From waveform to feature vector
Most industrial ML works on windows: short slices of a signal, for example one second of vibration. Each window becomes a row in a table, each feature a column, and the model learns from the table. This framing works for anomaly detection, classification and prognosis alike.
A good feature has three properties. It changes when the fault you care about appears. It stays stable when nothing is wrong. And it does not depend too much on things you do not care about, such as sensor mounting or load.
Classical baseline · one overall value
Overall velocity RMS in 10–1,000 Hz is a single feature. It is robust and standardised, but it misses faults that change the signal's shape before its energy. ML programmes usually keep it as one column among many.
Explore features on simulated faults
Each button generates a vibration signal from a motor running at 25 Hz (1,500 rpm) with a different condition. The table compares eight features with the healthy machine. Watch which features react to which fault: that is what a classifier learns to read.
Families of hand-crafted features
Time-domain statistics
Computed directly on the waveform. Cheap, robust and useful for detection.
| Feature | Formula idea | Reacts to |
|---|---|---|
| RMS | square root of mean square | overall energy: unbalance, severe faults |
| Peak, peak-to-peak | largest excursion | impacts, rubs |
| Crest factor | peak / RMS | early impacts (falls again when damage spreads) |
| Kurtosis | 4th moment / variance²; 3 for Gaussian | impulsiveness: bearing and gear tooth defects |
| Skewness | 3rd moment | asymmetry: rubbing, clipping |
| Shape, impulse, clearance factors | ratios of RMS, mean absolute, peak | impacts at different stages |
Frequency-domain features
The FFT spreads the signal over frequency. Rotating machines produce peaks at predictable multiples of running speed, so order-based features are the most informative: amplitude at 1×, 2×, 3×, the sum of higher harmonics, energy in bands, spectral centroid and spectral entropy.
Envelope features
Bearing defects excite a structural resonance at each impact. Band-pass filtering around that resonance and taking the envelope (the Hilbert transform magnitude) reveals the impact rate. The envelope amplitude at the bearing defect frequencies, BPFO, BPFI, BSF and FTF, are among the strongest bearing features available.
Context features
Speed, load, temperature and process setpoints are not fault symptoms, but a model needs them to know what normal looks like right now. Leaving them out is the most common reason a model false-alarms on operating changes.
Try it in the apps
The Vibration Analyzer computes these features on your files, including the kurtogram that picks the best envelope band automatically.
See features separate faults
The Feature Space Explorer shows which features pull fault classes apart, in a PCA view and with Fisher scores.
Learned features
Deep learning removes the hand-crafting step. A 1D convolutional neural network (CNN) applied to raw waveforms, or a 2D CNN applied to spectrogram images, learns its own filters during training. The first layer typically learns band-pass filters similar to the ones an analyst would choose, and deeper layers combine them into fault-specific patterns.
Hand-crafted features
- Need domain knowledge
- Work with small datasets (hundreds of windows)
- Explainable: "kurtosis went up"
- Transfer well between similar machines
Learned features
- Need little domain knowledge
- Need thousands of labelled windows
- Harder to explain without extra tools
- Can find patterns humans miss, and can also learn shortcuts
In practice the strongest systems combine both: physics-informed features for robustness and explainability, plus learned embeddings where data is plentiful. The computer vision page shows how spectrogram images feed a CNN.
Practical rules
- Normalise per asset. Express features relative to each machine's own healthy baseline, so one model can serve a fleet.
- Use orders, not hertz, when speed varies. A 2× peak should stay "2×" at any speed.
- Check sampling. Bearing envelope features need several kilohertz of bandwidth; a 1 kHz sample rate cannot see them.
- Avoid leakage. Split training and test data by time or by machine, never by randomly shuffled windows from the same run.
Key takeaways
- Features turn windows of raw signal into rows a model can learn from.
- Different faults move different features: there is no single best one.
- Context features (speed, load) are as important as symptom features.
- Learned features need more data but less domain knowledge; combining both works best.