Efficient Bayesian updating with two-step adaptive Kriging

Bayesian model updating is a powerful tool for system identification and model calibration as new measurements or observations become available. At present, Bayesian updating with structural reliability methods (BUS) is an efficient and easy-to-implement method, which can transform the multi-dimensional integration in Bayesian updating into a reliability problem by introducing an auxiliary variable. However, the efficiency and accuracy of BUS are dependent on the constant c in the performance function constructed in BUS for some reliability methods, while c is not available in advance generally. Therefore, this paper proposes an efficient Bayesian updating method with two-step adaptive Kriging (AK), which is named as BUS-AK2, where both c and the transformed reliability problem can be efficiently solved by AK. In the proposed method, BUS-AK2 first constructs the Kriging model of likelihood function by expected improvement (EI) learning function, and the maximum of likelihood function and c can be obtained. Then the Kriging model of the performance function in BUS is constructed, where U learning function is employed to obtain samples from the posterior distribution. In addition, for the BUS problem with a small acceptance rate, combined global and local sampling technique is incorporated into the proposed method to further improve modeling efficiency. Examples show that the proposed method has obvious computational advantages for the BUS problem with a small acceptance rate and multiple observations.