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Novelty Detection Augmented for Fault Detection In Variable Speed Machinery
As submitted to Mechanical Systems and Signal Processing
Jordan McBain, P.Eng.
Maintenance has advanced considerably from reactive policies
Modern sensors, computers and algorithms have set the stage
Health Monitoring of steady machinery widely available
Few techniques are available for monitoring unsteadily operating equipment
Techniques required for advanced equipment such as electromechanical shovel, variable duty hoists, etc.◦ Subject to variable loads, speed, ◦ temperatures, etc.
Problem
Theory◦ Condition Monitoring◦ Artificial Intelligence (AI) Background◦ AI for Monitoring Machinery◦ Monitoring Multi-Modal Machinery
Experimental Work◦ Methodology◦ Results◦ Future Work
Outline
Condition Monitoring
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
Artificial Intelligence Background
Savvy technicians employ(ed) a screw driver set atop a vibrating machine◦ Resultant vibration of screw driver used by
technician to classify health AUTOMATE THIS!
◦ More sensitive ◦ Earlier detection of faults◦ Consistent, reliable measurements
Consistent, reliable classification
AI in Condition Monitoring
One branch of artificial-intelligence domain Usually involves representing a state or
object to be indentified with a vector of commensurate numerical values
Representative vector called a “pattern” or “classification object”
Classification achieved by computing decision surfaces around classes of objects
Example: biometric classification of employees reporting to work
Pattern Recognition
Sensing SegmentationFeature
ExtractionClassification Post-
Processing
AI: Pattern Recognition
Measurements(height, weight, eye colour)
Selecting measurementinterval
Reducingsegmentedmeasurementsto key numbers
Plotting values in n-dimensionsand fitting a boundary
-Decision Support-Also detect enebriation-Pay-Etc.
Employing sensors to collect relevant data◦ Height, weight, eye colour, finger prints, image of
retina, DNA Conditioning signals
◦ Filtering noise
Sensing
Sensing SegmentationFeature
ExtractionClassification Post-
Processing
Sensor data divided into useful chunks◦ Separate employees from one another
Use a terminal for employees to sign in one at a time Use image processing and separate employees from
each other in picture One of the most difficult problems in pattern
recognition
Segmentation
Sensing SegmentationFeature
ExtractionClassification Post-
Processing
Characterizes an object to be recognized by measurements whose values are very similar for objects in the same category
Invariant to irrelevant transformations An ideal feature vector makes the job of
classification trivial (e.g. DNA) The curse of dimensionality
◦ A balance between improvements from increased dimensionality and increased need for data to describe the space and added complexities
Feature ExtractionSensing Segmentation
FeatureExtraction
Classification Post-Processing
Employs full feature vector provided by the feature extractor to assign the feature vector’s object to a category
Generalization – learning from a training set extends well to unexperienced data
E.g. Neural Networks◦ As one would fit a model to an experimental data set with
least-squares regression, in classification one would fit a boundary around a class’ data set
◦ Computationally equivalent tasks But in classification, the problem is non-linear
ClassificationSensing Segmentation
FeatureExtraction
Classification Post-Processing
Perform some action subsequent to classification
Improve classification error based on context◦ Employ multiple classifiers
Post Processing
Sensing SegmentationFeature
ExtractionClassification Post-
Processing
Artificial Intelligence (AI) for Machine Monitoring
Goal:◦ Divine state of machinery health from noisy
parameters Techniques
◦ Ranging from thermography, eddy-current measurement, oil analysis to vibration
AI in Machine Monitoring
Sensing
•Accelerometers, acoustic emission, temperature
•Filter stationary machinery elements (fans, EMI, etc)
Segmentation
•Use a standard length of vibration data (average other sensors according to the corresponding time interval)
•Use a variable length group of vibration data
Feature
Extraction
•Auto-regressive models, MUSIC spectrum, statistics (mean, RMS, etc), order domain, etc.
Classification
•Novelty detection (support vectors, neural network variants, etc)
Post-Processing
•The foregoing is considered fault detection
•Consider: diagnostics, prognostics
•Potential responses: stop machinery, inform technician, update database, etc.
Heavily used in literature Non-destructive, online, sensitive Faults in rotating machinery have
strongly representative features in the frequency domain
Consider bearings:◦ Frequency Response a function of
Fault, Slippage, Noise
Vibration Analysis
Diagrams from: Randall, B. State of the Art in Machinery Monitoring, JSV
Motivation: addresses imbalance of data from one class in relation to that of others◦ Data from faulted states are difficult to collect
(economics, operation) Sub problem of pattern recognition
◦ train on the “normal” class and then signal error when behaviour deviates from itDecision 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
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
Monitoring Multi-Modal Machinery
Multi-Modal Machinery
Simplest machine◦ damped spring system
◦ Frequency domain representation
◦ Forced with a function
Machinery Spectra
( )mx cx kx f t n
k
m 2
c
km
2 2
1 1( )
2n n
H wm w w j w w
0( ) *sin( )f t A t
With frequency-domain representation
The system’s output is given by
0 0( ) ( ) ( )2 2
A AF
( ) ( ) ( )X F H 0 02 2
0 0
1 1( ) ( ( ) ( ))
2 2 2n n
A AX
m w w j w w
Underground mines◦ Ventilation fans driven with VFD to optimize
efficiency◦ Fans driven at one speed one day and then
changed to a different constant speed New forcing function
Simple Machinery: Periodic Speed Changes
2 1
3 2
sin( ), 0( )
sin( ), 0
A t tf t
A t t
Examine function for one day (windowing)
Frequency representation (convolution operator):
System’s response to forcing, similar◦ Spectral leakage and smearing by windowing
4 3( ) ( )* sin( )t
f t rect A t
3 3
3 3
3 3
( ) Rect( ) ( ( ) ( ))2 2
sinc( ) ( ( ) ( ))2 2
(sinc( ) sinc( ))2
A AF
A A
A
Consider function including instant of change for a period of time 2*Tow
Resultant frequency representation
2 1 3 3
1 1( ) (2 )* sin( ) (2 )* sin( )
2 2
t tf t rect A t rect A t
1 1 2 21 1 2 2
1 1 2 2
( ) Rect( ) ( ( ) ( )) Rect( ) ( ( ) ( ))2 2 2 2 2 2 2 2
(sinc( ) sinc( )) (sinc( ) sinc( ))4 4
A A A AF
A A
Sinc functions with sidelobes◦ Introducing interference on spectrum◦ Central frequencies contaminated with frequency
info from windowing function◦ Info not solely indicative of health
Forced function with time varying frequency
◦ as modulating frequency◦ as carrier frequency◦ modulation index
No closed form solution of fourier integral Use bessel functions
Simple Machine: True Speed Changes
( ) cos(2 cos(2 ))c c mf t A f t f t
mf
cf
(Mathematically) unlimited bandwidth In practice 98% of bandwidth determined by
beta
Examining over a period of time (windowing)◦ Introduces sinc functions mounted on impulses◦ Consequence: spectral interference
Conclusion◦ Frequency domain contains valuable info on:
System behaviour Faults manifested in the form of changes in stiffness and
damping Forcing function
◦ Info in frequency bands not limited to system behaviour
Gear interaction modeled with:
As suggested by J- Kuang, A- Lin. Theoretical aspects of Torque responses in spur gearing due to mesh stiffness variation, Mechanical Systems and Signal Processing. 17 (2003) 255-271.
Assume◦ Fixed load of L (Nm)◦ Damping ratio of c=0.17◦ Spring value k = k(t)
Normal assumptions of spring constant◦ Clean frequency plot ◦ Obvious harmonics and sidebands
Gearbox’s Theoretical Frequency Response
( )mx cx kx f t
Spring stiffness varies with time
Consequence: non-linear frequency response ◦ Convolution introduced2 ( ) ( ) ( ) ( ) ( )m X cj X K X F
Frequency response of k(t), modeled as simple pulse train, is well known (RADAR, SONAR)◦ Sync function as envelop to impulse train
Variable speed machinery◦ Stiffness: variable pulse train◦ I.e. Pulse Width Modulation◦ No closed form Fourier integral
Bessel functions◦ Transfer function not discernible
Numerical analysis necessary Consequence
◦ Spectrum incredibly complex◦ No simple band to monitor
Primary aggravators: load and speed◦ Referred to as nuisance variables in the literature
In vibration monitoring◦ Power of vibration a product of the effects of load and
speed Relation between power and speed non-linear Resonances! Vibration a function of health and speed
Complex machinery an amalgamation of spring-like elements Vibration in most mechanical systems involves periodic
oscillation of energy from potential to kinetic (according to frequency response of spring approximation)
When machine is healthy, deviations in consequent vibrations are small
Impact of Multi-Modes
When machine is healthy, deviations in consequent vibrations are small
When health is poor, deviations due to speed become significant
Stack: Damping in undamaged machinery is largely insensitive to speed/load changes – damaged machinery is not
Experimental Methodology
Apparatus
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 SegmentationFeature
ExtractionClassification 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
Feature Vectors◦ Statistics of Vibration
RMS Crest Factor Kurtosis Mean Standard Deviation Impulse Factor
◦ Auto-regressive models Least-squares spectral approximation
◦ Acoustic Emissions
Sensing SegmentationFeature
ExtractionClassification Post-
Processing
Signal processing technique◦ Not a feature vector◦ Not a fault detection technique
Resamples data at constant angular shaft intervals ◦ Rather than constant time intervals
Tachometers employed (2500 pulses per rev) At max speed (500 rpm)
◦ 18 000 samples collected◦ Tach pulses: 37 500 samples
up-sampling x2 required At lowest speed (20 rpm)
◦ 450 000 samples collected◦ Tach pulses: 112 500
Up-sampling x4 required Up-sampling in the context of noise?
Order Tracking
Examined Techniques
Sensing SegmentationFeature
ExtractionClassification Post-
Processing
Statistical Parameterization
Thrust: Feature vectors are grouped according to speed and a statistical model fit as function of speed
Motivation: Effects of machinery resonances managed by subdividing novelty detection
Limitations: Double curse of dimensionality, assumption of Gaussianaity
Contribution:◦ Application to real world (machinery) data◦ Evaluated theoretical limitations with respect to machinery◦ Improved approach by suggesting whitening first followed
by normal novelty detection
Statistical Parameterization: Overview
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
Multi-Modal Novelty Detection
Variable Speed and Load
Thrust: One mode is included in the feature vector which are grouped into bins according to ranges of other mode (then employ multi-novelty detector dispatch)
Motivation: Advance the technique to higher modes Limitations: Curse of dimensionality, large number of
modes impractical, brute force Contribution:
◦ Very practical technique compared to literature (for load and speed)
◦ “Crossing” modes to enhance classification results Experimental Data: Laurentian’s TVS Status: Not yet validated
Multi-Modal Novelty Detection (Higher Modes): Overview
Approach so far only works with one mode Employ Timusk’s novelty detector dispatch
technique◦ Routine
Segment data into load bins For each load bin build a uni-modal novelty detector
for all speed data in that load bin◦ Improve results
Also build multiple detectors but based on speed bins
Combine classification results
Multi-Modal Novelty Detection
Averaging modes still a problem◦ Employ previous improvements
Curse of dimensionality increases◦ Some mitigation possible
Brute force ◦ Across of the spectrum of techniques, not as bad as
parzen windowing (enter dataset is memorized) Higher number of modes increases
computational complexities and curse of dimensionality
Multi-Modal Novelty Detection
Classification Results
Optimized Parameters: Number of Rotations in a Segment
Optimization: AR Order
Optimization: Order Tracking Subsampling
Results: No Speed Adaptation
Results: No Speed Adaptation
Results: No Speed Adaptation
Results: Speed in Feature Vector
Results: Speed in Feature Vector
Results: Speed in Feature Vector
Results: Speed in Feature Vector
Results: Statistical Parameterization
Results: Statistical Parameterization
Results: Statistical Parameterization
Results: Statistical Parameterization
Double Curse of Dimensionality
Generalization
Validate: Component Swapping
Different Gear Faults (96:32)
Different Gear Faults (96:32)
Different Gear Faults (96:32)
Conclusion and Future Work
Must account for speed! Worden’s Statistical Parameterization
◦ Good results◦ Subject to double curse of dimensionality and gaussianaity
Multi-Modal Novelty Detection◦ Results on par or better than Worden’s◦ Somewhat insensitive to double curse of dimensionality
Feature vectors◦ Statistics poor
Consequently, AE poor◦ AR models produced excellent results◦ Order Tracking poor
Why?
Conclusion
Thesis◦ Multi-Modal Novelty Detection for Higher No.
Modes◦ System Identification
No need to account for modes in novelty detection Curse of dimensionality?
◦ Cross-Correlation No need to measure modes Silver bullet?
◦ Software Architecture
Future Work
CEMI Dr. Mechefske (Queens) Dr. Timusk Greg Lakanen Greg Dalton
Thanks