Joint Estimation of Multi-Scale Structural Responses and Unknown Loadings Based on Modal Kalman Filter Without Using Collocated Acceleration Observations

Abstract

It has been proved that the usage of multi-type observations including global and local information for structural health monitoring (SHM) outperforms that of solo-type measurement. Kalman filter (KF) is a simple but powerful tool for the online state estimation. However, external force is required for the classic KF. Moreover, direct implementation of KF in time domain may be time consuming especially for large structures with many degrees-of-freedoms (DOFs) involved. From these points of view, the idea of modal Kalman filter (MKF) is introduced. An MKF-based approach is then proposed for joint estimation of multi-scale responses and unknown loadings with data fusion of multi-type observations. By using a projection matrix and the selected several modes, a modified observation equation in modal domain is derived. Limited multi-type measurements are fused together for online estimating multi-scale responses of structure at its critical locations. The unknown excitation is simultaneously identified by least squares estimation (LSE). The drift problem of the real time estimation of structural responses and unknown loads is avoided. The effectiveness of the proposed approach is numerically demonstrated via several examples. Results show that the proposed approach is capable of satisfactorily estimating the unmeasured multi-scale responses and identifying the unknown loadings.