Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. In this paper, we propose a methodology to quantify the sensitivity of the failure probability estimator to uncertainties generated by the Gaussian process and the sampling strategy. This quantification also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. Thus, an active learning approach integrating this analysis to reduce the main source of error and stopping when the global variability is sufficiently low is introduced. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities. Performance of the proposed strategy is then assessed on several examples.

对涉及复杂数值模型的工程问题运行可靠性分析在计算上可能非常昂贵，需要先进的模拟方法来降低整体数值成本。用于可靠性分析的基于高斯过程的主动学习方法已成为降低这种计算成本的有前途的方法。在本文中，我们提出了一种方法来量化故障概率估计器对高斯过程和采样策略产生的不确定性的敏感性。这种量化还能够控制与故障概率估计相关的整个误差，从而为估计提供准确度标准。因此，引入了一种主动学习方法，该方法集成了这种分析，以减少错误的主要来源，并在全局可变性足够低时停止。该方法被提议用于基于蒙特卡罗的方法以及基于重要性采样的方法，以寻求改进稀有事件概率的估计。然后根据几个示例评估所提议策略的性能。