The paper introduces the active learning Kriging (ALK) model into the structural fatigue reliability analysis. Firstly, the structural variable stress is obtained by experimental tests or finite element simulation (FES). On this basis, the cyclic stress corresponding to the fatigue life is analyzed based on the rain-flow counting method and the structural fatigue life is correspondingly computed using the Miner-Palmgren damage rule. Secondly, the uncertainties to affect the structural variable stress are considered and thus the prediction of structural fatigue lives can be obtained. Further, the structural fatigue reliability model is established, and its reliability is obtained by computing the probability that the predicted fatigue lives are greater than the allowable life. Finally, to balance the accuracy and efficiency for computing the structural fatigue reliability, a small number of boundary sample points for experiment or FES are produced and the corresponding fatigue lives are computed. Sequentially, the Kriging model is adopted to approximate the structural fatigue reliability model and it is adaptively updated by the active learning strategy. Several examples are also given to demonstrate the effectiveness of the proposed ALK-based structural fatigue reliability method.

本文将主动学习克里格（ALK）模型引入到结构疲劳可靠性分析中。首先，通过实验测试或有限元模拟（FES）获得结构变应力。在此基础上，基于雨流计数法分析疲劳寿命对应的循环应力，并利用Miner-Palmgren损伤规则计算相应的结构疲劳寿命。其次，考虑影响结构变应力的不确定性，从而得到结构疲劳寿命的预测值。进而建立结构疲劳可靠性模型，通过计算预测疲劳寿命大于许用寿命的概率得到其可靠性。最后，为了平衡结构疲劳可靠性计算的准确性和效率，产生了少量的实验或有限元边界样本点，并计算了相应的疲劳寿命。随后，采用克里金模型逼近结构疲劳可靠性模型，并通过主动学习策略进行自适应更新。还给出了几个例子来证明所提出的基于 ALK 的结构疲劳可靠性方法的有效性。