KF-Based Multiscale Response Reconstruction under Unknown Inputs with Data Fusion of Multitype Observations

Abstract

Utilization of multitype measurements including local and global information for structural health monitoring (SHM) has typically outperformed that using solo-type measurements. However, in many practical situations, only partial measurements can be obtained. Therefore, multiscale response reconstruction at the key locations of interest where sensors are not available is required. The Kalman filter (KF) is a powerful tool for optimally estimating the unknown structural states. The classical KF technique is, however, not applicable when the external excitations are unknown. In this paper, a KF-based multiscale response reconstruction under unknown input (MSRR-UI) approach is proposed to circumvent the aforementioned limitations. Based on the principle of KF, an analytical recursive solution of the proposed approach is derived and given. By using a projection matrix, a revised version of the observation equation is obtained. Multitype measurements in a few locations are fused together for response reconstruction. The unknown loading is simultaneously estimated by least-squares estimation (LSE). The effectiveness of the proposed approach is demonstrated via several numerical examples.