Bayesian updating using accelerated Hamiltonian Monte Carlo with gradient-enhanced Kriging model

Abstract

Bayesian methods have been widely used to improve the accuracy of finite element model in civil engineering. However, Bayesian methods generally suffer from the computational complexity involved in accurately identifying the posterior distribution. To address this issue, this paper proposes a novel method by combining the Hamiltonian Monte Carlo (HMC) algorithm with the gradient-enhanced Kriging (GEK) model, termed HMC-GEK, for more efficient model updating. The proposed method uses the potential function and gradient information generated during the burn-in phase of the HMC to train the GEK model. By replacing high-cost potential function with the GEK model, the original HMC sampling process is accelerated. An eight-story frame structure and a Y-shaped arch bridge are used to validate the accuracy and efficiency of the proposed method. Furthermore, the HMC-GEK method has been employed to identify damage of a real eight-story steel frame structure. Compared with the HMC method with the traditional Kriging model, HMC-GEK makes more full use of the gradient information of the potential function and significantly improves the sample acceptance rate and computational efficiency. In addition, the successful application of the method in damage identification of the real structure demonstrates its value for engineering applications.