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Local Sensitivity of Failure Probability through Polynomial Regression and Importance Sampling

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  • 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
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    References listed on IDEAS

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    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. 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).
    4. 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.
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