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 y8 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 inputsOutput: normal distribution

•Predicted mean •Prediction variance

-2 +2

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)

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