Ce travail porte sur la détection de l’endommagement de matériaux composites. Une première partie concerne l’élaboration de méthodes permettant d’estimer les termes sources de chaleur d’un matériau sollicité mécaniquement. Lors de ce processus, un ensemble de défauts mécaniques mènent à des productions de chaleur. La détection des sources peut permettre la détection de ces défauts. Deux principales méthodes sont présentées : une méthode dite « directe » basée sur une discrétisation du champ de température mesuré et une méthode « itérative » basée sur la méthode du gradient conjugué. A ces méthodes sont couplées des techniques de filtrages des données comme la SVD. Les équations sont résolues par différences finies sous leur forme linéaire. Des modifications sont apportées à l’algorithme itératif pour améliorer sa convergence ainsi que les résultats. Les problématiques envisagées font partie des problèmes inverses en thermique. L’objectif de la première partie est de trouver un lien entre l’apparition de macro-fissure et la localisation de termes sources de chaleur au sein d’un matériau composite. La seconde partie consiste à élaborer des méthodes d’estimation des diffusivités thermiques directionnelles. Les méthodes reposent sur une modélisation du transfert de chaleur à l’aide des quadripôles thermiques. Les estimations de paramètres sont réalisées sur des zones ciblées à risque sur un matériau déjà endommagé. Le but est de faire le lien entre un endommagement mécanique connu diffus et une dégradation des propriétés thermiques. Ce manuscrit est présenté en deux parties : une partie de validation des méthodes. Une partie expérimentale où sont analysés les composites. / This work deals with the damage detection of composite materials. These materials are used in the aeronautics industry. The first part concerns the development of methods to estimate the heat sources terms of a stressed material. During this process, a set of mechanical defects leads to heat productions. The sources detection can conduct to the detection of these defects. Two main methods are presented: a "direct" method based on a discretization of the measured temperature field and an "iterative" method based on the conjugate gradient method. These methods are coupled with data filtering techniques such as SVD. In order to optimize computation time, equations are solved by finite differences in their linear form. Modifications are also made for the iterative algorithm to improve its convergence as well as the results of the estimation. These problems are considered as thermal inverse problems. The main objective of the first part is to find an experimental link between the appearance of a macro fissure and the localization of a heat source term within a composite material. The second part consists in the elaboration of methods for estimating thermal directional diffusivities. The methods are based on a modeling of heat transfer using thermal quadrupoles. Parameter estimations are made on targeted "risked" areas on a material, which is already damaged but not under stress. The aim is to link a known mechanical damage, which is called "diffuse" to thermal properties degradation in the main directions. This manuscript is presented in two parts: a validation part of the methods, and an experimental part in which composites are analyzed.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-09T13:48:15Z No. of bitstreams: 1 renanpiazzarolifinottiamaral.pdf: 1172046 bytes, checksum: eb7bf10c813d64fbddcc572d39aecfc5 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-22T16:10:30Z (GMT) No. of bitstreams: 1 renanpiazzarolifinottiamaral.pdf: 1172046 bytes, checksum: eb7bf10c813d64fbddcc572d39aecfc5 (MD5) / Made available in DSpace on 2018-01-22T16:10:30Z (GMT). No. of bitstreams: 1 renanpiazzarolifinottiamaral.pdf: 1172046 bytes, checksum: eb7bf10c813d64fbddcc572d39aecfc5 (MD5) Previous issue date: 2017-09-01 / - / This thesis presents and discusses improvements in the type-1 and singleton fuzzy logic system for dealing with classification problems. Two training methods are addressed, the scaled conjugate gradient, which uses the second order information approximating the multiplication of the Hessian matrix H by the directional vector v (i.e. Hv), and the same method using the differential operator R {.} to compute the exact value of Hv. Also, in order to adapt the fuzzy model to handle multiclass classification problems, it is developed a novel fuzzy model with a vector as output. All proposals are tested through the performance metrics analysis based on data sets provided by UCI Machine Learning Repository. The reported results show the high convergence speed and better classification rates of the proposed training methods than others presented in the literature. Additionally, the novel fuzzy model has a significant reduction in computational and classifier complexity, especially when the number of classes in classification problem increases.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-03-31T14:47:16Z No. of bitstreams: 1 fellipelaraaparecida.pdf: 20651270 bytes, checksum: 48e88feb961f8d1446229cf83d322c3e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T02:58:29Z (GMT) No. of bitstreams: 1 fellipelaraaparecida.pdf: 20651270 bytes, checksum: 48e88feb961f8d1446229cf83d322c3e (MD5) / Made available in DSpace on 2016-04-24T02:58:29Z (GMT). No. of bitstreams: 1 fellipelaraaparecida.pdf: 20651270 bytes, checksum: 48e88feb961f8d1446229cf83d322c3e (MD5) Previous issue date: 2013-04-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho tem como objetivo o desenvolvimento de um código computacional para otimização de geometria de clusters metálicos. Para a otimização das coordenadas foi utilizado o método do gradiente conjugado não linear. Foi utilizado o potencial Tight- Binding com aproximação de segundos momentos (TB-SMA). As estruturas estudadas foram construídas nas direções cristalográficas fundamentais [1 0 0], [1 1 0] e [1 1 1]. Foi utilizado, também, o cálculo da função de distribuição radial para apresentar a goemetria das estruturas otimizadas. Um estudo complementar de compressão e alongamento foi realizado para as estruturas não otimizadas e otimizadas para verificar o comportamento das curvas de stress-strain das mesmas. Deste último estudo podese verificar uma situação limite em que estrutura sobrevive sem sofrer deformações permanentes. / This work aims to develop a computer code for geometry optimization of metal clusters. For the optimization of the coordinates we used the nonlinear conjugate gradient method. To describe the interactions between atoms we used the tight-binding potential with the second moments approximations (TB-SMA). The studied structures were built on the fundamental crystallographic directions [1 0 0] [1 1 0] and [1 1 1]. In order to elucidate good optimized structures we used the radial distribution function calculations. An additional study of compression and stretching was performed for the non-optimized and optimized structures to verify the behavior of the stressstrain curves. The stress-strain curves have shown the threshold situation in which the structures survives without permanet deformations.

This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.

A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.

This paper concerns the solution of plate bending problems in domains composed of rectangles. Domain decomposition (DD) is the basic tool used for both the parallelization of the conjugate gradient method and the construction of efficient parallel preconditioners. A so-called Dirich- let DD preconditioner for systems of linear equations arising from the fi- nite element approximation by non-conforming Adini elements is derived. It is based on the non-overlapping DD, a multilevel preconditioner for the Schur-complement and a fast, almost direct solution method for the Dirichlet problem in rectangular domains based on fast Fourier transform. Making use of Xu's theory of the auxiliary space method we construct an optimal preconditioner for plate problems discretized by conforming Bogner-Fox-Schmidt rectangles. Results of numerical experiments carried out on a multiprocessor sys- tem are given. For the test problems considered the number of iterations is bounded independent of the mesh sizes and independent of the number of subdomains. The resulting parallel preconditioned conjugate gradient method requiresO(h^-2 ln h^-1 ln epsilon^-11) arithmetical operations per processor in order to solve the finite element equations with the relative accuracy epsilon.

Orientadores: Aurélio Ribeiro Leite de Oliveira, Marta Ines Velazco Fontova / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T12:49:39Z (GMT). No. of bitstreams: 1 Coelho_AlessandroFonsecaEsteves_M.pdf: 2659631 bytes, checksum: fc1bec925179612ee07a4aaef7092d8a (MD5) Previous issue date: 2011 / Resumo: Um método frequentemente utilizado para a solução de problemas de programação linear é o método de pontos interiores. Nestes métodos precisamos resolver sistemas lineares para calcular a direção de Newton a cada iteração. A solução desses sistemas consiste no passo de maior esforço computacional nos métodos de pontos interiores. A fatoração de Cholesky é a opção mais utilizada para resolver estes sistemas. Contudo, quando trabalhamos com problemas de grande porte, esta fatoração pode ser densa e torna-se inviável trabalhar com esses métodos. Nestes casos, uma boa opção consiste no uso de métodos iterativos precondicionados. Estudos anteriores utilizam o método dos gradientes conjugados precondicionado para obter uma solução destes sistemas. Particularmente, os sistemas originados dos métodos de pontos interiores, são, naturalmente, sistemas de equações normais. Porém, a versão padrão do método dos gradientes conjugados, não considera a estrutura de equações normais do sistema. Neste trabalho propomos a utilização de duas versões do método de gradientes conjugados precondicionado que consideram a estrutura de equações normais destes sistemas. Estas versões serão comparadas com a versão de gradientes conjugados precondicionada que não considera a estrutura de equações normais do sistema. Resultados numéricos com problemas de grande porte mostram que uma dessas versões é competitiva em relação à versão padrão / Abstract: An often used method for solving linear programming problems is the interior point method. In these methods we need to solve linear systems to compute the Newton search direction at each iteration. The solution of these systems is the procedure of most computational effort in interior point methods. The Cholesky factorization is the most often used method to solve these systems. However, when dealing with large scale problems, this factorization can be dense and it become impossible to apply such methods. In such cases, a good option is the use of preconditioned iterative methods. Previous studies have used the preconditioned conjugate gradient method to find the solution of these systems. Particularly, the systems arising from interior point methods are, naturally, systems of normal equations type. Nevertheless, the standard version of the conjugate gradient method, does not take into account the normal equations system structure. This study proposes the use of two versions of preconditioned conjugate gradient method considering the normal equations structure of these systems. These versions are compared with the preconditioned conjugate gradient version that does not consider that structure. Numerical results with large scale problems show that one of these versions is competitive with the standard one / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Two alternative technologies of communication inside a parallelized Conjugate-Gradient algorithm are presented and compared to the well known hypercubecommunication. The amount of communication is diskussed in detail. A large range of numerical results corroborate the theoretical investigations.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第17968号 / 情博第512号 / 新制||情||91(附属図書館) / 30798 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 西村 直志, 准教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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