Two Efficient AK-Based Global Reliability Sensitivity Methods by Elaborative Combination of Bayes’ Theorem and the Law of Total Expectation in the Successive Intervals Without Overlapping

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.