Traditionally, analysis requires very large number of calculations; some engineering applications in particular require time-consuming numerical efforts. Classical reliability analysis methods with combinations of surrogate models can relieve the computational burden. An active learning reliability method that combines kriging and Monte Carlo simulation has drawn a great deal of attention in recent years. However, it is often challenging to find the most suitable sample point and speed up the convergence. In this paper, a method is proposed to deal with this problem, in which two strategies are employed: an active learning method is proposed to search the most suitable sample point in a specific region using the dichotomy method; an improved convergence criterion is developed based on standard deviation to improve the convergence speed. In addition, taking advantage of the excellent characteristics of Subset Simulation, a method for dealing with small failure probability problems is proposed based on the above strategies. The efficiency and accuracy of the proposed approaches are tested using three numerical examples and one finite element example. Results demonstrate its accuracy.
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