Summary The synthesis of structural identification with vibration control is cost‐effective and beneficial for developing smart building structures. In the past several decades, techniques have been put forward for the combination of structural identification and vibration control. However, it is still a challenging task to synthesize identification and vibration control of time‐varying structures under unknown earthquake excitation. First, structural dynamic responses collected by a structural health monitoring (SHM) system are absolute responses under unknown earthquake excitation, so existing identification approaches for unknown external excitations are not applicable for this situation. Moreover, it is essential to have an efficient algorithm for accurately tracking the various scenarios of time‐varying structural physical parameters with inexpensive computation to ensure the real‐time performance requested by structural vibration control. In this paper, an algorithm is put forward to tackle this challenging problem. It is proposed to treat structural time‐varying effect as “virtual unknown inputs” to the corresponding time‐invariant structure. A generalized extended Kalman filtering with unknown input (GEKF‐UI) is proposed to circumvent the limitations of the existing EKF‐UI approaches. The proposed GEKF‐UI can simultaneously identify structural system, unknown earthquake excitation, and the “virtual unknown inputs” using only partially measured structural absolute responses. Then, the identified structural state is synthesized in real time with the instantaneous optimal control strategy for optimal semiactive control provided by magnetorheological dampers. Therefore, the proposed algorithm can track various structural time‐varying with much less computation, which is more suitable for synthesis with structural control compared with other existing approaches. Some numerical cases of synthesizing identification and vibration control of various type time‐varying structures under unknown earthquake motion are adopted to investigate the feasibilities of the proposed algorithm.
The synthesis of structural health monitoring and vibration control is important in order to provide facilities for constructing smart structures. In recent years, some techniques have been developed to integrate structural identification and optimal vibration control. However, it is still challenging to integrate the identification and vibration control of time-varying structures subject to unknown earthquake excitation. The main difficulties are that structural dynamic responses collected by a simple harmonic motion system are absolute responses under unknown earthquake ground motion while previous identification approaches for unknown external excitation are not applicable for this situation and the need of an efficient algorithm to accurately track the various scenarios of time-varying structures with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, a novel algorithm is presented, in which structural time-varying parameters are treated as ‘virtual unknown inputs’ to the underlying time-invariant structure, a generalized Kalman filter with unknown inputs is proposed for joint identification of joint structural state, unknown earthquake excitation and ‘virtual unknown inputs’ with only partially measured structural absolute responses, and the identification results are integrated in real-time with the instantaneous optimal control scheme to reach the goal of optimal semi-active control provided by magneto-rheological dampers. Some numerical examples of integrated identification and vibration control of various time-varying structures subject to unknown earthquake excitation are used to demonstrate the performances of the proposed algorithm.
The exact information of seismic excitation and structural state is a prerequisite for structural seismic safety assessment and vibration control. When the seismic excitation to a structure is not measured, the seismic excitation can be identified as an inversed problem from measured structural responses. Although some relevant approaches have been developed, there are certain limitations or drawbacks in the existing approaches. To circumvent these problems, two generalized algorithms are proposed for the identification of seismic ground excitation to multi-story and tall buildings, respectively. When the seismic ground excitation to a structure is not measured, the data measured by a structural health monitoring system are structural absolute responses. So the structural motion equation in the absolute coordinate system is derived, in which the unknown seismic ground excitation is treated as unknown external force acting on the structure. First, the identification of unknown seismic excitations to multi-story building structures is studied. A generalized Kalman filtering under unknown input is proposed for the identification of structural state and unknown seismic excitation without the observation of structural absolute acceleration responses at the location of unknown external force. The derivation of the proposed generalized Kalman filtering under unknown input is based on the classical Kalman filter, but is more general than the existing identification approaches based on Kalman filter with unknown input in the deployments of accelerometers in the building structure. Then, it is extended to explore the identification of unknown seismic excitations to tall building structures. To avoid substructural identification from the top to bottom in a sequential manner, the motion equation in absolute coordinate system is reduced by modal expansion. Moreover, instead of the identification of unknown modal forces in previous approaches, the seismic excitation is directly identified without increasing the number of unknown forces. To demonstrate the proposed algorithms, numerical examples of identifying seismic excitations to a 6-story shear building and an 18-story tall building are investigated.
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.
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