High Efficiency Estimation of Failure Probability: A Fusion Method of Cross-Entropy Optimization and Back Propagation Neural Network

The estimation of failure probability in complex engineering structures suffers from low computational efficiency and challenges in handling with high-dimensional nonlinearity. Traditional methods are inefficient and require large sample sizes, making them difficult to meet the demands of practical engineering applications. This paper proposes a failure probability estimation framework that integrates cross-entropy (CE) optimization with a back propagation neural network (BPNN). The CE method is employed to adaptively optimize the sampling distribution, thereby enhancing the sampling efficiency for rare failure domains. By leveraging BPNN’s powerful nonlinear approximation capability, a surrogate model for the limit state function (LSF) is constructed, significantly reducing the number of LSF evaluations. Validation through numerical engineering examples demonstrates that, compared to cross-entropy-based importance sampling (CE-IS) and cross-entropy-based Gaussian mixture sampling (CE-GM) methods, the proposed CE-BPNN approach stably approximates the reference failure probability across varying sample sizes, with lower coefficient of variation (CoV) and mean absolute percentage error (MAPE). The predictive model achieves [Formula: see text]-square ([Formula: see text]) values consistently exceeding 0.97. Under identical sample sizes, CE-BPNN exhibits significant accuracy improvement and high stability. The results indicate that the CE-BPNN method offers superior accuracy and efficiency for structural reliability analysis involving high-dimensional nonlinearity and small failure probabilities, providing a promising new approach for reliability assessment of complex engineering structures.