Active Learning Kriging Model with Adaptive Uniform Design for Time-Dependent Reliability Analysis

Abstract

Due to uncertainties and time-varying parameters in design, manufacturing, and commissioning, many structural systems often exhibit uncertain and dynamic properties. These systems need time-dependent reliability analysis to help effectively estimate the safe state during their lifecycle. However, one of the challenging issues in doing so lies in computational efficiency. This paper develops an active learning Kriging technique to improve the computational efficiency of time-dependent reliability analysis. The Kriging model is employed first as a response surface to fit the extreme value response of time-dependent limit state functions. The most probable point of the Kriging response surface is then determined by solving an optimization problem in terms of a cumulative distribution function. Further, an adaptive iterative algorithm is developed to prepare the sampling points for updating the Kriging model based on an adaptive uniform design. Monte Carlo simulations are thus performed to facilitate evaluation using the final generated Kriging response surface. Several case studies are undertaken to test and validate the effectiveness of the proposed method and to demonstrate its applicability to engineering problems.