A new efficient simulation method based on Bayes' theorem and importance sampling Markov chain simulation to estimate the failure-probability-based global sensitivity measure

The failure-probability-based global sensitivity measure can detect the effect of input variables on the structural failure probability, which can provide useful information in reliability-based design. In this paper, a new efficient simulation method is proposed to estimate the failure-probability-based global sensitivity measure. The proposed method is based on the Bayes' theorem and importance sampling Markov chain simulation. The Bayes' theorem is used to provide a single-loop simulation method and the importance sampling Markov chain simulation is used to further reduce the computational cost. Compared to the traditional double-loop Monte Carlo simulation method, the proposed method requires only a single set of samples to estimate the failure-probability-based global sensitivity measure and its computational cost does not depend on the dimensionality of input variables. Finally, one numerical example and two engineering examples are presented to illustrate the accuracy and efficiency of the proposed method.