3.3.3 Modeling
A more general approach to feature extraction is modeling. A modeling ap-proach does not, unlike traditional condition indicators, make any assump-tions about features of importance, and does not require any a priori infor-mation about the geometry of the underlying assets.
General
parametric
signal
models
are
MA,
AR
and
ARMA
[4].
By
as-
suming that a signal power spectrum is stationary, this power spectrum can be approximated by any of these models. Fitting a model to an observed signal
can
be
done
by
a
number
of
algorithms
found
in
the
literature
[36].
The number of parameters for any of these models .tted to an observed sig-nal are far subsiding the number of DFT coe.cients for the same signal. Consequently, these parameters make a set of features suitable for classi.er input.
This
was
successfully
tested
in
[14]
[20],
using
a
cluster
classi.er.

A
similar
approach
is
using
the
lifting
scheme
[45]
to
generate
a
wavelet
capable of predicting a signal waveform. This method involves deriving a wavelet from a normal state transmission. The same wavelet can then be used for time domain prediction of subsequent observed signals. Any substantial prediction error indicates that the observed signal does not correspond to the normal
state
wavelet,
and
is
thus
an
indication
of
failure
[7]
[40]
[41].

3.4. CLASSIFICATION

3.4 Classi.cation
With the exception of the usage functions, which utilize simple and precise metrics for decision making, HUMS lies within the .eld of pattern recogni-tion. There are however a few characteristics which separate HUM Systems from most other pattern recognition systems. This is mainly due to the crit-icality of detecting all failure modes, regardless of their frequency of occur-rence. Consequently, the systems are set to detect failure modes for which they are not trained, even some of which have never even occurred (and maybe never will). It is to some extent possible to extrapolate the tested and con.rmed diagnosis functions of one component to other components for which training data does not exist. This is however not done without adding even more uncertainty to discipline which by default is quite "fuzzy", and is partially the reason for the high false alarm rate experienced with these systems.
3.4.1 Threshold Testing
Condition indicator threshold testing is the oldest classi.cation technique in the HUMS .eld, and is incorporated in several commercially available solu-tions. The technique consists simply of testing each indicator to a threshold (Fig. 3.2).
　
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