To identify a rolling element bearing (REB) failure under variable speed is mandatory to deal with highly non-stationary conditions, mainly caused by the variation of the speed, due to for REB failures the failure frequency is a function of the angular speed. Making the Instantaneous Angular Speed (IAS) one of the most important parameters to measure. However, the speed measurement is sensitive to disturbances like loss of samples or artefacts (Zimroz, R. et al.). Alternatively, the IAS can be extracted directly from the vibration signal, where this is the most challenging situation. Due to the multi-component nature of the signal, where different families of harmonics may coexist, alongside with the interaction between the orders and the structural resonances of the machine, and the low Signal to Noise Ratio (SNR) where noise comprises any component in the signal which is not of direct interest for the analysis (Leclere, Q et al.). As evidence of the continuous interest in REB fault detection under variable IAS, the subject was recently addressed in (Antoni, J., et al.); where two tasks are identified: the IAS extraction from the vibration signal and the posterior failure detection in the angular domain, a domain where the failure identification is possible only after a successful extraction of the IAS. As we will deal with low SNR our approach must be robust. For such reason, it is proposed the use of a Short-Time Non-Linear Least Squares (STNLS) method to estimate the IAS, if a signal is stationary in a short-time segment.

The second step is to highlight a REB failure under variable speed under highly non-stationary conditions. Recently, (Abboud, D. et al.) propose an extension of the cyclic spectral correlation for a time-varying speed scenario. However, it is assumed that time-dependent components are independent of the operating speed, which may be acceptable for modest speed variations; thus, its compensation constitutes an emerging field of investigation. Therefore, a methodology using a Short-Time/Angle frequency 2D filter based on Spectral Kurtosis (STSK), will be proposed in the present work, given that a signal it is expected to be piece-wise stationary regardless the domain (time or angle) if a window small enough is considered. The robustness of the STNLS method is tested in a simulated signal contaminated with different levels of two different types of noise (pink and white). Finally, the STNLS and STSK are applied in a case of study of an aircraft engine publicly available in (Antoni, J. et al.).

Zimroz, R., Urbanek, J., Barszcz, T., Bartelmus, W., Millioz, F., & Martin, N. (2011). Measurement of instantaneous shaft speed by advanced vibration signal processing application to wind turbine gearbox. Metrology and Measurement Systems.

Leclere, Q., André, H., & Antoni, J. (2016). A multi-order probabilistic approach for Instantaneous Angular Speed tracking debriefing of the CMMNO 14 diagnosis contest. Mechanical Systems and Signal Processing.

Antoni, J., Griffaton, J., André, H., Avendaño-Valencia, L. D., Bonnardot, F., Cardona- Morales, O., ... & Sierra-Alonso, E. F. (2017). Feedback on the Surveillance 8 challenge: Vibration-based diagnosis of a Safran aircraft engine. Mechanical Systems and Signal Processing, 97, 112-144.

Abboud, D., Baudin, S., Antoni, J., Rémond, D., Eltabach, M., & Sauvage, O. (2016). The spectral analysis of cyclo-non-stationary signals. Mechanical Systems and Signal Processing, 75, 1–21.