Adaptive Resonance Demodulation for Bearing Fault Diagnosis via Spectral Trend Reconstruction and Weighted Logarithmic Energy Ratio

Incipient fault signatures in rolling bearings are often compromised by intense background noise and stochastic impulses. Conventional resonance demodulation frequently relies on rigid frequency partitioning, which tends to disrupt the physical continuity of resonance bands and results in the incomplete capture of essential diagnostic information. Furthermore, the robustness of prevailing optimal demodulation frequency band (ODFB) selection indicators remains limited under heavy noise interference. This study develops the WLERgram framework, which utilizes regularized Fourier series to capture the global morphology of the vibration spectrum. By anchoring filter boundaries at natural energy troughs, the method mitigates spectral truncation based on inherent signal characteristics. The framework integrates an Adaptive Morphological Consensus (AMC) strategy, employing multi-scale operators to extract rotation-correlated components and enhance resistance to incoherent interference. By incorporating a Weighted Logarithmic Energy Ratio (WLER) metric, the method utilizes a nonlinear operator to implement differential mapping between coherent fault harmonics and stochastic noise, enabling autonomous optimization of the demodulation band. Validations using synthetic simulations and experimental benchmarks (CWRU and UORED) suggest that WLERgram offers reliable feature extraction performance and diagnostic robustness under harsh noise environments.