IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4357-d1263748.html
   My bibliography  Save this article

Local Sensitivity of Failure Probability through Polynomial Regression and Importance Sampling

Author

Listed:
  • Marie Chiron

    (ONERA/DTIS, Université de Toulouse, F-31055 Toulouse, France)

  • Jérôme Morio

    (ONERA/DTIS, Université de Toulouse, F-31055 Toulouse, France)

  • Sylvain Dubreuil

    (ONERA/DTIS, Université de Toulouse, F-31055 Toulouse, France)

Abstract

Evaluating the failure probability of a system is essential in order to assess its reliability. This probability may significantly depend on deterministic parameters such as distribution parameters or design parameters. The sensitivity of the failure probability with regard to these parameters is then critical for the reliability analysis of the system or in reliability-based design optimization. Here, we introduce a new approach to estimate the failure probability derivatives with respect to deterministic inputs, where the bias can be controlled and the simulation budget is kept low. The sensitivity estimate is obtained as a byproduct of a heteroscedastic polynomial regression with a database built with simulation methods. The polynomial comes from a Taylor series expansion of the approximated sensitivity domain integral obtained with the Weak approach. This new methodology is applied to two engineering use cases with the importance sampling strategy.

Suggested Citation

  • Marie Chiron & Jérôme Morio & Sylvain Dubreuil, 2023. "Local Sensitivity of Failure Probability through Polynomial Regression and Importance Sampling," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4357-:d:1263748
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4357/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4357/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    2. Rubinstein, Reuven Y., 1986. "The score function approach for sensitivity analysis of computer simulation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(5), pages 351-379.
    3. Proppe, Carsten, 2021. "Local reliability based sensitivity analysis with the moving particles method," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    4. Torii, André Jacomel & Novotny, Antonio André, 2021. "A priori error estimates for local reliability-based sensitivity analysis with Monte Carlo Simulation," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    5. Song, Shufang & Lu, Zhenzhou & Qiao, Hongwei, 2009. "Subset simulation for structural reliability sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 658-665.
    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. Marrel, Amandine & Chabridon, Vincent, 2021. "Statistical developments for target and conditional sensitivity analysis: Application on safety studies for nuclear reactor," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    2. Chabridon, Vincent & Balesdent, Mathieu & Bourinet, Jean-Marc & Morio, Jérôme & Gayton, Nicolas, 2018. "Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 164-178.
    3. R. M. Balan & Ioana Schiopu-Kratina, 2004. "Asymptotic Results with Generalized Estimating Equations for Longitudinal data II," RePAd Working Paper Series lrsp-TRS398, Département des sciences administratives, UQO.
    4. Norbert Christopeit & Michael Massmann, 2013. "A Note on an Estimation Problem in Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-151/III, Tinbergen Institute.
    5. Bakeer, Tammam, 2023. "General partial safety factor theory for the assessment of the reliability of nonlinear structural systems," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    6. Wenxuan Wang & Hangshan Gao & Pengfei Wei & Changcong Zhou, 2017. "Extending first-passage method to reliability sensitivity analysis of motion mechanisms," Journal of Risk and Reliability, , vol. 231(5), pages 573-586, October.
    7. Zio, E. & Pedroni, N., 2012. "Monte Carlo simulation-based sensitivity analysis of the model of a thermal–hydraulic passive system," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 90-106.
    8. Yuan-chin Chang, 2011. "Sequential estimation in generalized linear models when covariates are subject to errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(1), pages 93-120, January.
    9. Rubinstein, Reuven Y., 1991. "Modified importance sampling for performance evaluation and sensitivity analysis of computer simulation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 33(1), pages 1-22.
    10. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    11. Jiang, Chen & Qiu, Haobo & Yang, Zan & Chen, Liming & Gao, Liang & Li, Peigen, 2019. "A general failure-pursuing sampling framework for surrogate-based reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 47-59.
    12. Keshtegar, Behrooz & Chakraborty, Subrata, 2018. "An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 195-206.
    13. El Masri, Maxime & Morio, Jérôme & Simatos, Florian, 2021. "Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    14. Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2019. "Exponential structure of income inequality: evidence from 67 countries," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 345-376, June.
    15. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Shi, Congling, 2016. "Connectivity reliability and topological controllability of infrastructure networks: A comparative assessment," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 24-33.
    16. Jin Zhang, 2020. "Consistency of MLE, LSE and M-estimation under mild conditions," Statistical Papers, Springer, vol. 61(1), pages 189-199, February.
    17. Zhao, Enyong & Wang, Qihan & Alamdari, Mehrisadat Makki & Gao, Wei, 2023. "Advanced virtual model assisted most probable point capturing method for engineering structures," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    18. Norbert Christopeit & Michael Massmann, 2010. "Consistent Estimation of Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 10-077/4, Tinbergen Institute.
    19. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    20. Xu, Jun & Kong, Fan, 2018. "A new unequal-weighted sampling method for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 94-102.

    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:gam:jmathe:v:11:y:2023:i:20:p:4357-:d:1263748. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.