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Regular signal of a time-synchronous averaged signal

`Y = tsaregular(X,fs,rpm,orderList)`

`Y = tsaregular(X,t,rpm,orderList)`

`Y = tsaregular(XT,rpm,orderList)`

`[Y,S] = tsaregular(___)`

`___ = tsaregular(___,Name,Value)`

`tsaregular(___)`

computes the regular signal `Y`

= tsaregular(`X`

,`fs`

,`rpm`

,`orderList`

)`Y`

of the time-synchronous averaged (TSA)
signal vector `X`

using sampling rate `fs`

, the
rotational speed `rpm`

, and the orders to be retained
`orderList`

. `Y`

is computed by retaining the
primary frequency, the components in `orderList`

, and their respective
harmonics from `X`

. You can use `Y`

to further
extract condition indicators of rotating machinery for predictive maintenance. For
example, extracting the *FM0* indicator from `Y`

is useful in identifying major changes such as gear tooth breakage or heavy wear in a gear
box.

`___ = tsaregular(___,`

allows you to specify additional parameters using one or more name-value pair arguments.
You can use this syntax with any of the previous input and output arguments.`Name,Value`

)

`tsaregular(___)`

with no output arguments plots the
time-domain and frequency-domain plots of the raw and regular TSA signals.

**Regular Signal**

The regular signal is computed from the TSA signal by retaining the following from the signal spectrum:

Shaft frequency and its harmonics

Gear meshing frequencies and their harmonics

Optionally, the sidebands specified in '

`NumSidebands`

' at the gear meshing frequencies and their harmonics

`tsaregular`

uses a bandwidth equal to the shaft speed times the value of
'`NumSidebands`

', around the frequencies of interest, to compute
`Y`

from the TSA signal. The regular signal is related to the residual
signal through the equation $${Y}_{regular}=\text{}X-{Y}_{residual}$$. If the first-order sidebands are retained in the regular signal, then, $${Y}_{regular}=\text{}X-{Y}_{difference}$$.

**Amplitude Spectrum**

The amplitude spectrum of the regular signal is computed as follows,

$$\text{S=}\frac{\text{fft}(Y)}{\text{length}(Y)*2}$$

Here, `Y`

is the regular signal.

[1] McFadden, P.D. "Examination of a
Technique for the Early Detection of Failure in Gears by Signal Processing of the Time
Domain Average of the Meshing Vibration." *Aero Propulsion Technical Memorandum
434*. Melbourne, Australia: Aeronautical Research Laboratories, Apr.
1986.

[2] Večeř, P., Marcel Kreidl, and R. Šmíd.
"Condition Indicators for Gearbox Monitoring Systems." *Acta
Polytechnica* 45.6 (2005), pages 35-43.

[3] Zakrajsek, J. J., Townsend, D. P.,
and Decker, H. J. "An Analysis of Gear Fault Detection Methods as Applied to Pitting Fatigue
Failure Data." *Technical Memorandum 105950*. NASA, Apr.
1993.

[4] Zakrajsek, James J. "An investigation of gear mesh failure prediction techniques." National Aeronautics and Space Administration Cleveland OH Lewis Research Center, 1989. No. NASA-E-5049.