A Gaussian process-based dynamic surrogate model for complex engineering structural reliability analysis

The performance function of a complex engineering structure is always highly nonlinear and implicit, and its reliability needs to be evaluated through a time-consuming computer codes, such as finite element analysis (FEA). Thus, computational efficiency and precision are hard to unify when using traditional reliability methods in large-scale complex engineering structures. In this paper, a Dynamic Gaussian Process Regression surrogate model based on Monte Carlo Simulation (DGPR-based MCS) was proposed for the reliability analysis of complex engineering structures. A small number of training samples are created by random approach with FEA codes for building the Gaussian process regression (GPR) surrogate model, and the highly nonlinear and implicit performance function is approximated by GPR with an explicit formulation under a small sample condition. Then, combined with the trained GPR surrogate model, the most probable point (MPP) is quickly predicted using Monte Carlo sample technique without any further FEA. An iterative algorithm is presented to refine the GPR using the information of the MPP to continually improve the reconstruction precision in the important region, which significantly contributes to the probability of failure, and the probability of failure is taken as a convergence condition. The proposed method has advantages of high efficiency and high precision compared to the traditional response surface method (RSM). It can directly take advantage of existing engineering structural software without modification.