Active learning line sampling for rare event analysis

Line Sampling (LS) has been widely recognized as one of the most appealing stochastic simulation algorithms for rare event analysis, but when applying it to many real-world engineering problems, improvement of the algorithm with higher efficiency is still required. This paper aims to improve both the efficiency and accuracy of LS by active learning and Gaussian process regression (GPR). A new learning function is devised for informing the accuracy of the calculation of the intersection points between each line associated with LS and the failure surface. Then, an adaptive algorithm, with the learning function as an engine and a stopping criterion, is developed for adaptively training a GPR model to accurately estimate the intersection points for all lines in LS scheme, and the number of lines is actively increased if it is necessary for improving the accuracy of failure probability estimation. By introducing this adaptive GPR model, the number of required function calls has been largely reduced, and the accuracy for estimation of the intersection points has been largely improved, especially for highly nonlinear problems with extremely rare events. Numerical test examples and engineering applications show the superiority of the developed algorithm over the classical LS algorithm and some other active learning schemes.