Fault Diagnosis of Discrete-Event Systems Alejandro White, Doctoral - - PowerPoint PPT Presentation
Fault Diagnosis of Discrete-Event Systems Alejandro White, Doctoral Candidate Advisor: Dr. Karimoddini Motivation Faults are always u Faults are unwanted u Faults are arbitrary u Faults are costly u Faults are DEADLY u Our motivation
Alejandro White, Doctoral Candidate Advisor: Dr. Karimoddini
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Faults are always
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Faults are unwanted
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Faults are arbitrary
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Faults are costly
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Faults are DEADLY Our motivation for the provision of fault diagnostics is simple: we wish to minimize an everlasting, unpredictable, life destroying entity.
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Testing, Evaluation and Control of Heterogeneous Large-scale Autonomous systems of Vehicles (TECHLAV)
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Thrust 2: Resilient Control and Communication of Large-scale Autonomous Vehicle
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Task 2-1: Develop fault detection and isolation mechanism
Impact
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Objective
To develop techniques for automatic diagnosis of failures in the system to timely diagnose (detect, identify and locate) occurred. Upon a fault
a system will autonomously become aware of the fault’s
that isolates, identifies, and accommodates the fault in order to ensure proper utilization of the system’s remaining resources, allowing a resilient post fault system operation that is both safe and stable.
u Definition of Fault u Definition of Fault Diagnosis u Survey of Methods of Fault Diagnosis u Formulation of Fault Diagnosis within Discrete-Event System u Constructing the Diagnoser u Diagnosability Condition u Future Work
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Fault - a malfunction in system component(s) (actuators, sensors,…etc.) that results in unacceptable system performance, and/or system instability
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To better accommodate system behavior post fault occurrence
u Ensures system stability u Increases system reliability u Reduce number of failed missions u Save lives
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Fault Diagnosis - the detection of a fault’s occurrence conjoined with the identification of a fault’s nature, through examination of a system’s symptoms
u Fault detection: If a fault has occurred? u Fault identification: What is the type and nature of failure? u Fault isolation: Where in the system has occurred?
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Analytical Model Based: modelled system operation is compared to observed system operation
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Residuals - comparison of observed signals from the system with predicted values; residuals are usually designed to be zero if not fault present (Frank & Ding, 1997; Roth et al., 2011)
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T emplates – specify the expected correct timing and sequencing of events (Holloway & Chand, 1994)
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Fault free - observed system operation is compared to a nominal fault-free model (Pandalai & Holloway, 2000)
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Non-Model Based: a single abstract representation encompassing normal and faulty system operation is analyzed
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State based - system condition (failure status) is determined by state or set of states the system belongs to (Lin, 1993; Zad et al., 2003)
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Event based - system failure determined by observance of sequences of events (Sampath et al., 1995)
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Fault tree - fault diagnosis method based upon deductive fault analysis (Vesely et al., 1981; Lee et al., 1985)
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Knowledge Based: heuristic
u Expert system - past knowledge obtained by experts used to model unknown system aspects (Scherer & White, 1989;
Handelman & Stengel 1989)
u Artificial Neural Network - an abstract model of the brain’s neural pathways designed to actively “learn” the normal and
faulty behavior of a system (Elias Kosmatopoulos & Polycarpou, 1995; Diao & Passino, 2001)
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DES is an Event-driven time abstract formalism suitable for large-scale complex systems
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For diagnostic purposes, several large and complex real-world systems are successfully modeled as Discrete-Event Systems (e.g., cyber networks, manufacturing systems, smart grids)
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Naturally captures faults as abrupt changes (e.g., sequence of events)
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Matches human thinking
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coordination (e.g., interactions of systems) group
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cause and effect (e.g., a fault causing event sequence)
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Definition: a non-deterministic finite-state Discrete-Event System (DES) can be represented by a four-tuple
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State space:
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Event set:
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State-transition relation: a partial relation that determines all feasible system state transitions caused by system events
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Initial state:
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.
( , , , )
X x δ = Σ
Σ = Σ Σ U
X ∈
X
: 2X X δ ×Σ →
q Events (∑) : Notable occurrence of asynchronous discrete changes in a system q Observable events (∑"): Events observed by a sensor (e.g., opening of valve) q Unobservable events (∑#)– Events that are unable to be detected by sensors; possibly due to sensor absence/damage (e.g., failure event)
a b
X = {1,2} ∑ = {a,b} 𝜀 1, 𝑏 = 2; 𝜀 2,𝑐 = 2 x0 = 1 Am illustrative Example:
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Trace (string) - a sequence of events allowable by the system’s behavior 𝑡 = 𝑓.𝑓/ … 𝑓1 𝑥ℎ𝑓𝑠𝑓 𝑓6 ∈∑
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language – the set of all system traces which originate at the system’s initial state 𝑀 𝐻 = {𝑡 ∈ 𝑏∗|𝜀 𝑦>,𝑡 } Example: Definition: the system language is a discrete representation of the system’s behaviors (normal and faulty) in the form of sequences of events
∑= {a,b} L ={a, ab*}
system.
system’s language to the observable event set of the system.
∗ ∗
b
( ) P(e) e if e P(e) if e ( ) ( ) ( ) for and
P se P s P e s e ε ε ε
∗
= = ∈Σ = ∉Σ = ∈Σ ∈Σ
Extension of the natural projection to the languages: Am illustrative Example: 1 3 a 2 u
∑o= {a,b}, ∑u={u} L ={a, au,aub*} P(L)= {a,ab*} 𝑄
A B.(a)= {a,au}
∑= {a,b,u}
1(w)
L
Inverse of natural projection
b
Plant Natural Projection Diagnoser
( , , , )
X x δ = Σ ( ) L G ( ( )) P L G
detection time
: P
∗ ∗
Σ → Σ
How the diagnoser works?
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The diagnoser provides fault diagnostics by extracting information from the
current state and current condition (faulty or non-faulty).
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The diagnoser’s state transition rule is only defined over the original system’s
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Upon observance of the original system’s behavior , the diagnoser updates its estimation of the original system’s state and condition.
u Faults are unobservable
Otherwise their detection would be trivial.
u Understudied Faults do not bring the system to the halt mode.
This gives us enough time to diagnose the fault.
u No arbitrarily long strings of unobservable events.
This ensures that following the occurrence of an unobservable, sooner or later the system will produce an observable event. This is needed for detection of an unobservable event
u Live Language: state transition relation is defined for at least one event at all system
states This is to ensure that in the future the system will always produce a string of observable event to be used for diagnosis.
f u
Σ ⊆ Σ ⊆ Σ
, ( , ) . x X e suchthat x e is defined δ ∀ ∈ ∃ ∈∑
* *
, , , ,
suv L s v u n N suchthat u n ∀ ∈ ∈∑ ∈∑ ∃ ∈ ≤
1 2
: failure type
m
f f f f
m
= Σ Σ Σ = U UK U
Different faults may result in the same failure results. Example: An open circuit and a stuck closed valve may result in equivalent sensor reading. We can partition the failure event set into m disjoint subset, each representing a failure type
Plant Natural Projection Diagnoser
( , , , )
Q x δ = Σ
1
1 1 2 2 ( , ) ( )
( , , , ) Event set soley consisting of observable events 2 Initial diagnoser state = {( , ),( , ),...,( , )}, , , Diagnoser state space ( , ) {( ( , )
L
d d d d
n n i
d x l q t P e
G Q q q Q x l x l x l x X l q e x e δ δ δ
−
×Δ ∈ ∈
= Σ Σ = Σ = ∈ ∈Δ = U ,LP(( , ), ))} x l t
1 2 1 2
1 2
{ } 2 , { , ,... } isnormal { , ,..., } has reached by failures of type , ,...,
f k k
f m i i i i i i i i i
N F F F N if x l F F F if x F F F
Δ
Δ = ∪ Δ = ⎧ ⎪ = ⎨ ⎪ ⎩
Question: How to construct 𝑅D 𝑏𝑜𝑒 𝜀D?
if { }and for all 1,..., LP(( , ), ) { } if and
i i
F i F
N l N t i m x l t l F F l t = ∑ ∉ = ⎧ ⎪ = ⎨ ∉ ∑ ∈ ⎪ ⎩ U
Label propagation mechanism:
Algorithm
Let q {(x , N)} Let Q Repeat For q Q if ( , ) and ( , ) Q then Q Q ( , ) endif end for Until there is no new state ( , )for all q Q
d d
d d d d d d d
and e do q e q e q e q e and e δ δ δ δ = = ∈ ∈∑ ≠ ∅ ∉ = ∈ ∈∑ U
1 3 2 4 5 f2 a f1 a b b a b {1N} {5F2} {1N,3F1,4F2,5F2} {2N,3F1,4N,5F2} {3F1,4F2,5F2} a a a b b a b a b
Diagnosability - a system fault is considered diagnosable if upon its occurrence, all possible consequential system behaviors allow for the definitive diagnosis (detection, isolation, identification) of its occurrence. Question: An important question is that whether the diagnoser can detect and locate the failure?
A system with the live language L is said to be is said to be diagnmosable w.r.t. the natural projection if the following holds: ( )( )[ s ( )]( / ))[ ] where the dignosab
i
i f i f i
Definition f n t L s t n D ψ − ∀ ∈∑ ∃ ∈ ∀ ∈ ∑ ∀ ∈ ≥ ⇒
ility condition D is : ( ( ))
i
L f
D P P s s ω
−
∀ ∈ ⇒ ∑ ∈
1 3 2 4 5 f2 a f1 a b b a b 1 3 2 4 5 f2 a f1 a b b a
A Diagnosable plant An undiagnosable plant Question: How to check it based on the structure of the diagnoser?
Checking the diagnosability based the structure of the diagnoser Theorem: A language L without multiple failures of the same type is diagnosable, if and
Definition: Fi – Indeterminate Cycle:
1 3 2 4 5 f2 a f1 a b b a b {1N} {5F2} {1N,3F1,4F2,5F2} {2N,3F1,4N,5F2} {3F1,4F2,5F2} a a a b b a b a b
2
1 2 1 2 2
Faulty loop: 1 4 5 4 5 ( ) ( ) Normal loop: 1 2 1 2
f a b a a b a
s af ba P s P s aba s aba ⎫ ⎯⎯ → ⎯⎯ → ⎯⎯ → ⎯⎯ → = ⎪ ⇒ = = ⎬ ⎯⎯ → ⎯⎯ → ⎯⎯ → = ⎪ ⎭
Fi indeterminate Cycle
Challenges: 1- In many practical situations, only after a fault occurs, the diagnosis tool (e.g. a portable industrial computer) has to be brought and connected to the faulty plant to diagnose the occurred fault. In many cases, it is not possible, or it is time-consuming and costly, to restart the plant to be synchronized with the diagnoser. 2- Even if the plant and the diagnoser are initialized simultaneously, it is possible that for any particular reason, the diagnoser misses an observation, and thereafter, it cannot track the plant, in turn requiring both the plant and the diagnoser to be restarted again. In the existing methods (including the method presented here), it is required to initialize and run the diagnoser synchronously with the plant. This allows the diagnoser to diagnose failures based on a rich set of information including both pre- and post-failure behaviours in the system.
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Asynchronous Fault Diagnosis: To develop a systematic and analytical approach to construct a diagnoser that can be asynchronously turned on at anytime, even after the occurrence of a fault.
Problem formulation:
Challenges: 1- Unlike conventional diagnosis techniques, the past history of the system before the activation of the diagnoser is not available, leaving the diagnoser with the challenge of diagnosing faults using only the future behaviors of the plant, observed after the activation
2-In contrast to existing methods, where the initial state of the system and correspondingly the initial state of the diagnoser are generally assumed to be non-faulty, upon its initialization, the asynchronous diagnoser is no longer able to assume that the current state of the system is normal.