Multi-rate Kalman filtering for structural dynamic response reconstruction by fusing multi-type sensor data with different sampling frequencies

In this paper, a novel dynamic response reconstruction method based on multi-rate Kalman filtering (MRKF) is presented. The proposed method starts with representing the structural system by the state-space equation. Then, different observation equations are defined, and that selection is based on the availability of sensor types at a specific time. Not only can the multi-type sensor data sampled at different rates be fused directly, but the presented method also relaxes the collocated monitoring requirement. In addition, future observations are used to benefit the current state estimation by the Rauch, Tung, and Striebel smoothing procedure. The unobserved structural dynamic responses are estimated using the MRKF virtual sensing technique with multi-rate sensor data. Several demonstrative numerical tests are performed to verify the superiority and robustness of the presented MRKF method on one benchmark shear frame model. The experimental test employed a computer-vision-based displacement tracking technique. Results show that the proposed method surmounts the obstacle to deploying consumer-grade cameras in structural health monitoring applications, which provide a low-cost sensing solution without sacrificing response estimation accuracies.