Adaptive Kriging-based Bayesian updating of model and reliability

Bayesian updating is a powerful tool to reassess and calibrate models and their reliability as new observations emerge, and the Bayesian updating with structural reliability method (BUS) is an efficient approach that reformulates it as a structural reliability problem. However, the efficiency and accuracy of BUS depend on a constant $c$ determined by the maximum of likelihood function. To efficiently complete Bayesian updating with new observations related to implicit performance function, a method that combines adaptive Kriging with Bayesian updating is proposed. The proposed method involves three stages. Firstly, an innovatively advanced expected improvement (AEI) learning function is proposed to train the Kriging model of the likelihood function for estimating c, in which the convergence criterion and the strategy of selecting new training point guarantee the accuracy and efficiency of estimating c. Secondly, a new learning function based on expectation and variance of contribution uncertainty function (EVCUF) is proposed to adaptively train the Kriging model of the performance function constructed in BUS to extract posterior samples and complete Bayesian updating of model. By simultaneously taking the expectation and variance of the contribution of the candidate sample to improving accuracy of the Kriging model into consideration, the EVCUF learning function ensures the robust and efficient convergence of the Kriging model. Finally, based on the training points of the previous two stages, the traditional U learning function is employed to subsequentially update Kriging model of the performance function for classifying posterior samples and completing Bayesian updating of reliability. Additionally, a reduction strategy of the candidate sample pool is proposed to improve the efficiency of the proposed method. After demonstrating the basic principle and advantage of the proposed method, three examples are introduced to verify the efficiency and accuracy of the proposed method.