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An important challenge in structural reliability is to reduce the number of calls to evaluate the performance function, especially the complex implicit performance functions. To reduce the computational burden and improve the reliability analysis efficiency, a new active learning method is developed to consider the probability density function of samples based on the learning function U in an active learning reliability method that combines the kriging and Monte Carlo simulation. In the proposed method, the proposed active learning function contains two parts: part A is based on function U, and part B is based on the probability density function and function U. By changing the weights of parts A and B, the sample points close the limit-state function, and those in the region with a higher probability density function have more weight to be selected compared to the others. Subsequently, the kriging model can be constructed more effectively. The proposed method avoids a large number of time-consuming function evaluations, and the recommended weight is also reported. The performance of the proposed method is evaluated through three numerical examples and one engineering example. The results demonstrate the efficiency and accuracy of the proposed method.

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Structural reliability analysis is the key approach to assess uncertainties so that to increase the safety of engineering structures. Quantifying the failure probability (FP) is central to direct the result of the reliability assessment. In aerospace and military fields, normal samples collected from a structure are easily available, however, failure samples are extremely limited. Such imbalanced samples circumstance may lead to a large approximate bias of the failure probability. The critical problem in structural reliability analysis is how to use a smaller number of samples to get more precise failure probabilities. Although the Monte Carlo simulation (MCS) is the recognized benchmark, the high computational cost of calling limit state function has forced people to seek alternative ways. On the other hand, the surrogate model method, such as the adaptive Kriging model (abbreviated as AK-MCS), has been proposed to reduce the computational burden. To evaluate small failure probability, however, the number of the candidate points must be large for a convergent solution. To this end, this paper constructs a security domain identified model (SDIM) based on the one-class support vector machine (SVM) and imbalanced data. Different types of misjudged samples and approximate errors of the trained SDIM are analyzed. Two schemes are proposed accordingly to reduce the tested estimate error of the failure probability. Comparing with MCS and AK-MCS, the numerical and engineering examples demonstrate the accuracy and efficiency of the proposed method under different scenarios.