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10/16/02copyright Brian Williams, 20021 courtesy of JPL Diagnosing Multiple Faults Brian C. Williams 16.412J/6.834J October 16 th, 2002 Brian C. Williams,

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Presentation on theme: "10/16/02copyright Brian Williams, 20021 courtesy of JPL Diagnosing Multiple Faults Brian C. Williams 16.412J/6.834J October 16 th, 2002 Brian C. Williams,"— Presentation transcript:

1 10/16/02copyright Brian Williams, 20021 courtesy of JPL Diagnosing Multiple Faults Brian C. Williams 16.412J/6.834J October 16 th, 2002 Brian C. Williams, copyright 2000

2 10/16/02copyright Brian Williams, 20022 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely  Conflict-directed A*

3 10/16/02copyright Brian Williams, 20023 Failures may be hidden: STS-93 Symptoms: Engine temp sensor high LOX level low GN&C detects low thrust H2 level low (???) Problem : Liquid hydrogen leak Effect: LH2 used to cool engine Engine runs hot Consumes more LOX Failures may be detected by qualitative arguments

4 10/16/02copyright Brian Williams, 20024 Mars Observer courtesy of JPL Failures are Often Novel

5 10/16/02copyright Brian Williams, 20025

6 Multiple Faults Occur courtesy of NASA Quintuple fault occurs (three shorts, tank-line and pressure jacket burst, panel flies off). Power limitations too severe to perform new mission. Novel reconfiguration identified, exploiting LEM batteries for power. APOLLO 13

7 10/16/02copyright Brian Williams, 20027 Mars Observer.... Mars Climate Orbiter Mars Polar Lander Deep Space 2 courtesy of JPL Failures Are Subtle, Frequent and Remote

8 10/16/02copyright Brian Williams, 20028 Mars Polar Lander Diagnosis: Legs deployed during descent. Noise spike on leg sensors latched by software monitors. Laser altimeter registers 50ft. Begins polling leg monitors to determine touch down. Latched noise spike read as touchdown. Engine shutdown at ~50ft. Failures Involve Complex Software/Hardware Interactions

9 10/16/02copyright Brian Williams, 20029  Candidate: Assignment to all component modes. 3 2 2 3 3 M1 M2 M3 A1 A2 A B C D E F G X Y Z 10 Adder(i):  G(i): Out(i) = In1(i)+In2(i)  U(i): 12 Diagnosis identifies consistent modes Candidate = {G(A1) & G(A2) & G(M1) & G(M2) & G(M3)} Given Model and Observations:

10 10/16/02copyright Brian Williams, 200210 Diagnosis identifies consistent modes Adder(i):  G(i): Out(i) = In1(i)+In2(i)  U(i):  Candidate: Assignment to all component modes.  Diagnosis D: Candidate consistent with model Phi and observables OBS. 3 2 2 3 3 M1 M3 A1 A B C D E F G X Y Z 10 12 Diagnosis = {G(A1) & U(A2) & G(M1) & G(M2) & G(M3)} Given Model and Observations:

11 10/16/02copyright Brian Williams, 200211 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely

12 10/16/02copyright Brian Williams, 200212 sense P(s) WORLD observations actions AGENT Diagnostic Agent: Monitors & Diagnoses Repairs & Avoids Probes and Tests Plant act Consistency-based From Symptoms

13 10/16/02copyright Brian Williams, 200213 Goal: Support programmers with Embedded Languages that monitor, diagnose and repair (Model-based Programming) Programming Diagnostic Agents

14 System Model Control Program RMPL Model-based Program Control Sequencer Deductive Controller CommandsObservations Plant Titan Model-based Executive State goalsState estimates Mode Estimation Mode Reconfiguration Tracks likely plant states Tracks least cost goal states Executes concurrently Preempts Queries (hidden) states Asserts (hidden) state Closed Valve Open Stuckopen Stuckclosed OpenClose 0. 01 0.01 0.01 inflow = outflow = 0 Generates target goal states conditioned on state estimates

15 Example: The model-based program sets engine = thrusting, and the deductive controller... Determines that valves on the backup engine will achieve thrust, and plans needed actions. Deduces that a valve failed - stuck closed Plans actions to open six valves Fuel tank Oxidizer tank Deduces that thrust is off, and the engine is healthy

16 10/16/02copyright Brian Williams, 200216 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely

17 10/16/02copyright Brian Williams, 200217 Representing Inconsistent Candidates Compactly M1 M2 A1 A B C D E 3 2 2 3 F G X Y Z 10 Conflict A set of component modes M that are inconsistent with the model and observations. Every subset of a conflict is a conflict Only need conflicts that are minimal under subset Logically, not M is an implicate of model & Obs 6 6 12 M3 A2

18 10/16/02copyright Brian Williams, 200218 ? ? 3 2 2 3 3 M1 M3 A1 A B C D E F G X Y Z 10 12 ? Kernel Diagnosis = {U(A2) & U(M2)} Representing Diagnoses Compactly Partial Diagnosis: A set of component modes M all of whose extensions are diagnoses. M removes all symptoms M entails Model & Obs (implicant) Kernel Diagnosis: A minimal partial diagnosis K M is a prime implicant of model & obs

19 10/16/02copyright Brian Williams, 200219 Using Conflicts to Divide and Conquer Given model Phi and observations OBS 1.Find all symptoms and diagnose each symptom separately  2.Merge diagnoses  General Diagnostic Engine [de Kleer & Williams, 87]

20 10/16/02copyright Brian Williams, 200220 Using Conflicts to Divide and Conquer Given model Phi and observations OBS 1.Find all symptoms and diagnose each symptom separately  find minimal conflicts and constituent diagnoses 2.Merge diagnoses  find kernel diagnoses General Diagnostic Engine [de Kleer & Williams, 87]

21 10/16/02copyright Brian Williams, 200221 1. Find Symptom M1 M2 A1 A B C D E 3 2 2 3 F G X Y Z 10 Symptom: F is observed 10, but should be 12if M1 & M2 & A1 are okay. 6 6 12 M3 A2

22 10/16/02copyright Brian Williams, 200222 1. … and its Conflict M1 M2 A1 A B C D E 3 2 2 3 F G X Y Z Symptom: F is observed 10, but should be 12 if A1, M1& M2 are okay. Conflict:G(A1) & G(M1) & G(M2) is inconsistent F10 12 6 6

23 10/16/02copyright Brian Williams, 200223 M1 M2 A1 A B C D E 3 2 2 3 F G X Y Z Symptom: F is observed 10, but should be 12 Conflict:G(A1) & G(M1) & G(M2) is inconsistent U(A1) or U(M1) or U(M2) removes conflict. 10 12 6 6 1. … and its Conflict

24 10/16/02copyright Brian Williams, 200224 1. Find Another Symptom 3 2 3 M1 M3 A1 A2 A B C D E F G X Y Z 10 12 4 6 10 Symptom: G is observed 12, but should be 10...

25 10/16/02copyright Brian Williams, 200225 3 2 3 M1 M3 A1 A2 A B C D E F G X Y Z 10 12 4 6 10 Symptom: G is observed 12, but should be 10 Conflict:G(A1) & G(M2) & G(M1) & G(M3) is inconsistent Conflict not just upstream from symptom 1. … and its Conflict

26 10/16/02copyright Brian Williams, 200226 3 2 3 M1 M3 A1 A2 A B C D E F G X Y Z 10 12 4 6 10 Symptom: G is observed 12, but should be 10 Conflict:G(A1) & G(M2) & G(M1) & G(M3) is inconsistent U(A1) or U(A2) or U(M1) or U(M3) removes conflict Conflict not just upstream from symptom 1. … and its Conflict

27 10/16/02copyright Brian Williams, 200227 Kernel Diagnoses = 2. Merge Diagnoses U(A1) or U(M1) or U(M2) remove conflict 1. U(A1) or U(A2) or U(M1) or U(M3) remove conflict 2 “Smallest” sets of modes that remove all conflicts Constituent Kernel Diagnoses

28 10/16/02copyright Brian Williams, 200228 Kernel Diagnoses = {U(A1)} 3. Merge Diagnoses U(A1) or U(M1) or U(M2) remove conflict 1. U(A1) or U(A2) or U(M1) or U(M3) remove conflict 2 “Smallest” sets of modes that remove all conflicts Constituent Kernel Diagnoses

29 10/16/02copyright Brian Williams, 200229 Kernel Diagnoses = {U(M1)} {U(A1)} 3. Merge Diagnoses “Smallest” sets of modes that remove all conflicts U(A1) or U(M1) or U(M2) remove conflict 1. U(A1) or U(A2) or U(M1) or U(M3) remove conflict 2 Constituent Kernel Diagnoses

30 10/16/02copyright Brian Williams, 200230 3. Merge Diagnoses U(A1) or U(M1) or U(M2) remove conflict 1. U(A1) or U(A2) or U(M1) or U(M3) remove conflict 2 Kernel Diagnoses ={U(A2) & U(M2)} {U(M1)} {U(A1)} “Smallest” sets of modes that remove all conflicts Constituent Kernel Diagnoses

31 10/16/02copyright Brian Williams, 200231 Kernel Diagnoses = {U(M2) & U(M3)} {U(A2) & U(M2)} {U(M1)} {U(A1)} 3. Merge Diagnoses U(A1) or U(M1) or U(M2) remove conflict 1. U(A1) or U(A2) or U(M1) or U(M3) remove conflict 2 “Smallest” sets of modes that remove all conflicts Constituent Kernel Diagnoses

32 10/16/02copyright Brian Williams, 200232 Worst Case Complexity Given model Phi and observations OBS  Generate all minimal conflicts  An instance of Implicate generation - NP Hard  Generate kernel diagnosis from conflicts  An instance of Implicant generation - NP Hard Performance is a pragmatic question:  How large is the set of conflicts and kernels?  Is it faster to go through conflicts, than to go directly to the kernels?

33 10/16/02copyright Brian Williams, 200233 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely

34 10/16/02copyright Brian Williams, 200234 Diagnosis With Only the Unknown Inverter(i):  G(i):Out(i) = not(In(i))  U(i): X Y ABC 0 000 Nominal and Unknown Modes Isolates surprises Doesn’t explain

35 10/16/02copyright Brian Williams, 200235 Diagnosis With Only the Known Inverter(i):  G(i):Out(i) = not(In(i))  S1(i):Out(i) = 1  S0(i):Out(i) = 0 X Y ABC 0 000 Exhaustive Fault Modes No surprises Explains

36 10/16/02copyright Brian Williams, 200236 Solution: Diagnosis as Estimating Behavior Modes Inverter(i):  G(i):Out(i) = not(In(i))  S1(i):Out(i) = 1  S0(i):Out(i) = 0  U(i): X Y ABC 0 000 Nominal, Fault and Unknown Modes Isolates surprises Explains

37 10/16/02copyright Brian Williams, 200237 Example Diagnoses X Y ABC 0 0 1 Diagnosis: [S1(A),G(B),U(C)] 00 Sherlock [de Kleer & Williams, 89]

38 10/16/02copyright Brian Williams, 200238 Example Diagnoses X Y ABC 0 0 1 Diagnosis: [S1(A),G(B),U(C)] Kernel Diagnosis: [U(C)] X Y ABC 0 0 ?? 00 00 Sherlock [de Kleer & Williams, 89]

39 10/16/02copyright Brian Williams, 200239 1. Find Symptoms & Conflicts Conflict: not G(A), G(B) and G(C) X Y ABC 0 0 1 0 GG G 0 0 1 0 0

40 10/16/02copyright Brian Williams, 200240 More Symptoms & Conflicts Not S1(A), G(B), and G(C) X Y ABC 0 0 1 0 S1G G 0 0 1 0 0

41 10/16/02copyright Brian Williams, 200241 not S0(B) and G(C) X Y ABC 0 0 0 S0 G 0 0 1 More Symptoms & Conflicts 0 0

42 10/16/02copyright Brian Williams, 200242 not S1(C) X Y ABC 0 0 1 S1 0 0 More Symptoms & Conflicts

43 10/16/02copyright Brian Williams, 200243 All Conflicts 

44 10/16/02copyright Brian Williams, 200244 2. Constituent Diagnoses from Conflicts  => G(C),S0(C) or U(C)  => G(B),S1(B),U(B),S1(C),S0(C) or U(C)  => G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C) or U(C)  => S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C) or U(C)

45 10/16/02copyright Brian Williams, 200245 3. Generate Kernel Diagnoses  [U(C)]  [G(C),S0(C),U(C)]  [G(B),S1(B),U(B),S1(C),S0(C),U(C)]  [G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]

46 10/16/02copyright Brian Williams, 200246  [U(C)]  [S0(C)]  [G(C),S0(C),U(C)]  [G(B),S1(B),U(B),S1(C),S0(C),U(C)]  [G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)] 3. Generating Kernel Diagnoses

47 10/16/02copyright Brian Williams, 200247  [U(C)]  [S0(C)]  [U(B),G(C)]  [G(C),S0(C),U(C)]  [G(B),S1(B),U(B),S1(C),S0(C),U(C)]  [G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)] 3. Generating Kernel Diagnoses

48 10/16/02copyright Brian Williams, 200248  [U(C)]  [S0(C)]  [U(B),G(C)]  [G(C),S0(C),U(C)]  [G(B),S1(B),U(B),S1(C),S0(C),U(C)]  [G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(B),G(C)] 3. Generating Kernel Diagnoses

49 10/16/02copyright Brian Williams, 200249  [U(C)]  [S0(C)]  [U(B),G(C]  [S1(B),G(C)]  [U(A),G(B),G(C)]  [G(C),S0(C),U(C)]  [G(B),S1(B),U(B),S1(C),S0(C),U(C)]  [G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)] 3. Generating Kernel Diagnoses

50 10/16/02copyright Brian Williams, 200250  [U(C)]  [S0(C)]  [U(B),G(C]  [S1(B),G(C)]  [U(A),G(B),G(C)]  [S0(A),G(B),G(C)]  [G(C),S0(C),U(C)]  [G(B),S1(B),U(B),S1(C),S0(C),U(C)]  [G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]  [S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)] 3. Generate Kernel Diagnoses

51 10/16/02copyright Brian Williams, 200251 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely  Computing Likelihood  Conflict-directed A*

52 10/16/02copyright Brian Williams, 200252 Diagnoses: (42 of 64 candidates) Fault Models  [G(A),G(B),S0(C)]  [G(A),S1(B),S0(C)]  [S0(A),G(B),G(C)]... Fault Free  [G(A),G(B),U(C)]  [G(A),U(B),G(C)]  [U(A),G(B),G(C)] Partial Diagnoses  [G(A),U(B),S0(C)]  [U(A),S1(B),G(C)]  [S0(A),U(B),G(C)]... X Y ABC 0 0 00

53 10/16/02copyright Brian Williams, 200253 Changes to Event Space U Candidates with UNKNOWN failure modes Candidates with KNOWN failure modes Good G F1 Fn G U

54 10/16/02copyright Brian Williams, 200254 Candidate Initial (prior) Probabilities p([G(A),G(B),G(C)]) =.97 p([S1(A),G(B),G(C)]) =.008 p([S1(A),G(B),S0(C)]) =.00006 p([S1(A),S1(B),S0(C)]) =.0000005 Assume Failure Independence

55 10/16/02copyright Brian Williams, 200255 X Y ABC 0 0 0

56 10/16/02copyright Brian Williams, 200256 Posterior Probability, after Observation x = v P(x=v|c) estimated using Model:  If previous obs, c and Phi entails x = v Then p(x = v | c) = 1  If previous obs, c and Phi entails x <> v Then p(x = v | c) = 0  If Phi consistent with all values for x Then p(x = v | c) is based on priors  E.g., uniform prior = 1/m for m possible values of x Bayes’ Rule Normalization Term

57 10/16/02copyright Brian Williams, 200257 Observe out = 1:  C = [G(A),G(B),G(C)]  P(C) =.97  P(out = 1 | C) = ?  = 1  P(C | out = 0 ) = ?  =.97/p(x=v) X Y ABC 1 0

58 10/16/02copyright Brian Williams, 200258 Observe out = 0:  C = [G(A),G(B),G(C)]  P(C) =.97  P(out = 0 | C) = ?  = 0  P(C | out = 0 ) = ?  = 0 x.97/p(x=v) = 0 X Y ABC 0 0

59 10/16/02copyright Brian Williams, 200259 X Y ABC 0 0 How do the single faults change? which are eliminated? which predict observations? Which are agnostic? Priors for Single Fault Diagnoses:

60 10/16/02copyright Brian Williams, 200260 X Y ABC 0 0 0

61 10/16/02copyright Brian Williams, 200261 X Y ABC 0 0 00 Top 6 of 64 = 98.6% of P

62 10/16/02copyright Brian Williams, 200262 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely  Computing Likelihood  Conflict-directed A*

63 10/16/02copyright Brian Williams, 200263 When you have eliminated the impossible, whatever remains, however improbable, must be the truth. - Sherlock Holmes. The Sign of the Four. Exploring the Improbable

64 10/16/02copyright Brian Williams, 200264 Focusing on Probable Candidates: Conflict-directed A* Generate Candidate Test Candidate Consistent? Keep Compute Posterior p Below Threshold? Record Conflict Done YesNo YesNo Leading Candidate Based on Priors

65 10/16/02copyright Brian Williams, 200265 Increasing Cost Feasible Infeasible A*

66 10/16/02copyright Brian Williams, 200266 Increasing Cost Feasible Infeasible Conflict-directed A*

67 10/16/02copyright Brian Williams, 200267 Increasing Cost Feasible Infeasible Conflict 1 Conflict-directed A*

68 10/16/02copyright Brian Williams, 200268 Increasing Cost Feasible Infeasible Conflict 1 Conflict-directed A*

69 10/16/02copyright Brian Williams, 200269 Increasing Cost Feasible Infeasible Conflict 2 Conflict 1 Conflict-directed A*

70 10/16/02copyright Brian Williams, 200270 Increasing Cost Feasible Infeasible Conflict 2 Conflict 1 Conflict-directed A*

71 10/16/02copyright Brian Williams, 200271 Increasing Cost Feasible Infeasible Conflict 3 Conflict 2 Conflict 1 Conflict-directed A*

72 10/16/02copyright Brian Williams, 200272 Increasing Cost Feasible Infeasible Conflict 3 Conflict 2 Conflict 1 Conflict-directed A* Feasible regions described by the implicants of known conflicts (Kernel Assignments) Want kernel assignment containing the best cost candidate

73 10/16/02copyright Brian Williams, 200273 Conflict-directed A* Given Current Conflicts:  Generate best-cost kernel of conflicts  Extend best kernel to best candidate  Test consistency  Failure: new-conflict.

74 10/16/02copyright Brian Williams, 200274 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 Assume Independent failures:  P G(mi) >> P U(mi)  P single >> P double  P U(M2) > P U(M1) > P U(M3) > P U(A1) > P U(A2) Example: Diagnosis

75 10/16/02copyright Brian Williams, 200275 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12  Conflicts / Constituent Diagnoses  none  Best Kernel:  {}  Best Candidate: ?? First Iteration

76 10/16/02copyright Brian Williams, 200276 { } ?(M1) & ?(M2) & ?(M3) & ?(A1) & ?(A2) G(M1) & G(M2) & G(M3) & G(A1) & G(A2)  Select most likely value for unassigned modes

77 10/16/02copyright Brian Williams, 200277  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12

78 10/16/02copyright Brian Williams, 200278  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6

79 10/16/02copyright Brian Williams, 200279  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6

80 10/16/02copyright Brian Williams, 200280  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6

81 10/16/02copyright Brian Williams, 200281  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6

82 10/16/02copyright Brian Williams, 200282  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6  Extract Conflict and Constituent Diagnoses:

83 10/16/02copyright Brian Williams, 200283  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6  Extract Conflict and Constituent Diagnoses:

84 10/16/02copyright Brian Williams, 200284  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6  Extract Conflict and Constituent Diagnoses: Not [G(M2) & G(M1) & G(A1)]

85 10/16/02copyright Brian Williams, 200285  Test: G(M1) & G(M2) & G(M3) & G(A1) & G(A2)  Extract Conflict and Constituent Diagnoses: Not [G(M2) & G(M1) & G(A1)] U(M2) or U(M1) or U(A1) 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6

86 10/16/02copyright Brian Williams, 200286  Conflicts / Constituent Diagnoses  U(M2) or U(M1) or U(A1)  Best Kernel:  U(M2)  Best Candidate:  G(M1) & U(M2) & G(M3) & G(A1) & G(A2) Second Iteration 3 2 2 3 3 10 M1 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 6

87 10/16/02copyright Brian Williams, 200287  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 A1

88 10/16/02copyright Brian Williams, 200288 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1

89 10/16/02copyright Brian Williams, 200289 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 6  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1

90 10/16/02copyright Brian Williams, 200290 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 4 6  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1

91 10/16/02copyright Brian Williams, 200291 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 4 6 10  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1

92 10/16/02copyright Brian Williams, 200292 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 4 6 10  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1  Extract Conflict:

93 10/16/02copyright Brian Williams, 200293 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 4 6 10  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1  Extract Conflict: Not [G(M1) & G(M3) & G(A1) & G(A2)]

94 10/16/02copyright Brian Williams, 200294 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 4 6 10  Test: G(M1) & U(M2) & G(M3) & G(A1) & G(A2) A1  Extract Conflict: Not G(M1) & G(M3) & G(A1) & G(A2) U(M1) or U(M3) or U(A1) or U(A2)

95 10/16/02copyright Brian Williams, 200295  Conflicts / Constituent Diagnoses  U(M2) or U(M1) or U(A1)  U(M2) or U(M3) or U(A1) or U(A2)  Best Kernel:  U(M1)  Best Candidate:  U(M1) & U(M2) & G(M3) & G(A1) & G(A2) Second Iteration 3 2 2 3 3 10 M1 M3 A2 A B C D E F G X Y Z 12 6 4 6 10 A1

96 10/16/02copyright Brian Williams, 200296  Test: U(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M2 M3 A1 A2 A B C D E F G X Y Z 12

97 10/16/02copyright Brian Williams, 200297 3 2 2 3 3 10 M2 M3 A1 A2 A B C D E F G X Y Z 12  Test: U(M1) & G(M2) & G(M3) & G(A1) & G(A2)

98 10/16/02copyright Brian Williams, 200298 3 2 2 3 3 10 M2 M3 A1 A2 A B C D E F G X Y Z 12 6  Test: U(M1) & G(M2) & G(M3) & G(A1) & G(A2)

99 10/16/02copyright Brian Williams, 200299 3 2 2 3 3 10 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6  Test: U(M1) & G(M2) & G(M3) & G(A1) & G(A2)

100 10/16/02copyright Brian Williams, 2002100  Test: U(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 4

101 10/16/02copyright Brian Williams, 2002101  Test: U(M1) & G(M2) & G(M3) & G(A1) & G(A2) 3 2 2 3 3 10 M2 M3 A1 A2 A B C D E F G X Y Z 12 6 6 4 Consistent!

102 10/16/02copyright Brian Williams, 2002102 U(A2)U(M1) U(M3)U(A1) U(A1), U(A2), U(M1), U(M3) U(A1)U(M1)U(M2) U(A1) U(M1)U(M1) & U(A2) U(M2) & U(M3) Conflict-Directed A*: Generating Best Kernels U(A1), U(M1), U(M2) Constituent Diagnoses Kernel assignments found by minimal set covering To find the best kernel, expand tree in best first order

103 10/16/02copyright Brian Williams, 2002103 Outline  Properties of Diagnosis  Diagnostic Agents  Diagnosis using Conflicts  Estimating Modes  Finding the Most Likely  Computing Likelihood  Conflict-directed A*

104 10/16/02copyright Brian Williams, 2002104 Research in Model-based Diagnosis Methods exist for: Focusing on likely diagnoses Active probing Diagnosing dynamic systems and monitoring behavior Repairing and compensating for failures Diagnosing hybrid discrete/continuous systems Performing distributed diagnosis

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