On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals

The compressive sensing (CS) of mechanical signals is an emerging research topic for remote condition monitoring. The signals generated by machines are mostly periodic due to the rotating nature of its components. Often, these vibrations witness strong interactions among two or multiple rotating sources, leading to modulation phenomena. This paper is specifically concerned with the CS of this particular class of signals using a Bayesian approach. The main contribution of this paper is to consider the particular spectral structure of these signals through two families of hierarchical models. The first one adopts a block-sparse model that jointly estimates the sparse coefficients at identical or symmetrical positions around the carrier frequencies. The second is a spike-and-slab model where the spike component takes into account the symmetrical properties of the support of non-zero-coefficients in the spectrum. The resulting posterior distribution is approximated using a Gibbs sampler. Simulations show that considering the structure in the prior model yields better noise shrinkage and better reconstruction of small side-bands. Application to condition monitoring of a gearbox through CS of vibration signals highlights the good performance of the proposed models in reconstructing the signal, offering an accurate fault detection with relatively high compression rate.