1 / 17

Construction of Bayesian Networks for Diagnostics

Develop a Bayesian network model for diagnostic support using diverse information sources. Refine the model through experimental data to balance fidelity with design cost. Learn probability calculations and complexity integration for efficient decision support in diagnostics.

tracyo
Download Presentation

Construction of Bayesian Networks for Diagnostics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  11. Simple Network Model Example • FAULT NODE: • PLANT • SENSOR • CONNECTION • COMPUTER INCORRECT PHYSICAL VALUE SENSOR RESISTANCE INCORRECT SIGNAL

  12. Complex Network Model Example CONNECTION PLANT SENSOR COMPUTER 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(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. 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. Successful Elicitation • Given • {P(C1, C2, …, Cn|T)} • (distribution of all diagnostic probabilities) • P(C1, C2, …, Cn) • (single prior) • P(C1, C2, …, Cn|T’) • (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

  17. 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

More Related