Consequences of non-respect of the Bedrosian theorem when demodulating

Abstract

Vibration data acquired during system monitoring periods are rich in harmonics characterizing the presence of several mechanical parts in the system. Periodic variations of the torque or of the load create modulation side-bands around those harmonics. Even if the energy impact of the side-bands is small compared to the total energy of the signal, they are strong indicators of failures in mechanical systems. Unfortunately, these effects are of little concern in most of condition monitoring systems. When considering the problem with a signal processing point of view, a demodulation of those side-bands allows a time visualization of the modulating functions which are a precise image of the torque or the load variations. This demodulation can be done on the analytical signal directly derived from the original data. But to do that, data and specifically its spectrum should respect some constraints. The purpose of this paper is to underline those constraints, often forgotten. In particular, the respect of the non-overlapping condition in the Bedrosian theorem is discussed for signals and modulation rates that can be encountered on rotating machines. The respect of the constraints depends on the monitored phenomenon (e.g., gearmesh, rotating shaft), the modulation phenomenon (e.g., belt frequency, rotor current) and the type of medium (e.g., vibrations, electrical current). In the case where the constraints are not satisfied, we explain the consequences in terms of signal processing. These results are illustrated by two industrial case studies.