A stochastic process discretization method combing active learning Kriging model for efficient time-variant reliability analysis

Abstract

Time-variant reliability analysis (TRA) has attracted tremendous interest for evaluating product reliability in full life cycle. Discretization of stochastic process is considered one of the simplest ways to transform a time-variant problem into a time-invariant problem that becomes easier to handle. Its adoption in time-variant problem, nevertheless, requires overcoming two main issues on (1) the low efficiency of small discrete time interval, and (2) the low accuracy of large discrete time interval. To tackle these two challenges, we propose a Kriging-assisted time-variant reliability analysis method based upon stochastic process discretization (namely, K-TRPD for short). First, a complex time-variant reliability problem is converted into conventional time-invariant problem through discretization of stochastic process. Second, the most probable point (MPP) trajectory is approximated through a Kriging model over the entire time period concerned, whose input is identified from the discrete time points by an active learning approach; and the output is obtained by the first order reliability method (FORM) at the identified time points. Finally, the constructed Kriging model is utilized for time-invariant reliability analysis at each discrete time point, and the time-variant reliability is obtained by using the time-invariant reliability analysis results for analyzing the multivariate normal distribution function. In this study, three numerical analysis examples and one engineering design example are presented to demonstrate the effectiveness of the proposed method.