3.3. FEATURE EXTRACTION
size windows, where the number of windows equals the number of carrier rotations time the number of planets. Phase is adjusted so that each window contains one planet passing the accelerometer. The windows are then sorted by planet, forming one new signal for each planet.

3.3 Feature Extraction
Feature extraction is the process of extracting metrics about the system in-put which are more informative than evaluating at the raw input itself. Input features are the meta of the input, and constitutes a higher order interpre-tation. Feature extraction is a parameterization process which often reduces the data volume, though this is not always the case. Desirable properties for features are that they are sensitive to the characteristics of the input which di.ers between classes, while insensitive to characteristics which di.er within each class. The latter typically being insensitivity to measurement noise and other irrelevant factors which might confuse the classi.er.
In the case of vibration monitoring, a brute-force approach to feature extraction is extracting the Discrete Fourier Transform (DFT) of the vibra-tion signal. The absolute value of the DFT contains an estimate of the signal power spectrum, which displays substantially di.erent behavior be-tween health state and damaged state signals. Further, the absolute DFT is insensitive to the shaft phase o.set, which is random and thus a source of variation in signal characteristics within each class.
Given the geometry of a mechanical assembly, it is however possible to predict which frequencies, i.e. DFT coe.cients, are a.ected by di.erent failure modes. Consequently, any other coe.cient becomes less relevant. Further, some fault-indicating signal characteristics are not well captured by the DFT, but are better enhanced using other transforms. Thus, it is common to design feature extractors which outputs only the information relevant for detecting the failure modes to which the associated components are susceptible. This information are in the context of HUMS referred to as indicators.
3.3.1 Condition Indicators
The feature extraction part of a HUMS attempts to isolate signal features which have substantially di.erent behavior in normal state signals and signals recorded from damaged components. For shafts and bearing, this process is fairly straight forward. Normal state shafts do not produce much vibra-tion energy. Shaft failures, such as unbalance and miss-alignment, are easily identi.able as vibration energy increases at the frequencies corresponding to multiples of the shaft rotation frequency. Classical bearing failures are, as already explained, identi.able as periodic energy pulses with frequency given by the rotation speed and bearing geometry, as well the fault type.
For gears, feature extraction is not that simple. According
to
[30],
a
perfect
gear
produces
a
distinct
meshing
tone
　
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