1
© 1998 HRL Laboratories, LLC. All Rights Reserved
Construction of Bayesian Networks
for Diagnostics
K. Wojtek Przytula: HRL Laboratories
&
Don Thompson: Pepperdine University
Malibu, California
2
© 1998 HRL Laboratories, LLC. All Rights Reserved
Diagnostics / Troubleshooting
Problem Definition
Given a set of system observations ( symptoms,
sensor readings, error codes, test results)
determine a root cause of system failure
Typical Techniques for Problem Solution
•
Decision Trees
•
Cased Based Reasoning
•
Bayesian Networks
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Bayesian
Networks
-
Definition
Ob
1
Ob
2
Ob
3
Ob
4
F1
F2
Au
x
Bayesian Networks*
are a class of probabilistic
models for knowledge representation
•
Nodes represent random variables
•
Edges represent causal dependencies
between variables
•
Annotations are prior and conditional
probabilities
* (also known as belief networks or causal networks)
4
© 1998 HRL Laboratories, LLC. All Rights Reserved
Bayesian Networks
-
Features
•
Bayesian networks can be constructed from domain
knowledge and/or learned from data
•
Network structure reflects the causal reality of the domain
•
Query: given state of some variables, compute the
probability of states of remaining variables
•
Computation: efficient implementation of probabilistic
calculations
•
Application: decision support in presence of uncertainty
e.g. diagnostics
-
tool assist human in finding a fault
5
© 1998 HRL Laboratories, LLC. All Rights Reserved
Problem Definition
•
Create a Bayesian network model for a diagnostic
support tool using diverse information sources
(manuals, test & repair procedures, repair statistics,
experts)
•
Balance fidelity with design cost
•
Refine the model by learning from experimental data
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Subsystem Definition Example
PLANT
SENSOR
COMPUTER
CONNECTION
INCORRECT
SIGNAL
INCORRECT
PHYSICAL
VALUE
SENSOR
RESISTANCE
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Model Development
•
Decompose modeled system into small subsystems
•
Define model granularity
•
Create simple models for subsystems and test performance
•
Gradually increase model complexity
•
Integrate subsystem models into a single system model
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© 1998 HRL Laboratories, LLC. All Rights Reserved
System
Decomposition
•
Determine
system
complexity
by
combining
–
Number
of
replaceable
components
or
faults
–
Number
of
tests,
symptoms,
error
messages
•
Subdivide
system
by
functional
parts
•
Identify
experts
from
–
System
Design/Engineering
–
Maintenance/Repair
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Subsystem
Definition
•
Fault
list
•
Rank
faults
by
failure
frequency
•
Observation
list
–
Failure
symptoms
–
Computer
error
messages
–
Built
in
test
results
–
Fault
troubleshooting
data
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Simple
Subsystem
Model
•
One
fault,
conditionally
independent
observations
•
Causal
probability
determination
–
Only
necessary
for
fault
-
observation
pairs
–
All
others
zero
•
Thorough
testing
11
© 1998 HRL Laboratories, LLC. All Rights Reserved
INCORRECT
PHYSICAL
VALUE
INCORRECT
SIGNAL
FAULT NODE:
•
PLANT
•
SENSOR
•
CONNECTION
•
COMPUTER
Simple Network
Model Example
SENSOR
RESISTANCE
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© 1998 HRL Laboratories, LLC. All Rights Reserved
INCORRECT
SIGNAL
INCORRECT
PHYSICAL
VALUE
SENSOR
RESISTANCE
PHYSICAL
VALUE
SIGNAL
PLANT
COMPUTER
CONNECTION
SENSOR
Complex Network
Model Example
13
© 1998 HRL Laboratories, LLC. All Rights Reserved
Probability Calculations
Goal: computation of the joint probability
distribution of all components influencing a
given test, i.e. calculation of the ensemble
{P(C
1
, C
2
, …, C
n
,T)}
for all Tests T and corresponding
adjacent components
C
i
C
1
T
C
2
C
n
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Probability Elicitation
•
Diagnostic Probability
–
Intuitive to Diagnostic Experts
–
conditional probability of the form P(C|T), indicating the
likelihood that a component fails given a particular test has
returned a failure condition
–
Example: P(Generator Defective | Alternator Light = On) = 0.65
•
Causal Probability
–
Counter
-
Intuitive to Diagnostic
Experts
–
conditional probability of the form P(T|C), indicating the
likelihood of a particular test outcome given a component has
failed
–
Example: P(Alternator Light = On | Generator Defective) = 0.8
•
Prior
Probability
–
unconditional
probability
of
component
failure
P(C)
–
Example
:
P(Generator
Defective)
=
0
.
25
15
© 1998 HRL Laboratories, LLC. All Rights Reserved
What Probability
Information is Sufficient?
•
Question
:
Given
the
prior
component
probability
distribution
{P(C)},
and
the
diagnostic
probability
distribution
{P(C|T)},
is
it
possible
to
uniquely
determine
the
causal
probability
distribution
{P(T|C)}
and
therefore
the
joint
distribution
{P(C,T)}?
•
Answer
:
NO
.
Prior
and
diagnostic
probability
information
does
not
characterize
causal
and
joint
probabilities
.
There
are
infinitely
many
causal
and
joint
probability
distributions
resulting
from
fixed
prior
and
diagnostic
probability
information
.
16
© 1998 HRL Laboratories, LLC. All Rights Reserved
Successful Elicitation
Given
•
{P(C
1
,
C
2
,
…
,
C
n
|T)}
•
(distribution
of
all
diagnostic
probabilities)
•
P(C
1
,
C
2
,
…
,
C
n
)
•
(single
prior)
•
P(C
1
,
C
2
,
…
,
C
n
|T’)
•
(single
nonfailure
diagnostic)
we
can
calculate
•
{P(C
1
,
C
2
,
…
,
C
n
,T)}
•
(joint
distribution)
•
{P(T| C
1
, C
2
, …, C
n
)}
•
(distribution of all causal probabilities)
•
Implementation: Matlab
C
1
T
C
2
C
n
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© 1998 HRL Laboratories, LLC. All Rights Reserved
Conclusion
•
Methodology of Bayesian Network Design
–
Iterative
–
Hierarchical
–
Model fidelity control
–
Simplified verification and testing
•
Probability Elicitation
–
Natural for diagnostic expert
–
Automatic re
-
computation of probabilities for the network
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