Reliability sensitivity analysis based on a two-stage Markov chain Monte Carlo simulation

The reliability sensitivity index based on the safety/failure classification of model predictions is a valuable tool to measure how uncertain parameters affect the failure of engineering systems. The key to estimate this index is to estimate the failure-conditional probability density function (PDF) of parameters, which can be regarded as a posterior PDF from the perspective of Bayesian inference. Due to the binary property of the failure indicator function, it is difficult to directly sample the failure-conditional PDF. In this work, a new efficient sampling method is proposed to estimate the failure-conditional PDF and the reliability sensitivity index through a two-stage Markov chain Monte Carlo (MCMC) simulation. In the first stage, a different criterion based on the distance to the failure domain is adopted to update the chain and finally get a first sample in the failure domain. Then, starting with this sample, a normal Markov chain is run in the second stage to simulate the failure-conditional PDF and estimate the reliability sensitivity index. The preconditioned Crank-Nicolson algorithm (a special MCMC method) is adopted to deal with high-dimensional problems (with many uncertain parameters), and adaptive parameter tuning is used to enhance the performance of the proposed two-stage MCMC method. Several test examples show the high efficiency of the proposed two-stage MCMC method compared to subset simulation. The method is currently designed for problems with a single failure domain, yet it could be extended.