Construction of Bayesian Networks

lettuceescargatoireΤεχνίτη Νοημοσύνη και Ρομποτική

7 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

86 εμφανίσεις

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

3

© 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

6

© 1998 HRL Laboratories, LLC. All Rights Reserved

Subsystem Definition Example


PLANT

SENSOR

COMPUTER

CONNECTION

INCORRECT

SIGNAL

INCORRECT

PHYSICAL

VALUE

SENSOR

RESISTANCE

7

© 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


8

© 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

9

© 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

10

© 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

12

© 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

14

© 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

17

© 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