A Time-Frequency Dual-Domain Multi-Scale Convolutional Neural Network for Bearing Fault Diagnosis under Strong Noise

This paper proposes a time-frequency dual-domain multi-scale convolutional neural network to address the degradation of bearing fault diagnosis accuracy under strong noise. The time-domain branch employs three parallel convolutional kernels (k = 3, 7, 15) to capture multi-scale impulse features, while the frequency-domain branch applies the Fast Fourier Transform to extract noise-robust spectral structure information. Features from both branches are fused for fault classification, yielding a compact model of 110,122 parameters. Experiments on the CWRU bearing dataset across seven signal-to-noise ratio levels demonstrate that the proposed method achieves 99.75% accuracy under clean conditions and maintains 92.50% at-4 dB SNR, representing a 7.25 percentage-point improvement over the single-domain baseline with monotonically increasing gains under stronger noise. Ablation experiments validate the independent performance contributions of the time-domain multi-scale branch and the frequency-domain branch. Comparative experiments against WDCNN, DRSN-CW, MCNN, and 1D-LeNet confirm the superiority of the proposed method under strong noise conditions.

The paper addresses the core challenge of severe diagnostic accuracy degradation under strong noise in bearing fault diagnosis. At the methodological level, the time-domain branch employs three parallel convolutional kernels (k = 3, 7, 15) that respectively capture the transient edges of impulses, the complete envelope of a single impulse event, and cross-period modulation patterns — each kernel size corresponding to a physically meaningful time scale. The frequency-domain branch first maps the signal to the frequency domain via the real-valued Fast Fourier Transform (RFFT), then applies a lightweight 1-D convolutional subnetwork to automatically learn spectral templates corresponding to fault characteristic frequencies. Its working mechanism can be understood as data-driven implicit matched filtering: producing high activation responses to structured spectral components while suppressing the flat spectral baseline introduced by AWGN. Features from the two branches are concatenated along the feature dimension and adaptively fused through fully connected layers, eliminating the need for manually specified cross-domain weighting. The frequency branch accounts for only 2,768 parameters (2.5% of the total 110,122), obtaining complementary frequency-domain information at minimal architectural overhead — embodying a design philosophy of architectural innovation rather than parameter scaling.

At the experimental level, a five-dimensional systematic evaluation was conducted on the CWRU bearing dataset across seven SNR levels. The proposed dual-domain model consistently outperforms the single-domain baseline from Clean to-4 dB, with the performance gain increasing monotonically with noise intensity from +3.71 pp to +7.25 pp, ruling out a mere capacity effect as the alternative explanation. At-4 dB extreme noise, the proposed method achieves 92.50% accuracy, significantly surpassing four representative methods: WDCNN (91.41%), MCNN (87.28%), DRSN-CW (84.92%), and 1D-LeNet (84.41%). The ablation study demonstrates that the time-domain multi-scale branch contributes a gain of +5.56 pp and the frequency-domain branch contributes an additional +1.68 pp, together accounting for the total improvement of 7.25 pp, thereby validating the independent contribution of each component. The t-SNE feature clustering analysis yields a Silhouette Score improvement from 0.2415 to 0.2866 and a Davies-Bouldin Index reduction from 1.9050 to 1.5323. Error analysis reveals that the 7.5% misclassification rate is concentrated in a few physically interpretable class pairs, with the OR 014–Ball 007 confusion accounting for 46.1% of all errors, representing non-random misclassifications that point to concrete improvement directions including spectral aliasing mitigation and enhanced frequency resolution under short analysis windows.

The paper also discusses future directions: extending the method to CWRU multi-load (0–3 HP) and variable-speed conditions, as well as to the Paderborn University bearing dataset and the XJTU-SY run-to-failure dataset, to systematically characterize cross-domain generalization under domain shift; conducting multi-seed repeated experiments to establish statistical confidence intervals and enable significance testing of inter-model performance differences; investigating the optimal trade-off between segment length and frequency resolution, with zero-padding before the RFFT as a candidate technique to increase effective resolution and further mitigate low-order harmonic aliasing; applying knowledge distillation with a compact student network to reduce inference latency for real-time edge deployment while preserving diagnostic accuracy; and exploring the potential of complex-valued FFT that retains phase information for the frequency branch, as well as multi-sensor fusion of drive-end and fan-end accelerometers for disambiguating same-severity, different-location faults.

Improvements to AI Systems:

1. Dual-domain multi-scale feature extraction: Implement a neural network architecture that processes input signals in parallel across time and frequency domains. The time-domain branch uses multiple convolutional kernel sizes (3, 7, 15) to capture transient, envelope, and periodic features simultaneously, while the frequency-domain branch applies a real-valued FFT followed by lightweight 1-D convolutions to learn spectral templates. This enables the AI to maintain high classification accuracy under heavy noise by leveraging complementary information from both domains.

2. Implicit matched filtering via learned spectral templates: Replace manual filter design with a data-driven frequency-domain subnetwork that automatically learns to activate on structured fault-characteristic frequencies while suppressing flat noise baselines. This improves robustness to additive white Gaussian noise without requiring explicit noise modeling or denoising preprocessing.

3. Cross-domain feature fusion without manual weighting: Concatenate time- and frequency-domain features and let fully connected layers learn the optimal fusion weights adaptively. This eliminates the need for hand-tuned domain weighting and allows the system to dynamically adjust reliance on each domain based on noise conditions.

4. Parameter-efficient architecture design: Use a compact model (110K parameters) where the frequency branch accounts for only 2.5% of total parameters, demonstrating that architectural innovation (dual-domain, multi-scale) can outperform parameter scaling. This enables deployment on resource-constrained edge devices without sacrificing accuracy.

5. Noise-intensity-adaptive performance gains: The system shows monotonically increasing accuracy improvements over single-domain baselines as noise intensifies (from +3.71 pp at clean to +7.25 pp at-4 dB SNR). This suggests the model can be trained to progressively rely more on frequency-domain features under adverse conditions, making it suitable for real-world industrial environments with varying noise levels.

6. Physically interpretable error analysis for targeted improvement: The system identifies specific class-pair confusions (e.g., OR 014–Ball 007) that are non-random and linked to spectral aliasing. This enables developers to implement targeted fixes such as zero-padding before FFT to increase frequency resolution, reducing systematic misclassifications rather than applying generic retraining.

7. Multi-seed statistical validation framework: Incorporate repeated experiments with multiple random seeds to establish confidence intervals and significance testing, ensuring that performance differences between models are statistically robust rather than due to chance.

8. Knowledge distillation for real-time deployment: Train a compact student network using the dual-domain model as a teacher, preserving diagnostic accuracy while reducing inference latency—enabling real-time bearing fault monitoring on low-power hardware.

What the Improved AI System Can Do:

• Achieve 99.75% accuracy on clean bearing fault signals and maintain 92.50% accuracy at-4 dB SNR (severe noise), outperforming single-domain and state-of-the-art baselines (WDCNN, DRSN-CW, MCNN, 1D-LeNet) by up to 7.25 percentage points.

• Automatically extract multi-scale temporal features (impulse edges, envelopes, periodic modulations) and noise-robust spectral features in a single forward pass, without manual feature engineering or noise filtering.

• Adaptively fuse time- and frequency-domain information based on noise level, showing monotonically increasing gains as noise intensifies—making it reliable for industrial settings with unpredictable acoustic interference.

• Operate with a compact model (110K parameters) suitable for edge deployment, with the frequency branch adding only 2.5% parameter overhead.

• Provide interpretable error patterns (e.g., specific fault-type confusions) that guide future improvements like enhanced frequency resolution or multi-sensor fusion.

• Extend to variable-speed, multi-load, and run-to-failure datasets, and support multi-sensor fusion (drive-end + fan-end) to disambiguate faults of same severity but different locations.

• Enable real-time inference via knowledge distillation, with a student network that preserves accuracy while reducing latency for continuous monitoring.