Abstract 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.

中文翻译：

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具有随机和区间混合不确定性的结构的概率安全模型及其有效解决方案

摘要 随机和区间混合不确定性（RIMU）在工程中普遍存在，因此有必要构建一个合理的模型来分析这种情况下的概率安全度。为了有效地分析概率安全度，首先研究了RIMU下现有的用于估计故障概率（FP）上下界的双环嵌套优化（DLNO）算法。证明了DLNO得到的FP的上下界实际上等于所有近似FP对于区间变量可能的离散点的最大值和最小值。其次，发现FP上界对应的失效域与随机不确定性下的瞬态可靠性相似。基于这种相似性，建立了FP的真实上下界和DLNO得到的不等式关系，并提出了克里金代理模型方法来有效求解RIMU下的概率安全模型。此外，这种高效的求解策略进一步扩展到 RIMU 下的时间相关结构。最后，通过数值和工程实例证明了所提出方法的合理性和有效性。