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These methods use a reference wavelet or .lter as an approximate of the sig-nal, calculating the distance between each sample signal and the reference. Once a scalar feature is extracted, like the sum square di.erence, it is too late to perform any correction.
Another advantage is the possibility to piecewise normalize the raw signals before any further processing is performed. This is of interest for acquisitions where the recording period is su.ciently long for the environmental context to be subject to change throughout the recording period. Components re-quiring acquisitions of long duration are mainly rotors, as these rotate at slow speed.
This section attempts to de-correlates environmental context and signal power spectrum magnitude, giving the impression that all signals where ac-quired in the reference environment. Any correlation between environmental factors and power spectrum phase is however not considered. On the con-trary, the correction .lter does itself introduce a signi.cant phase distortion to the signal. If this is acceptable or not, depends on the classi.cation system for which the data is intended. Most systems in use today rely only on sig-nal magnitude at speci.c frequencies, and does not consider phase. Should the above method be used for pre-processing data for a phase-sensitive clas-si.cation system, the data must also be passed through a phase-equalizer correcting the distortions caused by the magnitude-equalizer.
To de-correlate vibration power spectrum and environmental context, it is necessary to create a model describing the environmental impact on the signal waveform. This can be done by evaluating the signal Power Spectral Density (PSD) as a function of signi.cant environmental factors, for example airspeed as
shown
in
.gure
5.5.
Note
that
frequency
is
given
in
shaft
order.
For
this
data set, a non-parametric PSD is obtained using a simple discrete Fourier transform, as the signals have already been averaged in the time-domain. The signal PSD magnitude and phase is thus an alternative representation
5.4. SIGNAL CORRECTION
of the time-domain signal, without any loss of information.
To model the spectral behavior as a function of the environmental context, it is however necessary to approximate the signal PSD using a parametric model.
As
seen
in
.gure
5.5,
gear
vibration
signals
consist
of
a
small
number
of high-energy regions, in this example only one, corresponding to the gear meshing harmonics and modulation sidebands, over a noise-.oor. Such a spectral shape can successfully be approximated by an autoregressive (AR) model (Eq. 5.6).
An AR model has a number K of high-energy regions, poles, over a base .oor. The frequency position of each pole is given by ωk ∈ [0, 2π], while the energy level is controlled by rk ∈ [0, 1). The general level is given by b0. All complex poles (ωk ∈{0, pi}), must have a complex
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