Multiscale three-dimensional Holo–Hilbert spectral entropy: a novel complexity-based early fault feature representation method for rotating machinery

The entropy-based complexity measurement tools have been widely used in extracting fault characteristics of rolling bearings. However, the fault information generally is hidden in both time and frequency domains, and thus one-dimensional entropy is unable to fully extract the comprehensive fault information from the measured vibration signals of rolling bearings. Focus on this shortcoming, a novel entropy-based complexity evaluation method called three-dimensional Holo–Hilbert spectral entropy (HHSE3D) is developed to extract the fault feature of rolling bearings, where the Holo–Hilbert spectral analysis is used to expand the one-dimensional signal to the three-dimensional relationship among time domain information, amplitude-modulated and frequency-modulated features. Meanwhile, to obtain a comprehensively nonlinear dynamic feature description in different scales, the proposed HHSE3D method is extended into the multiscale framework through the coarse-graining process, and thus the multiscale HHSE3D (MHHSE3D) method can be achieved. The robustness and effectiveness of MHHSE3D is verified using both simulated signals and experimental bearing data. The analysis results demonstrate that the proposed method exhibits the best feature extraction ability with highest diagnostic accuracy compared with the other four traditional entropy based diagnosis methods.