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