A New Adaptive Importance Sampling Scheme for Reliability Calculations

An adaptive importance sampling methodology is proposed to compute the multidimensional integrals encountered in reliability analysis. In the proposed methodology, samples are simulated as the states of a Markov chain and are distributed asymptotically according to the optimal importance sampling density. A kernel sampling density is then constructed from these samples which is used as the sampling density in an importance sampling simulation. The Markov chain samples populate the region of higher probability density in the failure domain and so the kernel sampling density approximates the optimal importance sampling density for a large variety of shapes of the failure domain. This adaptive feature is insensitive to the probability level to be estimated. A numerical example demonstrates the accuracy, efficiency and robustness of the method.