Bayesian operational modal analysis of structures with tuned mass damper

Tuned mass damper (TMD) is a common strategy to reduce structural vibration in a passive manner without the need for active power. The basic parameters of a TMD include its mass ratio, natural frequency and damping ratio. While these parameters are factory-calibrated before installation, it would be desirable to assess the in-situ properties of the TMD and the ‘primary’ structure under operational state, e.g., to validate/assess performance and detect detuning over the service life. In this work, a Bayesian approach is developed for identifying the modal parameters of the TMD and primary structure using only the ambient vibration data measured on the primary structure, i.e., ‘operational modal analysis’. The likelihood function and theoretical PSD matrix of ambient data are formulated, accounting for primary-secondary structure dynamics with non-classical damping that is not treated in existing Bayesian formulations. An Expectation-Maximisation (EM) algorithm is developed for efficient computation of the most probable value of modal parameters. Analytical expressions are derived so that the ‘posterior’ (i.e., given data) covariance matrix can be determined accurately and efficiently. The proposed method is verified using synthetic data and applied to field data of a chimney with close modes response attenuated by a TMD.