Reliability sensitivity analysis with multiple failure domains based on an extended two-stage Markov chain Monte Carlo simulation

Understanding how input variables affect the failure of structures is crucial in structural reliability design. The Reliability Sensitivity Index (RSI) based on Safety/failure Classification of model output (StarComp) quantifies the impact of these uncertain inputs on structural failure. The two-stage Markov Chain Monte Carlo (MCMC) algorithm is efficient for estimating the StarComp RSI, but it only works for problems with a single failure domain. This work extends the two-stage MCMC algorithm to handle problems with multiple disjoint failure domains. In the first stage, initial failure samples in different failure domains are obtained with multiple independent chains. Then, the second stage runs multiple independent Markov chains to sample the failure-conditional PDF. A set of weights is also constructed to obtain a proper estimation of the StarComp RSI. The proposed approach can effectively identify many failure domains with more chains and handle high-dimensional problems with the preconditioned Crank–Nicolson algorithm. It also works for single or overlapping failure domains. Three numerical examples with varying numbers of failure domains and dimensions, and an engineering example of vehicle side impact, are used to test the performance of the proposed approach. The results show that the proposed approach can capture multiple failure domains and obtain correct reliability sensitivity estimates compared to the original approach. It also outperforms subset simulation in computational accuracy and efficiency. With the proposed approach, useful information can be obtained to guide the reliability design of complex structures with multiple failure domains.