Generalized envelope harmonic product spectrum and GESHSgram with application to fault diagnosis of rolling element bearings

Accurate condition monitoring is crucial for implementing predictive maintenance of industrial machines, where the assessment of health status and the diagnosis of incipient faults rely heavily on the effective detection of machine fault-related information. In vibration analysis, the repetitive impulses induced by the fault of Rolling Element Bearings (REBs) operating at constant speed exhibit approximate periodicity, precisely pseudo-cyclostationarity. The Harmonic Product Spectrum (HPS) generated by the envelope spectrum or squared envelope spectrum has been applied to REB diagnostics by virtue of this property. However, there is a lack of adequate investigation and clear elucidation of their capabilities against multi-source interferences in industrial scenarios. To this end, a family of HPS, called Generalized Envelope Harmonic Product Spectrum (GEHPS), is proposed through the generalized envelope spectrum as the detector and estimator of cyclic frequencies. The performance and characteristics of GEHPS with different parameters are comprehensively verified and revealed by simulating interference noises from multiple sources in industrial scenarios and by comparing with the generalized envelope spectrum under the same parameter configurations. Additionally, taking advantage of the capability of GEHPS to detect cyclic transients, a normalized harmonic significance index with enhanced immunity to interference noise is newly proposed, which promotes a novel envelope analysis methodology, referred to as Generalized Envelope Spectrum Harmonics Significance-gram (GESHSgram), to be developed for fault diagnosis of REBs. The presented method is verified on one simulation case and three experimental cases from different test rigs, along with comparisons with four typical envelope analysis methods. The results demonstrate that the GESHSgram method can effectively and accurately detect various faults of REBs and outperforms four typical envelope analysis approaches.