New learning functions for active learning Kriging reliability analysis using a probabilistic approach: KO and WKO functions

Reducing the cost of calculation without compromising the accuracy of the solution is a recognized challenge for optimizing the reliability analysis, which became possible using surrogate models trained with robust techniques, such as active learning Kriging (AK) reliability methods. In the AK reliability method, a Kriging predictor is built with a small size of design of experiments (DoE) and becomes more accurate in the vicinity of the limit state function (LSF) in a stepwise manner, called the learning process, until a stopping criterion is met. The motivation of the current study is to enhance the accuracy and efficiency of AK reliability analysis by developing new learning functions, new stopping criteria, and a new method of selection of the next candidate for updating the DoE in the learning process. In this paper, two new learning functions named Kriging occurrence (KO) and weighted KO (WKO) are proposed based on a probability-based approach. A hybrid selection for the next candidate is introduced which simultaneously considers the probability of improvement and the density of DoE and a new stopping criterion is recommended based on the relative mean of the learning functions. A thorough study of the literature is conducted where 12 learning functions are summarized and their performances are compared to that of newly developed learning functions through five comparative examples. The result of the study shows that the new learning function can enhance the accuracy and efficiency of the learning process.