Normalized complex Teager energy operator demodulation method and its application to fault diagnosis in a rubbing rotor system

As a newer signal demodulation method composed of an empirical AM–FM decomposition and a Hilbert transform, the Normalized Hilbert transform (NHT) method has been proved effective to overcome several drawbacks of the direct Hilbert transform (HT) demodulation method to a certain extent, including limitation of Bedrosian theorem, negative frequency values and inevitable boundary fluctuations of the demodulation results. However, studies in this paper will show that the FM signal resulting from the empirical AM–FM decomposition may contain riding waves and its local extrema values may also deviate much from unity value in some cases. These two problems involved in the empirical AM–FM decomposition are not beneficial to extracting a desirable instantaneous frequency. Moreover, since the Hilbert transform is still used in the NHT method to extract instantaneous frequency from the FM signal, the boundary fluctuations will inevitably occur. Aiming at the drawbacks of NHT method, a new signal demodulation method named the normalized complex Teager energy operator (NCTEO) is proposed in this paper, which consists of an improved empirical AM–FM decomposition and a new instantaneous frequency estimate based on complex Teager energy operator (CTEO). In this demodulation method, the improved empirical AM–FM decomposition is firstly applied to a monocomponent signal for instantaneous amplitude extraction, achieving the separation of the envelope signal (AM part) and the carrier (FM part), then the proposed CTEO method is employed to extract the instantaneous frequency from the resulting FM signal. The results of comparative analysis on simulated signals and experimental rotor data demonstrate that NCTEO method can effectively extract the time-frequency information, and provide a reliable diagnostic basis for the rotor rubbing fault; moreover, comparisons with some other existing demodulation methods, such as HT, NHT and TEO methods, show the promising applications of NCTEO method.