Transcript Autocorrelation

Autocorrelation
Danny Vandeput & Lasse Hansen
Asset Optimization Division
Machinery Health Management
Company Confidential
October 29, 2015
Slide 1
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.
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October 29, 2015
Slide 2
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.
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October 29, 2015
Slide 3
Use of Autocorrelation, examples

Doppler Radar Techniques for Estimation of
target velocity

Imaging of Blood Flow used in Medical
Ultrasonography.

..

.

Vibration Analysis
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October 29, 2015
Slide 4
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)
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October 29, 2015
Slide 5
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
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October 29, 2015
Slide 6
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.
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Slide 7
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.
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October 29, 2015
Slide 8
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
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October 29, 2015
Slide 9
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
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Slide 10
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).
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Slide 11
Generated signal with almost all noise
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Slide 12
Generated signal with almost all noise
•Autocorrolation waveform shows no periodic energy
•Almost all energy is from random events
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Slide 13
Bearing with insufficient lubrication
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Slide 14
Bearing with insufficient lubrication
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Slide 15
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
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Slide 16
Generated signal with very little noise
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Slide 17
Autocorrolated waveform indicating a max amplitude of
value of 0,984 at the rate of the periodic energy
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Slide 18
Bearing with Outer Race Defect marked
Exhaust fan, 1698 RPM
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Slide 19
Autocorrolation amplitude is 0,93 indicating that
almost all the energy is from a periodic source
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Slide 20
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
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October 29, 2015
Slide 21
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
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October 29, 2015
Slide 22
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
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October 29, 2015
Slide 23
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
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October 29, 2015
Slide 24
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
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October 29, 2015
Slide 25
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
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October 29, 2015
Slide 26
Autocorrelation
Cases
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Slide 27
Cases

Looseness

Cage problem

Bearing Defect with Lube Fault

Ultra Low Speed bearing problem
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October 29, 2015
Slide 28
Case # 1 Looseness
1x and harmonics, not necessarily looseness
Data indicates some high frequency energy
excited by a low frequency event
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October 29, 2015
Slide 29
impacts up to 63.78 g’s and a very random pattern
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
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October 29, 2015
Slide 30
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
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October 29, 2015
Slide 31
Case # 2 Cage fault – bearing installation
Spectrum and Waveform indicating cage defect
Fan with a speed of 890 RPM
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Slide 32
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
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Slide 33
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
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Slide 34
Case # 3 Ultra Low Speed Bearing Problem
Outer race defect indicated in spectral data on
gearbox, 0,4 RPM
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Slide 35
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
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October 29, 2015
Slide 36
Case # 4 Bearing with Defect and Lube Fault
PeakVue spectrum and waveform
show a clear BPFO defect
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Slide 37
Case # 4 Bearing with Defect and Lube Fault
Only about 13.9% (√0.01933) of the
energy is coming from the BPFO
Rest of the energy is random
and related to a lube fault
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October 29, 2015
Slide 38
Autocorrelation Circular Plot

Combined with the Circular Plot the
Autocorrelation can also provide very good
information about the load zone
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October 29, 2015
Slide 39
Autocorrelation Circular Plot
Autocorrolation waveform
in circular format indicating
non-synchronous impacting
with amplitude modulation
at turning speed.
Typical for Inner Race defect
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October 29, 2015
Slide 40
The same can be applied to gearboxes
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
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October 29, 2015
Slide 41
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October 29, 2015
Slide 42
About 53% of the energy in the
waveform is coming from a BPFO defect
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October 29, 2015
Slide 43