Tradicionalmente, a técnica de síntese aditiva com funções base de Fourier é a que tem apresentado melhores resultados no que diz respeito à qualidade dos sons gerados. Entretanto, a carga computacional imposta por esta técnica é extremamente alta, dificultando assim a sua implementação em tempo real. Substituindo as funções de Fourier por outras mais complexas, derivadas das técnicas estatísticas de Karhunen-Loève, consegue-se uma redução na quantidade de operações necessárias. Neste trabalho foi estudado e implementado em microcomputador um modelo de síntese aditiva baseada em análise utilizando a transformada de Karhunen-Loève. / Traditionally, the Fourier based aditive synthesis is the method that have achieved the best results concerning to the quality of the generated sounds. However, the computacional load imposed by this technique is extremely high, difliculting its real time implementation. Substituting the Fourier functions by another set of more complex functions, derived from the Karhunen-Loève statistical techniques, one achieves a reduction on the amount of the necessary operations so as to viabilize its real time implementation.

The Karhunen–Loève Transform (KLT) is prevalent nowadays in communication and signal processing. This thesis aims at attaining the KLT in the encoders and achieving the minimum sum rate in the case of Gaussian multiterminal source coding. In the general multiterminal source coding case, the data collected at the terminals will be compressed in a distributed manner, then communicated the fusion center for reconstruction. The data source is assumed to be a Gaussian random vector in this thesis. We introduce the rate-distortion function to formulate the optimization problem. The rate-distortion function focuses on achieving the minimum encoding sum rate, subject to a given distortion. The main purpose in the thesis is to propose a distributed KLT for encoders to deal with the sampled data and produce the minimum sum rate. To determine the distributed Karhunen–Loève transform, we propose three kinds of algorithms. The rst iterative algorithm is derived directly from the saddle point analysis of the optimization problem. Then we come up with another algorithm by combining the original rate-distortion function with Wyner's common information, and this algorithm still has to be solved in an iterative way. Moreover, we also propose algorithms without iterations. This kind of algorithms will generate the unknown variables from the existing variables and calculate the result directly.All those algorithms can make the lower-bound and upper-bound of the minimum sum rate converge, for the gap can be reduced to a relatively small range comparing to the value of the upper-bound and lower-bound. / Thesis / Master of Applied Science (MASc)

The design of a face recognition system ( FRS ) can been separated into two major modules ¡V face detection and face recognition. In the face detection part, we combine image pre-processing techniques with maximum-likelihood estimation to detect the nearest frontal face in a single image. Under limited restrictions, our detection method overcomes some of the challenging tasks, such as variability in scale, location, orientation, facial expression, occlusion ( glasses ), and lighting change. In the face recognition part, we use both Karhunen-Loeve transform and linear discrimant analysis ( LDA ) to perform feature extraction. In this feature extraction process, the features are calculated from the inner products of the original samples and the selected eigenvectors. In general, as the size of the face database is increased, the recognition time will be proportionally increased. To solve this problem, hard-limited Karhunen-Loeve transform ( HLKLT ) is applied to reduce the computation time in our FRS.

[pt] Nesta tese, as vibrações não-lineares e a estabilidade de uma casca cilíndrica contendo um fluido são estudadas com base em modelos de dimensão reduzida, isto é, modelos com um número reduzido de graus de liberdade. A partir dos funcionais de energia potencial e cinética de uma casca cilíndrica, deduzem-se suas equações de movimento. O campo de deformações da casca cilíndrica segue a teoria não- linear de Donnell para cascas abatidas. O fluido é considerado interno à casca irrotacional, não-viscoso e incompressível, sendo descrito a partir de um potencial de velocidade que leva em consideração a interação entre o fluido e a estrutura. Para resolver o sistema de equações de equilíbrio da casca, desenvolve-se um procedimento analítico que permite obter os campos de deslocamento axial e circunferencial em função dos deslocamentos laterais, além de atender as condições de contorno do problema. Desta forma, reduz-se o sistema de equações de equilíbrio a uma única equação diferencial parcial que é resolvida com o método de Galerkin. A determinação dos deslocamentos laterais é feita a partir de técnicas de perturbação que ordena os modos não-lineares de acordo com sua importância na solução da casca cilíndrica. Comprova-se essa ordenação através do método de Karhunen-Loève que fornece, também, uma expansão ótima para os deslocamentos laterais. Além dessas técnicas, apresenta-se uma redução polinomial que relacionam as amplitudes dos modos não-lineares com a amplitude do modo linear, criando uma expansão modal com 1 GDL. Apresentam-se respostas no tempo, fronteiras de instabilidade e diagramas de bifurcação para uma casca cilíndrica submetida a dois tipos de carregamentos harmônicos, pressão lateral e carga axial. A seguir, são propostos alguns critérios para a análise da a integridade do sistema dinâmico tanto para um sistema com 1 GDL quanto para um sistema multidimensional através da evolução e erosão das bacias de atração. Por fim, estuda-se o comportamento de cascas cilíndricas parcialmente cheias, mostrando a influência da altura do fluido nas fronteiras de instabilidade e curvas de ressonância da casca cilíndrica. / [en] The nonlinear vibrations and stability of a fluid-filled cylindrical shell is investigated using reduced order models. First, the nonlinear equations of motion of the cylindrical shell are deduced based on the expressions for the potential and kinetic energy, which are obtained using Donnell shallow shell theory. The internal fluid is considered to be irrotational, non- viscous and incompressible. It is described by a velocity potential that takes into account the fluid-shell interaction. A procedure is proposed to obtain analytically the axial and circumferential displacements of the shell, satisfying the in-plane equations of motion and the associated boundary conditions. So, the problem is reduced to one partial differential equation of motion which is solved by the Galerkin method. The transversal displacement field is obtained by perturbation techniques. This enables one to identify the relevance of each term in the nonlinear expansion of the vibration modes. Then, the Karhunen-Loève method is employed to investigate de relative importance of each mode obtained by the perturbation analysis on the nonlinear response and to deduce optimal interpolation function to be used in the Galerkin procedure. A SDOF model is also obtained by relating the modal amplitudes of the nonlinear modes to the vibration amplitude of the linear mode. Time responses, instability boundaries and ifurcation diagrams are obtained for cylindrical shells subjected to harmonic lateral and axial loads. Different procedures for the analysis of the shell integrity are proposed based on the evolution and erosion of the basins of attraction in state-space. Finally, the influence of the fluid height on the stability boundaries and resonance curves is studied.

Made available in DSpace on 2014-12-17T14:08:40Z (GMT). No. of bitstreams: 1 PedroHCF_DISSERT.pdf: 3177377 bytes, checksum: aee262ba866eb8f7862d4fdf2b03cfdf (MD5) Previous issue date: 2010-08-07 / In geophysics there are several steps in the study of the Earth, one of them is the processing of seismic records. These records are obtained through observations made on the earth surface and are useful for information about the structure and composition of the inaccessible parts in great depths. Most of the tools and techniques developed for such studies has been applied in academic projects. The big problem is that the seismic processing power unwanted, recorded by receivers that do not bring any kind of information related to the reflectors can mask the information and/or generate erroneous information from the subsurface. This energy is known as unwanted seismic noise. To reduce the noise and improve a signal indicating a reflection, without losing desirable signals is sometimes a problem of difficult solution. The project aims to get rid of the ground roll noise, which shows a pattern characterized by low frequency, low rate of decay, low velocity and high amplituds. The Karhunen-Lo?ve Transform is a great tool for identification of patterns based on the eigenvalues and eigenvectors. Together with the Karhunen-Lo?ve Transform we will be using the Singular Value Decomposition, since it is a great mathematical technique for manipulating data / Na geof?sica existem diversas etapas no estudo da Terra, uma delas ? o processamento de registros s?smicos. Esses registros s?o obtidos atrav?s de observa??es realizadas na superf?cie, sendo ?teis para informa??es sobre a estrutura e a composi??o das zonas inacess?veis em grandes profundidades. Grande parte das ferramentas e t?cnicas desenvolvidas para tais estudos tem sido aplicada em pesquisas acad?micas. O grande problema do processamento s?smico ? a energia indesejada, registrada pelos receptores que n?o trazem nenhum tipo de informa??o em rela??o aos refletores podendo mascarar as informa??es e/ou gerar informa??es erradas da subsuperf?cie. Essa energia indesejada ? conhecida como ru?do s?smico. Atenuar esse ru?do para melhorar um sinal que indica uma reflex?o, sem perder sinal desej?vel ? algumas vezes um problema de dif?cil solu??o. O projeto tem como objetivo a atenua??o do ru?do ground roll , o qual apresenta um padr?o caracterizado pela baixa freq??ncia, baixa velocidade de propaga??o e forte amplitude. A Transformada de Karhunen-Lo?ve ? uma ?tima ferramenta para identifica??o de padr?es baseada nos autovalores e autovetores. Em conjunto com a Transformada de Karhunen-Lo?ve ser? utilizado a Decomposi??o em Valores Singulares, j? que a mesma ? uma ?tima t?cnica matem?tica para manipula??o dos dados

Ce travail de thèse est une contribution à l’analyse de santé structurale de la caisse de véhicules militaires terrestres à roues. Appartenant à la gamme 20 - 30 tonnes, de tels véhicules sont déployés dans des contextes opérationnels variés où les conditions de roulage sont sévères et difficilement caractérisables. De plus, faisant face à la concurrence, la fonction mobilité des véhicules est acquise auprès de fournisseurs et n’est plus développée par Nexter Systems. De ce fait, la définition complète de cette fonction n’est plus connue. S’appuyant sur ce contexte, l’objectif principal de la thèse est d’aborder l’état de santé de la structure porteuse par approche probabiliste, afin de maitriser les techniques de calcul permettant la prise en compte de l’aléa intrinsèque des chargements liés à la diversité d’emploi des véhicules militaires terrestres. En particulier, les stratégies les plus pertinentes pour propager les incertitudes de roulage au sein d’un modèle mécanique d’un véhicule terrestre sont définies. Ces travaux décrivent comment il est possible d’exploiter une grandeur d’intérêt au sein du véhicule dans un objectif d’évaluation de la fiabilité par rapport à un critère de dommage donné. Une application sur un démonstrateur entièrement conçu par Nexter Systems illustre l’approche proposée. / This thesis is a contribution to the structural health analysis of the body of ground military vehicles. Belonging to the 20 - 30 tons range, such vehicles are deployed in a variety of operational contexts where driving conditions are severe and difficult to characterize. In addition, due to a growing industrial competition, the mobility function of vehicles is acquired from suppliers and is no longer developed by Nexter Systems. As a result, the complete definition of this function is unknown. Based on this context, the main objective of this thesis is to analyze the health of the vehicle body using a probabilistic approach in order to control the calculation techniques allowing to take into account the random nature of loads related to the use of ground military vehicles. In particular, the most relevant strategies for propagating uncertainties due to the terrain within a vehicle dynamics model are defined. This work describes how it is possible to manage an observation data measured in the vehicle for the purpose of assessing the reliability with respect to a given damage criterion. An application on a demonstrator entirely designed by Nexter Systems illustrates the proposed approach.

[pt] Neste trabalho a Análise de Vibrações é tratada no contexto da formulação fraca. Um sistema contínuo é formulado abstratamente em um espaço de Hilbert e uma base de projeção é escolhida para a dinâmica. Um esquema de convergência para a aproximação é garantido à medida em que se aumenta o número de funções da base usada para representar a resposta do problema. Esta é a idéia por traz de métodos como o Método dos Elementos Finitos e o Método dos Modos Supostos, que derivam do Método de Galerkin. Esta estratégia é diferente do que comumente é ensinado nos cursos de vibrações, onde um sistema massa-mola é analisado, e sistemas discretos formados por massas, molas e amortecedores são discutidos. Nestes casos não se sabe qual é o erro cometido na análise numérica. A Análise de Vibrações é muito usada na manutenção preditiva de máquinas rotativas. Alguns fenômenos observados nesses equipamentos motivaram o desenvolvimento de um modelo numérico que pudesse reproduzir tais fenômenos para melhor entendê-los. Um sistema rotor-mancal é modelado e sua resposta dinâmica comparada qualitativamente com a resposta dinâmica captada através de acelerômetros fixados nos mancais de um exaustor da Companhia Siderúrgica de Tubarão (CST). Durante o trabalho diversos programas foram desenvolvidos através da plataforma MATLAB. / [en] Vibration Analysis is treated in the context of weak formulation. A continuous system is formulated in the Hilbert space and one base is selected to project the dynamics. An approximation scheme is guaranteed by increasing the number of functions in the base used to represent the response. This is the idea behind methods like the Finite Element Method and Assumed Modes Method, which derive from Galerkin Method. This strategy is different from what is commonly taught in vibration courses, where a mass-spring system is analyzed and discrete systems composed by masses, springs and dashpots are discussed. In those cases the error of the numerical analysis is not known. Vibration Analysis is very used in predictive maintenance of rotating machines. Some phenomenons observed in those machines motivated the development of a numerical model that could reproduce such phenomenons to better understand them. A rotor-bearing system is modelled and its dynamic response is qualitative compared to the dynamic response captured by accelerometers fixed on the bearings of a blower of the steel company Companhia Siderúrgica de Tubarão (CST). During this work several programs were developed using MATLAB software.

Master of Science / Department of Mechanical and Nuclear Engineering / Jeremy A. Roberts / A novel approach based on the Karhunen-Loéve Transform (KLT) is presented for treatment of the energy variable in response matrix methods, which are based on the partitioning of global domains into independent nodes linked by approximate boundary conditions. These conditions are defined using truncated expansions of nodal boundary fluxes in each phase-space variable (i.e., space, angle, and energy). There are several ways in which to represent the dependence on these variables, each of which results in a trade-off between accuracy and speed. This work provides a method to expand in energy that can reduce the number of energy degrees of freedom needed for sub-0.1% errors in nodal fission densities by up to an order of magnitude. The Karhunen-Loéve Transform is used to generate basis sets for expansion in the energy variable that maximize the amount of physics captured by low-order moments, thus permitting low-order expansions with less error than basis sets previously studied, e.g., the Discrete Legendre Polynomials (DLP) or modified DLPs. To test these basis functions, two 1-D test problems were developed: (1) a 10-pin representation of the junction between two heterogeneous fuel assemblies, and (2) a 70-pin representation of a boiling water reactor. Each of these problems utilized two cross-section libraries based on a 44-group and 238-group structure. Furthermore, a 2-D test problem based on the C5G7 benchmark is used to show applicability to higher dimensions.

L'analyse en composantes principales et l'analyse des correspondances sont généralisées pour étudier des ensembles de trajectoires de processus numériques ou qualitatifs. On étudie également certains problèmes de régression avec une infinité non dénombrable de variables: régression sur un processus, régression d'un processus sur un autre.

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