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.

This study proposes adaptive Studentized multi-kernel maximum mean discrepancy (MMD) for cross-condition machinery fault diagnosis. To account for sampling variation in mini-batch alignment, the multi-kernel MMD objective is normalized by empirical variability and integrated with domain-specific batch normalization. A label-free plateau criterion monitors fluctuations in the alignment loss and triggers joint cosine cooling of the learning rate and alignment weight, adapting the cooling onset to the observed training trajectory. The framework is evaluated on 18 window-level transfer tasks from the Paderborn bearing and PHM2009 gearbox datasets, with five random seeds per task and a fixed final-epoch reporting rule. Mean final-epoch accuracies reach 89.32% and 73.86%, exceeding DAN-style multi-kernel alignment by 2.16 and 2.39 percentage points, respectively. Compared with the fixed-schedule Studentized variant, adaptive scheduling improves accuracy by 0.57 and 0.37 percentage points, respectively. These results support combining variability-normalized alignment with label-free adaptive scheduling for cross-condition fault diagnosis.