An improved adaptive Kriging model for importance sampling reliability and reliability global sensitivity analysis

An improved adaptive Kriging model for importance sampling (IS) reliability and reliability global sensitivity analysis is proposed by introducing the IS density function into learning function. Considering the variance information of Kriging prediction, the formula of traditional IS method is extended to the form considering the uncertainty of symbol function. The estimated variance of failure probability caused by the prediction uncertainty of Kriging model is obtained, and the corresponding coefficient of variation (COV) is defined. Based on the standard deviation information of failure probability, a novel learning function considering the characteristic of IS density function is proposed, which are used to minimize the prediction uncertainty of Kriging. The corresponding stopping criterion is defined based on the COV information. In order to increase the likelihood that the selected sample points fall around the limit state boundary, the penalty function method is introduced to improve the learning function. Once the failure probability is obtained, the variable global sensitivity index is calculated through the failed sample set and Bayes theorem. The results show that: By introducing IS density function and penalty function into learning function, the sample points which contribute more to the failure probability can be obtained more effectively in IS method. The proposed method has high accuracy and efficiency compared with traditional Kriging-based IS method.