Subset simulation

About: Subset simulation is a research topic. Over the lifetime, 401 publications have been published within this topic receiving 10632 citations.

Reliability-based design optimization using kriging surrogates and subset simulation

Abstract: The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probable-failure-point-based approaches do not permit to quantify the error on the estimation of the failure probability, an approach based on both metamodels and advanced simulation techniques is explored. The kriging metamodeling technique is chosen in order to surrogate the performance functions because it allows one to genuinely quantify the surrogate error. The surrogate error onto the limit-state surfaces is propagated to the failure probabilities estimates in order to provide an empirical error measure. This error is then sequentially reduced by means of a population-based adaptive refinement technique until the kriging surrogates are accurate enough for reliability analysis. This original refinement strategy makes it possible to add several observations in the design of experiments at the same time. Reliability and reliability sensitivity analyses are performed by means of the subset simulation technique for the sake of numerical efficiency. The adaptive surrogate-based strategy for reliability estimation is finally involved into a classical gradient-based optimization algorithm in order to solve the RBDO problem. The kriging surrogates are built in a so-called augmented reliability space thus making them reusable from one nested RBDO iteration to the other. The strategy is compared to other approaches available in the literature on three academic examples in the field of structural mechanics.

Subset simulation and its application to seismic risk based on dynamic analysis

Abstract: A method is presented for efficiently computing small failure probabilities encountered in seismic risk problems involving dynamic analysis. It is based on a procedure recently developed by the writers called Subset Simulation in which the central idea is that a small failure probability can be expressed as a product of larger conditional failure probabilities, thereby turning the problem of simulating a rare failure event into several problems that involve the conditional simulation of more frequent events. Markov chain Monte Carlo simulation is used to efficiently generate the conditional samples, which is otherwise a nontrivial task. The original version of Subset Simulation is improved by allowing greater flexibility for incorporating prior information about the reliability problem so as to increase the efficiency of the method. The method is an effective simulation procedure for seismic performance assessment of structures in the context of modern performance-based design. This application is illustrated by considering the failure of linear and nonlinear hysteretic structures subjected to uncertain earthquake ground motions. Failure analysis is also carried out using the Markov chain samples generated during Subset Simulation to yield information about the probable scenarios that may occur when the structure fails.