3.4. CLASSIFICATION
given a series of alarms. This has successfully been applied to rotorcraft condition
indicators
in
[37].

The main drawback with the two latter methods is that they require a substantial amount of observations in order to produce a diagnosis. This means that there will be a delay between the occurrence of a problem and its detection. As far as Bayesian decision making is concerned, it is due to limited availability of training data di.cult to estimate the prior possibilities.
3.4.2 Clustering
Most failure modes tend to a.ect more than one indicator. A gradual shift in several indicators is thus a better indication of failure than random per-turbations in a single indicator. Consequently, a more robust indication of failure is measuring the total drift across all indicators for a given component, relative to their normal state baselines.

A classi.er taking this into account can be implemented through a cluster system
[16]
[18].
A
cluster
system
is
a
space
with
a
number
of
dimensions
equal to the number of inputs. Each class is a multi-dimensional region in this space. Any input vector is classi.ed by determining which sphere it falls within (Fig. 3.3),
or
alternatively
classi.ed
as
unknown
it
falls
in
the
void
between the regions.
A HUMS classi.er based on this method must as a minimum implement the normal state class. Consequently, any observation falling outside this sphere must be considered faulty. Such a system might also implement classes representing known failure modes. This technology has been adapted for several
commercial
solutions
[3]
[22],
and
provide
a
classi.cation
tool
which
is both .exible and transparent.

3.4.3 Feedforward Networks and Fuzzy Logic
Certain solutions based on feedforward networks and fuzzy logic exist in the academic
literature
[39]
[25].
Compared
to
cluster
solutions,
the
feedforward
network is more e.cient by allowing complex class regions to be de.ned with fewer neurons. The principal objection against feedforward networks working directly on DFTs or condition indicators is that training requires non-linear optimization. Using a non-linear optimization in the learning process will result in an even more complicated post-overhaul re-learning procedure for the operator. This can be circumvented by normalizing the inputs against learnt baselines before entering them into a factory-set network, although this solution has not been addressed in the literature. Moreover, feedforward networks require substantial amounts of training data and provide less insight to their inner logic. It should also be noted that .exibility similar to a feed forward network can be achieved with a cluster solution by adding a linear layer behind the radial basis layer.
　
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