Eleventh International Workshop on Principles of Diagnosis 2000/06/08 1 Meera Sampath, Wilson Center for Research & Technology Stéphane Lafortune, Dept. of EECS A Discrete Event Systems Approach to Failure Diagnosis: Theory & Applications Stéphane Lafortune Department of EECS, University of Michigan & Meera Sampath Joseph C.Wilson Center for Research & Technology Xerox Corporation DX-00 -Eleventh International Workshop on Principles of Diagnosis 2000/06/08
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Eleventh International Workshop on Principles of Diagnosis2000/06/08
1
Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
A Discrete Event Systems Approach to Failure Diagnosis:
Theory & Applications
Stéphane LafortuneDepartment of EECS, University of Michigan
&Meera Sampath
Joseph C.Wilson Center for Research & TechnologyXerox Corporation
DX-00 -Eleventh International Workshop on Principles of Diagnosis2000/06/08
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnostics in the Industrial World
• The Three C’s: Cost, Computation, and Customer Satisfaction
- Downtime is unproductive and undesirable. - Service is costly and competitive.
• Safety• Health Regulations
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Requirements for Industrial Systems
• Diagnostic engine must be easy to develop.
• Diagnostic engine must be simple to implement.
• Diagnosis must be achieved with minimal, cost-effective set of sensors.
• Diagnosis may need to be achieved with decentralized information
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The “Academic” Viewpoint
Automated Diagnostic Methodologies that:
• Are formal and model-based• Are applicable to dynamic systems• Allow analysis of diagnosability properties• Are “easy” to implement• Are extensible and versatile
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The “DES” Diagnostic Methodology
• Modeling: languages and automata
• Dynamic tracking and state-based inferencing: Diagnosers
• Ability to incorporate sensor information from multiple sources: real and virtual sensors
• Automated design of diagnostic inference engine
• Simple on-line implementation
DES: Discrete-Event Systems
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Conceptual View for Automated Systems
SYSTEM
SYSTEM SENSORSSYSTEM CONTROLLERS
INTERFACE
REAL-TIME CONTROL DIAGNOSTICS FAILURE RECOVERY
SUPERVISORY CONTROLLER
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Implementation
SYSTEM
SYSTEM SENSORSSYSTEM CONTROLLERS
EVENT GENERATOR
REAL-TIME CONTROL DES DIAGNOSER FAILURE RECOVERY
SUPERVISORY CONTROLLER
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Motivating Example 1:Heating, Ventilation, and Air Conditioning Systems
• Components hard to access, few sensors
• Valve, pump, controller faults, etc.
• Sinnamohideen,Sampath et al., JCI
Courtesy, Johnson Controls, Inc.
Variable Air-Volume Controller
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Motivating Example 2:Document Processing Systems
• Complex processes, few sensors
• Electro-mechanical and image quality faults
• Sampath et al., Xerox Corp.
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Motivating Example 3:Automated Highway Systems (AHS)
• Platoons of vehicles
• Transmitterand receiverfaults
• Sengupta et al., PATH, UC-Berkeley
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Contents of Presentation• “Basic” theory
– Notion of diagnosability – Model construction – Diagnosers: synthesis and analysis
• Industrial applications– “Hybrid” techniques for Document Processing
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnosability: The Premise
• Event-based model: traces of events
• Language: set of traces of events
• Fault or failure events: unobservable
• Partition failures into types
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnosability: Intuitive Statement
A language (i.e., DES) is diagnosable with respect to a partition of the failure events and with respect to a set of observable events if
it is possible to detect occurrences of any type of failure with finite delay, based on
observed event sequences only
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
s
fi
t
• trace s ends with unobservable failure event fi• trace t is a sufficiently long continuation of trace s
• “any trace of the system that looks like st must contain a failure event of same type as fi”
• multiple failures may occur
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Definition of Diagnosability
A prefix-closed and live language L is said to be diagnosable with respect to the projection P and with respect to the partition Πf on Εf if the following holds:( ∀ i ∈ Π f ) ( ∃ ni ∈ Ν) ( ∀ s ∈ Ψ(Ε fi) )
( ∀ t ∈ L/s) [ || t || ≥ ni ⇒ D ]
where the diagnosability condition D is: ω ∈ PL
-1 [P(st)] ⇒ Ε fi ∈ ω .
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Explanation of Notation
• Projection P : “erases” unobservable events
P( o1 uo1 uo2 o2 uo3 o3 ) = o1 o2 o3
• Inverse Projection PL-1 :
PL-1 (y) = { s ∈ L : P(s) = y }
• Traces ending in failure of type i :
Ψ(Εfi) = { sa ∈ L : a ∈ Ε fi }
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnosability: Illustrative Example
b fa
fc
fb
uo c
d
• If F1 = {fa}, F2 = {fb}, and F3 = {fc}, then not diagnosable
• If F1 = {fa, fb} and F2 = {fc}, then diagnosable
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Why a Formal Notion of Diagnosability?
! Analysis:
! Is this DES diagnosable?
! Design:
! What sensors to use
! How to use them
! What changes to make to the system
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Steps in the DES Approach
Fault SymptomTables
ComponentModels
DiagnoserSystemModel Diagnoser
Diagnostic Requirements
Test Sequence/Controller Model
Step 1: Build Discrete Event Model of SystemStep 1: Build Discrete Event Model of System Step 2: Build Diagnoser
Analysis: Is it Diagnosable?
Design: How to Diagnose?
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Building Discrete-Event Model of System
• Use automata (or state machines) as basic building blocks to model components
• Obtain the parallel composition of components
• Incorporate the sensor information in the event set
• Obtain the complete model as an automaton
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
OPEN_VALVE, CLOSE_VALVE
CLOSE_VALVE
STOP_PUMP
SC
VC
C1 C3
C4
C2
POFF PON
VO
SO
OPEN_VALVE, CLOSE_VALVE
OPEN_VALVE
OPEN_VALVE
OPEN_VALVE
CLOSE_VALVE
CLOSE_VALVE
START_PUMP
START_PUMP
START_PUMP
STOP_PUMP
STOP_PUMP
STUCK_OPEN
STUCK_CLOSED
Simple Pump-Valve-Controller Example
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The Global Sensor Map
STATES SENSOR MAP 1-6, 10-12: (POFF, -, -) NP, NF 7: (PON, VO,C3) PP, F 8: (PON, SO,C3) PP, F 9: (PON, SC,C3) PP, NF
Flow Sensor (NF/F)
Pump Pressure Sensor (NP/P)
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
3
6
SC
SC
<OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
<STOP_PUMP,NP,NF>
9
12
SC
SC <START_PUMP,PP,F>
1 2
4 5
S0
S0
<OPEN_VALVE, NP,NF><OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
7 8
10 11
S0
S0
<START_PUMP,PP,F>
<START_PUMP,PP,F>
<STOP_PUMP,NP,NF>
<STOP_PUMP,NP,NF>
< F -> NF >
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The Event Set of the Composite Model
• Observable events:– Commands issued by controller (with sensor
readings)– Changes in sensor readings– “Generalized events”: changes in virtual sensor
readings, test outcomes, etc.• Unobservable events:
– Failures of components, controllers, sensors– Changes in system state not recorded by sensors
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
(Part of) HVAC System
FAN
PUMP
BOILER CONTROLLER
VALVE
HTG. COIL
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
PON
PON
POFF
POFF P1 P2
PUMP
FON
FONFOFF
FOFF
F1 F2
FAN
L1 L2
FOFF FOFF
SPD
LOADL0
SPD SPISPI
OV
OV
CV
CV V1 V2
VALVE
V3
V4
CV, OV
CV, OV
SO1
SC1
S02
SC2
BON
BONBOFF
BOFF
B1 B2
BOILER
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
C11 C12
C13 C14 C15 C16
C17C18C19C20
C21 C22
C23
C24
C1 C2 C3 C4 C5 C6
C7C8C9C10
FOFF
FONSPD
SPDSPI
SPIFOFFCFOFF
FON SPI
SPISPDFOFF SPD
SPI
CFON
FON
BOFF POFF CV
SPD
OV PON BON
SPISPD
OV PON BON
OV PON BON
CONTROLLER
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Steps in the DES Approach
Fault SymptomTables
ComponentModels
DiagnoserSystemModel Diagnoser
Diagnostic Requirements
Test Sequence/Controller Model
Step 1: Build Discrete Event Model of System Step 2: BuildStep 2: Build DiagnoserDiagnoser
Analysis: Is it Diagnosable?
Design: How to Diagnose?
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Tool for Analysis and On-line Diagnosis
!Let the composite model generate language L
!Pick any automaton G that generates L
!The diagnoser Gd is an automaton built from G
!Think of Gd as a “refined” observer:
! Gd carries state estimates
! Gd carries failure labels
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Illustrative Example: Gd1 N
4 N 5 F2 6 F1
7 N 8 F2
10 N 11 F2
1 N 2 F2 3 F1
9 F1
12 F1
3 F1
6 F1
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF> <CLOSE_VALVE, NP,NF>
<START_PUMP,PP,F>
<START_PUMP,PP,NF>
<START_PUMP,PP,NF>
<STOP_PUMP,NP,NF> <STOP_PUMP,NP,NF>
< F -> NF >
F1: SC
F2: SO
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
3
6
SC
SC
<OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
<STOP_PUMP,NP,NF>
9
12
SC
SC <START_PUMP,PP,F>
1 2
4 5
S0
S0
<OPEN_VALVE, NP,NF><OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
7 8
10 11
S0
S0
<START_PUMP,PP,F>
<START_PUMP,PP,F>
<STOP_PUMP,NP,NF>
<STOP_PUMP,NP,NF>
< F -> NF >
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Construction of the Diagnoser
• States are of the form: {(x1,l1), …, (xn, ln)}
• xi are states of system G
• li are labels: N or subsets of {F1 ,…, Fn}
• Transitions are due to observable events only
• Update of state estimates: similar to conversion of nondeterministic automaton to deterministic one
• Failure labels are propagated and updated by failures encountered along unobservable subtraces
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
State Transition Function of Diagnoser
7 N 8 F2
10 N 11 F2
9 F1<STOP_PUMP,NP,NF>
< F -> NF >
7 8 9
10 11
S0
S0
SC
<STOP_PUMP,NP,NF><STOP_PUMP,NP,NF>
< F -> NF >F1: SC
F2: SO
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnoser Gd
1 N
4 N 5 F2 6 F1
7 N 8 F2
10 N 11 F2
1 N 2 F2 3 F1
9 F1
12 F1
3 F1
6 F1
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF> <CLOSE_VALVE, NP,NF>
<START_PUMP,PP,F>
<START_PUMP,PP,NF>
<START_PUMP,PP,NF>
<STOP_PUMP,NP,NF> <STOP_PUMP,NP,NF>
< F -> NF >
F1: SC
F2: SO
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
What Should We Worry About?1 N
9 F1
12 F1
3 F1
6 F1
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF> <CLOSE_VALVE, NP,NF>
<START_PUMP,PP,NF>
<START_PUMP,PP,NF>4 N 5 F2 6 F1
7 N 8 F2
10 N 11 F2
1 N 2 F2 3 F1
<START_PUMP,PP,F>
<STOP_PUMP,NP,NF> <STOP_PUMP,NP,NF>
< F -> NF >
F1: SC
F2: SO
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Formal Result
• The language L is diagnosable iff the diagnoser Gd does not contain any indeterminate cycles
• Indeterminate cycles in Gd are cycles of uncertain states that have corresponding cycles in G involving their failed states
• This necessary and sufficient condition is implementable (polynomial complexity)
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Example of Indeterminate Cycle
4 N 5 F2 6 F1
7 N 8 F2
10 N 11 F2
1 N 2 F2 3 F1
<START_PUMP,PP,F>
<STOP_PUMP,NP,NF>
<OPEN_VALVE, NP,NF><CLOSE_VALVE, NP,NF>
1 2
4 5
S0
S0
<OPEN_VALVE, NP,NF>
<OPEN_VALVE, NP,NF>
<CLOSE_VALVE, NP,NF>
7 8
10 11
S0
S0
<START_PUMP,PP,F>
<START_PUMP,PP,F>
<STOP_PUMP,NP,NF>
<STOP_PUMP,NP,NF>
<CLOSE_VALVE, NP,NF>
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The Notion of Indeterminate Cycle
• Intuition: An indeterminate cycle corresponds to the situation where there are two traces in L, of arbitrary long length, that have the same observable projection, and where
" one trace contains a failure event of a certain type
" the other trace does not
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The Notion of Indeterminate Cycle
• Formally: An Fi-indeterminate cycle in Gd is a cycle of Fi-uncertain states for which there exists:
" a corresponding cycle (of observable events) in G involving only states that carry Fi in their labels in the cycle in Gd
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Not all Uncertain Cycles are Indeterminate!
fbgdbgt
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Steps in the DES Approach
Fault SymptomTables
ComponentModels
DiagnoserSystemModel Diagnoser
Diagnostic Requirements
Test Sequence/Controller Model
Step 1: Build Discrete Event Model of System Step 2: BuildStep 2: Build DiagnoserDiagnoser
Analysis: Analysis: Is it Diagnosable?Is it Diagnosable?
Design: How to Diagnose?
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
On-Line Diagnosis Using Diagnosers• Store transition function of diagnoser• Update state after each observable event• Report failure status based on labels in state• Formal Result:
• If a given system (language) is diagnosable, then the diagnoser detects occurrences of failure events of any type in a bounded number of events after the occurrence of the failure event
• “Detects” h Enters a Certain State
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Steps in the DES Approach:Case of “On-the-Fly” Computations
Fault SymptomTables
ComponentModels
Test Sequence/Controller Model Diagnoser
On-the-fly calculationof diagnoser state
Diagnostic Requirements
Diagnostic decisionDiagnostic decision
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
On-Line Diagnosis Using Diagnosers:Case of “On-the-Fly” Computations
• Store component models and sensor tables• Calculate current diagnoser state after each
observable event:• Using component models and sensor
tables, build current state of system plus some limited lookahead (until next observable event)
• Build current diagnoser state
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
How to Achieve Diagnosability?
Fault SymptomTables
ComponentModels
DiagnoserSystemModel Diagnoser
Diagnostic Requirements
Test Sequence/Controller Model
Step 1: Build Discrete Event Model of System Step 2: Build Diagnoser
Analysis: Analysis: Is it Diagnosable?Is it Diagnosable?
Design:Design:How to make systemHow to make system
diagnosable?diagnosable?
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
How to Make System Diagnosable?
• Select new set of sensors (i.e., observable events), and repeat process of building and testing diagnoser
• Problem of optimal sensor selection:– Given set A of available sensors, select minimum-
cost subset of A for which system is diagnosable" Need efficient testing strategy" See Debouk et al., CDC 99
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
How to Make System Diagnosable?
• Integrate supervisory control and failure diagnosis:• Design a control protocol that makes system
diagnosable and that achieves control objectives
• Different control protocols lead to different diagnosability properties!
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
OPEN_VALVE, CLOSE_VALVE
CLOSE_VALVE
STOP_PUMP
SC
VC
C1 C3
C4
C2
POFF PON
VO
SO
OPEN_VALVE, CLOSE_VALVE
OPEN_VALVE
OPEN_VALVE
OPEN_VALVE
CLOSE_VALVE
CLOSE_VALVE
START_PUMP
START_PUMP
START_PUMP
STOP_PUMP
STOP_PUMP
STUCK_OPEN
STUCK_CLOSED
Modified Pump-Valve-Controller Example
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Active Diagnosis Problem
• Need results from supervisory control theory• See Sampath et al., CDC 97 and TAC 98
System
Controller
P
Observable events
Controllableevents
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
How to Make System Diagnosable?
• Do more “intelligent” processing of available information, using complementary diagnostic techniques" Concept of virtual sensor
Sampath et al., Xerox Corp.
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Contents of Presentation• “Basic” theory
– Notion of diagnosability – Model construction – Diagnosers: synthesis and analysis
• Industrial applications– “Hybrid” techniques for Document Processing
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Other Hybrid Approaches to Diagnosis
• Passino & Antsaklis - Expert Systems & FDI Schemes (1988) • Frank, P.M. - Expert Systems & FDI Schemes (1990)• Pomeroy et. al. - Model based Diagnosis & FDI Schemes
(1990)• McIlraith et al. - Model based Diagnosis & Parameter
Estimation (1999)• Zhao et. al - Model based Diagnosis & Signal Processing
(2000)
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Two Examples from the Document Processing Industry
• Embedded Diagnostics of the Paper Feeder System in a Digital Copier
- Signature Analysis based Virtual Sensor
• A System for Automated Diagnosis of Image Quality Problems
- Image Processing based Virtual Sensor
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Application 1: Real Time Diagnosis of the Paper Feeder System in a Digital Copier
The Xerox Document Center DC265
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
The DC265 Paper Feeder System ComponentsPaper Trays Feed Roll CartridgeWait Station Sensor Stack Height Sensor Drives Plate - Feed & Elevator Motors, Nudger Solenoid,
Paper Size Sensors
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
• Drives Plate ground current is a “good” diagnostic indicator• Feature extraction based analysis computationally less expensive• Choice of Features for Paper Feeder Assembly:
- Peak Current - Power Spectral amplitudes
• Feature Extraction followed by Statistical Discriminant Analysis• Choice of Classifiers:
- Linear Classifiers- Quadratic classifiers
Signature Analysis & Feature Extraction based Virtual Sensor
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Discriminant Analysis -Sample Results
iiSi;iMiXiSimxiSimxxid
Cluster of CovarianceCluster of MeannObservatio Sample
ClassifierQuadratic −−−
+−−−= ;
ln)()1(')()(2:
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
DIAGNOSER DESIGN
Fault SymptomTables
ComponentModels
DiagnoserSystemModel Diagnoser
DiagnosticRequirements
Test Sequence/Controller Model
Step 2: Build Diagnoser
Analysis: Is it Diagnosable?
Design: How to Diagnose?
Step 1: Build Discrete Event Model of System
SENSOR MAPS & VIRTUAL SENSOR OUTPUTS
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
(Part of The) Diagnoser for the Paper Feeder System
N F1 F2 F3 F4 F5 F6
Feed Motor OnN F1 F2 F3 F4 F5 F6
Solenoid OnN F1 F2 F3 F4 F5 F6
Feed Motor Off, Wait Sensor Low
F1 F2 F3 F4 F6Peak Current High
F1 F3 F6Stack Height Counter High
F1 F6
Start Feed CycleF1 - Out Of Paper
F2 - Stalled Feed Motor
F3- Stalled Elev Motor
F4 - Broken Solenoid
F5 - Degraded Solenoid
F6 - Broken Feed CRU
CONTROL/SENSOR
DATA
VIRTUALSENSOR
DATA
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Experimental Setup
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnostic System Output
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Motivating Example 3:Automated Highway Systems (AHS)
• Platoons of vehicles
• Transmitterand receiverfaults
• Sengupta et al., PATH, UC-Berkeley
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
AHS: Platoon Communication
n 3 2 Lead
• Wireless LAN, TDMA, 20 msec, for velocity and acceleration data
• Separate (reliable) communication channel to exchange diagnostic information about LAN
• Model considered: leader and two followers
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
l: leader
fi: follower i
Partial system model
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Questions:
• Can the vehicles “jointly” diagnose the LAN faults, by sharing “some” information
• How to proceed? " Sengupta et al." Debouk et al.
Issue:• LAN faults cannot be diagnosed “individually” (namely, by running three independent diagnosers)
• A centralized diagnostic scheme is not practical
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Decentralized Diagnosis with Coordinator
SITE 2SITE 1
INTERFACE 1
DIAGNOSTICS
SUPERVISORY CONTROLLER 1
INTERFACE 2
DIAGNOSTICS
SUPERVISORY CONTROLLER 2
COORDINATOR FAILURE RECOVERY
Local Observations
Communications
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Key Ingredients
• Local processing for diagnostics• Communication rule• Decision rule at coordinator
We call these a PROTOCOL
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Diagnosability in this New Architecture
A language (i.e., DES) is diagnosable with respect to a protocol, a partition of the failure events, and sets of locally observable events if
under this protocol, the coordinator site can detect the occurrence of any type of failure
with finite delay
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Modified Definition of Diagnosability
A prefix-closed and live language L is said to be diagnosable with respect to the given protocol, the projections P1 and P2, and the partition Πf on Ef if the following holds:( ∀ i ∈ Π f ) ( ∃ ni ∈ Ν) ( ∀ s ∈ Ψ(Ε fi) )
( ∀ t ∈ L/s) [ || t || ≥ ni ⇒ C is Fi-certain ]
C: register holding diagnostic information at the coordinator site
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Key Assumptions
• System is diagnosable in a centralized set up• One site alone cannot diagnose all faults• Communication is reliable:
– Global ordering is preserved at the coordinator– No raw data is communicated– Communication may be interrupted
• Coordinator should be “simple”memory, processing, no system model
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Objective
• Design a set of protocols and analyze their “complexity – performance” tradeoff
• Compare their performance to the centralized diagnoser
The centralized scheme is the “only” one available for comparison purposes…
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Work Done So Far
Protocol 1
Protocol 2
Protocol 3
Perfo
rman
ce d
ecre
ases
Perfo
rman
ce d
ecre
ases
Com
plex
ity in
crea
ses
Com
plex
ity in
crea
ses
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Brief Description of Protocol 3
• Diagnosers are used at local sites• Communicate nothing but failures detected
(Fi-certain)• Coordinator is “trivial”• Test to determine if protocol works
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Brief Description of Protocol 2
• Diagnosers are used at local sites• Communicate current diagnoser state to
coordinator– Communicate after each observable event– May interrupt communication
• Do simple “intersections” at coordinator
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Protocol 2: A Few More Details
• Communicate also:• status bit (common event or not)• the unobservable reach
• Coordinator only stores most recent messagefrom each site
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Protocol 2: Decision Rule:Upon Reception of Message R1 from Site 1
0R1 3 R211Decision Rule 5
1Wait10Decision Rule 3
0R1 3 R400Decision Rule 1
Status Bit
UpdateCoordinatorStatus Bit
Received
Current Status
BitRule
Eleventh International Workshop on Principles of Diagnosis2000/06/08
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
Protocol 2: Decision Rule:Upon Reception of Message R1 from Site 1
R2: last message from site 2 w/out
unobservable reach
R4: last message from site 2 with unobservable
reach
obs. by 2 unobs.
obs. by 1
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS
AHS: Platoon Communication
n 3 2 Lead
Protocol 3 does not work
Protocol 2 works!
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Meera Sampath, Wilson Center for Research & TechnologyStéphane Lafortune, Dept. of EECS