LSTM-augmented probability-informed neural network-driven evolution estimation for time-dependent reliability analysis

Abstract

For time-dependent dynamic systems, the inputs include not only random variables but also stochastic processes, posing significant challenges to traditional Time-Dependent Reliability Analysis (TDRA) methods regarding efficiency, accuracy, and generality. To address these challenges, this paper develops a Long Short-Term Memory (LSTM)-Augmented Probability-Informed Neural Network Evolution (LPNE) framework for TDRA of dynamic systems. A set of local performance functions is introduced by selecting representative points for time-independent random variables. Subsequently, an LSTM network is trained to learn the time-dependent behavior of the dynamic system for each local limit state function. Multiple local surrogate LSTM models are then employed to assemble an enhanced dataset accordingly. Based on the enriched dataset, point-evolution estimation is performed with a more ample sample size, integrating Deep Neural Networks (DNN) with the physical equation information of the generalized probability density evolution equation (GDEE). The proposed framework can effectively compensate for the limitations of existing point-evolution approaches that struggle to consider scenarios with stochastic process inputs. The proposed LPNE is validated through four benchmark cases: a simple numerical example, scenarios involving corroded steel beams, corrosion-induced deterioration of steel structures, and the seismic response of multi-story shear frame structure. The results demonstrate that LPNE can accurately and efficiently estimate time-dependent failure probabilities with a limited number of representative points without requiring additional samples.