New importance sampling Markov chain simulation based reliability sensitivity method

Importance sampling has wide application as an efficient reliability analysis approach. On condition that the failure probability is analyzed by the importance sampling, a new method for the reliability sensitivity is presented on the basis of the importance sampling Markov Chain simulation. According to the integration form of the failure probability, the reliability sensitivity, measured by the partial differential of the failure probability with respect to the distribution parameter of the basic random variable, is transformed into an expectation of a feature function. Then, the importance sampling Markov Chain simulation is employed to generate the failure samples, called conditional samples, distributing as the conditional probability density function. At last, the average of the feature function values at these conditional samples is used to evaluate the conditional expectation and further complete the reliability sensitivity. Since a little computation cost is increased during the importance sampling procedure, the efficiency of the presented method is very high. Additionally, no hypothesis of the linear limit state equation is introduced in the construction of the presented method; hence, the effect of the non-linearity of the limit state equation can be accounted on the reliability sensitivity. A few examples illustrate the advantages of the presented method.