Industrial Diagnostics Using Algebra of Uncertain Temporal Relations

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Industrial Diagnostics Using Algebra of Uncertain
Temporal Relations

• Vladimir Ryabov, Vagan Terziyan
• IASTED-2003
• Innsbruck, Austria

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

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

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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.

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Industrial Temporal Diagnostics (conceptual
schema)
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Real-Time Predictive Maintenance in FDM
Predicted maintenance activity
Data
Diagnosis
Field Agent
Maintenance Agent
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Imperfect Relation Between Temporal Point Events
Definition

• lt a1 a2 a3 gt - 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
lt a1 a2 a3 gt
Event 2
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Example of Imperfect Relation

• lt 0.5 0.2 0.3 gt - 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
lt 0.5 0.2 0.3 gt
1
Event 2
lt
gt

R(Event 1,Event 2)
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Axiom 1 (no other alternatives)
a1 a2 a3 1
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One Unknown Value Estimation
x
Unknown, free value
lt E1 E2 x gt lt E1 E2 1 - E1 - E2 gt
Evidence (fixed values) E1 E2 lt 1
Evidence, fixed value
1
Similar for lt E1 x E2 gt and lt x E1 E2 gt
E2
x

E1
gt
lt
R(Event 1,Event 2)
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One Unknown Value Estimation
lt E1 E2 x gt
x P(event 1, after, event 2)P(event 1,
before, event 2) E1 , P(event 1, same time,
event 2) E2
Similar for lt E1 x E2 gt and lt x E1 E2 gt
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Axiom 2 Two Asymmetric Unknown Values Estimation
(Exponential)
x
y
Unknown, free values
lt E x y gt
Evidence, fixed value
Similar for lt y x E gt
1
E
x
lt
y

gt
R(Event 1,Event 2)
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Two Asymmetric Unknown Values Estimation
lt E x y gt
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 lt y x E gt
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Axiom 3 Two Symmetric Unknown Values Estimation
(Normal)
x
y
Unknown, free values
Unknown, free values
lt x E y gt
Evidence, fixed value
1
y
x
E
gt
lt

R(Event 1,Event 2)
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Two Symmetric Unknown Values Estimation
lt x E y gt
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
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Axiom 4 All Three Unknown Values Estimation
(Temporal Freedom)
Unknown, free values
Unknown, free values
Unknown, free values
x
z
? gt 0
lt x y z gt lt (1- ? )/2 ? (1- ? )/2 gt
y
x P(event 1, before, event 2)
y P(event 1,same time, event 2)
z P(event 1, after, event 2)
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Operations with Temporal Relations

• Inversion
• Composition
• Sum

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Operations for Reasoning with Temporal Relations
Composition
Inversion
Addition
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Inversion of Point Relations
Event 1
x1 a3
lt a1 a2 a3 gt
lt x1 x2 x3 gt
x2 a2
x3 a1
Event 3
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Inversion of Point Relations (Example)
Event 1
lt 0.5 0.2 0.3 gt
lt 0.3 0.2 0.5 gt
Event 2
lt 0.5 0.2 0.3 gt lt 0.3 0.2 0.5 gt
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Composition of Point Relations
lt x1 x2 x3 gt lt a1 a2 a3 gt lt b1 b2 b3 gt
Event 1
b1
b2
b3
lt a1 a2 a3 gt
lt x1 x2 x3 gt
Event 2
a1
lt b1 b2 b3 gt
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)
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Composition of Point Relations (Example)
Event 1
lt 0.5 0.2 0.3 gt
? 1/3
lt 0.52 0.15 0.33 gt
Event 2
x1 a1 b1 a1 b2 a2 b1 1/3 (a1 b3
a3 b1)
x2 a2 b2 1/3 (a1 b3 a3 b1)
lt 0.4 0.3 0.3 gt
x3 a2 b3 a3 b2 a3 b3 1/3 (a1 b3
a3 b1)
Event 3
lt 0.5 0.2 0.3 gt lt 0.4 0.3 0.3 gt lt 0.52
0.15 0.33 gt
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Sum of Point Relations
Event 1
lt a1 a2 a3 gt
lt x1 x2 x3 gt
lt b1 b2 b3 gt
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)
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Sum of Point Relations (example)
Event 1
lt 0.5 0.2 0.3 gt
lt 0.4 0.3 0.3 gt
lt 0.45 0.24 0.31 gt
Event 2
lt 0.5 0.2 0.3 gt lt 0.4 0.3 0.3 gt lt 0.22
/ 0.49 0.12 / 0.49 0.15 / 0.49 gt lt 0.45
0.24 0.31 gt
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Temporal Interval Relations

• The basic interval relations are the thirteen
  Allens 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
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Imperfect Relation Between Temporal Intervals
Definition

• lt a1 a2 a13 gt - 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
lt a1 a2 a13 gt
interval 2
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From Imperfect Point Relations to Imperfect
Interval Relations
A
B
R .
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Industrial Temporal Diagnostics (composing a
network of relations)
Sensor 1
Relational network representing the particular
case
Sensor 2
Sensor 3
Industrial object
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Industrial Temporal Diagnostics (generating
temporal scenarios)
Object A
Object B
Object C
N2
N1
N3
Scenario S
1. for i1 to n do 2. for ji1 to n do 3.
if (??R1) oror (??Rk) then 4. begin 5.
for g1 to n do 6. if not (??Rg)
then Reasoning(, Rg) 7. // if
Reasoning False then (?Rg)TUR 8.
(? R) Å (? Rt), where t1,..k 9. end
10. else go to line 2
DB of scenarios
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Scenario Generation Example
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Recognition of Temporal Scenario
Bal(RA,B)
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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

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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/a
gora-center/indexEng.html
InBCT Project (2000-2004) Innovations in
Business, Communication and Technology
http//www.jyu.fi/agora-center/inbct.html