Order-frequency Holo-Hilbert spectral analysis for machinery fault diagnosis under time-varying operating conditions

Holo-Hilbert spectral analysis (HHSA) has been demonstrated to be an effective instantaneous feature demodulation tool for revealing the coupling relationship between the frequency-modulated (FM) carriers and amplitude-modulated (AM) characteristics within nonlinear and non-stationary mechanical vibration signals. However, it is unable to acquire the time varying AM characteristics from the vibration signals of the equipment operates under variable speed conditions. To decode such signals, inspired by HHSA, a novel angle-time double-layer decomposition structure termed order-frequency HHSA (OFHHSA) is established to demodulate the fault information from the time varying vibration signals in this paper. The corresponding spectrogram, namely, order-frequency Holo-Hilbert spectrum (OFHHS) is acquired for describing the interaction relationship between time and angle domains. Besides, the order AM-marginal spectrum is derived from the OFHHS via integrating the carrier variable to exhibit the fault characteristic-related orders. Moreover, the differences between OFHHSA and angle-time cyclo-stationary framework-based order-frequency spectral correlation (OFSC) are analyzed for time varying machinery fault diagnosis. Finally, from the analyses of simulated and tested data of mechanical equipment, the OFHHSA method has avoided the limitations of the two OFSC estimators on periodic assumption and the maximum cut-off order, and the proposed method obtained a more accurate rate in fault identification and more robust ability of anti-noise.