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

Abstract

Summary 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.

System Identification of a Structure Equipped with a Cable‐Bracing Inerter System Using Adaptive Extended Kalman Filter

“…Recently, some KF-based methods with unknown input have been proposed to simultaneously estimate the system state and unknown input [35][36][37][38][39][40][41]. Particularly, several EKF-based model-free approaches have been developed to identify the restoring forces rather than the parameters of structural control systems [42][43][44][45].…”

Integration of locating baseline-free nonlinear elements and identifying model-free nonlinear restoring forces in structures

“…The authors [35][36] also developed model-free NRF identification methods, e.g., taking power series polynomial model to approximate NRF and then utilizing Kalman filter to conduct NRF identification, however, it is difficult to determine the polynomial series. Later on, the authors [37][38][39] treated structural NRFs as the 'unknown virtual forces' acting on the linear structure, then the NRFs are identified by the proposed Kalman filter under unknown input (KF-UI). However, the locations of structural nonlinearity need to be known in prior.…”

Hysteresis and dynamic loading nonparametric identification for multi‐degree‐of‐freedom structures using an updated general extended Kalman filter and a Legendre polynomial model

“…Subsequently, considering the difficulties in measuring complete excitation information, Xu et al 44 also put forward a nonparametric nonlinear restoring force (NRF) and excitation identification approach with EKF and data fusion, where NRF was expressed in the form of a Legendre polynomial model (LPM). Aiming at the identification of the hysteretic forces of a nonlinear structure in a nonparametric way, Lei et al 45 proposed a two stage model‐free hysteresis force identification approach for MR dampers with GEKF‐UI and GKF‐UI, where the hysteresis force is treated as a “unknown fictitious forces” applied to the corresponding linear bare structure identified in the first stage. Zhao et al 46 discussed the nonuniqueness problem in the stiffness and damping coefficients identification results on the first floor of a linear structure under base excitation.…”