Probabilistic safety model and its efficient solution for structure with random and interval mixed uncertainties

Random and interval mixed uncertainties (RIMU) universally exist in engineering, thus it is necessary to construct a reasonable model for analyzing the probabilistic safety degree in this case. Aiming at analyzing the probabilistic safety degree efficiently, the existing double-loop nested optimization (DLNO) algorithm for estimating the upper and lower bounds of failure probability (FP) is firstly investigated under RIMU. It is proved that the upper and lower bounds of FP obtained by DLNO actually equal to the maximum and minimum of all approximate FPs with respect to the possible discrete points of interval variables. Secondly, it is found that the failure domain corresponding to the upper bound of FP is similar to that of time-dependent reliability under random uncertainty. Based on this similarity, the inequality relations are established for the real upper and lower bounds of FP and those obtained by DLNO, and the Kriging surrogate model methods are proposed to solve probabilistic safety model under RIMU efficiently. Additionally, this efficient solution strategy is further extended to the time-dependent structure under RIMU. Finally, numerical and engineering examples are used to demonstrate the reasonability and efficiency of proposed methods.