Industrial Diagnostics Using Algebra of Uncertain Temporal Relations

Industrial Diagnostics Using Algebra of Uncertain Temporal Relations

Vladimir Ryabov, Vagan Terziyan*

IASTED-2003

Innsbruck, Austria

Contact info.

Vagan TerziyanE-mail: [email protected]://http://www.cs.jyu.fi/ai/vagan/

Vladimir Ryabov

E-mail: [email protected]

InBCT Project, Agora Center, University of Jyvaskyla, P.O.Box 35, FIN-40014, Jyvaskyla, FINLAND

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.

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.

Real-Time Predictive Maintenance in FDM

Field Agent Maintenance Agent

Data Diagnosis

Predicted maintenance activity

Symptoms Recognition in Field Device Monitoring

Device ParametersHistory Local

Database

RecognizedPatterns

Ontology of Patterns

MonitoringAgent

PatternRecognitionAgent

"Symptoms" HistoryLocal Data

(Knowledge) Base

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.

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.

Device ParametersHistory LocalA Database

RecognizedC-Patterns

Ontology of Patterns

FieldAgent

C

A

B

Device ParametersHistory LocalB Database

Device ParametersHistory LocalC Database

RecognizedA-Patterns

Ontologyof "Diseases"

Diagnosis

Symptoms HistoryLocal C Data

(Knowledge) Base

Symptoms HistoryLocal B Data

(Knowledge) Base

Symptoms HistoryLocal A Data

(Knowledge) Base

RecognizedB-Patterns

Diagnoses HistoryLocal Data

(Knowledge) Base

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.

Ontology of"Symptoms"

Field AgentInfrastructure

Ontology of"Diseases"

Diagnosis

Diagnoses HistoryLocal Data

(Knowledge) Base

Field AgentInfrastructure

Diagnosis

Diagnoses HistoryLocal Data

(Knowledge) Base

DistributedDisjoint Devicesof a Similar Type

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.

Ontology of"Symptoms"

Field AgentInfrastructure

Ontology of"Diseases"

Diagnosis

Diagnoses HistoryLocal Data

(Knowledge) Base

Field AgentInfrastructure

Diagnosis

Diagnoses HistoryLocal Data

(Knowledge) Base

System ofInteractedDevices

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.

Conceptual Schema for Temporal Diagnostics

N

S1 S2 … Sn

Temporal scenarios

1,SND2,SND

nSND ,

Recognition of temporal scenarios

• We estimate the probability of belonging of the particular relational network to known temporal scenarios.

Generating 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.

N1

N2

N3

N4N5

S

Industrial Temporal Diagnostics (conceptual schema)

Industrial object

Temporal data

Relational network

DB ofscenarios

Estimation Recognition Diagnosis

Learning

Real-Time Predictive Maintenance in FDM

Field Agent Maintenance Agent

Data Diagnosis

Predicted maintenance activity

Imperfect Relation Between Temporal Point Events: Definition

Event 2

< 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 >

Example of Imperfect Relation

Event 2

< 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

<= >

R(Event 1,Event 2)

Axiom 1 (“no other alternatives”)

a1+ a2 + a3 = 1

One Unknown Value Estimation

< E1; E2; x > = < E1; E2; 1 - E1 - E2 >

1

<

=>

R(Event 1,Event 2)

Evidence, fixed value

Unknown, free value

Similar for:

< E1; x ; E2 >and

< x; E1; E2 >

x

E1

x

Evidence (fixed values):E1 + E2 < 1

E2

One Unknown Value Estimation

< E1; E2; x >

Similar for:

< E1; x ; E2 >and

< x; E1; E2 >

x = P(event 1, after, event 2)||[P(event 1, before, event 2) = E1 , P(event 1, same time, event 2) = E2]

Axiom 2: Two Asymmetric Unknown Values Estimation (Exponential)

< E; x; y > =

1

<= >

R(Event 1,Event 2)

Evidence, fixed value

Unknown, free values

2

)34(2 ;

2

)34( ;

EEEEEEE

Similar for < y; x; E >

x y

E

xy

Two Asymmetric Unknown Values Estimation

Similar for < y; x; E >

x = P(event 1, same time, event 2)||P(event 1, before, event 2) = E

< E; x; y >

y = P(event 1, after, event 2)||P(event 1, before, event 2) = E

Axiom 3: Two Symmetric Unknown Values Estimation (Normal)

< x; E; y > =

1

<=

>

R(Event 1,Event 2)

Evidence, fixed value

Unknown, free values

2

1 ; ;

2

1 EE

E

x y

E

x y

Unknown, free values

Two Symmetric Unknown Values Estimation

x = P(event 1, before, event 2)||P(event 1, same time, event 2) = E

< x; E; y >

y = P(event 1, after, event 2)||P(event 1, same time, event 2) = E

Axiom 4: All Three Unknown Values Estimation (Temporal FreedomTemporal Freedom)

< x; y; z > = < (1- )/2; ; (1- )/2 >

Unknown, free values x zUnknown, free valuesUnknown, free values

y

> 0

x = P(event 1, before, event 2)

y = P(event 1,same time, event 2)

z = P(event 1, after, event 2)

Operations with Temporal Relations

InversionCompositionSum

Operations for Reasoning with Temporal Relations

rb,a = bar,~

ra,b

a b

ra,b rb,c

ra,c = ra,b rb,c

a

b

c

r r ra b a b a b, , , 1 2

r 1 a , br 2 a , b

a b

Inversion

Addition

Composition

Inversion of Point Relations

Event 1

< a1; a2; a3 >

Event 3

< x1; x2; x3 >

x1 = a3

x3 = a1

x2 = a2

Inversion of Point Relations (Example)

Event 2

Event 1

< 0.5; 0.2; 0.3 >

< 0.3; 0.2; 0.5 >

~ < 0.5; 0.2; 0.3 > = < 0.3; 0.2; 0.5 >

Composition of Point Relations

Event 2

Event 1

< a1; a2; a3 >

Event 3

< b1; b2; b3 >

< x1; x2; x3 >

< x1; x2; x3 > = < a1; a2; a3 > * < b1; b2; b3 >

x1 = a1 · b1 + a1 · b2 + a2 · b1 + (1- )/2 · (a1 · b3 + a3 · b1)

x3 = a2 · b3 + a3 · b2 + a3 · b3 + (1- )/2 · (a1 · b3 + a3 · b1)

x2 = a2 · b2 + · (a1 · b3 + a3 · b1)

* < = >

< < < ?

= < = >

> ? > >

b1 b2 b3

a1

a2

a3

Composition of Point Relations (Example)

Event 2

Event 1

< 0.5; 0.2; 0.3 >

Event 3

< 0.4; 0.3; 0.3 >

< 0.52; 0.15; 0.33 >

< 0.5; 0.2; 0.3 > * < 0.4; 0.3; 0.3 > = < 0.52; 0.15; 0.33 >

x1 = a1 · b1 + a1 · b2 + a2 · b1 + 1/3 · (a1 · b3 + a3 · b1)

x3 = a2 · b3 + a3 · b2 + a3 · b3 + 1/3 · (a1 · b3 + a3 · b1)

x2 = a2 · b2 + 1/3 · (a1 · b3 + a3 · b1)

= 1/3

Sum of Point Relations

Event 1

Event 2

< a1; a2; a3 >

< b1; b2; b3 >

< x1; x2; x3 >

x1 = k · a1 · b1 / (a1 + b1)

x3 = k · a3 · b3 / (a3 + b3)

x2 = k · a2 · b2 / (a2 + b2) k = 1 / [a1 · b1 / (a1 + b1) + a2 · b2 / (a2 + b2) + a3 · b3 / (a3 + b3)]

Sum of Point Relations (example)

Event 1

< 0.5; 0.2; 0.3 >

Event 2

< 0.4; 0.3; 0.3 >

< 0.45; 0.24; 0.31 >

< 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 >

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

A B

AB

AB

BA

AB

AB

BA

Imperfect Relation Between Temporal Intervals: Definition

interval 2

< 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 >

From Imperfect Point Relations to Imperfect Interval Relations

e2

sl u2 2 s

B

s2

ue2le2

s1 e1

us1ls1

ue1le1

A

r12r21

r22

r11

R = = . r r

r rA B

11 12

21 22

,

e e e e e e

e e e e e er r

r rA B

, , , ,

, , , ,,

11 12

21 22

Industrial Temporal Diagnostics (composing a network of relations)

Sensor 3Sensor 2

Relational network representing the particular caseIndustrial object

Sensor 1

Estimation of temporal relations between

symptoms

Industrial Temporal Diagnostics (generating temporal scenarios)

N1

Scenario S

N3N2

Object A Object B Object C

Generating the temporal scenario

for “Failure X”DB of

scenarios

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

Scenario Generation Exampleb

a c

d

b

a c

d

b

a c

d

Generating the temporal

scenario

Recognition of Temporal Scenario

m

ii

m

iii

w

dwD

1

1SN,

)Bal()Bal(,, , DC,BA,DCBA

RRd RR

12

0,

1

12

1

i

iei BABal(RA,B) =

Industrial object

Temporal data

Relational network

DB ofscenarios

Estimation Recognition Diagnosis

Learning

bm

ofi

disi eq

sd

foi

mi

bi

wbi =1

weq

=0.5

wb =0 wf =0.75

Balance point for RA,B

Balance point for RC,D

Probability value

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

AcknowledgementsAgora 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