Laplace Prior-Based Bayesian Compressive Sensing Using K-SVD for Vibration Signal Transmission and Fault Detection

Vibration signal transmission plays a fundamental role in equipment prognostics and health management. However, long-term condition monitoring requires signal compression before transmission because of the high sampling frequency. In this paper, an efficient Bayesian compressive sensing algorithm is proposed. The contribution is explicitly decomposed into two components: a multitask scenario and a Laplace prior-based hierarchical model. This combination makes full use of the sparse promotion under Laplace priors and the correlation between sparse blocks to improve the efficiency. Moreover, a K-singular value decomposition (K-SVD) dictionary learning method is used to find the best sparse representation of the signal. Simulation results show that the Laplace prior-based reconstruction performs better than typical algorithms. The comparison between a fixed dictionary and learning dictionary also illustrates the advantage of the K-SVD method. Finally, a fault detection case of a reconstructed signal is analyzed. The effectiveness of the proposed method is validated by simulation and experimental tests.