CBM Variable Speed Machinery

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


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


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



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



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



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)



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



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



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


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


Classification Results

Optimized Parameters: Number of Rotations in a Segment

Optimization: AR Order

Optimization: Order Tracking Subsampling

Results: No Speed Adaptation



Results: Speed in Feature Vector




Results: Statistical Parameterization




Double Curse of Dimensionality

Generalization

Validate: Component Swapping

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

Documents

CBM Variable Speed Machinery