An active learning method using deep adversarial autoencoder-based sufficient dimension reduction neural network for high-dimensional reliability analysis

Reliability analysis often requires time-consuming evaluations, especially when dealing with high-dimensional and nonlinear problems. To address this challenge, surrogate model methods are frequently employed. One way to improve the efficiency of surrogate model methods involves selecting informative samples that significantly enhance the accuracy of the surrogate model. This paper introduces a novel approach to facilitate the construction of surrogate models and selection of informative samples in high-dimensional reliability analysis, through an active learning method based on a deep adversarial autoencoder-based sufficient dimension reduction (AAE-SDR) neural network. The AAE-SDR neural network serves as a surrogate model, transforming complex high-dimensional variables into tractable, low-dimensional embeddings relevant to the target. These embeddings are Gaussian-distributed with a distinct latent limit state boundary. A new sampling strategy is proposed to select informative misclassified samples by iteratively identifying candidate samples near the latent limit state boundary and uniformly sampling from the candidate sample dataset based on the latent Gaussian distribution. The effectiveness of the proposed approach is demonstrated through two high-dimensional numerical examples and a cable-stayed bridge case study. Results show that the proposed method simplifies complex high-dimensional reliability problems and provides a relatively accurate estimated failure probability with a limited number of samples.