| 1. |
- Bergman, Niclas
(författare)
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Recursive Bayesian Estimation : Navigation and Tracking Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recursive estimation deals with the problem of extracting information about parameters, or states, of a dynamical system in real time, given noisy measurements of the system output. Recursive estimation plays a central role in many applications of signal processing, system identification and automatic control. In this thesis we study nonlinear and non-Gaussian recursive estimation problems in discrete time. Our interest in these problems stems from the airborne applications of target tracking, and autonomous aircraft navigation using terrain information.In the Bayesian framework of recursive estimation, both the sought parameters and the observations are considered as stochastic processes. The conceptual solution to the estimation problem is found as a recursive expression for the posterior probability density function of the parameters conditioned on the observed measurements. This optimal solution to nonlinear recursive estimation is usually impossible to compute in practice, since it involves several integrals that lack analytical solutions.We phrase the application of terrain navigation in the Bayesian framework, and develop a numerical approximation to the optimal but intractable recursive solution. The designed point-mass filter computes a discretized version of the posterior filter density in a uniform mesh over the interesting region of the parameter space. Both the uniform mesh resolution and the grid point locations are automatically adjusted at each iteration of the algorithm. This Bayesian point-mass solution is shown to yield high navigation performance in a simulated realistic environment.Even though the optimal Bayesian solution is intractable to implement, the performance of the optimal solution is assessable and can be used for comparative evaluation of suboptimal implementations. We derive explicit expressions for the Cramér-Rao bound of general nonlinear filtering, smoothing and prediction problems. We consider both the cases of random and nonrandom modeling of the parameters. The bounds are recursively expressed and are connected to linear recursive estimation. The newly developed Cramér-Rao bounds are applied to the terrain navigation problem, and the point-mass filter is verified to reach the bound in exhaustive simulations.The uniform mesh of the point-mass filter limits it to estimation problems of low dimension. Monte Carlo methods offer an alternative approach to recursive estimation and promise tractable solutions to general high dimensional estimation problems. We provide a review over the active field of statistical Monte Carlo methods. In particular, we study the particle filters for recursive estimation. Three different particle filters are applied to terrain navigation, and evaluated against the Cramér-Rao bound and the point-mass filter. The particle filters utilize an adaptive grid representation of the filter density and are shown to yield a performance equal to the point-mass method.A Markov Chain Monte Carlo (MCMC) method is developed for a highly complex data association problem in target tracking. This algorithm is compared to previously proposed methods and is shown to yield competitive results in a simulation study.
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| 2. |
- Stenman, Anders
(författare)
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Model on Demand : Algorithms, Analysis and Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification deals with the problem of estimating models of dynamical systems from observed data. In this thesis, we focus on the identification of nonlinear models, and, in particular, on the situation that occurs when a very large amount of data is available.Traditional treatments of the estimation problem in statistics and system identification have mainly focused on global modeling approaches, i.e., the model has been optimized on basis of the entire data set. However, when the number of observations grows very large, this approach becomes less attractive to deal with because of the difficulties in specifying model structure and the complexity of the associated optimization problem. Inspired by ideas from local modeling and database systems technology, we have taken a conceptually different point of view. We assume that all available data are stored in a database, and that models are built “on demand” as the actual need arises. When doing so, the bias/variance trade-off inherent to all modeling is optimized locally by adapting the number of data and their relative weighting. For this concept, the name model-on-demand has been adopted.In this thesis we have adopted a weighted regression approach for the modeling part, where a weight sequence is introduced to localize the estimation problem. Two conceptually different approaches for weight selection are discussed, where the first is based on traditional kernel assumptions and the other relies on an explicit optimization stage. Furthermore, two algorithms corresponding to these approaches are presented and their asymptotic properties are analyzed. It is concluded that the optimization approach might produce more accurate predictions, but that it at the same time is more demanding in terms of computational efforts.Compared to global methods, and advantage with the model-on-demand concept is that the models are optimized locally, which might decrease the modeling error. A potential drawback is the computational complexity, both since we have to search for neighborhoods in a multidimensional regressor space, and since the derived estimators are quite demanding in terms of computational resources.Three important applications for the concept are presented. The first one addresses the problem of nonlinear time-domain identification. A number of nonlinear model structures are evaluated from a model-on-demand perspective and it is concluded that the method isuseful for predicting and simulating nonlinear systems provided sufficiently large datasets are available. It is demonstrated through simulations that the prediction errors are in order of magnitude directly comparable to more established modeling tools such as artificial neural nets and fuzzy identification.The second application addresses the frequency-domain identification problems that occur when estimating spectra of time series or frequency responses of linear systems. We show that the model-on-demand approach provides a very good way of estimating such quantities using automatic, adaptive and frequency-dependent choices of frequency resolution. This gives several advantages over traditional spectral analysis techniques.The third application, which is closely related to the first one, is control of nonlinear processes. Here we utilize the predictive power of the model-on-demand estimator for online optimization of control actions. A particular method, model-free predictive control, is presented, that combines model-on-demand estimation with established model predictive control techniques.
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| 3. |
- Andersson, Magnus
(författare)
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Experimental Design and Updating of Finite Element Models
- 1997
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis deals with two partly related topics: model updating and actuator/sensor placement concerning finite element (FE) models of large, flexible mechanical structures.The importance of accurate dynamical FE models of mechanical structures in, e.g., aviation/aerospace applications are steadily increasing. For instance, a sufficient accurate model may reduce the expenses for ground vibration testing and wind-tunnel experiments substantially. It is therefore of high industrial interest to obtain accurate models of flexible structures. One approach is to improve a parameterized, initial FE model using measurements of the real structure, so-called model updating. For a fast, successful model updating, three requirements must be fulfilled. The model updating must be computationally cheap, which requires an efficient model reduction technique. The cost function describing the deviation between the model output and the measurements must have good convexity properties so that an estimation of the parameters corresponding to the global optimum is likely to be obtained. Finally, the optimization methods must be reliable. A novel mode-pairing free cost function is presented, and together with a proposed general procedure for model updating, a cheap model updating formulation with good parameter estimation properties is obtained.Actuator and sensor placement is a part of the experimental design. It is performed in advance of the vibrational experiment in order to ensure high quality measurements. Using a nominal FE model of the structure, an actuator/sensor placement can be made. Actuator/sensor placement tasks are generally discrete, non-convex optimization problems of high complexity. One is therefore restricted to the use of sub-optimal algorithms in order to fulfill time and memory storage requirements. A computationally cheap algorithm for general actuator/sensor placement objectives are proposed. A generalization of an actuator/sensor placement criterion for model updating, and a novel noise-robust actuator placement criterion for experimental modal analysis are proposed.
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| 4. |
- Edström, Krister
(författare)
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Simulation of Mode Switching Systems Using Switched Bond Graphs
- 1996
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis one approach to model and simulate mode switching systems is studied. This approach, switched bond graphs, is an extension of the bond graph language in the sense that it allows modeling of mode switching phenomena. The classical bond graph language as well as the switched bond graph language are presented. Different aspects of these tools are discussed, and one aspect specially considered is causality. Computational causality shows in what order the variables in a model should be calculated to get efficient simulation code. Causality can also be used to make analysis of the model. For classical bond graphs, causality is a fixed property. For switched bond graphs causality becomes mode varying. With the mode varying causality, it follows that there will be a different continuous model for each mode. Many other and similar approaches do not allow one model for each mode. They express the description of all modes in one single model. The reason for this is the exponential increase of modes for a linear increase in the number of modeled switching phenomena.The main contribution of the thesis is mediated by an actual implementation, where it is shown that the simulation procedure is algorithmic from a switched bond graph model. Two different simulation procedures are presented: MTS simulation and mode-by-mode simulation. Of these procedures, MTS-simulation is implemented. In the MTS-simulation algorithm, the complete mathematical description of all modes will be derived before the simulation starts. In mode-by-mode simulation, the mathematical description will be derived for one mode at a time. The simulation of one mode will take place before equations for the next mode are derived. This algorithm circumvents the combinatorial explosion in the number of modes.The modes can be categorized by their properties in different ways. Two different categorizations are discussed in the thesis. The first categorization is to divide the modes into conflicting and non-conflicting modes. Conflicting modes may reflect errors in the model or undesired behaviors of the system. The other categorization is made by how fast the different modes are left when activated during simulation. These properties are interesting when dealing with the transition conditions. Two mode switching systems, modeled using switched bond graphs, are simulated using the presented algorithms. The models are analyzed, and a discussion about the properties of the different modes in these models is conducted.
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| 5. |
- Forssell, Urban
(författare)
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Closed-loop Identification : Methods, Theory, and Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification deals with constructing mathematical models of dynamical systems from measured data. Such models have important applications in many technical and nontechnical areas, such as diagnosis, simulation, prediction, and control. The theme in this thesis is to study how the use of closed-loop data for identication of open-loop processes affects dierent identification methods. The focus is on prediction error methods for closed-loop identification and a main resultis that we show that most common methods correspond to diefferent parameterizations of the general prediction error method. This provides a unifying framework for analyzing the statistical properties of the different methods. Here we concentrate on asymptotic variance expressions for the resulting estimates and on explicit characterizations of the bias distribution for the different methods. Furthermore, we present and analyze a new method for closed-loop identification, called the projection method, which allows approximation of the open-loop dynamics in a fixed, user-specified frequency domain norm, even in the case of an unknown, nonlinear regulator.In prediction error identification it is common to use some gradient-type search algorithm for the parameter estimation. A requirement is then that the predictor filters along with their derivatives are stable for all admissible values of the parameters. The standard output error and Box-Jenkins model structures cannot beused if the underlying system is unstable, since the predictor filters will generically be unstable under these circumstances. In the thesis, modified versions of these model structures are derived that are applicable also to unstable systems. Another way to handle the problems associated with output error identification of unstable systems is to implement the search algorithm using noncausal filtering. Several such approaches are also studied and compared.Another topic covered in the thesis is the use of periodic excitation signals for time domain identification of errors-in-variables systems. A number of compensation strategies for the least-squares and total least-squares methods are suggested. The main idea is to use a nonparametric noise model, estimated directly from data, to whiten the noise and to remove the bias in the estimates."Identication for Control" deals specically with the problem of constructing models from data that are good for control. A main idea has been to try to match the identication and control criteria to obtain a control-relevant model fit. The use of closed-loop experiments has been an important tool for achieving this. We study a number of iterative methods for dealing with this problem and show how they can be implemented using the indirect method. Several problems with the iterative schemes are observed and it is argued that performing iterated identification experiments with the current controller in the loop is suboptimal. Related to this is the problem of designing the identification experiment so that the quality of the resulting model is maximized. Here we concentrate on minimizing the variance error and a main result is that we give explicit expressions for the optimal regulator and reference signal spectrum to use in the identification experiment in case both the input and the output variances are constrained
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| 6. |
- Forssell, Urban
(författare)
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Properties and Usage of Closed-loop Identification Methods
- 1997
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification deals with the construction of mathematical models of dynamical systems using measured data. Closed-loop identification is what results when performing the identification experiment under output feedback, that is, in closed loop. In this thesis we study a number of closed-loop identification methods, both classical and more recently suggested ones. A common feature of the methods considered is that they all are derived in the prediction error framework. We provide a comprehensive treatment of the statistical properties of the different methods for closed-loop identification. A focus will be on accuracy aspects of different closed-loop identification methods and we show that indirect and joint input-output methods fail to give better accuracy than the direct method.The question of whether is is possible to design a closed-loop method that allows fitting the model to the data with arbitrary frequency weighting has long been open. We describe and analyze a new method for closed-loop identication - the projection method - that has this desirable property. A strong feature of the projection method is that it can be applied to systems with arbitrary feedback mechanisms, just as the direct method. A drawback is that the projection method gives worse accuracy than the direct method.Substantial interest has been devoted to the problem of linking identification and control. One mainstream approach has been to try to match the identification and control criteria by using proper frequency weighting in the identification. Obviously the projection method is well suited for this problem. In the literature various indirect methods have been employed. The motivation for this has been that by using indirect methods the bias error will be shaped by the sensitivity function which generally is considered advantageous. We show how the identification step in several identification-for-control schemes based on this idea can be performed in a unified manner using a simple indirect method.A related approach to identification for control is to try to minimize the degradation in closed-loop performance due to control design based on identified models by carefully tuning the experiment design parameters. We focus on closed-loop issues and starting with a quite general problem formulation we show how to optimally choose the feedback regulator and the reference signal.
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| 7. |
- Gunnarsson, Johan
(författare)
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On Modeling of Discrete Event Dynamic Systems : Using Symbolic Algebraic Methods
- 1995
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The interest in discrete event systems (DEDS) has increased during the last years, due to the lack of methods and tools that are capable to handle the complexity of problems and tasks present in industry to day. In this thesis we will consider a symbolic and algebraic framework which will be used for modeling, analysis, and synthesis of DEDS.We will use polynomials belonging to a polynomial ring over finite fields to represent finite quantities, functions, and relations of a DEDS system. The polynomials make it possible to improve efficiency and scalability of DEDS computations, as shown in this thesis by the modeling and analysis of the landing gear controller of the Swedish fighter aircraft JAS 39 Gripen. A polynomial model, represented by binary decision diagram (BDD), is automatically generated from a 1200 lines Pascal implementation, which contains 105 binary variables of which 26 are state variables. Function specifications expressed with temporal algebra, are verified using tools for dynamic analysis, which we also use to compute a polynomial representing the set of all reachable states in the model.To explore the ability and applicability of the polynomial approach when doing synthesis, we use a tank system containing actuators (pump and valves) and sensors (the tank level and measurable disturbances). We propose a synthesis method that uses actuator priority, weighting of states, and Gröbner bases to compute explicit control laws for the actuators, fulfilling the control objectives even if one of the actuators (the pump) is defective.Modeling aspects are emphasized further by comparing the polynomial approach which we have used, with Boolean expressions and established DEDS approaches in the community of automatic control like Ramadge-Wonham, Petri nets, and COCOLOG. We discuss how to handle transformation between signals and events for DEDS and how to modularize DEDS to gain complexity advantages. Model description languages are discussed and desirable features are stated, using the experiences achieved from the modeling of the tank system and the landing gear controller.
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| 8. |
- Gunnarsson, Johan
(författare)
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Symbolic Methods and Tools for Discrete Event Dynamic Systems
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The interest in Discrete Event Dynamic Systems (DEDS) has increased during the last years, due to the lack of methods and tools that are capable of handling the complexity of problems and tasks present in industry today. In this thesis we will consider a framework based on relations over finite domains. The framework is used for modeling, analysis, and synthesis of DEDS.Binary Decision Diagrams (BDDs) are used to represent relations, as well as the operations for modeling, analysis and synthesis of DEDS. To utilized the structure of integers and arithmetic operation, Integer Decision Diagrams (IDDs) are developed and implemented. Polynomials over finite fields are another type of representation that is used for the relational framework. Here Gröbner bases, and Integrated Monomial Diagrams (IMDs) are the tools that are used. IDDs and IMDs are both developed, by the author, to represent integer structures and arithmetic operations efficiently.With tools for efficient relational representation, it possible to improve scalability of DEDS computations, as shown in this thesis by the modeling and analysis of the landing gear controller of the Swedish fighter aircraft JAS 39 Gripen. A relational model, represented by a BDD, is automatically generated from a 1200 lines Pascal implementation, which contains 105 binary variables of which 26 are state variables. Function specifications expressed with temporal algebra, are verified using tools for dynamic analysis, which we also use to compute a polynomial representing the set of all reachable states in the model. The landing gear controller serves as a benchmark test of BDDs and IDDs. The IDDs reduced the computation time by 50%.To explore the ability and applicability of using a polynomial relational representation when doing synthesis, we use a tank system containing actuators (pump and valves) and sensors (the tank level and measurable disturbances). We propose a synthesis method that uses actuator priority, weighting of states, and Gröbner bases to compute explicit control laws for the actuators, fulfilling the control objectives even if one of the actuators (the pump) is defective.Modeling aspects are emphasized further, by comparing the polynomial approach which we have used, with Boolean expressions and established DEDS approaches in the community of automatic control like Ramadge-Wonham, Petri nets, and COCOLOG. We discuss how to handle transformation between signals and events for DEDS and how to modularize DEDS to gain complexity advantages. Model description languages are discussed and desirable features are stated, using the experiences achieved from the modeling of the tank system and the landing gear controller.
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| 9. |
- Hagenblad, Anna
(författare)
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Aspects of the Identification of Wiener Models
- 1999
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification deals with the problem of constructing models of systems from observations of the inputs and outputs to the systems. In this thesis, a particular class of models, Wiener models, is studied. The Wiener model consists of a linear dynamic block, followed by a static nonlinearity.The prediction error method is formulated for the Wiener model case, and it is discussed how the predictor depends on the noise assumptions. It is shown that under certain conditions, the prediction error estimate is consistent. Conditions that certify consistency for a simplied, approximative predictor are also stated.Consistent in theory, the prediction error estimate is much too complicated to calculate analytically in practice, and numerical methods must be used. Furthermore, the prediction error criterion may have several local minima, so a good initial estimate is needed. A considerable part of this thesis deals with how to calculate such an initial estimate.By a particular choice of parameterization of the linear subsystem and the inverse of the nonlinearity, it is possible to formulate an error criterion where the parameters enter quadratically. It is discussed how this error criterion may be minimized using linear regression, quadratic programming or the total least squares method. This initial estimate may then be used in the numerical minimization of the prediction error criterion.An algorithm for identication of Wiener models is presented, and it is shown that the algorithm under some conditions gives a consistent estimate. The algorithm is also applied to both simulated and experimental data.
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| 10. |
- Helmersson, Anders
(författare)
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Methods for robust gain scheduling
- 1995
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Regulatorer används i många tillämpningar för att förbättra prestanda ochegenskaper hos fordon och farkoster av olika slag, t ex flygplan och raketer.Beroende på olika faktorer, som hastighet och höjd, kan dynamiken ochuppträdandet av dessa farkoster variera. Man vill därför låta regulatorn tahänsyn till dessa variationer genom att ändra sitt uppförande i motsvarandegrad.Regulatorn kan konstrueras på olika sätt. En möjlighet är att styrsignalernaberor linjärt eller proportionellt på regulatorns insignaler, till exempelavvikelser från önskad bana. Regulatorn bestäms av ett antal parametrarsom kan ändras efter de yttre betingelserna (t ex hastighet och höjd för ett flygplan). Denna metod kallas för parameterstyrning.Vid konstruktionen av regulatorn använder man en modell av det systemsom ska styras. En viktig och önskad egenskap hos en regulator är att denska kunna fungera bra även om systemet den ska styra varierar eller avvikerfrån modellen. Ett flygplan beter sig på olika sätt beroende på hur mycketlast den har och hur lasten är placerad. Det är därför önskvärt att användaregulatorer som inte är känsliga för variationer, t ex i last, och som uppförsig bra i olika situationer. En sådan regulator sägs vara robust.Avhandlingen behandlar hur man kan analysera och konstruera regulatorersom är robusta och parameterstyrda. Det visar sig att båda dessaproblem är likartade och att de kan behandlas med samma metoder.
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