Adaptive active subspace-based metamodeling for high-dimensional reliability analysis

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.