Compressive sensing of wireless sensors based on group sparse optimization for structural health monitoring

Vibration signals of most civil infrastructures have sparse characteristics (i.e. only a few modes contribute to the vibration of the structures). Therefore, the vibration data usually have sparse representation. Additionally, the vibration data measured by the sensors placed on different locations of structure have almost the same sparse structure in the frequency domain. On basis of the group sparsity of the structural vibration data, we proposed a group sparse optimization algorithm based on compressive sensing for wireless sensors. Different from the Nyquist sampling theorem, the data are first acquired by a nonuniform low-rate random sampling method according to compressive sensing theory. We then developed the group sparse optimization algorithm to reconstruct the original data from incomplete measurements. By conducting a field test on Xiamen Haicang Bridge with wireless sensors, we illustrate the effectiveness of the proposed approach. The results show that smaller reconstruction errors can be achieved using data from multiple sensors with the group sparse optimization method than using data from only single sensor. Even using only 10% random sampling data, the original data can be reconstructed using the group sparse optimization method with a small reconstruction error. In addition, the modal parameters can also be identified from the reconstruction data with small identification errors.