For the reliability analysis with imprecise probability distributions, the failure probability and its sensitivity are always denoted as the functions of distribution parameters. The computation of those functional relationships remains a challenging task due to the intensive computational burden. To further improve the computational efficiency, this work proposes a new computational method based on the classical active learning Kriging model with U learning function. The Kriging model is constructed with a group of initial point and updated by the best contributing samples selected from different sample spaces corresponding to discrete distribution parameters, which guarantees the prediction ability in the variation range of distribution parameters. Consequently, the functions of failure probability and sensitivity can be estimated by the same Kriging model, which avoids re-constructing Kriging models corresponding to different distribution parameters. Several examples including two numerical examples and three engineering practices are investigated to validate the reasonability and superiority of the proposed method. Finally, the proposed method is applied to the fatigue life reliability and sensitivity analyses of a turbine disk structure.

对于具有不精确概率分布的可靠性分析，失效概率及其敏感性始终被表示为分布参数的函数。由于大量的计算负担，这些功能关系的计算仍然是一项艰巨的任务。为了进一步提高计算效率，本文提出了一种基于经典主动学习克里格模型的新的计算方法，该模型具有U学习功能。克里格模型由一组初始点构成，并通过从与离散分布参数相对应的不同样本空间中选择的贡献最大的样本进行更新，从而保证了分布参数变化范围内的预测能力。所以，失效概率和灵敏度的函数可以通过相同的克里格模型来估计，从而避免了重构对应于不同分布参数的克里格模型。研究了包括两个数值示例和三个工程实践的几个示例，以验证所提出方法的合理性和优越性。最后，将所提出的方法应用于涡轮盘结构的疲劳寿命可靠性和灵敏度分析。