Research on iterated Hilbert transform and its application in mechanical fault diagnosis

Multicomponent AM–FM demodulation is an available method for machinery fault vibration signal analysis, so a new method for mechanical fault diagnosis based on iterated Hilbert transform (IHT) is proposed. The principle of computing the asymptotically exact multicomponent sinusoidal model for an arbitrary signal by iterating Hilbert transform is introduced, and some properties of IHT are analyzed. Theoretical analysis for the generic two-component signal shows that there are limitations in the direct estimation of instantaneous frequencies via the phase signals of the previously obtained model. Therefore, a smoothed instantaneous frequency estimation (SIFE) method based on difference operator and zero-phase digital low-pass filtering is proposed, and then the accuracy and validity of this method have been proved by the simulation results. The analysis results of the mechanical fault signals show that the weak features of these signals can be efficiently extracted with the proposed approach.