A Fourth-Order Moment Method Based on Back Propagation Neural Network for High-Dimensional Nonlinear Reliability Analysis

Reliability analysis of complex engineering products often involves high-dimensional nonlinear state functions, with random variable distributions hard to determine due to limited samples, restricting the fourth-order moment method that fails to link moments of variables and state functions. This study proposes a method combining a back propagation (BP) neural network and a fourth-order moment method: a BP neural network surrogates the mapping between the model approximation variables and the state function, generating samples for estimating the first-fourth-order moments of the state function, and thus performing reliability analyses based on the fourth-order moment method. Validation shows the BP model outperforms Kriging in predicting high-dimensional nonlinear functions; it aligns with Monte Carlo simulation (MCS) results in rolling bearing reliability analysis with higher efficiency and applies to time-varying fatigue analysis. This method overcomes limitations of the fourth-order moment method, offers higher accuracy than existing surrogate-based methods, and retains the efficiency of moment methods, suitable for limited-sample and time-varying scenarios.