when the model output is smooth with regards to the inputs, a spectral convergence of the computed sensitivity indices is achieved. However, even for smooth outputs the method is limited to a moderate number of inputs, say 10–20, as it becomes computationally too demanding to reach the convergence domain. Alternative methods (such as sampling strategies) are then more attractive. The method is also challenged when the output is non-smooth even when the number of inputs is limited.

Suggested Citation

  • Crestaux, Thierry & Le Maıˆtre, Olivier & Martinez, Jean-Marc, 2009. "Polynomial chaos expansion for sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1161-1172.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:7:p:1161-1172
    DOI: 10.1016/j.ress.2008.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832008002561
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2008.10.008?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. 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.
    2. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    3. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Mara, Thierry A. & Tarantola, Stefano, 2012. "Variance-based sensitivity indices for models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 115-121.
    3. Shahsavani, D. & Grimvall, A., 2009. "An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1173-1182.
    4. Gatelli, D. & Kucherenko, S. & Ratto, M. & Tarantola, S., 2009. "Calculating first-order sensitivity measures: A benchmark of some recent methodologies," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1212-1219.
    5. 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.
    6. 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.
    7. Plischke, Elmar, 2012. "An adaptive correlation ratio method using the cumulative sum of the reordered output," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 149-156.
    8. 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.
    9. Storlie, Curtis B. & Reich, Brian J. & Helton, Jon C. & Swiler, Laura P. & Sallaberry, Cedric J., 2013. "Analysis of computationally demanding models with continuous and categorical inputs," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 30-41.
    10. Mirko Ginocchi & Ferdinanda Ponci & Antonello Monti, 2021. "Sensitivity Analysis and Power Systems: Can We Bridge the Gap? A Review and a Guide to Getting Started," Energies, MDPI, vol. 14(24), pages 1-59, December.
    11. Helton, Jon C. & Johnson, Jay D. & Sallaberry, Cédric J., 2011. "Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1014-1033.
    12. Martorell, S. & Villamizar, M. & Martón, I. & Villanueva, J.F. & Carlos, S. & Sánchez, A.I., 2014. "Evaluation of risk impact of changes to surveillance requirements addressing model and parameter uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 153-165.
    13. Hao, Wenrui & Lu, Zhenzhou & Wei, Pengfei, 2013. "Uncertainty importance measure for models with correlated normal variables," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 48-58.
    14. Torossian, Léonard & Picheny, Victor & Faivre, Robert & Garivier, Aurélien, 2020. "A review on quantile regression for stochastic computer experiments," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    15. Deman, G. & Kerrou, J. & Benabderrahmane, H. & Perrochet, P., 2015. "Sensitivity analysis of groundwater lifetime expectancy to hydro-dispersive parameters: The case of ANDRA Meuse/Haute-Marne site," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 276-286.
    16. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    17. Hansen, C.W. & Behie, G.A. & Bier, A. & Brooks, K.M. & Chen, Y. & Helton, J.C. & Hommel, S.P. & Lee, K.P. & Lester, B. & Mattie, P.D. & Mehta, S. & Miller, S.P. & Sallaberry, C.J. & Sevougian, S.D. & , 2014. "Uncertainty and sensitivity analysis for the nominal scenario class in the 2008 performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 122(C), pages 272-296.
    18. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2020. "Margins associated with loss of assured safety for systems with multiple weak links and strong links," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    19. Helton, Jon C. & Hansen, Clifford W. & Sallaberry, Cédric J., 2012. "Uncertainty and sensitivity analysis in performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 44-63.
    20. Di Maio, Francesco & Bandini, Alessandro & Zio, Enrico & Alberola, Sofia Carlos & Sanchez-Saez, Francisco & Martorell, Sebastián, 2016. "Bootstrapped-ensemble-based Sensitivity Analysis of a trace thermal-hydraulic model based on a limited number of PWR large break loca simulations," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 122-134.

    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:94:y:2009:i:7:p:1161-1172. 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.