Outline 1. Introduction to fault diagnosis of DES 2. Seminal work - PowerPoint PPT Presentation

On Fault Diagnosis Methods of Discrete Event Systems Janan Zaytoon University of Reims Champagne Ardenne, France Janan.zaytoon@univ-reims.fr 1

Outline 1. Introduction to fault diagnosis of DES 2. Seminal work of Sampath-Sengupta-Lafortune-Sinnamohideen- Teneketzis 3. Classification of diagnosis methods with respect to: Fault compilation, modeling tools, fault representation, decision structure and architecture 4. Related and induced problems Fault prediction, design problems, sensor selection & reliability, robust diagnosis, active diagnosis, fault-tolerant control 5. Contribution of our research team 6. Conclusion 2

Outline 1. Introduction to fault diagnosis of DES 2. Seminal work of Sampath et al. 3. Classification of diagnosis methods with respect to: Fault compilation, modeling tools, fault representation, decision structure and architecture 4. Related and induced problems Fault prediction, design problems, sensor selection and reliability, robust diagnosis, active diagnosis, fault-tolerant control 5. Contribution of our research team 6. Conclusion 3

Modeling for fault diagnosis  Fault causes a non desired deviation of a system or one of its components from its normal or intended behavior  Fault : Tolerant deviation of system performance  Failure : Critical deviation (breakdown)  Fault diagnosis has two tasks  Fault detection: confirms whether a system works in normal conditions or a fault has occurred  Fault isolation: localizes responsible element(s) and fault nature (criticality, size, importance, ...) 4

Modeling for fault diagnosis  Faults are considered as an additional input for the system modeling  Faults are usualy partitioned into set of fault partitions, each associated with a fault model and fault label F i Faults f Real output y Real input u System Normal Fault Fault Predicted Faulty behaviors behavior Diagnostic result isolation detection output y models + model ∈ ( N , F i ), i {1,..., } d - G N G F 1 G Fd 5

Fault classification  With respect to their dynamics (time dependency)  permanent faults (motor failure)  Incipient faults (drift-like)  Intermittent faults (bad contact, vibration) Intermittent Drift-like permanent faults faults faults Faulty behavior Normal Time functioning Time Time  With respect to the related physical elements  Sensors faults: Discrepancies between measured and real values of system variables (Sensors offset, Sensors stuck-off/stuck-on)  Actuators faults: Discrepancies between input commands of actuators and their real output (Actuators stuck-off/stuck-on)  Plant faults: Changes in system dynamics (Tanks leakages, corked pipes, …) 6

Historical Background  Partial observation and observability: Caines et al. 1991; Cieslak et al. 1988; Lin and Wonham 1988; Ramadge 1986  not directly concerned with the partition of failures and the identification of failure types  (initial) state estimation and supervisory control  State-based approach to diagnosability ( Lin 1994 ):  off-line and on-line diagnosis  computing a sequence of test commands for diagnosing failures  Sensor optimisation for diagnosis: Bavishi and Chong 1994  Petri net based fault detection:  monitoring the tokens in P-invariants ( Prock 1991 )  backfiring transitions to determine if a given state is invalid ( Sreenivas and Jafari 1993 ) 7

Outline 1. Introduction to fault diagnosis of DES 2. Seminal work of Sampath, Sengupta, Lafortune, Sinnamohideen, Teneketzis (1995) 3. Classification of diagnosis methods with respect to: Fault compilation, modeling tools, fault representation, decision structure and architecture 4. Related and induced problems Fault prediction, design problems, sensor selection and reliability, robust diagnosis, active diagnosis, fault-tolerant control 5. Contribution of our research team 6. Conclusion 8

Automata modeling for fault diagnosis Some of the events are unobservable (no sensors)!! 9

Dealing with unobservable events  What are the faults that explain the observations?  build a state observer (deterministic automaton) staring from the original automaton: Transitions are due to observable events A state is an estimation of the state of the original model Observer size is exponential in the size of the model f 3 1 a {2,4,5} {1,3} b 2 consecutive b b a a a is a symptom a of f b {3} {4,5} uo a 2 5 4 a a a 10

Diagosability of a fault  A fault is (n-)diagnosable if it can be detected with certainty within a finite number of (n) observable events after its occurrence  A fault f is diagnosable if: for every trace s ending with f , there exists a sufficiently long continuation t such that: … any other trace indistinguishable from st (producing the same record of observable events) contains f (are also faulty) t f s Sampath, Sengupta, Lafortune, Sinnamohideen, Teneketzis (1995) 11

Diagnoser  Refine the observer: add labels F ( f occurred) and N ( f didn’t occur)  Diagnoser: FSM based on off-line compilation of observed trajectories:  can be used off-line or on-the-fly  F-indeterminate cycle in diagnoser: presence of 2 cycled traces with the same observable projection, such that F occurs in the 1 st trace but not in the 2 nd  Condition for diagnosability: no indeterminate cycles in the diagnoser for all fault types {1N} f a 3 1 a a {2N,4F} {4F,5F} Indeterminate b b a a cycle: f is not b F-certain a b diagnosable! state {1N,3F} {3F} uo 5 2 4 ambiguous state a 12 a

Diagnosability and Diagnosers  General hypothesis: system is live, no cycle of unobservable events  A diagnoser is an ideal and efficient machine: having a diagnoser implies  a complete characterization of the diagnosis problem : every state of the diagnoser is a possible diagnosis & every possible diagnosis is a state of the diagnoser  an efficient diagnosis algorithm : updating the diagnosis after a new observation only requires the firing of a transition  But having a diagnoser is an utopia: constructing a diagnoser implies  availability of an exhaustif and correct fault model  complex calculations and state explosion: Worst case diagnoser size = 2 X x 2 F  example: a system with 4 components, 10 states per component, 5 faults: worst case size of diagnoser =10 10000 ! (number of atoms in the universe: 10 80 )  Twins machine ( Jiang et al. 2001; Yoo-Lafortune 2002 ):  polynomial test for diagnosability without constructing a diagnoser: a fault f is diagnosable if there is no couple of infinite traces having the same observation such that f occurs in the first trace but not in the second 13

Roadmap New New New Efficient Properties Models Algorithms solutions 1995 On going Diagnoser approach Slide from A.Paoli, CASY 2007 14

Publications ≈10 -12% of WODES papers ≈ 20 -23% of DCDS papers 1 to 3 papers/year in JDEDS since 1998 15

Outline 1. Introduction to fault diagnosis of DES 2. Seminal work of Sampath et al. 3. Classification of diagnosis methods with respect to: Fault compilation, modeling tools, fault representation, decision structure and architecture 4. Related and induced problems Fault prediction, design problems, sensor selection and reliability, robust diagnosis, active diagnosis, fault-tolerant control 5. Contribution of our research team 6. Conclusion 16

Classification of Diagnosis methods wrt fault compilation  Off-line compilation of a diagnoser: system in test-bed  All observations are known in advance  Efficient in terms of diagnosis response time but computationally intractable!  On-line computation of the set of faults after each observed event: system is operational  Higher on-line computational effort (higher time to do diagnosis), but gain in memory space because no need to store the complete diagnoser 17

Classification of diagnosis methods wrt the modeling tool  Diagnoser is built using:  Automata and their extensions: Sampath et al., 1995; Debouk et al., 2000; Wang et al., 2007  Petri nets: Lefebvre-Delherm, 2007; Ramírez-Treviño, 2007; Genc-Lafortune, 2007; Cabasino et al, 2010; Dotoli et al., 2009; Basile et al., 2008  Statecharts – hierarchical state machines: Paoli-Lafortune, 2008; Idghamishi-Zad, 2004 18

Timed and Probabilistic Automata  Timed Systems based on special class of timed automata: Chan-Provan, 1997; Tripakis, 2002; Bouyer et al., 2005; Cassez, 2009; Jiang-Kumar, 2006 :  time diagnosability requiring the diagnosability condition to hold after a bounded time interval, instead of a bounded number of events  Issues: time semantics (tick event or dense times), diagnosability, diagnoser construction, complexity, relation with untimed systems, …  Probabilistic systems and probabilistic diagnosers: Fabre- Jezequel, 10; Thorsley et al., 2008; Wang et al., 2004, Athanasopoulou-Hadjicostis, 2005; Lunze and Schröder, 2001 :  build deterministic FSM that gives the probability distribution on states and diagnosis values, given any observed sequence  diagnosability notions for stochastic and probabilistic automata 19