prognosis of gear health using gaussian process model department of adaptive systems, institute of...
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Prognosis of Gear Health Using Gaussian Process
Model
Department of Adaptive systems, Institute of Information Theory and Automation, May 2011, Prague
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Motivation
An estimated 95% of installed drives belong to older generation - no embedded diagnostics
functionality- poorly or not monitored
These machines will still be in operation for some time!
Goal: to design a low cost, intelligent condition monitoring module
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Outline
Problem description Experimental setup Gaussian Process models Time series modelling and prediction Conclusions
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Problem description
Gear health prognosis using feature values from vibration sensors
Model the time series using discrete-time stochastic model
Time series prediction using the identified model
Prediction of first passage time (FPT)
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Experimental setup
Experimental test bed with motor-generator pair and single stage gearbox
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Experimental setup
Vibration sensors
Signal acquisition
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Experimental setup
Experiment description• 65 hours• constant torque (82.5Nm)• constant speed (990rpm)• accelerated damage mechanism
(decreased surface area)
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Mechanical damage
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Feature extraction
For each sensor, a time series of feature value evolution is obtained, only y8 used
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Outline
Problem description Experimental setup Gaussian Process models Time series modelling and prediction Conclusions
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Probabilistic (Bayes) nonparametric model
GP model
Prediction of the output based on similarity test input – training inputsOutput: normal distribution
•Predicted mean •Prediction variance
-2 +2
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Static illustrative example
Static example: 9 learning points: Prediction
Rare data density increased variance (higher uncertainty).
-1.5 -1 -0.5 0 0.5 1 1.5 2-4
-2
0
2
4
6
8
xy
Nonlinear function to be modelled from learning points
y=f(x)
Learning points
-1.5 -1 -0.5 0 0.5 1 1.5 2-6
-4
-2
0
2
4
6
8
10
x
y
Nonlinear fuction and GP model
-1.5 -1 -0.5 0 0.5 1 1.5 20
2
4
6
x
e
Prediction error and double standard deviation of prediction
2|e|
Learning points
2f(x)
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GP model attributes (vs. e.g. ANN) Smaller number of parameters Measure of confidence in prediction, depending on data Data smoothing Incorporation of prior knowledge * Easy to use (engineering practice)
Computational cost increases with amount of data
Recent method, still in development Nonparametrical model
* (also possible in some other models)
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Outline
Problem description Experimental setup Gaussian Process models Time series modelling and prediction Conclusions
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Prediction of first passage time
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The modelling of feature evolution as time series and its prediction
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Prediction of the time when harmonic component feature reaches critical value
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Conclusions Application of GP models for:
• modelling of time-series describing gear wearing
• prediction of the critical value of harmonic component feature
Two models useful:• Matérn + polynomial + constant
covariance function• Neural-network covariance function
Useful information 15 to 20 hours ahead – soon enough for maintenance