Structural reliability sensitivity analysis method based on Markov Chain Monte Carlo subset simulation

Based on subset simulation for reliability analysis with small failure probability, a novel reliability sensitivity (RS) algorithm, Markov Chain Monte Carlo (MCMC) based subset simulation, is presented. By introducing a set of intermediate failure events in the subset simulation method, the original variable space is separated into a sequence of subsets. And then the small failure probability can be expressed as a product of larger conditional failure probabilities, which indicates the possibility of turning a rare failure event simulation problem into several more frequent event conditional simulation problems. MCMC simulation is implemented to efficiently generate conditional samples for estimating the conditional failure probabilities. Using the failure probability formula of the subset simulation, the RS of the failure probability with respect to the distribution parameter of the basic variable is transformed as that of a set of conditional failure probabilities with respect to the distribution parameter of the basic variable. By use of the conditional samples, a procedure is established to estimate the RS of the conditional failure probabilities, and estimate the RS of the failure probability finally. The results of the illustrations show that the presented RS algorithm is efficient and precise, and the presented algorithm is suitable for highly nonlinear limit state equation.