Industrial Diagnostics Using Algebra of Uncertain Temporal Relations

1. Industrial Diagnostics Using Algebra of Uncertain Temporal Relations Vladimir Ryabov, Vagan Terziyan* IASTED-2003 Innsbruck, Austria

2. Contact info. InBCT Project, Agora Center, University of Jyvaskyla, P.O.Box 35, FIN-40014, Jyvaskyla, FINLAND Vladimir Ryabov E-mail: vlad@it.jyu.fi Vagan Terziyan E-mail: vagan@it.jyu.fi URL://http://www.cs.jyu.fi/ai/vagan/

3. Wider Research Objective: Agent-Based Field Device Management in Semantic Web The expectations from smart field devices include advanced diagnostics and predictive maintenance capabilities. The concerns are to develop a diagnostics system that automatically follows up the performance and maintenance needs of field devices offering also easy access to this information. The emerging agent and communication technologies give new possibilities also in this field. The primer goal is to implement the benefits of the Semantic Web (ontological support and semantic annotations) and (Multi)Agent technologies (agents communication and coordination) together with modern data mining, knowledge discovery and decision support algorithms to substantially improve the performance of the Field Device Management Process.

4. Issues in Field Device Management • Data Mining and Knowledge Discovery in FDM; • Online Learning in FDM; • Metadata and Ontologies in FDM; • Multiagent Architectures in FDM; • Temporal Diagnostics in FDM; • Online Stochastic Prediction in FDM; • Real-Time Maintenance in FDM.

5. Real-Time Predictive Maintenance in FDM Predicted maintenance activity Data Diagnosis Field Agent Maintenance Agent

6. Symptoms Recognition in Field Device Monitoring While monitoring device via one information channel we can get useful information about some dimension of the device state, then derive online some useful patterns from this information, which can be considered as “symptoms” of the device “health”, and finally recognise these symptoms using Ontology of Patterns.

7. Device Diagnostics with Field Agent Infrastructure If we are monitoring a device via several information channels then appropriate Field Agent Infrastructure allows us not only to derive and recognise “symptoms” of the device “health”, but also derive and recognise a disease itself using Ontology of Diseases. History of online derived diagnoses would be also useful to store locally.

8. When Interactions between Field Agents Reasonable ? Case 1. If we are monitoring a group of distributed devices which are physically and logically disjoint, however they all are of the same type, then any history of derived patterns and diagnoses from one device can be useful to better interpret current state of any other device from the group. Thus appropriate field agents should communicate with each other to share history information and thus improving the performance of diagnostic algorithms.

9. When Interactions between Field Agents Reasonable ? Case 2. If we are monitoring a group of distributed devices which are considered as a system of physically or logically interacting components, then it will be extremely important for every field agent to use outcomes from other field agents as a context for interpretation of the produced diagnosis. Thus appropriate field agents should communicate with each other to share online and historical information and thus to improve the performance of the diagnostic algorithms.

10. Specific Objective: Temporal Diagnostics in FDM • The proposed approach to temporal diagnostics uses the algebra of uncertain temporal relations. • Uncertain temporal relations are formalized using probabilistic representation. • Relational networks are composed of uncertain relations between some events (set of symptoms) • A number of relational networks can be combined into a temporal scenario describing some particular course of events (diagnosis). • In future, a newly composed relational network can be compared with existing temporal scenarios, and the probabilities of belonging to each particular scenario are derived.

11. Temporal scenarios … N S1 S2 Sn N1 N2 N3 N5 N4 S Conceptual Schema for Temporal Diagnostics Generating temporal scenarios Recognition of temporal scenarios • We compose a temporal scenario combining a number of relational networks consisting of the same set of symptoms and possibly different temporal relations between them. • We estimate the probability of belonging of the particular relational network to known temporal scenarios.

12. Diagnosis Temporal data Relational network Industrial object DB of scenarios Estimation Recognition Learning Industrial Temporal Diagnostics (conceptual schema)

13. Real-Time Predictive Maintenance in FDM Predicted maintenance activity Data Diagnosis Field Agent Maintenance Agent

14. Imperfect Relation Between Temporal Point Events: Definition • < a1; a2; a3 >- imperfect temporal relation between temporal points (Event 1 and Event 2): • P(event 1, before, event 2) = a1; • P(event 1, same time, event 2) = a2; • P(event 1, after, event 2) = a3. Event 1 < a1; a2; a3 > Event 2

15. Example of Imperfect Relation • < 0.5; 0.2; 0.3 > - imperfect temporal relation between temporal points: • P(event 1, before, event 2) = 0.5; • P(event 1, same time, event 2) = 0.2; • P(event 1, after, event 2) = 0.3. Event 1 < 0.5; 0.2; 0.3 > 1 Event 2 < > = R(Event 1,Event 2)

16. Axiom 1 (“no other alternatives”) a1+ a2 + a3 = 1

17. One Unknown Value Estimation x Unknown, free value < E1; E2;x > = < E1; E2;1 - E1 - E2 > Evidence (fixed values): E1 + E2 < 1 Evidence, fixed value 1 Similar for: < E1; x ; E2 > and < x;E1; E2> E2 x = E1 > < R(Event 1,Event 2)

18. One Unknown Value Estimation < E1; E2;x > x = P(event 1, after, event 2)|[P(event 1, before, event 2) = E1 , P(event 1, same time, event 2) = E2] Similar for: < E1; x ; E2 > and < x;E1; E2>

19. Axiom 2: Two Asymmetric Unknown Values Estimation (Exponential) x y Unknown, free values < E; x; y > = Evidence, fixed value Similar for < y; x; E > 1 E x < y = > R(Event 1,Event 2)

20. Two Asymmetric Unknown Values Estimation < E; x; y > x = P(event 1, same time, event 2)|P(event 1, before, event 2) = E y = P(event 1, after, event 2)|P(event 1, before, event 2) = E Similar for < y; x; E >

21. Axiom 3: Two Symmetric Unknown Values Estimation (Normal) x y Unknown, free values Unknown, free values < x; E; y > = Evidence, fixed value 1 y x E > < = R(Event 1,Event 2)

22. Two Symmetric Unknown Values Estimation < x; E; y > x = P(event 1, before, event 2)|P(event 1, same time, event 2) = E y = P(event 1, after, event 2)|P(event 1, same time, event 2) = E

23. Axiom 4: All Three Unknown Values Estimation (Temporal Freedom) Unknown, free values Unknown, free values Unknown, free values z x  > 0 < x; y; z > = < (1-  )/2; ; (1-  )/2 > y x = P(event 1, before, event 2) y = P(event 1,same time, event 2) z = P(event 1, after, event 2)

24. Operations with Temporal Relations • Inversion • Composition • Sum

25. b r r a,b b,c c a Ä r r r = a,c a,b b,c Operations for Reasoning with Temporal Relations Composition Inversion Addition

26. Inversion of Point Relations Event 1 x1 = a3 < a1; a2; a3 > < x1; x2; x3 > x2 = a2 x3 = a1 Event 3

27. Inversion of Point Relations (Example) Event 1 < 0.5; 0.2; 0.3 > < 0.3; 0.2; 0.5 > Event 2 ~ < 0.5; 0.2; 0.3 > = < 0.3; 0.2; 0.5 >

28. Composition of Point Relations < x1; x2; x3 > = < a1; a2; a3 > * < b1; b2; b3 > Event 1 b1 b2 b3 < a1; a2; a3 > < x1; x2; x3 > Event 2 a1 < b1; b2; b3 > a2 Event 3 a3 x1 = a1 ·b1 + a1 ·b2 + a2 ·b1 + (1-  )/2 · (a1 ·b3 + a3 ·b1) x2 = a2 ·b2 + · (a1 ·b3 + a3 ·b1) x3 = a2 ·b3 + a3 ·b2 + a3 ·b3 + (1-  )/2 · (a1 ·b3 + a3 ·b1)

29. Composition of Point Relations (Example) Event 1 < 0.5; 0.2; 0.3 >  = 1/3 < 0.52; 0.15; 0.33 > Event 2 x1 = a1 ·b1 + a1 ·b2 + a2 ·b1 + 1/3 · (a1 ·b3 + a3 ·b1) x2 = a2 ·b2 + 1/3 · (a1 ·b3 + a3 ·b1) < 0.4; 0.3; 0.3 > x3 = a2 ·b3 + a3 ·b2 + a3 ·b3 + 1/3 · (a1 ·b3 + a3 ·b1) Event 3 < 0.5; 0.2; 0.3 > * < 0.4; 0.3; 0.3 > = < 0.52; 0.15; 0.33 >

30. Sum of Point Relations Event 1 < a1; a2; a3 > < x1; x2; x3 > < b1; b2; b3 > Event 2 x1 = k·a1 ·b1 / (a1 +b1) x2 = k·a2 ·b2 / (a2 +b2) k = 1 / [a1 ·b1 / (a1 +b1) + a2 ·b2 / (a2 +b2) + a3 ·b3 / (a3 +b3)] x3 = k·a3 ·b3 / (a3 +b3)

31. Sum of Point Relations (example) Event 1 < 0.5; 0.2; 0.3 > < 0.4; 0.3; 0.3 > < 0.45; 0.24; 0.31 > Event 2 < 0.5; 0.2; 0.3 > + < 0.4; 0.3; 0.3 > = = < 0.22 / 0.49 ; 0.12 / 0.49 ; 0.15 / 0.49 > = < 0.45; 0.24; 0.31 >

32. A A A A A B B B B B A A B B Temporal Interval Relations • The basic interval relations are the thirteen Allen’s relations: A before (b) B B after (bi) A A meets (m) B B met-by (mi) A A overlaps (o) B B overlapped-by (oi) A A starts (s) B B started-by (si) A A during (d) B B contains (di) A A finishes (f) B B finished-by (fi) A A equals (eq) B B equals A

33. Imperfect Relation Between Temporal Intervals: Definition • < a1; a2;… ; a13 >- imperfect temporal relation between temporal intervals (interval 1 and interval 2): • P(interval 1, before, interval 2) = a1; • P(interval , meets, interval 2) = a2; • P(interval 1, overlaps, interval 2) = a3; • … • P(interval 1, equals, interval 2) = a13; interval 1 < a1; a2 ;… ; a13 > interval 2

34. l u l u s s e e 1 1 1 1 s e r 1 1 21 r r 12 11 r 22 e s 2 2 u e l u l s s e 2 2 2 2 From Imperfect Point Relations to Imperfect Interval Relations A B R = = .

35. Estimation of temporal relations between symptoms Industrial Temporal Diagnostics (composing a network of relations) Sensor 1 Relational network representing the particular case Sensor 2 Industrial object Sensor 3

36. Generating the temporal scenario for “Failure X” Industrial Temporal Diagnostics (generating temporal scenarios) Object B Object A Object C N2 N3 N1 Scenario S 1. for i=1 to n do 2. for j=i+1 to n do 3. if (R1) or…or (Rk) then 4. begin 5. for g=1 to n do 6. if not (Rg) then Reasoning(, Rg) 7. // if “Reasoning” = False then (Rg)=TUR 8. ( R) = Å ( Rt), where t=1,..k 9. end 10. else go to line 2 DB of scenarios

37. Generating the temporal scenario b b b a a a c c c d d d Scenario Generation Example

38. Diagnosis Temporal data Relational network Industrial object DB of scenarios Estimation Recognition Learning Probability value si d eq wb =0 b o di wf =0.75 wbi =1 weq =0.5 mi s f fi bi m oi Balance point for RC,D Balance point for RA,B Recognition of Temporal Scenario Bal(RA,B) =

39. Conclusions • temporal diagnostics considers not only a static set of symptoms, but also the time during which they were monitored. This often allows having a broader view on the situation, and sometimes only considering temporal relations between different symptoms can give us a hint to precise diagnostics; • This might be relevant in cases when appropriate casual relationships between events (symptoms) are not yet known and the only available for study are temporal relationships

40. Acknowledgements Agora Center (University of Jyvaskyla): Agora Center includes a network of good-quality research groups from various disciplines. These groups have numerous international contacts in their own research fields. Agora Center also coordinates and administrates research and development projects that are done in cooperation with different units of university, business life, public sector and other actors. The mutual vision is to develop future's knowledge society from the human point of view. http://www.jyu.fi/agora-center/indexEng.html InBCT Project (2000-2004): Innovations in Business, Communication and Technology http://www.jyu.fi/agora-center/inbct.html