Two-Stage Harmonic Optimization-Gram Based on Spectral Amplitude Modulation for Rolling Bearing Fault Diagnosis

To address the challenge of effectively extracting early-stage failure features in rolling bearings, this paper proposes a two-stage harmonic optimization-gram method based on spectral amplitude modulation (SAM-TSHOgram). The method first employs amplitude spectra with varying weighting exponents to preprocess the signal, performing nonlinear adjustments to the vibration signal’s spectrum to enhance weak periodic impact characteristics. Subsequently, a two-stage evaluation strategy based on spectral coherence (SCoh) was designed to adaptively identify the optimal frequency band (OFB). The first stage employs the Periodic Harmonic Correlation Strength (PHCS) metric, based on autocorrelation, to coarsely screen candidate bands with strong periodic structures. The second stage utilizes the Sparse Harmonic Significance (SHS) metric, based on spectral negative entropy, to refine the candidate set, selecting bands with the most prominent harmonic features. Finally, SCoh is integrated over the selected OFB to generate an Improved Envelope Spectrum (IES). The proposed method was validated using both simulated and experimental vibration signals from bearings and gearboxes. The results demonstrate that SAM-TSHOgram significantly outperforms conventional approaches such as EES, Fast Kurtogram, and IESFOgram in terms of signal-to-noise ratio (SNR) enhancement, harmonic clarity, and diagnostic robustness. These findings confirm its potential for reliable early fault detection in rolling bearings.