Orientadores: João Marcos Travassos Romano, Francisco Rodrigo Porto Cavalcanti / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-04T00:19:46Z (GMT). No. of bitstreams: 1 Cavalcante_CharlesCasimiro_D.pdf: 8652621 bytes, checksum: bf432c4988b60a8e2465828f4f748b47 (MD5) Previous issue date: 2004 / Resumo: Esta tese é dedicada ao estudo de tecnicas de separação cega de fontes aplicadas ao contexto de processamento multiusuario em comunicações digitais. Utilizando estrategias de estimação da função de densidade de probabilidade (fdp), são propostos dois metodos de processamento multiusuario que permitem recuperar os sinais transmitidos pela medida de similaridade de Kullback-Leibler entre a fdp dos sinais a saida do dispositivo de separação e um modelo parametrico que contem as caracteristicas dos sinais transmitidos. Alem desta medida de similaridade, são empregados diferentes metodos que garantem a descorrelação entre as estimativas das fontes de tal forma que os sinais recuperados sejam provenientes de diferentes fontes. E ainda realizada a analise de convergencia dos metodos e suas equivalencias com tecnicas classicas resultando em algumas importantes relações entre criterios cegos e supervisionados, tais como o criterio proposto e o criterio de maxima a posteriori. Estes novos metodos aliam a capacidade de recuperação da informação uma baixa complexidade computacional. A proposição de metodos baseados na estimativa da fdp permitiu a realização de um estudo sobre o impacto das estatisticas de ordem superior em algoritmos adaptativos para separação cega de fontes. A utilização da expansão da fdp em series ortonormais permite avaliar atraves dos cumulantes a dinamica de um processo de separação de fontes. Para tratar com problemas de comunicação digital e proposta uma nova serie ortonormal, desenvolvida em torno de uma função de densidade de probabilidade dada por um somatorio de gaussianas. Esta serie e utilizada para evidenciar as diferenças em relação ao desempenho em tempo real ao se reter mais estatisticas de ordem superior. Simulações computacionais são realizadas para evidenciar o desempenho das propostas frente a tecnicas conhecidas da literatura em varias situações de necessidade de alguma estrategia de recuperação de sinais / Abstract: This thesis is devoted to study blind source separation techniques applied to multiuser processing in digital communications. Using probability density function (pdf) estimation strategies, two multiuser processing methods are proposed. They aim for recovering transmitted signal by using the Kullback-Leibler similarity measure between the signals pdf and a parametric model that contains the signals characteristics. Besides the similarity measure, different methods are employed to guarantee the decorrelation of the sources estimates, providing that the recovered signals origin from different sources. The convergence analysis of the methods as well as their equivalences with classical techniques are presented, resulting on important relationships between blind and supervised criteria such as the proposal and the maximum a posteriori one. Those new methods have a good trade-off between the recovering ability and computational complexity. The proposal os pdf estimation-based methods had allowed the investigation on the impact of higher order statistics on adaptive algorithms for blind source separation. Using pdf orthonormal series expansion we are able to evaluate through cumulants the dynamics of a source separation process. To be able to deal with digital communication signals, a new orthonormal series expansion is proposed. Such expansion is developed in terms of a Gaussian mixture pdf. This new expansion is used to evaluate the differences in real time processing when we retain more higher order statistics. Computational simulations are carried out to stress the performance of the proposals, faced to well known techniques reported in the literature, under the situations where a recovering signal strategy is required. / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

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This thesis develops theoretical and computational methods for the robustness analysis of uncertain systems. The considered systems are linearized and depend rationally on random parameters with an associated probability distribution. The uncertainty is tackled by applying a polynomial chaos expansion (PCE), a series expansion for random variables similar to the well-known Fourier series for periodic time signals. We consider the linear perturbations around a system's operating point, i.e., reference trajectory, both from a probabilistic and worst-case point of view. A chief contribution is the polynomial chaos series expansion of uncertain linear systems in linear fractional representation (LFR). This leads to significant computational benefits when analyzing the probabilistic perturbations around a system's reference trajectory. The series expansion of uncertain interconnections in LFR further delivers important theoretical insights. For instance, it is shown that the PCE of rational parameter-dependent linear systems in LFR is equivalent to applying Gaussian quadrature for numerical integration. We further approximate the worst-case performance of uncertain linear systems with respect to quadratic performance metrics. This is achieved by approximately solving the underlying parametric Riccati differential equation after applying a polynomial chaos series expansion. The utility of the proposed probabilistic robustness analysis is demonstrated on the example of an industry-sized autolanding system for an Airbus A330 aircraft. Mean and standard deviation of the stochastic perturbations are quantified efficiently by applying a PCE to a linearization of the system along the nominal approach trajectory. Random uncertainty in the aerodynamic coefficients and mass parameters are considered, as well as atmospheric turbulence and static wind shear. The approximate worst-case analysis is compared with Monte Carlo simulations of the complete nonlinear model. The methods proposed throughout the thesis rapidly provide analysis results in good agreement with the Monte Carlo benchmark, at reduced computational cost.

Estudamos o diagrama de fases e o ponto tricrítico da transição de colapso em um modelo de animais na rede quadrada, a partir da expansão em série da compressibilidade isotérmica KT do sistema. Como função das variáveis x (fugacidade) e y = e1/T (T é a temperatura reduzida), a serie KT é analisada utilizando-se a técnica dos aproximantes diferenciais parciais. Determinamos o padrão de fluxo das trajetórias características de um típico aproximante diferencial parcial com ponto fixo estável. Obtemos estimativas satisfatórias para a fugacidade tricrítica Xt = 0.024 &#177 0.005 e a temperatura tricritica Tt = 0.54 &#177 0.04. Considerando somente campos de escala lineares, obtemos também o expoente de escala &#947 = 1.4 &#177 0.2 e o expoente \"crossover\" &#934 = 0.66 &#177 0.08. Nossos resultados estão em boa concordância com estimativas prévias obtidas por outros métodos. Também estudamos um processo de polimerização ramifIcada através de simulações computacionais na rede quadrada baseadas em um modelo de crescimento cinético generalizado para se incorporar ramifIcações e impurezas. A configuração do polímero e identificada com uma árvore-ligação (\"bond tree\") a fim de se examinar os aspectos topológicos. As dimensões fractais dos aglomerados (\"clusters\") são obtidas na criticalidade. As simulações também permitem o estudo da evolução temporal dos aglomerados bem como a determinação das auto-correlações temporais e expoentes críticos dinâmicos. Com relação aos efeitos de tamanho finito, uma técnica de cumulantes de quarta ordem e empregada para se estimar a probabilidade de ramificação critica bc e os expoentes críticos v e &#946. Na ausência de impurezas, a rugosidade da superfície e descrita em termos dos expoentes de Hurst. Finalmente, simulamos este modelo de crescimento cinético na rede quadrada utilizando um método de Monte Carlo para estudar a polimerização ramificada com interações atrativas de curto alcance entre os monômeros. O diagrama de fases que separa os regimes de crescimento finito e infinito e obtido no plano (T,b) (T é a temperatura reduzida e b é a probabilidade de ramificação). No limite termodinâmico, extrapolamos a temperatura T&#8727 = 0.102 &#177 0.005 abaixo da qual a fase e sempre infinita. Observamos também a ocorrência de uma transição de rugosidade na superfície do polímero. / The phase diagram and the tricritical point of a collapsing lattice animal are studied through an extended series expansion of the isothermal compressibility KT on a square lattice. As a function of the variables x (fugacity) and y = e1/T (T is the reduced temperature), this series KT is investigated using the partial differential approximants technique. The characteristic flow pattern of partial differential approximant trajectories is determined for a typical stable fixed point. We obtain satisfactory estimates for the tricritical fugacity Xt = 0.024 &#177 0.005and temperature Tt = 0.54 &#177 0.04.Taking into account only linear scaling fields we are also able to get the scaling exponent &#947 = 1.4 &#177 0.2 and the crossover exponent &#934 = 0.66 &#177 0.08. Our results are in good agreement with previous estimates from other methods. We also study ramified polymerization through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities. The polymer configuration is identified with a bond tree in order to examine its topology. The fractal dimensions of clusters are obtained at criticality. Simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents. In regard to finite size effects, a fourth-order cumulant technique is employed to estimate the critical branching probability be and the critical exponents v and &#946. In the absence of impurities, the surface roughness is described in terms of the Hurst exponents. Finally we simulate this kinetic growth model on the square lattice using a Monte Carlo approach in order to study ramified polymerization with short distance attractive interactions between monomers. The phase boundary separating finite from infinite growth regimes is obtained in the (T,b) space (T is the reduced temperature and b is the branching probability). In the thermodynamic limit, we extrapolate the temperature T = 0.102 &#177 0.005 below which the phase is found to be always infinite. We also observe the occurrence of a roughening transition at the polymer surface.

量子擾動及挫折性兩者均可破壞絕對零溫的磁序，為近代凝態物 理關注的有趣現象。在外加橫場下的三角晶格易辛反鐵磁兼具量子臨 界現象(quantum criticality)及幾何挫折性，可謂量子磁性物質之一典 範理論模型。本論文利用平衡態及非平衡態量子蒙地卡羅(quantum Monte Carlo)方法探測三角晶格易辛反鐵磁之量子相變，其界定零溫 時無磁性的順磁態及具 Z6 對稱破缺的有序態(所謂時鐘態)。這裡的 量子蒙地卡羅方法為運用算符的零溫投射(zero-temperature projector) 及隨機序列展開(stochastic series expansion)演算法。在非平衡模擬 中，我們分別沿降溫過程及量子絕熱過程逼近量子相變點，藉此我們 得到動力學指數，及其它相關臨界指數。 / The destruction of magnetic long-range order at absolute zero temperature arising from quantum fluctuations and frustration is an interesting theme in modern condensed-matter physics. The triangular lattice Ising antiferromag- net in a transverse field provides a playground for the study of the combined effects of quantum criticality and geometrical frustration. In this thesis we use quantum Monte Carlo methods both in equilibrium and non-equilibrium setups to study the properties of the quantum critical point in the triangular lattice antiferromagnet, which separates a disordered paramagnetic state and an ordered clock state exhibiting Z6 symmetry breaking; The methods are based on a zero-temperature projector algorithm and the stochastic series ex- pansion algorithm. For the non-equilibrium setups, we obtain the dynamical exponent and other critical exponents at the quantum critical point approached by slowly decreasing temperature and through quantum annealing.

Estudamos o diagrama de fases e o ponto tricrítico da transição de colapso em um modelo de animais na rede quadrada, a partir da expansão em série da compressibilidade isotérmica KT do sistema. Como função das variáveis x (fugacidade) e y = e1/T (T é a temperatura reduzida), a serie KT é analisada utilizando-se a técnica dos aproximantes diferenciais parciais. Determinamos o padrão de fluxo das trajetórias características de um típico aproximante diferencial parcial com ponto fixo estável. Obtemos estimativas satisfatórias para a fugacidade tricrítica Xt = 0.024 &#177 0.005 e a temperatura tricritica Tt = 0.54 &#177 0.04. Considerando somente campos de escala lineares, obtemos também o expoente de escala &#947 = 1.4 &#177 0.2 e o expoente \"crossover\" &#934 = 0.66 &#177 0.08. Nossos resultados estão em boa concordância com estimativas prévias obtidas por outros métodos. Também estudamos um processo de polimerização ramifIcada através de simulações computacionais na rede quadrada baseadas em um modelo de crescimento cinético generalizado para se incorporar ramifIcações e impurezas. A configuração do polímero e identificada com uma árvore-ligação (\"bond tree\") a fim de se examinar os aspectos topológicos. As dimensões fractais dos aglomerados (\"clusters\") são obtidas na criticalidade. As simulações também permitem o estudo da evolução temporal dos aglomerados bem como a determinação das auto-correlações temporais e expoentes críticos dinâmicos. Com relação aos efeitos de tamanho finito, uma técnica de cumulantes de quarta ordem e empregada para se estimar a probabilidade de ramificação critica bc e os expoentes críticos v e &#946. Na ausência de impurezas, a rugosidade da superfície e descrita em termos dos expoentes de Hurst. Finalmente, simulamos este modelo de crescimento cinético na rede quadrada utilizando um método de Monte Carlo para estudar a polimerização ramificada com interações atrativas de curto alcance entre os monômeros. O diagrama de fases que separa os regimes de crescimento finito e infinito e obtido no plano (T,b) (T é a temperatura reduzida e b é a probabilidade de ramificação). No limite termodinâmico, extrapolamos a temperatura T&#8727 = 0.102 &#177 0.005 abaixo da qual a fase e sempre infinita. Observamos também a ocorrência de uma transição de rugosidade na superfície do polímero. / The phase diagram and the tricritical point of a collapsing lattice animal are studied through an extended series expansion of the isothermal compressibility KT on a square lattice. As a function of the variables x (fugacity) and y = e1/T (T is the reduced temperature), this series KT is investigated using the partial differential approximants technique. The characteristic flow pattern of partial differential approximant trajectories is determined for a typical stable fixed point. We obtain satisfactory estimates for the tricritical fugacity Xt = 0.024 &#177 0.005and temperature Tt = 0.54 &#177 0.04.Taking into account only linear scaling fields we are also able to get the scaling exponent &#947 = 1.4 &#177 0.2 and the crossover exponent &#934 = 0.66 &#177 0.08. Our results are in good agreement with previous estimates from other methods. We also study ramified polymerization through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities. The polymer configuration is identified with a bond tree in order to examine its topology. The fractal dimensions of clusters are obtained at criticality. Simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents. In regard to finite size effects, a fourth-order cumulant technique is employed to estimate the critical branching probability be and the critical exponents v and &#946. In the absence of impurities, the surface roughness is described in terms of the Hurst exponents. Finally we simulate this kinetic growth model on the square lattice using a Monte Carlo approach in order to study ramified polymerization with short distance attractive interactions between monomers. The phase boundary separating finite from infinite growth regimes is obtained in the (T,b) space (T is the reduced temperature and b is the branching probability). In the thermodynamic limit, we extrapolate the temperature T = 0.102 &#177 0.005 below which the phase is found to be always infinite. We also observe the occurrence of a roughening transition at the polymer surface.

Le développement de la fabrication additive permet d'élaborer des pièces de forme extrêmement complexes, en particulier des structures alvéolaires ou "lattices", où l'allégement est recherché. Toutefois, cette technologie, en très forte croissance dans de nombreux secteurs d'activités, n'est pas encore totalement mature, ce qui ne facilite pas les corrélations entre les mesures expérimentales et les simulations déterministes. Afin de prendre en compte les variations de comportement, les approches multiparamétriques sont, de nos jours, des solutions pour tendre vers des conceptions fiables et robustes. L'objectif de cette thèse est d'intégrer des incertitudes matérielles et géométriques, quantifiées expérimentalement, dans des analyses de flambement. Pour y parvenir, nous avons, dans un premier temps, évalué différentes méthodes de substitution, basées sur des régressions et corrélations, et différentes réductions de modèles afin de réduire les temps de calcul prohibitifs. Les projections utilisent des modes issus soit de la décomposition orthogonale aux valeurs propres, soit de développements homotopiques ou encore des développements de Taylor. Dans un second temps, le modèle mathématique, ainsi créé, est exploité dans des analyses ensemblistes et probabilistes pour estimer les évolutions de la charge critique de flambement de structures lattices. / The development of additive manufacturing allows structures with highly complex shapes to be produced. Complex lattice shapes are particularly interesting in the context of lightweight structures. However, although the use of this technology is growing in numerous engineering domains, this one is not enough matured and the correlations between the experimental data and deterministic simulations are not obvious. To take into account observed variations of behavior, multiparametric approaches are nowadays efficient solutions to tend to robust and reliable designs. The aim of this thesis is to integrate material and geometric uncertainty, experimentally quantified, in buckling analyses. To achieve this objective, different surrogate models, based on regression and correlation techniques as well as different reduced order models have been first evaluated to reduce the prohibitive computational time. The selected projections rely on modes calculated either from Proper Orthogonal Decomposition, from homotopy developments or from Taylor series expansion. Second, the proposed mathematical model is integrated in fuzzy and probabilistic analyses to estimate the evolution of the critical buckling load for lattice structures.

Cette thèse traite de l'évitement de collision entre un engin spatial opérationnel, appelé objet primaire, et un débris orbital, dit secondaire. Ces travaux concernent aussi bien la question de l'estimation du risque pour une paire d'objets sphériques que celle du calcul d'un plan de manoeuvres d'évitement pour le primaire. Pour ce qui est du premier point, sous certaines hypothèses, la probabilité de collision s'exprime comme l'intégrale d'une fonction gaussienne sur une boule euclidienne, en dimension deux ou trois. On en propose ici une nouvelle méthode de calcul, basée sur les théories de la transformée de Laplace et des fonctions holonomes. En ce qui concerne le calcul de manoeuvres de propulsion, différentes méthodes sont développées en fonction du modèle considéré. En toute généralité, le problème peut être formulé dans le cadre de l'optimisation sous contrainte probabiliste et s'avère difficile à résoudre. Dans le cas d'un mouvement considéré comme relatif rectiligne, l'approche par scénarios se prête bien au problème et permet d'obtenir des solutions admissibles. Concernant les rapprochements lents, une linéarisation de la dynamique des objets et un recouvrement polyédral de l'objet combiné sont à la base de la construction d'un problème de substitution. Deux approches sont proposées pour sa résolution : une première directe et une seconde par sélection du risque. Enfin, la question du calcul de manoeuvres de proximité en consommation optimale et temps fixé, sans contrainte d'évitement, est abordée. Par l'intermédiaire de la théorie du vecteur efficacité, la solution analytique est obtenue pour la partie hors-plan de la dynamique képlérienne linéarisée. / This thesis is about collision avoidance for a pair of spherical orbiting objects. The primary object - the operational satellite - is active in the sense that it can use its thrusters to change its trajectory, while the secondary object is a space debris that cannot be controlled in any way. Onground radars or other means allow to foresee a conjunction involving an operational space craft,leading in the production of a collision alert. The latter contains statistical data on the position and velocity of the two objects, enabling for the construction of a probabilistic collision model.The work is divided in two parts : the computation of collision probabilities and the design of maneuvers to lower the collision risk. In the first part, two kinds of probabilities - that can be written as integrals of a Gaussian distribution over an Euclidean ball in 2 and 3 dimensions -are expanded in convergent power series with positive terms. It is done using the theories of Laplace transform and Definite functions. In the second part, the question of collision avoidance is formulated as a chance-constrained optimization problem. Depending on the collision model, namely short or long-term encounters, it is respectively tackled via the scenario approach or relaxed using polyhedral collision sets. For the latter, two methods are proposed. The first one directly tackles the joint chance constraints while the second uses another relaxation called risk selection to obtain a mixed-integer program. Additionaly, the solution to the problem of fixed-time fuel minimizing out-of-plane proximity maneuvers is derived. This optimal control problem is solved via the primer vector theory.

This thesis considers new methods that exploit recent developments in computer technology to address three extant problems in the area of Finance and Econometrics. The problem of Asian option pricing has endured for the last two decades in spite of many attempts to find a robust solution across all parameter values. All recently proposed methods are shown to fail when computations are conducted using standard machine precision because as more and more accuracy is forced upon the problem, round-off error begins to propagate. Using recent methods from numerical analysis based on multi-precision arithmetic, we show using the Mathematica platform that all extant methods have efficacy when computations use sufficient arithmetic precision. This creates the proper framework to compare and contrast the methods based on criteria such as computational speed for a given accuracy. Numerical methods based on a deformation of the Bromwich contour in the Geman-Yor Laplace transform are found to perform best provided the normalized strike price is above a given threshold; otherwise methods based on Euler approximation are preferred. The same methods are applied in two other contexts: the simulation of stable distributions and the computation of unit root densities in Econometrics. The stable densities are all nested in a general function called a Fox H function. The same computational difficulties as above apply when using only double-precision arithmetic but are again solved using higher arithmetic precision. We also consider simulating the densities of infinitely divisible distributions associated with hyperbolic functions. Finally, our methods are applied to unit root densities. Focusing on the two fundamental densities, we show our methods perform favorably against the extant methods of Monte Carlo simulation, the Imhof algorithm and some analytical expressions derived principally by Abadir. Using Mathematica, the main two-dimensional Laplace transform in this context is reduced to a one-dimensional problem.