Subspace enhanced active learning method for high-dimensional reliability analysis

Subspace-based surrogate modeling methods are extensively used for high-dimensional reliability analysis due to their ability to mitigate the "curse of dimensionality". The accuracy of the subspace fundamentally determines the credibility of the reliability analysis. However, existing methods may construct the subspace with poor accuracy because they reduce the dimensionality only based on responses and gradients of limited samples, making the results of the failure probability inaccurate. To tackle this issue, this paper proposes a novel high-dimensional reliability analysis method by combining subspace enhancement and active learning. First, we calculate a projection matrix using slice inverse regression to obtain an initial subspace. To calibrate the projection direction, a nested optimization strategy is developed to refine the parameters of the projection matrix using the manifold optimization technique. In the early stages of active learning, a similarity-preserving global sampling strategy is proposed to select samples that are most beneficial for enhancing dimensionality reduction accuracy. Once the dimensionality reduction reaches sufficient precision, a local sampling strategy is implemented to identify samples near the limit state boundary, enhancing the accuracy of failure probability estimation. Finally, the learning process is terminated using a stopping criterion based on the upper bound estimate of relative error. The performance of the proposed method is validated through two numerical cases and two engineering cases.