SESC: A new subset simulation method for rare-events estimation

Abstract

A sequential space conversion (SESC) method is proposed to solve complex and high dimensional rare event problems. While the conventional Subset Simulation (SubSim) formulation is based on the Bayes theorem, that of the SESC is derived from the control variate technique. This approach first estimates a fast imprecise failure probability and then improves the estimation using refining terms. It designs a set of scaled limit state functions similar to the original one but with higher failure probabilities, then uses the set as the control variates, and, finally, conducts the Markov chain Monte Carlo samples toward the important failure region. Hence, unlike the conventional SubSim, the SESC performance does not depend on the geometry of the performance function away from the limit state surface. The reliability analysis of complex and high dimensional problems that involve several counterexamples of subset simulations shows that the proposed method is capable of solving problems with complex/misleading performance functions that cannot be solved with conventional SubSim or other existing approaches.