Combined Importance Sampling and Separable Monte Carlo: Analytical Variance Estimator and applications to Structural Reliability
Résumé
This paper considers reliability analysis problems where the limit state function, characterizing the failure domain, can be expressed in terms of two independent components: response and capacity. An approach called Separable Importance Sampling has been proposed in the literature as an extension of Importance Sampling, allowing improved sampling efficiency due to separable sampling of response and capacity. 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. 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 numerical experiments, allowing us to provide a comprehensive analysis of situations where Separable Importance Sampling would be most beneficial.
Mots clés
reliability analysis structural reliability separable limit state Monte Carlo methods separable Monte Carlo importance sampling sampling methods analytical variance estimator
reliability analysis
structural reliability
separable limit state
Monte Carlo methods
separable Monte Carlo
importance sampling
sampling methods
analytical variance estimator
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Licence : Copyright (Tous droits réservés)