Estimation of failure probability-based-global-sensitivity using the theorem of Bayes and subset simulation

The failure probability-based-global-sensitivity can measure the effect of the uncertainty of model input on the failure probability of the structure or system. In this paper, a novel simulation method based on the theorem of Bayes and subset simulation is proposed to efficiently estimate the failure probability-based-global -sensitivity. In the proposed method, the unconditional failure probability is estimated by the efficient subset simulation through the estimation of the probability of a series of conditional failure domain. Then, based on the Bayes formula in the conditional failure domain involved in subset simulation, an equivalent transformation formula is derived for the conditional failure probability on fixed model inputs. Next, according to the deduced equivalent transformation formula and the failure samples obtained by the subset simulation, the conditional failure probability on arbitrary inputs realization can be directly computed without any extra model evaluations. Finally, the failure probability-based-global-sensitivity can be estimated by the unconditional failure probability acquired by the subset simulation and those conditional failure probabilities obtained by the proposed equivalent transformation formula. Additionally, the preconditioned Crank-Nicolson algorithm is used in the subset simulation and the interval approximation approach is employed in estimating the conditional failure probability so as to further improve the robustness of the proposed method.