A new adaptive importance sampling scheme for reliability calculations

An adaptive importance sampling methodology is proposed to compute the mult idimensional integrals encountered in reliability analysis. It is based on a Markov simulation algorithm due to Metropolis et al. (Metropolis, Rosenbl uth, Rosenbluth and Teller, Equations of state calculatons by fast computin g machines. Journal of Chemical Physics, 1953;21(6): 1087-1092). In the pro posed methodology, samples are simulated as the states of a Markov chain an d are distributed asymptotically according to the optimal importance sampli ng density. A kernel sampling density is then constructed from these sample s which is used as the sampling density in an importance sampling simulatio n. The Markov chain samples populate the region of higher probability densi ty in the failure region and so the kernel sampling density approximates th e optimal importance sampling density for a large variety of shapes of the failure region. This adaptive feature is insensitive to the probability lev el to be estimated. A variety of numerical examples demonstrates the accura cy, efficiency and robustness of the methodology, (C) 1999 Elsevier Science Ltd. All rights reserved.