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.

为了解决高维概率空间中可靠性分析的挑战，本文提出了一种将主动子空间、异方差高斯过程和主动学习相结合的新元建模方法。利用活动子空间来识别高维计算模型的低维显着特征。通过异方差高斯过程在低维特征空间中建立代理计算模型。主动学习自适应地引导代理模型训练到对故障概率有显着影响的关键区域。该方法的一个关键特征是，三个主要成分——主动子空间、异方差高斯过程和主动学习——耦合在一起，结合代理建模自适应地优化特征空间映射。这种耦合使得所提出的方法能够通过低维代理建模准确地解决重要的高维可靠性问题。最后，研究了高维非线性函数的数值例子和结构工程应用，以验证所提出方法的性能。