Title: Combined importance sampling and separable Monte Carlo: analytical variance estimator and applications to structural reliability

Authors: Gabriele Capasso; Christian Gogu; Christian Bès; Jean-Philippe Navarro; Martin Kempeneers

Addresses: Université de Toulouse, CNRS, UPS, INSA, Mines Albi, ISAE-SUPAERO, Institut Clément Ader, Toulouse, France; Airbus Operations SAS, Toulouse, France ' Université de Toulouse, CNRS, UPS, INSA, Mines Albi, ISAE-SUPAERO, Institut Clément Ader, Toulouse, France ' Université de Toulouse, CNRS, UPS, INSA, Mines Albi, ISAE-SUPAERO, Institut Clément Ader, Toulouse, France ' Airbus Operations SAS, Toulouse, France ' Airbus Operations SAS, Toulouse, France

Abstract: In this paper, we derive a new analytical variance estimator for the probability of failure estimated by Separable Importance Sampling, allowing to analytically determine the number of samples required to reach a given coefficient of variation on the probability of failure. The proposed method can be applied in all reliability problems where response and capacity of a given system are independent. Numerical investigations have been conducted on two benchmark reliability problems. Thanks to this variance estimator we were able to carry out a large number of statistical simulations, allowing us to provide a comprehensive analysis of situations where Separable Importance Sampling would be most beneficial.

Keywords: reliability analysis; structural reliability; separable limit state; Monte Carlo methods; separable Monte Carlo; importance sampling; sampling methods; analytical variance estimator.

DOI: 10.1504/IJRS.2023.135679

International Journal of Reliability and Safety, 2023 Vol.17 No.3/4, pp.200 - 227

Received: 01 Sep 2022
Accepted: 05 Jun 2023
Published online: 21 Dec 2023 *

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