Prognosis of Gear Health Using Gaussian Process Model

1. Prognosis of Gear Health Using Gaussian ProcessModel Department of Adaptive systems, Institute of Information Theory and Automation, May 2011, Prague

2. 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

3. Outline • Problem description • Experimental setup • Gaussian Process models • Time series modelling and prediction • Conclusions

4. 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)

5. Experimental setup Experimental test bed with motor-generator pair and single stage gearbox

6. Experimental setup Vibration sensors Signal acquisition

7. Experimental setup • Experiment description • 65 hours • constant torque (82.5Nm) • constant speed (990rpm) • accelerated damage mechanism (decreased surface area)

8. Mechanical damage

9. Feature extraction For each sensor, a time series of feature value evolution is obtained, only y8 used

10. Outline • Problem description • Experimental setup • Gaussian Process models • Time series modelling and prediction • Conclusions

11. GP model • Probabilistic (Bayes) nonparametric model • Prediction of the output based on similarity test input – training inputs • Output: normal distribution • Predicted mean • Prediction variance

12. Nonlinear fuctionand GP model 10 8 Nonlinear function to be modelled from learning points 8 y=f(x) 6 Learning points 6 4 y 2 4 0 y 2 -2 0 -4 Learning points m ± s 2 -2 -6 m -1.5 -1 -0.5 0 0.5 1 1.5 2 f(x) x -4 Prediction error and double standard deviation of prediction -1.5 -1 -0.5 0 0.5 1 1.5 2 x s 2 6 |e| 4 e 2 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 x Static illustrative example • Static example: • 9 learning points: • Prediction • Rare data density  increased variance (higher uncertainty).

13. 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)

14. Outline • Problem description • Experimental setup • Gaussian Process models • Time series modelling and prediction • Conclusions

15. Prediction of first passage time

16. The modelling of feature evolution as time series and its prediction

17. Prediction of the time when harmonic component feature reaches critical value

18. 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