Fourier Neural Network
Spectral Learning for Predictive Maintenance on CWRU Bearing Dataset
Status
Research Published
Accuracy
~96% vs 92% CNN
Role
ML Researcher
Research Motivation
Why Fourier Neural Networks beat traditional approaches for bearing fault detection:
- LSTM Limitation: Processes signals sequentially O(N), misses long-range periodic patterns
- CNN Limitation: Fixed receptive field, struggles with frequency-domain features
- FNN Advantage: Global receptive field via FFT in O(N log N) time. Naturally detects characteristic fault frequencies
- Bearing Faults Create Peaks: Outer race faults produce energy spikes at ~107 Hz. FNN detects these directly in frequency domain
Key Insight: Bearing failure is a frequency phenomenon. By learning in frequency domain with learnable complex weights, the model directly captures fault signatures.
Architecture: Fourier Neural Operator
Key Equation per Fourier Block:
v_{t+1} (x) = Ο( WΒ·v_{t} (x) + Fβ»ΒΉ(R_Ο Β· F(v_{t})) (x) )
Where F = FFT, Fβ»ΒΉ = IFFT, R_Ο = learnable complex weights (first k_max modes only)
Why This Works for Bearing Faults:
- β’ FFT extracts characteristic frequencies of each fault type
- β’ R_Ο (complex weights) learns to amplify fault-specific frequencies
- β’ IFFT reconstructs time-domain signal with emphasis on fault features
- β’ Global view of spectrum = O(N log N) instead of O(NΒ²) attention
Experimental Results
| Model | Accuracy | F1 Score | Train Time | Parameters |
|---|---|---|---|---|
| CNN | ~92% | ~0.91 | 60s | 180K |
| LSTM | ~88% | ~0.87 | 120s | 130K |
| FNN | ~96% | ~0.95 | 45s | 85K |
Key Finding: FNN achieves highest accuracy with fewest parameters and fastest training. Superior noise robustness compared to baselines.
FNN vs Baselines: Property Comparison
| Property | LSTM | CNN | FNN |
|---|---|---|---|
| Receptive Field | Local (sequential) | Local (kernel) | Global (full signal) |
| Complexity | O(N) | O(NΒ·k) | O(N log N) |
| Periodic Patterns | Indirect | Indirect | Direct (spectral) |
| Noise Robustness | Low | Medium | High |
Dataset & Methodology
CWRU Bearing Dataset
- β’ 4 classes: Normal, Inner Race, Ball Fault, Outer Race
- β’ Sampling rate: 12,000 Hz
- β’ Drive-end accelerometer (DE_time)
- β’ Source: engineering.case.edu/bearingdatacenter
Signal Processing
- β’ Butterworth filtering (2-8 kHz)
- β’ Windowed segmentation (2048 samples)
- β’ FFT-based feature extraction
- β’ Spectral subtraction for noise robustness
Deliverables
7 Research Notebooks
01_data_inspection.ipynb β 02_signal_visualization β 03_fft_analysis β 04_feature_engineering β 05_baseline_models β 06_fourier_neural_network β 07_model_comparison
Streamlit Dashboard
Real-time signal upload, FFT visualization, live fault probability prediction. Engineers can upload `.mat` files and get predictions instantly.
CLI Inference
Command-line tool for batch predictions: `python app/inference.py --file data.mat --model fnn`
Tech Stack
ML & Research
- β’ PyTorch (model architecture)
- β’ NumPy/SciPy (signal processing)
- β’ Matplotlib/Seaborn (visualization)
- β’ Jupyter Notebooks
Deployment
- β’ Streamlit (interactive dashboard)
- β’ Python Click (CLI)
- β’ Pytest (unit tests)
- β’ Docker (containerization)