# An efficient method for estimating the parameter global reliability sensitivity analysis by innovative single-loop process and embedded Kriging model

Abstract

Abstract For evaluating the effect of uncertain distribution parameter on the uncertainty of the failure probability function, the parameter global reliability sensitivity index (PGRSI) is researched and the high efficient estimation algorithm is proposed to approximately estimate the PGRSI. The used definition form of the PGRSI is the expectation of absolute differences between the unconditional expectation of failure probability function and the conditional expectation of failure probability function, which involves a triple-loop evaluation. For efficiently estimating the PGRSI, this paper innovatively inducts the Bayes theorem and the law of total expectation in the successive intervals without overlapping in order to convert the triple-loop evaluation to a single-loop one. The number of actual model evaluations of the single-loop Monte Carlo simulation (MCS) is independent of the dimensionality of uncertain distribution parameters, and the single-loop MCS only needs one set of input-output samples. Besides, the single-loop MCS can be regarded as a classification problem which needs to identify the failure or safety states of samples in the one set. To further enhance the computational efficiency of the proposed single-loop process, the adaptive Kriging (AK) model is embedded in the single-loop MCS, where the Kriging model is used to approximate the actual limit state function to classify the samples. The number of actual model evaluations of the Kriging model nested single-loop process only generates in the process of constructing the AK model. The results of case studies illustrate the accuracy and efficiency of the proposed method.