A new active learning method based on the learning function U of the AK-MCS reliability analysis method

In recent years, reliability analysis methods based on the Kriging surrogate model have often been employed to obtain accurate failure probabilities of problems since the Kriging model can be used to provide predictions of the performance function at sample points and the corresponding variance of these predictions. Several learning functions have been explored to update the design of experiments and to complete the iterative process. However, it is still not easy to reduce the number of times the performance function or finite element model (FEM) is called for problems using the Kriging model. In this paper, a new active learning method based on a widely used learning function U is proposed to improve the speed of convergence of the AK-MCS method for problems with a connected domain of failure. Then, three academic examples and one three-unequal-span continuous girder with an implicit performance function are used to verify the accuracy and validity of the AK-MCS method based on the proposed learning method. Comparisons with AK-MCS based on the learning function U and MCS indicate that AK-MCS based on the proposed learning method requires calling the performance function or FEM fewer times than required by AK-MCS based on the learning function U to obtain accurate failure probabilities of the four examples, especially for six-dimensional problems.