An efficient Kriging model-based importance sampling method for estimating the failure probability-based parameter global sensitivity index with uncertain distribution parameters

Abstract

The failure probability-based parameter global sensitivity index measures the importance of each uncertain distribution parameter on the uncertainty of failure probability. The crude Monte Carlo simulation for estimating the failure probability-based parameter global sensitivity index involves a complicated nested triple-loop process, and the huge amount of computational burden restricts the application of the failure probability-based parameter global sensitivity. For efficiently analyzing the failure probability-based parameter global sensitivity index, this paper proposes an efficient Kriging model-based importance sampling method. First, the standard normal auxiliary variables are inducted by using the equivalent probability transformation, in which the equivalent limit state function with respect to the uncertain distribution parameters and the standard normal auxiliary variables are constructed, so that the importance sampling samples of uncertain distribution parameters and the standard normal auxiliary variables can be generated based on the equivalent limit state function. Secondly, based on the importance sampling technique, the formula of single-loop method for estimating the failure probability-based parameter global sensitivity index is derived in which the importance sampling samples can be reused to obtain all uncertain distribution parameters' failure probability-based global sensitivity indices. Thirdly, the equivalent probability transformation is used again to transform the importance sampling samples in the high-dimensional space into the relatively low-dimensional input space, and the Kriging model of the original limit state function with relatively low-dimensional input space is adaptively constructed to recognize the states (failure or safety) of all high-dimensional importance sampling samples. Then, the failure probability-based parameter global sensitivity indices can be efficiently estimated. The results of three case studies verify the accuracy and efficiency of the proposed method.