Reliability assessment of stochastic dynamical systems based on physics-informed gaussian process regression

The dynamic reliability function (DRF) can measure the performance of stochastic dynamic systems under random parameters or excitation in the whole life cycle, and it is required in the reliability-based design optimization under dynamic uncertainty. To construct a high-fidelity predictive model for analyzing complex dynamic systems and enhancing system reliability, a novel surrogate-based approach is proposed in this paper, leveraging physics-informed gaussian process regression (PIGPR). Two PIGPR-based frameworks are established, including PIGPR combined with Monte Carlo Simulation (PIGPR-MCS) for time-variant reliability under random parameters and PIGPR combined with first-passage (PIGPR-FP) for first-passage reliability under stochastic excitations. PIGPR-MCS applies PIGPR for the solution of the original dynamic equation and solves the DRF using MCS, while PIGPR-FP directly uses PIGPR to solve the backward Kolmogorov equation satisfied by the first-passage reliability. Compared with the traditional surrogate-based methods, the proposed PIGPR-based frameworks, by embedding the physical laws in DRF into the covariance function of Gaussian process, can handle uncertain and noisy data, offering better estimation of DRF as well as its uncertainty. Since PIGPR can effectively utilize the physical information of DRF, it effectively reduces the dependence on label samples and improve the physical interpretability, which is well illustrated by a numerical example. The effectiveness and applicability of the PIGPR-MCS and PIGPR-FP are demonstrated through two engineering examples, respectively. Through the proposed PIGPR approach, the safety degree of the stochastic dynamic systems can be efficiently evaluated.