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 F1F2 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 C1C1 T C2C2 CnCn

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 C1C1 T C2C2 CnCn

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