Este trabalho apresenta uma nova metodologia para estimar parâmetros de geradores síncronos baseada na análise de sensibilidade de trajetória. Esta nova metodologia foi concebida com o objetivo de suplantar dificuldades de convergência que a metodologia de sensibilidade de trajetória tradicional apresenta devido a: (i) baixa robustez com relação aos valores iniciais dos parâmetros e ruído nas medidas, (ii) impossibilidade de lidar com singularidades que podem se apresentar nas equações algébricas do modelo de EAD (equações algébrica-diferenciais) que levam a inexistência de soluções, especialmente quando os parâmetros estão distantes dos valores verdadeiros. Apesar de ter sido desenvolvida para resolver o problema de estimação de parâmetros do gerador síncrono, a metodologia é geral e pode ser aplicada para uma classe grande de sistemas dinâmicos não-lineares. Neste sentido, a principal contribuição desta tese é a proposição de uma nova metodologia baseada na sensibilidade de trajetória para estimar parâmetros de sistemas dinâmicos não-lineares restritos, ou seja, modelados por EADs. Mais precisamente, relaxa-se a restrição de igualdade do sistema dinâmico, substituindo-a por uma formulação alternativa baseada na minimização da função algébrica do modelo de EAD. Uma segunda contribuição desta tese está relacionada à modelagem do gerador. Neste sentido...

Nesta dissertação estudamos uma versão do Teorema de Trotter-Kato que estabelece uma equivalência entre a continuidade, relativamente a um parâmetro, de operadores resolvente e a continuidade dos semigrupos lineares associados. Os operadores ilimitados envolvidos (geradores de semigrupos analíticos) estão definidos em espaços que variam com o parâmetro e isto nos leva a ter que comparar elementos de espaços de Banach diferentes. Este resultado é aplicado a um problema de Neumann em um domínio fino com fronteira altamente oscilante e que se degenera a um intervalo quando o parâmetro varia. Nesta aplicação, utilizamos o método das múltiplas escalas (comum em teoria de homogeneização) para obter formalmente o problema limite (veja [17]) e, em seguida, provamos a convergência compacta dos operadores resolventes utilizando as funções teste oscilantes de Tartar [15], [16] (veja também Cioranescu e Saint Jean Paulin [12]), obtidas através de um problema auxiliar, juntamente com operadores de extensão; In this work we study a version of Trotter-Katos Theorem that establishes an equivalence between the continuity, with respect to a parameter, of the resolvent operators and the continuity of the associated linear semigroups. The unbounded operators involved (generators of analytic semigroups) are defined spaces that vary with the parameter leading us to introduce methods to compare vectors in different Banach spaces. We apply this theorem to an elliptic boundary value problem with Neumann boundary condition in a highly oscillating thin domain that degenerates to a line segment as the parameter varies. In this application we use the multiple scale method (frequently used in the homogenization theory) to obtain...

Neste trabalho, uma abordagem micromecânica com aproximação da geometria dada por funções de Bézier triangulares com continuidade geométrica G1 é inserida ao Método dos Elementos de Contorno, o qual é aplicado em problemas da elastostática tridimensional. Para consideração do efeito microestrutural, foi utilizado a teoria gradiente elástica simplificada de Aifantis, a qual é uma particularização da teoria geral de Mindlin. Nesta teoria, um argumento variacional é estabelecido para determinar todas as possíveis condições de contorno, clássica e não-clássica, para o problema de valor de contorno geral. A partir deste argumento, a solução fundamental da elasticidade gradiente é explicitada e com o auxílio da identidade integral recíproca é construído a representação integral de contorno. Para tornar o problema de valor de contorno bem-posto, em adição à representação integral de contorno para deslocamento, uma segunda representação integral para derivada normal do deslocamento foi utilizada. Expressões integrais para deslocamento e tensão em pontos internos são apresentadas. Todos os núcleos das equações integrais são explicitamente desenvolvidos. Para a discretização do MEC foram utilizados elementos triangulares curvos...

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

We are not seeing faster progress against poverty amongst the poorest developing countries. Yet this is implied by widely accepted "stylized facts" about the development process. The paper tries to explain what is missing from those stylized facts. Consistently with models of economic growth incorporating borrowing constraints, the analysis of a new data set for 100 developing countries reveals an adverse effect on consumption growth of high initial poverty incidence at a given initial mean. A high incidence of poverty also entails a lower subsequent rate of progress against poverty at any given growth rate (and poor countries tend to experience less steep increases in poverty during recessions). Thus, for many poor countries, the growth advantage of starting out with a low mean ("conditional convergence") is lost due to their high poverty rates. The size of the middle class--measured by developing-country, not Western, standards--appears to be an important channel linking current poverty to subsequent growth and poverty reduction. However...

Comparing changes in inequality with initial levels, using new data, the author finds that within-country inequality in income or per capita consumption is converging toward medium levels--a Gini index around 40 percent. The finding is robust to allow for serially independent measurement error in inequality data and for short-run dynamics around longer-term trends. However, the convergence process is neither rapid nor certain, and more observations over time are needed to be confident of the pattern. The author offers an approach to modeling the determinants of inequality that may be a starting point for estimating richer models.

The AR(1) and power models of spatial correlation are popular in the analysis of field trial data. Numerical difficulties in estimation and interpretation of these models may occur when the autocorrelation parameter ρ tends to either zero or unity. These problems are considered here using three different examples. The first example is based on simulated data for a partially replicated design, where the true underlying variance-covariance structure is known. The other two examples involve real data from a precision farming trial and a plant breeding trial. We suggest four options to deal with the observed numerical problems and illustrate their use with the examples. It is shown in the examples that re-scaling of the spatial coordinates or a re-parameterization of the AR(1) model as an exponential model can be useful to help the model converge. We conclude that individual parameter estimates of the AR(1) model should be interpreted with care, especially when the autocorrelation estimate is close to either zero or unity.; Hans-Peter Piepho and Jens Möhring acknowledge support by DFG grant PI 377/13-1.

The management of Water Distribution Systems (WDSs) involves making decisions about various operations in the network, including the scheduling of pump operations and setting of disinfectant dosing rates. There are often conflicting objectives in making these operational decisions, such as minimising costs while maximising the quality of the water supplied. Hence, the operation of WDSs can be very difficult, and there is generally considerable scope to improve the operational efficiency of these systems by improving the associated decision making process. In order to achieve this goal, optimisation methods known as Genetic Algorithms (GAs) have been successfully adopted to assist in determining the best possible solutions to WDS optimisation problems for a number of years. Even though there has been extensive research demonstrating the potential of GAs for improving the design and operation of WDSs, the method has not been widely adopted in practice. There are a number of reasons that may contribute to this lack of uptake, including the following difficulties: (a) developing an appropriate fitness function that is a suitable description of the objective of the optimisation including all constraints, (b) making decisions that are required to select the most appropriate variant of the algorithm...

An important research area in computer vision is parameter estimation. Given a mathematical model and a sample of image measurement data, key parameters are sought to encapsulate geometric properties of a relevant entity. An optimisation problem is often formulated in order to find these parameters. This thesis presents an elaboration of fundamental numerical algorithms for estimating parameters of multi-objective models of importance in computer vision applications. The work examines ways to solve unconstrained and constrained minimisation problems from the view points of theory, computational methods, and numerical performance. The research starts by considering a particular form of multi-equation constraint function that characterises a wide class of unconstrained optimisation tasks. Increasingly sophisticated cost functions are developed within a consistent framework, ultimately resulting in the creation of a new iterative estimation method. The scheme operates in a maximum likelihood setting and yields near-optimal estimate of the parameters. Salient features of themethod are that it has simple update rules and exhibits fast convergence. Then, to accommodate models with functional dependencies, two variant of this initial algorithm are proposed. These methods are improved again by reshaping the objective function in a way that presents the original estimation problem in a reduced form. This procedure leads to a novel algorithm with enhanced stability and convergence properties. To extend the capacity of these schemes to deal with constrained optimisation problems...

In this paper, we employ low-rank matrix approximation to solve a general parameter estimation problem: where a non-linear system is linearized by treating the carrier terms as separate variables, thereby introducing heteroscedastic noise. We extend the bilinear approach to handle cases with heteroscedastic noise, in the framework of low-rank approximation. The ellipse fitting problem is investigated as a specific example of the general theory. Despite the impression given in the literature, the ellipse fitting problem is still unsolved when the data comes from a small section of the ellipse. Although there are already some good approaches to the problem of ellipse fitting, such as FNS and HEIV, convergence in these iterative approaches is not ensured, as pointed out in the literature. Another limitation of these approaches is that they cannot model the correlations among different rows of the “general measurement matrix”. Our method, of employing the bilinear approach to solve the general heteroscedastic parameter estimation problem, overcomes these limitations: it is convergent, at least to a local optimum, and can cope with a general heteroscedastic problem. Experiments show that the proposed bilinear approach performs better than other competing approaches: although it is still far short of a solution when the data comes from a very small arc of the ellipse.; Pei Chen and David Suter

In this paper, we study the parameter estimation problem in a general heteroscedastic linear system, by putting the problem in the framework of the bilinear approach to low-rank matrix approximation. The ellipse fitting problem is studied as a specific example of the general theory. Despite the impression given in the literature, the ellipse fitting problem is still unsolved when the data comes from a small section of the ellipse. Although there are already some good approaches to the problem of conic fitting, such as FNS and HEIV, convergence in these iterative approaches is not ensured, as pointed out in the literature. Another limitation of these approaches is that they can’t model the correlations among different rows of the “general measurement matrix”. Our method, of employing the bilinear approach to solve the general heteroscedastic parameter estimation problem, overcomes these limitations: it is convergent and can cope with a general heteroscedastic problem. Experiments show that the proposed bilinear approach performs slightly better than other competing approaches; Pei Chen and David Suter

The objective of this thesis is to study optimal control problems subject to equations arising in the field of fluid dynamics. This thesis is split into two essential parts. Each of them deals with an important partial differential equation, that are of interest in various applications and are widely considered in current research: The density dependent Navier--Stokes equation and the thin-film equation. These optimal control problems are motivated in many ways: First, the equations are mathematically interesting due to strong nonlinear effects occurring additionally as coupling effects in the context of optimization. Also, it is not immediate that properties (such as convergence of numerical approximations) are inherited by the optimal control problem. The literature on optimal control subject to nonlinear partial differential equation is rare, while the knowledge on those problems subject to the mentioned equations is even more rare: Only very few works are known, and the content of this thesis is a big contribution to this topic. Finally, for both control problems, there are industrial applications requiring the optimal control of fluid flows (which will also be addressed within the this thesis) such as the control of the interface in aluminum production...

Approved for public release; distribution is unlimited; In this thesis we present an algorithm for the precise determination of the Mie extinction efficiency parameter. The mathematical representation of the Mie parameters is in the form of an infinite series, and any technique that could be found to accelerate the convergence of the Mie series would have great commercial and military application. Results are presented that show the comparison of the rate of convergence obtained by directly summing the individual terms of the extinction efficiency parameter and the rate obtained using an existing series acceleration technique. It was found that the acceleration method we employed, known as the Levin method of series transformation, proved unsuccessful in accelerating the convergence of the Mie series. However, other acceleration techniques exist and should be explored. In this thesis we present an algorithm for the precise determination of the Mie extinction efficiency parameter. The mathematical representation of the Mie parameters is in the form of an infinite series, and any technique that could be found to accelerate the convergence of the Mie series would have great commercial and military application. Results are presented rate of convergence obtained by directly summing the individual terms of the extinction efficiency parameter and the rate obtained using an existing series acceleration technique. It was found that the acceleration method we employed...

The problem of parameter and state estimation of a class of nonlinear systems is addressed. An adaptive identifier and observer are used to estimate the parameters and the state variables simultaneously. The proposed method is derived using a new formulation. Uncertainty sets are defined for the parameters and a set of auxiliary variables for the state variables. An algorithm is developed to update these sets using the available information. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. In addition to its application in difficult estimation problems, the algorithm has also been adapted to handle fault detection problems. The technique of estimation is applied to two broad classes of systems. The first involves a class of continuous time nonlinear systems subject to bounded unknown exogenous disturbance with constant parameters. Using the proposed set-based adaptive estimation, the parameters are updated only when an improvement in the precision of the parameter estimates can be guaranteed. The formulation provides robustness to parameter estimation error and bounded disturbance. The parameter uncertainty set and the uncertainty associated with an auxiliary variable is updated such that the set is guaranteed to contain the unknown true values. The second class of system considered is a class of nonlinear systems with timevarying parameters. Using a generalization of the set-based adaptive estimation technique proposed...

A maioria dos trabalhos sobre convergência de renda pressupõe que os países são unidades geográficas isoladas, não considerando a interação espacial subjacente. Este artigo investiga a análise de convergência de renda entre países, incorporando o efeito de vizinhança proporcionado pela interação espacial, e, portanto, controlando-se para os efeitos espaciais, a saber, a dependência espacial e a heterogeneidade espacial observável e não observável. Para se conseguir isso, foram construídos modelos de painel de dados espacial para 148 países no período quinquenal entre 1985 e 2005. Os principais resultados revelam que o valor do parâmetro b se eleva consideravelmente quando se controla para os efeitos fixos e a dependência espacial. Ao não considerar os efeitos fixos e a autocorrelação espacial, o valor do b, o coeficiente que indica convergência, é consideravelmente subestimado e a meia-vida aumentada.; The moststudiesonincome convergenceimplythat countriesareisolated geographic units, not considering the underlying spatial interaction.This paper investigates theanalysis of income convergenceamong countries incorporing the neighborhood effect provided by the spatial interaction and, thereby, controlling forspatial dependenceand spatial heterogeneity.To do so...

Since Bayes' Theorem was first published in 1762, many have argued for the Bayesian paradigm on purely philosophical grounds. For much of this time, however, practical implementation of Bayesian methods was limited to a relatively small class of "conjugate" or otherwise computationally tractable problems. With the development of Markov chain Monte Carlo (MCMC) and improvements in computers over the last few decades, the number of problems amenable to Bayesian analysis has increased dramatically. The ensuing spread of Bayesian modeling has led to new computational challenges as models become more complex and higher-dimensional, and both parameter sets and data sets become orders of magnitude larger. This dissertation introduces methodological improvements to deal with these challenges. These include methods for enhanced convergence assessment, for parallelization of MCMC, for estimation of the convergence rate, and for estimation of normalizing constants. A recurring theme across these methods is the utilization of one or more chain-dependent partitions of the state space.

; Dissertation

Genetic Algorithms are powerful tools, which when set upon a solution space will search for the optimal answer. These algorithms though have some associated problems, which are inherent to the method such as pre-mature convergence and lack of population diversity. These problems can be controlled with changes to certain parameters such as crossover, selection, and mutation. This paper attempts to tackle these problems in GA by having another GA controlling these parameters. The values for crossover parameter are: one point, two point, and uniform. The values for selection parameters are: best, worst, roulette wheel, inside 50%, outside 50%. The values for the mutation parameter are: random and swap. The system will include a control GA whose population will consist of different parameters settings. While this GA is attempting to find the best parameters it will be advancing into the search space of the problem and refining the population. As the population changes due to the search so will the optimal parameters. For every control GA generation each of the individuals in the population will be tested for fitness by being run through the problem GA with the assigned parameters. During these runs the population used in the next control generation is compiled. Thus...

Gilbert, Robert; Guyenne, Philippe; In this work we use a finite difference scheme to solve relevant boundary value problems modeling ultrasound propagation through a cancellous bone specimen. In one boundary value problem we consider the bone as an orthotropic medium. In the second boundary value problem the bone is considered to be an isotropic medium. After the boundary value problems are solved numerically we perform various numerical tests to show convergence of the schemes. After convergence is exhibited we deem the problem suitable for performing an inverse problem where certain parameters of interest are tried to be recovered. In addition we develop a new model where we consider the bone specimen to be circular and we also add a layer of muscle to the configuration. For this model, we assume scattering of an infinite cylinder by an incoming plane compressional wave. Analytical solutions are derived using a Helmholtz type decomposition. In deriving the analytical solutions in this model, the solutions are assumed to be time harmonic. We recover time dependence by performing a numerical inverse fast Fourier transform. Plots of the radial displacements will be provided to suggest that the model is physically acceptable. Finally we propose a generalization of the circular problem by assuming the specimen contains a layer of cortical bone. Analytical solutions can still be derived in the time harmonic case. A method for generating these solutions is discussed using a generalization of a method proposed by Vekua.; University of Delaware...

In this paper we discuss parameter estimators for fully and partially observed discrete-time linear stochastic systems (in state-space form) with known noise characteristics. We propose finite-dimensional parameter estimators that are based on estimates of summed functions of the state, rather than of the states themselves. We limit our investigation to estimation of the state transition matrix and the observation matrix. We establish almost-sure convergence results for our proposed parameter estimators using standard martingale convergence results, the Kronecker lemma and an ordinary differential equation approach. We also provide simulation studies which illustrate the performance of these estimators.

We propose a recursive identification algorithm for a class of discrete-time linear hybrid systems known as Switched ARX models. The key to our approach is to view the identification of multiple ARX models as the identification of a single, though more complex, lifted dynamical model in a higher dimensional space. Since the dynamics of this lifted model do not depend on the value of the discrete state or the switching mechanism, we propose to use a standard recursive identifier in the lifted space. We derive persistence of excitation conditions on the input/output data guarantee the exponential convergence of the recursive identifier. Such conditions are a natural generalization of the well known result for ARX models. We then use the estimates of the lifted model parameters to build a homogenous polynomial whose derivatives at a regressor give an estimate of the parameters of the ARX model generating that regressor. Although our algorithm is designed for the case of perfect input/output data, our experiments also show its performance with noisy data.