Harmonic Fourier decomposition and its application in fault identification of rotating machinery system

As one of the most failure-prone critical components in rotating machinery, rolling bearings generate fault signatures exhibiting energy concentration in spectral distributions, thereby offering significant opportunities for deploying one-dimensional signal decomposition techniques in condition monitoring applications. To address the enduring challenge of weak fault feature extraction in practical bearing diagnostics, this study proposes a Harmonic Fourier Decomposition (HFD) framework. The methodology derives mode boundaries through Fourier trend analysis of power spectral density (PSD), effectively reducing computational complexity and eliminating spurious components. A zero-phase Fourier filter bank is employed for frequency-band segmentation, achieving simultaneous minimization of spectral leakage and enhancement of computational efficiency. Furthermore, Harmonic Spectral Kurtosis (HSK) is innovatively integrated to quantify cyclostationary impulse components while suppressing transient interference and background noise. Experimental validation using both simulated signals and bearing test-rig data confirms the method's capability to reliably identify localized defects in inner raceways and outer raceways.