Efficient global reliability sensitivity method by combining dimensional reduction integral with stochastic collocation

Defined as the mean square difference between unconditional failure probability (FP) and conditional FP on fixed input realization, global reliability sensitivity (GRS) can quantify the effect of random input on FP. For efficiently estimating the GRS, a novel method is proposed by combining truncated dimensional reduction integral with stochastic collocation (DRI-SC). In the DRI-SC, the unconditional and conditional FPs are equivalently converted into the expected cumulative distribution function (CDF) of a selected reduction input. Then, using the continuity of CDF, a truncated DRI is combined with SC to efficiently estimate the expected CDF. To further enhance the efficiency of DRI-SC, an adaptive Kriging model is trained to provide the integrand CDF values at the SC nodes. The novelties of the DRI-SC include deriving the unconditional and conditional FPs required by GRS as the expected CDF, designing an SC node-sharing strategy, and training the Kriging model in the SC node set. DRI-SC inherits the universality of numerical simulation but avoids its prohibitive computation, and the DRI-SC maintains the efficiency of the existing SC-based GRS methods but avoids the density fitting. The superiority of the DRI-SC over existing methods is verified by the presented examples.