Distributed Diagnosis of Discrete-Event Systems Using Petri Nets Sahika Genc and St´ ephane Lafortune Department of Electrical Engineering and Computer Science, University of Michigan, {sgenc,stephane}@eecs.umich.edu; www.eecs.umich.edu/umdes June 25, ATPN 2003, Eindhoven, Netherlands
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Distributed Diagnosis of Discrete-Event Systems Using ...€¦ · Introduction • Why fault diagnosis?? Limited sensor information: Faults are unobservable events. • Problem:?
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Distributed Diagnosis of Discrete-EventSystems Using Petri Nets
Sahika Genc and Stephane Lafortune
Department of Electrical Engineering and Computer Science,University of Michigan,
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 1
Introduction
• Why fault diagnosis?
? Limited sensor information: Faults are unobservable events.
• Problem:
? Detect and isolate faults during the operation of the system.
• Model-based approach: Normal and failed behaviour.
? Discrete-Event System(DES) models are adequate for large class offaults.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 2
Introduction: Previous Work
• DES Modelling Formalism: Automata (languages)
? “Failure Diagnosis Using Discrete Event Models” by M. Sampath, R.Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis IEEETransactions on Control Systems Technology Vol. 4, No. 2, March1996, pp. 105-124
? “Diagnosability of Discrete Event Systems” by M. Sampath, R.Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis IEEETransactions on Automatic Control Vol. 40, No. 9, September 1995,pp. 1555-1575
• Previous theory successfully applied to ...
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 3
Introduction: Areas of Application
• HEATING, VENTILATION AND AIR CONDITIONING SYSTEMS
Sinnamohideen, Sampath, et al., Johnson’s Control Inc.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 4
Introduction: Areas of Application
• DOCUMENT PROCESSING SYSTEMSSampath, et al., Xerox Corp.
Document Centre 265 DC/LP/ST
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 5
Introduction: Areas of Application
• AUTOMATED HIGHWAY SYSTEMS(AHS)
Sengupta, et al., PATH, UC-Berkeley
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 6
Introduction: Diagnoser Approach
• Previous work: Solution methodology based on diagnoser automata.
Theory of diagnosability Which faults can be diagnosed?
Online diagnosis How to diagnose?
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 7
Introduction: Diagnoser Approach
• Previous work: Solution methodology based on diagnoser automata.
Theory of diagnosability Which faults can be diagnosed?
Online diagnosis How to diagnose?
• Objective: Develop an analogous methodology based on Petri netmodels and deal with distributed systems.
• Why Petri nets?
? A good mathematical tool to model concurrent, asynchronous anddistributed systems.
• Online diagnosis.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 7
Outline
• Introduction
• Centralized Diagnosis
• Distributed Diagnosis with Communication
• Main Result
• Summary
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 8
Centralized Diagnosis: Notation
• A Petri net graph: N = 〈P, T,A, w〉.
• A labeled Petri net: (N ,Σ, l, x0, f).
• The labeling function: l : T → Σ.
• The labeling function is extended to strings of transitions: l : T ∗ → Σ∗
l(t) = a, l(t′) = a′ ⇒ l(tt′) = l(t)l(t′) = aa′.
• The set of events: Σ = Σo ∪ Σuo.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 9
Centralized Diagnosis
N Nd
System
LabeledPetri Net
LabeledPetri Net
Diagnoser
• The system to be diagnosed is modelled by a labeled Petri net.
• The diagnoser is a labeled Petri net.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 10
Centralized Diagnosis
N Nd
System DiagnoserObservable
EventFaultType
LabeledPetri Net
LabeledPetri Net
• The system to be diagnosed is modelled by a labeled Petri net.
• The diagnoser is a labeled Petri net.
• The Petri net diagnoser observes the system online and outputs whichfault types have occurred.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 10
Centralized Diagnosis
The diagnoser for the labeled Petri net (N ,Σ, l, x0, f) is
Nd = (N ,Σ, l, xd0,∆f , fd)
where
• xd0 is the initial diagnoser state,
• ∆f = {F1, . . . , Fk}: Finite set of fault types,
• fd: Diagnoser state transition function.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 11
Centralized Diagnosis: Diagnoser States
Diagnoser state =States F1 · · ·Fk[
|||
]
• A diagnoser state has multiple states(markings).
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 12
Centralized Diagnosis: Diagnoser States
Diagnoser state =States F1 · · ·Fk[
|||
]
• A diagnoser state has multiple states(markings).
• Each state in the diagnoser state has a fault label. The fault labelshows which type of faults have occurred.
? If a fault of type i has occurred, then the ith entry in the fault labelis 1, otherwise 0.
• The fault label of the initial state, x0, is lx0f = [0 . . . 0].
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 12
Centralized Diagnosis: Diagnoser States
Given (N ,Σ, l, x0, f) and Nd = (N ,Σ, l, xd0,∆f , fd),
• Unobservable reach of a state x, UR(x), is found by firing thetransitions labeled with unobservable events.
• The initial diagnoser state is the unobservable reach of the initial stateof the system:
xd0 = UR(x0lx0f ).
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 13
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 16
Centralized Diagnosis
Certain or Uncertain?
Diagnoser state =F1 F2 F3[
| 1 0 1| 1 0 1| 1 0 0
]
• Certain?
? Fault of type 1 (F1) has occurred.? Fault of type 2 (F2) has not occurred.
• Uncertain?
? Fault of type 3 (F3) may or may not have occurred.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 17
Outline
• Introduction
• Centralized Diagnosis
• Distributed Diagnosis with Communication
• Main Result
• Summary
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 18
Distributed Diagnosis with Communication
• Objective : Achieve same performance of centralized diagnosis withdistributed diagnosis.
• Why distributed diagnosis? System to be diagnosed is
? too large to perform centralized diagnosis
� large automated manufacturing systems, etc.? truly distributed
� networked systems, etc.
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 19
Distributed Diagnosis with Communication: Centralizedvs. Distributed
Centralized Diagnosis
N Nd
System DiagnoserObservable
EventFaultType
Distributed Diagnosis with Communication
Nd,1Nd,1
Nd,2Nd,2
FiFi
FjFj
System
Diagnoser
Diagnoser
Observable Event ofFirst Diagnoser
Observable Event ofSecond Diagnoser
FaultType
FaultType
Communication
N1N1
NN
N2N2
CommonPlaces
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 20
Distributed Diagnosis with Communication
• Based on design considerations, the labeled Petri net (N ,Σ, l, x0, f) ispartitioned into two labeled Petri nets (N1,Σ1, l1, x0,1, f1) and(N2,Σ2, l2, x0,2, f2) as follows
? Σ = Σ1∪Σ2,
? ∀t ∈ T if l(t) ∈ Σ1, then t ∈ T1; ∀t ∈ T if l(t) ∈ Σ2, then t ∈ T2,
? P1 = ∪t∈T1 (I(t) ∪O(t)), P2 = ∪t∈T2 (I(t) ∪O(t)).Result: Common places; disjoint sets of events, transitions and arcs.
N1N1
NN
N2N2
CommonPlaces
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 21
Distributed Diagnosis with Communication
• The partitions must satisfy the following assumptions
1. ∀t ∈ T if (I(t) ∪O(t)) ∩ (P1 ∩ P2) 6= ∅ , then l(t) ∈ Σo.2. ∀t1 ∈ T1 and ∀t2 ∈ T2, if l(t1) ∈ ΣFi and l(t2) ∈ ΣFj, then i 6= j.
N1N1NN
N2N2
CommonPlaces
so
s’os’o
s’o
so
so
N1N1NN
N2N2
Fi
Fj
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 22
Centralized vs. Distributed
Centralized Diagnosis
N Nd
System DiagnoserObservable
EventFaultType
Distributed Diagnosis with Communication
Nd,1Nd,1
Nd,2Nd,2
FiFi
FjFj
System
Diagnoser
Diagnoser
Observable Event ofFirst Diagnoser
Observable Event ofSecond Diagnoser
FaultType
FaultType
Communication
N1N1
NN
N2N2
CommonPlaces
Sahika Genc and Stephane Lafortune, University of Michigan / June 25, 2003 23
Distributed Diagnosis with Communication: Messages
• Given Pc the set of common places, define the weighting vector