Asymptotic sampling for high-dimensional reliability analysis

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Active learning for structural reliability: Survey, general framework and benchmark (2021, methodology): “Faravelli (1989) uses a second-order polynomial while Bucher and Bourgund (1990) introduced a two-stage approach where a first quadratic response surface is used to locate the MPFP.”
Rare event estimation with sequential directional importance sampling (2022, methodology): “To improve the sampling efficiency, one can amplify the standard deviation of all the input variables [37-39], resulting in the following auxiliary failure probability”
MCMC algorithms for Subset Simulation (2015, methodology): “…of random variables, a number of advanced simulation methods have been developed, including Subset Simulation (Au & Beck 2001), Spherical Subset Simulation (Katafygiotis & Cheung 2007), Line Sampling (Hohenbichler & Rackwitz 1988, Koutsourelakis et al. 2004) and Asymptotic Sampling (Bucher 2009).”
A new adaptive response surface method for reliability analysis (2013, methodology): “In order to be independant of the dimension, it is proposed in [9,42,43,34] to keep a crude Monte Carlo method but to make use of the regularity of tail probabilities.”