Rolling element bearings are critical parts of rotating machinery, as they support the loads applied to the rotating components. Therefore, continuous monitoring of the health state of the operational bearings is applied in order to detect early damages before any unexpected breakdown of the rotating machinery occurs. Bearing diagnostics is a field of intensive research, focusing nowadays mainly in complicated machinery (e.g. planetary gearboxes, multi-stage gearboxes, etc.) operating under varying conditions (e.g. varying speed and load), as they still provide challenges in terms of accuracy and time of detection/diagnosis.

One of the most common methods for bearings diagnostics is the Envelope Analysis. A filter is usually applied around an excited frequency band (by impulsive damage) and the signal is enveloped, thus obtaining the Squared Envelope Spectrum. For the detection of the filtering frequency band, several band selection tools have been proposed in the past that extract the optimal band in a semi-autonomous or fully autonomous manner. The most widely used tool for band selection is the Kurtogram, where the band that returns the highest Spectral Kurtosis value is selected as the optimal band for demodulation [1]. However, as the bearing damage may excite several frequency bands simultaneously, band-pass filtering around only one frequency band may not be sufficient for the detection of the bearing fault under the presence of noise. One proposed method to circumvent this case is to filter around several bands that carry the Signal of Interest (bearing damage signature). Recently, multi-band filtering based on the Autogram feature values, used as a pre-step in order to extract the Combined Squared Envelope Spectrum (CSES) has been presented, providing better detection performance of faulty bearings compared to the extraction of the SES after filtering over a single optimal band returned by the Autogram [2].

Recently, a particular interest had been target to the Cyclic Spectral Correlation (CSC) and to the derived methods, due to their effectiveness in describing second-order cyclostationary signals. One of such methods is the Cyclic Spectral Coherence (CSCoh) which is a normalized version of the CSC bivariable map [3]. Both methods are represented in the frequency-frequency domain. It has been shown that the integration of the bivariable functions over discrete spectral frequency bands is analogous to band-pass filtering. The IESFOgram has been proposed [4] as a band selection tool, based on either the CSC or CSCoh, in order to extract the optimal frequency band. The integration on the frequency band of the bivariable map further enhances the detectability of faulty bearings on the resulting Improved Envelope Spectrum (IES). However, the method has been proposed with the integration of one single band. In this paper the method is extended towards the extraction of the Combined Improved Envelope Spectrum (CIES), performing a multi-band integration of the bivariable map around multiple resonant frequencies that are carriers of the bearing damage signature. The proposed method is applied, tested and evaluated on experimental data and the results are compared with other state-of-the-art band-selection tools.

[1] Antoni, J., Fast computation of the kurtogram for the detection of transient faults. Mechanical Systems and Signal Processing, 21, pp. 108-124 (2007).

[2] Moshrefzadeh, A., Fasana, A., The Autogram: An effective approach for selecting the optimal demodulation band in rolling element bearings diagnosis. Mechanical Systems and Signal Processing, 15, pp. 294-318 (2018).

[3] Antoni, J., Abboud, D., Xin, G.,, Cyclostationarity in Condition Monitoring: 10 years after. Proceedings of ISMA 2016 including USD 2016, Leuven, Belgium, (2016).

 [4] Mauricio, A., Smith, W., Qi, J., Randall, R., Gryllias, K., Cyclo-non-stationarity based bearings diagnostics of planetary bearings. International Conference on Condition Monitoring of Machinery under non-stationary conditions of CMMNO 2018, Santander, Spain, (2018).