A robust autocorrelation-based strategy for early gear fault feature extraction under strong Gaussian noise and random impulsive interference

Gearbox fault diagnosis is often hindered by the presence of strong Gaussian white noise and random impulsive noise, which tend to mask weak modulation components associated with early-stage faults. To overcome this challenge, this study proposes a novel demodulation-based signal analysis method, termed LEARCgram, specifically designed to extract cyclic fault features under complex noise conditions. The proposed method introduces the logarithmic envelope autocorrelation average power spectrum (LEAPS), which effectively enhances periodic fault-related components while suppressing non-Gaussian interference. Furthermore, a new indicator called the relative cyclic frequency index (RCFI) is developed to evaluate the periodicity strength of each frequency band, thereby enabling the selection of the optimal demodulation band in a data-driven and fault-targeted manner. By integrating the advantages of logarithmic envelope transformation, autocorrelation analysis, and spectral averaging, LEARCgram improves the signal-to-noise ratio and enhances the detectability of subtle fault signatures. The method is validated using both simulated gear fault signals and experimental vibration data collected from industrial gearboxes. Comparative results demonstrate that LEARCgram outperforms conventional methods in isolating fault-related harmonics and exhibits superior robustness against noise and impulsive interference, making it a promising tool for early and reliable fault diagnosis in rotating machinery.