Improved Envelope Spectrum via Feature Optimisation-gram (IESFOgram): A novel tool for rolling element bearing diagnostics under non-stationary operating conditions

Demodulation methods are widely used for bearing diagnostics, based often on the (Squared) Envelope Spectrum after band pass filtering. One of the main challenges of these methods is the detection of a suitable band for signal demodulation under varying speed conditions. Angular resampling methods may synchronize the impulsive nature of bearing damages with a certain periodicity, in the case of large speed fluctuations. On the other hand, the time-invariant carrier frequencies may spread over the broadband of the spectrum, making impossible the application of many band selection tools. Lately, focus has been targeted to cyclostationary-based tools, such as the Cyclic Spectral Correlation and the Cyclic Spectral Coherence, which achieve a high performance in detecting hidden cyclic periodicities. Initially, these methods have been represented in the Frequency-Frequency domain, however they have been extended, to the Order-Order and the Order-Frequency domains, to be able to describe signals under varying speed conditions. The integration of these bi-variable maps over a specific frequency band results to an equivalent to a demodulated spectrum. Therefore, the challenge is the selection of the proper integration band to obtain these demodulated spectra for bearing diagnostics. In this paper, a novel tool called the Improved Envelope Spectrum via Feature Optimization-gram (IESFOgram) is proposed as a band selection tool for the demodulation of the bi-variable map (CSC or CSCoh) for bearing diagnostics. The method is represented in a 1/3-binary tree and is applicable under constant and variable speed conditions. The methodology is tested and validated on real data captured on a laboratory planetary gearbox and on an aircraft engine gearbox, under both constant and varying speed conditions. Furthermore, the methodology is compared in terms of performance with the Fast Kurtogram and the Autogram-based methods.