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Institutionen för systemteknik Department of Electrical Engineering Examensarbete Design of Automated Generation of Residual Generators for Diagnosis of Dynamic Systems Examensarbete utfört i Fordonssystem

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Institutionen för systemteknik Department of Electrical Engineering Examensarbete Design of Automated Generation of Residual Generators for Diagnosis of Dynamic Systems Examensarbete utfört i Fordonssystem vid Tekniska högskolan vid Linköpings universitet av Isac Duhan LiTH-ISY-EX--11/444--SE Linköping 211 Department of Electrical Engineering Linköpings universitet SE Linköping, Sweden Linköpings tekniska högskola Linköpings universitet Linköping Design of Automated Generation of Residual Generators for Diagnosis of Dynamic Systems Examensarbete utfört i Fordonssystem vid Tekniska högskolan i Linköping av Isac Duhan LiTH-ISY-EX--11/444--SE Handledare: Examinator: Daniel Eriksson isy, Linköpings universitet Mattias Krysander isy, Linköpings universitet Linköping, 26 October, 211 Avdelning, Institution Division, Department Division of Vehicular Systems Department of Electrical Engineering Linköpings universitet SE Linköping, Sweden Datum Date Språk Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport ISBN ISRN LiTH-ISY-EX--11/444--SE Serietitel och serienummer Title of series, numbering ISSN URL för elektronisk version Titel Title Design av automatgenerering av residualgeneratorer för diagnos av dynamiska system Design of Automated Generation of Residual Generators for Diagnosis of Dynamic Systems Författare Author Isac Duhan Sammanfattning Abstract Diagnosis and Supervision of technical systems is used to detect faults when they occur. To make a diagnosis, tests based on residuals can be used. Residuals are used to compare observations of the system with a model of the system, to detect inconsistencies. There are often many different types of faults which affects the state of the system. These states are modeled as fault modes. The difference between fault modes are the presence of faults in the model. For each fault mode a different set of model equations is used to describe the behaviour of the real system. When doing fault diagnosis in real time it is good, and sometimes vital, to be able to change fault mode of the model, when a fault suddenly occurs in the real system. If multiple faults can occur the number of combinations of faults is often so big, even for relatively small systems, that residuals for all fault modes can not be prepared. To handle this problem, the residuals are to be generated when they are needed. The main task in this thesis has been to investigate how residuals can be automatically generated, given a fault mode with a corresponding model. An algorithm has been developed and to verify the algorithm a model of a satellite power system, called ADAPT-Lite, has been used. The algorithm has been made in two versions. One is focusing on numerical calculations and the other is allowing algebraical calculations. A numerical algorithm is preferred in an automatized process because of generally shorter calculation times and the possibility to apply it to systems which can not be solved algebraically but the algebraical algorithm gives slightly more accurate results in some cases. Nyckelord Keywords Model Based Diagnosis, Dynamic Systems, Supervision Abstract Diagnosis and Supervision of technical systems is used to detect faults when they occur. To make a diagnosis, tests based on residuals can be used. Residuals are used to compare observations of the system with a model of the system, to detect inconsistencies. There are often many different types of faults which affects the state of the system. These states are modeled as fault modes. The difference between fault modes are the presence of faults in the model. For each fault mode a different set of model equations is used to describe the behaviour of the real system. When doing fault diagnosis in real time it is good, and sometimes vital, to be able to change fault mode of the model, when a fault suddenly occurs in the real system. If multiple faults can occur the number of combinations of faults is often so big, even for relatively small systems, that residuals for all fault modes can not be prepared. To handle this problem, the residuals are to be generated when they are needed. The main task in this thesis has been to investigate how residuals can be automatically generated, given a fault mode with a corresponding model. An algorithm has been developed and to verify the algorithm a model of a satellite power system, called ADAPT-Lite, has been used. The algorithm has been made in two versions. One is focusing on numerical calculations and the other is allowing algebraical calculations. A numerical algorithm is preferred in an automatized process because of generally shorter calculation times and the possibility to apply it to systems which can not be solved algebraically but the algebraical algorithm gives slightly more accurate results in some cases. Sammanfattning Diagnos och övervakning av tekniska system används för att upptäcka fel när de inträffar. För att ställa en diagnos kan tester baserade på residualer användas. Residualer används för att jämföra observationer av ett system med en model av system för att upptäcka inkonsistens. Det finns ofta många typer av fel som påverkar ett systems tillstånd. Dessa tillstånd modelleras med olika felmoder. För varje felmod används olika uppsättningar av modellekvationer för att beskriva systemets beteende. När diagnoser ska ställas i realtid är det ofta bra och ibland avgörande att kunna byta felmod när ett fel plötsligt inträffar i systemet. Om multipelfel kan inträffa blir antalet kombinationer av fel ofta så stort att residualekvationerna för alla felmoder inte kan v vi förberedas. Detta gäller även för relativt små system. För att hantera problemet bör residualerna kunna genereras vid den tidpunkt då de behövs. Examensarbetets huvuduppgift handlar om att undersöka hur residualerna kan genereras automatiskt, givet en felmod och en modell. En algoritm har utvecklats och verifierats med en model av ett kraftsystem för en satellit, kallad ADAPT-Lite. Algoritmen har gjorts i två versioner. Den ena tillåts göra algebraiska beräkningar men den andra, i så stor utsträckning som möjligt, tillåts endast göra numeriska beräkningar. En numerisk algoritm föredras i en automatiserad process p.g.a. generellt sett kortare beräkningstid och dess egenskap att kunna lösa vissa problem som inte kan lösas algebraiskt. Den algebraiska algoritmen har dock visats sig ge aningen noggrannare resultat i många fall. Acknowledgments I would like to thank my supervisor, Ph.D. student Daniel Eriksson for the support and for all the help he has given me reviewing my report. I would like to thank my examinor, associate professor Mattias Krysander with whom I ve had many technical and theoretical discussions. I would also like to thank associate professor Erik Frisk who has also given me much support with technical and theoretical questions. Isac Duhan, Linköping October 211 vii Contents 1 Introduction Diagnosis and Supervision Model Based Diagnosis Fault Modes Automatic Generation of Residual Equations ADAPT-Lite Problem Formulation Thesis Outline Theory Models State Space Models Differential Algebraic Equations The Index of a DAE Model Linearization Nonlinear Least Square Estimation of Parameters Diagnosis Residuals Observers using Kalman Filters Modeling Modeling of Components Equation Set Generation Parameter Estimation The Algorithm Equation Structuring About dividing g alg Using Algebraic Part-Solution Using Non-Algebraic Part-Solution Observers Linearization Linearization in the Algebraic Algorithm Linearization in the Numerical Algorithm ix x Contents Tuning the Kalman Filter Simulation Simulation in the Algebraical Algorithm Simulation in the Numerical Algorithm Application on ADAPT-Lite ADAPT-Lite Overview Starting Point of the Project Estimated Model Parameters Generated Equations Dynamic Equations The Residual Equations The Conditional Relation The Kalman Gain Algebraical Shortcuts for Numerical Algorithm Linearization Point and Initial Simulation Point Reformulation of the Algebraic Constraints Simulation Simulation Tolerances Defining the Fault Modes and the Faults Fault Mode NF without Faults Fault Mode NF with Fault f Fault Mode F 1 with Fault f Fault Mode NF with Fault f Fault Mode F 2 with Fault f Fault Mode NF with Fault f Fault Mode F 3 with fault f Variance Estimations for the Kalman Filter The Numerical Algorithm s Sensitivity to λ About Approximation in the Linearization Conclusions Generation of Residual Equations Simulation Method Algebraical Shortcuts Linearization and Simulation Initialization Point Reformulation of the Algebraic Constraints Estimation of Variances for the Kalman Filter Approximation in the Linearization Future Work Improved Model Multiple Faults Automatic Model Parameter Estimation Automatic Estimation of λ Improved Numerical Simulation Method Contents xi 7.6 Real Time Implementation Bibliography 51 A Component Models of ADAPT-Lite 53 A.1 Battery A.2 Circuit Breaker and Relay A.3 Complex Circuit Breaker and Complex Relay A.4 Fan A.5 Inverter A.6 Real Load A.7 Real AC Load A.8 Sensors Chapter 1 Introduction This work has been carried out at the division of Vehicular Systems, which is a part of the department of Electrical Engineering at Linköping University. The purpose has been to design and implement an algorithm to automatically generate tests, to detect possible faults in a system, based on theory of model based diagnosis. In Section 1.1 there is an overview of model based diagnosis followed by an introductory explanation of automatic residual generation in Section 1.2. In Section 1.3 the ADAPT-Lite system, which will be used for the evaluation of the residual generator, is introduced. A problem description is formulated in Section 1.4. Finally an overview of the structure and content of the report is presented in Section Diagnosis and Supervision Diagnosis and supervision of technical systems is in general about detecting and isolating faults occurring in the system. In many industrial systems it is important to have correct knowledge about the condition of the system and to be able to find and handle faults systematically. The reason for this can be many but often it is a safety and an economical issue, see e.g., [9]. When an industrial machine breaks down it can be dangerous for the operators working close to the machine. Using diagnosis to detect faults can prevent many hazardous situations. If left alone, a fault in a system can grow from minor to severe and cause additional faults. If a fault can be detected and corrected in an early stage, lots of money can be saved by preventing long production stops or more expensive repairs. There are many different methods within the field of diagnosis. When the examined system can be described with mathematical models it may be possible to use model based diagnosis Model Based Diagnosis In model based diagnosis a mathematical model, describing the observed system, is used to make a diagnosis. A diagnosis is, according to [9], a conclusion of 1 2 Introduction which combinations of faults that can explain the process behavior. Faults can be discovered by detecting inconsistencies between the model and the real system. With an accurate model and well placed sensors it may sometimes be possible to not only say that a fault has occurred but also where in the system it is situated and what kind of fault it is. One type of test to detect the inconsistencies between a model and a real system can be created by using a residual together with a criteria for when the residual show the inconsistencies. A residual can be written as r(t) = f(y(t)) (1.1) where r(t) is the residual, y(t) are measurements and f(y(t)) is the residual generator, which is constructed out of model equations. When there are no model uncertainties in f and no measurement noise in y(t), the following is true r(t) =. Example 1.1: Making residuals of a model A model, where two sensors, y 1 (t) and y 2 (t), are measuring an unknown signal x(t), is given as y 1 (t) = x(t) y 2 (t) = x(t). (1.2) Using a variable substitution of x(t) gives y 1 (t) y 2 (t) = (1.3) which is a consistency relation. A residual generator f(y(t)) is made of the left hand side in (1.3) which is then written as y 1 (t) y 2 (t) = f(y(t)) (1.4) and the residual is the resulting signal when input is put into the residual generator as r(t) = f(y(t)), (1.5) where r(t) is the residual. The model, which the residual generator f is made of, is seldom perfect and measured signals often contain noise. Therefore the residuals in most cases slightly deviate from zero even when the real system has no faults. Because of this the residuals are often filtered and thresholded. The thresholds are chosen to separate the deviation in the fault free case from the bigger deviation caused by faults in the system. In other words, the threshold makes the criteria for when there is an 1.1 Diagnosis and Supervision 3 inconsistency between the model and the real system. An example of this can be seen in Figure 1.1, where a residual is affected by a fault after 5 seconds. Despite the signal being noisy, it is possible to detected the fault with a threshold, drawn with a dashed line in the figure. Understanding the use of thresholds is important for this thesis but no thresholds will be designed. The focus in this work is on generating residuals. 1 Example of a Residual.8.6 Amplitude Figure 1.1. Example of a residual with a fault occurring at 5s. With a threshold at.5 on the y-axis the fault will be detected. With information from several residuals it is often possible to make use of fault isolation algorithms which will say more precisely where in the system the faults have occured. Fault isolation is not in the scope of the thesis and will therefore not be further explained here but examples of fault isolation algorithms can be found in [3] and [8] Fault Modes To describe what state the system is in, in regard to what faults that are present in the system, the term fault mode is used, see [9]. The fault mode is used to tell which faults are present or if the system is free of faults. To be able to describe the behavior of the system when the system is in a certain state the equations which describe the corresponding fault mode are needed. Different fault modes are described by different sets of model equations. If one component in a system breaks it may however be that only the equations for that component changes in the set in the transition between the fault modes. The fault mode only says how the system is currently modelled, i.e., which equations are used. It does not necessarily tell the truth about what faults are actually present in the system. With the nomenclature used in this thesis the fault free case is a fault mode. Only component one broken in the model is also a fault mode and only component two broken is another fault mode. A multiple fault of component one and component two broken in the model is yet another fault mode and so on. 4 Introduction Example 1.2: Fault Modes The model equations y(t) = x(t) [ fault free mode ] y(t) = x(t) + k [ fault mode 1 ] y(t) = [ fault mode 2 ] (1.6) represent three different fault modes for a sensor y measureing a variable x. The first fault mode represents the fault free case, the second when there is a bias error present, and the third fault mode represents when the sensor is dead. The three equations in (1.6) will never be used at the same time. 1.2 Automatic Generation of Residual Equations Designing residuals for a diagnosis algorithm can be made by hand for small systems which have few measured signals. In bigger and more complex systems with a larger amount of measured signals, the number of possible residuals that can be made grows rapidly. To be able to get good fault isolation, that is to tell different faults apart when they are detected, more then a handful of the possible residuals might be needed for a large system. In this case it can be hard and time consuming to create all these by hand. Therefore to create residuals automatically would have several advantages. One is to save development time. Another is to avoid mistakes during development that are easy to make in a manual procedure, especially for large systems. One important aspect is that even for relatively small systems, the number of possible residuals needed to detect and isolate faults in all possible fault modes is too large to be precalculated and prepared. Thus it is not only important but necessary to be able to automatically generate new residuals while the system is running and goes from one fault mode into another. This is especially true when there is a need to use different sets of model equations for different fault modes of the system. During simulation in this thesis it is however assumed that the fault mode is constant and does not do a transition into another fault mode. It is still however a background and motivation for generating the residual equations automatically. 1.3 ADAPT-Lite During the past two years NASA has organized a diagnosis competition which in 21 ran under the name Second International Diagnostic Competition (DXC 1), see [11]. In the competition there were three different entry categories. The competition category of interest for this thesis concerns the so called ADAPT-Lite system. What is given is the following: 1.4 Problem Formulation 5 Abbreviation BAT2 INV2 FAN CB IT EY AC ST, TE, ISH, ESH Component battery inverter fan circuit breaker current sensor relay load position sensor Table 1.1. The components and their abbreviations in the ADAPT-Lite system. A sketch of the system, shown in Figure 1.2, which shows how all the components are connected. All fault modes for each component. Measurement data from the sensors in the real system from a number of different fault scenarios. What is not given are models for the components and model parameter values. The models have to be made and the parameters, e.g., resistance of resistors, have to be estimated with the use of the data series. The ADAPT-Lite system is a suitable platform for evaluating a diagnosis algorithm and is therefore used for this in the thesis. Figure 1.2. Schematic over the ADAPT-Lite satellite system. The figure comes from [11]. In Table 1.1 the abbreviations are explained. 1.4 Problem Formulation The purpose of this thesis is to develop an algorithm which automatically generates tests from model equations to detect faults. This includes modeling of the system, 6 Introduction developing an algorithm which automatically generates residuals and observer relations and creating a simulator to simulate the generated tests. The residuals are to be generated numerically. To evaluate the method it will be applied to the ADAPT-Lite system and the results from this will be analyzed. The problem can be summed up in the following bullets: An algorithm to automatically generate residual generators from model equations shall be made. The algorithm shall handle equations that contain first order derivatives. If possible the algorithm shall operate completely numerical without assistance from algebraic solvers so that in the future an online implementation is made possible. The algorithm shall be evaluated on the ADAPT-Lite system. All the components in the ADAPT-Lite system that have not yet been modeled at the start of the thesis project need to be modeled. The work does not need to consider the following: The algorithm does not have to work online in real time which also means that the simulation time can be long. To make or use a fault isolation algorithm is not in the scope of this thesis. 1.5 Thesis Outline The thesis includes the following chapters: Chapter 2, Theory The chapter presents a state space model and differential algebraic equations

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