A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models

By B. Echard, Nicolas Gayton, Maurice Lemaire, N. Relun. Reliability Engineering & System Safety, 2013

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LIF: A new Kriging based learning function and its application to structural reliability analysis (2017, background): “Various kinds of sequential DoE based on the Kriging model have been proposed to improve the accuracy of structural reliability analysis and reduce the number of calls to the real performance function [8,29,32,38,41,42].”
Active learning for structural reliability: Survey, general framework and benchmark (2021, methodology): “For instance, replacing the Monte Carlo simulation part of the algorithm with importance sampling or subset simulation leads respectively to AK-IS (Echard et al., 2013) or AK-SS (Huang et al., 2016).”
Polynomial-Chaos-based Kriging (2015, neutral): “This characteristics is exploited when devising adaptive experimental designs in structural reliability analysis, see [42, 46, 82, 83].”
Rare event estimation with sequential directional importance sampling (2022, methodology): “Existing methods in the literature can be categorized into four types: approximate analytical methods [2, 3], moment-based methods [4-8], surrogate-assisted methods [9-13] and numerical simulation methods [14-16].”