Kickoff Meeting Presentation

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Defense and Security Symposium 2007
Online Tribology Ball Bearing Fault Detection and
Identification
Dr. Bo Ling Migma Systems, Inc. Dr. Michael
Khonsari Louisiana State University
April 11, 2007
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Presentation Outline
- Problem Statement
- Laboratory Experimental System
- Ball Bearing Transient Data Analysis
- Feature Space Construction
- HMM-GMM Based Fault States Classification
- Laboratory Data Test Results
- Conclusion
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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
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Laboratory System
Precision Universal MicroTribometer
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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
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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
where X(f) is the Fourier transform of x(n).
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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.
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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
where k is the time index (horizontal axis), f is
the frequency index (vertical axis).
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Fault Event Trigger
From the trend of Shannon entropy, we can
estimate the fault event trigger and progress of
fault events.
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Fault Events Identification
From these triggers, we identify three stages
Normal, Fault A, and Fault B.
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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.
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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 N?N state transition matrix, A, whose (i,
j) entry is the probability of a transition from
state i to state j.
? The N?M 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, ?.
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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).
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Gaussian Mixture Model
The general Gaussian mixture model is defined as
where ?k is the probability that an observation
belongs to the kth cluster (?k ? 0 ), ?k is
given as
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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.
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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.
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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.
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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.
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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.
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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.