I think I am getting a grasp on autocorrelation but am still confused by the idea of a negative correlation factor.

Can anyone explain the sinusiodal nature of the autocorrelated PeakVue TWF attached?

autocorrelate.doc (64 Kb, 76 downloads)

Let Rxx(t) be the true autocorrelation function (unknown) and Rxx_hat(t) be our estimate of the autocorrelation function.

Rxx(t) = E [X(tau) X(tau-t)] / E[(X(tau)^2)]
Rxx_hat(t) = Int [ X(tau) X(tau-t)] dtau / Int [ X(tau)^2] dtau

Both functions can in general be positive or negative.

BUT if X(t) is always above 0 as it is for a peakview waveform, then the autocorrelation function should stay positive.

So as far as I know, your peakvue autocorrelation should be positive. It looks as if the autocorrelation waveform has been inadvertantly filtered to remove the dc component. That is fine for normal time waveforms but destroys the meaning of an autocorrelation waveform.

Wher computing the Autocorrelation coefficient function from the PeakVue waveform, the first task is to shift the PeakVue waveform so that the mean value is zero. This leads to the very important property of removing the random (uncorrelated) component from the autocorrelation coefficient data. If you have a sine wave with no noise, the autocorrelation coefficient function will be a cosine wave ranging between + and - 1.0.

The data you are showing is suggesting you may have rubbing occuring with a period of one revolution. The peakVue spectra is showing activity (impacting, rub, or so) at the running speed. If the activity was a simple impact event occuring at once per rev, you would expect the duration of the impact would be short relative to one revolution and hence the duration would be short in the autocorrelation data. Yours is activity occuring over much of the revolution where the energy from the assumed rub is varying from 'most' to 'little' in a very repetitive (cyclic) nature through a shaft revolution.

Dr. Robinson,

This bearing has a guard attached that forms a cylinder around the shaft and extends axially between the bearing housing and the fan housing. When they over grease the bearing (SOP), it sometimes gets packed into this guard. That would seem to constitute a rub to me. I'll have it checked out, since it has happened before.

Thanks. I'll post if I get any response.

And thanks for the explanations Pete and Dr. Robinson. They both helped, I think

http://en.wikipedia.org/wiki/Autocorrelation

I see from the above wikipedia link there are various flavors of autocorrelation. The signal processing flavor does not subtract out the mean and is similar to what I was describing. The statistical flavor subtracts out the mean as Mr Robinson described. I can see the value in eliminating the mean (dc component) since the dc component would give a positive dc correlation component that doesn't tell us anything about the nature of the spacing of impacts.