Reliability is a fundamental aspect of modern structural engineering due to the inherent randomness of materials, loads, and environmental conditions. However, as system complexity increases, a substantial computational cost is typically required to evaluate the failure probability, often involving 105–106 limit state function evaluations in a conventional Monte Carlo simulation. To address this challenge, this study presents an active-learning-driven deep neural network (ALDNN) meta model algorithm to improve both efficiency and accuracy in reliability analysis. To substantially reduce the computational costs, a multi-phase active learning framework incorporating weighted sampling and adaptive threshold-based candidate filtering is implemented by iteratively selecting more important points and adaptively training deep neural networks. Thresholds for candidate sample points and training datasets are gradually adjusted based on feedback from estimated responses. The proposed method reduces the number of true limit state evaluations to the order of 102 in the benchmark problems considered, while maintaining high accuracy. Its performance is assessed using widely referenced benchmark problems, and finite-element-method-based implicit examples for frame structures are further employed to verify applicability. The results demonstrate the high efficiency, accuracy, and scalability of the ALDNN meta model as system complexity increases.
Sangik Lee (Thu,) studied this question.