| 1. |
- Abd-Elrady, Emad, 1970-
(författare)
-
Nonlinear Approaches to Periodic Signal Modeling
- 2005
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Periodic signal modeling plays an important role in different fields. The unifying theme of this thesis is using nonlinear techniques to model periodic signals. The suggested techniques utilize the user pre-knowledge about the signal waveform. This gives these techniques an advantage as compared to others that do not consider such priors. The technique of Part I relies on the fact that a sine wave that is passed through a static nonlinear function produces a harmonic spectrum of overtones. Consequently, the estimated signal model can be parameterized as a known periodic function (with unknown frequency) in cascade with an unknown static nonlinearity. The unknown frequency and the parameters of the static nonlinearity are estimated simultaneously using the recursive prediction error method (RPEM). A treatment of the local convergence properties of the RPEM is provided. Also, an adaptive grid point algorithm is introduced to estimate the unknown frequency and the parameters of the static nonlinearity in a number of adaptively estimated grid points. This gives the RPEM more freedom to select the grid points and hence reduces modeling errors. Limit cycle oscillations problem are encountered in many applications. Therefore, mathematical modeling of limit cycles becomes an essential topic that helps to better understand and/or to avoid limit cycle oscillations in different fields. In Part II, a second-order nonlinear ODE is used to model the periodic signal as a limit cycle oscillation. The right hand side of the ODE model is parameterized using a polynomial function in the states, and then discretized to allow for the implementation of different identification algorithms. Hence, it is possible to obtain highly accurate models by only estimating a few parameters. In Part III, different user aspects for the two nonlinear approaches of the thesis are discussed. Finally, topics for future research are presented.
|
|
| 2. |
- Bhikkaji, Bharath, 1974-
(författare)
-
Model Reduction and Parameter Estimation for Diffusion Systems
- 2004
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Diffusion is a phenomenon in which particles move from regions of higher density to regions of lower density. Many physical systems, in fields as diverse as plant biology and finance, are known to involve diffusion phenomena. Typically, diffusion systems are modeled by partial differential equations (PDEs), which include certain parameters. These parameters characterize a given diffusion system. Therefore, for both modeling and simulation of a diffusion system, one has to either know or determine these parameters. Moreover, as PDEs are infinite order dynamic systems, for computational purposes one has to approximate them by a finite order model. In this thesis, we investigate these two issues of model reduction and parameter estimation by considering certain specific cases of heat diffusion systems. We first address model reduction by considering two specific cases of heat diffusion systems. The first case is a one-dimensional heat diffusion across a homogeneous wall, and the second case is a two-dimensional heat diffusion across a homogeneous rectangular plate. In the one-dimensional case we construct finite order approximations by using some well known PDE solvers and evaluate their effectiveness in approximating the true system. We also construct certain other alternative approximations for the one-dimensional diffusion system by exploiting the different modal structures inherently present in it. For the two-dimensional heat diffusion system, we construct finite order approximations first using the standard finite difference approximation (FD) scheme, and then refine the FD approximation by using its asymptotic limit. As for parameter estimation, we consider the same one-dimensional heat diffusion system, as in model reduction. We estimate the parameters involved, first using the standard batch estimation technique. The convergence of the estimates are investigated both numerically and theoretically. We also estimate the parameters of the one-dimensional heat diffusion system recursively, initially by adopting the standard recursive prediction error method (RPEM), and later by using two different recursive algorithms devised in the frequency domain. The convergence of the frequency domain recursive estimates is also investigated.
|
|
| 3. |
- Ebadat, Afrooz, 1986-
(författare)
-
On Application Oriented Experiment Design for Closed-loop System Identification
- 2015
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification concerns how to construct mathematical models of dynamic systems based on experimental data. A very important application of system identification is in model-based control design. In such applications it is often possible to externally excite the system during the data collection experiment. The properties of the exciting input signal influence the quality of the identified model, and well-designed input signals can reduce both the experimental time and effort. The objective of this thesis is to develop algorithms and theory for minimum cost experiment design for system identification while guaranteeing that the estimated model results in an acceptable control performance. We will use the framework of application oriented Optimal Input Design (OID). First, we study how to find a convex approximation of the set of models that results in acceptable control performance. The main contribution is analytical methods to determine application sets for controllers with no explicit control law, for instance Model Predictive Control (MPC). The application oriented OID problem is then formulated in time domain to enable the handling of signals constraints, which often comes from the physical limitations on the plant and actuators. The framework is the extended to closed-loopsystems. Here two different cases are considered. The first case assumes that the plant is controlled by a general (either linear or non-linear) but known controller. The main contribution here is a method to design an external stationary signal via graph theory such that the identification requirements and signal constraints are satisfied. In the second case application oriented OID problem is studied for MPC. The proposed approach here is a modification of a results where the experiment design requirements are integrated to the MPC as a constraint. The main idea is to back off from the identification requirements when the control requirements are violating from their acceptable bounds. We evaluate the effectiveness of all the proposed algorithms by several simulation examples.
|
|
| 4. |
- Larsson, Erik, 1975-
(författare)
-
Identification of Stochastic Continuous-time Systems : Algorithms, Irregular Sampling and Cramér-Rao Bounds
- 2004
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The problem of identifying continuous-time systems is of fundamental interest in various areas, such as astrophysics, economics, control and signal processing. The most obvious reason for working with continuous-time models is that most physical systems are inherently continuous in time. Therefore, the parameters in the models often have a physical interpretation. The unifying theme of this thesis is identification of continuous-time stochastic systems using discrete-time data. Firstly, a thorough introduction to the topic is given. Basic concepts are described and previous results in the field are stated. A detailed description of various methods for identifying continuous-time systems is also provided. Secondly, some specific problems concerning identification of continuous-time autoregressive moving average (CARMA) processes, and continuous-time autoregressive (CAR) processes are studied. The effects of sampling a CARMA process are examined in detail. For example, more precise expressions than those available in the literature for how the zeros are transformed under sampling are derived. These results are then use in order to develop some simple schemes for estimating the parameters of CAR models. The more difficult problem of estimating the parameters of CARMA models is also treated. Irregular sampling is another major topic of this thesis. Some of the existing methods for identifying CAR processes are extended to handle the case of unevenly sampled data. The methods are computationally very efficient compared to standard methods for handling unevenly sampled data. Finally, the problem of computing the CRB for estimating the parameters of CAR and CARMA models, given arbitrary sampling patterns, is considered.
|
|
| 5. |
- Mahata, Kaushik, 1973-
(författare)
-
Estimation Using Low Rank Signal Models
- 2003
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.
|
|
| 6. |
- Rensfelt, Agnes, 1976-
(författare)
-
Viscoelastic Materials : Identification and Experiment Design
- 2010
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Viscoelastic materials can today be found in a wide range of practical applications. In order to make efficient use of these materials in construction, it is of importance to know how they behave when subjected to dynamic load. Characterization of viscoelastic materials is therefore an important topic, that has received a lot of attention over the years. This thesis treats different methods for identifying the complex modulus of an viscoelastic material. The complex modulus is a frequency dependent material function, that describes the deformation of the material when subjected to stress. With knowledge of this and other material functions, it is possible to simulate and predict how the material behaves under different kinds of dynamic load. The complex modulus is often identified through wave propagation testing, where the viscoelastic material is subjected to some kind of load and the response then measured. Models describing the wave propagation in the setups are then needed. In order for the identification to be accurate, it is important that these models can describe the wave propagation in an adequate way. A statistical test quantity is therefore derived and used to evaluate the wave propagation models in this thesis. Both nonparametric and parametric identification of the complex modulus is considered in this thesis. An important aspect of the identification is the accuracy of the estimates. Theoretical expressions for the variance of the estimates are therefore derived, both for the nonparametric and the parametric identification. In order for the identification to be as accurate as possible, it is also important that the experimental data contains as much valuable information as possible. Different experimental conditions, such as sensor locations and choice of excitation, can influence the amount of information in the data. The procedure of determining optimal values for such design parameters is known as optimal experiment design. In this thesis, both optimal sensor locations and optimal excitation are considered.
|
|
| 7. |
- Sorelius, Joakim, 1969-
(författare)
-
Subspace-Based Parameter Estimation Problems in Signal Processing
- 1999
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The effects of multipath-induced angular spread and non-zero band-width on narrow-band direction-of-arrival (DOA) estimation are investigated. In both cases expressions for the resulting estimation error are developed for the MUSIC, ESPRIT and WSF DOA estimators. The bias expressions are obtained by assuming that the source angular spread and the source bandwidth are small and by then performing a perturbation analysis on the covariance matrix of the array output.Blind (and semi-blind) linear equalizers for direct sequence code division multiple access (DS-CDMA) systems are derived, using multiple antennas in asynchronous intersymbol interference channels. An optimal, in the min-imum mean-square error (MMSE) sense, multi-user DS-CDMA receiver is estimated in a blind (and semi-blind) setting. Simple relations existing between DS-CDMA receivers at the symbol rate and at the chip rate are exploited and deterministic constraints are derived that can be used to determine these receivers in a blind manner, with small sample sizes. The chip rate receiver is shown to be close to a (non-blind) MMSE receiver.A number of subspace-based order estimation methodologies are presented and compared. The methods are all based on matrix rank tests of a Hankel matrix of covariances. Order estimation for both scalar and multi-variable autoregressive moving average (ARMA) processes is emphasized.
|
|
| 8. |
- Abd-Elrady, Emad
(författare)
-
Harmonic signal modeling based on the Wiener model structure
- 2002
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The estimation of frequencies and corresponding harmonic overtones is a problem of great importance in many situations. Applications can, for example, be found in supervision of electrical power transmission lines, in seismology and in acoustics. Generally, a periodic function with an unknown fundamental frequency in cascade with a parameterized and unknown nonlinear function can be used as a signal model for an arbitrary periodic signal. The main objective of the proposed modeling technique is to estimate the fundamental frequency of the periodic function in addition to the parameters of the nonlinear function.The thesis is divided into four parts. In the first part, a general introduction to the harmonic signal modeling problem and different approaches to solve the problem are given. Also, an outline of the thesis and future research topics are introduced.In the second part, a previously suggested recursive prediction error method (RPEM) for harmonic signal modeling is studied by numerical examples to explore the ability of the algorithm to converge to the true parameter vector. Also, the algorithm is modified to increase its ability to track the fundamental frequency variations.A modified algorithm is introduced in the third part to give the algorithm of the second part a more stable performance. The modifications in the RPEM are obtained by introducing an interval in the nonlinear block with fixed static gain. The modifications that result in the convergence analysis are, however, substantial and allows a complete treatment of the local convergence properties of the algorithm. Moreover, the Cramér–Rao bound (CRB) is derived for the modified algorithm and numerical simulations indicate that the method gives good results especially for moderate signal to noise ratios (SNR).In the fourth part, the idea is to give the algorithm of the third part the ability to estimate the driving frequency and the parameters of the nonlinear output function parameterized also in a number of adaptively estimated grid points. Allowing the algorithm to automatically adapt the grid points as well as the parameters of the nonlinear block, reduces the modeling errors and gives the algorithm more freedom to choose the suitable grid points. Numerical simulations indicate that the algorithm converges to the true parameter vector and gives better performance than the fixed grid point technique. Also, the CRB is derived for the adaptive grid point technique.
|
|
| 9. |
- Bhikkaji, Bharath
(författare)
-
Model reduction for diffusion systems
- 2000
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Diffusion phenomena has been studied with a lot of interest, for a long time, due to its historical and practical significance. In the recent days it has thrown a lot of interest among control engineers, as more and more practical systems, varying from stock markets to environmental pollution, have been observed to involve diffusion.Diffusion systems are normally modeled by linear partial differential equations (LPDEs) of the form(1) ∂T(x,t)/∂t = £T(x,t),where £ is a second order linear spatial differential operator and T(x,t) is the physical quantity, whose variations in the spatial domain cause diffusion. To characterise diffusion phenomena, one has to obtain the solution of (1) either analytically or numerically. Note that, since (1) involves a second order spatial operator and a first order time derivative, one needs at least two boundary conditions in the spatial domain, x, and an initial condition at time t = 0, for determining T(x,t).LPDEs of the type (1) can be interpreted as infinite order linear time invariant (LTI) systems with inputs as boundary conditions. To compute the solution of (1) numerically, one has to approximate, explicitly or implicitly, the underlying infinite order system by a finite order system. Any numerical scheme, which computes the solution of (1), essentially approximates the underlying infinite order LTI system by a finite order LTI system. The efficiency of the approximation, for a given problem, varies for the different numerical schemes.In this thesis, we make an attempt to explore more about diffusion systems in general. As a starting point, we consider a simple case of one-dimensional heat diffusion across a homogeneous region. The resulting LPDE is first shown explicitly to be an infinite order dynamical system. An approximate solution is computed from a finite order approximation of the true infinite order dynamical system. In this thesis, we first construct the finite order approximations using certain standard PDE solvers based on Chebyshev polynomials. From these finite order approximations we choose the best one, from a model reduction perspective, and use it as a benchmark model. We later construct two more approximate models, by exploiting the given structure of the problem and we show by simulations that these models perform better than the chosen benchmark.
|
|
| 10. |
- Hong, Mei, 1972-
(författare)
-
Analysis of Some Methods for Identifying Dynamic Errors-in-variables Systems
- 2008
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A system where errors or noises are present on both the inputs and the outputs is called an errors-in-variables (EIV) system. EIV systems appear in industrial and agricultural processes, medical sciences, economical systems, biotechnology, as well as in many other areas. Until now, a considerable number of methods for identifying dynamic errors-in-variables systems have been proposed. This thesis studies the statistic properties of different EIV methods and explores the relationships between some of the existing methods. An EIV approach, based on a bias-compensated least squares scheme, is considered in this thesis. Three promising estimators are in focus, namely, Zheng's bias-eliminated least squares (BELS) methods, Frisch scheme methods and extended compensated least squares (ECLS) methods. A simplified form of the BELS equation is first proposed. The new equation will simplify the computation and the theoretical analysis. Next, an important relationship between the BELS, Frisch and ECLS methods is found. The defining non-linear equations used by these three methods are equivalent, providing that the same extended model is used. This means that despite the use of different techniques to solve these equations, the three methods will have the same asymptotic estimation accuracy. Furthermore, the thesis studies the convergence properties of BELS. An alternative BELS algorithm is proposed, which has less of a divergence problem under low SNR situations as compared to the classic BELS methods. Another important problem which is investigated in the thesis is the asymptotic accuracy of the estimates. For the BELS method and a third-order cumulants based method, explicit expressions for the covariance matrices of the parameter estimates are derived. With such expressions available, one may obtain insight into how different user choices in the algorithms influence the accuracy. By using the expressions for the covariance matrices, comparisons of the estimation accuracies are made between three Frisch methods and between the time-domain maximum likelihood method and the sample maximum likelihood method. Finally, identification of errors-in-variables systems with periodic input signals is considered. How to utilize the periodic data and how to design instrumental variables in order to achieve the optimal estimation accuracy are analyzed as well.
|
|
