I frequently see references to the auto-correlation of the time wave form but am unclear as to how to interpret an autocorelated waveform.

Could someone please explain this function?

Thanks,

For a random signal (component of a signal) one thinks of the value at a future time as being independent (statistically – knowing the value at time t gives one no knowledge of its value at time s). Correlation (auto or cross) relates the correlated (non-independent features of a waveform).

For a random waveform (with independent incremements), the auto-correlation is zero except at time lag 0. The repeatable (harmonic) components will have a peak or valley at repeatable time lags.

One can use cross-correlations to look for time delays in signals.

If you have a noisy signal off a pipe with flow, one might show peaks at the lags corresponding to the number of vanes in the pump times running speed (in time values, so the inverse of this) with the flow noise significantly diminished (in practical case, 1X of pump [time period] would also be present as peaks).

Bill,
I'll play around with it some, but I think I get the gist.

Does this mean that autocorrelation can be used to identify correlated impacts in a seemingly random twf? In other words allow you to see the forrest among the trees?

Thanks,

Danny

I assume you are referrring to the RBM auto-correlated waveform, huh?

Its interputation might be simple or difficult depending on how one looks at it.

From what I have seen, the original waveform is divided in half, then the calculations are performed that determines what in the first half is repeated the most often in the second half and trashes the rest of the data.Sometimes the new waveform might have little left to show and sometimes cramped full of data.

If an inner race defect is most predominant in the original then it is what is shown in the correlated, along with most anything else that is in a repeated state.
I believe there are some things in the original waveform that might not be in the correlated one because maybe it only is repeated once or twice.
One might say that the auto-correlated waveform is showing basically what is seen in the spectrum.

Correlation functions are defined as convolutions. The value at T = Sum x(t-T)*x(t) - I've seen the - replaced with a plus.

The operation of convolution creates a product in the frequency domain (fft). The fft of a convolution is the product of the fft's.

Autocorrelation can be thought of as similiar to Synchronous averaging where synchronous averaging is a first moment vector averaging and autocorrelation is a second moment scalar averaging. For a time waveform with random events occuring (such as friction in general), the autocorrelation coefficient will be zero for all delay times greater than zero. For a time waveform of periodic events, the autocorrelation coefficient will have values between + or - 1.0 at the delay times corresponding to integer multiples of the period of the periodic event (values will trend toward + or - 1.0 if little random noise is present in the time waveform).

The strengths (relative to spectral data) of the autocorrelation coefficient data are:

1. Separate periodic events from
random events.

2. Identify the presence of periodic
events at low frequency (such as
cage in bearing faults or felts
in paper machines).

3. Provides distinct patterns with
class of faults (such as BSF
and BPFI faults).