Determining the number of measurements for compressive sensing of traffic-induced vibration data

Abstract Compressive Sensing (CS) is an emerging signal sampling technique, which can be useful in the long-term monitoring of civil infrastructures by reducing the storage space and transmission bandwidth drastically. In this paper, a fully deterministic approach is adopted to enhance the previously proposed CS-based methods. First, the sparsifying dictionary is trained using a vibration data set. Then, a deterministic projection matrix is computed based on the trained dictionary. Second, a new index is defined to determine the number of measurements in advance, without any trial and error in the reconstruction stage. This index which is coined as NPI (Normalized Power Index) is derived using the singular value decomposition of the trained dictionary. The capability of the proposed method is investigated using vibration signals of the Tianjin Yonghe Bridge with traffic excitation. Both accuracy and computational time of the deterministic CS was compared to different data compression algorithms.