Reducing the surrogate model-based method computation without loss of prediction accuracy remains a significant challenge in structural reliability analysis. The unbalanced probability density, important information in critical region and information redundancy of added sample points are ignored in most of traditional surrogate-based methods, resulting in heavy computational burden. In this work, an active learning combining adaptive Kriging method and weighted penalty (AK-WP) is proposed to analyze the reliability of engineering structures. Firstly, an active learning and weighted penalty function (WPLF) is the result of integrating active learning method, weighted function and penalty function, which is proposed to find the most probable point (MPP). Meanwhile, to avoid redundant information, the best suitable MPP is determined by a proposed distance law established between the found MPP and the existing design of experiment (DoE). Secondly, the Kriging model is refined according to best suitable MPP in each iteration. Thirdly, the failure probability is estimated by the Monte Carlo sample points from the n-ball domain until the convergence condition is satisfied. The accuracy and efficiency of the proposed method are demonstrated by some numerical examples including the highly nonlinear, the small probability problems and implicit function, as well as a real engineering application.

在不降低预测精度的情况下，减少基于替代模型的方法计算仍然是结构可靠性分析中的重大挑战。在大多数传统的基于代理的方法中，不平衡的概率密度，关键区域中的重要信息以及添加的采样点的信息冗余都被忽略，从而导致沉重的计算负担。在这项工作中，提出了一种主动学习结合自适应克里格法和加权罚分法（AK-WP）来分析工程结构的可靠性。首先，主动学习和加权罚分函数（WPLF）是将主动学习方法，加权函数和罚分函数相结合的结果，旨在找到最可能的点（MPP）。同时，为了避免多余的信息，最合适的MPP由找到的MPP与现有实验设计（DoE）之间建立的拟议距离定律确定。其次，在每次迭代中根据最适合的MPP完善Kriging模型。第三，失效概率是由蒙特卡洛样本点从n球域，直到满足收敛条件为止。通过数值例子证明了所提方法的准确性和有效性，包括高度非线性，小概率问题和隐函数，以及实际的工程应用。