Learnable Band-Selective Envelope-Spectrum Residual Fusion for Bearing Fault Diagnosis Under Matched Noise Conditions

Strong noise can obscure the transient and modulation signatures used for bearing fault diagnosis, while envelope-based methods remain sensitive to the frequency band selected before demodulation. This study proposes a learnable band-selective envelope fusion WDCNN (LBEF-WDCNN). A raw-waveform branch extracts temporal features, whereas an auxiliary branch applies four differentiable Gaussian masks, reconstructs the corresponding spectrally selected waveforms, and encodes their Hilbert envelope spectra. Both branches are trained jointly and combined using a fixed, sample-independent residual coefficient of 0.1. The method was evaluated on HUST using a matched-noise protocol comprising additive white Gaussian noise (AWGN), colored noise, and impulse noise at 0, −6, and −10 dB, with additional dataset-specific evaluations on CWRU and PU. Across the nine HUST conditions, LBEF-WDCNN achieved the highest average Macro-F1 of 98.53% using 74,065 trainable parameters. At −10 dB AWGN, it reached 95.30% Macro-F1, exceeding DRSN-CW by 7.68 percentage points. Ablation results showed that learnable band selection improved the three-noise average at −10 dB from 94.79% for fixed bands to 96.73%. DRSN-CW remained stronger under severe impulse noise. These results indicate that the proposed representation is particularly effective under severe broadband contamination while retaining a compact model size.