ASS-GPR: Adaptive Sequential Sampling Method Based on Gaussian Process Regression for Reliability Analysis of Complex Geotechnical Engineering

Abstract

Reliability analysis of complex geotechnical engineering is time-consuming since its performance function is highly nonlinear and implicit. In this paper, an adaptive sequential sampling metamodeling-based method is proposed to deal with such problems. Gaussian process regression (GPR), utilized to approximate the real performance function, is constructed by the initial design of experiments (DOEs). Based on the geometric meaning of the most probable point (MPP) in the first-order reliability method (FORM), the potential MPP, which is a point infinitely close to the limit-state surface and with the minimum distance to the origin while considering a distance constraint, is searched and added to the DOE to refine the GPR. Then, the Monte Carlo simulation (MCS) is adopted to evaluate the failure probability by the refined GPR. The above two procedures are repeated until the stopping criterion is reached. Three examples, including one mathematical example and two geotechnical engineering problems, are analyzed. The results show the proposed method requires fewer performance function calls and is an efficient, accurate, and robust reliability analysis method.