A Structural Dynamic Response Reconstruction Method for Continuous System Based on Kalman Filter

The structural dynamic response reconstruction technology can extract unmeasured information from limited measured data， significantly impacting vibration control， load identification， parameter identification， fault diagnosis， and related fields. This paper proposes a dynamic response reconstruction method based on the Kalman filter， which simultaneously identifies external excitation and reconstructs dynamic responses at unmeasured positions. The weighted least squares method determines the load weighting matrix for excitation identification， while the minimum variance unbiased estimation determines the Kalman filter gain. The excitation prediction Kalman filter is constructed through time， excitation， and measurement updates. Subsequently， the response at the target point is reconstructed using the state vector， observation matrix， and excitation influence matrix obtained through the excitation prediction Kalman filter algorithm. An algorithm for reconstructing responses in continuous system using the excitation prediction Kalman filtering algorithm in modal space is derived. The proposed structural dynamic response reconstruction method evaluates the response reconstruction and the load identification performance under various load types and errors through simulation examples. Results demonstrate the accurate excitation identification under different load conditions and simultaneous reconstruction of target point responses， verifying the feasibility and reliability of the proposed method.