Kriging has gained significant attention for reliability analysis primarily because of the analytical form of its uncertainty information, which facilitates adaptive training and establishing stopping criteria for the training process. Learning functions play a significant role in both selection of training points and stoppage of the training. For these functions, most existing learning functions evaluate candidate training points individually. However, lack of consideration for the global effects can lead to suboptimal training. In addition, the subjectivity of these stopping criteria may result in over or undertraining of surrogate models. To overcome these gaps, we propose Global Error-based Learning Function (GELF) for optimal refinement of Kriging surrogate models for the specific purpose of reliability analysis. Instead of prioritizing training points based on their uncertainty and proximity to the limit state like the existing learning functions, GELF for the first time directly and analytically associates the maximum error in the failure probability estimate to the global effect of choosing a candidate training point. This development subsequently facilitates an adaptive training scheme that minimizes the error in adaptive reliability estimation to the highest degree. For this purpose, GELF uses hypothetical future uncertainty information by treating the current construction of the surrogate model as a generative model. The proposed method is tested on three classic benchmark problems and one practical engineering problem. Results indicate that the proposed method has significantly better computational efficiency than the state-of-the-art methods while achieving high accuracy in all the numerical examples.

中文翻译：

---

GELF：基于全局误差的学习函数，用于全局最优自适应可靠性分析

克里金法在可靠性分析中获得了极大的关注，主要是因为其不确定性信息的分析形式，这有利于自适应训练和建立训练过程的停止标准。学习功能在训练点的选择和训练的停止方面都起着重要作用。对于这些函数，大多数现有的学习函数单独评估候选训练点。然而，缺乏对全局影响的考虑可能会导致训练效果不佳。此外，这些停止标准的主观性可能会导致替代模型训练过度或不足。为了克服这些差距，我们提出了基于全局误差的学习函数（GELF），用于优化克里金代理模型的细化，以实现可靠性分析的特定目的。 GELF 不像现有的学习函数那样根据训练点的不确定性和接近极限状态来确定训练点的优先级，而是首次直接分析地将故障概率估计中的最大误差与选择候选训练点的全局效果相关联。这一发展随后促进了自适应训练方案，该方案将自适应可靠性估计中的误差最小化到最高程度。为此，GELF 通过将当前的替代模型构建视为生成模型来使用假设的未来不确定性信息。该方法在三个经典基准问题和一个实际工程问题上进行了测试。结果表明，所提出的方法比最先进的方法具有明显更好的计算效率，同时在所有数值示例中实现了高精度。