To address the challenges of reliability analysis in high-dimensional probability spaces, this paper proposes a new metamodeling method that couples active subspace, heteroscedastic Gaussian process, and active learning. The active subspace is leveraged to identify low-dimensional salient features of a high-dimensional computational model. A surrogate computational model is built in the low-dimensional feature space by a heteroscedastic Gaussian process. Active learning adaptively guides the surrogate model training toward the critical region that significantly contributes to the failure probability. A critical trait of the proposed method is that the three main ingredients-active subspace, heteroscedastic Gaussian process, and active learning-are coupled to adaptively optimize the feature space mapping in conjunction with the surrogate modeling. This coupling empowers the proposed method to accurately solve nontrivial high-dimensional reliability problems via low-dimensional surrogate modeling. Finally, numerical examples of a high-dimensional nonlinear function and structural engineering applications are investigated to verify the performance of the proposed method.

翻译：为解决高维概率空间中可靠度分析的挑战，本文提出一种耦合活性子空间、异方差高斯过程与主动学习的新型元建模方法。利用活性子空间识别高维计算模型的低维显著特征，在低维特征空间中通过异方差高斯过程构建替代计算模型。主动学习自适应地将代理模型训练引导至对失效概率具有显著贡献的关键区域。该方法的关键特性在于：通过将活性子空间、异方差高斯过程与主动学习三大核心要素耦合，实现特征空间映射与代理建模的协同自适应优化。这种耦合机制使得本文方法能够通过低维代理建模精确解决非平凡的高维可靠性问题。最后，通过高维非线性函数算例与结构工程应用实例验证了所提方法的有效性。