An adaptive failure boundary approximation method for reliability analysis and its applications

In practical engineering problems, accurate reliability assessment often is computationally expensive with time-consuming numerical models or simulation models. How to obtain an accurate reliability index with a fewer number of calls to original performance function in reliability analysis has become an important challenge. For the purpose of reducing the computational cost in reliability analysis, this work develops an adaptive failure boundary approximation method (AFBAM) by combining Kriging and uniform sampling with a new adaptive learning strategy. The proposed AFBAM makes full use of the binary classification feature of reliability analysis in the way that the failure boundary of the original model can be efficiently approximated. The number of experimental design samples is constantly updated by selecting informative samples with the proposed learning strategy. In order to ensure classification accuracy of the constructed Kriging model, a new stopping criterion is designed based on average misclassification probability and misclassification ratio. The proposed AFBAM technically makes reliability evaluation phase independent of adaptive iterative process, which greatly improves the efficiency of model refinement phase. At last, five examples involving nonlinearity problem, small failure probability problem and practical engineering problem are tested to verify the efficiency of the proposed AFBAM.