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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Static Analysis for Efficient Affine Arithmetic on GPUs

Chan, Bryan January 2007 (has links)
Range arithmetic is a way of calculating with variables that hold ranges of real values. This ability to manage uncertainty during computation has many applications. Examples in graphics include rendering and surface modeling, and there are more general applications like global optimization and solving systems of nonlinear equations. This thesis focuses on affine arithmetic, one kind of range arithmetic. The main drawbacks of affine arithmetic are that it taxes processors with heavy use of floating point arithmetic and uses expensive sparse vectors to represent noise symbols. Stream processors like graphics processing units (GPUs) excel at intense computation, since they were originally designed for high throughput media applications. Heavy control flow and irregular data structures pose problems though, so the conventional implementation of affine arithmetic with dynamically managed sparse vectors runs slowly at best. The goal of this thesis is to map affine arithmetic efficiently onto GPUs by turning sparse vectors into shorter dense vectors at compile time using static analysis. In addition, we look at how to improve efficiency further during the static analysis using unique symbol condensation. We demonstrate our implementation and performance of the condensation on several graphics applications.
2

Static Analysis for Efficient Affine Arithmetic on GPUs

Chan, Bryan January 2007 (has links)
Range arithmetic is a way of calculating with variables that hold ranges of real values. This ability to manage uncertainty during computation has many applications. Examples in graphics include rendering and surface modeling, and there are more general applications like global optimization and solving systems of nonlinear equations. This thesis focuses on affine arithmetic, one kind of range arithmetic. The main drawbacks of affine arithmetic are that it taxes processors with heavy use of floating point arithmetic and uses expensive sparse vectors to represent noise symbols. Stream processors like graphics processing units (GPUs) excel at intense computation, since they were originally designed for high throughput media applications. Heavy control flow and irregular data structures pose problems though, so the conventional implementation of affine arithmetic with dynamically managed sparse vectors runs slowly at best. The goal of this thesis is to map affine arithmetic efficiently onto GPUs by turning sparse vectors into shorter dense vectors at compile time using static analysis. In addition, we look at how to improve efficiency further during the static analysis using unique symbol condensation. We demonstrate our implementation and performance of the condensation on several graphics applications.
3

Affine Arithmetic Based Methods for Power Systems Analysis Considering Intermittent Sources of Power

Munoz Guerrero, Juan Carlos January 2013 (has links)
Intermittent power sources such as wind and solar are increasingly penetrating electrical grids, mainly motivated by global warming concerns and government policies. These intermittent and non-dispatchable sources of power affect the operation and control of the power system because of the uncertainties associated with their output power. Depending on the penetration level of intermittent sources of power, the electric grid may experience considerable changes in power flows and synchronizing torques associated with system stability, because of the variability of the power injections, among several other factors. Thus, adequate and efficient techniques are required to properly analyze the system stability under such uncertainties. A variety of methods are available in the literature to perform power flow, transient, and voltage stability analyses considering uncertainties associated with electrical parameters. Some of these methods are computationally inefficient and require assumptions regarding the probability density functions (pdfs) of the uncertain variables that may be unrealistic in some cases. Thus, this thesis proposes computationally efficient Affine Arithmetic (AA)-based approaches for voltage and transient stability assessment of power systems, considering uncertainties associated with power injections due to intermittent sources of power. In the proposed AA-based methods, the estimation of the output power of the intermittent sources and their associated uncertainty are modeled as intervals, without any need for assumptions regarding pdfs. This is a more desirable characteristic when dealing with intermittent sources of power, since the pdfs of the output power depends on the planning horizon and prediction method, among several other factors. The proposed AA-based approaches take into account the correlations among variables, thus avoiding error explosions attributed to other self-validated techniques such as Interval Arithmetic (IA).
4

SWITCH LEVEL SIMULATION IN THE PRESENCE OF UNCERTAINTIES

RAGUPATHY, MANOJ KUMAR 22 April 2008 (has links)
No description available.
5

Aproximação poligonal robusta de curvas implícitas / Robust polygonal approximation of implicit curves

Filipe de Carvalho Nascimento 19 May 2016 (has links)
Modelagem geométrica envolvendo objetos implícitos é um tema de intensa pesquisa em Computação Gráfica. Portanto, obter técnicas eficientes para representar esses objetos é de extrema importância. Dois grupos de objetos implícitos relevantes para Computação Gráfica são as curvas implícitas e superfícies implícitas. As técnicas tradicionais para se aproximar curvas e superfícies implícitas envolvem dividir o domínio e buscar em suas partições partes da curva ou da superfície. Neste projeto propomos um novo métodos de poligonização robusta de curvas implícitas usando uma ferramenta numérica auto-validada chamada de Aritmética Afim. O método consiste na poligonização adaptativa de curvas implícitas em malhas triangulares tridimensionais. / Geometric modeling involving implicit objects is a topic of intense research in Computer Graphics. Thus, obtain efficient techniques for representing these objects is of utmost importance. Two groups of relevant implicit objects for Computer Graphics are implicit curves and implicit surfaces. Traditional techniques for approximating implicit curves and surfaces involve splitting the domain and searching for parts of the curve or the surface. In this project we propose a new methods of robust polygonization of implicit curves using the self-validated numerical tool called Affine Arithmetic. The method consists in the adaptive polygonization of implicit curves in three-dimensional triangular meshes.
6

Stochastic Modeling and Analysis of Power Systems with Intermittent Energy Sources

Pirnia, Mehrdad 10 February 2014 (has links)
Electric power systems continue to increase in complexity because of the deployment of market mechanisms, the integration of renewable generation and distributed energy resources (DER) (e.g., wind and solar), the penetration of electric vehicles and other price sensitive loads. These revolutionary changes and the consequent increase in uncertainty and dynamicity call for significant modifications to power system operation models including unit commitment (UC), economic load dispatch (ELD) and optimal power flow (OPF). Planning and operation of these ???smart??? electric grids are expected to be impacted significantly, because of the intermittent nature of various supply and demand resources that have penetrated into the system with the recent advances. The main focus of this thesis is on the application of the Affine Arithmetic (AA) method to power system operational problems. The AA method is a very efficient and accurate tool to incorporate uncertainties, as it takes into account all the information amongst dependent variables, by considering their correlations, and hence provides less conservative bounds compared to the Interval Arithmetic (IA) method. Moreover, the AA method does not require assumptions to approximate the probability distribution function (pdf) of random variables. In order to take advantage of the AA method in power flow analysis problems, first a novel formulation of the power flow problem within an optimization framework that includes complementarity constraints is proposed. The power flow problem is formulated as a mixed complementarity problem (MCP), which can take advantage of robust and efficient state-of-the-art nonlinear programming (NLP) and complementarity problems solvers. Based on the proposed MCP formulation, it is formally demonstrated that the Newton-Raphson (NR) solution of the power flow problem is essentially a step of the traditional General Reduced Gradient (GRG) algorithm. The solution of the proposed MCP model is compared with the commonly used NR method using a variety of small-, medium-, and large-sized systems in order to examine the flexibility and robustness of this approach. The MCP-based approach is then used in a power flow problem under uncertainties, in order to obtain the operational ranges for the variables based on the AA method considering active and reactive power demand uncertainties. The proposed approach does not rely on the pdf of the uncertain variables and is therefore shown to be more efficient than the traditional solution methodologies, such as Monte Carlo Simulation (MCS). Also, because of the characteristics of the MCP-based method, the resulting bounds take into consideration the limits of real and reactive power generation. The thesis furthermore proposes a novel AA-based method to solve the OPF problem with uncertain generation sources and hence determine the operating margins of the thermal generators in systems under these conditions. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a pdf. The AA-based approach is benchmarked against the MCS-based intervals, and is shown to obtain bounds close to the ones obtained using the MCS method, although they are slightly more conservative. Furthermore, the proposed algorithm to solve the AA-based OPF problem is shown to be efficient as it does not need the pdf approximations of the random variables and does not rely on iterations to converge to a solution. The applicability of the suggested approach is tested on a large real European power system.
7

Optimisation Globale basée sur l'Analyse d'Intervalles : relaxation Affine et Limitation de la Mémoire / Global Optimization based on Interval Analysis : affine Relaxation and Limited Memory

Ninin, Jordan 08 December 2010 (has links)
Depuis une vingtaine d’années, la résolution de problèmes d’optimisation globale non convexes avec contraintes a connu un formidable essor. Les algorithmes de branch and bound basée sur l’analyse d’intervalles ont su trouver leur place, car ils ont l’avantage de prouver l’optimalité de la solution de façon déterministe, avec un niveau de certitude pouvant aller jusqu’à la précision machine. Cependant, la complexité exponentielle en temps et en mémoire de ces algorithmes induit une limite intrinsèque, c’est pourquoi il est toujours nécessaire d’améliorer les techniques actuelles. Dans cette thèse, nous avons développé de nouvelles arithmétiques basées sur l’arithmétique d’intervalles et l’arithmétique affine, afin de calculer des minorants et des majorants de meilleure qualité de fonctions explicites sur un intervalle. Nous avons ensuite développé une nouvelle méthode automatique de construction de relaxations linéaires. Cette construction est basée sur l’arithmétique affine et procède par surcharge des opérateurs. Les programmes linéaires ainsi générés ont exactement le même nombre de variables et de contraintes d’inégalité que les problèmes originaux, les contraintes d’égalité étant remplacées par deux inégalités. Cette nouvelle procédure permet de calculer des minorants fiables et des certificats d’infaisabilité pour chaque sous-domaine à chaque itération de notre algorithme de branch and bound par intervalles. De nombreux tests numériques issus du site COCONUT viennent confirmer l’efficacité de cette approche. Un autre aspect de cette thèse a été l’étude d’une extension de ce type d’algorithmes en introduisant une limite sur mémoire disponible. L’idée principale de cette approche est de proposer un processus inverse de l’optimisation par le biais d’un principe métaheuristique : plutôt que d’améliorer des solutions locales à l’aide de métaheuristiques telles que les algorithmes Taboo ou VNS, nous partons d’une méthode exacte et nous la modifions en une heuristique. De cette façon, la qualité de la solution trouvée peut être évaluée. Une étude de la complexité de ce principe métaheuristique a également été effectuée. Enfin, pour finir l’étude, nous avons appliqué notre algorithme à la résolution de problème en géométrie plane, ainsi qu’à la résolution d’un problème de dimensionnement de moteur électrique. Les résultats obtenus ont permis de confirmer l’intérêt de ce type d’algorithme, en résolvant des problèmes ouverts sur les polygones convexes et proposant des structures innovantes en génie électrique. / Since about thirty years, interval Branch and Bound algorithms are increasingly used to solve constrained global optimization problems in a deterministic way. Such algorithms are reliable, i.e., they provide an optimal solution and its value with guaranteed bounds on the error, or a proof that the problem under study is infeasible. Other approaches to global optimization, while useful and often less time-consuming than interval methods, do not provide such a guarantee. However, the exponential complexity in time and memory of interval Branch and Bound algorithms implies a limitation, so it is always necessary to improve these methods. In this thesis, we have developed new arithmetics based on interval arithmetic and affine arithmetic, to compute better lower and upper bounds of a factorable function over an interval. An automatic method for constructing linear relaxations of constrained global optimization problems is proposed. Such a construction is based on affine and interval arithmetics and uses operator overloading. These linear programs have exactly the same numbers of variables and of inequality constraints as the given problems. Each equality constraint is replaced by two inequalities. This new procedure for computing reliable bounds and certificates of infeasibility is inserted into a classical interval Branch and Bound algorithm. Extensive computation experiments, made on a sample of test problems from the COCONUT database, prove its effectiveness. Another aspect is the study of an extension of such a global optimization code by limiting the available memory. The main idea of this new kind of metaheuristique is to propose a reverse process of optimization via heuristics : rather than improving local solutions by using metaheuristics such as Taboo or VNS, we begin with an exact method and we modify it into a heuristic one. In such a way, the quality of the solution could be evaluated. Moreover, a study of the complexity of this metaheurisque has been done. Finally, we applied our algorithm to solve open problem in geometry, and to solve a design problem of an electric motor. The results have confirmed the usefulness of this kind of algorithms, solving open problems on convex polygons and offering innovative structures in electrical engineering.
8

Aritméticas intervalares aplicadas à solução do problema de fluxo de potência via equações de injeção de corrente

Araújo, Bianca Maria Costa 03 February 2016 (has links)
Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-12T12:40:39Z No. of bitstreams: 1 biancamariacostaaraujo.pdf: 4585632 bytes, checksum: 78f37e18164b9b5f82a0867bf14ee884 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-15T13:32:18Z (GMT) No. of bitstreams: 1 biancamariacostaaraujo.pdf: 4585632 bytes, checksum: 78f37e18164b9b5f82a0867bf14ee884 (MD5) / Made available in DSpace on 2016-08-15T13:32:18Z (GMT). No. of bitstreams: 1 biancamariacostaaraujo.pdf: 4585632 bytes, checksum: 78f37e18164b9b5f82a0867bf14ee884 (MD5) Previous issue date: 2016-02-03 / Estudos de fluxo de potência são tipicamente utilizados para determinar as condições de operação em estado permanente de um sistema de energia elétrica, avaliadas para um determinado conjunto de valores de geração e carga. Quando os dados de entrada são incertos, vários cenários precisam ser analisados para cobrir a faixa de incerteza. Sob tais condições, torna-se necessária a utilização de algoritmos que incorporem o efeito da incerteza dos dados de geração e carga na análise do fluxo de potência. Como uma alternativa para este problema, um novo metódo de solução é proposto com base na utilização da aritmética afim, que é um modelo melhorado para análise numérica de auto-validação. Nesta aritmética, as quantidades de interesse são representadas como combinações afim de certas variáveis primitivas, que representam as fontes de incerteza nos dados ou aproximações feitas durante o cálculo. Esta técnica é incorporada ao fluxo de potência expresso em termos das equações de injeção de corrente, com as tensões escritas na forma retangular. Posteriomente, os resultados obtidos aplicando-se a aritmética intervalar e a Simulação de Monte Carlo na resolução do problema de incertezas no fluxo de potência em redes de energia elétrica são comparados. / Power flow analysis typically uses a given set of generation and loading profiles to determine steady state operating conditions of electric power systems. When the input data are imprecise, several scenarios need to be analysed to cover the range of uncertainties. Under these conditions, it is necessary to utilise algorithms to incorporate the effect of the uncertainties within the power flow analysis. As an alternative solution to this issue, a new method has been proposed, based on the use of affine arithmetic. This alternative technique has been developed to improve the self-validated numerical analysis. Within affine arithmetic, the quantities of interest are represented by affine combinations of certain primitive variables. The affine combinations can signify both the source of the uncertainties in the data and the approximations during calculations. This technique is incorporated at the power flow which is expressed in terms of current injection equations, with the voltages represented in the rectangular form. The proposed results are later compared with the Monte Carlo Simulation and interval arithmetic, both of which solve the same issue: uncertainties in the power flow analysis of electric power grids.
9

Analyse Statique de Programmes Numériques: Ensembles Affines Contraints

Ghorbal, Khalil 28 July 2011 (has links) (PDF)
Nous nous plaçons dans le cadre de l'analyse statique de programmes, et nous nous intéressons aux propriétés numériques, c'est a dire celles qui concernent les valeurs numériques des variables de programmes. Nous essayons en particulier de déterminer une sur-approximation garantie de l'ensemble de valeurs possibles pour chaque variable numérique utilisée dans le programme à analyser. Cette analyse statique est faite dans le cadre de la théorie de l'interprétation abstraite, théorie présentant un compromis entre les limites théoriques d'indécidabilite et de calculabilite et la précision des résultats obtenus. Nous sommes partis des travaux d'Eric Goubault et Sylvie Putot, que nous avons étendus et généralisés. Notre nouveau domaine abstrait, appelé ensembles affines contraints, combine à la fois l'efficacite de calcul des domaines à base de formes affines et le pouvoir ex- pressif des domaines relationnels classiques tels que les octogones ou les polyèdres. Le nouveau domaine a été implémenté pour mettre en évidence l'intérêt de cette combinaison, ses avantages, ses performances et ses limites par rapport aux autres domaines numériques déjà existants. Le formalisme ainsi que les résultats pra- tiques ont fait l'objet de plusieurs publications [CAV 2009, CAV 2010].
10

Avaliação do ponto de conexão de geração intermitente através de Aritmética Affine e solução da curva de carga

Altomar, Mariana Brinati 01 September 2017 (has links)
Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2017-12-21T17:39:10Z No. of bitstreams: 1 marianabrinatialtomar.pdf: 5565205 bytes, checksum: aed1136ebbc66049baea19e7b7da34fb (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-12-22T12:17:48Z (GMT) No. of bitstreams: 1 marianabrinatialtomar.pdf: 5565205 bytes, checksum: aed1136ebbc66049baea19e7b7da34fb (MD5) / Made available in DSpace on 2017-12-22T12:17:48Z (GMT). No. of bitstreams: 1 marianabrinatialtomar.pdf: 5565205 bytes, checksum: aed1136ebbc66049baea19e7b7da34fb (MD5) Previous issue date: 2017-09-01 / A inserção de geração distribuída em sistemas de potência do mundo todo vem crescendo em ritmo acelerado nos últimos anos. Grandes investimentos em fontes limpas e renováveis, especialmente a eólica e solar, estão sendo feitos pelos países com o objetivo de minimizar os impactos ambientais causados pela geração de energia a partir de combustíveis fósseis. A conexão de uma geração distribuída utilizando fontes intermitentes pode trazer algumas vantagens para o funcionamento do sistema de distribuição, como melhora dos níveis de tensão, aumento da confiabilidade e redução de perdas elétricas. Porém, do ponto de vista do sistema de transmissão, a conexão desse tipo de geração em algumas áreas do sistema pode acabar tendo um impacto negativo em sua operação, causando variações de tensão que podem afetar alguns equipamentos da rede e aumentar a complexidade de sua operação. Além disso, deve ser avaliado seu impacto no controle de frequência de carga e controle de tensão entre outros aspectos. Desta forma, pode-se verificar que esse tipo de conexão deve ser estudado com um maior nível de profundidade. A partir deste contexto, neste trabalho serão analisados os impactos sistêmicos da conexão de uma geração solar em sistemas elétricos de potência, avaliando os níveis de perdas elétricas e variações nos níveis de tensão. Duas metodologias de solução do fluxo de potência na presença de incertezas são avaliadas. As incertezas consideradas estão nos dados de geração e também de carga do sistema. A primeira metodologia é baseada na solução do fluxo de carga determinístico sequencial ao longo da curva de carga. Para esta metodologia são consideradas curvas de carga e de geração, obtidas através do Sistema Teste de Confiabilidade IEEE24 barras e do Laboratório Solar da UFJF, respectivamente. São analisados os impactos nos níveis de perdas elétricas, assim como a variação dos níveis de tensão nas barras para diferentes situações de geração. A segunda metodologia avaliada é baseada na utilização de aritmética affine para determinação dos impactos destas incertezas. Os resultados de perdas obtidos serão tratados considerando-se o ponto médio dos intervalos para fins de comparação com outras metodologias. Os resultados das duas metodologias são comparados aos obtidos pelas Simulações de Monte Carlo, com o objetivo de serem validados. / The insertion of distributed generation into worldwide power systems has been increasing at a rapid pace in the last few years. Large investments in clean and renewable sources, especially wind and solar, are being made by countries to minimize the environmental impacts caused by fossil fuel power generation. Connecting a distributed generation using intermittent sources can bring some benefits for the operation of the distribution system, such as improved voltage levels, increased reliability and reduction of electrical losses. However, from the point of view of the transmission system, the connection of this type of generation in some areas of the system can end up having a negative impact on its operation, causing voltage variations which can affect network equipments and increase the operation complexity. In addition, impacts on the load frequency control and voltage control among other aspects must be evaluated. Thus, this type of connection must be studied with greater level of depth. In this context, the systemic impacts of the connection of a solar plant to electrical power systems, evaluating the levels of electrical losses and variations in voltage levels are analysed. Two methodologies for solving the power flow in the presence of uncertainties are evaluated. The uncertainties considered are the generation and system load data. The first methodology is based on sequential Newton power flow solutions along the load curve, in which load and generation curves obtained from the IEEE24 Bus Test System and from the UFJF Solar Laboratory, respectively. The impacts on the electrical losses are analyzed, as well as the variation on bus voltage levels in the bars for various generation conditions. The second methodology is based on the use of affine arithmetic to determine the impacts of these uncertainties. The results of losses obtained will be treated considering the average point of the intervals for comparisons with other methodologies. The results obtained from the two methods are compared with those obtained by the Monte Carlo Simulations, in order to validate them.

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