Interval response reconstruction based on Kalman filter

The purpose of structural response reconstruction is to determine the responses at the unmeasured nodes based on the responses at the measured nodes. This study focuses on utilizing Kalman filtering for structural response reconstruction under the influence of random noise, aiming to obtain the interval boundaries of acceleration responses at the unmeasured structure nodes. Considering the reconstruction errors caused by random model noise and measurement noise within the Kalman filter, an Interval Response Reconstruction (IRR) method based on Kalman filtering is proposed. The IRR method utilizes the state error set to capture error information during the Kalman filter-based response reconstruction process. By leveraging the Gaussian distribution properties, it establishes an error boundary set to calculate the error radius of the posterior state estimation of Kalman filter. Through response reconstruction and radius reconstruction equations, the acceleration response and response interval of the unmeasured structural nodes are obtained, achieving interval-based reconstruction of structural acceleration responses. The method is validated through both numerical simulations and experimental analyses. Results indicate that under different sensor configurations and noise levels, the percentage errors of the response intervals are within 1.9 % for the crane numerical example and 0.3 % for the simply supported beam experiment. The deviation of the actual acceleration response from the reconstructed interval bounds does not exceed 0.08. Compared to traditional Kalman filter-based response reconstruction, the proposed IRR method shows minimal sensitivity to sensor configurations and effectively mitigates the influence of random noise through interval representation. When compared to the Zonotopic Kalman filter (ZKF) and Interval Observer filtering (IOF) methods, the proposed IRR method demonstrates superior performance in reconstructing acceleration response intervals at the unmeasured nodes, exhibiting robust interval reconstruction capabilities.