Company Confidential June 1, 2014 Slide 1 Autocorrelation Danny Vandeput & Lasse Hansen Asset...

Company ConfidentialApril 10, 2023Slide 1

AutocorrelationAutocorrelationAutocorrelationAutocorrelationDanny Vandeput & Lasse Hansen

Asset Optimization Division

Machinery Health Management


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.

DefinitionDefinition


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.

DefinitionDefinition


Use of Autocorrelation, examplesUse of Autocorrelation, examples Doppler Radar Techniques for Estimation of target

velocity

Imaging of Blood Flow used in Medical Ultrasonography.

..

.

Vibration Analysis


Common tools in Vibration Analysis on Rotating Machinery are: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)


Common tools in Vibration Analysis on Rotating Machinery are: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


Why use Autocorrelation in Vibration AnalysisWhy 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.


Why use Autocorrelation in Vibration AnalysisWhy 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.


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

How to use Autocorrelation in Vibration AnalysisHow 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

How to use Autocorrelation in Vibration AnalysisHow to use Autocorrelation in Vibration Analysis


Useful PropertiesUseful 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).


Generated signal with Generated signal with almost all noisealmost all noiseGenerated signal with Generated signal with almost all noisealmost all noise


Generated signal with Generated signal with almost all noisealmost all noiseGenerated signal with Generated signal with almost all noisealmost all noise

•Autocorrolation waveform shows no periodic energy•Almost all energy is from random events


Bearing with Bearing with insufficient lubricationinsufficient lubricationBearing with Bearing with insufficient lubricationinsufficient lubrication


Bearing with Bearing with insufficient lubricationinsufficient lubricationBearing with Bearing with insufficient lubricationinsufficient lubrication


Useful Properties (partially repeated)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


Generated signal with Generated signal with very little noisevery little noiseGenerated signal with Generated signal with very little noisevery little noise


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


Bearing with Outer Race Defect markedBearing with Outer Race Defect marked

Exhaust fan, 1698 RPM

Bearing with Outer Race Defect markedBearing with Outer Race Defect marked

Exhaust fan, 1698 RPM


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


The period of the autocorrolated waveform is The period of the autocorrolated waveform is 86,5 Hz being generated by bearing outer race86,5 Hz being generated by bearing outer raceThe period of the autocorrolated waveform is The period of the autocorrolated waveform is 86,5 Hz being generated by bearing outer race86,5 Hz being generated by bearing outer race

Autocorrelation function allows adding fault frequencies to indicate the cause of the periodicity


Useful Properties (partially repeated)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


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

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


SummarySummary 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


SummarySummary 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


SummarySummary 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


AutocorrelationAutocorrelationCasesCasesAutocorrelationAutocorrelationCasesCases


CasesCases Looseness

Cage problem

Bearing Defect with Lube Fault

Ultra Low Speed bearing problem


Case # 1 LoosenessCase # 1 Looseness

1x and harmonics, not necessarily looseness

Data indicates some high frequency energy excited by a low frequency event

impacts up to 63.78 g’s and a very random pattern



Autocorrelated waveform indicates a change in speed during the acquisition time

Period of 1x seems regular for the first half of waveformBut then it changesSecond half of the Autocorrelated waveformalso indicates a 1x, it is only slightly changed



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


Case # 2 Cage fault – bearing installationSpectrum and Waveform indicating cage defectCase # 2 Cage fault – bearing installationSpectrum and Waveform indicating cage defect

Fan with a speed of 890 RPM


Case # 2 Cage fault – bearing installationNot sharp peaks like a cracked or broken cageCase # 2 Cage fault – bearing installationNot sharp peaks like a cracked or broken cage

No indication of high frequency riding on low frequency content


Photo of bearing in Pillow Block HousingPhoto 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


Case # 3 Ultra Low Speed Bearing ProblemOuter race defect indicated in spectral data on gearbox, 0,4 RPM

Case # 3 Ultra Low Speed Bearing ProblemOuter race defect indicated in spectral data on gearbox, 0,4 RPM


Case # 3 Ultra Low Speed Bearing ProblemCase # 3 Ultra Low Speed Bearing Problem

Highest value is 0,118 indicating aprox 34% energyFrom 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


Case # 4 Bearing with Defect and Lube FaultCase # 4 Bearing with Defect and Lube Fault

PeakVue spectrum and waveform show a clear BPFO defect


Case # 4 Bearing with Defect and Lube FaultCase # 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


Autocorrelation Circular PlotAutocorrelation Circular Plot Combined with the Circular Plot the

Autocorrelation can also provide very good information about the load zone


Autocorrelation Circular PlotAutocorrelation Circular Plot

Autocorrolation waveformin circular format indicatingnon-synchronous impactingwith amplitude modulationat turning speed.Typical for Inner Race defect

The same can be applied to gearboxes


How to use Autocorrelation?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



About 53% of the energy in thewaveform is coming from a BPFO defectAbout 53% of the energy in thewaveform is coming from a BPFO defect

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Company Confidential June 1, 2014 Slide 1 Autocorrelation Danny Vandeput & Lasse Hansen Asset...

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