An improved complex multi-task Bayesian compressive sensing approach for compression and reconstruction of SHM data

The long-term structural health monitoring (SHM) provides massive data, leading to a high demand for data transmission and storage. Compressive sensing (CS) has great potential in alleviating this problem by using less samples to recover the complete signals utilizing the sparsity. Vibration data collected by an SHM system is usually sparse in the frequency domain, and the peaks in their Fourier spectra most often correspond to the same frequencies. This underlying commonality among the signals can be utilized by multi-task learning technique to improve the computational efficiency and accuracy. While being real-valued originally, the data after discrete Fourier transformation are in general complex-valued. In this paper, an improved complex multi-task Bayesian CS (CMT-BCS) method is developed for compression and reconstruction of SHM data requiring a high sampling rate. The novelty of the proposed method is twofold: (i) it overcomes the invalidity of the conventional CMT-BCS approach in dealing with the ‘incomplete’ CS problem, and (ii) it improves the computational efficiency of conventional CMT-BCS approach. The former is achieved by restructuring the CMT-BCS formulation, and the latter is realized by sharing a common sampling matrix across all tasks of concern. The improved CMT-BCS is evaluated using the shaking table test data of a scale-down frame model and the real-world SHM data acquired from a supertall building. A comparison with several existing BCS methods that enable to deal with complex values is also provided to demonstrate the effectiveness of the proposed method.