Company Confidential June 1, 2014 Slide 1 Autocorrelation Danny Vandeput & Lasse Hansen Asset...
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Transcript of 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
Company ConfidentialApril 10, 2023Slide 2
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
Company ConfidentialApril 10, 2023Slide 3
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
Company ConfidentialApril 10, 2023Slide 4
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
Company ConfidentialApril 10, 2023Slide 5
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)
Company ConfidentialApril 10, 2023Slide 6
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
Company ConfidentialApril 10, 2023Slide 7
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.
Company ConfidentialApril 10, 2023Slide 8
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.
Company ConfidentialApril 10, 2023Slide 9
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
Company ConfidentialApril 10, 2023Slide 10
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
Company ConfidentialApril 10, 2023Slide 11
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).
Company ConfidentialApril 10, 2023Slide 12
Generated signal with Generated signal with almost all noisealmost all noiseGenerated signal with Generated signal with almost all noisealmost all noise
Company ConfidentialApril 10, 2023Slide 13
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
Company ConfidentialApril 10, 2023Slide 14
Bearing with Bearing with insufficient lubricationinsufficient lubricationBearing with Bearing with insufficient lubricationinsufficient lubrication
Company ConfidentialApril 10, 2023Slide 15
Bearing with Bearing with insufficient lubricationinsufficient lubricationBearing with Bearing with insufficient lubricationinsufficient lubrication
Company ConfidentialApril 10, 2023Slide 16
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
Company ConfidentialApril 10, 2023Slide 17
Generated signal with Generated signal with very little noisevery little noiseGenerated signal with Generated signal with very little noisevery little noise
Company ConfidentialApril 10, 2023Slide 18
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
Company ConfidentialApril 10, 2023Slide 19
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
Company ConfidentialApril 10, 2023Slide 20
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
Company ConfidentialApril 10, 2023Slide 21
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
Company ConfidentialApril 10, 2023Slide 22
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
Company ConfidentialApril 10, 2023Slide 23
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
Company ConfidentialApril 10, 2023Slide 24
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
Company ConfidentialApril 10, 2023Slide 25
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
Company ConfidentialApril 10, 2023Slide 26
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
Company ConfidentialApril 10, 2023Slide 27
AutocorrelationAutocorrelationCasesCasesAutocorrelationAutocorrelationCasesCases
Company ConfidentialApril 10, 2023Slide 28
CasesCases Looseness
Cage problem
Bearing Defect with Lube Fault
Ultra Low Speed bearing problem
Company ConfidentialApril 10, 2023Slide 29
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
Company ConfidentialApril 10, 2023Slide 30
Case # 1 LoosenessCase # 1 Looseness
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
Company ConfidentialApril 10, 2023Slide 31
Case # 1 LoosenessCase # 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
Company ConfidentialApril 10, 2023Slide 32
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
Company ConfidentialApril 10, 2023Slide 33
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
Company ConfidentialApril 10, 2023Slide 34
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
Company ConfidentialApril 10, 2023Slide 35
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
Company ConfidentialApril 10, 2023Slide 36
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
Company ConfidentialApril 10, 2023Slide 37
Case # 4 Bearing with Defect and Lube FaultCase # 4 Bearing with Defect and Lube Fault
PeakVue spectrum and waveform show a clear BPFO defect
Company ConfidentialApril 10, 2023Slide 38
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
Company ConfidentialApril 10, 2023Slide 39
Autocorrelation Circular PlotAutocorrelation Circular Plot Combined with the Circular Plot the
Autocorrelation can also provide very good information about the load zone
Company ConfidentialApril 10, 2023Slide 40
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
Company ConfidentialApril 10, 2023Slide 41
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
Company ConfidentialApril 10, 2023Slide 42
Company ConfidentialApril 10, 2023Slide 43
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