Study on Simultaneous Identification of External Excitation and Response Reconstruction for Continuous System

This paper proposes a novel dynamic response reconstruction method based on the Kalman filter which can simultaneously identify external excitation and reconstruct dynamic responses at unmeasured positions. The weighted least squares method determines the load weighting matrix for excitation identification, while 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 DRR method evaluates response reconstruction and load identification performance under various load types and errors through simulation examples. Finally, a test system for structural DRR on simply supported beams is constructed and tested. Results demonstrate accurate excitation identification under different load conditions and simultaneous reconstruction of target point responses, verifying the feasibility and reliability of the method.