Bayesian Operational Modal Analysis of Structures with Tuned Mass Damper

Tuned mass dampers (TMDs) are general used as a common strategy for reducing structural vibration, e.g., to improve structural safety and human comfort under various dynamic loadings. It can operate in a passive manner without active control algorithm or external power. For a given mass of the TMD (which may be determined by practical constraints), the design of TMD involves the specification of optimal natural frequency and damping ratio, which are determined according to the properties (i.e., mass, natural frequency and damping ratio) of the ‘primary’ structure. The latter is better informed by the in-situ modal properties, which can differ significantly from the predictions based on design blueprints. After installation, TMD is susceptible to detuning (i.e., its parameters are no longer optimal as designed) due to deterioration or changes of the system, resulting in degradation in performance. It is therefore desirable to assess the in-situ properties of the TMD and the primary structure under operational state. This thesis aims at developing a Bayesian approach for identifying the modal parameters of a structure equipped with TMD, using only ambient vibration data measured on the primary structure, i.e., ‘operational modal analysis’ (OMA). The work covers formulation, computational algorithms, verification and application. A Bayesian OMA approach provides a rigorous means for making inference about modal properties and quantifying the identification uncertainty. The identification results include the posterior (i.e., given data) most probable value and covariance matrix, informing the ‘best estimate’ and identification uncertainty, respectively. The likelihood function and theoretical power spectral density matrix of ambient data are mathematically formulated, accounting for non-classically damped modal dynamics that is not treated in existing Bayesian formulations. An Expectation-Maximisation algorithm is developed for efficient computation of the most probable value of modal parameters. Analytical expressions are derived so that the posterior covariance matrix can be determined accurately and efficiently. The proposed algorithms are verified based on synthetic data and then applied to field data of structures with closed-mode response attenuated by TMD