Orientador: Petronio Pulino / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-23T01:06:26Z (GMT). No. of bitstreams: 1 RodriguezMiranda_JuanCarlos_M.pdf: 6493367 bytes, checksum: 4c92920b543f2973fc3063991c696c72 (MD5) Previous issue date: 2013 / Resumo: O Método dos Elementos Finitos representou nos últimos anos uma ferramenta fundamental no estudo de problemas de contorno. A evolução desde sua formulação fundamental a partir do Método de Galerkin clássico até sua versão com refinamento hp, se tornou na base dos métodos numéricos mais avançados como é o Método de Galerkin Descontinuo. O Método dos Elementos Finitos de Alta Ordem juntamente com os Métodos Espectrais usados na obtenção de soluções numéricas para problemas de contorno com fronteira descontinua, serão nosso objeto de estudo nesta Dissertação. Desde sua formulação matemática fundamental, por intermédio da escolha apropriada das funções hierárquicas que compõem os espaços de aproximação, assim como a montagem dos sistemas lineares locais e sua respectiva utilização no sistema linear global esparso, cuja solução é obtida pelo método iterativo de Gradiente Conjugado usando diversos Precondicionadores, será o caminho a seguir / Abstract: The Finite Element Method developed in the last decades has been the most important tool in the study of Boundary Value Problems. Your evolution from its fundamental formulation using the Galerkin Method to the hp-adaptive finite element methods (hp-FEM), provided the necessary foundation for more advanced Numerical Methods like the Galerkin Discontinuous Method. The Finite Element Method of Higher Order, together with the Spectral formulation as a numerical method to solve Boundary Problems with Discontinuous Boundary, is the objective of study to this dissertation. The fundamental mathematical formulation of the finite element methods, passing through of to choose of hierarchical basis functions, also the assembly of local linear systems and it posteriorly use to construct a Sparse Linear System, whose solution is obtained for an iterative Preconditioner Gradient Method / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

La porosité d'une plaque composite carbone / époxy de type RTM est connue par tomographie X. Une méthode de détermination de cette porosité par mesure de l'atténuation des ondes longitudinales à travers l'épaisseur de cette plaque est proposée. Ces mesures sont effectuées sur des surfaces de dimensions variables (quelques cm2 à quelques mm2) et permettent l’obtention de cartographies. Une correspondance porosité (tomo X) – atténuation (onde US) est déduite et analysée en fonction de la structure du matériau composite. Dans chaque cas, on estime la qualité des relations obtenues et on en déduit les limites de validité de la correspondance porosité-atténuation. Des premiers résultats de tomographie acoustiques sont obtenus. / The porosity of a composite plate in carbon / epoxy of type RTM is known by used of tomography X. A method of determination of this porosity by measure of the mitigation of the longitudinal waves through the thickness of this kind of plate is proposed. These measures are made on surfaces of different sizes (from some cm2 to some mm2) and allow the obtaining of cartographies. A correspondence porosity (tomo X) - Mitigation (US wave) is deducted and analyzed according to the structure of the composite material. In every case, we estimate the quality of the obtained relations and we deduct the limits of validity of the correspondence between porosity and mitigation. First results of acoustic tomography are obtained.

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This thesis covers the development of a series of new methods and the application of adaptive filter theory which are combined to produce a generalised adaptive filter system which may be used to perform such tasks as pattern recognition. Firstly, the relevant background adaptive filter theory is discussed in Chapter 1 and methods and results which are important to the rest of the thesis are derived or referenced. Chapter 2 of this thesis covers the development of a new adaptive algorithm which is designed to give faster convergence than the LMS algorithm but unlike the Recursive Least Squares family of algorithms it does not require storage of a matrix with n2 elements, where n is the number of filter taps. In Chapter 3 a new extension of the LMS adaptive notch filter is derived and applied which gives an adaptive notch filter the ability to lock and track signals of varying pitch without sacrificing notch depth. This application of the LMS filter is of interest as it demonstrates a time varying filter solution to a stationary problem. The LMS filter is next extended to the multidimensional case which allows the application of LMS filters to image processing. The multidimensional filter is then applied to the problem of image registration and this new application of the LMS filter is shown to have significant advantages over current image registration methods. A consideration of the multidimensional LMS filter as a template matcher and pattern recogniser is given. In Chapter 5 a brief review of statistical pattern recognition is given, and in Chapter 6 a review of relevant connectionist models. In Chapter 7 the generalised adaptive filter is derived. This is an adaptive filter with the ability to model non-linear input-output relationships. The Volterra functional analysis of non-linear systems is given and this is combined with adaptive filter methods to give a generalised non-linear adaptive digital filter. This filter is then considered as a linear adaptive filter operating in a non-linearly extended vector space. This new filter is shown to have desirable properties as a pattern recognition system. The performance and properties of the new filter is compared with current connectionist models and results demonstrated in Chapter 8. In Chapter 9 further mathematical analysis of the networks leads to suggested methods to greatly reduce network complexity for a given problem by choosing suitable pattern classification indices and allowing it to define its own internal structure. In Chapter 10 robustness of the network to imperfections in its implementation is considered. Chapter 11 finishes the thesis with some conclusions and suggestions for future work.

L'augmentation des performances des futurs systèmes dynamiques nécessite la prise en compte des phénomènes physiques non linéaires. Cette thèse apporte un éclairage et des contributions sur deux sujets complémentaires liés aux phénomènes dynamiques non linéaires. Le mémoire de thèse est divisé en deux parties.La première partie porte sur les non-linéarités des amplificateurs de puissance dans le cadre d'applications destinées aux télécommunications ou à la diffusion audio-visuelle. Plusieurs méthodes de modélisation et de linéarisation des amplificateurs de puissance ont été conçues et discutées. Un banc de test a été développé afin d'évaluer les méthodes sur des amplificateurs réels. La robustesse de ces techniques à un mauvais alignement temporel des signaux ainsi que leur capacité à faire face à des artefacts spectraux ont été évaluées. Par ailleurs, nous avons effectué une étude théorique sur l'existence et la prise en compte de solutions multiples dans l'approche adaptative par apprentissage indirect. La deuxième partie traite des systèmes dynamiques non linéaires qui présentent des solutions chaotiques. Ces systèmes sont bien connus, mais les techniques d'identification de ces solutions manquent de fiabilité ou nécessitent une puissance de calcul importante. Dans cette thèse, plusieurs méthodes utilisant également le calcul parallèle sont présentées. Les systèmes à commande différentielle fractionnaire sont brièvement discutés. Il est aussi montré, qu'il existe des systèmes liés à des fonctions de transfert non linéaires avec quantification pour lesquels les méthodes d'analyse classiques échouent / In order to achieve better performance of modern communication devices, that have to be operated on its physical limits, the nonlinear phenomena need to be taken into the account. This thesis brings insight into two different subjects related with nonlinear dynamical phenomena. The thesis itself is divided into two parts : the first part is focused on the domain of nonlinear power amplifiers from the system point of view. Several methods for modelization and linearization of power amplifiers have been designed and discussed. A test-bench has been assembled in order to evaluate the proposed methods on real power amplifiers. Then the robustness to time misalignment in the system and the ability to deal with spectral artifacts in the system of presented methods have been evaluated. Also a theoretical study has been conducted on the existence and management of multiple solutions in the frame of adaptive indirect learning approach. The second part deals with nonlinear dynamical systems that are exhibiting chaotic solutions. Such systems are well known, but techniques for identifying reliable such solutions are either missing or are computational intense. In this thesis several methods using also parallel computing are presented. Systems with fractional differential order are briefly discussed. It is as well shown, that there exists systems related with quantified nonlinear transfer functions for which the standard analyzing methods fails

Orientadores: Christiano Lyra Filho, Aurelio Ribeiro Leite de Oliveira / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-27T01:38:37Z (GMT). No. of bitstreams: 1 Casacio_Luciana_D.pdf: 3240577 bytes, checksum: f49bb4444bbbfacf0559d3b88d8feee5 (MD5) Previous issue date: 2015 / Resumo: A solução de problemas de otimização linear através de métodos de pontos interiores envolve a solução de sistemas lineares. Esses sistemas quase sempre possuem dimensões elevadas e alto grau de esparsidade em aplicações reais. Para solução, tipicamente são realizadas operações algébricas que os reduzem a duas formulações mais simples: uma delas, conhecida por "sistema aumentado", envolve matrizes simétricas indefinidas e geralmente esparsas; a outra, denominada "sistema de equações normais", usa matrizes de menor dimensão, simétricas e definidas positivas. A solução dos sistemas lineares é a fase que requer a maior parte do tempo de processamento dos métodos de pontos interiores. Consequentemente, a escolha dos métodos de solução é de extrema importância para que se tenha uma implementação eficiente. Normalmente, aplicam-se métodos diretos para a solução como, por exemplo, a fatoração de Bunch-Parllett ou a fatoração de Cholesky. No entanto, em problemas de grande porte, o uso de métodos diretos torna-se desaconselhável, por limitações de tempo e memória. Nesses casos, abordagens iterativas se tornam mais atraentes. O sucesso da implementação de métodos iterativos depende do uso de bons precondicionadores, pois a matriz de coeficientes torna-se muito mal condicionada, principalmente próximo da solução ótima. Uma alternativa para tratar o problema de mal condicionamento é o uso de abordagens híbridas com duas fases: a fase I utiliza um precondicionador para o sistema de equações normais construído com informações de fatorações incompletas, denominado fatoração controlada de Cholesky; a fase II, utilizada nas últimas iterações, adota o precondicionador separador desenvolvido especificamente para sistemas mal condicionados. O trabalho propõe um novo critério de ordenamento das colunas para construção do precondicionador separador, que preserva a estrutura esparsa da matriz de coeficientes original. Os resultados teóricos desenvolvidos mostram que a matriz precondicionada tem o número de condição limitado quando o ordenamento proposto é adotado. Experimentos computacionais realizados com todos os problemas da biblioteca NETLIB mostram que a abordagem é competitiva com métodos diretos e que o número de condição da matriz precondicionada é muito menor do que o da matriz original. Foram também realizadas comparações com a abordagem híbrida anterior, baseada em precondicionadores que reduzem a esparsidade do sistema de equações. Esses experimentos confirmaram o bom desempenho da metodologia em relação ao número de iterações dos métodos de pontos interiores, aos tempos computacionais e à qualidade das soluções. Esses benefícios foram obtidos com a preservação da esparsidade dos sistemas de equações, o que destaca a adequação da abordagem proposta para a solução de problemas de grande porte / Abstract: The solution of linear optimization problems through interior point methods involves the solution of linear systems. These systems often have high dimensions and high sparsity degree, specially in real applications. Typically algebraic operations are performed to reduce the systems in two simpler formulations: one of them is known as the augmented system, and the other one, referred as normal equation systems, has a smaller dimension matrix which is symmetric positive definite. The solution of linear systems is the interior point methods step that requires most of the processing time. Consequently, the choice of the solution methods are extremely important in order to have an efficient implementation. Usually, direct methods are applied for solving these systems as, for example, Bunch-Parllett factorization or Cholesky factorization. However, in large scale problems, the use of direct methods becomes discouraging by limitations of time and memory. In such cases, iterative approaches are more attractive. The success of iterative method approaches depends on good preconditioners once the coefficient matrix becomes very ill-conditioned, especially close to an optimal solution. An alternative to treat the problem of ill conditioning is to use hybrid approaches with two phases: phase I uses a preconditioner for the normal equation systems built with incomplete factorizations information, called controlled Cholesky factorization; phase II, used in the final iterations, adopts the splitting preconditioner, which was developed specifically for such ill conditioned systems. This work proposes a new ordering criterion for the columns of the splitting preconditioner that preserves the sparse structure of the original coefficient matrix. Theoretical results show that the preconditioned matrix has a limited condition number when the proposed idea is adopted. Computational experiments performed with all NETLIB problems show that the approach is competitive with direct methods and the condition number of the preconditioned matrix is much smaller than the original matrix. Comparisons are also performed with the previous hybrid approach. These experiments confirm the good performance of the methodology. The final number of iterations, processing time and quality of solutions of interior point methods are suitable. These benefits are obtained preserving the sparse structure of the systems, which highlights the suitability of the proposed approach for large scale problems / Doutorado / Automação / Doutora em Engenharia Elétrica

Neste trabalho estudamos a estabilidade assintótica de Lagrange para duas classes de sistemas, sob as hipóteses de detetabilidade fraca e de limitação do custo medio a longo prazo. Para sistemas lineares com saltos markovianos com rudo aditivo, a equivalência entre estabilidade e as condições mencionadas sera provada. Para sistemas dinâmicos generalizados, provaremos a estabilidade sob uma condição adicional / In this work we study Lagrange asymptotic stability for two classes of systems, under conditions of weak detectability and boundedness of the long run average cost. For Markov jump linear systems with additive noise, the equivalence between stability and the aforementioned conditions is proved. For generalized dynamical systems, we prove stability under an additional condition

Neste trabalho estudamos um controlador denominado rastreador linear quadrático (RLQ) com custo médio de longo prazo (CMLP) para sistemas lineares com saltos markovianos (SLSM). Mostramos que o conceito de detetabilidade uniforme, juntamente com a hipótese de que o regulador linear quadrático associado ao RLQ tenha custo uniformemente limitado, são suficientes para que o controle obtido seja estabilizante em um certo sentido. A partir deste resultado, e considerando as mesmas hipóteses, demonstramos a existência do CMLP. Com isto, estendemos os resultados dispostos na literatura desde que consideramos um sistema variante no tempo e uma estrutura mais geral para a cadeia deMarkov. Além disto, avaliamos a aplicação deste controlador no planejamento da operação de um sistema hidrotérmico. Para isto, utilizamos o sistema de usinas do rio São Francisco, em dois casos de estudo, para comparar o desempenho do controlador estudado em relação à solução ótima para o problema, encontrada com o uso da programação dinâmica estocástica, e em relação à solução obtida via programação dinâmica determinística. Os resultados sugerem que o RLQ pode representar uma alternativa interessante para o problema de planejamento hidrotérmico / In the present work we study the reference tracking controller (RTC) for the long run average cost (LRAC) problem for Markov jump linear systems. We show that uniform detectability and an hypothesis that the linear quadratic regulator associated with the RTC has uniformly bounded cost, together, are sufficient conditions for the obtained control be exponentially stabilizing in a certain sense. This result allows us to demonstrate the existence of the LTAC under the same hypotheses. The results can be regarded as an extension of previous works, since we have considered a more general framework with time-varying systems and quite general Markov chains. As an applicatioin, we consider the operational planning of hydrothermal systems. We have considered some power plants of the Sao Francisco river, in two different scenarios, and we have compared the performances of the RTC and standard controls obtained by deterministic and stochastic dynamic programming, indicating that the RTC may be an interesting alternative for the hydrothermal planning problem

Dans cette thèse, nous nous intéressons à la contrôlabilité interne et à son coût pour une ou plusieurs équations aux dérivées partielles conservatives. ?Dans la première partie, nous introduisons et détaillons deux méthodes permettant d'estimer le coût du contrôle (et par dualité, de la constante d'observabilité) de l'équation des ondes avec potentiel $l^{\infty}$ en dimension un d'espace. La première utilise la propagation des ondes le long des caractéristiques en s'appuyant sur le rôle symétrique de la variable de temps et d'espace. La deuxième méthode repose sur la décomposition spectrale de l'équation des ondes et sur l'utilisation des inégalités d'ingham. L'estimation de la constante d'observabilité se ramène alors à l'étude d'un problème d'optimisation faisant intervenir les vecteurs propres du laplacien-dirichlet avec potentiel. Nous fournissons ensuite des propriétés qualitatives sur le minimiseurs ainsi qu'une estimation du minimum ne dépendant que de la mesure de l'ensemble d'observation. ?Dans la deuxième partie, nous étudions la contrôlabilité de certains systèmes d'équations avec un nombre de contrôles réduits, autrement dit le nombre de contrôles est plus petit que le nombre d'équations. En particulier, nous caractérisons exactement les données initiales qui peuvent être contrôlées pour des systèmes d'équations couplées de type schrödinger et nous énonçons une condition nécessaire et suffisante de type kalman pour des systèmes d'équations des ondes couplées. La preuve repose sur une méthode de contrôle fictif combinée à la résolution algébrique d'un système sous-déterminé et sur certains résultats de régularité. / In this work, we focus on the internal controllability and its cost for some linear partial differential equations. In the first part, we introduce and describe two methods to provide precise estimates of the cost of control (and by duality, of the observability constant) for general one dimensional wave equations with potential. The first one is based on a propagation argument along the characteristics relying on the symmetrical roles of the time and space variables. The second one uses a spectral decomposition of the solution of the wave equation and ingham's inequalities. This relates the estimation of the observability constant to the study of an optimal problem involving dirichlet eigenfunctions of laplacian with potential. We provide some qualitative properties of the minimizers, and also precise bounds on the minimum. In the second part, we are concerned with the controllability of some systems of equations by a reduced number of controls (i.e. the number of controls is less that the number of equations). In particular, in the case of coupled systems of schrödinger equations, we exactly characterize the initial conditions that can be controlled and we give a necessary and sufficient condition of kalman type for the controllability of coupled systems of wave equations. The proof relies on the fictitious control method coupled with the proof of an algebraic solvabilityproperty for some related underdetermined system, as well as on some regularity results.

[pt] O desenvolvimento e/ou a adaptação de métodos numéricos para aplicação em análises computacionais de estabilidade de sistemas elétricos no domínio do tempo costumam despertar interesse em função das dificuldades de solução das equações diferenciais e algébricas (EDAs) que representam a rede e seus componentes. Condições de operações muito carregadas e compensadas dificultam a solução, devido, p.ex., ao mau condicionamento da matriz Jacobiana, instabilidade numérica e singularidade. Uma dessas dificuldades pode surgir durante a solução de equações não lineares, especificamente no problema linear do tipo Ax = b. Para contornar estas e outras dificuldades, a presente tese procurou contribuir no aspecto numérico do problema destacando a aplicação do método iterativo Resíduo Mínimo Generalizado - GMRES na solução do problema. Optou-se por trabalhar na qualidade do pré-condicionador construído com base na matriz Jacobiana calculada no início do processo de solução. Verificou-se que, se esta matriz estiver bem condicionada, a qualidade do pré-condicionador resultante dela é boa para o GMRES atingir a convergência em poucas iterações. Comprovou-se através de experimentos numéricos com diferentes sistemas-teste e diferentes condições de operação, que o condicionamento da matriz Jacobiana é melhorado se escalonada, normalizada e reordenada antes da construção do pré-condicionador, resultando, de fato, num pré-condicionador de boa qualidade, agindo positivamente no desempenho do GMRES e consequentemente no processo global de solução. / [en] The development and/or adaptation of numerical methods when applied to power systems stability computer simulations in time domain are of interest due to the difficulties related to the solution of the algebraic differential equations (ADEs) which represent the network and its components. The solution of networks operating under heavy load conditions and extremely compensated is difficult due to the ill-conditioning of the Jacobian matrix, numerical instability and singularity. It can happen, for instance, when solving linear problems of type Ax = b. In order to overcome this and other difficulties, this thesis aims to contribute in the numerical aspect of the problem applying the Generalized Minimal Residual method – GMRES to solve the problem. The idea is to work over the preconditioner quality constructed based on the Jacobian matrix. It is shown that, if this matrix is well conditioned, the quality of the resulting preconditioner is good enough to the GMRES reaches convergence in few iterations. It is seen through numerical experiments using different test-systems and different operating conditions as well, that the Jacobian matrix conditioning is improved if scaled, normalized and reordered before the preconditioner construction, resulting, in fact, in a high quality preconditioner, improving the GMRES performance.