Kernel method in Monte Carlo importance sampling

A new approach to evaluate the reliability of structural systems using a Monte Carlo variance reduction technique called the Importance Sampling is presented. Since the efficiency of the importance sampling method depends primarily on the choice of the importance sampling density, the use of the kernel method to estimate the optimal importance sampling density is proposed.; The first step in implementing the proposed method involves generating samples from the original distribution. The kernel sampling density is then constructed using these samples. A second set of samples is then generated from the kernel sampling density, and the failure probability is estimated by taking the average of the two sets of samples.; A number of example problems were examined to illustrate the application of the proposed kernel method. The method was shown to be more efficient than the basic Monte Carlo method and yielded unbiased probability of failure estimates. It was demonstrated to perform better than the adaptive sampling method. The method was also shown to be versatile because it can be applied to problems with very complex performance functions that can not be expressible in explicit form, and to produce unbiased estimate of the failure probability even in problems with multiple failure modes. In problems with large number of random variables, the efficiency of the kernel method increased after treating the unimportant random variables as constants.