Two-stage Bayesian system identification using Gaussian discrepancy model

System identification aims at updating the model parameters (e.g., mass, stiffness) associated with the mathematical model of a structure based on measured structural response. In this process, a two-stage approach is commonly adopted. In Stage I, modal parameters including natural frequencies and mode shapes are identified. In Stage II, the modal parameters are used to update structural parameters such as those related to stiffness, mass and boundary conditions. A recent Bayesian formulation allows the identification results in the first stage to be incorporated in the second stage directly via Bayes' rule without using a heuristic model (often based on classical statistics) that transfers the information from Stage I to II. This opens up opportunities for explicitly accounting for modeling error in the structural model (Stage II) through the conditional distribution of modal parameters given structural model parameters. Following this approach, this paper investigates a methodology where the modeling error between the two stages is incorporated with Gaussian distributions whose statistical parameters are also updated with available data. Leveraging on special mathematical structure induced by the model, computational issues are resolved and an analytical investigation is performed that yields insights on the role of modeling error and whether its statistics can be distinguished from those of identification uncertainty (defined for given structural model). The proposed methodology is verified using synthetic data and applied to a laboratory-scale structure.Nanyang Technological UniversityAccepted versionThis paper is funded by the National Natural Science Foundation of China (Grant No.: 51878484; F.-L.Z.), Natural Science Foundation of Shenzhen (Grant No.: JCYJ20190806143618723; F.-L.Z.), a start-up grant SUG/4 (S.-K.A.) from Nanyang Technological University, Singapore, and Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (Grant No.: 2019 EEEVL0401; Y.-C.N.). The financial support is gratefully acknowledged