The global reliability sensitivity index (GRSI) can measure the effect of model input variable on the failure probability of the structure and provide guidance for the reliability-based design optimization. In this paper, to efficiently estimate the GRSI, an equivalent form of the GRSI is derived by elaborative combination of Bayes’ theorem and the law of total expectation in the successive intervals without overlapping, and it not only makes the total computational cost independent of the dimensionality of model inputs, but also avoids approximating the probability density function approximation used in the existing Bayes’ theorem based global reliability sensitivity analysis. For further improving the efficiency of estimating the GRSI by the equivalent form, two algorithms are presented by nesting the adaptive Kriging (AK) into Monte Carlo simulation (MCS) and importance sampling (IS), respectively, which are abbreviated as AK-MCS and AK-IS. Results of one numerical example and four engineering applications show that the number of model evaluations by the AK-IS is less than $\text{2}\% $ of that by direct IS, and the model evaluation number by AK-MCS is less than $\text{4}\% $ of that by direct MCS under the convergent condition. The results illustrate that the proposed methods for estimating the GRSI are practical for engineering applications.

中文翻译：

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结合贝叶斯定理和连续区间总期望定律的两种有效的基于AK的全局可靠性敏感性方法，不重叠

全局可靠性敏感性指数（GRSI）可以衡量模型输入变量对结构失效概率的影响，为基于可靠性的设计优化提供指导。在本文中，为了有效地估计 GRSI，通过在不重叠的连续区间内精心组合贝叶斯定理和总期望定律，推导出 GRSI 的等价形式，它不仅使总计算成本独立于模型输入的维度，但也避免了在现有的基于贝叶斯定理的全局可靠性敏感性分析中使用的概率密度函数近似。为了进一步提高等价形式估计 GRSI 的效率，通过将自适应克里金法（AK）分别嵌套到蒙特卡洛模拟（MCS）和重要性采样（IS）中，提出了两种算法，分别简称为 AK-MCS 和 AK-IS。1个算例和4个工程应用的结果表明，AK-IS的模型评估次数少于直接IS的模型评估次数，AK-MCS的模型评估次数更少比收敛条件下直接 MCS 的 $\text{4}\% $。结果表明，所提出的估计 GRSI 的方法对于工程应用是实用的。1个算例和4个工程应用的结果表明，AK-IS的模型评估次数少于直接IS的模型评估次数，AK-MCS的模型评估次数更少比收敛条件下直接 MCS 的 $\text{4}\% $。结果表明，所提出的估计 GRSI 的方法对于工程应用是实用的。1个算例和4个工程应用的结果表明，AK-IS的模型评估次数少于直接IS的模型评估次数，AK-MCS的模型评估次数更少比收敛条件下直接 MCS 的 $\text{4}\% $。结果表明，所提出的估计 GRSI 的方法对于工程应用是实用的。