Abstract Reliability analysis for structural systems with multiple failure modes and expensive-to-evaluate simulations is challenging. In this paper, a new and efficient system reliability method is proposed based on the adaptive importance sampling and kriging models. The Metropolis–Hastings (M–H) algorithm is used to construct several Markov chains to fully explore complex failure regions. A number of Markov chain states are selected as the center of the component importance sampling functions to generate samples for reliability analysis. Based on the component importance sampling function of each selected chain state, the system importance sampling function is constructed with the weighting index. The system importance sampling function can be constructed effectively because it does not involve time-consuming simulations and the most probable point (MPP) search. The new learning function, which is directly linked to the system failure probability, is developed to adaptively select the best added samples for refining the kriging models at each iteration. The adaptive importance sampling method and kriging models are well-combined for system reliability analysis in the proposed method. Compared with existing methods, the proposed method, generally, offers the following advantages: (1) The learning function and stopping criterion are directly linked to system failure probability; (2)the adaptive importance sampling and kriging models are well-combined to yield accurate results based on a small sample size for small failure probability problems; (3) the weights of sampling centers are considered, and the MPP search is not required at each iteration; (4) it is applicable for complex systems regardless of the structure and system failure probability level. Three numerical examples are analyzed, which demonstrate that the proposed method is effective for complex system reliability analysis.

中文翻译：

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自适应重要性抽样与代理模型相结合的小故障概率问题可靠性新方法

摘要 具有多种失效模式和昂贵的模拟评估结构系统的可靠性分析具有挑战性。在本文中，基于自适应重要性采样和克里金模型，提出了一种新的、高效的系统可靠性方法。Metropolis-Hastings (M-H) 算法用于构建多个马尔可夫链以充分探索复杂的故障区域。选取多个马尔可夫链状态作为组件重要性采样函数的中心，生成用于可靠性分析的样本。基于每个选定链状态的组件重要性采样函数，构建系统重要性采样函数，并带有权重指标。系统重要性采样函数可以有效构建，因为它不涉及耗时的模拟和最可能点（MPP）搜索。新的学习函数与系统故障概率直接相关，它被开发来自适应地选择最佳添加样本，以在每次迭代时细化克里金模型。在该方法中，自适应重要性采样方法和克里金模型很好地结合用于系统可靠性分析。与现有方法相比，所提出的方法总体上具有以下优点： (1) 学习函数和停止准则与系统故障概率直接相关；(2)自适应重要性采样和克里金模型结合得很好，基于小样本量，对于小故障概率问题产生准确的结果；(3)考虑了采样中心的权重，不需要每次迭代都进行MPP搜索；(4) 适用于复杂系统，无论其结构和系统故障概率水平如何。对三个数值算例进行了分析，表明该方法对复杂系统可靠性分析是有效的。