Prognosis of Gear Health Using Gaussian Process Model Department of Adaptive systems, Institute of Information Theory and Automation, May 2011, Prague

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

Outline  Problem description  Experimental setup  Gaussian Process models  Time series modelling and prediction  Conclusions

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)

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

Experimental setup  Vibration sensors  Signal acquisition

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

Mechanical damage

Feature extraction  For each sensor, a time series of feature value evolution is obtained, only y 8 used

Outline  Problem description  Experimental setup  Gaussian Process models  Time series modelling and prediction  Conclusions

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

Static illustrative example  Static example:  9 learning points:  Prediction  Rare data density  increased variance (higher uncertainty) x y Nonlinear function to be modelled from learning points y=f(x) Learning points x y Nonlinear fuction and GP model x e Prediction error and double standard deviation of prediction 2  |e| Learning points   2   f(x)

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)

Outline  Problem description  Experimental setup  Gaussian Process models  Time series modelling and prediction  Conclusions

Prediction of first passage time

The modelling of feature evolution as time series and its prediction

Prediction of the time when harmonic component feature reaches critical value

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