Adaptive Deep Neural Network Method for Engineering Structural Reliability Analysis with Imbalanced Samples

To improve the accuracy and efficiency of engineering structural reliability analysis under imbalanced sample conditions, an adaptive deep neural network (ADNN) method is pro-posed. The method integrates limit state surface (LSS)-based stratified splitting, a composite loss function, and an adaptive training strategy into the DNN framework. In the proposed method, the DNN is employed to establish the mapping relationship between input variables and output responses. The LSS-based stratified splitting improves the representativeness of samples near the LSS; the composite loss function assigns greater importance to samples in critical regions, thereby enhancing the model’s ability to learn the LSS; and the adaptive training strategy is used to improve model robustness. The proposed method is validated through two nonlinear function examples and a cable-stayed bridge engineering example, in which the failure-sample proportions in the model-construction datasets range from 0.10 to 0.33. The results show that ADNN improves the approximation capability of the LSS and maintains good reliability analysis performance as the failure-sample proportion decreases. Compared with conventional surrogate models, the ADNN method achieves higher accuracy and efficiency in reliability analysis. This study provides methodological support for structural reliability analysis under imbalanced sample conditions.