| 1. |
- Andersson, Magnus
(author)
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Experimental Design and Updating of Finite Element Models
- 1997
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Licentiate thesis (other academic/artistic)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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| 2. |
- Barenthin Syberg, Märta, 1979-
(author)
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Complexity Issues, Validation and Input Design for Control in System Identification
- 2008
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Doctoral thesis (other academic/artistic)abstract
- System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.
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| 3. |
- Bergman, Niclas
(author)
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Recursive Bayesian Estimation : Navigation and Tracking Applications
- 1999
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Doctoral thesis (other academic/artistic)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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| 4. |
- Björklund, Svante
(author)
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A Survey and Comparison of Time-Delay Estimation Methods in Linear Systems
- 2003
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Licentiate thesis (other academic/artistic)abstract
- In this thesis the problem of time-delay estimation (TDE) in linear dynamic systems is treated. The TDE is studied for signal-to-noise ratios, input signals, and systems that are common in process industry. This also implies that both open-loop and closed-loop cases are of interest. The true time-delay is estimated, which may be different from the time-delay giving the best model approximation of the true system. Time-delays which are not a multiple of the sampling interval are also of interest to estimate.In this thesis, a review and a classification according to underlying principles of TDE methods in the literature are made. The main classes are: 1) Time-Delay Approximation Methods: The time-delay is estimated from a relation (a model) between the input and output signals expressed in a certain basis. The time-delay is not an explicit parameter in the model. 2) Explicit Time-Delay Parameter Methods: The time-delay is an explicit parameter in the model. 3) Area and Moment Methods: The time-delay is estimated from certain integrals of the impulse and step responses. 4) Higher Order Statistics Methods.Some new methods and variants of old ones are suggested and evaluated, some of which have good estimation performance and some poor performance. Properties of TDE methods are analyzed, both theoretically and experimentally. Recommendations are given on how to choose estimation method and input signal. Generally, prediction error methods where the time-delay parameter is explicit and is optimized simultaneously with the other model parameters give good estimation quality.Most evaluations have been conducted with factorial experiments using Monte Carlo simulations in open and closed loop. Some statistical analysis methods have been utilized: The RMS error of the time-delay estimates gives an absolute measure of the performance. ANOVA (ANalysis Of VAriance) and confidence intervals give conclusions with a certain level of confidence.
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| 5. |
- Edström, Krister
(author)
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Simulation of Mode Switching Systems Using Switched Bond Graphs
- 1996
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Licentiate thesis (other academic/artistic)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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| 6. |
- Forssell, Urban
(author)
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Closed-loop Identification : Methods, Theory, and Applications
- 1999
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Doctoral thesis (other academic/artistic)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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| 7. |
- Forssell, Urban
(author)
-
Properties and Usage of Closed-loop Identification Methods
- 1997
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Licentiate thesis (other academic/artistic)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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| 8. |
- Galrinho, Miguel
(author)
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Least Squares Methods for System Identification of Structured Models
- 2016
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Licentiate thesis (other academic/artistic)abstract
- The purpose of system identification is to build mathematical models for dynamical systems from experimental data. With the current increase in complexity of engineering systems, an important challenge is to develop accurate and computationally efficient algorithms.For estimation of parametric models, the prediction error method (PEM) is a benchmark in the field. When the noise is Gaussian and a quadratic cost function is used, PEM provides asymptotically efficient estimates if the model orders are correct. A disadvantage with PEM is that, in general, it requires minimizing a non-convex function. Alternative methods are then needed to provide initialization points for the optimization. Two important classes of such methods are subspace and instrumental variables.Other methods, such as Steiglitz-McBride, use iterative least squares to avoid the non-convexity of PEM. This thesis focuses on this class of methods, with the purpose of addressing common limitations in existing algorithms and suggesting more accurate and computationally efficient ones. In particular, the proposed methods first estimate a high order non-parametric model and then reduce this estimate to a model of lower order by iteratively applying least squares.Two methods are proposed. First, the weighted null-space fitting (WNSF) uses iterative weighted least squares to reduce the high order model to a parametric model of interest. Second, the model order reduction Steiglitz-McBride (MORSM) uses pre-filtering and Steiglitz-McBride to estimate a parametric model of the plant. The asymptotic properties of the methods are studied, which show that one iteration provides asymptotically efficient estimates. We also discuss two extensions for this type of methods: transient estimation and estimation of unstable systems.Simulation studies provide promising results regarding accuracy and convergence properties in comparison with PEM.
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| 9. |
- Gillberg, Jonas, 1975-
(author)
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Methods for Frequency Domain Estimation of Continuous-Time Models
- 2004
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Licentiate thesis (other academic/artistic)abstract
- Approaching parameter estimation from the discrete-time domain is the dominating paradigm in system identification. Identification of continuous-time models on the other hand is motivated by the fact that modelling of physical systems often take place in continuous-time. For many practical applications there is also a genuine interest in the parameters connected to these physical models. In the black-box discrete-time modelling framework however, the identified parameters often lack a physical interpretation.Uniform sampling has also been a standard assumption. A single sensor delivering measurements at a constant rate has been considered as the ideal situation. With the advent of networked asynchronous sensors the validity of this assumption has however changed. In fields such as economics and finance, uniform sampling might not be practically possible. This indicates a need for methods coping with non-uniform sampling.In the first part of this thesis the problem of estimation of irregularly sampled continuous-time ARMA models in the frequency domain is treated. In this process, the mode! output is assumed to be piecewise constant or piecewise linear, and an approximation of the continuous-time spectral density is calculated. Maximum Likelihood estimation in the frequency domain is then used to obtain parameter estimates. Rules of thumb concerning the mode! bias and variance are derived and used in order to select the frequencies to be used in estimation. Finally, the methods are applied to a tire pressure estimation problem.The second part ofthe thesis treats frequency domain identification of continuoustime ARMA and OE models for uniformly sampled data. Here the end objective is to inspire improved interpolation schemes which excel over the piecewise-linear and piecewise-constant approximations used in the first part. The result is a method which estimates the continuous-time spectrum/Fourier transform from its discretetime counterpart.
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| 10. |
- Gunnarsson, Johan
(author)
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On Modeling of Discrete Event Dynamic Systems : Using Symbolic Algebraic Methods
- 1995
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Licentiate thesis (other academic/artistic)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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