An Extremum-Based BP Neural Network Method and Its Application in Time-Dependent Structural System Reliability Analysis

Time-dependent structural systems (TDSSs) in engineering involve high dimensionality, nonlinearity, and complex uncertainties, complicating the reliability analysis compared to time-independent assessments. To address these challenges, this paper proposes an extremum-based back propagation neural network (BPNN) method for TDSS reliability analysis. The method adopts a double-loop structure. Specifically, the inner loop finds the minimum of the time-dependent performance function for a given realization of the random variables. This transformation converts the time-dependent problem into an equivalent time-invariant one. Then, the outer loop constructs a BPNN surrogate model to map the relationship between the random variables and the performance function minima. To improve computational efficiency, an adaptive sample selection strategy is integrated into the training process. This technique selects samples near the failure boundary to iteratively update the BPNN, ensuring high accuracy with a small training set. Once the stopping criterion is satisfied, the failure probability is estimated using Monte Carlo simulation (MCS). The trained BPNN model is used to rapidly predict the extremum for the large-scale sample pool. The proposed method is verified through three practical engineering cases: a four-bar mechanism, an aero-engine turbine disc, and a cantilever tube. Results show that the method remains accurate and efficient. The successful applications confirm the rationality and engineering applicability of the proposed model.