Geometric models, such as for use in CAD/CAM or animation, are often constructed in a piece-wise fashion. Historically, these models have been made of NURBS surfaces. For various reasons it is problematic and often times mathematically impossible to combine several NURBS models into one continuous surface. The recent invention of a surface type called T-splines has made the combining of NURBS surfaces into a single continuous surface possible, but much of the mathematics has yet to be explored. This thesis explores the mathematics and algorithms necessary to merge multiple NURBS, T-spline, or T-NURCC surfaces into a single continuous surface. This thesis addresses two main problems. The first problem is merging surfaces with different parameterizations. In order to merge surfaces with different parameterizations, it is often necessary to modify the parameter values of the surface, which can change the shape of the surface. This change can be alleviated through shape control methods. The second problem is merging surfaces that meet at extraordinary points, or points with a valence other than four. Results show that the merging algorithm is able to successfully convert models composed of multiple NURBS, T-spline, or T-NURCCS surfaces into models composed of a single T-spline or T-NURCC surface. The resulting models are gap-free and contain little distortion in the parameterization.

We propose a family of search directions based on primal-dual entropy in the context of interior point methods for linear programming. This new family contains previously proposed search directions in the context of primal-dual entropy. We analyze the new family of search directions by studying their primal-dual affine-scaling and constant-gap centering components. We then design primal-dual interior-point algorithms by utilizing our search directions in a homogeneous and self-dual framework. We present iteration complexity analysis of our algorithms and provide the results of computational experiments on NETLIB problems.

We propose a family of search directions based on primal-dual entropy in the context of interior point methods for linear programming. This new family contains previously proposed search directions in the context of primal-dual entropy. We analyze the new family of search directions by studying their primal-dual affine-scaling and constant-gap centering components. We then design primal-dual interior-point algorithms by utilizing our search directions in a homogeneous and self-dual framework. We present iteration complexity analysis of our algorithms and provide the results of computational experiments on NETLIB problems.

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One of heavy oils upgrading processes is hydroconversion. As it is a complex process involving many chemical reactions, the mathematical model of hydroconversion process often has more kinetic parameters than can be estimated from the data. In this thesis, a model for hydroconversion processing of vacuum residue is proposed. It is proved that the model is structurally identifiable, but shown that it is inestimable and good parameter estimates may be impossible to obtain even if the model fit is good. As a proof to the model inestimability, it is shown that literature data can be fitted using a subset of only three (of seven) parameters. To improve parameter estimability, a method is proposed for designing additional experiments. The method is based on designing experiments that provide data that is complementary (in an appropriate sense) to existing data. The approach is illustrated using the hydroconversion model. For the hydroconversion model, using two additional experiments provides a good balance between parameter estimation and experimental effort. / Process Control

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao–Cramer lower bound) in the limit of small noise.

With the emergence of the concept of Smart Grid (SG), the Power Distribution Systems are undergoing major changes in the way it is operated, studied and analyzed. The breakthrough technology of measurement, automation, control and telecommunication equipment, together with the reduction of the costs of acquisition and implementation, allowed Brazilian electric utilities to invest in automation, control and telecommunication, facing distribution networks. This technological development applied in the networks allows new studies and new methodologies to be developed and implemented by utilities in order to improve their technical and operational performance. Many studies are being conducted in order to propose automatic reconfiguration in the distribution networks, automatic restoration and distribution management system in real time, aiming to optimize the loads distribution, reduce energy losses, improve system reliability and the quality indicators of power supply, among other possible needs of the distribution company. Nowadays a fairly explored point is the switching through automatic devices, which have criteria and assumptions for execution in the network. Among the criteria and assumptions, there is the guarantee of coordination and selectivity of protective devices involved in the reconfiguration after switching and consequent topological change. The need for analysis of protective devices and possible reparameterization of them, justifies the development of a methodology through computational solution, able to analyze the coordination and selectivity of the devices (microprocessor reclosers) after network changes. It is due to this niche opportunities caused by technological development and changes in operating philosophy of distribution networks, that this dissertation has as main objective to develop a methodology to validate the operation condition of protective devices, ensuring the safety and system reliability and proposing new protection settings when needed, which consequently will allow network reconfigurations. / Com o surgimento do conceito de Smart Grid (SG), os Sistemas de Distribuição de Energia vêm sofrendo grandes modificações em sua forma de operação, estudo e análise. O grande avanço tecnológico dos equipamentos de medição, automação, controle e telecomunicação, aliado à redução dos custos de aquisição e implementação, permitiu que as distribuidoras brasileiras de energia elétrica realizassem grandes investimentos em automação, controle e telecomunicação, voltados para redes de distribuição. Este avanço tecnológico aplicado nas redes permite que novos estudos e novas metodologias sejam desenvolvidos e aplicados pelas concessionárias, a fim de melhorar o seu desempenho técnico operacional. Muitos estudos estão sendo realizados com o intuito de propor reconfigurações automáticas nas redes de distribuição, recomposição automática e gerenciamento do sistema em tempo real, sempre com o objetivo de otimizar a distribuição das cargas, reduzir as perdas de energia, melhorar a confiabilidade do sistema e os indicadores de qualidade do fornecimento de energia, entre outras possíveis necessidades da respectiva distribuidora. Atualmente um ponto bastante explorado são os chaveamentos através de dispositivos automatizados, os quais possuem critérios e premissas para efetivação em campo. Dentre os critérios e premissas, destaca-se a garantia da coordenação e seletividade dos equipamentos de proteção envolvidos na reconfiguração após a realização do chaveamento e consequente mudança topológica. A necessidade de análise dos dispositivos de proteção e possível reparametrização dos mesmos justifica o desenvolvimento de uma metodologia através de solução computacional, capaz de analisar a coordenação e seletividade dos dispositivos (religadores microprocessados), após mudanças na rede. É devido a este nicho de oportunidades causadas pelo desenvolvimento tecnológico e pelas mudanças na filosofia de operação das redes de distribuição, que esta dissertação tem por objetivo principal desenvolver uma metodologia que permita validar a condição de operação dos dispositivos de proteção, garantindo a segurança e a confiabilidade do sistema e propondo novos ajustes de proteção quando necessário, o que consequentemente permitirá reconfigurações de rede.