Abstract The stochastic uncertainties affecting the models used to describe the behavior of structural/mechanical systems may give rise to unfavorable scenarios leading to failures. In this framework, the quantification of the failure probability is a recognized fundamental task for structural safety and reliability analyses. Unfortunately, the estimation of the failure probability of structural/mechanical systems is a computationally demanding task, especially when the failure is a rare event and the computer codes used to model the system response require large computational efforts. One major issue further complicates the estimation process, i.e., the parameters of the probability distributions of the random variables used to describe the uncertainties involved can, in turn, be imprecise, since they are typically estimated by means of statistical inference based on observations and engineering judgment. In this context, reliability sensitivity analysis aims at estimating the influence of this additional source of uncertainty on the system failure probability in order to assess the robustness of the system to the modeling of uncertainties. Intuitively, reliability sensitivity analyses may easily become prohibitive by standard sampling-based methods (e.g., Monte Carlo method), since a nested, second level of uncertainties is involved. To overcome this issue, in this work we embed the efficient AK-IS algorithm for estimating small failure probabilities within an original computational framework that allows to perform a Sobol-based, global sensitivity analysis of the failure probability at an affordable number of computer model evaluations. The algorithm is demonstrated with reference to two case studies of literature of structural/mechanical reliability, often used in the literature as benchmark tests.

中文翻译：

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基于 Sobol 的动态自适应克里金重要性抽样的全局可靠性敏感性分析

摘要 影响用于描述结构/机械系统行为的模型的随机不确定性可能会导致导致故障的不利情况。在这个框架中，失效概率的量化是结构安全和可靠性分析公认的基本任务。不幸的是，结构/机械系统故障概率的估计是一项计算要求很高的任务，尤其是当故障是罕见事件并且用于模拟系统响应的计算机代码需要大量计算工作时。一个主要问题使估计过程进一步复杂化，即用于描述所涉及的不确定性的随机变量的概率分布参数反过来可能不精确，因为它们通常是通过基于观察和工程判断的统计推断来估计的。在这种情况下，可靠性敏感性分析旨在估计这种额外的不确定性来源对系统故障概率的影响，以评估系统对不确定性建模的稳健性。直观地说，可靠性敏感性分析很容易被标准的基于抽样的方法（例如蒙特卡罗方法）所禁止，因为涉及到嵌套的第二级不确定性。为了克服这个问题，在这项工作中，我们嵌入了高效的 AK-IS 算法，用于在允许执行基于 Sobol 的原始计算框架内估计小故障概率，在负担得起的计算机模型评估数量下对故障概率进行全局敏感性分析。该算法参考了结构/机械可靠性文献的两个案例研究，在文献中经常用作基准测试。