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Consistency-based diagnosis

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  1. Consistency-based diagnosis 1 Introduction 2 Diagnosis as constrain propagation plus register of dependencies 3 General Diagnostic Engine:GDE 4 A theory of diagnosis from first principles 5 CBD without on-line dependency-recording: the possible conflict approach 6 Current research areas and open problems

  2. Model-based Reasoning process oriented component oriented causal models process models structural models functional models behavioural models teleological models (similar to comp. oriented.) ... ... ... crisp probabilistic correct behaviour fault models .… extensional intensional .… time- varying quantitative qualitative static dynamic hierarchical flat discrete state change landmarks orders of magnitude ... derivatives intervals Automated Diagnosis Introduction Machine Learning Case-Based Reasoning Knowledge-Based Sytems Devices Software… Processes Medicine Application fields

  3. Model-based diagnosis approaches • Control Theory / Engineering (FDI community) • Robuts Fault Detection and Isolation • (Global) Analytical Models, mainly • Generation and Analysis of Residuals (discrepancy) • Most commonly used techniques • State-observers • Parity-equations (Analytical Redundancy Relations) • Parameter Identification (or Estimation) • Artificial Inteligence (DX community) • Fault Isolation and Identification • (assumption: robust fault detection is available) • Qualitative Models (causal, constraints, semi-qualitative, etc.) • Conflict detection and candidate (diagnosis) generation • Diagnosis based on structure and behaviour • Consistency-based diagnosis • Abductive diagnosis • Consistency-based Diagnosis with fault models • BRIDGE (integration of DX and FDI) GDE

  4. Consistency Based DiagnosisIntroduction Historical background • Second generation Expert Systems (Davis, 1982-84) • First works in USA, late 70s – early 80s (@ MIT, Stanford Univ.) • Solid theoretical theory (Reiter, 1987) • Early results: • mid/late-80s: static systems • late 80s, early 90s: dynamic systems • late 90s (mature)  large systems GDE

  5. Model-based diagnosis fundamental Behaviour Model Real System Diagnosis Predicted Behaviour Observed Behaviour Discrepancy (symptom) GDE

  6. Consistency Based DiagnosisIntroduction • Main Model Based Diagnosis framework from DX community • Component oriented (ontology) • May be extended to processes / constraints • Knowledge: • structural + behavioural (local) models • models of components • Only models of correct behaviour GDE

  7. Basic Assumptions (de Kleer 03) • Physical system • Set of interconnected components • Known desired function • Design achieves function • System is correct instance of design • All malfunctions caused by faulty component(s) • Behavioural information • Only indirect evidence GDE

  8. Behavioural information: Behavioural models • Components are in some physical condition • e.g. a wire • Different physical conditions result in different behaviours Condition 1 Condition 2 Condition 3 Behaviour 1 Behaviour 3 Behaviour 2 GDE

  9. Behavioural information: Ruling out behaviours • We cannot verify the presence of behaviours, but we can falsify them • After observing • We cannot infer behaviour 2, but we can reject behaviour 1 GDE

  10. Consistency Based Diagnosis Intuition • Search for the model that is “compliant” with the observations Behaviour Model Real System Diagnosis Predicted Behaviour Observed Behaviour Discrepancy GDE

  11. General Diagnostic Engine • GDE, de Kleer and Williams, 87 • First model based computational system for multiple faults • Main computational paradigm • Still in use! • Still a reference to compare any model- based proposal on DX community GDE

  12. A X F M1 A1 B C Y M2 D G A2 Z M3 E A classic expository example:the polybox (de Kleer 87, 03) GDE

  13. Model based approach to diagnosis Textbooks, design, first principles Model Real System Predicted Behaviour Observed Behaviour Discrepancy Diagnosis GDE

  14. A [3] B [2] C [2] D [3] E [3] Observed Behaviour X F F M1 A1 [10] Y M2 G A2 [12] Z M3 GDE

  15. Model based approach to diagnosis Textbooks, design, first principles Model Real System Predicted Behaviour Observed Behaviour Discrepancy Diagnosis GDE

  16. A [3] B [2] C X 6 [2] F M1 D A1 [3] E Y M2 [3] G A2 Z M3 Local propagation (I) GDE

  17. A [3] B X 6 F [2] M1 C A1 [2] D 6 [3] Y M2 E G [3] A2 Z M3 Local propagation (II) GDE

  18. A [3] B [2] X 6 F F C M1 [2] A1 12 D [3] 6 Y M2 E [3] G A2 Z M3 Local propagation (III) GDE

  19. A [3] B [2] X 6 F F C M1 [2] A1 12 D [3] 6 Y M2 E [3] G A2 Z M3 6 Local propagation (IV) GDE

  20. A [3] B [2] X 6 F F C M1 [2] A1 12 D [3] 6 Y M2 E [3] G A2 12 Z M3 6 Local propagation (V) GDE

  21. A [3] B [2] X 6 F F C M1 [2] A1 12 D [3] 6 Y M2 E [3] G A2 12 Z M3 6 Predicted Behaviour GDE

  22. Model based approach to diagnosis Textbooks, design, first principles Model Real System Predicted Behaviour Observed Behaviour Discrepancy Diagnosis GDE

  23. A [3] X 6 12 F F M1 B A1 [10] [2] C 6 [2] Y D M2 12 [3] G A2 [12] Z E M3 [3] 6 Candidates • Detect Symptoms: F=12 and F=10 • Generate Candidates: {M1}, {A1}, {M2, S2}, {M2, M3} GDE

  24. A [3] B [2] C [2] D [3] E [3] Diagnosis for the polybox X 4 12 F F M1 A1 [10] 6 Y M2 12 G A2 [12] Z M3 6 GDE

  25. A [3] B [2] C [2] D [3] E [3] Diagnosis for the polybox X 6 12 F F M1 A1 [10] 6 Y M2 10 G A2 [12] Z M3 6 GDE

  26. A [3] B [2] C [2] D [3] E [3] Diagnosis for the polybox X 6 12 F F M1 A1 [10] 4 Y M2 12 G A2 [12] Z M3 6 GDE

  27. A [3] B [2] C [2] D [3] E [3] M3 Diagnosis for the polybox X 6 12 F F M1 A1 10 4 Y M2 12 G A2 [12] Z 8 GDE

  28. How GDE works? • Detecting every SYMPTOM Prediction: propagating on every direction (even non causal!) • Identifying CONFLICTS • Generating CANDIDATES GDE

  29. A [3] B [2] X 6 F F C M1 [2] A1 12 D [3] 6 Y M2 E [3] G A2 12 Z M3 6 Prediction - Requirements • Modeling Structure • Modeling component behaviour • Predict overall behaviour GDE

  30. Modelling Structure - Requirements • Determine the structural elements and interconections • Which entities can be the origin of malfunction? • Which parts can be replaced? • Which variables can be observed? • Reflect aspects and levels of (diagnostic) reasoning about the device behaviour GDE

  31. Component-Oriented Modelling: Components and Connections • Systems: components linked by connections via terminals • Components: Normally physical objects • Resistors, diodes, voltage sources, tanks, valves • Terminals: unique comunication link • Connections:ideal connections (but may be modelled as components) • No resistance wires, loadless pipes... • Possible faults: defect components, broken connection GDE

  32. Modelling Behaviour -Requirements • Describe behaviour of the structural elements: Locality • Goal: detecting discrepancies • Consider aspecs like • Generality: which kind of devices are to be diagnosed? • Robustness: which type of failure are to be detected • Reflect the diagnostic reasonig process (e.g. simplifications) • Which kind of information is (easily) available (e. g. qualitative information) GDE

  33. Local behaviour models • Constrains / relations among • Input/Output variables • Internal parameters • Various directions • No implicit reference to or implicit assumptions about context (existence or state of other components) • Locality • Necessary for diagnosis: different context because something is broken; otherwise implicit hypothesys must be revised • Reusability: model library, compositionality GDE

  34. Local behaviour model - Example • Or-gate • Variables: in1, in2,out • Domain dom(in1)=dom(in2)=dom(out)={0,1} • Relation {{0,0,0}, {1,0,1}, {0,1,1}, {1,1,1}}  dom(in1)  dom(in2)  dom(out) • Inferences • in1 = 1  out = 1 • in2 = 1  out = 1 • in1=0  in2=0  out = 1 • out=0  in1=0  in2=0 • out=1  in1=0  in2=1 • out=1  in2=0  in1=1 causal direction non causal direction GDE

  35. A f B p1 p2 Behaviour model of a valve • Relation: f = k  A • Implicit assumption: pump is on and ok • Relation: IF on(B) and ok(B) THEN f= k  A • Implicit assumption: a pump exists and is connected as in the diagram • Better: f = k’  (p1 – p2)  A • Principle: no function in structure GDE

  36. A B F F C M1 A1 D M2 E G A2 M3 Abstract model • Domain for each variable, var dom(var) = {OK, BAD, ?} • Model for each correct component, C IF for all input-variables, vari of C, vari = OK THEN for each output-variable, varo of C, varo = OK • To avoid masking of faults by correct components IF there exists an input-variable, vari of C, vari = BAD THEN for each output-variable, varo of C, varo = BAD GDE

  37. Prediction - Principles • Infer the behaviour of the entire device from • Observations • Component models • Structural description • Preserve dependencies on component models • Propagate the effects of local models along the interaction paths (connections) • Propagate not only in the causal direction GDE

  38. A [3] B [2] C X 6 [2] F M1 D A1 [3] E Y M2 [3] G A2 Z M3 PropagationCausal direction (I) • [A]=3  [C]=2  X=6 (M1) GDE

  39. A [3] B X 6 F [2] M1 C A1 [2] D 6 [3] Y M2 E G [3] A2 Z M3 PropagationCausal direction (II) • [B]=2  [D]=3  Y=6 (M2) GDE

  40. A [3] B [2] X 6 F F C M1 [2] A1 12 D [3] 6 Y M2 E [3] G A2 Z M3 PropagationCausal direction (III) • X=6  Y=6  F=12 (A1) GDE

  41. A [3] B [2] X 6 F F C M1 [2] A1 [10] D [3] 4 Y M2 E [3] G A2 Z M3 Propagation“Backward” direction (II) • [F]=10  X=6  Y=4 (A1) GDE

  42. Candidate Generation • Detecting SYMPTOMS (DISCREPANCIES) • Identifying (minimal) CONFLICTS • Generating (minimal) CANDIDATES GDE

  43. Symptoms Real System Model Predicted Behaviour Observed Behaviour Discrepancy Diagnosis • Symptoms are contradictions that indicate an inconsistency between observations and correct behaviour • But other potential sources of contradictions • Imprecise measurements • Bugs in the model • Bugs in propagation GDE

  44. Symptoms Detection • Symptoms occurs as contradictory values for one variable • Predicted plus observed • Predicted following two different paths • Discrete Variables • Static x=val1  x=val2  val1  val2 • Dynamic x=(val1, t1)  x=(val2, t2)  val1  val2  (t1  t2)   • Continuous Variables • Quantitatives (static): • Intervals: x=i1  x=i2  (i1  i2)   • Values: x=val1  x=val2  val1  val2 • Relations: xval1  xval2 • Qualitatives: distance,distance >Threshold GDE

  45. A [3] B [2] C [2] D [3] E [3] Some symptoms for the polybox (I) 12 X 6 F F M1 [10] A1 6 Y M2 G [12] A2 Z M3 GDE

  46. A [3] B [2] C [2] D [3] E [3] Some symptoms for the polybox (II) X 6 F F M1 [10] A1 4 Y M2 6 G [12] A2 Z M3 GDE

  47. A [3] B [2] C [2] D [3] E [3] Some symptoms for the polybox (III) X X X 6 6 F F F F M1 [10] A1 4 Y Y M2 M2 10 G G [12] A2 Z Z M3 6 6 GDE

  48. A [3] B [2] C [2] D [3] E [3] Some symptoms for the polybox (IV) 6 X 12 F F M1 4 A1 [10] 6 Y M2 4 10 G A2 [12] 6 Z M3 8 GDE

  49. Identify conflicts • Conflict (informal):set of correctness assumtions underlying discrepancies • Polybox (minimal) conflicts • F=[10]  F=12 {M1, M2, A1}, {M1, M3, A1, A2} • X=6  X=4 {M1, M2, A1}, {M1, M3, A1, A2} • Y=6  Y=4 {M1, M2, A1}, {M1, M3, A1, A2} • Z=6  Z=8 {M1, M3, A1, A2} • G=[12]  G=10 {M1, M3, A1, A2} • By definition,any superset of a conflic set is a conflict • {M1, M2, A1}  {M1, M2, A1, A2}  {M1,M2, M3, A1, A2} • Minimal conflict: conflict no proper subset of which is a conflict • It is essential to represent the conflicts through the set of minimal conflicts (to avoid combinatorial explosion) GDE

  50. Conflicts latice [M1, M2, M3, A1, A2] [M1, M2, M3, A2] [M1, M3, A1, A2] [M2, M3, A1, A2] [M1, M2, A1, A2] [M1, M2, M3, A1] [ M3, A1, A2] [M1, M2, M3] [M1, M2, A1] [M1, M2, A2] [M1, M3, A1] [M1, M3, A2] [M2, M3 A1] [M1, A1, A2] [M2, M3, A2] [M2, A1, A2] [M1, M2] [M1, M3] [M1, A1] [M2, M3] [M1, A2] [M2, A1] [M2, A2] [ M3, A1] [ M3, A2] [ A1, A2] [M1] [M2] [M3] [A1] [A2] GDE [ ]