State-Input System Identification of Tall Buildings under Unknown Seismic Excitations Based on Modal Kalman Filter with Unknown Input

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Abstract
The seismic safety evaluation of tall building structures is necessary, but the multidegree-of-freedom feature of tall buildings increases the difficulty of joint identification of structural states, structural parameters, and unknown seismic excitations. Therefore, the state-input-system identification of tall buildings under unknown seismic excitations is the focus of this paper. To avoid the complex work of establishing a structural motion equation in absolute coordinate system, the simple structural motion equation in relative coordinates is directly adopted, but the measured absolute accelerations are used to establish the observation equation. In this way, the establishment of approximate assumptions is avoided, and direct feedback is not reflected in the observation equation. Also, the modal expansion technique is adopted to reduce the dimension of the motion equations and the size of the structural state to be identified. Different from the previous methods based on modal Kalman filtering, the unknown seismic excitation is treated as an unknown input instead of unknown modal forces in this paper, so the dimension of unknown forces in the identification process is not increased. When structural parameters of tall buildings are known, the generalized modal Kalman filtering with unknown input (GMKF-UI) proposed by the authors can simultaneously identify structural states and unknown seismic excitations by observing partial absolute acceleration responses. When extended to the case of unknown structural parameters, a generalized modal extended Kalman filtering with unknown input (GMEKF-UI) is proposed in this paper to simultaneously identify structural states, the unknown seismic inputs, and tall building systems using only partial absolute acceleration responses. Two numerical examples are used to verify the effectiveness of the proposed method.

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