Condition Monitoring Of Unsteadily Operating Equipment
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Transcript of Condition Monitoring Of Unsteadily Operating Equipment
Condition Monitoring of Unsteadily Operating
EquipmentJordan McBain, B.Eng.Mgt, EIT
Health Monitoring of steady speed/load machinery a well established practice
However, few techniques are available for monitoring unsteadily operating equipment
Techniques required for advanced equipment such as electromechanical shovel, variable duty hoists, etc.
Problem
Condition Monitoring Pattern Recognition Vibration Analysis Condition Monitoring of Unsteadily Operating
Equipment◦ Suggested Approach: Statistical Parameterization◦ Novelty Detection
Experimental Methodology◦ Classification Results
Conclusions Future Work
Outline
Machinery Maintenance Policy driven by:◦ Availability of resources (spare parts, pers., capital)◦ Importance of equipment◦ Availability of technology and expertise
Modern Maintenance Policy evolved through:◦ Run-to-Failure◦ Periodic Maintenance◦ Predictive Maintenance
Maintenance is delayed until some monitored parameter of the equipment becomes erratic
Proactive Balances resources
Condition Monitoring
Benefits:◦ Environment◦ Safety◦ Production◦ Staff Shortages/Costs◦ Scheduling◦ Spare Parts (JIT)◦ Insurance◦ Life Extension
Condition Monitoring
Faults in rotating machinery have very representative features in the frequency domain
Consider bearing:◦ Frequency Response a
function of Fault, Slippage, Noise
Vibration Analysis
Diagrams from: Randall, B. State of the Art in Machinery Monitoring, JSV
One branch of artificial-intelligence domain Usually involves representing a state or
object to be indentified with a vector of commensurate numerical values◦ E.g. In classifying fruit: weight, spectroscopic
values, etc. Representative vector called a “pattern” or
“classification object” Classification achieved by computing
decision surfaces around classes of objects
Pattern Recognition
Sensing
Segmentation
Feature
Extraction
Classification
Post-Processing
Pattern Recognition
Vibration Measurement
DividingVibration Signal
Choosing RepresentativeNumeric Values
CalculatingClassificationBoundaries
-Decision Support-Prognostics-Etc.
Condition Monitoring of Unsteadily Operating
EquipmentStatistical Parameterization
Explore a technique developed for monitoring health of structures first established in◦ K Worden, H Sohn, CR Farrar. Novelty detection in a
changing environment: Regression and inter polation approaches, J.Sound Vibrat. 258 (2002).
Essential idea: clustering of patterns will vary with modal parameters (speed/load/temp)
Technique improves the segmentation step; rendering classification almost trivial
Statistical Parameterization
Variable speed machinery◦ Elements of a machine’s vibratory response are
assumed to have a strong relation to the speed of the given machinery
Distribution for speeds:◦ Means vary with speed◦ Variances vary with resonance response
x
y
* C10
*C20
*C30
Segment vibration signal Group segments according to the machine’s
speed Calculate Gaussian parameters for small
segments of speed (sample statistics assumed to be population statistics)◦ Curse of Dimensionality
Interpolate or Regress each component of statistical parameters
Decision boundary function of speed (and other modal parameters)
Method
Sub problem of pattern recognition◦ Rather than train a classifier on all classes, we train on
the “normal” class and then signal an error when behaviour deviates from it
◦ Employed where knowledge of all classes (of faults) not practical to attain
Decision boundary encircles normal patterns A wide variety of techniques available Examine two:
◦ Boundaries containing a certain quantile of data (i.e. a discordance test)
◦ Boundaries derived by Support Vectors
Novelty Detection
For uni-variate data – a simple task:◦ Classify as normal if test pattern falls within nth
quantile of training data◦ Think confidence level
Novelty Detection: Discordance
(| | ) 0.95P x R | |1.96
x
1.96 1.96x
For multi-variate data:◦ Build multi-variate model from multiple uni-
variate ones – assuming independence
Novelty Detection: Discordance
( ) ( )* ( )P A B P A P B
Assuming independence
Novelty Detection: Discordance
2
21
1
1( )
2
1 1
1 1( ) ( ) ( )2 2
1
1( ) ( )
2
1 1
(2 ) | |(2 )
i i
i
di i t
ii
xd d
ii i i
xx x
d dd
ii
p x p x e
e e
Example:◦ Distr. #1 µ= 5 and σ=4◦ Distr. #2 µ= 10 and σ=8◦ Joint Distr. therefore has µ= [5,10] and
◦ The level curves of the distribution are determined by the Mahalanobis squared distance given by
Novelty Detection: Discordance
4 0
0 8
2 1( ) ( )tr x x
This is the equation of an ellipsoid
In practice, covariance matrix non-diagonal (ie. Cross terms present)◦ Consequence: ellipses not
aligned with central axis◦ PCA required to
determine orientation Decision boundary, for
d-dimensional problem, containing n-th quantile given by:
1 1 1 12 1
2 2 2 2
1
11 2
2
11 2
2
11 2
2
2 22 1 2
( ) ( )
54 05 10
100 8
10 545 10
1010
8
55 10
104 8
( 5) ( 10)
4 8
tx xr
x x
xx x
x
xx x
x
xx x
x
x xr
2 ( , )k chi inv q d
Is independence a reasonable assumption in the context of variable load/speed machinery?◦ Many spectral components of vib. Machinery
strongly related Consider Bearings Consider Gear Meshing Etc.
◦ Gaussian fit depends on independence of probabilities of individual parameters
◦ May prove poor in this context
Novelty Detection: Discordance
This ellipsoidal boundary is very rigid and will not work well if the data is not perfectly Gaussian
Rather than computing the quantile for a test patterns given speed◦ Center each speed bin’s data about the origin and alter
its distribution from ellipsoidal to spherical with the whitening transform
◦ Consequence: All modal data is centered at the origin with faulted data orbiting the healthy data
◦ Now draw a decision boundary around the healthy data: use Support Vectors
N.B. There is still some dependence on the assumption of a Gaussian fit
Novelty Detection: Support Vectors
x
y
* C10
*C20
*C30
x
y
Healthy Data for all Speeds
Faulted Data
Support Vector Technique: Tax’s Support Vector Data Description (for Novelty Detection)◦ Attempts to fit a sphere of minimal radius around
normal data◦ But a in a higher dimensional space (using the
“kernel trick”) Generates a very flexible decision boundary in the
input space
Support Vectors
Experimental Methodology
Dr. Timusk’s PhD data Spectraquest gear dynamics simulator
◦ Variable frequency drive ◦ Gearbox (two stage parallel reduction)
Subject to variable loads (particle brake) Data acquisition system: NI PXI
◦ Ceramic Shear ICP Accelerometers (0.5 to 6500 Hz)◦ Sampling 4kHz/channel
Faults: ◦ motor with bearing faults, broken rotor bars, rotor unbalance◦ gear faults: missing tooth, chipped pinion, outer race bearing
Appartus
Segment vibration data into segments of ‘steady’ speed and load◦ Segments defined by n-shaft rotations
Accounts for varying speed Ensures coherent signal
Windowed (Gaussian Window – 70% overlap)
Sensing
Segmentation
Feature
Extraction
Classification
Post-Processing
Steady speed/load not guaranteed◦ But can generate segments with reasonable steadiness
and variance can be computed Group vibration segments into bins of a selected
size◦ Size effects how many classification objects in each bin
curse of dimensionality balanced against need for very fine modal resolution
Segmentation
A number of parameters could be employed to represent a vibration segment◦ Crest factor, average power, kurtosis, impulse factor, etc.◦ Autoregressive Models (AR)
AR models◦ Think Root Locus Method from Control Systems: You
determine the placement of poles to shape the frequency response of the CS AR models control placement of poles to shape model’s
frequency response to be representative of a signal’s frequency response in the least squares sense
◦ User selects the number of poles The more poles, the more representative the signal is Balanced against the curse of dimensionality
Sensing
Segmentation
Feature
Extraction
Classification
Post-Processing
Segmentation step makes data almost perfectly separable
Sensing
Segmentation
Feature
Extraction
Classification
Post-Processing
Fit each component of each statistical parameter (mean and covariance matrix) to model
Components of mean vector could be fit with polynomial
Components of covariance matrix not traceable
Classification: Regression
Covariance matrix components vary wildly Additional concern:
◦ Covariance matrix derived from regression may not be positive semi-definite
Method available to deal with issue (added complexity)
Classification results are poor
0tx x
Instead, we must store each bin’s statistical parameters◦ Any bins which are ill-conditioned or under
sampled could then simply be interpolated over◦ Positive semi definitenessguaranteed◦ Good classification results
Classification: Interpolation
High acceptance rate of healthy data generates poor rejection rate of faulted data (ellipsoidal boundaries)
Interpolating over missing/ill-conditioned bins◦ One missing bin: interpolated statistics almost the
same as those of measured values◦ Three bins missing:
SVDD has one parameter – sigma◦ Integer value [1,inf)◦ Low values – Tight
bound Choice of sigma has
very little effect No frustrating trade
off between classification error on normal and faulted data
Superior classification
Classification: Whitening with Support Vectors
Too good to be true?◦ Tax explored variable load/speed machinery
without our segmentation steps Training SVDD over all speeds, he achieved an
average error of 8% Our average error of 2% is very plausible!
Segmentation step removes overlap between faulted data of one speed bin and healthy data of others
The errors shown on the right are based on data from one accelerometer
Faults are not all located near this accelerometer
Segmentation has made classifications sensitive enough so that accelerometers can measure spatially disparate faults
Plausible: Underwater warfare analogy
Key Observation
For a fixed amount of data, increasing the dimensionality of the space increase classification error
Statistical Parameterization is doubly cursed
Curse of Dimensionality
Statistical parameterization◦ Approach extends well to variable speed
machinery Gaussian/independence assumption not theoretically
correct but the data cluster well anyway◦ Prefer interpolation over regression
Memory requirements not a concern (but might try piece-wise linear regression in the
future)◦ Interpolation possible over missing/ill-conditioned
bins
Conclusion
◦ Whitened data with Support Vectors Statistics for each bin still required Produces a less rigid decision boundary Better classification results Still somewhat dependent on assumption of
Gaussianaity ◦ Segmentation essentially renders classification
stage trivial◦ Segmentation makes it possible for sensors to
detect faults on physically distant machinery components
◦ Suffers doubly from the curse of dimensionality
Verification of methodology on real world machinery (diamond drill head with dyno)
Develop classifier variants for multi-modal processes which are less susceptible to the curse of dimensionality
Develop ONLINE prognostics techniques◦ When will failure occur?◦ What is the probability a machine will fail at time x?
Develop economic means of measuring torsional load for this application
Develop complete software architecture (software engineering principles) and prototype
Future Work