General Diagnostic Engine: GDE

Transcription

1 eneral iagnostic ngine: onsistency based diagnosis 1 Introduction 2 omputational approach: arlos lonso onzález elarmino Pulido Junquera SI. pto. Informática, Universidad de Valladolid

2 onsistency ased iagnosis Main Model ased iagnosis framework from X community omponent oriented May be extended to processes Knowledge: structure + behavioural (local) models of components Only models of correct behaviour 2

3 asic ssumptions (de Kleer 03) Physical system Set of interconnected components Known desired function esign achieves function System is correct instance of design ll malfunctions caused by faulty component(s) ehavioural information Only indirect evidence 3

4 ehavioural information: ehavioural models omponents are in some physical condition e.g. a wire ondition 1 ondition 2 ondition 3 ifferent physical conditions result in different behaviours ehaviour 1 ehaviour 2 ehaviour 3 v i v i v i

5 ehavioural information: Ruling out behaviours We cannot verify the presence of behaviours, but we can falsify them fter observing v i We cannot infer behaviour 2, but we can reject behaviour 1 5

6 onsistency ased iagnosis Intuition Search for the model that is compliant with the observations Real System ehaviour Model iagnosis Observed ehaviour iscrepancy Predicted ehaviour

7 eneral iagnostic ngine, de Kleer and Williams, 87 irst model based computational system for multiple faults Main computational paradigm Still in use! Still a reference to compare any model base proposal on X community 7

8 classic expository example: the polybox (de Kleer 87, 03) X 1 Z Y 2 8

9 Model based approach to diagnosis Textbooks, design, first principles Real System Model Observed ehaviour iscrepancy Predicted ehaviour iagnosis 9

10 Observed ehaviour X Z Y 1 2 [10] [12] 10

11 Model based approach to diagnosis Textbooks, design, first principles Real System Model Observed ehaviour iscrepancy Predicted ehaviour iagnosis 11

12 Local propagation (I) X Y Z

13 Local propagation (II) X Y Z

14 Local propagation (III) X Y Z

15 Local propagation (IV) X Y Z

16 Local propagation (V) X Y Z

17 Predicted ehaviour X Y Z

18 Model based approach to diagnosis Textbooks, design, first principles Real System Model Observed ehaviour iscrepancy Predicted ehaviour iagnosis 18

19 andidates X Y Z [10] 12 [12] etect Symptoms: =12 and =10 enerate andidates: {}, {1}, {, S2}, {, } 19

20 iagnosis for the polybox X 4 Y Z [10] 12 [12] 20

21 iagnosis for the polybox X Y Z [10] 10 [12] 21

22 iagnosis for the polybox 4 X Y Z [10] 12 [12] 22

23 iagnosis for the polybox 4 X Y Z [12] 23

24 How works? 1. etecting every SYMPTOM Prediction: propagating on every direction (even non causal!) 2. Identifying ONLITS 3. enerating NITS 24

25 Prediction - Requirements X Y Z Modelling structure Modelling component behaviour Predict overall behaviour 25

26 Modelling Structure - Requirements etermine the structural elements and interconnections 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 2

27 omponent-oriented Modelling: omponents and onnections Systems: components linked by connections via terminals omponents: Normally physical objects Resistors, diodes, voltage sources, tanks, valves Terminals: unique communication link onnections:ideal connections (but may be modelled as components) No resistance wires, load less pipes... Possible faults: defect components, broken connection 27

28 Modelling ehaviour - Requirements escribe behaviour of the structural elements: Locality oal: detecting discrepancies onsider aspects like enerality: which kind of devices are to be diagnosed? Robustness: which type of failure are to be detected Reflect the diagnostic reasoning process (e.g. simplifications) Which kind of information is (easily) available (e. g. qualitative information) 28

29 Local behaviour models onstrains / 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 hypothesis must be revised Reusability: model library, compositionally 29

30 Local behaviour model - xample Or-gate Variables: in1, in2,out omain 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 causal direction out=0 in1=0 in2=0 out=1 in1=0 in2=1 out=1 in2=0 in1=1 non causal direction

31 ehaviour model of a valve f p 1 p 2 Relation: f = k Implicit assumption: pump is on and ok Relation: I on() and ok() THN f= k Implicit assumption: a pump exists and is connected as in the diagram etter: f k (p1 p2) Principle: no function in structure

32 bstract model 1 2 omain for each variable, var dom(var) = {OK,,?} Model for each correct component, I for all input-variables, var i of, var i = OK THN for each output-variable, var o of, var o = OK To avoid masking of faults by correct components I there exists an input-variable, var i of, var i = THN for each output-variable, var o of, var o = 32

33 Prediction - Principles Infer the behaviour of the entire device from Observations omponent 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 33

34 Propagation ausal direction (I) X Y Z 1 2 []=3 []=2 X= () 34

35 Propagation ausal direction (II) X Y Z 1 2 []=2 []=3 Y= () 35

36 Propagation ausal direction (III) X Y Z X= Y= =12 (1) 3

37 Propagation ackward direction (II) 4 X Y Z 1 2 [10] []=10 X= Y=4 (1) 37

38 andidate eneration etecting SYMPTOMS (ISRPNIS) Identifying (minimal) ONLITS enerating (minimal) NITS 38

39 Symptoms Real System Model Observed ehaviour iscrepancy Predicted ehaviour iagnosis Symptoms are contradictions that indicate an inconsistency between observations and correct behaviour ut other potential sources of contradictions Imprecise measurements ugs in the model ugs in propagation 39

40 Symptoms etection Symptoms occurs as contradictory values for one variable Predicted plus observed Predicted following two different paths iscrete Variables Static x=val1 x=val2 val1 val2 ynamic x=(val1, t1) x=(val2, t2) val1 val2 (t1 t2) ontinuous Variables Qualitatives (static): Intervals: x=i1 x=i2 (i1 i2) Values: x=val1 x=val2 val1 val2 Relations: x val1 x <val2 Quantitatives : distance, distance >Threshold

41 Some symptoms for the polybox (I) X Y Z [10] [12] 41

42 Some symptoms for the polybox (II) X 4 Y Z 1 2 [10] [12] 42

43 Some symptoms for the polybox (III) 4 X Y Z 1 2 [10] 10 [12] 43

44 Some symptoms for the polybox (IV) X 4 Y 4 Z [10] 10 [12] 44

45 Identify conflicts onflict (informal):set of correctness assumptions underlying discrepancies Polybox (minimal) conflicts =[10] =12 {,, 1}, {,, 1, 2} X= X=4 {,, 1}, {,, 1, 2} Y= Y=4 {,, 1}, {,, 1, 2} Z= Z=8 {,, 1, 2} =[12] =10 {,, 1, 2} y definition,any superset of a conflict set is a conflict {,, 1} {,, 1, 2} {,,, 1, 2} 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) 45

46 onflicts lattice [,,, 1, 2] [,,, 1] [,,, 2] [,, 1, 2] [,, 1, 2] [,, 1, 2] [,, ][,, 1][,, 2] [,, 1][,, 2] [, 1] [, 1, 2] [,, 2] [, 1, 2] [, 1, 2] [, ] [, ] [, 1] [, ] [, 2] [, 1] [, 2] [, 1] [, 2] [ 1, 2] [] [] [] [1] [2] [ ] 4

47 onflicts generation with TMS The problem solver performs inferences The TMS records the dependencies between inferences Introduce observations as facts Support each local propagation with a correctness assumption for the component Label of a node:(minimal) environments that entails the prediction Records components that support prediction voids recomputation Symptoms: produce NOOOS NOOOS are the MINIML ONLITS 47

48 onflicts generation, detailed model, first minimal conflict (I) {{}} X Y Z

49 onflicts generation, detailed model, first minimal conflict (II) {{}} X Y Z 1 {{}} 2 49

50 onflicts generation, detailed model, first minimal conflict (III) {{}} X Y Z 1 {{}} 2 {{,, 1}} 12 50

51 onflicts generation, detailed model, first minimal conflict (IV) {{}} X Y Z 1 {{}} 2 {{,, 1}} 12 [10] { } =[10] =12 {,, 1} 51

52 onflicts generation, detailed model, second minimal conflict (I) X Y Z {{,, 1, 2}} [12] 52

53 onflicts generation, detailed model, second minimal conflict (II) X Y Z {{,, 1, 2}} 12 1 [10] { } 2 [12] =[10] =12 {,, 1, 2} 53

54 onflicts generation, abstract model, first minimal conflict (I) {{}} X ok Y Z

55 onflicts generation, abstract model, first minimal conflict (II) {{}} X ok ok Y Z 1 {{}} 2 55

56 onflicts generation, abstract model, first minimal conflict (III) {{}} X ok ok Y Z 1 {{}} 2 {{,, 1}} ok 5

57 onflicts generation, abstract model, first minimal conflict (IV) {{}} X ok ok Y Z 1 {{}} 2 {{,, 1}} ok [bad] { } =[bad] =ok {,, 1} 57

58 onflicts generation, abstract model, second minimal conflict (I) {{}} X ok bad Y Z 1 {{, 1}} 2 [bad] bad {{, 1, 2}} 58

59 onflicts generation, abstract model, second minimal conflict (II) {{}} X ok bad Y Z 1 {{, 1}} 2 [bad] { } bad {{, 1, 2}} =[bad] =ok {, 1, 2} 59

60 andidates andidate: hypothesis of how the device differs from model Represented as a set of assumptions ssumptions included: false ssumptions not included: true andidate example: {, 2} Meaning:, 2 are faulty,, 1 are correct iagnosis: identify every candidate consistent with observations 0

61 andidate generation ach candidate has to account for all conflicts ach candidate has to retract at least one correctness assumption out of each conflict onstruct candidates as Hitting Set of (minimal) conflicts a candidate, i conflict, a i i a, a i i ach superset of a candidate is also a candidate: Minimal candidates:minimal hitting set of minimal conflicts 1

62 andidate generation example X 4 4 Z 8 Y [10] 10 [12] Minimal conflicts {, 1, } {, 1,, 2 } Minimal candidates {}, {1}, {, }, {, 2} 2

63 onflict irected Search 1. Let M be the set of putative minimal diagnoses, initially containing only []. 2. If no more minimal conflicts, the M is the set of minimal diagnoses 3. or every new minimal conflict 1. or every diagnosis in M 1. If identifies one component in as faulted, do nothing. 2. lse remove from M and add to M all which have some component of faulted. 2. Remove duplicates from M 4. o to 2. 3

64 andidate lattice: parsimonious representation (I) [,,, 1, 2] [,,, 1] [,,, 2] [,, 1, 2] [,, 1, 2] [,, 1, 2] [,, ][,, 1][,, 2] [,, 1][,, 2] [, 1] [, 1, 2] [,, 2] [, 1, 2] [, 1, 2] [, ] [, ] [, 1] [, ] [, 2] [, 1] [, 2] [, 1] [, 2] [ 1, 2] [] [] [] [1] [2] 1:[,, 1] [ ]

65 andidate lattice: parsimonious representation (II) [,,, 1, 2] [,,, 1] [,,, 2] [,, 1, 2] [,, 1, 2] [,, 1, 2] [,, ][,, 1][,, 2] [,, 1][,, 2] [, 1] [, 1, 2] [,, 2] [, 1, 2] [, 1, 2] [, ] [, ] [, 1] [, ] [, 2] [, 1] [, 2] [, 1] [, 2] [ 1, 2] [] [] [] [1] [2] 1:[,, 1] [ ] 2 :[,, 1, 2]

66 andidate lattice: parsimonious representation (III) [,,, 1, 2] [,,, 1] [,,, 2] [,, 1, 2] [,, 1, 2] [,, 1, 2] [,, ][,, 1][,, 2] [,, 1][,, 2] [, 1] [, 1, 2] [,, 2] [, 1, 2] [, 1, 2] [, ] [, ] [, 1] [, ] [, 2] [, 1] [, 2] [, 1] [, 2] [ 1, 2] [] [] [] [1] [2] 1:[,, 1] [ ] 2 :[,, 1, 2]

67 andidate lattice: parsimonious representation (IV) [,,, 1, 2] [,,, 1] [,,, 2] [,, 1, 2] [,, 1, 2] [,, 1, 2] [,, ][,, 1][,, 2] [,, 1][,, 2] [, 1] [, 1, 2] [,, 2] [, 1, 2] [, 1, 2] [, ] [, ] [, 1] [, ] [, 2] [, 1] [, 2] [, 1] [, 2] [ 1, 2] [] [] [] [1] [2] 1 & 2 1:[,, 1] [ ] 2 :[,, 1, 2]

68 andidate generation abstract model Minimal conflicts Minimal candidates ok ok X bad Z Y {, 1, } {, 1, 2 } 1 2 ok [bad] bad {}, {1}, {, 2} 8

69 andidate generation: problems Undetected symptoms Insufficient observations Imprecise Not available Insufficient models Quantitative accuracy Qualitative ambiguity Limitations of conflict generation Inherent in the prediction algorithm Inherent in the model 9

70 onflict generation: limitations due to local propagation [1] [1] [1] I X1 X2 X3 [1] onflicts: {I, X1, X2, X3} andidates: {I }, {X1}, {X2}, {X3} {I} should not be a candidate {X1, X2, X3} ought to be a conflict 70

71 onflict generation: limitations due to the model (I) W-1 W-3 W-5 S W-2 W-4 W- Observations: 1, 2 O,3 ON Minimal conflicts {S, W1, 1, W2}, {S, W1, W3, 2, W4, W2}, {3, W5, 2, W}, {3,W5, W3, 1, W4, W} 22 minimal candidates! {1, 2}, {S, 3}, {W1, W5} (?) 71

72 onflict generation: limitations due to the model (II) W-1 W-3 W-5 S W-2 W-4 W- Observations: 1, 2 O,3 ON andidate {S, 3} Logically possible Physically impossible ue to the absence of information about faulty behaviour (only models of correct behaviour) 72