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Industrial Diagnostics Using Algebra of Uncertain Temporal Relations. Vladimir Ryabov, Vagan Terziyan * IASTED-2003 Innsbruck, Austria. Contact info. InBCT Project, Agora Center, University of Jyvaskyla, P.O.Box 35, FIN-40014, Jyvaskyla, FINLAND. Vladimir Ryabov E-mail: [email protected]. - PowerPoint PPT Presentation
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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