Identifying nonlinear characteristics of model-free MR dampers in structures with partial response data

MR dampers have been widely applied in passive and semi-active vibration control over the past decades. The modeling of hysteretic behavior of structural components is a prerequisite for optimal performances of MR dampers and the predication of nonlinear dynamic responses of structures subjected to severe dynamic loads. However, it is hard to establish proper mathematical models for the nonlinear hysteretic behaviors of MR dampers in service due to the complexities of nonlinearities and the degradations of the construction materials. Consequently, it is strongly desired to develop model-free methodologies for the nonlinear hysteretic performance identification with no assumption on the nonlinear hysteretic models of MR dampers. In this paper, a novel method is proposed for this purpose. Firstly, the MR dampers are in the linear state when the structure is under the weak external excitations, the restoring force of the MR dampers is only provided by linear stiffness and viscous damping of MR dampers, the structural physical parameters can be estimated based on the extended Kalman filter (EKF) approach. Then, MR dampers are in the nonlinear state when the structure is under the strong external excitations. The nonlinear restoring forces from MR dampers in a structure are treated as 'unknown fictitious inputs' to the corresponding structural systems without MR dampers. The recent Kalman filter with unknown input (KF-UI) algorithm developed by the authors is adopted for the simultaneous identification of the corresponding structural systems and the 'unknown fictitious inputs'. No real information about the structure is needed, so the proposed method is capable of identifying hysteretic restoring forces of MR dampers by the direct use of partial structural dynamic response measurements, which are usually available from an employed structural health monitoring (SHM) system. To validate the performances of the proposed method, some numerical simulation examples of identifying nonlinear hysteretic restoring forces of MR dampers in different models are used.