Presentation on theme: "Autocorrelation Danny Vandeput & Lasse Hansen"— Presentation transcript:
1Autocorrelation Danny Vandeput & Lasse Hansen 3/31/2017AutocorrelationDanny Vandeput & Lasse HansenAsset Optimization DivisionMachinery Health Management
2DefinitionAutocorrelation, R, is a mathematical tool for finding repetitive patterns, such asfind the presence of a periodic signal which has been buried under noise, oridentify the missing fundamental frequency in a signal implied by its harmonic frequencies.
3DefinitionIt 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.
4Use of Autocorrelation, examples Doppler Radar Techniques for Estimation of target velocityImaging of Blood Flow used in Medical Ultrasonography....Vibration Analysis
5Common tools in Vibration Analysis on Rotating Machinery are: Digitally capture of a Band Limited Time Waveformat a predetermined sampling (digitization) ratefor a specified data block sizeSpectral 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)
6Common tools in Vibration Analysis on Rotating Machinery are: In addition to the velocity spectral analysis, a special analysis recommended by EPM is thecapture 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 dataAnother tool available with EPM is the Autocorrelation Waveform.The autocorrelated waveform is a method for determining the periodic or random energy in the waveform
7Why use Autocorrelation in Vibration Analysis The strength in the autocorrelation function is itsability to identify low repetition rate events with low duty cycleability to separate random events from periodic eventsThe autocorrelation function also supplies a means to approximate the percentage of energy in the time waveform that iseither from the periodic energy orfrom the random energy.
8Why 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.
9How 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 zeroFor periodic data with no (or little) noise, the value will approach 1 at the period (1/frequency) of the periodic data
10How 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
11Useful PropertiesThe 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).
16Useful 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
18Autocorrolated waveform indicating a max amplitude of value of 0,984 at the rate of the periodic energy
19Bearing with Outer Race Defect marked Exhaust fan, 1698 RPM
20Autocorrolation amplitude is 0,93 indicating that almost all the energy is from a periodic source
21The 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
22Useful 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 faultThe amplitude value of the periodic event will be somewhere between 0 and 1The square root of the peak amplitude will be the approximate percentage (fraction) of energy contributed by the fault with that period
23Square 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
24SummaryTime 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
25SummarySpectra has an advantage for defects generating higher frequenciesAutocorrelation has an advantage for lower frequency defectsAutocorrelation provides a means to determine the approximate percentage of the waveform energy which is due to the periodic event
26SummaryAutocorrelation 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
28Cases Looseness Cage problem Bearing Defect with Lube Fault Ultra Low Speed bearing problem
29Case # 1 Looseness 1x and harmonics, not necessarily looseness Data indicates some high frequency energyexcited by a low frequency eventimpacts up to g’s and a very random pattern
30Case # 1 LoosenessAutocorrelated waveform indicates a change in speed during the acquisition timePeriod 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
31Case # 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
32Case # 2 Cage fault – bearing installation Spectrum and Waveform indicating cage defect Fan with a speed of 890 RPM
33Case # 2 Cage fault – bearing installation Not sharp peaks like a cracked or broken cage No indication of high frequencyriding on low frequency content
34Photo of bearing in Pillow Block Housing The axial trust with the misaligned races generated highfrequency energy as the cage rotated through the tight spot
35Case # 3 Ultra Low Speed Bearing Problem Outer race defect indicated in spectral data on gearbox, 0,4 RPM
36Case # 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 rpmindicates here alert value to 0,2g and fault level 0,4g
37Case # 4 Bearing with Defect and Lube Fault PeakVue spectrum and waveformshow a clear BPFO defect
38Case # 4 Bearing with Defect and Lube Fault Only about 13.9% (√ ) of the energy is coming from the BPFORest of the energy is random and related to a lube fault
39Autocorrelation Circular Plot Combined with the Circular Plot the Autocorrelation can also provide very good information about the load zone
40Autocorrelation Circular Plot Autocorrolation waveformin circular format indicatingnon-synchronous impactingwith amplitude modulationat turning speed.Typical for Inner Race defectThe same can be applied to gearboxes
41How 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