A Physics-Informed Neural Network-Based Method for Reliability Analysis of Stochastic Degradation Systems

This study presents a reliability analysis method for stochastic degradation systems using a physics-informed neural network (PINN). The system degradation process is modelled by continuous diffusion-type stochastic differential equations. Based on stochastic differential theory, the reliability problem is transformed into solving the governing equation of the probability density function of the degradation state, such as the Fokker-Planck equation. A loss function is constructed by embedding these physical constraints into the deep learning framework, enabling the PINN to solve the forward problem efficiently. The proposed approach is validated through numerical examples involving Wiener and Ornstein-Uhlenbeck processes. The results demonstrate good agreement between the PINN-based solutions and Monte Carlo simulations, indicating that the proposed method offers a promising alternative for computationally intensive reliability analyses.

Keywords: Stochastic differential equations, PINN, reliability analysis.