Online Tribology Ball Bearing Fault Detection and Identification

April 11, 2007

Defense and Security Symposium 2007

Dr. Bo LingMigma Systems, Inc.

Dr. Michael KhonsariLouisiana State University

Presentation Outline

- Problem Statement

- Ball Bearing Transient Data Analysis

- Feature Space Construction

- HMM-GMM Based Fault States Classification

- Laboratory Experimental System

- Laboratory Data Test Results

- Conclusion

Problem Statement

Successful operation of many precision machinery used in space instruments require very stringent position accuracy – in the range of microns.

Theses systems must be designed to operate reliably with little or no maintenance and long service-life duration.

In many instances, the accuracy of the instruments and devices used to monitor and control the mechanical system is highly dependent on the dynamic performance of ball bearings

Laboratory System

Precision Universal MicroTribometer

Laboratory Data Collection System

The sampling time is 50 ms, the angle of the oscillatory motion is 14.4o, and the rotational speed is

10 rpm.

X-directional force Y-directional force

Transient Torque Data Analysis

The first step in our fault identification method is to calculate the bispectrum from the raw torque data. Let {x(n)}, n = 0, 1, …, N-1, be a discrete time signal. Its bispectrum can be defined as:

)()()(1

),( 2121213 ffXfXfXN

ffB x

where X(f) is the Fourier transform of {x(n)}.

Bispectrum Analysis

As bispectrum is a 2-D function, it is difficult to analyze.

A 1-D slice of the bispectrum is obtained by freezing one of is two frequency indices.

There are many types of 1-D slices including diagonal, vertical, or horizontal.

Instead of taking 1-D slices, we add bispectra along one frequency index, thus, generating dynamics in the time-frequency domain.

Shannon Entropy for Fault Trend Detection

From the bispectrum data, we then calculate the Shannon entropy which is a measure of its spectral distribution of the bispectrum. It is defined as

)(log)( 2 fxfxSE kf

kk

where k is the time index (horizontal axis), f is the frequency index (vertical axis).

Fault Event Trigger

From the trend of Shannon entropy, we can estimate the fault event trigger and progress of fault events.

Fault Events Identification

From these triggers, we identify three stages: Normal, Fault A, and Fault B.

Fault Features

We then extract the features from the raw torque data. Our feature space is made of the 2nd moment and kurtosis.

The kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. The 2nd moment is a measure of data variation around the statistical mean value.

Hidden Markov Model

To identify the fault states, we have further developed a set of stochastic models using hidden Markov model (HMM)

characterized as follows:

The number of states in the model, N.

The number of distinct observation symbols, M.

The NN state transition matrix, A, whose (i, j) entry is the probability of a transition from state i to state j.

The NM observation matrix, B, whose (i, k) entry is the probability of emitting observation symbol vk

given that the model is in state i. The initial state distribution, .

HMM-GMM Models

In most HMM applications, the observation is assumed to take the discrete values in a set. However, for our application, there are no specific discrete observations. In other words, we are dealing with a continuous feature space with certain underlying statistical

distribution.

In our system, we model the distribution of feature vectors as Gaussian Mixture Model (GMM).

Gaussian Mixture Model

The general Gaussian mixture model is defined as

n

i

G

kkkikkGGL

1 111 ),|()|,...,;,...,( yy

)2det(

)(21

),|(

1

k

kikT

ki

kkik

yyy

-exp

where k is the probability that an observation belongs to the kth cluster (k 0; ), k is given as

HMM-GMM Based Classifier

We have identified two fault states, Fault A and Fault B. Therefore, we have built three independent HMM-GMM models for three states including NRMAL state, respectively.

Initial Data Processing

The bearing tested had 8 balls with races coated with MoS2. The bearing was tested over a continuous period of 25 days under an imposed normal load of 42 N.

The sampling time was 50 ms.

There are tremendous amount of data available for processing. Given that the ball bearing coating is wearing out gradually, it was decided to analyze the data at every 10-second.

Classifier Training

We have trained three HMM-GMM models, HMM-GMMnormal, HMM-GMMfaultA, HMM-GMMfaultB.

We then process all torque data through these three models.

Hidden States Transition

Observations

(a) Three stages are distinctive, indicating that our HMM-GMM models are accurate;

(b) Different stages can be observed during the transitions of stages; and

(c) The trend of stage transition is clear and conclusive.

Test Results

It is clear that the HMM-GMM models have accurately predicted the ball bearing stages, namely, Fault A, Fault B, and Normal.

These three stages are difficult to identify from the raw torque data. In fact, under the conditions tested the torque data did not show useful trend as ball bearing coating is wearing out.

The HMM-GMM models can be used to identify the fault stages, thus, providing valuable prognosis information for the ball bearings.

Conclusion

- We have developed a system to monitor the health status of ball bearings.

- Bispectrum and Shannon entropy for the transient torque data are used to capture the fault trend.

- HMM-GMM based classifier can be used to actually identify the fault states of ball bearings, thus providing valuable prognosis information for their operation.

- Under NASA Phase II funding, we will develop a fully functional system and test it in a realistic space operation environment.