Estimation of the instantaneous rotation speed using complex shifted Morlet wavelets

The ability of the complex continuous wavelet transform (CCWT) to provide also an estimation of the instantaneous frequency of a signal, parallel to the estimation of the instantaneous amplitude of the signal, is proposed as an approach for the estimation of the instantaneous rotation speed of machinery. Complex shifted Morlet wavelets (CSMW) present a number of advantages. The concept of shifting the Morlet wavelet in the frequency domain allows the simultaneous optimal selection of both the wavelet center frequency and the wavelet bandwidth. In this paper it is shown that the recovery of the signal frequency can be performed accurately, without the requirement that the wavelet center frequency coincides to the signal frequency. Contrarily, the accurate recovery of the signal amplitude requires additionally this last condition. The algorithm is tested on two synthetic signals and four non-stationary experimental vibration signals, in an experimental fault test rig and in a motorcycle engine. The proposed instantaneous frequency estimation approach presents very good results and in comparison to the Hilbert Transform achieves a significantly lower RMSE. ► The CSMW can be used for the estimation of the inst. rotation speed of machinery. ► The method is evaluated on 2 synthetic signals and 4 non-stationary vibration signals. ► The proposed IF estimation approach presents a lower RMSE compared to the HT.