1. Autocorrelation Danny Vandeput & Lasse Hansen
3/31/2017
Autocorrelation
Danny Vandeput & Lasse Hansen
Asset Optimization Division
Machinery Health Management

2. Definition
Autocorrelation, R, is a mathematical tool for finding repetitive patterns, such as
find the presence of a periodic signal which has been buried under noise, or
identify the missing fundamental frequency in a signal implied by its harmonic frequencies.

3. Definition
It is used frequently in signal processing for analyzing functions or series of values, such as time domain signals.
Informally, it is the similarity between observations as a function of the time separation between them.
More precisely, it is the cross-correlation of a signal with itself.

4. Use of Autocorrelation, examples
Doppler Radar Techniques for Estimation of target velocity
Imaging of Blood Flow used in Medical Ultrasonography. .. .
Vibration Analysis

5. Common tools in Vibration Analysis on Rotating Machinery are:
Digitally capture of a Band Limited Time Waveform
at a predetermined sampling (digitization) rate
for a specified data block size
Spectral Analysis (usually via FFT) of the Time Waveform.
For standard vibration analysis, it is customary to carry the spectral analysis out in the velocity domain (mm/sec, RMS)

6. Common tools in Vibration Analysis on Rotating Machinery are:
In addition to the velocity spectral analysis, a special analysis recommended by EPM is the
capture of a time block consisting of acceleration “peak values” (PeakVueTM time waveform)
compute the PeakVue spectral data in a manner analogous to the velocity (or acceleration) spectral data
Another tool available with EPM is the Autocorrelation Waveform.
The autocorrelated waveform is a method for determining the periodic or random energy in the waveform

7. Why use Autocorrelation in Vibration Analysis
The strength in the autocorrelation function is its
ability to identify low repetition rate events with low duty cycle
ability to separate random events from periodic events
The autocorrelation function also supplies a means to approximate the percentage of energy in the time waveform that is
either from the periodic energy or
from the random energy.

8. Why use Autocorrelation in Vibration Analysis
The Autocorrelation Coefficient function is not an average value obtained over the entire block of data at a specific narrow band such as the spectral data.
The resultant fact is, that low duty cycle (low frequency) periodic data shows up very strongly in the Autocorrelation Coefficient data.
The higher frequency periodic data (high duty cycle) is more obvious in the spectral data than in the autocorrelation data.

9. How to use Autocorrelation in Vibration Analysis
The Autocorrelation Coefficient function has proven valuable as a tool to aid in the interpretation of vibration data (especially for the PeakVue analysis). The key properties are:
For random data, the value will approach zero
For periodic data with no (or little) noise, the value will approach 1 at the period (1/frequency) of the periodic data

10. How to use Autocorrelation in Vibration Analysis
The pattern of the periodic peaks can be very helpful in identifying the fault type.
Any defect that is amplitude modulated will clearly have the modulation frequency shown.
When autocorrelation is performed, the waveform will be reduced to ½ its original length in time due to the autocorrelation function process.
This should be remembered when using it as a diagnostics tool to identify very slow speed faults

11. Useful Properties
The autocorrelation coefficient function is a mathematical process used to determine how much of the waveform energy is periodic.
The amplitude scale is always -1 to +1.
The scale is not related to normal vibration units (acceleration, velocity, displacement).
If the amplitude value is near zero, almost all of the waveform energy is from a fault generating mostly random impacting, (e.g. lubrication fault).

12. Generated signal with almost all noise

13. Generated signal with almost all noise
Autocorrolation waveform shows no periodic energy
Almost all energy is from random events

14. Bearing with insufficient lubrication

15. Bearing with insufficient lubrication

16. Useful Properties (partially repeated)
If the amplitude value is near zero, almost all of the waveform energy is from a fault generating mostly random impacting ( e.g. lubrication fault).
If the amplitude is near 1, almost all of the energy is from a periodic fault.
The period between the peaks will determine the frequency of the fault

17. Generated signal with very little noise

18. Autocorrolated waveform indicating a max amplitude of value of 0,984 at the rate of the periodic energy

19. Bearing with Outer Race Defect marked Exhaust fan, 1698 RPM

20. Autocorrolation amplitude is 0,93 indicating that almost all the energy is from a periodic source

21. The period of the autocorrolated waveform is 86,5 Hz being generated by bearing outer race
Autocorrelation function allows adding fault frequencies to indicate the cause of the periodicity

22. Useful Properties (partially repeated)
If the amplitude value is near zero, almost all of the waveform energy is from a fault generating mostly random impacting ( e.g. lubrication fault).
If the amplitude is near 1, almost all of the energy is from a periodic fault.
The period between the peaks will determine the frequency of the fault
The amplitude value of the periodic event will be somewhere between 0 and 1
The square root of the peak amplitude will be the approximate percentage (fraction) of energy contributed by the fault with that period

23. Square root of 0,92 is 0,96, so 96% of the energy (aprox 21,5 g of the 22,35 g) is generated by the outer race fault

24. Summary
Time Synchronous Averaging (vector averaging) highlights events synchronous to the trigger event.
Energy not synchronous to the trigger will be removed.
Autocorrelation averaging (scalar averaging) highlights periodic events
(including synchronous and non-synchronous events)
Periodic events are highlighted by both normal FFT spectra and autocorrelation

25. Summary
Spectra has an advantage for defects generating higher frequencies
Autocorrelation has an advantage for lower frequency defects
Autocorrelation provides a means to determine the approximate percentage of the waveform energy which is due to the periodic event

26. Summary
Autocorrelation is a very useful feature to detect cage problems and BSF problems.
Both are typically very low in amplitude and are hidden into the random time waveform.
Also defects like gear mesh problems can be diagnosed using autocorrelation

27. Autocorrelation Cases
3/31/2017
Autocorrelation Cases 27

28. Cases Looseness Cage problem Bearing Defect with Lube Fault
Ultra Low Speed bearing problem

29. Case # 1 Looseness 1x and harmonics, not necessarily looseness
Data indicates some high frequency energy
excited by a low frequency event
impacts up to g’s and a very random pattern

30. Case # 1 Looseness
Autocorrelated waveform indicates a change in speed during the acquisition time
Period of 1x seems regular for the first half of waveform
But then it changes
Second half of the Autocorrelated waveform
also indicates a 1x, it is only slightly changed

31. Case # 1 Looseness This zoom indicates little periodic content
Bearing Inner Race was very loose on the shaft,
turning slightly at the shaft, so the 1x period was shifted

32. Case # 2 Cage fault – bearing installation Spectrum and Waveform indicating cage defect
Fan with a speed of 890 RPM

33. Case # 2 Cage fault – bearing installation Not sharp peaks like a cracked or broken cage
No indication of high frequency
riding on low frequency content

34. Photo of bearing in Pillow Block Housing
The axial trust with the misaligned races generated high
frequency energy as the cage rotated through the tight spot

35. Case # 3 Ultra Low Speed Bearing Problem Outer race defect indicated in spectral data on gearbox, 0,4 RPM

36. Case # 3 Ultra Low Speed Bearing Problem
Highest value is 0,118 indicating aprox 34% energy
From outer race fault or 0,41g’s.
PeakVue Assistant does not calculate below 4 rpm
indicates here alert value to 0,2g and fault level 0,4g

37. Case # 4 Bearing with Defect and Lube Fault
PeakVue spectrum and waveform
show a clear BPFO defect

38. Case # 4 Bearing with Defect and Lube Fault
Only about 13.9% (√ ) of the energy is coming from the BPFO
Rest of the energy is random and related to a lube fault

39. Autocorrelation Circular Plot
Combined with the Circular Plot the Autocorrelation can also provide very good information about the load zone

40. Autocorrelation Circular Plot
Autocorrolation waveform
in circular format indicating
non-synchronous impacting
with amplitude modulation
at turning speed.
Typical for Inner Race defect
The same can be applied to gearboxes

41. How to use Autocorrelation?
The use of Autocorrelation does not require any special setup or knowledge.
Simply go to the time waveform (either the standard TWF or the PeakVue TWF)
Right mouse click – choose Autocorrelate and perform the function

43. About 53% of the energy in the waveform is coming from a BPFO defect