Accounting for amplitude of excitation in model updating through a hierarchical Bayesian approach: Application to a two-story reinforced concrete building

•A Hierarchical Bayesian updating method is proposed to account for excitation level.•The approach estimates stiffness-amplitude relationship as well as modeling errors.•It is applied for updating of an RC building using ambient and shaker test data.•Estimated uncertainties are propagated in predicted response time histories.•Improved confidence bounds are obtained when accounting for excitation level. Calibrated linear equivalent models of civil structures are often used for response prediction and performance assessment. However, these models are only valid for a narrow range of excitation level for which these models are calibrated. In this paper a hierarchical Bayesian model updating approach is proposed for model calibration and response prediction of dynamic structural systems in a wide range of excitation levels where the linear equivalent stiffness of different structural components are updated as functions of excitation amplitude. The proposed approach is implemented on a two-story reinforced concrete building with masonry infills. The building, located in El Centro California, has suffered severe damage during past earthquakes. Ambient and forced vibration tests were performed on the building using an eccentric mass shaker, and its dynamic response was measured using an array of accelerometers. The modal parameters of the structure are identified under different amplitudes of vibration and the natural frequencies exhibit significant decrease at higher vibration levels. The hierarchical Bayesian model updating approach is used to estimate the probability distribution of effective stiffness of considered structural components which is characterized by the stiffness mean and covariance as hyperparameters, as well as modeling errors. To account for the effect of vibration amplitude, the effective stiffness mean is considered as a function of vibration level. A two-step sampling approach is proposed to evaluate the joint posterior probability distribution of updating parameters. The calibrated model is then used to predict time history response of the building under forced vibration which is compared with measured data. The good agreement observed from this comparison verifies the calibrated model and the proposed approach to account for the excitation level in updating process.