Identification of joint structural state and earthquake input based on a generalized Kalman filter with unknown input

Abstract

Accurate and real-time information of structural states and earthquake input is the prerequisite for structural seismic safety assessment and vibration control. When the earthquake input to a structure is not measured, it has been tried to identify structural state and the unknown earthquake input using the measured structural responses as an inverse problem. However, only structural absolute acceleration responses instead of the relative ones can be measured in this case, which limits the real-time performance of the existing Kalman filter with unknown input (KF-UI). In this paper, a generalized Kalman filter with unknown input (GKF-UI) is proposed to identify structural states and unknown earthquake inputs in real-time. Structural motion equations are established in the relative coordinate system and the observation equations are structural absolute acceleration-only measurements. The analytical derivation of the proposed GKF-UI is a direct extension of the classical Kalman filter (KF). It is also proven that the identification by the proposed GKF-UI using the absolute acceleration-only measurements under unknown earthquake excitation does not lead to the so-called drifted results in the previous identifications under unknown external excitations. Moreover, structural modeling errors can be considered in the identification by the proposed method. Then, it is extended to investigate the identification of the structural state of high-rise shear buildings and unknown earthquake inputs by combining the proposed GKF-UI with the modal expansion. Hybrid dynamic motion equations in modal space and observation equations in physical space are established to both reduce the state dimension and keep the one-dimension of unknown earthquake input instead of the increased number of unknown modal inputs. In addition, absolute accelerations are used in the observation equations, which avoids the dilemma that absolute accelerations cannot be converted into relative modal accelerations in the relative coordinate system under unknown earthquake input. Some numerical examples are used to verify the proposed method. Moreover, a shaking table test is adopted to further validate the performances of the proposed method.