The infogram: Entropic evidence of the signature of repetitive transients

A classical symptom of rotating machines faults in vibration signals is the presence of repetitive transients, whose distinctive signature is both impulsive and cyclostationary. Typical approaches for their detection proceed in the time or frequency domains, with tools such as the spectral kurtosis, the kurtogram, or the envelope spectrum. The object of this paper is to extend and somehow connect these concepts in order to capture the signature of repetitive transients in both domains. Motivated by ideas borrowed from the field of thermodynamics where transients are seen as departures from a state of equilibrium, it is proposed to measure the negentropy of the squared envelope (SE) and of the squared envelope spectrum (SES) of the signal. This defines the SE infogram, the SES infogram, and their average which is theoretically maximum for a Dirac comb according to Hirschman's uncertainty principle. It is demonstrated that the joint consideration of the infograms significantly extends the domain of applicability of the kurtogram, in particular to situations corrupted with impulsive noise or when the relaxation time of the transients is low as compared to their rate of repetition. This is illustrated on both synthetic and actual vibration signals. This paper is part of a special issue in honor of Professor Simon Braun and pays tribute to his early contribution to the field of mechanical signature analysis. (C) 2015 Elsevier Ltd. All rights reserved.