Extension of AK-MCS for the efficient computation of very small failure probabilities

Nassim Razaaly and Pietro Marco Congedo

Reliability Engineering and System Safety, 2020, vol. 203, issue C

Abstract: We consider the problem of estimating a probability of failure pf, defined as the volume of the excursion set of a complex (e.g. output of an expensive-to-run finite element model) scalar performance function J below a given threshold, under a probability measure that can be recast as a multivariate standard gaussian law using an isoprobabilistic transformation. We propose a method able to deal with cases characterized by multiple failure regions, possibly very small failure probability pf (say ∼10−6−10−9), and when the number of evaluations of J is limited. The present work is an extension of the popular Kriging-based active learning algorithm known as AK-MCS, as presented in [1], permitting to deal with very low failure probabilities. The key idea merely consists in replacing the Monte-Carlo sampling, used in the original formulation to propose candidates and evaluate the failure probability, by a centered isotropic Gaussian sampling in the standard space, whose standard deviation is iteratively tuned. This extreme AK-MCS (eAK-MCS) inherits its former multi-point enrichment algorithm allowing to add several points at each iteration step, and provide an estimated failure probability based on the Gaussian nature of the Kriging surrogate.

Keywords: Tail probability; AK-MCS; Importance sampling; Risk analysis; Multiple failure regions; Low failure probability; Rare event (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:203:y:2020:i:c:s0951832020305858

DOI: 10.1016/j.ress.2020.107084

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