The dissertation forms part of an ongoing project for the modelling and eventual control of an electric arc furnace (EAF) process. The main motivation behind such a project is the potential benefits that can result from automation of a process that has largely been operator controlled, often with results that leave sufficient room for improvement. Previous work in the project has resulted in the development of a generic model of the process. A later study concentrated on the control of the EAF where economic factors were taken into account. Simulation results from both studies clearly demonstrate the benefits that can accrue from successful implementation of process control. A major drawback to the practical implementation of the results is the lack of a model that is proven to be an accurate depiction of the specific plant where control is to be applied. Furthermore, the accuracy of any process model can only be verified against actual process data. There lies the raison d'etre for this dissertation: to take the existing model from the simulation environment to the real process. The main objective is to obtain a model that is able to mimic a selected set of process outputs. This is commonly a problem of system identification (SID): to select an appropriate model then fit the model to plant input/output data until the model response is similar to the plant under the same inputs (and initial conditions). The model fitting is carried out on an existing EAF model primarily by estimation of the model parameters for the EAF refining stage. Therefore the contribution of this dissertation is a model that is able to depict the EAF refining stage with reasonable accuracy. An important aspect of model fitting is experiment design. This deals with the selection of inputs and outputs that must be measured in order to estimate the desired parameters. This constitutes the problem of identifiability: what possibilities exist for estimating parameters using available I/O data or, what additional data is necessary to estimate desired parameters. In the dissertation an analysis is carried out to determine which parameters are estimable from available data. For parameters that are not estimable recommendations are made about additional measurements required to remedy the situation. Additional modelling is carried out to adapt the model to the particular process. This includes modelling to incorporate the oxyfuel subsystem, the bath oxygen content, water cooling and the effect of foaming on the arc efficiency. / Dissertation (MEng (Electronic Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted

This thesis presents the formulation and solution of a new problem in systems and control theory, called the Network Realization Problem. Its relationship to other problems, such as State Realization and Structural Identifiability, is shown. The motivation for this work is the desire to completely quantify the conditions for transitioning between different mathematical representations of linear time-invariant systems. The solution to this problem is useful for theorists because it lays a foundation for quantifying the information cost of identifying a system's complete network structure from the transfer function.

In the system identification community a popular framework for the problem of estimating a parametrized model structure given a sequence of input and output pairs is given by the prediction-error method. This method tries to find the parameters which maximize the prediction capability of the corresponding model via the minimization of some chosen cost function that depends on the prediction error. This optimization problem is often quite complex with several local minima and is commonly solved using a local search algorithm. Thus, it is important to find a good initial estimate for the local search algorithm. This is the main topic of this thesis. The first problem considered is the regressor selection problem for estimating the order of dynamical systems. The general problem formulation is difficult to solve and the worst case complexity equals the complexity of the exhaustive search of all possible combinations of regressors. To circumvent this complexity, we propose a relaxation of the general formulation as an extension of the nonnegative garrote regularization method. The proposed method provides means to order the regressors via their time lag and a novel algorithmic approach for the \textsc{arx} and \textsc{lpv-arx} case is given.   Thereafter, the initialization of linear time-invariant polynomial models is considered. Usually, this problem is solved via some multi-step instrumental variables method. For the estimation of state-space models, which are closely related to the polynomial models via canonical forms, the state of the art estimation method is given by the subspace identification method. It turns out that this method can be easily extended to handle the estimation of polynomial models. The modifications are minor and only involve some intermediate calculations where already available tools can be used. Furthermore, with the proposed method other a priori information about the structure can be readily handled, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models.   The final topic in this thesis is the initialization of discrete-time systems containing polynomial nonlinearities. In the continuous-time case, the tools of differential algebra, especially Ritt's algorithm, have been used to prove that such a model structure is globally identifiable if and only if it can be written as a linear regression model. In particular, this implies that once Ritt's algorithm has been used to rewrite the nonlinear model structure into a linear regression model, the parameter estimation problem becomes trivial. Motivated by the above and the fact that most system identification problems involve sampled data, a version of Ritt's algorithm for the discrete-time case is provided. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.

This thesis reports the identification of linear and nonlinear handling models for road vehicles starting from structural identifiability analysis, continuing with the experiments to acquire data on a vehicle equipped with a sensor set and data acquisition system and ending with the estimation of parameters using the collected data. The 2 degrees of freedom (dof) linear model structure originates from the well known linear bicycle model that is frequently used in handling analysis of road vehicles. Physical parameters of the bicycle model structure are selected as the unknown parameter set that is to be identified. Global identifiability of the model structure is analysed, in detail, and concluded according to various available sensor sets. Physical parameters of the bicycle model structure are estimated using prediction error estimation method. Genetic algorithms are used in the optimization phase of the identification algorithm to overcome the difficulty in the selection of initial values for parameter estimates. Validation analysis of the identified model is also presented. Identified model is shown to track the system response successfully. Following the linear model identification, identification of 3 dof nonlinear models are studied. Local identifiability analysis is done and optimal input is designed using the same procedure for linear model structure identification. Practical identifiability analysis is performed using Fisher Information Matrix. Physical parameters are estimated using the data from simulated experiments. High accuracy estimates are obtained. Methodology for nonlinear handling model identification is presented.

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

Differential-algebraic equations (DAEs) form the natural way in which models of physical systems are delivered from an object-oriented modeling tool like Modelica. Differential-algebraic equations are also known as descriptor systems, singular systems, and implicit systems. If some constant parameters in such models are unknown, one might need to estimate them from measured data from the modeled system. This is a form of system identification called gray box identification. It may also be of interest to estimate the value of time-varying variables in the model. This is often referred to as state estimation. The objective of this work is to examine how gray box identification and estimation of time-varying variables can be performed for models described by differential-algebraic equations. If a model has external stimuli that are not measured or uncertain measurements, it is often appropriate to model this as stochastic processes. This is called noise modeling. Noise modeling is an important part of system identification and state estimation, so we examine how well-posedness of noise models for differential-algebraic equations can be characterized. For well-posed models, we then discuss how particle filters can be implemented for estimation of time-varying variables. We also discuss how constant parameters can be estimated. When estimating time-varying variables, it is of interest to examine if the problem is observable, that is, if it has a unique solution. The corresponding property when estimating constant parameters is identifiability. In this thesis, we discuss how observability and identifiability can be determined for DAEs. We propose three approaches, where one can be seen as an extension of standard methods for state-space systems based on rank tests. For linear DAEs, a more detailed analysis is performed. We use some well-known canonical forms to examine well-posedness of noise models and to implement estimation of time-varying variables and constant parameters. This includes formulation of Kalman filters for linear DAE models. To be able to implement the suggested methods, we show how the canonical forms can be computed using numerical software from the linear algebra package LAPACK.

Vehicle handling models are commonly used in the design and analysis of vehicle dynamics. Especially, with the advances in vehicle control systems need for accurate and simple vehicle handling models have increased. These models have parameters, some of which are known or easily obtainable, yet some of which are unknown or difficult to obtain. These parameters are obtained by system identification, which is the study of building model from experimental data. In this thesis, identification of vehicle handling models is based on data obtained from the simulation of complex vehicle dynamics model from ADAMS representing the real vehicle and a general methodology has been developed. Identified vehicle handling models are the linear bicycle model and vehicle roll models with different tire models. Changes of sensitivity of the model outputs to model parameters with steering input frequency have been examined by sensitivity analysis to design the test input. To show that unknown parameters of the model can be identified uniquely, structural identifiability analysis has been performed. Minimizing the difference between the data obtained from the simulation of ADAMS vehicle model and the data obtained from the simulation of simple handling models by mathematical optimization methods, unknown parameters have been estimated and handling models have been identified. Estimation task has been performed using MATLAB Simulink Parameter Estimation Toolbox. By model validation it has been shown that identified handling models represent the vehicle system successfully.

<p>Progress in individualized drug treatment is of increasing importance, promising to avoid much human suffering and reducing medical treatment costs for society. The strategy is to maximize the therapeutic effects and minimize the negative side effects of a drug on individual or group basis. To reach the goal, interactions between the human body and different drugs must be further clarified, for instance by using mathematical models. Whether clinical studies or laboratory experiments are used as primary sources of information, greatly</p><p>influences the possibilities of obtaining data. This must be considered both prior and during model development and different strategies must be used. The character of the data may also restrict the level of complexity for the models, thus limiting their usage as tools for individualized treatment.</p><p>In this thesis work two case studies have been made, each with the aim to develop a model for a specific human-drug interaction. The first case study concerns treatment of inflammatory bowel disease with thiopurines, whereas the second is about treatment of ovarian cancer with paclitaxel. Although both case studies make use of similar amounts of experimental data, model development depends considerably on prior knowledge about the systems, the character of the data and the choice of modelling tools. All these factors are presented for</p><p>each of the case studies along with current results. Further, a system for classifying different but related models is also proposed with the intention that an increased understanding will contribute to advancement in individualized drug dosage.</p> / Report code: LiU-Tek-Lic-2007:41.

This thesis considers two distinct topics in phylogenetic analysis. The first is construction of empirical rate matrices for amino acid models. The second topic, which constitutes the majority of the thesis, involves analysis of and extensions to the BH model of Barry and Hartigan (1987). There are a number of rate matrices used for phylogenetic analysis including the PAM (Dayhoff et al. 1979), JTT (Jones et al. 1992) and WAG (Whelan and Goldman 2001). The construction of each of these has difficulties. To avoid adjusting for multiple substitutions, the PAM and JTT matrices were constructed using only a subset of the data consisting of closely related species. The WAG model used an incomplete maximum likelihood estimation to reduce computational cost. We develop a modification of the pairwise methods first described in Arvestad and Bruno that better adjusts for some of the sparseness difficulties that arise with amino acid data. The BH model is very flexible, allowing separate discrete-time Markov processes to occur along different edges. We show, however, that an identifiability problem arises for the BH model making it difficult to estimate character state frequencies at internal nodes. To obtain such frequencies and edge-lengths for BH model fits, we define a nonstationary GTR (NSGTR) model along an edge, and find the NSGTR model that best approximates the fitted BH model. The NSGTR model is slightly more restrictive but allows for estimation of internal node frequencies and interpretable edge lengths. While adjusting for rates-across-sites variation is now common practice in phylogenetic analyses, it is widely recognized that in reality evolutionary processes can change over both sites and lineages. As an adjustment for this, we introduce a BH mixture model that not only allows completely different models along edges of a topology, but also allows for different site classes whose evolutionary dynamics can take any form.

Engineers who develop fundamental models for chemical processes are often unable to estimate all of the model parameters due to problems with parameter identifiability and estimability. The literature concerning these two concepts is reviewed and techniques for assessing parameter identifiability and estimability in nonlinear dynamic models are summarized. Modellers often face estimability problems when the available data are limited or noisy. In this situation, modellers must decide whether to conduct new experiments, change the model structure, or to estimate only a subset of the parameters and leave others at fixed values. Estimating only a subset of important model parameters is a technique often used by modellers who face estimability problems and it may lead to better model predictions with lower mean squared error (MSE) than the full model with all parameters estimated. Different methods in the literature for parameter subset selection are discussed and compared. An orthogonalization algorithm combined with a recent MSE-based criterion has been used successfully to rank parameters from most to least estimable and to determine the parameter subset that should be estimated to obtain the best predictions. In this work, this strategy is applied to a batch reactor model using additional data and results are compared with computationally-expensive leave-one-out cross-validation. A new simultaneous ranking and selection technique based on this MSE criterion is also described. Unfortunately, results from these parameter selection techniques are sensitive to the initial parameter values and the uncertainty factors used to calculate sensitivity coefficients. A robustness test is proposed and applied to assess the sensitivity of the selected parameter subset to the initial parameter guesses. The selected parameter subsets are compared with those selected using another MSE-based method proposed by Chu et al. (2009). The computational efforts of these methods are compared and recommendations are provided to modellers. / Thesis (Master, Chemical Engineering) -- Queen's University, 2011-09-27 10:52:31.588