Two-stage fundamental Bayesian model updating method based on MCMC algorithm

Model updating plays an important role in obtaining a more accurate finite element model (FEM) based on measured vibration data. Based on the updated FEM, it is more convenient to carry out further analysis, e.g., structural health monitoring, digital twin, and so on. Bayesian model updating methods are attracting more attention since they can provide rigorous models and evaluate the uncertainty of the updated results. However, in the real application, it still has some problems such as computational efficiency and accuracy. In this paper, a two-stage Bayesian function combined with MCMC algorithm is proposed and used to perform model updating of a real complicated long-span cable-stayed bridge. The two-stage Bayesian function can automatically consider the heteroscedasticity of each utilized modal degree and it allows for incomplete modal information for model updating. Before conducting model updating, two different sensitivity analysis functions are used for local and global sensitivity analysis of bridge model. A set of interaction process between different computation tools has been established to improve computational speed by using an improved stopping criterion. The updated results are demonstrated for both model classes, and ultimately a Bayesian model class evidence was used to judge their superiority. The proposed method was verified by a numerical example and then applied in the updating of the bridge. The experimental results show that the model updating method successfully corrects initial FEMs with reverse mode order errors using incomplete modal information. Simultaneously, the results exhibit a relatively low level of uncertainty. Furthermore, the Bayesian model class selection algorithm proves that new sensitivity analysis functions are superior.