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 for the provision of fault diagnostics is simple: we wish to minimize an everlasting, unpredictable, life destroying entity.
TECHLAV Project Testing, Evaluation and Control of Heterogeneous Large-scale Autonomous u systems of Vehicles (TECHLAV)� Thrust 2: Resilient Control and Communication of Large-scale Autonomous u Vehicle Task 2-1: Develop fault detection and isolation mechanism u
TECHLAV Project Objective Impact Upon a fault occurrence, a system will To develop techniques for automatic diagnosis of autonomously become aware of the fault’s failures in the system to timely diagnose occurrence, and initiate a systematic procedure that isolates, identifies, and accommodates the (detect, identify and locate) occurred. 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. 4
Outline 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
What is fault? Fault - a malfunction in system component(s) (actuators, sensors,…etc.) that u results in unacceptable system performance, and/or system instability
Fault Diagnosis Fault Diagnosis - the detection of a fault’s occurrence conjoined with the u 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? Why do we need Fault Diagnosis? To better accommodate system behavior post fault occurrence u u Ensures system stability u Increases system reliability u Reduce number of failed missions u Save lives
State of the Art Analytical Model Based: modelled system operation is compared to observed system operation u Residuals - comparison of observed signals from the system with predicted values; residuals are usually u designed to be zero if not fault present (Frank & Ding, 1997; Roth et al., 2011) T emplates – specify the expected correct timing and sequencing of events (Holloway & Chand, 1994) u Fault free - observed system operation is compared to a nominal fault-free model (Pandalai & Holloway, u 2000) Non-Model Based: a single abstract representation encompassing normal and faulty system operation is u analyzed State based - system condition (failure status) is determined by state or set of states the system belongs to u (Lin, 1993; Zad et al., 2003) Event based - system failure determined by observance of sequences of events (Sampath et al., 1995) u Fault tree - fault diagnosis method based upon deductive fault analysis (Vesely et al., 1981; Lee et al., u 1985) Knowledge Based: heuristic u 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)
Why Discrete Event System Framework? DES is an Event-driven time abstract formalism suitable for large-scale complex u systems For diagnostic purposes, several large and complex real-world systems are u successfully modeled as Discrete-Event Systems (e.g., cyber networks, manufacturing systems, smart grids) Naturally captures faults as abrupt changes (e.g., sequence of events) u Matches human thinking u coordination (e.g., interactions of systems) group u cause and effect (e.g., a fault causing event sequence) u
Automaton Definition: a non-deterministic finite-state Discrete-Event System (DES) can be u represented by a four-tuple G ( X , , , x ) = Σ δ X o State space: u U Event set: Σ = Σ Σ u o u 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) b Am illustrative Example: 1 a 2 State-transition relation: a partial relation that determines all feasible system state u transitions caused by system events 2 X : X δ ×Σ → X = {1,2} ∑ = {a,b} Initial state: x X u ∈ 𝜀 1, 𝑏 = 2; 𝜀 2,𝑐 = 2 o x 0 = 1 . u
Language Definition: the system language is a discrete representation of the system’s behaviors (normal and faulty) in the form of sequences of events Trace (string) - a sequence of events allowable by the system’s behavior u 𝑡 = 𝑓 . 𝑓 / … 𝑓 1 𝑥ℎ𝑓𝑠𝑓 𝑓 6 ∈ ∑ language – the set of all system traces which originate at the system’s initial u state 𝑀 𝐻 = {𝑡 ∈ 𝑏 ∗ |𝜀 𝑦 > ,𝑡 } Example: ∑ = {a,b} L ={a, ab*}
Natural Projection Our purpose is to diagnose unobservable faults from the observable behavior of the • system. The system’s observable behavior can be described by the natural projection of the • P : system’s language to the observable event set of the system. ∗ ∗ Σ → Σ 0 P ( ) ε = ε Am illustrative Example: P(e) e if e b = ∈Σ o a P(e) if e u = ε ∉Σ o 1 2 3 b P se ( ) P s P e ( ) ( ) for s and e ∗ = ∈Σ ∈Σ ∑ = {a,b,u} Extension of the natural projection to the languages: ∑ o = {a,b}, ∑ u ={u} P L ( ) { ( ) | P s s L } = ∈ L ={a, au,aub*} P(L)= {a,ab*} B. (a)= {a,au} 𝑄 1 (w) P − {s L | P(s) w} A = ∈ = Inverse of natural projection L
Diagnosis within DES Framework Detected failures • L G ( ) P L G ( ( )) Natural Plant Type of detected failures • Diagnoser Projection G ( X , , , x ) = Σ δ Location of the system at • o P : ∗ ∗ detection time Σ → Σ 0 How the diagnoser works? The diagnoser provides fault diagnostics by extracting information from the u original system’s observable behaviors, in order to estimate the original system’s current state and current condition (faulty or non-faulty). The diagnoser’s state transition rule is only defined over the original system’s Ø observable events. Upon observance of the original system’s behavior , the diagnoser updates its u estimation of the original system’s state and condition.
Assumptions u Faults are unobservable Σ ⊆ Σ ⊆ Σ f u 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. * * suv L s v , , , u , n N suchthat u n ∀ ∈ ∈∑ ∈∑ ∃ ∈ ≤ o u 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 x X , e suchthat ( , ) x e is defined . ∀ ∈ ∃ ∈∑ δ This is to ensure that in the future the system will always produce a string of observable event to be used for diagnosis.
Capturing different types of faults 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 • • • U UK U m : failure type Σ = Σ Σ Σ = f f f f 1 2 m
Diagnoser Natural Plant Diagnoser Projection G ( , Q , , x ) = Σ δ G ( Q , , , q ) = Σ δ o d d d d o Event set soley consisting of observable events Σ = Σ d o x q 2 ×Δ Initial diagnoser state = 0 o Q = {( , ),( x l x l , ),...,( x l , )}, x X , l , Diagnoser state space ∈ ∈Δ d 1 1 2 2 n n i o i = U ( , ) q e {( ( , ) x e ,LP(( , ), ))} x l t δ δ d ( , ) x l q ∈ 1 − t P ( ) e ∈ L Δ { } N 2 , { F F , ,... F } f Δ = ∪ Δ = f 1 2 m N if x isnormal ⎧ ⎪ i l = ⎨ i { F F , ,..., F } if x has reached by failures of type F F , ,..., F ⎪ ⎩ i i i i i i i 1 2 k 1 2 k Label propagation mechanism: N if l { }and N t for all i 1,..., m = ∑ ∉ = ⎧ ⎪ F LP(( , ), ) x l t i = ⎨ ⎩ U l { } if F F l and t ∉ ∑ ∈ ⎪ i F i Question: How to construct 𝑅 D 𝑏𝑜𝑒 𝜀 D ?
Constructing the diagnoser b b 1 2 3 f 1 a Algorithm a b Let q {(x , N)} = 0 0 a Let Q q = 4 5 f 2 d 0 Repeat For q Q and e do a ∈ ∈∑ d o if ( , ) q e and ( , ) q e Q then δ ≠ ∅ δ ∉ d d d U Q Q ( , ) q e = δ b a {1N} {2N,3F1,4N,5F2} {1N,3F1,4F2,5F2} d d d endif end for Until there is no new state ( , )for all q q e Q and e δ ∈ ∈∑ a b d d o b {5F2} {3F1,4F2,5F2} a b a
Recommend
More recommend
