International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, California / Dryden real-time flight simulators encompass the simulation of pulse code modulation (PCM) telemetry signals. This paper presents a new method whereby the calibration polynomial (from first to sixth order), representing the conversion from counts to engineering units (EU), is numerically inverted in real time. The result is less than onecount error for valid EU inputs. The Newton-Raphson method is used to numerically invert the polynomial. A reverse linear interpolation between the EU limits is used to obtain an initial value for the desired telemetry count. The method presented here is not new. What is new is how classical numerical techniques are optimized to take advantage of modern computer power to perform the desired calculations in real time. This technique makes the method simple to understand and implement. There are no interpolation tables to store in memory as in traditional methods. The NASA F-15 simulation converts and transmits over 1000 parameters at 80 times/sec. This paper presents algorithm development, FORTRAN code, and performance results.

La complexification de la modélisation multi-physique conduit d'une part à devoir simuler des systèmes d'équations différentielles ordinaires et d'équations différentielles algébriques de plus en plus grands en nombre d'inconnues et sur des temps de simulation longs. D'autre part l'évolution des architectures de calcul parallèle nécessite d'autres voies de parallélisation que la décomposition de système en sous-systèmes. Dans ce travail, nous proposons de concevoir des méthodes de décomposition de domaine pour la résolution d'EDO en temps. Nous reformulons le problème à valeur initiale en un problème aux valeurs frontières sur l'intervalle de temps symétrisé, sous l'hypothèse de réversibilité du flot. Nous développons deux méthodes, la première apparentée à une méthode de complément de Schur, la seconde basée sur une méthode de type Schwarz dont nous montrons la convergence pouvant être accélérée par la méthode d'Aitken dans le cadre linéaire. Afin d'accélérer la convergence de cette dernière dans le cadre non-linéaire, nous introduisons les techniques d'extrapolation et d'accélération de la convergence des suites non-linéaires. Nous montrons les avantages et les limites de ces techniques. Les résultats obtenus nous conduisent à développer l'accélération de la méthode de type Schwarz par une méthode de Newton. Enfin nous nous intéressons à l'étude de conditions de raccord non-linéaires adaptées à la décomposition de domaine de problèmes non-linéaires. Nous nous servons du formalisme hamiltonien à ports, issu du domaine de l'automatique, pour déduire les conditions de raccord dans le cadre l'équation de Saint-Venant et de l'équation de la chaleur non-linéaire. Après une étude analytique de la convergence de la DDM associée à ces conditions de transmission, nous proposons et étudions une formulation de Lagrangien augmenté sous l'hypothèse de séparabilité de la contrainte.

The goal of this thesis is to develop a new, fast, adaptive load flow algorithm that "automatically alternates" numerical methods including Newton-Raphson method, Gauss-Seidel method and Gauss method for a load flow run to achieve less run time. Unlike the proposed method, the traditional load flow analysis uses only one numerical method at a time. This adaptive algorithm performs all the computation for finding the bus voltage angles and magnitudes, real and reactive powers for the given generation and load values, while keeping track of the proximity to convergence of a solution. This work focuses on finding the algorithm that uses multiple numerical techniques, rather than investigating programming techniques and programming languages. The convergence time is compared with those from using each of the numerical techniques. The proposed method is implemented on the IEEE 39-bus system with different contingencies and the solutions obtained are verified with PowerWorld Simulator, a commercial software for load flow analysis.

Convex optimization has developed a wide variety of useful tools critical to many applications in machine learning. However, unlike linear and quadratic programming, general convex solvers have not yet reached sufficient maturity to fully decouple the convex programming model from the numerical algorithms required for implementation. Especially as datasets grow in size, there is a significant gap in speed and scalability between general solvers and specialized algorithms. This thesis addresses this gap with a new model for convex programming based on an intermediate representation of convex problems as a sum of functions with efficient proximal operators. This representation serves two purposes: 1) many problems can be expressed in terms of functions with simple proximal operators, and 2) the proximal operator form serves as a general interface to any specialized algorithm that can incorporate additional `2-regularization. On a single CPU core, numerical results demonstrate that the prox-affine form results in significantly faster algorithms than existing general solvers based on conic forms. In addition, splitting problems into separable sums is attractive from the perspective of distributing solver work amongst multiple cores and machines. We apply large-scale convex programming to several problems arising from building the next-generation, information-enabled electrical grid. In these problems (as is common in many domains) large, high-dimensional datasets present opportunities for novel data-driven solutions. We present approaches based on convex models for several problems: probabilistic forecasting of electricity generation and demand, preventing failures in microgrids and source separation for whole-home energy disaggregation.

Orientador: Sérgio Kurokawa / Banca: Ailton Akira Shinoda / Banca: Mariangela Carvalho Bovolato / Banca: Marcos de Araujo Paz / Banca: Damásio Fernandes Júnior / Resumo: Este trabalho apresenta um modelo analítico para uma linha de transmissão trifásica com plano de simetria vertical. Devido às características físicas dessa linha, é possível representá-la por um sistema constituído por uma linha monofásica e por uma linha bifásica. Nesse sistema, as equações que descrevem o comportamento das grandezas nos terminais da linha monofásica são conhecidas, enquanto que as equações da linha bifásica foram obtidas utilizando uma matriz de transformação escrita explicitamente em função dos parâmetros da linha trifásica. Em seguida, as grandezas modais da linha trifásica foram convertidas para o domínio das fases e as equações resultantes representam um modelo analítico desenvolvido diretamente no domínio das fases dessa linha. Para verificar o desempenho do modelo, foram realizadas simulações considerando a energização e a incidência de uma descarga atmosférica em uma linha trifásica de 440 kV. Esses resultados foram comparados aos resultados obtidos com a linha representada por meio de um método clássico (representação nos modos) e as simulações mostraram que o modelo responde adequadamente na faixa de frequência correspondente aos procedimentos de manobra e chaveamento. O modelo desenvolvido leva em conta o efeito da frequência sobre os parâmetros longitudinais da linha e também o fato de que os parâmetros da linha são distribuídos ao longo de seu comprimento. Acredita-se que a análise das matrizes, que dão suporte ao modelo, e a validação do modelo no domínio do tempo possa dar origem, futuramente, a um modelo de linha de transmissão desenvolvido diretamente no domínio do tempo. Tal modelo, pelo fato de ser obtido diretamente das equações de propagação da linha, permitirá a obtenção de resultados de simulações, de transitórios eletromagnéticos que ocorrem... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This paper presents an analytical model to a three-phase transmission line with vertical symmetry plane. Because of physical characteristics of this line, it is possible to represent it by a system consisting of a single-phase and a two-phase line. In this system, the equations that describe the behavior of single-phase terminals quantities are known, while the two-phase equations were obtained using a transformation matrix written explicitly in terms of the parameters of three-phase line. Then, the modal quantities of three-phase line were converted into phase domain and the resulting equations represent an analytical model developed directly in phase domain of this line. To verify the performance of the model, were performed simulations considering the energization and impact of a lighting surge in a 440 kV three-phase line. These results were compared to results obtained with the line represented by a classical method (presentation modes) and simulations show that the model responds appropriately in the frequency range corresponding to the operation and switching procedures. The model developed takes into account the frequency effect on the longitudinal line parameters and also the fact that the line parameters are distributed along their length. It is believed that the matrix analysis, that support the model and the model validation in time domain may give rise in the future to a transmission line model developed directly in time domain. Such a model, because it is obtained directly from the propagation equations of line, will enable the more accurate results of simulations of electromagnetic transients that... (Complete abstract click electronic access below) / Doutor

Many optimization problems for a smooth cost function f on a manifold M can be solved by determining the zeros of a vector field F; such as e.g. the gradient F of the cost function f. If F does not depend on additional parameters, numerous zero-finding techniques are available for this purpose. It is a natural generalization however, to consider time-dependent optimization problems that require the computation of time-varying zeros of time-dependent vector fields F(x,t). Such parametric optimization problems arise in many fields of applied mathematics, in particular path-following problems in robotics, recursive eigenvalue and singular value estimation in signal processing, as well as numerical linear algebra and inverse eigenvalue problems in control theory. In the literature, there are already some tracking algorithms for these tasks, but these do not always adequately respect the manifold structure. Hence, available tracking results can often be improved by implementing methods working directly on the manifold. Thus, intrinsic methods are of interests that evolve during the entire computation on the manifold. It is the task of this thesis, to develop such intrinsic zero finding methods. The main results of this thesis are as follows: - A new class of continuous and discrete tracking algorithms is proposed for computing zeros of time-varying vector fields on Riemannian manifolds. This was achieved by studying the newly introduced time-varying Newton Flow and the time-varying Newton Algorithm on Riemannian manifolds. - Convergence analysis is performed on arbitrary Riemannian manifolds. - Concretization of these results on submanifolds, including for a new class of algorithms via local parameterizations. - More specific results in Euclidean space are obtained by considering inexact and underdetermined time-varying Newton Flows. - Illustration of these newly introduced algorithms by examining time-varying tracking tasks in three application areas: Subspace analysis, matrix decompositions (in particular EVD and SVD) and computer vision. / Das Optimieren einer glatten Kostenfunktion f auf einer Mannigfaltigkeit M kann oft dadurch erreicht werden, dass man die Nullstellen eines Vektorfeldes F bestimmt; z.B. dann, wenn F der Gradient von f ist. Für solche Problemstellungen gibt es zahlreiche Nullstellensuchmethoden, sofern F nicht von zusätzlichen Parametern abhängt. Es ist jedoch eine nahe liegende Erweiterung, zeitvariante Optimierungsaufgaben zu betrachten, für die dann Verfahren zur Berechnung der zeitvarianten Nullstelle von Vektorfeldern F(x,t) benötigt werden. Solche parametrisierte Optimierungsprobleme tauchen in vielen Teilgebieten der angewandten Mathematik auf, insbesondere Verfolgungsprobleme in der Robotik, rekursive Eigenwert- und Singulärwertbestimmung in der Signalverarbeitung sowie in der numerischen linearen Algebra und inverse Eigenwertprobleme in der Kontrolltheorie. In der Literatur gibt es bereits einige Nullstellen-Verfolgungsmethoden für solche Aufgaben. Jedoch wird dabei meistens nicht die Struktur der Mannigfaltigkeit hinreichend berücksichtigt, was aber wünschenswert wäre. Methoden, die direkt auf M arbeiten liefern nämlich andere und ggf. bessere Ergebnisse. Dies begründet unser Interesse an intrinsische Methoden, und es ist die zentrale Aufgabe dieser Arbeit, solche Methoden herzuleiten. Die Hauptergebnisse sind wie folgt: - Neue Klassen von diskreten und kontinuierlichen Methoden zur Verfolgung von Nullstellen von zeitvarianten Vektorfeldern auf Riemannschen Mannigfaltigkeiten werden etabliert. Dazu wurden der zeitvariante Newton Fluss und der zeitvariante Newton Algorithmus auf Riemannschen Mannigfaltigkeiten neu eingeführt und studiert. - Die Konvergenzanalyse wird auf beliebigen Riemannschen Mannigfaltigkeiten durchgeführt. - Die Ergebnisse werden durch Betrachtung von Untermannigfaltigkeiten konkretisiert. Dabei wird eine neue Klasse von Algorithmen hergeleitet, die lokalen Parametrisierungen der Mannigfaltigkeit nutzt. - Durch Betrachtung der Ergebnisse im euklidischen Raum werden diese zunächst weiter vereinfacht und dann um inexakte und unterbestimmte zeitvariante Verfahren erweitert. - Die neu eingeführten Algorithmen werden durch das ausführliche Studium von zeitvarianten Verfolgungsproblemen in drei Anwendungsgebieten veranschaulicht: Unterraumberechnung, Matrizenzerlegungen (insbesondere Diagonalisierung von Matrizen und Singulärwertzerlegung) und Bewegungsrekonstruktion aus Kamerabildern.

In dieser Arbeit befassen wir uns mit einem reaktiven Transportmodell mit Niederschlags-Auflösung Reaktionen das aus den Geowissenschaften stammt. Es besteht aus PDGs, gewöhnlichen Differentialgleichungen, algebraischen Gleichungen und Komplementaritätsbedingungen. Nach Diskretisation dieses Modells erhalten wir eine großes nichtlineares und nichtglattes Gleichungssystem. Wir lösen dieses System mit der semismoothen Newtonverfahren, das von Qi und Sun eingeführt wurde. Der Fokus dieser Arbeit ist in der Anwendung und Konvergenz dieses Algorithmus. Wir zeigen, dass dieser Algorithmus für dieses Problem wohldefiniert ist und sogar lokal quadratisch konvergiert gegen eine BD-reguläre Lösung. Wir befassen uns auch mit den dabei entstehenden linearen Gleichungssystemen, die sehr groß und dünn besetzt sind, und wie sie effizient gelöst werden können. Ein wichtiger Bestandteil dieser Untersuchung ist die Beschränktheit einer gewissen matrixwertigen Funktion, die in einem eigenen Kapitel gezeigt wird. Als Seitenbetrachtung untersuchen wir wie die extremalen Eigenwerte (und Singulärwerte) von gewissen PDE-Operatoren, welche in unserem diskretisierten Modell vorkommen, genau abgeschätzt werden können. / In this thesis we consider a reactive transport model with precipitation dissolution reactions from the geosciences. It consists of PDEs, ODEs, algebraic equations (AEs) and complementary conditions (CCs). After discretization of this model we get a huge nonlinear and nonsmooth equation system. We tackle this system with the semismooth Newton method introduced by Qi and Sun. The focus of this thesis is on the application and convergence of this algorithm. We proof that this algorithm is well defined for this problem and local even quadratic convergent for a BD-regular solution. We also deal with the arising linear equation systems, which are large and sparse, and how they can be solved efficiently. An integral part of this investigation is the boundedness of a certain matrix-valued function, which is shown in a separate chapter. As a side quest we study how extremal eigenvalues (and singular values) of certain PDE-operators, which are involved in our discretized model, can be estimated accurately.

Resumo: Nesse trabalho propõe-se uma adaptação do método barreira penalidade quasi-Newton apresentado por P. Armand em 2003, para a resolução do problema do Fluxo de Potência Ótimo (FPO). Este método é denominado de método da função langrangiana barreira penalidade adaptada. Neste método as restrições de desigualdade são transformadas em igualdade pelo uso de variáveis de folga positivas. Estas variáveis são relaxadas, utilizando-se variáveis positivas, as quais, são incorporadas na função objetivo através de um termo de penalização. O novo problema restrito é então transformado em irrestrito associando a uma função lagrangiana às restrições de igualdade e uma função barreira penalidade às restrições de desigualdade. o algoritmo é composto por um ciclo interno e um externo. No ciclo interno é utilizado um método quasi-Newton para o cálculo das direções de busca e é determinado o tamanho do passo. No ciclo externo os parâmetros de barreira e penalidade são atualizados através de regras pré-definidas até que as condições de KKT sejam satisfeitas. Testes computacionais foram realizados utilizando problemas matemáticos e o problema de FPO, os quais demonstram a eficiência da adaptação proposta / Abstract: This work proposes an adaptation of the quasi-Newton penalty barrier method presented by P. Armand in 2003. for the solution of the Optimal Power Flow (OPD) problem. This method is called method adapted penalty barrier lagrangian function. In this method the inequalities constraint are transformed in equality by adding non-negative slack variable. These variables are relaxed by positive auxiliary variables which are incorporated in the objective function through a penalty term. The new constraint problem is transformed in unconstraint by associating an lagrangian function for handling the equality constraint and an penalty barrier function for treating the inequality constraints. The algorithm is composed by an internal and external cycle. In the interanal cycle is used the quasi-Newton method to determine the search directions and the step size is calculated. In the external cycle the barrier parameters are updated through predefined rules until the KKT conditions are satisfied. Computational tests were accomplished using mathematical problems and the OPF problem which demonstrate the efficiency of the propose adaptation / Orientador: Edméa Cássia Baptista / Coorientador: Vanusa Alves de Sousa / Banca: Geraldo Roberto Martins da Costa / Banca: Antonio Roberto Balbo / Mestre

Este projeto de pesquisa teve o objetivo de desenvolver uma nova abordagem para a resolução do Fluxo de Potência Ótimo. Para isso, foram obtidos dados teóricos, a partir de um levantamento bibliográfico, que explicitaram os conceitos de otimização aplicados ao sistema estático de energia elétrica. A pesquisa fundamentou-se metodologicamente nos métodos: Newton-Langragiano, Penalidade e Função Barreira Logarítmica de Newton Projetada. Os sistemas de equações resultantes das condições de estacionaridade da função Lagrangiana foram resolvidos pelo método de Newton. Na implementação computacional foram utilizadas técnicas de esparsidade. Foram realizadas estudos para validação e a verificação da abordagem proposta nos sistemas de 3, 14, 30 e 118 barras. / This research project had the objective of developing a new approach for the resolution of the Optimum Power Flow. For this purpose, theoretical data were obtained through a bibliographical survey, which explained the optimization concepts applied to the electrical energy static system. The research was based on the methods: Newton-Lagrangian, Penalty and Projected Newton Barrier Function. The systems of equations resulting from the Lagrangian function stationarity conditions were resolved through the Newton\'s method. In the computational implementation, sparsity techniques had been used. Studies had been carried out for the proposed approach validation and verification in the systems of 3, 14, 30 and 118 buses.

by Hau-Leung Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 41-42). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Paper I --- p.5 / Chapter 1.2 --- Paper II --- p.6 / Chapter 2 --- The Inexact Newton-Like Method for Inverse Eigen- value Problem --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- The Newton-Like Method --- p.9 / Chapter 2.3 --- The Inexact Newton-Like Method --- p.11 / Chapter 2.4 --- Convergence Analysis --- p.14 / Chapter 2.5 --- Numerical Experiments --- p.22 / Chapter 3 --- A DCT Based Watermarking Scheme for Copyright Protection of Images --- p.26 / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Preliminary --- p.28 / Chapter 3.2.1 --- Gray-level image --- p.28 / Chapter 3.2.2 --- Color image --- p.29 / Chapter 3.2.3 --- The Discrete Cosine transform --- p.30 / Chapter 3.3 --- Watermarking Approaches --- p.31 / Chapter 3.3.1 --- Insertion procedures --- p.31 / Chapter 3.3.2 --- Retrieval procedures --- p.33 / Chapter 3.4 --- Experimental results --- p.34 / Chapter 3.5 --- Other Applications --- p.38 / Chapter 3.5.1 --- Data Hiding --- p.38 / Chapter 3.5.2 --- Authentication --- p.39 / Chapter 3.5.3 --- Fingerprinting --- p.39 / Chapter 3.5.4 --- Copy Control --- p.39 / Chapter 3.6 --- Conclusion --- p.40 / Bibliography --- p.41