Estimating effective damping introduced by a Pendulum Tuned Mass Damper using the Extended Kalman Filter

July 29, 2014
Publication: Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014, Porto, Portugal
Author(s): Roffel, Aaron J. Narasimhan, Sriram

Abstract: Pendulum tuned mass dampers (PTMDs) are common auxiliary damping devices used to attenuate excessive motion in tall structures. The concept of effective or equivalent damping is commonly referenced when quantifying tuned mass damper (TMD) performance. Effective damping refers to determining the damping in a single-degree-of-freedom (SDOF) oscillator operating at the same natural frequency that would produce an equal mean squared displacement response as the combined main and auxiliary system. Despite its simplicity, effective damping introduced by a TMD has experienced relatively little use in describing the performance of in-service TMDs, since its theoretical computation is based on the displacement response of the structure, which is seldom measured. Instead, acceleration response measurements are taken from which displacements need to be inferred. The proposed method applies the extended Kalman filter for combined state and parameter estimation for the purpose of estimating the effective damping introduced by a PTMD. The acceleration response measurements are fitted to the response of a SDOF system, where the unknown modal damping is appended to the state vector and estimated.|The assumption of known bare structure natural frequency is subsequently relaxed and the natural frequency of the structure without the PTMD is estimated alongside the effective damping. The algorithm is first demonstrated using a numerical example and compared to the theoretical calculation. The methodology is also shown using full-scale acceleration response measurements collected from a structure equipped with a PTMD. The results of the study demonstrate the approach is an accurate and reliable means of quantifying the performance of in-service PTMDs without a direct measure of the displacement response of the attenuated structure and a priori knowledge of the underlying structure’s natural frequency.