1. Jordan McBain, B.Eng.Mgt, EIT

2.  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.

3.  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

4.  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

5.  Benefits:
◦ Environment
◦ Safety
◦ Production
◦ Staff Shortages/Costs
◦ Scheduling
◦ Spare Parts (JIT)
◦ Insurance
◦ Life Extension

6.  Faults in rotating
machinery have very
representative features in
the frequency domain
 Consider bearing:
◦ Frequency Response a
function of Fault, Slippage,
Noise
Diagrams from: Randall, B. State
of the Art in Machinery Monitoring, JSV

7.  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

8. Feature Post-
Sensing Segmentation Classification
Extraction Processing
Vibration Dividing Choosing Calculating -Decision Support
Measurement Vibration Representative Classification -Prognostics
Signal Numeric Boundaries -Etc.
Values

9. Statistical Parameterization

10.  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

11.  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 *C30
◦ Variances vary with resonance response
*C20
y
* C10
x

12.  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)

13.  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

14.  For uni-variate data – a simple task:
◦ Classify as normal if test pattern falls within nth
quantile of training data
◦ Think confidence level
P(| x   | R)  0.95 | x| 1.96    x  1.96  
 1.96


15.  For multi-variate data:
◦ Build multi-variate model from multiple uni-variate
ones – assuming independence
P( A  B)  P( A)* P( B)

16.  Assuming independence
1 x 
d d  ( i i )2
 1
p ( x )   p ( xi )   e 2 i
i 1 i 1 2 i
d
x 

1
 ( i i )2 1    
 ( x   )t  1 ( x   )
1 2 i 1  i 1
 d
e  e 2
(2 ) d   i (2 ) |  |
d
i 1

17.  Example:
◦ Distr. #1 µ= 5 and σ=4
◦ Distr. #2 µ= 10 and σ=8
4 0
◦ Joint Distr. therefore has µ= [5,10] and   
 0 8

◦ The level curves of the distribution are determined
by the Mahalanobis squared distance given by
  t 1  
r  (x  )  (x  )
2

18.  x1   1  t 1  x1   1 
r  (    )  (    )
2  This is the equation of an
 x2    2   x2    2  ellipsoid
In practice, covariance
1
 4 0   x1  5  
  x1  5 x2  10 
 0 8   x2  10 
   matrix non-diagonal (ie.
1
0
 Cross terms present)
4  x1  5 
  x1  5 x2  10   ◦ Consequence: ellipses not
0 1   x2  10 
  aligned with central axis

 8 ◦ PCA required to determine
 x1  5 x2  10   x1  5  orientation

 4 8   x2  10 
   Decision boundary, for
( x  5) ( x2  10) d-dimensional problem,
2 2
r  1
2

4 8 containing n-th quantile
given by:
k  chi 2inv(q, d )

19.  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

20.  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

21. *C30
Faulted Data
y
Healthy Data
*C20 for all Speeds
y x
* C10
x

22.  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

24.  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

25. Feature Post-
Sensing Segmentation Classification
Extraction Processing
 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)

26.  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

27. Feature Post-
Sensing Segmentation Classification
Extraction Processing
 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

29. Feature Post-
Sensing Segmentation Classification
Extraction Processing
 Segmentation step makes data almost
perfectly separable

31.  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

32.  Covariance matrix components vary wildly
 Additional concern:
◦ Covariance matrix derived from regression may not
be positive semi-definite
x x  0
t
 Method available to deal with issue (added complexity)
 Classification results are poor

33.  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

34.  High acceptance rate of healthy data generates poor
rejection rate of faulted data (ellipsoidal boundaries)

35.  Interpolating over missing/ill-conditioned
bins
◦ One missing bin: interpolated statistics almost the
same as those of measured values
◦ Three bins missing:

36.  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

37.  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

38.  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

39.  For a fixed amount of data, increasing the
dimensionality of the space increase
classification error
 Statistical Parameterization is doubly cursed

40.  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

41. ◦ 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

42.  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