Reliability-based Bayesian Updating using Machine Learning

Abstract

Bayesian updating is a powerful tool for model calibration and uncertainty quantification when new observations are available. By reformulating Bayesian updating into a structural reliability problem and introducing an auxiliary random variable, the state-of-the-art BUS algorithm has showcased large potential to achieve higher accuracy and efficiency compared with the conventional Markov-Chain-Monte-Carlo approach. However, BUS faces a number of limitations. The transformed reliability problem often investigates a very rare event problem especially when the number of measurements increases. Moreover, conventional reliability analysis techniques are not efficient and in some cases not capable of accurately estimating the probability of rare events. To overcome the aforementioned limitations, we propose integrating BUS algorithm with adaptive Kriging-based reliability analysis method. This approach improves the accuracy of the Bayesian updating and requires considerably smaller number of evaluations of the time-consuming likelihood function, compared to BUS.