Signal transmission plays an important role in the daily operation of structural health monitoring (SHM) systems. In wireless sensor networks, transmission loss often occurs and threatens reliable data delivery. The massive amount of data monitoring also leads to a high signal transmission and storage cost throughout the system's service life. Compressive Sensing (CS) provides a novel perspective on alleviating these problems. Based on the sparsity of vibration signals in the frequency domain, CS can reconstruct a nearly complete signal from just a few measurements. This can improve the robustness of data loss while facilitating data compression to reduce transmission demands. Extended from CS methods, distributed compressive sensing (DCS) can exploit the correlation across multiple measurement vectors (MMV) to jointly recover the multi-channel signals with similar sparse patterns, which can effectively enhance the reconstruction quality. In this paper, a comprehensive DCS framework for wireless signal transmission in SHM is constructed, incorporating the process of data compression and transmission loss together. Unlike the basic DCS formulation, the proposed framework not only activates the inter-correlation among channels but also provides flexibility and independence to single-channel transmission. To promote signal sparsity, a hierarchical Bayesian model using Laplace priors is built and further improved as the fast iterative DCS-Laplace algorithm for large-scale reconstruction tasks. Vibration signals (e.g., dynamic displacement and accelerations) acquired from real-life SHM systems are used to simulate the whole process of wireless transmission and test the algorithm's performance. The results demonstrate that (1) DCS-Laplace is an adaptative algorithm that can actively adapt to signals with various sparsity by adjusting the penalty term to achieve optimal performance; (2) compared with CS methods, DCS methods can effectively improve the reconstruction quality of multi-channel signals; (3) the Laplace method has advantages over the OMP method in terms of reconstruction performance and applicability, which is a better choice in SHM wireless signal transmission.
Keywords: Laplace prior; distributed compressive sensing; hierarchical Bayesian model; structural health monitoring; wireless signal transmission.