LAUSR

Abstract The small first passage probability of nonlinear dynamic structures under nonstationary seismic excitation implies a prohibitive computational demand because of the epistemic uncertainties rooted in structure system. In this work, a hybrid Kriging-high dimensional model representation (Kriging-HDMR) methodology for drastically simplifying this task is proposed. The epistemic uncertainties with well-defined bounds but no concrete distribution forms are addressed by interval model. Therefore, the first passage probability of the generic response process that the epistemic uncertainties involved, is represented by the conditional univariate extreme value distribution (EVD) of structural parameters with interval form. Then, a Kriging assisted HDMR together with third moment saddle point approximation (TMSA) is proposed to alleviate the computational burden and provides an accurate depiction of possible model outcome. The differential evolution (DE) interval optimization strategy is performed to accelerate the post process of searching the lower bound (LB) and upper bound (UB) of first passage probability with interval form. Finally, a nine-story shear frame with Bouc–Wen model is presented to demonstrate the accuracy and efficiency of proposed method.