Subset simulation method

Katafygiotis, L. 6c Cheung, S. 2007. Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study. Structural Safety 29(3), 194—207. 

Ching, J., Au, S-K. Beck, J.L. 2005b. Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation. Probabilistic Engineering Mechanics 20 199-214. 

Subset Simulation Method for Rare Event Estimation An Introduction... 

Some variants of the subset simulation method, which are based on splitting of trajectories, are as follows ... 

Different variance reduction strategies can be combined into a single framework so as to leverage advantages associated with each one of them. Thus, for example, the subset simulation method and the Girsanov transformation-based method can be combined in such a way that subset simulations handle the uncertainties associated with parameters, and the Girsanov transformation takes care of the random excitations (Sundar and Manohar 2014b). Performance of few simulation-based variance reduction techniques with respect to few benchmark problems has been documented by Schueller and Pradlwarter (2007). 

This section attempts to briefly introduce the main concepts of the subset simulation as an advanced stochastic simulation method for estimation of small probabilities corresponding to rare failure events. However, a detailed introductory description of methodology can be found in the chapter Subset Simulation Method for Rare Event Estimation An Introduction of the general section Reliability and Robustness of the Encyclopedia of Earthquake Engineering. 

Subset Simulation Method for Rare Event Estimation An Introduction, Fig. 1 Monte Carlo samples and the failure domain F. xq and Xo" are, respectively, the closest to failure and the safest samples among xj). .., xj," ... 

Subset Simulation Method for Rare Event Estimation An Introduction, Fig. 2 The first intermediate failure domain Fi. In this schematic illustration, n = 10, p = 0 2, so that there are exactly np = 2 Monte Carlo samples in FI, xj) xj > 6 fi... 

Subset Simulation Method for Rare Event Estimation An Introduction, Fig. 7 Failure probability pp versus the... 

Subset Simulation Method for Rare Event Estima- threshold is y = 200, and the corresponding true value tion An Introduction, Fig. 10 Performance of Subset of the failure probability is pp = 1.27 x 10 [Example... 

---