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.

结构可靠性方面的一个重要挑战是减少评估性能函数（尤其是复杂的隐式性能函数）的调用次数。为了减少计算量并提高可靠性分析效率，开发了一种新的主​​动学习方法，在结合克里金法和蒙特卡洛模拟的主动学习可靠性方法中，基于学习函数U考虑样本的概率密度函数。在提出的方法中，提出的主动学习功能包括两部分：部分A基于函数U，部分B基于概率密度函数和函数U。通过更改部分A和B的权重，采样点接近极限状态函数，与其他概率点相比，具有较高概率密度函数的区域中的采样点具有更多的权重可供选择。随后，可以更有效地构建克里金模型。所提出的方法避免了大量耗时的功能评估，并且还报告了推荐的权重。通过三个数值实例和一个工程实例对所提方法的性能进行了评估。结果证明了该方法的有效性和准确性。