Data Correction
5.1 Introduction
The spectral signature of HUMS vibration acquisitions are a.ected not only by
the
underlying
assets,
but
also
environmental
factors
[50].
During
opera-
tion, acquisitions are performed at di.erent airspeeds, engine torques and oil-temperatures, as well as during level .ight, turning, climbing and so on. As the environmental context of an acquisition is random, relative to when the acquisition is performed, the impact of the various conditions is manifested as random variations between the signals. This impact is manifested di.er-ently for each frequency on each acquisition. The energy at some indicators / frequencies at some acquisitions are heavily in.uenced by environmental factors, while others are not.
These random variations are manifested as noise clouding the vibration measurements. Working with fault detection, it is desirable to reduce ran-dom noise as much as possible, in order to avoid erroneous diagnosis as a result of unreliable measurements. Methods to limit contextual variations in the measurements currently implemented in commercial solutions are mainly limited to contextual windows for when acquisition is enabled. I.e. the use of min and max criteria for signature-in.uential parameters, such as airspeed and torque. A disadvantage of this approach is that variations can still be considerable within these windows. Further, applying strict contextual win-dows poses problems for aircraft with diverse operating envelopes, such as search and rescue aircraft, resulting in low .ight time within the contextual window and consequently a low data volume per .ight.
This chapter tries to compensate for contextual variations through mod-eling. After an initial theoretical framework is developed, methods for both indicator correction and raw signal correction are presented. The purpose
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of the methods is to de-correlate the vibration signatures and their environ-mental context, thus reducing variance between observations representing the same condition of the underlying asset. The better choice of correction method, indicator correction or raw signal correction, depends on the type of indicator and diagnosis methods are deployed on the corrected data, and will be discussed in the following.

5.2 Modeling
In this study, it is assumed that the observed .nite length signal x recorded at time t can be seen as the product of a number of models Mk, each depending on the linear or nonlinear combinations of the elements in a vector of model parameters pk(t) (Eq.
5.1).

x(t)= Mk(pk(t)) (5.1)
k
It is further assumed that this expression can be simpli.ed by considering only the in.uence by the condition of the associated component Mc and the environmental factors Me (Eq.
5.2).

x(t)= Mc.Me(pc(t)) (5.2)
The environmental in.uence, Me, is given by the environment at the time of acquisition. Each HUMS acquisition is accompanied by a set of contextual parameters describing this environment. These are .ight data parameters such as airspeed, torque and oil temperature, where the selection of parameters available depends on HUMS model and version. Consequently, Me can be made as a function of an array of contextual parameters pc(t).
　
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