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

Yosra Marnissi,Dany Abboud,Amadou Assoumane,Mohamed El-Badaoui,Yasmine Hawwari

doi:10.3390/app11062626

Abstract

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.

Highlights

This paper investigates the reconstruction of smoothly modulated signals in a Bayesian framework by exploiting, for the first time, the structured support of their spectrum
In our analysis, the choice of the proposed models and their effect on the structure of the reconstructed support set
Mechanical vibration signals are very often acquired by accelerometers that are mounted on operating mechanical components

Summary

Introduction

The challenge for remote monitoring is managing the transmission of these volumes of data.there is a need to reduce the size of the samples that are acquired while preserving the useful information. In this context, an alternative to the sampling theory has recently emerged, which shows that data can be recovered from far fewer measurements than what the Shannon–Nyquist theorem states. An alternative to the sampling theory has recently emerged, which shows that data can be recovered from far fewer measurements than what the Shannon–Nyquist theorem states This new theory, coined compressive sensing (CS) introduced in [2,3], relies on the sparsity or compressibility of data. This technique was applied in several fields, such as the medical, communication, presence detection, electromagnetic radiation, and structural health monitoring fields [4,5,6,7,8,9], respectively

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