Construction of Bayesian Networks for Diagnostics

1
Construction of Bayesian Networks for Diagnostics

• K. Wojtek Przytula HRL Laboratories
• Don Thompson Pepperdine University
• Malibu, California

2
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
Bayesian Networks - Definition

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)

F1
F2
Aux
Ob1
Ob2
Ob3
Ob4
4
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
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
Subsystem Definition Example
COMPUTER
PLANT
SENSOR
CONNECTION
INCORRECT SIGNAL
SENSOR RESISTANCE
INCORRECT PHYSICAL VALUE
7
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
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
Subsystem Definition

• Fault list
• Rank faults by failure frequency
• Observation list
• Failure symptoms
• Computer error messages
• Built in test results
• Fault troubleshooting data

10
Simple Subsystem Model

• One fault, conditionally independent observations
• Causal probability determination
• Only necessary for fault-observation pairs
• All others zero
• Thorough testing

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Simple Network Model Example

• FAULT NODE
• PLANT
• SENSOR
• CONNECTION
• COMPUTER

INCORRECT PHYSICAL VALUE
INCORRECT SIGNAL
SENSOR RESISTANCE
12
Complex Network Model Example
PLANT
CONNECTION
COMPUTER
SENSOR
PHYSICAL VALUE
SIGNAL
INCORRECT SIGNAL
INCORRECT PHYSICAL VALUE
SENSOR RESISTANCE
13
Probability Calculations

• Goal computation of the joint probability
• distribution of all components influencing a
• given test, i.e. calculation of the ensemble
• P(C1, C2, , Cn,T)
• for all Tests T and corresponding
• adjacent components Ci

C1
C2
Cn
T
14
Probability Elicitation

• Diagnostic Probability Intuitive to Diagnostic
  Experts
• conditional probability of the form P(CT),
  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(TC),
  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

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What Probability Information is Sufficient?

• Question Given the prior component probability
  distribution P(C), and the diagnostic
  probability distribution P(CT), is it possible
  to uniquely determine the causal probability
  distribution P(TC) 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.

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Successful Elicitation

• Given
• P(C1, C2, , CnT)
• (distribution of all diagnostic probabilities)
• P(C1, C2, , Cn)
• (single prior)
• P(C1, C2, , CnT)
• (single nonfailure diagnostic)
• we can calculate
• P(C1, C2, , Cn,T)
• (joint distribution)
• P(T C1, C2, , Cn)
• (distribution of all causal probabilities)
• Implementation Matlab

C1
C2
Cn
T

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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