Identification of model‐free hysteretic forces of magnetorheological dampers embedded in buildings under unknown excitations using incomplete structural responses

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Magnetorheological (MR) damper is efficient to mitigate vibration of the structure subject to severe excitations. The identification of nonlinear characteristics of MR damper has attracted increasing attention. However, it is still challenging to identify model-free hysteresis of MR dampers embedded in structures using only incomplete measurements of structural responses under unknown excitations. In this paper, an identification technique is proposed for this tough task, namely, nonparametric identification of MR nonlinear restoring forces in building structures under unknown excitations. The proposed technique involves identifications in two stages. In the first stage, the identification of linear parameters of bare structure and MR dampers under low-level unknown excitations is conducted based on the generalized extended Kalman filter with unknown input (GEKF-UI) by the authors. In the second stage, the hysteretic forces of MR dampers are proposed to be treated as “unknown fictitious forces” to the corresponding linear bare structure identified in the first stage. The generalized Kalman filter with unknown inputs (GKF-UI) by the authors is adopted to identify all unknown inputs including the “unknown fictitious forces” originated from MR dampers. To demonstrate the proposed technique, some numerical examples are used to identify model-free hysteresis of single or multi MR dampers with different nonlinear restoring force models in shear frames under unknown external force excitations or unknown seismic excitations, respectively. Furthermore, experimental testing of the identification of model-free MR damper in a multi-story shear frame under unknown external excitation is conducted.