Profust reliability analysis, in which the failure state of a load-bearing structure is assumed to be fuzzy, is investigated in this paper. A novel active learning method based on the Kriging model is proposed to minimize the number of function evaluations. The new method is termed ALK-Pfst. The sign of performance function at a given random threshold determines the profust failure probability. Therefore, the expected risk function at an arbitrary threshold is derived as the learning function of ALK-Pfst. By making full use of the prediction information of Kriging model, the prediction error of profust failure probability is carefully derived into a closed-form expression. Aided by the prediction error, the accuracy of Kriging model during the learning process can be monitored in real time. As a result, the learning process can be timely terminated with little loss of accuracy. Four examples are provided to demonstrate the advantages of the proposed method.

本文研究了假设承重结构的失效状态为模糊状态的可靠可靠性分析。提出了一种基于克里金模型的新型主动学习方法来最小化函数评估的数量。新方法称为 ALK-Pfst。给定随机阈值下的性能函数符号决定了profust 故障概率。因此，将任意阈值处的预期风险函数导出为 ALK-Pfst 的学习函数。通过充分利用Kriging模型的预测信息，将profust失效概率的预测误差精心推导为一个封闭式的表达式。借助预测误差，可以实时监控 Kriging 模型在学习过程中的准确性。因此，学习过程可以及时终止，而准确性几乎没有损失。提供了四个例子来证明所提出方法的优点。