Sequential importance sampling for structural reliability analysis

• We develop an adaptive simulation method for reliability analysis based on sequential importance sampling.
• The method samples a sequence of distributions that gradually approach the optimal importance sampling density.
• We propose two MCMC algorithms for sampling the intermediate distributions.
• We demonstrate accuracy and efficiency of the method in low and high dimensional component and system problems.

This paper proposes the application of sequential importance sampling (SIS) to the estimation of the probability of failure in structural reliability. SIS was developed originally in the statistical community for exploring posterior distributions and estimating normalizing constants in the context of Bayesian analysis. The basic idea of SIS is to gradually translate samples from the prior distribution to samples from the posterior distribution through a sequential reweighting operation. In the context of structural reliability, SIS can be applied to produce samples of an approximately optimal importance sampling density, which can then be used for estimating the sought probability. The transition of the samples is defined through the construction of a sequence of intermediate distributions. We present a particular choice of the intermediate distributions and discuss the properties of the derived algorithm. Moreover, we introduce two MCMC algorithms for application within the SIS procedure; one that is applicable to general problems with small to moderate number of random variables and one that is especially efficient for tackling high-dimensional problems.