An efficient method for estimating global reliability sensitivity indices

Abstract

Global reliability sensitivity index, defined as the average absolute difference between the original probability density function (PDF) of input and the conditional one on the failure event, can measure the effect of input on the failure probability and provide information for the safety design. However, efficiently estimating the global reliability sensitivity index is still a challenge for engineering structures with rare failure events and implicit complex limit state functions. Thus, a novel method by combining the dynamic Kriging with Monte Carlo simulation (abbreviated as DK-MCS) is proposed for addressing this issue. The novelty of DK-MCS is twofold. One advantage is that the DK model is inserted in MCS process for accurately recognizing failure samples from all MCS samples by the iteratively updated DK model instead of the actual implicit limit state function, thus the computational cost of DK-MCS is significantly less than that of MCS while the precision of DK-MCS is the same as that of MCS. The other is that a new criteria is presented for selecting informative training points to effectively refine the DK model, where the informative training points with the largest contribution to the failure probability are selected by the cross validation method. Therefore, the iteration process for building the DK model can converge more rapidly. Several examples demonstrate the proposed DK-MCS method can greatly save computational cost of estimating the global reliability sensitivity indices and keep the same precision as MCS.