Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation

By Siu-Kui Au, James L. Beck. 2001

2,350 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/31959860c7bb06b93d1090ce0132e2cfe740f91a

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In Civil and Structural Engineering

In Statistics and Probability

Citations in the corpus

Conditional (2019, neutral): “To effectively accomplish face de-identification, we meticulously integrate multidimensional conditions to ensure the protection of individual identities while navigating the nuances of privacy preservation.”
Sequential design of computer experiments for the estimation of a probability of failure (2010, methodology): “…a host of refined random sampling methods have been proposed to improve over the basic Monte Carlo convergence rate; for instance, methods based on importance sampling with cross-entropy (Rubinstein and Kroese, 2004), subset sampling (Au and Beck, 2001) or line sampling (Pradlwarter et al., 2007).”
Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach (2012, methodology): “…the coefficient of variation of Pe computed by subset simulation was determined using the following equation: COVPe ¼ Xm j¼1 ½COVPðFjÞ 2 (12) where COVPðFjÞ is the coefficient of variation at an intermediate level j. Details on the computation of COVPðFjÞ may be found in Au and Beck (2001, 2003).”
Reliability-based design optimization using kriging surrogates and subset simulation (2011, methodology): “The nested reliability and reliability sensitivity analyses are performed with the subset simulation variance reduction technique (Au and Beck, 2001) onto the kriging surrogates.”
Energetic–statistical size effect simulated by SFEM with stratified sampling and crack band model (2007, background): “To compute the tolerable loads of such extremely low Pf, effective SFEMs for extreme value statistics have been developed; they include the ‘importance sampling’ [5, 7, 8], ‘subset simulation’ [9, 10], ‘line sampling’ [11], von Neumann’s ‘splitting’, ‘Russian roulette’ [11], etc.”
The stochastic finite element method: Past, present and future (2009, methodology): “In order to overcome the inefficiency of direct MCS in calculating small failure probabilities, a novel approach called subset simulation (SS) has been recently proposed [7].”