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Supervision Systems Design Prof. Belkacem OULD BOUAMAMA Research Director Ecole Polytechnique de Lille Head of the research group “Bond Graphs” «LAGIS UMR CNRS8219» Laboratory Avenue Paul Langevin, F59655 Villeneuve d'Ascq cedex Tel : +33(0) , GSM: +33(0) Prof. Belkacem OULD BOUAMAMA Research Director Ecole Polytechnique de Lille Head of the research group “Bond Graphs” «LAGIS UMR CNRS8219» Laboratory Avenue Paul Langevin, F59655 Villeneuve d'Ascq cedex Tel : +33(0) , GSM: +33(0)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» PLAN Supervision : Introduction and definitions Supervision software's Synthesis of monitoring systems Structural analysis and bipartite graph Information redundancy for FDI Observers for FDI LFT Bond graphs for robust FDI Design of supervision system. Application to a industrial systems Conclusions and bibliography

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Prof. B. Ould Bouamama Polytech’Lille « Supervision Systems Design » Part 1: Introduction

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Bibliography Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (Eds)(2007) Diagnosis and Fault-Tolerant Control, Berlin:Springer-Verlag. "Automatique et statistiques pour le diagnostic". T1 et 2 sous la direction de Bernard Dubuisson, Collection IC2 Edition Hermes, 204 pages, Paris A.K. Samantaray and B. Ould Bouamama "Model-based Process Supervision. A Bond Graph Approach". Springer Verlag, Series: Advances in Industrial Control, 490 p. ISBN: , Berlin D. Macquin et J. Ragot : "Diagnostic des systèmes linéaires", Collection Pédagogique d'Automatique, 143 p., ISBN X, Hermès Science Publications, Paris, B. Ould Bouamama, M. Staroswiecki and A.K. Samantaray. « Software for Supervision System Design In Process Engineering Industry ». 6th IFAC, SAFEPROCESS,, pp Beijing, China. B. Ould Bouamama, K. Medjaher, A.K. Samantary et M. Staroswiecki. "Supervision of an industrial steam generator. Part I: Bond graph modelling". Control Engineering Practice, CEP, Vol 1 14/1 pp 71-83, Vol 2. 14/1 pp 85-96, B. Ould-Bouamama. Contrôle en ligne d'une installation de générateur de vapeur par Bond Graph. Techniques de l'Ingénieurs AG pages 2014 B. Ould-Bouamama. La conception intégrée pour la surveillance robuste des systemes. Approche Bond Graph. Techniques de l'Ingénieurs AG pages 2013 R.Merzouki, A.K.Samantaray, M.Pathak and B. Ould-Bouamama. Intelligent Mechatronic Systems: Modelling, Control and Diagnosis. Springer Verlag, ISBN: , 943 pages, PhD Thesis, several lectures can be doownloaded at : //www.mocis-lagis.fr/membres/belkacem-ould-bouamama /

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Publications and co publications in the BG and FDI domain 5 BG for Modelling Bg for Supervision mechatronics BG theory LFT BG Intelligent transport FDI software

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Aims Acquire the methodological and practical knowledge on development and implementation of online monitoring systems (detection and isolation of faults) Understanding and acquire the structural analysis methodology for integrated design of complex systems supervision Understanding how online monitoring systems (SCADA system) can be developed and implemented Understanding the links between maintenance, control, on-line diagnosis, reconfiguration and analysis of operating modes and criticality 6

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» What is a supervision : two levels FDI FTC? Supervision : Set of tools and methods used to operate an industrial process in normal situation as well as in the presence of failures. Supervision (IFAC): Monitoring a physical system and taking appropriate actions to maintain the operation in the case of faults. Activities concerned with the supervision : Fault Detection and Isolation (FDI) in the diagnosis level, and the Fault Tolerant Control (FTC) through necessary reconfiguration, whenever possible, in the fault accommodation level. SUPERVISIONSUPERVISION FDI : How to detect and to isolate a faults ? FTC : How to continue to control a process ?

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Supervision Graphical User Interface (GUI) Monitoring of variables (Data acquisition)? Surveillance (Alarms) ControlControl

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9 Synoptique fonction essentielle de la supervision, fournit une représentation synth étique, dynamique et instantanée de l'ensemble des moyens de production de l'unité permet à l'opérateur d'interagir avec le processus et de visualiser le comportement normal Courbes: donne une représentation graphique de différentes données du processus Historisation du procédé : - permet la sauvegarde périodique de grandeurs (archivage au fil de l'eau) - permet la sauvegarde d'événements horodatés (archivage sélectif) - fournit les outils de recherche dans les données archivées - fournit la possibilité de refaire fonctionner le synoptique avec les données archivées ( fonction de magnétoscope ou de replay) - permet de garder une trace validée de données critiques (traçabilité de données de production) Gestion des Alarmes Role of GUI (IHM)

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Fonction of supervision systems Management ERP : Enterprise Resource planning : planning of resources integration of different business functions in a centralized computer system configured according to the client-server mode. MRP : Manufacturing Resource Planning : planning of production Planning system which determines the component requirements from requests of finished products and existing suppliesPRODUCTION Process SCADA : Supervisory Control & Data Acquisition PC & PLC Process Control/ Programmable Logic Controller Supervisor A system that performs supervision by means of fault detection and isolation, determination of remedial actions, and execution a corrective actions.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision and Monitoring Monitoring A continuous real time task of determining the conditions of a physical system, by recording information recognising and indicating anomalies of the behaviour (local security) Automatic control Control of parameters (to maintain the quality of products) Supervision Centralize monitoring and control tasks Two parts of SCADA system hardware (collect of datas) Software (control, display, monitoring)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision in the hierarchy of a manufacturing company 12

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Global Function of the supervision 13

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision softwares Les logiciels de supervision sont une classe de programmes applicatifs dédiés à la production dont les buts sont : - l'assistance de l'opérateur dans ses actions de commande du processus de production (interface IHM dynamique...) - la visualisation de l'état et de l'évolution d'une installation automatisée de contrôle de processus, avec une mise en évidence des anomalies (alarmes) - la collecte d'informations en temps réel sur des processus depuis des sites distants (machines, ateliers, usines...) et leur archivage - l' aide à l'opérateur dans son travail (séquence d'actions/batch, recette/receipe) et dans ses décisions (propositions de paramètres, signalisation de valeurs en défaut, aide à la résolution d'un problème...) - fournir des données pour l'atteinte d'objectifs de production (quantité, qualité, traçabilité, sécurité...)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision softwares

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision softwares Wonderware InTouch Wonderware InTouch is the world’s number one Human Machine Interface (HMI), Used in over one-third of the world’s industrial facilities open and extensible solution that enables the rapid creation of standardized, reusable visualization applications and deployment across an entire enterprise. Extensible library with more than 500 graphical symbols to build the system.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision softwares PANORAMA : Ergonomic HMI module for alarms and events, an operating unit of historical datas. SIMATIC WinCC (Siemens) Supervision system with scalable features for monitoring automated processes, provides a full SCADA functionality in Windows Totally Integrated Automation System : Engennering, Communication, Diagnosis, Safety, Security, Robustess

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Supervision softwares DSPACE MATLAB-Simulink More used for fast prototyping based on RealTime Interface (RTI) Simulink model RTI Residuals

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» How to select SCADA systems Simplicity, Usability Solvers Image processing (icons, libraries, …) Supervision Control Surveillance Alarm processing Archiving Programing Performances/Price : Price : hardware + Operating system, software, support, documentation

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Supervision system Architecture Réseau d’entreprise Réseau d’atelier (Ethernet) Réseau de terrain (Profibus, Modbus, Asi…) Postes de Supervision Automate (PID, TOR…) Opérateur Terminal d’atelier Actionneurs Capteurs

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Prof. B. Ould Bouamama Polytech’Lille « Supervision Systems Design » Part 2: Objectives and definitions

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Definitions Safety (sûreté) Ability of a system to dispose of its functional performance (reliability, maintainability, availability) and not to cause a danger for persons or equipment or environment Safety is rather protection against accidental events. Security (sécurité) The condition of being protected from or not exposed to danger. Security is rather protection against intentional damages. Example : Aircraft security is about protecting the aircraft and it's contents from criminal activity and terrorism (Control of documents ) Aircraft safety is about protecting the people by making the aircraft less likely to be involved in a crash (maintenance…)

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Somme definitions Fault Unpermitted deviation of at least one characteristic property or parameter of the system from acceptable / usual / standard condition Incipient fault (naissante): A fault where the effect develops slowly e.g. clogging of a valve). In opposite to an abrupt fault. Abrupt fault : A fault where the effect develops rapidly (e.g. a step function). In opposite to an incipient fault. Active fault- tolerant system : A fault-tolerant system where faults are explicitly detected and accommodated. Contrary to a passive fault-tolerant system. Failure (Défaillance) Permanent interruption of a systems ability to perform a required function under specified operating conditions – incipient failures (naissantes), – Having a transitory nature – constants – Evolving over time – catastrophic Types of fault

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Somme definitions Fault detection : Determination of faults present in a system and time of detection Fault diagnosis: Determination of kind, size, location, and time of occurrence of a fault. Includes fault detection, isolation and identification Fault isolation : Determination of kind, location, and time of detection of a fault. Follows fault detection. Fault modeling : Determination of a mathematical model to describe a specific fault effect. Fault-tolerance : The ability of a controlled system to maintain control objectives, despite the occurrence of a fault. A degradation of control performance may be accepted. Fault-tolerance can be obtained through fault accommodation or through system and /or controller reconfiguration. Fault-tolerant system : A system where a fault is accommodated with or without performance degradation, but a single fault does not develop into a failure on subsystem or system level. Sensor fusion Integration of correlated signals from different sensors (information sources) into a single representation or action.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Somme definitions Fault accommodation (1) - A correcting action that prevents a certain fault to propagate into an undesired end-effect. (2) - Change in controller parameters or structure to avoid the consequences of a fault. The original control objective is achieved although performance may degrade. Disturbance: An unknown (and uncontrolled) input acting on a system Perturbation: An input acting on a system which results in a temporary departure from current state Constraint: The limitation imposed by nature (physical laws) or man. It permits the variables to take certain values in the variable space. Decision logic The functionality that determines which remedial action(s) to execute in case of a reported fault and which alarm(s) shall be generated. Detector An algorithm that performs fault detection and isolation

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Somme definitions Analytical redundancy Use of more than one not necessarily identical ways to determine a variable, where one way uses a mathematical process model in analytical form. Hardware redundancy Use of more than one independent instrument to accomplish a given function. Availability: Probability that a system or equipment will operate satisfactorily and effectively at any point of time. MTTR: Mean Time To Repair MTTR = 1/µ; µ: rate of repair Reliability: Ability of a system to perform a required function under stated conditions, within a given scope, during a given period of time. Measure: MTBF = Mean Time Between Failure. MTBF = 1\la; la is rate of failure [e.g. failures per year]

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Somme definitions : Models Qualitative model A system model describing the behavior with relations among system variables and parameters in heuristic terms such as causalities or if-then rules. Qualitative equation Equations whose functional form and coefficient values are not completely specified. Quantitative model A system model describing the behavior with relations among system variables and parameters in analytical terms such as differential or difference equations. Residual Fault information carrying signals, based on deviation between measurements and model based computations. Threshold Limit value of a residual's deviation from zero, so if exceeded, a fault is declared as detected Symptom Change of an observable quantity from normal behaviour

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Introduction From 1840: automatic control (Watt regulator) Task: improve the quality of finished products, from 1980, new Challenge : Supervision Rôles : Provide the human operator assistance in its emergency management tasks alarm situations to increase the reliability, availability and dependability of the process. Apparition of integrated automation Control, diagnosis, optimization …

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Integrated automation Supervision Monitoring Regulation Instrumentation Input Outputs FDI, FTC, aided decision tools Monitoring the state of the process, user interface Control, optimisation Selection and implementation of sensors and actuators Observations Decisions level 3 level 2 level 1 level 0

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Hazardous area Hazardous Area Relation between FDI et FTC Perf=F(Y1,Y2) UNACCEPTABLE PERFORMANCES DEGRADED PERFORMANCES Y1 Y2 Degraded performances Required Performances Reconfiguration Fault

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SUPERVISION in INDUSTRY FTC Level Fault accommodation Reconfiguration FTC Level Fault accommodation Reconfiguration List of faulty components Corrective maintenance (after fault occurs) Set points Sensors y x u urur Controllers Actuator Process FDI Level On line Fault Detection and isolation FDI Level On line Fault Detection and isolation

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Supervision system : different steps

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» FDI Purpose Objectives : given I/O pair (u,y), find the fault f. It will be done in 3 steps : DETECTION detect malfunctions in real time, as soon and as surely as possible : decides whether the fault has occured or not ISOLATION find their root cause, by isolating the system component(s) whose operation mode is not nominal : find in which component the fault has occured DIAGNOSIS diagnose the fault by identifying some fault model : determines the kind and severity of the fault

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FDI: Medical interpretaion 0 T NON OUI Clinical examination (DETECTION) Diagnosis (ISOLATION)

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FDI steps in technological process supervisions 35 Alarms generation Datas from Actual process Model + - DIAGNOSIS Type of failures Detection : Is it really a fault ? isolation : Which component is faulty ? Identification : What is the type of fault? DECISION List of faulty components Technical specifications

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FT (Fault Tolerance) and FTC (Fault Tolerant Control) FT (Fault Tolerance) Analysis of fault tolerance : The system is runing under faulty mode Since the system is faulty, is it still able to achieve its objective(s) ? Design of fault tolerance : The goal is to propose a system (hardware architecture and sofware which will allow, if possible, to achieve a given objective not only in normal operation, but also in faulty situations. Control and Fault Tolerant Control Control algorithms : implement the solution of control problems : according to the way the system objectives are expressed FTC algorithms implements the solution of control problems : controls the faulty system the system objectives have to be achieved, in spite of the occurence of a pre-specified set of faults

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Control Problem Traditional control : two kinds of objectives control of the system, estimation of its variables Problematic : Given a set U of a control law ( open loop, closed loop, continuous or discrete variables, linear or non-linear) a set of control objective(s) O, set of uncertain constraints C( ), (dynamic models) The solution is completely defined by the triple

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» FTC problem FTC Controls the faulty system: 2 cases 1) fault adaptation, fault accommodation, controller reconfiguration change the control law without changing the system 2) system reconfiguration change both the control and the system : The difference with Control problem System constraints may change. System constraints may change. Admissible control laws may change. Admissible control laws may change.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Passive and active fault tolerance Passive fault tolerance Active fault tolerance control law unchanged when faults occur Normal mode Control law solves Faulty mode Control law also solves f F specific solution for normal and faulty mode and f F ROBUST TO FAULTS Knowledge about C f ( f ) and U f must be available. FDI layer must give information.

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Fault accommodation and System reconfiguration FDI system System reconfiguration Provide estimation of C f ( f ) U f of the fault impact Provide estimation of C f ( f ) U f of the fault impact solve Fault solve Provide estimation of f ( f ), U f of the fault impact Provide estimation of f ( f ), U f of the fault impact Fault FDI cannot provide any estimation of the fault impact FDI cannot provide any estimation of the fault impact solve Fault Fault accommodation

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Process Controller FDI Fault Accommodation Fault Accommodation Controller parameters Ref. Y u Supervision Control system

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Fault Reconfiguration FDI New control configuration Reconfiguration Yref Nominal Controller Process Y u u' New Controller Y’ref Y’ Supervision Control system

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Part 3: HOW TO DESIGN SUPERVISION SYSTEMS ?

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» DIAGNOSTIC METHODS (2/2)

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Model-based FDI S E N SO R S Process actual operation RESIDUAL GENERATOR RESIDUAL GENERATOR MODEL OF THE NORMAL OPERATION ALARM GENERATION 0 Isolation Identification ALARM INTERPRETAION Detection

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» FDI based on Identification and observer y Modèle U y Residual + - y Observateur U y Residual + - identification based Observer based

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No model based Pattern recognition methods Determination of a set of classes (learning step) For each class is associated an operating mode (normal and faulty) Advantage Methods : statistical learning, data analysis, pattern recognition, neuronal networks, etc. Only experimental data are exploited No complex analytical model Advantage Methods : statistical learning, data analysis, pattern recognition, neuronal networks, etc. Only experimental data are exploited No complex analytical model ? ? ? Problems need historical data in normal and in abnormal situations, every fault mode represented ??? generalisation capability ?? Problems need historical data in normal and in abnormal situations, every fault mode represented ??? generalisation capability ??

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D2 Example : FDI of a valve 48 1) No model based Pressure difference Pr = P 1 -P 2 Flow Q(t) * * * * * * * * * * * * * * * * * D1 1) Pattern recognition step (classification of different modes) Q P1P1 P2P2 2) On line surveillance step

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» QUALITATIVE METHODS Use expert knowledge based on « If then else » : applying models of human thinking to physical systems Example : « If P1 increase then Q increase, else valve is blocked» advantage of qualitative methods: No need of numerical value of parameters neither deep knowledge of the system système. Easy to be implemented Issue Sensor faults not detected Lower and upper values of the deviation cannot be fixed precisely Combinatory problem can appear for complex systems (multivariable)

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Model based : example 50 Step 1 determination of fault indicator offline) Q P1 P2 Analytical model, parameters Threshold Residual signal

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Steps in FDI system (1/4) 1. DETECTION Logic operation : We state the system is faulty or not Criteria No detection or too late detection ➽ Catastrophic consequences for the process False alarms ➽ Unnecessary stops of the production unit. There are 4 hypothesis H0 : Assumption of normal operation (Decision domain D0) H1 : Assumption of faulty mode operation (Decision domain D0) Dx : No decision domain

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Steps in FDI system (2/4) Problematic Given R=[r 1, ….r n ] fault indicators Two distributions are known p(Z/H 0 ) and p(Z/H 1 ) One of two hypotheses, H 0 or H 1 is true What to do ? Verify if each r i (i=1,..n) belongs to p(Z/H 0 ) and p(Z/H 1 ) 4 possibilités

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Steps in FDI system (4/4) 2. ISOLATION To be able to isolate the failed components (Alarm filtering) using logic operations Criteria No isolability ➽ Catastrophic consequences for the process False isolability ➽ Unnecessary stops of the production unit or equipment. 3. IDENTIFICATION (DIAGNOSIS) When the fault is located, it is then necessary to identify the specific causes of this anomaly. Are the used logic operation based on signatures identified by experts and validated through expertise and repair faults.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Technical specifications Specifications Which parameters must be supervized ? What are the non acceptable values ? Objectives Performances false alarm missed detection detection delay Available data other (cost, complexity, memory,...) Constraints

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Logic Diagnosis : Systems and faults (1) COMPS = {comp1, comp2, comp3, comp4, comp5} x a b c d y z e f comp1 comp2 comp3 comp4 comp5 A system is a set of interconnected components A system is a triplet (SD, COMPS, OBS) SD : System Description, COMPS : Set of components OBS: set of observations

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System (2) COMPS = {input valve, tank, output pipe, level sensor} x = a b y = b z = c d e = x y f = z ( y) x a b c d y z e f comp1 comp2 comp3 comp4 comp5 Continuous Hydraulic system Discrete electronic system SD

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» SM (or SD) is the set of all those constraints Input valve Tank Output pipe Level sensor System (4)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Examples of internal faults (1) y b OK(comp2) is false x a b c d y z e f comp1 comp2 comp3 comp4 comp5

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Examples of internal faults (2) Process fault : the tank is leaking Sensor fault : noise has improper statistical characteristics Actuator fault : input valve is blocked open

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Examples of external faults (2) Control algorithm objective : cannot be achieved for too large output flows Control algorithm objective : cannot be achieved for too large output flows Controller a = 2 !! (it should equal to 1) x a b c d y z e f comp1 comp2 comp3 comp4 comp5

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Diagnosis algorithm SD is now... OK(input valve) OK(tank) OK(output pipe) OK(level sensor) OK(comp1) x = a b OK(comp2) y = b OK(comp3) z = c d OK(comp4) e = x y OK(comp5) f = z ( y)

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Problems 1) For some given S COMPS, how to check the consistency of SD {OK(X) X S} OBS 2) How to find the collection of the NOGOODS How to check the consistency Problem statement

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Two means to check consistency Analytical Redundancy properties that OBS should satisfy if actual system healthy properties that are satisfied by the nominal system trajectories check whether they are true or not Observers values that OBS should have if actual system healthy simulate / reconstruct the nominal system trajectories check whether they coincide with actual system trajectories

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Chap.2 : ANALYTICAL REDUNDANCY

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Representation PROCESS Capteurs pp d x0x0 x(t) y(t) u(t) mm PROCESS Capteurs pp d x0x0 x(t) y(t) u(t) mm ss pp Model of the faulty system Model of the healthy system

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» State space representation Faults Disturbances Linear case Nonlinear case Faults Disturbances

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» When the system is faulty ? Given a system The system works in normal regime (hypothesis H0) means : y is produced according law C and x is produced according law f and is produced according law of probability P The system works in failure mode hypothesis H1) means : y is not produced according law C, or x is not produced according law f, or is not produced according law of probability P

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Analytical redundancy :How to generate ARRS ? Given The ARR express the difference between information provided by the actual system and that delivered by its normal operation model What is Residual ? 68 u y r All variables are known

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Analytical Redundancy Relations (ARR) and Residuals (r) Definition ARR ARR is a mathematical model where all variables are known. The known variables are available from sensors, set points and control signal. ARR : F(u,x 0, y, ) Residual r Residual is the numerical value of ARR (evaluation of ARR) R is a signal, ARR is an expression R= Eval (ARR) Problematic : How to generate ARRs ? Issue : Elimination of unknown variables theory

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» General principle Analytic model measurement equations or state and measurement equations Off-line Elimination of unknown variables techniques On-line Computation of ARRs (actual system)

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Hardware and analytical redundancy 71 R S 1 or S 2 S2S2S2S2 Hardware redundancy Detection Isolation Sensors S3S3 S2S2 S1S1 F2F2 F1F1 Analytical redundancy ? Leakage S1S1S1S1 F1F1F1F1 Valve R F2F2F2F2 r1r1 r2r Signature Fault Matrix (SFM)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Detectability and isolability S ij : boolean value (0,1) E j (j=1,m) : Fault which may affect the j th component Fault Signature Matrix (FSM) Ib : Isolability Mb: Detectability DEFINITION

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Detectability and isolability Detectability A component fault E j is detectable (M bj =1) if at least one s ij (j=1,m) of its signature vector V Eij is different than zero Isolability A component fault E j is isolable (I bj =1) if it is detectable and its signature vector V Eij is different from others. The signature vector V Ej (j=1,m) of each component fault E j is given by the column vector:

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Detectability and isolability example Faults and ARR Fault Signature Matrix (FSM) Signature vectors Hamming Distance C: Binary coherence vector S j : Signature vector of the j th component to be monitored to isolate k failures, the distance should be equal to 2k + 1.

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Hamming Distance Hamming Distance of given example Signature vectors The Hamming distance shows the ability to isolate two faults. Hamming distance (example)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Hardware redundancy : Simplest redundancy Hardware redundancy uses only measurement equations (therefore it can detect only sensor faults) Example : duplex redundancy Model : y 1 = x y 2 = x Static ARR : y 1 - y 2 = 0

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Duplex redundancy r t Max threshold Min threshold Alarm Fn. normal Low pass filter + - m1m1 m2m2 m 1f m 2f Alarm generator Max threshold Min threshold Alarms Sensor 1 Sensor 2 Noised signal Low pass filter Process Variable x r1r1 r2r2

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Triplex redundancy r1r1 t r2r2 t r3r3 t Residuals r 1 = m 1f - m 2 f r 2 = m 1f – m 3f r 3 = m 2f – m 3f Low pass filter m1m1 m2m2 m 1f Thresholds Alarms Low pass filter Residual generation m 2f m 3f m3m3 Decision procedure r2r2 r3r3 r1r1 Sensor 2 Variable x Low pass filter Sensor 1 Sensor 3

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Fault detection : three steps y1y1 y2y2 Sensors acquisition Sensors acquisition Residual generation r = y 1 - y Residual evaluation = 0 ? yes no

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Fault detection : Problematic y 1 - y 2 = 0 it is not impossible (but it is not certain) that both sensors are healthy Why is it so ??? because there might be non detectable faults

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non detectable faults y 1 = x + f 1 y 2 = x + f 2 y 1 = x + f 1 y 2 = x + f 2 r = y 1 - y 2 = f 1 - f 2 r = 0 even when there is a combination of faults f 1 and f 2 such that : f 1 - f 2 = 0 Example : common mode failures Computation form Evaluation form Redundancy with Non detectable faults Given fault model

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» yes is never true no is always true because y 1 = x + 1 y 2 = x + 2 we need a model of the uncertainties Assume we know 1 [a 1, b 1 ], 2 [a 2, b 2 ], then we know 1 - 2 [a 12, b 12 ] r = y 1 - y 2 = 1 - 2 Redundancy with uncertainties y1y1 y2y2 = 0 ? Residual Generation r

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» y 1 = x + 1 y 2 = x + 2 r = y 1 - y 2 = 1 - 2 Redundancy with noises Assume we know P( 1 ) and P( 2 ), then we know P( 1 - 2) is r distributed according to P( 1 - 2) ??? r P( 1 - 2) r d( 1 - 2) we need a Statistical decision theory

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» triplex redundancy y 1 = x y 2 = x y 3 = x triplex redundancy y 1 = x y 2 = x y 3 = x two residuals r 1 = y 1 - y 2 = 0 r 2 = y 2 - y 3 = 0 two residuals r 1 = y 1 - y 2 = 0 r 2 = y 2 - y 3 = 0 Remarks * any linear combination of residuals is a residual (r 3 = y 2 - y 3 ) How to isolate the fault ? The set {r 1, r 2 } is a residual basis in the following sense :

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Fault isolation (fault model) Triplex redundancy y 1 = x + f 1 x = y 1 - f 1 y 2 = x + f 2 x = y 2 - f 2 y 3 = x + f 3 x = y 3 - f 3 Triplex redundancy y 1 = x + f 1 x = y 1 - f 1 y 2 = x + f 2 x = y 2 - f 2 y 3 = x + f 3 x = y 3 - f 3 y 1 - f 1 = y 2 - f 2 y 2 - f 2 = y 3 - f 3 y 1 - f 1 = y 2 - f 2 y 2 - f 2 = y 3 - f 3 r 1 = y 1 - y 2 = f 1 - f 2 r 2 = y 2 - y 3 = f 2 - f 3 r 1 = y 1 - y 2 = f 1 - f 2 r 2 = y 2 - y 3 = f 2 - f 3 Computation formEvaluation form

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Fault isolation r 1 = y 1 - y 2 = f 1 - f 2 r 2 = y 2 - y 3 = f 2 - f 3 r 1 = y 1 - y 2 = f 1 - f 2 r 2 = y 2 - y 3 = f 2 - f 3 f1f2f3r1110r2011f1f2f3r1110r2011 f1f2f3r1110r2011f1f2f3r1110r2011 Structured and directional residuals Directional residuals

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Conclusion about hardware redundancy detect sensor faults (if detectable) isolate sensor faults (if enough redundancy) needs noise models for statistical decision needs uncertainty models for set theoretic based decision powerful approach but multiplies weight and costs limited to sensor faults

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Static Analytical redundancy

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Parity Space Given linear system Static redundancy Suppose m>n : Then, a decomposition of matrix C can be given under following form as : Such that C 1 is inversible then measurement equation y(t) can be written : d: fault, : uncertainties

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Parity Space Then unknown variable X is calculated from y 1, and eliminated by replacing x(t) in Y 2 : we obtain an ARR Evaluation and calculation form can be obtained

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Parity space approach Parity space approach to eliminate unknown variable x (Chow 84). : Find an orthogonal matrix W to C such that (WC=0) by multiplying measurement equation y=CX by W : Then The system of measurement equation is overdertermined w.r.t. to x : We have m-n ARR, while W has m-n linearly independent rows

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Static Parity space Given measurement equation : Columns of C : vector subspace of dimension R(C) : we note C R(C) Given additional subspace to C R(C) noted W m-R(C) W m-R(C) is named parity space Thus : C R(C) W m-R(C) =R m ( sum of vector space)

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Projection of measurement equation onto parity space ARR: in the absence of faults and disturbances (d(k)=f(k)=0) =0 Calculation formEvaluation form

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Forms of vector parity Evaluation formCalculation form

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Hardware redundancy based on substitution Example : triplex redundancy y 1 = x + f 1 x = y 1 - f 1 y 2 = x + f 2 x = y 2 - f 2 y 3 = x + f 3 x = y 3 - f 3 y 1 - f 1 = y 2 - f 2 y 2 - f 2 = y 3 - f 3 r 1 = y 1 - y 2 = f 1 - f 2 r 2 = y 2 - y 3 = f 2 - f 3 r 1 = y 1 - y 2 = f 1 - f 2 r 2 = y 2 - y 3 = f 2 - f 3

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Hardware redundancy based on parity space ARR generation using parity space Parity space of dimension 2. Then a basis W can be choosen WC=0 (2 vectors orthogonal to C). Among those solutions, Parmi toutes les solutions choisissons : Projection of Y(t) onto parity space gives:

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Directional residuals r(k) can be expressed as : Dimension of the parity space is 2. The direction of the residual vector depends on the specific direction of each fault. r1r1 r2r2 f1f1 f2f2 f3f3

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Example of static redundancy Given parity space u y2 y1y1 y2y2 x1x2 y3y3 To eliminate x, one find W such that : Wy = WCx = 0

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Example of static redundancy Residuals are : While dim(W)=1x3, then W = (a b c) All vectors under form : W= [a 0 -a] cancels WC One find thus the hardware redundancy:

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Conclusion about hardware redundancy There is a static redundancy if one can find : A set of vectors W orthogonal to C such that : WC = 0 Row vectors of W define parity space : Projection of measurement equation onto parity space gives : –Static ARR: W.Y = W.C.X = 0 Hardware redundancy concerns only sensor FDI Widely used in industry

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» A bit more complex Analytical redundancy (dynamic)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» State space model Continuous time Discrete time If there exists W such that WC = 0 then static redundancy relations can be found If there exists W such that WC = 0 then static redundancy relations can be found Dynamic Analytical Redundancy

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Dynamical Analytical redundancy (continuous) Differenciation of y

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Dynamical Analytical redundancy (Discrete) Differenciation of y

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» If there exists W such that W then Analytical redundancy (dynamic)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Observability matrix OBS(A, C, p) Toeplitz matrix T(A, B, C, D, p) Analytical redundancy (general) Dérivation de y Dérivation de y (n)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Expressions of dynamical ARRs If there exists W such that ARRs are : Rows of W are a basis of Ker(OBS), define the parity space Parity space dimension is number of sensors

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RESUME REDONDANCE DYNAMIQUE Given the system At time K+1 Using (1) we have Then: generalizing until the order p (1) (2) (3) (4)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Computation form Evaluation form = 0 when no fault 0 when fault is present Fault detection

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Cayley-Hamilton Theorem Consequence of Cayley-Hamilton Theorem It exists order p such that rank of OBS(A,C,p) matrix is smaller than the number of rows : thus we can find a matrix W such that : W.OBS(A,C,p) = 0 Additional space to OBS, defined by W, is named « Parity space ». By projection of measurement equation (3) onto this space, we obtain: Dynamic ARR : The residual is

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Application Calcul W : derivation first order : Derivation up to second order CB D D

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Application Find two linearly independent vectors W We fix arbitrarily 2 unknowns Residuals expressions are then : W3 is linear combination of W1 and W2

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Application If r=0, we obtain initial model

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Second order residual Matrices OBS and T will be : We obtain after claculation Analysis 2 nd order residual (cf r 4 ) is sensible only to Y 2 (Good for isolation) If the order is increased, are obtained the same ARRS but time shifted RRAs (filtered) 1st order residual (obtained before) 2 nd order Residual

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Conclusions detects any fault (if detectable) isolates any fault (if enough redundancy) estimates the unknown variable with several estimation versions needs noise models for statistical decision needs uncertainty models for set theoretic based decision

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» CHAP3: Structural Analysis Structural analysis Motivations Structural description Structural properties Matching Causal interpretation of matchings Subystems characterization System decomposition Conclusion

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Motivations Complex systems : hundreds of variables and equations Many different configurations Many different kinds of models (qualitative, quantitative, static, dynamic, rules, look-up tables, …) Description of physical plants as interconnected subsystems Analytic models not available The structural description of a system expresses only the links between the variables and the constraints Structural analysis Analysis of the structural properties of the models, i.e. properties that are independent on the actual values of the parameter.

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Graphs : some definitions 118 A graph is an ordered pair G = (V, E) which consists of a set V of vertices or nodes together with a set E of edges or lines A graph is used to specify relationships among a collection of items. The are Simple (undirected graphs) and oriented (directed) graphs Examples social networks, in which nodes are people or groups of people, and edges represent some kind of social interaction Communication networks : computers are nodes, and the edges represent direct links along which messages can be transmitted. A A B B C C D D A A B B C C D D Undirected (simple) Graph Directed (oriented) Graph (A points to B but not vice versa

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Digraph: definitions Given the state equation The digraph ? [ Blanke and al. 2003] Graph whose set of vertices corresponds to the set of inputs u i, output y j and state variables x k Edges are defined as : An edge exists from vertex x k (respectively from vertex u l ) to vertex x j if and only if the state variable x k (respectively the input variable u l ) really occurs in the function F (i.e. vertex u i ) in the function An edge exists from vertex x k to vertex y j if and only if the state variable x k really occurs in the function g Physical means Digraph is a structural abstraction of the behaviour model where Edges represent mutual influence between variables : The time evolution of the derivative x i depends to the time evolution of x k

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Directed graph representation Edge represents mutual influence between variables (x 1 influences y Means : the time evolution of the derivative depends to the time evolution of x 2 Directed graph representation u u x2x2 x2x2 x1x1 x1x1 y y

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Structural description Behaviour model of a system : a pair (C, Z) Z = {z 1, z 2,...z N } is a set of variables and parameters, C = {c 1, c 2,...c M } is a set of constraints Variables quantitative, qualitative, fuzzy Constraints algebraic and differential equations, difference equations, rules, etc. time continuous, discrete

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Sensor Controller Structure of controlled system Process X Y U Yref U, subset of control variables Y, subset of measured variables X, subset of unknown variables - + C : set of constraints CcCc CpCp CmCm Z : set of variables Structure = binary relation S : C x Z {0, 1} (c i, z j ) S(c i, z j ) Structure = binary relation S : C x Z {0, 1} (c i, z j ) S(c i, z j ) S=(C,Z)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Bipartite graph A graph is bipartite if its vertices can be partitioned into two disjoint subsets C and Z such that each edge has one endpoint in C and the other one in Z. Bi-partite graph : links between variables and constraints

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Definition The structural model of the system (C,Z) is a bipartite graphe (C,Z,A), Where A is a set of edges defined as follows : Example C1C2C1C2 C1C2C1C2 iyuiyu iyuiyu CZ

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Example bipartite graph (1) ueue uCuC C0C0 uRuR i uLuL R0R0 umum L0L0 Remark ! In some papers are introduced 2 additional constraints (differential) and corresponding variables to express just the derivative of variable:

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Example : bipartite graph (2) K=known variables X=Unknown variables C umum ueue uLuL uCuC uRuR i c1c1 c2c2 c3c3 c4c4 c5c5 Z Cardinal = size (dimension) of a vector

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Example : bipartite graph (3) C umum ueue uLuL uCuC uRuR i z1z1 z2z2 c1c1 c2c2 c3c3 c4c4 c5c5 c6c6 c7c7 Z The differential constraints could be added Differential constraints and variables

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Incidence matrix A bipartite graph can be represented by an adjacency matrix (named incidence matrix). This is a Boolean matrix where each row corresponds to a constraint c i and each column to a variable z j. A “1” at position ( i, j ) indicates that there is an edge connecting the constraint c i and the variable z j. Variables Z UnKnown variables Known variables Constraints C The incidence matrix B is the matrix whose rows and column represent the set of constraints or variables, respectively. Every edge (c i, z j ) is represented by « 1 » in the intersection of c i and z j. The incidence matrix B is the matrix whose rows and column represent the set of constraints or variables, respectively. Every edge (c i, z j ) is represented by « 1 » in the intersection of c i and z j.

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Subsystem : definition Definition 1. The Structure of a system is a bipartite graph G(C, Z, A), where A is a set of edges such that : (c, z) C Z, a = (c, z) A the variable z appears in the constraint c Definition 2. The structure of a constraint c is a subset of variables Z(c) such that : z Z(c), (c, z) A Definition 3. A subsystem is a pair ( , Z( )) where is a subsystem of C and Z( ) = c Z(c ).

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Example of a subsystem A subsystem is a pair ( , Z( )) where is a subset of C and Z( ) = c , Z(c). C/Z uRuR uLuL uCuC iumum ueue c1c c2c c3c c4c c5c uRuR uLuL i c1c1 101 c2c2 011 Subsystem (R,L)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Differential and algebraic equations Are used three kinds of equations: Differential Algebraic Measure Used variables are

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Hydraulic example Tank dx(t)/dt - q i (t) + q o (t) = 0 Input valve c 2 : q i (t) - αu(t) = 0 Output pipe c 3 : q 0 (t) - k v (x(t)) = 0 Level sensor 1 c 4 : y 1 (t) - x(t) = 0 Level sensor 2 c 5 : y 2 (t) - x(t) = 0 Output flow sensor c 6 : y 3 (t) - q o (t) = 0 Control algorithm c 7 : u(t) = 1 if lmin y 1 (t) lmax u(t) = 0 else U(t) y1y1 y2y2 y3y3 qiqi q0q0 LC x=volume

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Bipartite graph and incidence matrix c 1 : dx(t)/dt - q i (t) - q o (t) = 0 c 2 : q i (t) - αu(t) = 0 c 3 : q 0 (t) - k v (x(t)) = 0 c 4 : y 1 (t) - x(t) = 0 c 5 : y 2 (t) - x(t) = 0 c 6 : y 3 (t) - q o (t) = 0 c 7 : u(t) = 1 if lmin x(t) lmax u(t) = 0 else c1c2c3c4c5c6c7c1c2c3c4c5c6c7 c1c2c3c4c5c6c7c1c2c3c4c5c6c7 x(t) q i (t) q o (t) u(t) y 1 (t) y 2 (t) y 3 (t) x(t) q i (t) q o (t) u(t) y 1 (t) y 2 (t) y 3 (t)

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State space model and digraph Bipartie graph representation Digraph representation

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Subsystems A subsystem : is a pair (C i,,Q(C i ) where Q(C i ) is the set of variables constrained by constraints C i Q(C i ) consists of 2 parts Qc(C i ): correspond to known variables and Qx(C i ): correspond aux unknown variables Example : Hydraulic system C1C1 Q(C 1 )

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Dulmage-Mendelsohn decomposition The number of solutions for Qx(C i ) obtained from Qc(C i ) characterize each subsystem Any system can be uniquely decomposed into 3 subsystems : Over-constrained (C +,X + ) Just-constrained (C 0,X 0 ) Under-constrained (C -,X - ) Only the over-constrained subsystem is monitorable C/Z x X-{x}y1y1 y2y2 f1f f2f c 1 : F 1 (y 1, x) = 0 c 2 : F 2 (y 2, x) = 0 Subsystem {c 1, c 2 } overdetermines the unknown variable x : x can be computed via two different ways, The two results have to be identical Subsystem {c 1, c 2 } overdetermines the unknown variable x : x can be computed via two different ways, The two results have to be identical Example of overdetermined system x=(F 2 ) -1 (y 2 ) x=(F 1 ) -1 (y 1 )

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Under determined subsystem (C, Q(C)) is under determined if, For each value of known variable Qc(C), the set of unknown variables Qx(C) verifying the constraints C has a cardinal higher than one. : card(C)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Just and over determined subsystems (C, Q(C)) is just determined if : card(C)=card(Qx(C)) The unknown variables Qx(C) can be calculated uniquely from known variables Qc(C) and constraints C. (C, Q(C)) is over determined : card(C)>card(Qx(C)) Causes Variables Qx(C) can be calculated in different ways from the known variables Qc (C) and the constraints C Each subset C i C provides a different way to calculate Qx (C). Since the results of these calculations are identical (they are the same physical variables), there are some analytical redundancy

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Examples (1/2) Z={X} U {K} X={u, i}, K={y 1, } C1: u-Ri=0 C2: y 1 -u=0 Z={X} U {K} X={u, i}, K={y 1, } C1: u-Ri=0 C2: y 1 -u=0 i R R u y1y1 y1y1 0 C 2 (y 1, U)= Subsystem : C 1 (i,u)=0 (C 1, Q(C 1 )) is under determined Card(C 1 )=1

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Example (2/2) 1 1 y1y1 0 C 2 (y 1, u)= C 1 (i,, u)=0 ui y2y2 0 C 3 (i, y 2 )= (C, Q(C)) is over determined: Card(C)=3>Card(Q x (C)=2 (C, Q(C)) is over determined: Card(C)=3>Card(Q x (C)=2 i R R u y1y1 y2y2 Z=XUK X={u, i}, K={y 1, y 2, } C1: U-Ri=0 C2: y1-u=0 C3: y2-i=0 Z=XUK X={u, i}, K={y 1, y 2, } C1: U-Ri=0 C2: y1-u=0 C3: y2-i=0

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Example : Incidence matrix C/Zui C 1 (i,u)=0 1 1 y1y1 0 C 2 (y 1, u)= y2y2 0 C 3 (u, y 2 )= y2y2 x={u, i} K={} C 1 : U-Ri=0 x={u, i} K={} C 1 : U-Ri=0 x={u, i} K={y 1 } C 1 : U-Ri=0 C 2 : y 1 –U=0 x={u, i} K={y 1 } C 1 : U-Ri=0 C 2 : y 1 –U=0 x={u, i} K={y 1,y 2, } C 1 : U-Ri=0 C 2 : y 1 –U=0 C 3 : y 2 -U=0 x={u, i} K={y 1,y 2, } C 1 : U-Ri=0 C 2 : y 1 –U=0 C 3 : y 2 -U=0 i R u y1y1

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Prof. B. Ould Bouamama Polytech’Lille « Supervision Systems Design » Matching and ARRs

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Definition of a matching Consider the graph G(Cx, X, Ax), restriction of the structural graph of the system where Cx : Constraints related to unknown variables X Ax : set of edges linking Cx to X. Let a A X, We note X(a) the end of a in X and C X (a) extremity of a in C X. The edge can be written as : a = (C x (a), X(a)) X X C C A A={a 1, a 2, …a n ) X={x 1, x 2, …x n ) C={c 1, c 2, …c n ) X C(x) X(a) Cx(a) a

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Matching : Definition (1/2) G(Cx, X, A) is a matching on G(Cx, X, Ax) if and only if 1) A Ax 2) a1, a2 A a1 a2 Cx(a1) Cx(a2) X(a1) X(a2) Interpretation A matching is : a set of pairs (c i,x i ) s.t. the variable x i can be computed by solving the constraint c i, under the hypothesis that all other variables are known X C(x) X(a 1 ) Cx(a 1 ) X C(x) X(a 2 ) Cx(a 2 ) a1a1 a2a2

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Matching : Definition (2/2) 145 Definition A mathing is a subset of edges such that any two edges have non common node (neither in C nor in Z) Differents matchins can be defined on a bi-partite graph C 1 (i,, u)=0 C 2 (y 1, u)=0 C 3 (i, y 2 )=0 C 1 (i,, u)=0 C 2 (y 1, u)=0 C 3 (i, y 2 )=0 C1C1 C2C2 C3C3 i u y1y1 y2y2 C1C1 C2C2 C3C3 i u y1y1 y2y2 Different matchings of unknown variables

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Maximal matching A maximal matching on G(Cx, X, Ax) is a matching G(Cx, X, A) s.t.: A' A, A' A G(Cx, X, A') is not a matching. What is it ? A maximal matching is a matching such that no edge can be added without violating the no common node property C1C1 C2C2 C3C3 i u y1y1 y2y2 This matching is not maximal w.r.t X (C 3,u) can be added C1C1 C2C2 C3C3 i u y1y1 y2y2 This matching is maximal w.r.t X : Any matching can be added

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Complete and incomplete matching 147 A matching β is complete w.r.t to C (set of constraints ) respectively to X (set of variables) if : x X, c C such that (c,x) β : complete w.r.t. C c C, x X such that (c,x) β : complete w.r.t. X C1C1 C2C2 C3C3 i u y1y1 y2y2 This matching is incomplete w.r.t. to C (C 3 is not matched) but complete w.r.t. to X This matching is incomplete w.r.t. to C (C 3 is not matched) but complete w.r.t. to X C 1 (i,, u)=0 C 2 (y 1, u)=0 C 3 (u, y 2 )=0 C 1 (i,, u)=0 C 2 (y 1, u)=0 C 3 (u, y 2 )=0 C1C1 i u C 1 (i,, u)=0 This matching is complete w.r.t. to C But incomplete w.r.t. to X This matching is complete w.r.t. to C But incomplete w.r.t. to X X (unknown variables) K (known variables while measured) C X

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Matching and the incidence matrix 1/2 Select at most one "1" in each row and in each column Each selected "1" represents an edge of the matching No other edge should contain the same variable : it is the only one in the row No other edge should contain the same constraint : it is the only one in the column.

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Matching and the incidence matrix 2/2 149 C1C1 C2C2 C3C3 i u y1y1 y2y2 y2y2 C/Zui y1y1 C 2 (y 1, u)=0 C 1 (u,i)=0 C 3 (u, y 2 )= y2y2 y2y2 C/Zui y1y1 C 2 (y 1, u)=0 C 1 (u,i)=0 C 3 (u, y 2 )= y2y2 C1C1 C2C2 C3C3 i u y1y1 y2y2

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Causal interpretation of matchings Causal graph ? The oriented bipartite graph which results from a causality assignment is named Causal graph Algebraic constraints At least one variable can be matched in a given constraint Non invertible algebraic constraints Consider C(x 1,x 2 )=0 C x1x1 x2x2 Possible matching x1x1 x2x2 C Impossible matching C/Zx1x1 x2x2 C11 1 x1x1 x2x2 C11 x

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Oriented graph associated with a matching Causal and acausal constraint u-Ri=0 : acausal constraint have not a direction. The variables have the same status: the graph is non oriented U = Ri : causal constraint : i is known, u is calculated. Here the matching is chosen. The matched constraint is associated with one matched variable and with some non matched one 0 u i C C: u-Ri=0 Non matched constraint u i C: U=RI Matched constraint Oriented graph

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Oriented graph associated with a matching Matched constraints the output is computed : the inputs are supposed to be known. The edges adjacent to a matched constraints are oriented C/Zxx1x1 x 2 x3x3 C1C1 111 C2C2 xxx C 3 xxx C 4 xxx C -1 (x 1,x 2,x 3 ) x1x1 x2x2 x3x3 x

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Oriented graph associated with a matching Non-matched constraints all the edges adjacent to a non-matched constraint are inputs. The relation C is redundant. All variables are inputs C/Zx1x1 x 2 x3x3 C1C1 111 C2C2 C 3 C 4 x3x3 c1c1 Maximal matching w.r.t. to X But incomplete w.r.t. to C Maximal matching w.r.t. to X But incomplete w.r.t. to C C 1 is redundant (is not used to eliminate X) 1 1 1

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Structural properties Diagnosability conditions

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Structural observability Under derivative causality, the system is structurally observable if and only if : 1. All the unknown variables are reachable from the known ones (measure) 2. the over constrained and just-constrained subsystems are causal (no differential loop) 3. the under-constrained subsystems is empty

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Over and just constrained system The system is over-constrained if There is a causal matching which is complete w.r.t. all the unknown variables but not w.r.t. all the constraints. The unknown variables can be expressed (in several ways) as functions of the known variables. The subsystem is observable and redundant The system is just-constrained if : There is a causal matching which is complete w.r.t. all the unknown variables and all the constraints. The unknown variables can be expressed as functions of the known variables. The subsystem is observable

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Under-constrained system The system is under-constrained if There is no causal matching which is complete w.r.t. the unknown variables. The subsystem is not observable, and not monitorable. Structural monitorability The conditions for a fault to be monitoable are : 1. the subsustem is observable 2. the fault belongs to the structurally observable over constrained part of the subsystemm to be monitored

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Under and juste constrained system C1C1 i u C1: u-Ri=0 i R R No solution C1: u-Ri=0 C2: y 1 -u=0 C1: u-Ri=0 C2: y 1 -u=0 i R R u y1y1 One solution (non redundancy) C1C1 C2C2 i u y1y1 u i C1C1 y1y1 C2C2 C1C1 ❸ Oriented graph Oriented graph All constraints are used: there is no a redundancy ❷ Bipartite graph ❶ System ❷ Bipartite graph ❸ Oriented graph

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Over constrained system (matching 1) x={u, i}, K={y 1,y 2, } C 1 : U-Ri=0, C 2 : y 1 –U=0, C 3 : y 2 -U=0 x={u, i}, K={y 1,y 2, } C 1 : U-Ri=0, C 2 : y 1 –U=0, C 3 : y 2 -U=0 Maximal matching w.r.t. to X Incomplète matching w.r.t. to C Maximal matching w.r.t. to X Incomplète matching w.r.t. to C y1y1 C2C2 C1C1 C3C3 0 edge y2y2 ❶ System ❷ Bipartite graph and incidence matrix ❸ Oriented graph and ARR

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Over constrained system (matching 2) y1y1 C3C3 C1C1 C2C2 0 edge y2y2

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Exercise y2y2 i R u y1y1 ❷ Constraints ❸ Bipartite graph and incidence matrix ❶ System ❹ Oriented graph and ARR

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Alternated chain What is alternated chains ? A path between two nodes (variables or constraints) alternates always successively variables and constraints nodes : this path is said alternated chain Lenth of alternated chain ? Number of constraints accrosed along the path Reachability A variable x 1 is reachable from variable x 2 if there exists an alternated chain from x 1 to x2 Example C2C2 C1C1 Number of constraints : 2 Number of variables : 3 Lenth of alternated chain : 2 The variable i is reachable from y 1 The path between i and y 1 is : y 1 →C 1 →u →C 1 →i Number of constraints : 2 Number of variables : 3 Lenth of alternated chain : 2 The variable i is reachable from y 1 The path between i and y 1 is : y 1 →C 1 →u →C 1 →i y1y1 Nodes

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Hydraulic example : differential constraint R y V C1C1 C2C2 C3C3 V y qiqi qoqo z C4C4 y C3C3 V C2C2 qoqo C4C4 z qiqi C1C1 Zero Zero edge Maximal matching w.r.t. to X Incomplète matching w.r.t. to C Maximal matching w.r.t. to X Incomplète matching w.r.t. to C Graphe bipartite

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Differential constraints Differential constraints can always be represented under the form: x 2 = dx 1 / dt Derivative and integral causality Derivative causality Integral causality Initial conditions must be known

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Loops Definitions In the oriented graph, loops are a special subset of constraints, which have to be solved simultaneously, because the output signals of some constraints in the loop are the inputs are some others in the same loop : the number of matched variables is equal to the number of constraints (length of the loop). Algebraic loop C/Zx1x1 x2x2 C1C1 11 C2C C3C3 V C2C2 qoqo x2x2 C1C1 x1x1 C2C2

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Differential loop: example V C2C2 C4C4 qiqi C1C1 z q0q0 R V Differential loop 1) Using derivative causality : there is no solution 2) Using integral causality : there is one solution if initial condition is known V C2C2 qiqi C1C1 q0q0 q0q0

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Differential loop How to broke the loop Adding a sensor A matching without any differential loop is called a causal matching V C2C2 C4C4 qiqi C1C1 z q0q0 C3C3 y

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Example just-constrained system V C2C2 C4C4 C1C1 z q0q0 C3C3 y qiqi C/Zz=dV/dtVqiqi qoqo y C1C C2C C3C C4C All unknown variables matched All constraints are matched Suppose input flow q i is unknown

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Example Over-constrained system V C2C2 C4C4 C1C1 z q0q0 C3C3 y u C5C5 qiqi C/Z z=dV/dt Vqiqi qoqo yu C1C C2C C3C C4C C5C All unknown variables matched C 1 is not matched Redundancy

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What is happened in integral causality? V C2C2 C1C1 q0q0 C3C3 y u qiqi V(0) C5C5 C/Z V(0) Vqiqi qoqo yu C1C C2C C3C C5C X :All unknown variables matched C : All constraintsare matched The system is now just-determined : the matching is complete w.r.t to X and C. The system is now just-determined : the matching is complete w.r.t to X and C. 1

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Example under-constrained system V C2C2 C4C4 C1C1 z q0q0 u qiqi C5C5 C/Z z=dV/dt Vqiqi qoqo u C1C C2C C4C C5C The system is not observable There is a differential loop The system is not observable There is a differential loop

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Conclusions (1/2) Structural analysis based on bipartite graphs is easy to understand, easy to apply, Shows the relation between constraints and components, Allows to : identify the monitorable part of the system, i.e. the subset of the system components whose faults can be detected and isolated, Advantages Easy to implement and suited for complex systems Allows to determine the FDI/FTC possibilities No a priori knowledge of the model equations is necessary Lack Structural analysis produces only structural properties

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Conclusiosn (2/2) :What we can do with structural analysis ? can the system be observed ? can all the system variables be computed from the knowledge of the sensors outputs can the system be controlled ? can the system be monitored ? can the malfunction of the system components be detected and isolated can the system be reconfigured ? can the system achieve some objective in spite of the malfunction of some components Actual properties are only potential when structural properties are satisfied. They can certainly not be true when structural properties are not satisfied. Structural properties are properties which hold for actual systems almost everywhere in the space of their independent parameters

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Chapter 3 : Observer-based approaches

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Introduction Principle of FDI methods observer based Reconstruction of the output from sensor and comparison of this estimation with the real output In function of the system: deterministe case : estimation with observers Stochastic case : Kalman filter Observer ? Is a state reconstructor that from measured variables preform estimation of state vector Software sensor !

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» What is observer ? Given How to reconstruct based on output error Process u x C y

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Simulation of the observer C A-KC

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Observer and process A C + B PROCESS B K AA C OBSERVER

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Convergence (1/2) Convergence conditions

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Convergence (2/2) Erreur d’estimation s’annule exponentiellement si (A-KC) est asymptotiquement stable i.e. valeurs propres (modes) sont à partie réelles négatives : Comment ? : Bien choisir K

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Remarks Conclusion The reconstruction error is not zero because The IC of the observer is choosen arbitraly and IC of the process are unknowns How to cacal the error: We can act only on K: then choose K to stabilize the matrix A-KC ensuring convergence to zero the error Used Techniques: Poles Placement used to set the speed of convergence by adjusting the coefficient K (see the instructions on Matlab place and acker

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Idea of diagnosis based observer Estimation error cannot be generated (the state is not measured) But : error of the recontructor can be calculated while Y is measured mesurée Scheme : Residual Process Observer CompareCompare u u

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How to generate residuals ? 1. Par simulation C A-KC Sensor y + - Residual + + y process

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Calculation of residual using z transform Residual

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Calcul du résidu en p (2) L (1)

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Using P transform (1)-(2) : Rsidual Aprés quelques simplifications Lemme d’inversion de matrice : Residual

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Convergence and sensitivity to the noise Analysis of r(p) 1. The reconstruction error of the output depends on the estimation error of the CI 2. Dilemma between : convergence of the observer and the residue sensitivity to noise Choose the gain K so that the error converges rapidly (by imposing the eigenvalues of the matrix very low) : But if K becomes too sensitive to random noise residue

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Example Simple monovariable case Convergence de l’erreur Stability conditions

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Simulation SIMULATION

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Generalized Luenberger Observer Given: 1. We want to estimate the output y(t) Is used observer of gain K X(t) : state, u(t) : input d(t) : faults e(t) : distubancess or noises (1) (2)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Erreurs estimation 2. Dynamic equations of the error estimation (1)- (2) 3. Laplace trasnform of output error

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Remarks about the residual 1. Le résidue is sensitive to fault d(p), to disturbances and noises e(p), but also to the IC. Observation converge to 0 for t , we can neglect transitory due of CI. 2.If d=0, e=0, we have the expression obtained previously.. 3.The gain K of the observer affects similarly d and e: So it is difficult to generate a residual sensitive to faults but not to disturbances 4. Analysis of matrices G indicates whether components are to be isolated from other

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Different influences to the residue 1. Influence of the noise Let e(t) noise realization of a Esp (e (t) = 0 random variable ² Find the residue in frequential Using the above equations the terms of reconstruction errors are obtained (assuming D = 1 Ey = 0) Observer Fréquentiel

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Influence of the noise to the residue Négligeons d’abord l’influence des CI Etude de l’influence du point de vue fréquentiel de e sur r(p) Reduction of the noise e(jω) and r(jω) : Find a gain K, by placing the cut-off frequency of the filter such as the influence of noise is reduced

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Calcul du seuil d’alarmes du résidu Soit données les hypotheses statistiques du bruit : Consider the estimator If average noise e is null it is the same for the estimator

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Calculation of the alarm threshold of the residue Equation variance propagation Application to the error estimation

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Calculation of the alarm threshold of the residue Threshold in stationary regim Determine a threshold in the decision process of the presence of faults based on the variance of y beyond which the residue will be considered null (there is really an alarm) K V0V0 Détermination of variance of the residual t Threshold 0 ALARM NORMAL

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» 2. Influence d’une erreur de modélisation Problematic In practice there is always a modeling error Observer built from the model, then the reconstructed output is sensitive to modeling errors Diagnosis is based on the difference between real and reconstructed output Difficult to separate due to modeling errors and those due to faults Goal Build an observer sensitive to faults and insensitive to modeling errors

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Développement Let uncertain state model : consider error only on A Estimation of the state Cet observateur doit alors détecter, au travers de l’erreur de reconstruction de la sortie, la perturbation du système A Traduit l’apparition d’une perturbation A sur le système Représente un observateur calé sur le système nominal Représente un observateur calé sur le système nominal

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Error hypothesis Assumptions about the error Bounded : i.e slight inaccuracy of the model coefficients Problem to solve : générate residuals 1. less sensitive to A 2. with a maximum sensitivity to faults

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Influence of parameter uncertainties 1. Influence of variations of A to the residues Error estimation (from previous equations) : Frequential domain The reconstruction error is sensitive to inaccuracies A and to the state x(t) (not eliminated here)

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Influence of input and A Influence of input u to the resdiue For IC=0, and replacing x(p) by its expression we have : Then residue depends on u and A We exploit this property to distinguish the influences to the residue of faults and uncertainties How ? : While A is unknown, the error estimation is expressed in terms of what is applied (i.e. u) for ( A ) we calculate the threshold for max A

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Decision Scheme of the decision procedure 1. If the residual value is below the threshold then diagnosis is reserved because the error may be due to uncertainties 2. Beyond this threshold amplitude of the residue indicates the presence of a fault different from model errors 1. If the residual value is below the threshold then diagnosis is reserved because the error may be due to uncertainties 2. Beyond this threshold amplitude of the residue indicates the presence of a fault different from model errors U (bornée) Upper bound of the construction error (residue) t 0 ALARM NORMAL

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Unknown Input Observers (UIO) Problematic Models where the output of the actuators is not measured Evaluation of RRAs requires knowledge measures and inputs So: is used unknown input observers (UIO: Unknown Input Observers) Principle Let a system with known inputs u(t) And unknown inputs

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Observateur à entrée inconnue Let system with UI Consider then the following observer : The error estimation will be :

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Differentiating and substituting x (t) and z (t), then:: Let : P = I+EC

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» The reconstruction error of the state of the UIO While the input is unknown, we try to have : This reconstruction tends then asymptotically to zero iff :

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Calculation of UIO Procedure to calculate the UIO Calculate the generalized inverse of CF Deduct P and G We fix the poles of N and then we deduce K and N L is calculated The unknown input is not involved in the expression of residue.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Estimation of UI Initial equation of the system : If (CF) -1 exists we will have :

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Different UIO schemes SOS : Simplified Observer Scheme Only one UIO Allows to detect faults. No isolation possibilities DOS : Dedicated Observer Scheme Bank of UIO Each observer is sensitive to one fault (diagonal structure)

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D.O.S w.r.t. actuators Actuators System Sensors u y UIO 1 u1u1 u mu e1e1 e mu UIO m u Diagonal structure w.r.t. actuator faults

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D.O.S w.r.t. sensors Actuators System Sensors u y UIO 1 u1u1 u mu e1e1 e mu UIO m u Diagonal structure w.r.t. sensor faults

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G.O.S w.r.t. actuators Actuators System Sensors u y UIO 1 u1u1 u mu e1e1 e mu UIO m u Each residual is affected by all faults except for one sensor fault

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» BOND GRAPH FOR ROBUST FDI Chap.5/ 214

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» PLAN 1) Motivations et positionnement 2) Problématique des méthodes à base de modèles 3) Bond graph et le diagnostic 4) Conception d’un système de supervision 5) Outil logiciel pour la conception de systèmes de supervision 6) Application a un générateur de vapeur

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Contexte Résultats de recherche depuis 12 ans B. Ould Bouamama and A.K. Samantaray. "Model-based Process Supervision. A Bond Graph Approach". Springer Verlag, To be published on 2007, Berlin. Thoma J.U. et B. Ould Bouamama. "Modeling and Simulation in Thermal and Chemical Engineering". A Bond Graph Approach. Springer Verlag, 219 pages, Berlin More : Web : Applications Projet Européens (CHEM, damadics) supervision de procédés chimiques et pétrochimiques, raffinerie de sucre,.. Projet nationaux : EDF Filtrage d’alarmes Projet régional : supervision de procédés non stationnaires Outils logiciels développés Model Builder « FDIPAD » Génération de modèles et d’indicateurs de fautes formels à partir des PIDs Analyse de la surveillabilité : placement de capteurs Génération de S-function ou code C pour la simulation La supervision aujourd’hui dans l’industrie

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Integrated design for supervision P&ID Generate a dynamic and formal models Generate a formal and robust ARRS Optimal sensor placement Diagnosability results New sensor architecture Process Online implementation Data from sensors Sensors Technical specifications Diagnosability analysis ARRs Uncertain Parameters

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Conception intégrée de systèmes pilotés : Démarche Thème 1 Propriétés formelles et comportementales Indicateurs de fautes formels Dimension- nement Synthèse de lois de commande Thème 2 Placement de Capteurs et actionneurs Propriétés structurelles et causales Commandabilité, Observabilité Commandabilité, Observabilité Surveillabilité, Reconfigurabilité Surveillabilité, Reconfigurabilité Simplification de modèles Thème 2 Thème 3 Informatisation Test en ligne

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Pourquoi les BGs pour la conception intégrée ? Graphes et Bond Graphs : quelles différences ? 219

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Génération automatique des modèles 220

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Why Graphical Approach for integrated design? Graphical methods that are based essentially on structural models Graph structures independent of the numerical values of the syst. parameters. Structural properties are independent of the values of the system Structural description of a system expresses only the links between the variables and the constraints Visualization of the system topology Many different kinds of models linear, non linear can be used (qualitative, quantitative, static, dynamic, rules, look-up tables, …) Lack Structural analysis produces only structural properties 221

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» State of art 222 BOND GRAPH For MODELLING (1959) Control (Vergé, Gawtrop, Dauphin, Sueur, Rahmani..) 1991 DiagnosisSizing Qualitative approach (1993) Linkens, Mosterman, Kohda,.. Quantitative approche (1995) Coupled BG (Ould Bouamama 198) Robust Diagnosis Extension to coupled BG Automated Diagnosis Design of supervision system Opend loop system Linear Systems Sensor and actuator Faults Monoenergy Bond Graph (Tagina 95) Hybrid Bond Graph (Biswas, Mosterman (USA)

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Model based approach : Issues MODELLING Modelling step is most important in FDI design obtaining the model is a difficult task The constraints are not deduced in a systematic way It is not trivial in the real systems to write the model under a "beautiful" form x=f(x,u,θ ). RESIDUAL GENERATION Eliminate the unknowns : analytic redundancy approach Existing methodology : parity space for linear, elimination theory (constraints under polynomial forms) Variables to be considered : all quantities constrained by the system components (process, actuators, sensors, algorithms) How to generate directly from the process ARRs and models : Bond graph tool well suited because of its causal and structural properties.

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DEFINITION, REPRESENTATION DEFINITION REPRESENTATION P = e.f e f 1 1 2 2 Mechanical power :

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Notion de causalités

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Electrical DOMAIN Mechanical (rotation) Hydraulic Chemical Thermal Economic Mechanical (translation) POWER VARIABLES FOR SEVERAL DOMAINS VOLTAGE u [V] CURRENT i [A] FORCE F [N] VELOCITY v [m/s] FLOW (f) EFFORT (e) TORQUE [Nm] ANGULAR VELOCITY [rad/s] UNIT PRICE P u [$/unit] FLOW OF ORDERS f c [unit/period] CHEM. POTENTIAL [J/mole ] MOLAR FLOW PRESSURE P [pa] VOLUME FLOW TEMPERATURE T [K] ENTROPY FLOW

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T2T2 On-Off VoVo QO QO PI T1T1

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Tank2 0 C:C 1 De2 6 Tank1 0 C:C 1 De1 2 Pump MSf 1 1 T2T2 On-Off Valve1 1 R:R Valve 2 1 R:R 1 Se PI u1u1 On-offUSER u3u3 PI T1T1 VoVo QO QO Outflow to consumer

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Specialized software for Bond graph modelling

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Prof. B. Ould Bouamama Polytech’Lille « Supervision Systems Design » 3) Bond graph and diagnostic : determinsit and robust case 230

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» 231 Bipartite graphs and Bond graphs The structural model of the system (C,Z) is a bipartite graphe (C,Z,A) The constraints C from the bond graph model consist of structural C s, behavioral C b and measurement equations C m : The structural constraints are deduced from the set of junction equations which represent the mass and energy conservation laws. The number of junction equations is then equal to the number of equations in 0-junction (common effort), 1-junction (common flow) and 2-ports elements (transformer TF, gyrator GY):,

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232 Behavior equations (C b ) describe the physical phenomena occurred in passive BG elements (Resistive R, Capacitive C and Inertial I): Measurement (C m ) equations represent the sensor equations De and Df are effort and flow detectors respectively. The set of variables The set of variables Z consists of known ( K ) and unknown ( X ) variables. The known variable set K contains the effort (Se) and flow (Sf) source variables : Unknown variables X are the pair of conjugated power variables (flow and effort):

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Cardinality from BG model Consider the j th junction structure (JS) where occur several phenomena represented by set of n bond graph elements E : E 1, …E m To this junctions are connected m sensors : S 1, …S m This junction is completely defined by one structural equation (energy conservation), n behavioral equations (how this energy is transformed) and m measurement equations.

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The cardinal of unknown variables The number of unknown variables in 0-junction is equal to the set of flow variables plus the common effort variable which links all elements Similarly on the 1-junction, the number of unknown variables is the sum of effort variables labeling the components bond graph plus the common flow variable General case, the unknown variables cardinal can be written by the relation: For global system Consider now the global bond graph model of the system to be monitored which consists of junctions. The cardinal of the unknown variables and the cardinal of constraints can be given through the following relations:

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» ARRs generation from Bond Graphs ARR is a constraint calculated from over determined subsystem where all variables are known: In a bond graph representation ARR is

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Covering causal path Définion (Causal path) A causal path between two ports is an alternation of bonds and basic bond graph elements (named nodes) such that ( i) all nodes have a correct and complete causality, and (ii) two bonds of the path have in the same node opposite causal stroke direction. Simple direct Causal path : covered following only one variable (effort or flow). Indirect causal path : one element (R,C, I) should be crossed along the path Mixad causal path : it comprises a gyrator (GY) imposing the change of followed variable 236 e 1 01 f e 0 10 f Passive element (R, C, I f e f f e 1GY f e f

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Causal path and causality E C iCiC UCUC i F C iCiC UCUC Se:E UCUC iCiC Sf:i UCUC i UCUC iCiC UCUC i C 0 Se:E iCiC Derivative causality 0 C Sf: i Integral causality

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How causal path can help for simulation ! E R1R1 g C i UcUc URUR 1 R:R 1 C:C 1 Se:E E URUR UcUc ieie icic irir For R elemnt URUR irir URUR R:R 1 For C element UcUc icic C:C 1 icic For 1 junction ❶ E UcUc URUR + - E UcUc URUR Df:i

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Dualised sensors I Se Df R SSf R L i A R L i A R L Se: u i A RL circuit I Se Df R Bond graph model in integral causality For control and simulation Bond graph model in derivative causality with dualised sensor why ? Initial Conditions no knowns Df : as source of information

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De I Se Df C R SSe SSf I Se Df C R SSf Pas de conflit de causalité, Système sur-déterminé Conflit de causalité, Système sous-Déterminé ?

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Example a DC motor ELECTRICAL PART u a iaia MECHANICALPARTMECHANICALPART LOADLOAD

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Systematic State equations generation 242 uaua iaia (J,f) RaRa LaLa imim mm MSe:U a iaia uaua 1 LL I:J R:f Se:- L ff JJ 1 R:R a I:L a uMuM iaia u Ra u La iaia MGY:K Df: m Df:i m

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» 243 Automated Control analysis

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Algorithme de génération des RRAs à partir du modèle BG 244 ❶ Put the BG model in derivative causality dualising sensors MSe:U a iaia uaua 1 LL I:J R:f Se:- L ff JJ 1 R:R a I:L a uMuM iaia u Ra u La iaia MGY:K SSf: m SSf:i m

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Structural analysis Cardinal of constraints Cardinal of Unknown variables 245

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Incidence matrix and Bipartie graph of the Dc motor 246

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❷ The structure junction (conservative law equation) associated with at least one sensor represents the candidate 247

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❸ The unknown variables are eliminated using covering causal paths from unknwn to known variables (measured and control signal) MSe:U a uaua 1 LL I:J R:R M Se:- L ff JJ 1 R:R A I:L a uMuM iaia u Ra u La iaia MGY:K SSf: m SSf:i m

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Oriented graph

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Decision procedure: monitorability analysis R i /fautesLReUaImWmJmRm R1R R2R

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Decision procedure: monitorability analysis

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Informatisation FDIPAD

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Robustness problem

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How to fix threshold ? Défaut sur capteur du courant égal à 15% de sa valeur nominale Fonctionnement normal Seuil simple: 3*std

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What about parameter uncertainties ? False alam because of parameter uncertainties !!!! introduction of 5% of nominal value of R M

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Linear Fractional Transformation Any rational expression can be written under LFT form 256 LFT Representation Transfert Function LFT Représentation State space representation

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LFT Modelling Physical system Modele bloc diagramme Mathematical model R fRfR eReR R fRfR eReR δRδR eReR e inc + + R n fRfR e Rn fRfR eReR

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LFT modelling R n f Rn e Rn eReR e inc + + δR δR R:R fRfR eReR R fRfR eReR 1 0 R:R n De*:z R MSe*:w R -δ R e Rn f 1 =f Rn e Rn e inc fRfR eReR zRzR wRwR -δ R

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Example R L i A R L i A R L Se: u i A 1 4 R:R n De*:z R MSe:w R Df: i I:L n 3 10 MSf:w L 7 Df*:z L 8 R:R 2222 I:L 3

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ARR generation : determinist (1/1) I:L 3 1 Se: u R:R SSf: i Df: i 1- Se SSf- 2-R-2 SSf- 3- L- 3 R L i A R L i A R L Se: u i A

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MSe:w L R:R n I:L n De*:z L De*:z R Se: u SSf: i MSe:w R Se SSf R n SSf L n MSe:w R 7- MSe:w L

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MSe:w L R:R n I:L n De*:z L De*:z R Se: u SSf: i MSe:w R

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OUR DC MOTOR 263

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Robust ARR From BG DC motor Uncertain ARRs 264 R(t) (t) adaptive thresholds

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Simulation results 265 Residuals in normal operation

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Simulation results 266 Réaction des deux résidus robustes suite à une variation des paramètres RA et RM d'une valeur supérieure à leur incertitude relative

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Simulation results 267 Réaction des deux résidus robustes suite à une variation des paramètres RA et RM d'une valeur égale à leur incertitude relative

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Fault detectability index DI The fault detectability index DI is the difference in absolute value between the effort (or flow) provided by faults and those granted by all the uncertainties. 268

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» CONCLUSIONS The interest of the presented approach : consists in the use of only one representation (bond graph modelling) for ARRs and dynamics models generation in symbolic format. the industrial designer can easily (because of integration of the functional tool as interface with the human operator) build the thermofluid dynamic model and ARRs Propose to the user a sensor placement to satisfy a given technical specification To add a new component in the data base in a generic way What are the limits in model based supervision ? The performances depend on the accuracy of the model Processes are no stationary : the models change There is not “the” method for supervision… but integration of tools is needed Real time applications are not yet used in industry : maintenance of implemented algorithms is difficult.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» APPLICATION to A steam generator Installation

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Steps of performing a supervisory system Failure Modes Analysis, Effects and Criticality Analysis,(AMDEC) Offline monitorability and reconfigurability analysis conditions List of pertinent equipments Elaboration of the supervision system Results of monitorability and reconfigurability analysis Sensor Placement Online test of the supervision system Algorithms Online Ofline

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Different steps for on line diagnosis system design Isolation decision procedure On line FDI Measurements for FDI and control List of faulty components Decision making tool for supervision (FDI and FTC levels) Dynamic model Model Validation Ofline diagnosability analysis Diagnosis algorithms generation Measurements for monitoring ARRs

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Process delay system FIR 10 PR 11 PIR 16 TR 17 PC 2 PR 14 PR 15 TR 38 PR 38 TR 29 PR 31 V1 V6 User PR 13 PR 12 ZC 1 V2 V11 BOILER LIR 9 8 LG 1 TR 5 PC 1 PIR 7 TR 6 Q 4 Thermal resistor LC 1 V10 60kW FIR 3 P2 P1 V9 STORAGE TANK TIR 2 LIR 1 LG 3 STEAM FLOW FEED WATER CONDENSER HEAT-EXCHANGER Steam generator : P &IDiagram

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General views 274 GUI Data acquisition system

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» 275

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Architecture of the supervisions system 276

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General Informations Number of sensors 28 10 Pressure sensors, 12 Temperature sensors, 5 Level sensors, 4 Flow sensors, 1 Power sensor Number of actuators 8 1 Pump (switching level control in the boiler) 1 Thermal resistor (switching pressure control in the boiler) 1 Valve (Continuous pressure control in the condenser) 1 Valve (Continuous valve position) 3 discharge valves (switching level control in the condenser) 1 Three way-valve (continuous cooling water temperature control ) Number of equipment units 1 storage tank of 0.4 m 3, 4 Pumps, 1 Boiler of m 3, 5 controlled valves, 1 Controlled three- way-valve 1 Condenser coupled with an exchanger, 1 Aero-refrigerator, 1 Thermal resistor of 60 KW, 1 PC- based digital control system, 1 process delay system Automation System: Conventional instrumentation The used technology is the 4-20 mA Control system Two types of digital controllers are used: « On-off » and PI Controlled parameters: –Boiler pressure, boiler level, condenser level, condenser pressure, Steam flow valve position and Cooling water temperature.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Failure scenarios Plant faults Water leak in the boiler by opening valve V11 Thermal insulation fault taking off the calorifuge sheet Pressure leak in the steam flow system by opening valve V3 Water leak in the storage tank by opening valve V10 Steam pipe blocked out by closing the manual valve V13 Actuator faults Any valve can be blocked open or closed Pump fault by switching off the power supply The actuator control signals can be modified Failure Discharge valves leak by opening valve V8 et V9 Sensor abrupt faults Any sensor can be temporary disconnected The sensor signals can be modified Reconfigurability Degraded mode: one or two discharge valves in running Use of one or two controlled valves in the steam flow system The long loop of the heat-exchanger in fault mode: degraded mode, only the short loop is in running mode Feeding pumps are redundant Sensor system can be reconfigured General Informations

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» 279/13 Modelling hypothesis For the feeding circuit the liquid is incompressible. I n the steam boiler, water and steam are in thermodynamic equilibrium, This is justified by the fact that we have a good homogenous mixture of the emulsion water-steam. The mixture is at uniform pressure, which means that we neglect surface tension of the steam bubbles. The boiler has a thermal capacity and is subject to heat losses towards the environment All variables are described by lumped parameters.

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» 280 \93 WORD BOND GRAPH OF THE INSTALLATION Condenser Cooling circuit Condenser-Heat exchanger Boiler Steam expansion Feed water circuit Receiver Discharge valves Voltage source i U Thermal resistor

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Bond graph model 281

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Dynamic simulation using Bond graph and Matlab Simulink

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Modular Approach using library models

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Model Validation yr(t) ym(t) + < adm ? u(t) No Validated model Real system Model Sensors (Acquisition card) - yes

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» ARRs generation

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Diagnosability analysis : Fault Signature matrix RRAs générées Modèle bond graph sous forme icone métier Bibliothèque de modèles Matrice de surveillabilité

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Control algorithm based on Panorama software

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Variable definition based on Panorama software

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Diagnosis Decision procedure based on Panorama software

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Diagnosis Decision procedures based on Panorama software

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» Determination of thresholds

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Prof. B. Ould Bouamama Polytech Lille « Supervision Systems Design» CONCLUSIONS The interest of the presented approach : consists in the use of only one representation (bond graph modelling) for ARRs and dynamics models generation in symbolic format. the industrial designer can easily (because of integration of the functional tool as interface with the human operator) build the thermofluid dynamic model and ARRs Propose to the user a sensor placement to satisfy a given technical specification To add a new component in the data base in a generic way What are the limits in model based supervision ? The performances depend on the accuracy of the model Processes are no stationary : the models change There is not “the” method for supervision… but integration of tools is needed Real time applications are not yet used in industry : maintenance of implemented algorithms is difficult.

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