MIT16_410F10_lec12b

MIT16_410F10_lec12b - Model-based Monitoring Brian C...

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Unformatted text preview: 3/6/00 Model-based Monitoring Brian C. Williams 16.412J/6.834J March 6 th , 2006 Brian C. Williams, copyright 2000 Due to the unknown mode, there tends to be an exponential number of diagnoses. U Good Candidates with UNKNOWN failure modes G Good Candidates with KNOWN failure modes U Fault Models don’t help. F1 Fn G U 1 Image credit: NASA. 3/6/00 2 Due to the unknown mode, there tends to be an exponential number of diagnoses. U Candidates with UNKNOWN failure modes Good G Candidates with KNOWN failure modes Good F1 Fn G U Fault Models don’t help. Most of the density space may be approximated by enumerating the few most likely diagnoses But “unknown” diagnoses represent a small fraction of the probability density space. U Sequential Model-based Diagnosis Input: • Set of component mode variables M, with finite domains. • Set of observables X, with finite domains. • Device model Φ over M and X, in propositional logic. • Prior distribution P(M i ) of mode assignments for each component i. • Observation sequence X 1,n = x 1,n provided dynamically. Output: • P(M) Prior Probability of Failure • P(M | X 1,n = x 1,n ) Posterior Given Observation updated after each observation is received. Assume: • Independence of component mode prior distribution. • Conditional independence of observations given candidate (Naïve Bayes). • Uniform distribution of observables, given candidate. 3/6/00 3 Mode Estimation Example Inverter(i): • G(i): Out(i) = not(In(i)) • S1(i): Out(i) = 1 • S0(i): Out(i) = 0 • U(i): X Y A B C 0 0 Nominal, Fault and Unknown Modes • Isolates surprises • Explains Sherlock...
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MIT16_410F10_lec12b - Model-based Monitoring Brian C...

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