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Silva, Renato de Sousa e. "Raiz de função polinomial pelo método de Newton-Raphson." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8735.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Determining roots of polynomial functions is a quite frequent content in the subject of Mathematics in Primary and Higher Education. But Galois has shown that it is not possible to develop algebraic formulas to find such roots in polynomials with a degree greater than 4. The present work aims to use Newton-Raphson’s Numerical and Iterative method to find roots of polynomial function. For this, the GeoGebra software is used as a computational and pedagogical tool to illustrate the procedure adopted by the mentioned method through spreadsheets, Geometry and algebraic calculations. Thus, the proposed methodology can help in the understanding of the Newton-Raphson Method and contribute to the process of teaching and learning the content of polynomials for teachers and students of Basic Education.
Determinar raízes de funções polinomiais é um conteúdo bastante frequente na disciplina de Matemática do Ensino Básico e Superior. Mas, Galois demonstrou que não é possível desenvolver fórmulas algébricas para encontrar tais raízes em polinômios com grau maior que 4. Então o presente trabalho tem o objetivo de utilizar o Método Numérico e Iterativo de Newton-Raphson para encontrar raízes de função polinomial. Para isto, utiliza-se o software GeoGebra como ferramenta computacional e pedagógica para ilustrar o procedimento adotado pelo método citado por meio de planilhas eletrônicas, da Geometria e de cálculos algébricos. Assim, a metodologia proposta pode auxiliar na compreensão do Método de Newton-Raphson e colaborar para o processo de ensino e aprendizagem do conteúdo de polinômios para professores e alunos do Ensino Básico.
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Miller, Shannon N. "The dynamics of Newton's method on cubic polynomials." Huntington, WV : [Marshall University Libraries], 2006. http://www.marshall.edu/etd/descript.asp?ref=658.
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Garcia-Valle, Rodrigo Joel. "Dynamic modelling and simulation of electric power systems using the Newton-Raphson method." Thesis, University of Glasgow, 2007. http://theses.gla.ac.uk/435/.
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The research work presented in this thesis is concerned with the development of a dynamic power flow computer algorithm using Newton's method. It addresses both the development of a positive sequence dynamic power flow algorithm for the dynamic study of balanced power systems and a fully-fledged three-phase dynamic power flow algorithm for the dynamic study of power systems exhibiting a significant degree of either structural or operational unbalance. As a prelude to the research work on dynamic power flows, a three-phase Newton-Raphson power flow algorithm in rectangular co-ordinates with conventional HVDC power plant modelling is presented in this thesis, emphasising the representation of converter control modes. The solution approach takes advantage of the strong numerical solutions for combined HVAC-HVDC systems, where power plant and operational imbalances are explicitly taken into account. The dynamic algorithm is particularly suited to carrying out long-term dynamic simulations and voltage stability assessments. Dynamic model representations of the power plants components and the load tap changing transformer are considered, and to widen the study range of dynamic voltage phenomena using this method, extensions have been made to include induction motor and polynomial load modelling features. Besides, reactive power compensators that base their modus operandi on the switching of power electronic valves, such as HVDC-VSC and the STATCOM are taken into account. The dynamic power flow algorithm has primarily been developed making use of the positive sequence and [dq] representations. Extensions are made to developing a three-phase power flows dynamic algorithm. Test cases for the various dynamic elements developed in this research are presented to show the versatility of the models and simulation tool, including a trip cascading event leading up to a wide-area voltage collaps. Comparisons with the output of a conventional transient stability program carried out where appropriate.
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Simonis, Joseph P. "Inexact Newton methods applied to under-determined systems." Link to electronic dissertation, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-050406-103442/.
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Dissertation (Ph.D.)--Worcester Polytechnic Institute.Keywords: Periodic Solutions, Under-Determined Systems, Continuation, Nonlinear Eigenvalue, Inexact Newton Methods, Newton's Method, Trust Region Methods Includes bibliographical references (p.93-95).
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Choi, Yan-yu. "Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's method." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37680948.
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Choi, Yan-yu, and 蔡欣榆. "Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37680948.
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Baur, Robin. "An Investigation of Rupture in Thin Fluid Films." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/177.
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The behavior of a fluid with a thin capillary meniscus can be modelled on a one-dimensional domain Ω = [−L, L] by the thin film equation ht = −(hnhxxx)x with boundary conditions hx(±L) = ±α (giving a fixed contact angle) and hxxx(±L) = 0 (prohibiting mass flux). It is desirable to know whether or not such a film experiences rupture; that is, whether there exists some x0, t0 (with t0 possibly ∞) such that h(x0, t0) = 0, corresponding to the appearance of a dry spot. We approach this problem using energy methods, which use the conservation or dissipation of quantities such as mass, surface area, coating energy, and other more abstract quantities to describe the behavior of the fluid. We present a brief analysis of the behavior of some of these energies, as well as a proof that, given certain assumptions, rupture cannot occur in a thin capillary meniscus for n > 4 and, in more restricted cases, for n > 7/2. We also show that rupture must occur for 0 < n < 1/2. We describe the asymptotic behavior of the regions in which rupture occurs. We also describe the numerical implementation of this problem and the advantages and drawbacks of using certain prewritten solvers in MATLAB and new implementations of θ-weighted schemes and the Newton-Raphson method. We propose uses of these numerical methods to make further progress on the problem.
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Tran, Vanthu Thy. "Newton's method as a mean value method." Akron, OH : University of Akron, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1176739678.
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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007."May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.
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Santos, Elma Pereira 1982. "Despacho integrado da geração termeletrica e da produção e transporte de gas natural com metodo de Newton." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259919.
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Orientador: Takaaki OhishiDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: O gás natural é um combustível fóssil que pode ser utilizado tanto na indústria como no comércio, residências e veículos. Uma aplicação importante do gás natural é como fonte primária para geração de energia elétrica em usinas termelétricas. Seu uso possibilita uma maior estabilidade ao Sistema Elétrico Brasileiro, pelo fato de depender menos do nível de água nos reservatórios para atendimento da demanda de energia elétrica. Como o gás natural possui uma estocagem complexa e onerosa, a quantidade de demanda de gás afeta diretamente as suas etapas de produção e transporte, já que toda a quantidade produzida e transportada deverá ser consumida. Desse modo, a operação do sistema de suprimento de gás natural é fortemente dependente das decisões de seus consumidores. As usinas termelétricas estão entre os maiores consumidores de gás, de forma que o despacho das usinas termelétricas afeta fortemente a operação do sistema de gás. Por outro lado, restrições no sistema de suprimento de gás também podem afetar a operação das usinas termelétricas. Esta forte dependência operativa entre estes dois sistemas requer uma operação coordenada para se obter uma operação mais eficiente e segura. Esta tese apresenta um modelo de despacho econômico aplicado a usinas termelétricas que usam gás natural como fonte primária, considerando os custos de produção, transporte de gás natural e de geração de energia elétrica. A modelagem matemática resulta em um problema misto não linear. Para resolução foi utilizada uma abordagem híbrida, que combina um modelo baseado em Programação Linear e um modelo não linear. O problema não linear é resolvido através do método de Newton.
Abstract: Natural gas is a fossil fuel that can be used in industry, trade, residence and vehicles, among others. An important application of natural gas is as a primary source for electricity generation in thermoelectric power plants. In the Brazilian Electric System this source increase the system stability, once it is less dependent of the water level in tanks to serve the demand for power. As natural gas storage it is more complex and expensive, the amount of gas directly affects the production and transportation stages, once the entire amount that is produced and transported must be consumed. Thus, the operation of the supply system of natural gas is strongly dependent on decisions of their consumers. The thermoelectric power plants are among the largest gas consumers, so the dispatch of thermoelectric plants affects strongly the gas system operation. On the other hand, restrictions in the gas supply system may also affect the operation of thermoelectric plants. This strong operative dependence between these two kinds of systems, requires a coordinated operation with the aim of obtaining a more efficient and safer operation. This thesis presents a model of economic dispatch applied to thermoelectric power plants that use natural gas as a primary energy source, considering the costs of production, transportation of the natural gas and electricity generation. The mathematical modeling results in a nonlinear mixed problem. For resolution was used a hybrid approach that combines a model based on Linear Programming and a nonlinear. The nonlinear problem is solved by the Newton's method.
Mestrado
Engenharia de Computação
Mestre em Engenharia Elétrica
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Meireles, Eduardo David. "Uma contribuição ao estudo do problema de mal condicionamento de redes eletricas de potencia sob o ponto de vista de estabilidade de tensão." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261719.
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Orientadores: Carlos Alberto de Castro Junior, Luiz Carlos Pereira da SilvaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: A literatura técnica registra uma série de metodologias propostas para a obtenção do estado de operação das chamadas redes mal condicionadas, ou seja, redes cujos modelos resultam em sistemas de equações de difícil resolução [1, 2]. Estas metodologias mostraram-se úteis também em situações em que a operação da rede é infactível, ou seja, situações em que o sistema de equações que representa a rede não apresenta soluções. Nestes casos, os métodos de resolução do problema de fluxo de carga convencionais divergem, não oferecendo informações úteis sobre a rede. Já as metodologias específicas para redes mal condicionadas oferecem, mesmo na situação de divergência, informações que podem ser úteis no sentido de apontar suas possíveis causas. Recentemente, foi levantada a possibilidade de que estas supostas redes mal condicionadas não existissem de fato, mas estivessem simplesmente operando em torno do seu limite de estabilidade de tensão [3], ou seja, o mal condicionamento seria resultado de problemas de estabilidade de tensão e não do mal condicionamento propriamente dito. De acordo com [3], após uma série de simulações não foram encontradas situações em que a rede fosse mal condicionada e estivesse operando em condições normais de operação no que diz respeito à estabilidade de tensão. Os testes mostrados em [3] foram realizados utilizando-se o fluxo de carga da continuação [4]. O objetivo deste trabalho é realizar alguns testes para analisar e discutir as conclusões de [3]. Para isso, algumas simulações adicionais foram realizadas para redes teste mal condicionadas apresentadas em [2], dentre outras. As conclusões deste trabalho apontam para a importância de se continuar a pesquisa para o desenvolvimento de métodos para a resolução de sistemas mal condicionados
Abstract: A number of methods for computing the operating state of the so-called ill-conditioned systems can be found in the literature. A power system is called ill-conditioned if its model results in a set of equations for which the resolution presents numerical difficulties [1, 2]. Those methods also showed to be useful tools in situations where the operation is unfeasible, that is, situations in which the set of equations that represents the network do not present any solution. In these cases the conventional load flow methods diverge and do not provide any useful information about the system operating condition. On the other hand, specific load flow methods for ill-conditioned systems do provide such information, even in divergence situations, and the possible causes of the numerical problems may be inferred. Recently, the possibility that the alleged ill-conditioned systems are in fact systems operating close to or beyond their voltage stability limit was discussed [3]. Therefore, the ill-conditioning would be the result of voltage stability problems rather than ill-conditioning itself. According to [3], after a number of simulations no situations where found such that the system was indeed ill-conditioned and was operating in normal condition as far as voltage stability is concerned. The tests carried out in [3] used continuation load method [4]. The main goal of this work is to carry out some simulation tests to analyze and discuss the conclusion presented in [3]. Also, some additional simulations were done for other ill-conditioned systems shown in [2], among others. The conclusions of this work point towards the importance of a continuing effort in the development of efficient methods for solving ill-conditioned systems
Mestrado
Energia Eletrica
Mestre em Engenharia Elétrica
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D'Orto, Manolo. "Comparing Different Approaches for Solving Large Scale Power Flow Problems on the CPU and GPU with the Newton-Raphson Method." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-289369.
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Power system modelling is increasing in importance. It is vital for power system operations and transmission grid expansions, and therefore the future energy transition. The Swedish power system is under fast development to face the progress of more flexible demand, a higher share of distributed renewable sources, and updated capacities. In order to ensure the power system’s secure physical capacities on a real-time basis in the future, the power system models must be able to handle this increased complexity. Hence, more efficient modelling and reduced computational time are necessary in order to secure the efficient daily operation of the Swedish grid. This thesis focuses on using the Newton-Raphson method to solve the power flow problem. The most computationally demanding part of the Newton- Raphson method is solving the linear equations at each iteration. Therefore, this study investigates different approaches to solve the linear equations on both CPU and GPU. Six different approaches were developed and evaluated in this thesis. Two of these run entirely on CPU while other two of these run entirely on GPU. The remaining two are hybrid approaches that run on both CPU and GPU. The main difference between the six approaches is where the linear equations are executed. However, all approaches either use LU or QR factorization to solve the linear equations. Two different hardware platforms were used to conduct the experiments, namely one single NVIDIA Quadro T2000 GPU on a laptop and one single NVIDIA V100 GPU on Kebnekaise system at HPC2N. The results show that the GPU gives better performance compared to the CPU for larger power flow problems. The results also show that the best performing version is a hybrid method where the Jacobian matrix is assembled on GPU; the preprocessing with KLU analysis is preformed on the CPU; and finally the linear equations are solved on the GPU. If the data transfers between the CPU and GPU are not considered, the hybrid version yielded a speedup factor of 46 in comparison with the baseline CPU version using the LU algorithm on the laptop. This speedup was obtained on the largest case with 9241 buses. Furthermore, the execution time of the hybrid version on the Kebnekaise system was approximately 114 times faster than the baseline CPU version on the laptop.Modellering av kraftsystem ökar i betydelse. Det är avgörande för driften av kraftsystemet och utbyggnad av nätet och därmed den framtida energiomställningen. Det svenska kraftsystemet är under snabb utveckling för att möta en mer varierande efterfrågan, en högre andel förnybara energikällor och uppdaterade kapacitetsbestämningsmetoder. För att i framtiden kunna säkerställa kraftsystemets säkra fysiska kapaciteter i realtid, måste kraftsystemmodellerna kunna hantera denna ökade komplexitet. Därför är effektivare modellering och reducerad beräkningstid nödvändig för att säkerställa effektiv daglig drift av det svenska nätet. Detta examensarbete fokuserar på Newton-Raphsons metod för att lösa stora lastflödesproblem. Den mest beräkningstunga delen av Newton-Raphsons metod är att lösa de linjära ekvationerna vid varje iteration. Därför undersöker denna studie olika metoder för att lösa dessa ekvationer både på CPU och GPU. Sex olika metoder har utvecklats och utvärderats. Två av dessa körs endast på CPU, ytterligare två körs enbart på GPU och de två sista är hybridmetoder som körs både på CPU och GPU. Den största skillnaden mellan de sex versionerna är var de exekverades. Alla tillvägagångssätt använder någon form av LU-faktorisering eller QR-faktorisering för att lösa de linjära ekvationerna. Två olika hårdvaruplattformar användes för att genomföra experimenten, nämligen ett NVIDIA Quadro T2000 GPU på en bärbar dator och ett NVIDIA V100 GPU på HPC2Ns Kebnekaise-system. Resultaten visar att GPU ger bättre prestanda jämfört med CPU för stora lastflödesproblem. Resultaten visar även att den version med bäst prestanda är en hybridmetod där Jacobimatrisen har konstruerats på GPU; förbehandlingarna sker med hjälp av KLU-analys på CPU; och slutligen löses de linjära ekvationerna på GPU. När dataöverföringarna mellan CPU och GPU inte togs i beaktande, var hybridversionen 46 gånger snabbare än CPU-version med LU- faktorisering på den bärbara datorn i fallet med 9241 bussar. Dessutom var hybridversionen ungefär 114 gånger snabbare när den exekverades på V100 GPU-systemet jämfört med CPU-versionen med LU-faktorisering på den bärbara datorn.
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Alves, Paulo Cesar. "Percepção de aprendizagens de alunos de cursos de engenharia sobre o Método de Newton-Raphson pelo uso de mapas conceituais." Pontifícia Universidade Católica de São Paulo, 2016. https://tede2.pucsp.br/handle/handle/19418.
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This developed search has the objective of analyse the conceptuals maps as a reflection instrument related to the understandment of a method to calculate the aproaches of real roots for high degree students. The chosen method is known as Newton-Raphson Method (NRM), that is normally part of the Numerical Calculus or Quantitative Methods and Computer subjects, that use the Derivated contant studied for first-year-engeneer students mainly in the subject of Differencial and Integral Cauculus. What was investigated was: how conceptuals maps can be used to understand as engeneer students can understan the NRM and its relation to Differencial and Integral Cauculus? Was used a quantitative aproache to this search that is situated at the educational field of Mathmatics. The theorical part is fundamented to the Learning Significative Theory of David Ausubel, using the Conceptual Maping of Joseph Novak. This search was developed with engeneer high degree students of a private institutuion, it was used the CmapTools software to the elaboration of digital conceptuals maps for the students. The final results were analysed with the objective of: firstly, try to realize students learnings about the NRM, obtained when students studied the subject of Numerical Calculus or Quantitative Methods and Computer. After we tryed to identify possible learnings that had an assimilation obliteradora. For this, the participants developed two conceptual maps using the CmapTools, the first map was elaborated with no influence of the searcher and the second was elaborated after a presentation of the method. The first conceptual digital maps elaborated for the participants revealed they understood how to elaborate a conceptual map using the CmapTools program, although they elaborated simple maps, with little relation to the used concepts. They also could present a NRM description in a logic way, revealing the students still remember some concepts envolved NRM and they also could present some relation that envolve these concepts. In relation to the second digital conceptual map, the students demostrated concepts that were not presented at the first digital conceptual map, some were elaborated with different structures and presented new terms of logic and coherence. In some maps is possible to realize the students remembered concepts studied in NRM and tryed to related to their maps by propositions. However, in some maps it is possible to detect the students only tryed to insert some NRM elements presented by the teacher. We also could realize that some studied concepts related to NRM seem to be interacting in the cognitive structure with previous knowledge, and with the NRM presentation, we concluded that some of these concepts seem to be present in a assimilation obliteradora
A pesquisa desenvolvida teve por objetivo analisar o uso de mapas conceituais como instrumento de reflexão a respeito da compreensão de um método para calcular aproximações de raízes reais por alunos do ensino superior. O método escolhido é conhecido como Método de Newton-Raphson (MNR), normalmente trabalhado na disciplina de Cálculo Numérico ou de Métodos Quantitativos e Computacionais, que utiliza o conteúdo de Derivada estudado por alunos no primeiro ano de cursos de Engenharia, principalmente na disciplina de Cálculo Diferencial e Integral. A questão a investigar foi: Como Mapas Conceituais podem ser utilizados para entender como alunos de cursos de Engenharia compreendem o MNR e sua relação com o Cálculo Diferencial e Integral? Foi utilizada uma abordagem qualitativa para a pesquisa que está situada na área da Educação Matemática. O referente teórico está fundamentado na Teoria da Aprendizagem Significativa de David Ausubel, utilizando a técnica de Mapeamento Conceitual de Joseph Novak. A pesquisa foi desenvolvida junto a alunos de cursos de Engenharia de uma instituição privada de ensino superior, com a utilização do software CmapTools para que os alunos elaborassem mapas conceituais digitais. Os dados foram analisados com o objetivo de, primeiramente, tentar perceber aprendizagens de alunos sobre o MNR, obtidas quando os alunos cursaram a disciplina de Cálculo Numérico ou Métodos Quantitativos e Computacionais. Depois, tentar identificar possíveis aprendizagens que tiveram uma assimilação obliteradora. Para tanto, os participantes desenvolveram dois mapas conceituais utilizando a ferramenta CmapTools, sendo o primeiro mapa elaborado sem nenhuma influência do pesquisador e o segundo após uma apresentação do referido método. As análises dos primeiros mapas conceituais digitais elaborados pelos participantes revelou que os mesmos entenderam como elaborar um mapa conceitual por meio do programa CmapTools, embora tenham elaborado mapas simples, com poucas relações entre os conceitos utilizados. Também conseguiram apresentar de maneira lógica uma descrição do MNR, revelando que os alunos ainda possuíam lembranças de alguns conceitos envolvidos no MNR e conseguiram apresentar algumas relações entre esses conceitos. Em relação ao segundo mapa conceitual digital, os alunos apresentaram conceitos que não estavam presentes no primeiro mapa conceitual digital, alguns foram elaborados com estruturas diferentes e apresentaram novos termos de ligações com lógica e coerência. Em alguns mapas é possível perceber que os alunos relembraram conceitos estudados no MNR e tentaram relacioná-los em seus mapas por meio de proposições. Entretanto, em alguns mapas é possível perceber que os referidos alunos apenas tentaram inseriram alguns elementos do MNR apresentado pelo professor. Notamos, ainda, que alguns conceitos estudados relacionados ao MNR parecem estar interagindo na estrutura cognitiva com conhecimentos prévios e que, com a apresentação do MNR, inferimos que alguns desses conceitos parecem estar presentes em uma assimilação obliteradora
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Sassi, Carlos Alberto. "Sobre o desempenho de métodos Quase-Newton e aplicações." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306041.
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Orientador: Maria Aparecida Diniz EhrhardtDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Iniciamos este trabalho com o estudo de equações não lineares, transcendentais de uma única variável, com o objetivo principal de abordar sistemas de equações não lineares, analisar os métodos, algoritmos e realizar testes computacionais, embasados na plataforma MatLab "The Language of Technical computer - R2008a - version 7.6.0.324_. Os algoritmos tratados se referem ao método de Newton, métodos Quase-Newton, método Secante e aplicações, com enfoque na H-equação de Chandrasekhar. Estudamos aspectos de convergência de cada um destes métodos que puderam ser analisados na prática, a partir dos experimentos numéricos realizados
Abstract: This work begins with the study of nonlinear and transcendental equations, with only one variable, which has the main purpose to study systems of nonlinear equations, methods and algoritms, in order to accomplish computational tests using MatLab Codes "The Language of Technical computer - R2008a - version 7.6.0.324". These algoritms were concerned to Newton's method, Quasi-Newton method, Secant method, and the main application was the Chandrasekhar H-Equation. Convergence studies for these methods were analysed with the applied numerical methods
Mestrado
Matematica
Mestre em Matemática
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Kuhn, Wolfgang. "Rigorous and reasonable error bounds for the numerical solution of dynamical systems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28941.
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Akhtar, Naeem, and Ahmad Alzghoul. "Time performance comparison in determining the weak parts in wooden logs." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5703.
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The steadily increasing demand of wood forces sawmills to increase the efficiency and effectiveness of their equipments. The weak parts and the twist in wooden logs have been documented as the most common and crucial defect in sawn lumber.
In this thesis we are going to implement a program which is able to determine the weak parts in wooden logs. The implementation will be in two languages C++ and Matlab. Parts of the program are going to be implemented sometimes by C++ and sometimes by Matlab therefore different designs are going to be tested. The aim of this thesis is to check whether these designs will meet the real time bound of 10 m/s.
The result shows that there is a huge difference in time performance for the different designs. Therefore, different discretization levels were used in order to meet the deadline of 10m/s. We found that in order to get better speed one should calculate the matrix for the function F and the Jacobian function J by using C++ not by Matlab. Also we found that when we called functions from one language to another an extra time is added.
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Bokka, Naveen. "Comparison of Power Flow Algorithms for inclusion in On-line Power Systems Operation Tools." ScholarWorks@UNO, 2010. http://scholarworks.uno.edu/td/1237.
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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.
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Santos, Janio Cesar Alencar dos. "O método de Newton-Raphson na solução da equação 2 x = x 2: uma motivação para o estudo da existência de logaritmo de números negativos." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8756.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work are discussed about two central problems: the solution for equation 2 x = x 2 and the existence of logarithm of negative numbers. In this sense, the Newton- Raphson method, some aspects about complex numbers and Taylor's series are presented with detail. Our aim was produce a good research and study material directed for teachers of basic education and undergraduate students.
Neste trabalho são discutidos dois problemas centrais: a solução da equação 2 x = x 2 e a existência de logaritmos de números negativos. Nesse sentido, são apresentados de forma detalhada o método de Newton-Raphson, alguns tópicos sobre números complexos e a fórmula de Taylor. A equação 2 x = x 2 será resolvida por meio do métodonumérico de Newton-Raphson. A análise desta equação nos conduzirá à definição de logaritmos de números negativos. Nosso principal objetivo ao escrever este trabalho foi confeccionar uma bom material de pesquisa direcionado a professores da educação básica e estudantes de graduação de ciências exatas.
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Gerardin, Rodrigo Ceccatto. "Modelo dinamico do sistema pistão-biela-manivela com mancais hidrodinamicos." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263457.
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Orientador: Marco Lucio BittencourtDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Atualmente, devido as exigências comerciais e técnicas, os motores de combustão interna operam com pressões de combustão cada vez mais altas. Ao mesmo tempo, deve-se otimizar a operação de todo sistema e a forma dos componentes levando-se em conta a melhor performance e redução de peso. Para um melhor entendimento do comportamento dinâmico de um motor de multi cilindros, é necessário verificar a cinemática e a dinâmica para apenas um cilindro como feito neste trabalho. O foco principal deste trabalho é desenvolver um modelo matemático para determinar as distribuições de pressão e as forças atuantes nos mancais hidrodinâmicos para um cilindro de um motor de combustão interna. Um modelo dinâmico do sistema de pistão-biela-manivela é apresentado e permite calcular as forças dinâmicas e folgas no mancal principal, olhais maior e menor da biela derivados da pressão de combustão. O modelo matemático do mancal hidrodinâmico radial é oriundo da equação de Reynolds e resolvido utilizando o Método de Elementos Finitos. O sistema dinâmico não-linear é resolvido utilizando o método iterativo de Newton-Raphson para cada passo de integração no tempo
Abstract: Due to the current commercial and technical requirements, the internal combustion engines must operate under higher pressures. It is also necessary to optimize the system operation and the shape of the components aiming at increasing the performance and weight reducing. For a better understanding of the dynamical behavior of a multi-cylinder engine, it is necessary to verify the kinematics and dynamics for just one cylinder, as considered in this work. The main focus of this work is the development of a mathematical model to determine the pressure distributions and the hydrodynamic bearing forces for one cylinder internal combustion engine. The dynamical model of the piston-conrod-crank system is presented and allows the calculation of the dynamic forces and clearances obtained from the combustion pressure for the main, big-end and small-end bearings. The mathematical model of the hydrodynamic bearing comes from the Reynolds equation and is solved by the Finite Element Method. The non-linear dynamic system is solved by the iterative Newton-Rhapson method for each time integration step
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
19
Barbosa, Neto Antonio Marinho 1989. "Desenvolvimento de um simulador PVT composicional para fluidos de petróleo." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265808.
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Orientador: Antonio Carlos BannwartDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências
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Resumo: Fluidos de petróleo, incluindo gás, condensado e óleo leve, são misturas complexas de hidrocarbonetos. O conhecimento sobre o comportamento de fases destas misturas é de interesse para a indústria de petróleo, desde o reservatório, produção, transporte, até o processamento e refino de petróleo. Além disso, pacotes termodinâmicos computacionais para predizer o comportamento de tais misturas são de grande interesse nesta indústria. Neste sentido, uma ferramenta computacional para prever com precisão as propriedades termodinâmicas utilizando cálculos de equilíbrio de fases pode desempenhar um papel importante para aplicações de projeto e operações de campo. Equações de estado cúbicas tem sido amplamente utilizada para predizer o comportamento de fases e propriedades volumétricas de fluidos de petróleo devido a sua simplicidade e alto desempenho computacional. Diante deste contexto, o presente trabalho teve como objetivo principal desenvolver um simulador PVT composicional, de fácil manuseio, porém completo, capaz de avaliar o comportamento volumétrico e de fases de fluidos de petróleo em diferentes condições operacionais (P, T) a partir da modelagem do equilíbrio líquido-vapor e do equilíbrio líquido-líquido-vapor. A ferramenta computacional foi desenvolvida na linguagem de programação Visual Basic Applications (VBA) em aplicativo Excel. Uma interface gráfica foi construída em aplicativo Excel. O programa, denominado PVTpetro, consiste basicamente em três módulos computacionais e suas funções auxiliares. O módulo de cálculo de flash (P, T) 2 fases isotérmico para misturas de hidrocarbonetos consiste no equilíbrio líquido-vapor (ELV) para sistemas óleo-gás multicomponentes. O módulo de cálculo de flash (P, T) 3 fases isotérmico avalia sistemas envolvendo óleo, água e gás (OWG). E, o módulo de cálculo de propriedades volumétricas de fluidos de petróleo que calcula o peso molecular, o volume e a massa específica das fases existentes no sistema. A ferramenta foi validada via comparação entre os resultados de pacotes termodinâmicos comerciais (Wimprop, Hysys, COMThermo) e os do programa desenvolvido. Os resultados gerados pelo PVTpetro foram avaliados através do cálculo do desvio relativo em relação às respostas dos softwares comerciais. Desta forma, verificou-se para o módulo de cálculo flash (P, T) 2 fases que os valores de desvio em relação ao Wimprop e Hysys foram inferiores a 1% para os estudos realizados. Enquanto que, para o módulo de cálculo flash (P, T) 3 fases os valores de erro relativo se concentraram na faixa de 0 ¿ 5% quando comparados com os pacotes termodinâmicos Hysys e COMThermo. De uma maneira geral, os resultados gerados pelo PVTpetro apresentaram-se satisfatórios em todos os cálculos propostos. Na validação do módulo de cálculo das propriedades volumétricas, feita de forma qualitativa, observou-se que o comportamento das propriedades em função da pressão e em diferentes temperaturas, gerado pelo PVTpetro, reproduziram as curvas fornecidas pelo Hysys, em todas as condições investigadas. Portanto, além de se apresentar confiável em seus cálculos o PVTpetro mostrou ser de fácil manuseio e intuitivo para o usuário, facilitando assim o trabalho em vários casos
Abstract: Petroleum fluids, which include gas, condensate and light oil, are complex hydrocarbons mixtures. There is a great deal of interest in the oil industry in computational thermodynamic packages able to predict the phase behavior of such mixtures, from the reservoir, production, transportation until the oil processing and refining. In this sense, a computational tool that accurately predicts thermodynamic properties using phase equilibrium calculations have an important role in designing applications and field operations. Cubic equations of state have been widely used to predict the phase behavior and bulk properties of petroleum fluids due to its simplicity and high computational performance. This study focused on developing a PVT compositional simulator, easy to use, able to assess the bulk properties and phase behavior of petroleum fluids at different operating conditions (P, T) from the modeling of the vapor-liquid equilibrium (VLE) and the vapor-liquid-liquid equilibrium (VLLE). The computational tool was developed in Visual Basic Applications (VBA) programming language, with a graphic interface built in Excel. The program, named PVTpetro, consists in three basic computational modules and their auxiliary functions. The isothermal two phase flash (P, T) module calculation to hydrocarbon mixtures consists of VLE for multi-component oil-gas systems. The isothermal three phase flash (P, T) module calculation evaluates oil, water and gas (OWG) systems. Lastly, the bulk properties of petroleum fluids calculation module calculates the molecular weight, the volume and density of the system phases. The tool has been validated through the comparison between the results of commercial thermodynamic packages (Wimprop, Hysys, COMThermo) with the developed program. The results were evaluated by the relative deviation calculation between these commercial software and PVTpetro results. For the isothermal two-phase flash (P, T) calculation module were observed deviations below 1% for Wimprop and Hysys results. For the isothermal three phase flash (P, T) calculation module the deviations were about 0 and 5% for Hysys and COMThermo. For the bulk properties calculation module the results by PVTpetro and Hysys showed a good agreement in all investigated conditions, ensuring the PVTpetro reliability
Mestrado
Explotação
Mestre em Ciências e Engenharia de Petróleo
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Shaterzadeh-Yazdi, Mohammad Hossein 1991. "Análise de contato entre dois corpos elásticos usando o Método dos Elementos de Contorno." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265747.
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Orientadores: Paulo Sollero, Eder Lima de AlbuquerqueDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: Em problemas de contato mecânico entre dois corpos elásticos, o cálculo de tensões e deformações dos componentes é de grande importância. Em casos particulares os corpos estão sujeitos a cargas normal e tangencial na presença de atrito, o qual aumenta a complexidade do problema. O estudo do fenômeno e a modelagem do problema, empregando o método dos elementos de contorno (MEC), é apresentado neste trabalho. Devido à presença de atrito e restrições de contato, esse problema torna-se um caso não linear. A não linearidade do problema foi contornada com a aplicação incremental de carga e o uso de um método de resolução de sistemas não lineares. A zona de contato é uma das variáveis do problema e pode conter estados de adesão e escorregamento, simultaneamente. Esses estados dependem dos esforços normais e tangenciais no componente e podem variar durante o processo de aplicação de carga. Dessa forma, cada incremento de carga pode perturbar em relação ao estado anterior. Portanto, o cálculo de variáveis e a atualização do sistema de equações em cada iteração é indispensável. Por este motivo, um algoritmo robusto para definição dos estados de contato é proposto. Como o sistema de equações obtido é não linear, o uso de um método numérico adequado é exigido. Para a solução deste sistema, o método de Newton foi aplicado, o qual permite a verificação do estado de contato em cada incremento. A análise é feita com o uso de elementos quadráticos contínuos, apresentando resultados contínuos e sem oscilação. A comparação dos resultados com as soluções analíticas de Hertz e Mindlin-Cattaneo mostram boa concordância
Abstract: The computation of stresses and strains on the components is of great importance, when the contact mechanics problems between two elastic bodies are analyzed. In particular cases, bodies are subjected to normal and shear loading in the presence of friction, which increases the complexity of the problem. The study of the phenomenon and modeling of the problem, using the boundary element method (BEM), are presented in this work. Due to the presence of friction and natural restrictions, this problem becomes non-linear. The non-linearity of the problem was solved with an incremental applied load and with the use of solvers to non linear systems. The contact zone can contain stick and slip states, simultaneously. These states are dependent on the normal and shear forces on the component and can vary during the application load process. Thus, each load increment can violate the previous state and therefore, the evaluation of variables and the updating of the system of equations after each iteration is indispensable For this reason, a robust algorithm for contact state definition is suggested. Since a non linear system of equations is obtained, an appropriate numerical method is required. To solve this system, Newton¿s method is applied, which allows the verification of the state of contact at each increment. The analysis is done with the use of quadratic continuous elements and provides continuous and non-oscillatory results. Comparisons of the results with the analytical solutions of Hertz and Mindlin-Cattaneo show good agreement
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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Picart, Philippe. "Contribution à la résolution numérique des problèmes élasto-plastiques et élasto-viscoplastiques en transformations finies." Valenciennes, 1986. https://ged.uphf.fr/nuxeo/site/esupversions/c0aa3577-2ebe-4da6-82da-563b9f60f2ea.
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La première partie des travaux concerne la construction, la mise au point et l'implémentation de quelques méthodes numériques de résolution du problème non linéaire en élasto-plasticité ou élasto-viscoplasticité en transformations finies. Une étude comparative globale des méthodes de Newton-Raphson, de Newton-Raphson modifiées et de quasi-Newton sur des tests numériques appropriés nous a permis de déterminer les stratégies de résolution à adopter en fonction des critères suivants: fiabilité, précision, rapidité de convergence et temps de calcul. Dans la seconde partie nous avons développé un algorithme implicite de calcul en élasto-viscoplasticité incluant les effets thermiques adiabatiques. Une configuration intermédiaire d'intégration est utilisée pour le calcul des contraintes, les variables internes sont actualisées selon un schéma implicite. Nous en déduisons une expression analytique de l'opérateur élasto-viscoplastique tangent associé de manière consistante au schéma d'intégration proposé. Nous présentons une série de tests de validation ainsi qu'un certain nombre de tests complémentaires en élasto-plasticité et élasto-viscoplasticité permettant d'évaluer les capacités et l'aptitude de notre code de calcul à résoudre les problèmes industriels de mise en forme des métaux.
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Wang, Chen. "Transient performance simulation of gas turbine engine integrated with fuel and control systems." Thesis, Cranfield University, 2016. http://dspace.lib.cranfield.ac.uk/handle/1826/9881.
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Two new methods for the simulation of gas turbine fuel systems, one based on an inter-component volume (ICV) method, and the other based on the iterative Newton Raphson (NR) method, have been developed in this study. They are able to simulate the performance behaviour of each of the hydraulic components such as pumps, valves, metering unit of a fuel system, using physics-based models, which potentially offer more accurate results compared with those using transfer functions. A transient performance simulation system has been set up for gas turbine engines based on an inter-component volume (ICV). A proportional- integral (PI) control strategy is used for the simulation of engine control systems. An integrated engine and its control and hydraulic fuel systems has been set up to investigate their coupling effect during engine transient processes. The developed simulation methods and the systems have been applied to a model turbojet and a model turboshaft gas turbine engine to demonstrate the effectiveness of both two methods. The comparison between the results of engines with and without the ICV method simulated fuel system models shows that the delay of the engine transient response due to the inclusion of the fuel system components and introduced inter-component volumes is noticeable, although relatively small. The comparison of two developed methods applied to engine fuel system simulation demonstrate that both methods introduce delay effect to the engine transient response but the NR method is ahead than the ICV method due to the omission of inter-component volumes on engine fuel system simulation. The developed simulation methods are generic and can be applied to the performance simulation of any other gas turbines and their control and fuel systems. A sensitivity analysis of fuel system key parameters that may affect the engine transient behaviours has also been achieved and represented in this thesis. Three sets of fuel system key parameters have been introduced to investigate their sensitivities, which are, the volumes introduced for ICV method applied to fuel system simulation; the time constants introduced into those first order lags tosimulate the valve movements delay and fuel spray delay effect; and the fuel system key performance and structural parameters.
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Ciftci, Guclu Koray. "Nonlinear Analysis Of Reinforced Concrete Frame Structures." Master's thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615549/index.pdf.
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Reinforced concrete frames display nonlinear behavior both due to its composite nature and
the material properties of concrete itself. The yielding of the reinforcement, the non-uniform
distribution of aggregates and the development of cracks under loading are the main
reasons of nonlinearity. The stiffness of a frame element depends on the combination of the
modulus of elasticity and the geometric properties of its section - area and the moment of
inertia. In practice, the elastic modulus is assumed to be constant throughout the element
and the sectional properties are assumed to remain constant under loading.
In this study, it is assumed that the material elasticity depends on the reinforcement ratio and
its distribution over the section. Also, the cracks developing in the frame element reduces the
sectional properties. In case of linear analysis, the material and sectional parameters are
assumed to be constant. In practice, the modulus of elasticity E is a predefined value based
on previous experiments and the moment of inertia I is assumed to be constant throughout
the analysis. However, in this study, E and I are assumed to be combined. In other words,
they cannot be separated from each other throughout the analysis. These two parameters
are handled as a single parameter as EI . This parameter is controlled by the reinforcement
ratio and its configuration, sectional properties and deformation of the member.
Two types of analysis, namely a sectional and a finite element analyses, are used in this
study. From the sectional analysis, the parameter EI is calculated based on the sectional
geometry, material properties and the axial load applied on the section. The parameter EI is
then used in the finite element analysis to calculate the sectional forces and the nodal
displacements. For the nonlinear analysis, the Newton-Raphson iterative approach is
followed until convergence is obtained.
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Magadi, Suma. "Use of an Integrate Method to Trace Coexistence Curves: Application to Pure and Multi-Component Mixtures." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1399555573.
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Pontes, Rafael de Paiva. "Nova metodologia full Newton para consideração dos limites de geração de potência reativa no problema de fluxo de potência." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/6933.
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Este trabalho, realiza uma revisão da metodologia tradicional, de representação dos limites de geração de potência reativa, na solução do problema de fluxo de potência, em coordenadas polares, pelo método de Newton-Raphson. Apresenta uma nova modelagem para o tratamento destes limites, baseada em uma formulação full Newton do problema. Para tanto, utiliza-se um conjunto de chaves sigmoides, que incorporam novas equações à matriz Jacobiana, de acordo com a geração de potência reativa da barra. De forma a tornar o sistema possível e determinado, a geração de potência reativa, é tratada como uma nova variável de estado do problema, corrigida a cada iteração do método de Newton. A formulação proposta, utiliza duas chaves sigmoides para o tratamento dos limites de geração de potência reativa, em barras PV e, duas chaves, que consideram o procedimento de retomada do controle (conhecido como estratégia de backoff ), das barras que atingiram limites, caso necessário. Dessa forma, não há uma mudança explícita no tipo da barra, como na metodologia tradicional, e a dimensão da matriz Jacobiana é mantida constante. Neste trabalho, todo o equacionamento e formulação, foi desenvolvido através do programa Matlab, e os resultados foram validados, utilizando-se o programa de análise de redes – ANAREDE, versão acadêmica, disponibilizada pelo Centro de Pesquisas de Energia Elétrica (CEPEL). São avaliados alguns sistemas benchmark IEEE e os resultados obtidos, demonstram a eficácia das formulações propostas.
This work, presents a review of the traditional methodology, of representing the limits of reactive power generation, in the solution of the power flow problem, in polar coordinates, by the Newton-Raphson method. Presents a new modeling for the treatment of these limits, based on a formulation full Newton of the problem. For this purpose, a set of sigmoid switches is used, to incorporate new equations to the Jacobian matrix, according to the generation of reactive power of the bus. In order to produce a system possible and determined, reactive power generation, is treated as a new problem state variable, corrected at each iteration of the Newton’s method. The proposed formulation, use two sigmoid switches for the tratment of reactive power generation limits, in PV buses and also, two switches, that consider the procedure of resumption of control (procedure known as backoff strategy), of the buses that reached some limit, if necessary. Thus, there is no explicit change in the bus type, as in traditional methodology, and the Jacobian matrix dimension is kept constant. In this work, all equation and formulation, were developed through Matlab software, and the results were checked, using the network analysis program – ANAREDE, academic version provided by Electrical Energy Research Center (CEPEL). Some IEEE benchmark systems are evaluated, and the results obtained, demonstrates the efficacy of the proposed formulations.
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Anzai, Alexandre Haruiti 1978. "Um modelo de fluxo de carga para sistemas de distribuição contendo diferentes tecnologias de geração distribuida." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260000.
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Orientadores: Walmir de Freitas Filho, Luiz Carlos Pereira da SilvaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Esta dissertação de mestrado apresenta um modelo monofásico de fluxo de carga para sistemas de distribuição capaz de representar as tecnologias mais comumente utilizadas em geração distribuída. Tal ferramenta permite a realização de estudos técnicos e de diagnósticos em relação à conexão de um novo gerador nos alimentadores de sistemas de distribuição. Propõe-se um método de cálculo de fluxo de carga expandido, no qual os modelos dos geradores, turbinas e seus controles são levados em conta na resolução das equações do fluxo de carga. O método de fluxo de carga expandido considera que o sistema é modelado através de equações algébricas e diferenciais num ponto de equilíbrio, ao invés da modelagem convencional baseada apenas em equações algébricas de balanço de potência. As tecnologias de geração analisadas são compostas por máquinas síncronas, máquinas de indução e geradores conectados via conversores estáticos de potência. Diferentes fontes primárias de energia são consideradas, incluindo turbinas a vapor, hidráulicas e eólicas, além dos sistemas de controle associados às partes elétrica e mecânica de caqa tecnologia. O método de fluxo de carga proposto é testado usando uma rede de distribuição real do Estado de São Paulo
Abstract: This dissertation presents a monophasic load flow model for distribution systems capable of representing the most common technologies used for distributed generation. The developed computational tool allows the accomplishment of technical studies and diagnosis related to the impacts of connecting new generators on distribution feeders. It is proposed an expanded load flow method, including models for generators, turbines and associated controllers, for the solution of load flow equations. The expanded load flow method represents the system by using algebraic and differential equations in a equilibrium point, instead of the conventional modeling based only on the power balance algebraic equations. The technologies used for generation are composed by synchronous machines, induction machines and inverter based generators. Different prime mover technologies are considered, including steam turbines, hydraulic turbines, wind turbines, and control systems associated with the electric and mechanical operation of each technology. The proposed load flow method is tested by using a real distribution network of the State of São Paulo
Mestrado
Energia Eletrica
Mestre em Engenharia Elétrica
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Bravenec, Ladislav. "Porovnání různých metod nelineárního výpočtu konstrukcí s hlediska rychlosti, přesnosti a robustnosti." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2013. http://www.nusl.cz/ntk/nusl-226458.
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The aim of the thesis is to compare the iterative methods which program RFEM 5 uses the non-linear calculations of structures, namely the analysis of large deformations and post critical analysis. Comparison should serve as a basis for which calculation method is the most accurate, fastest and most reliable in terms of getting results. Time-consuming will be judged according to the calculation of the solution and the time needed to compute one iterativ. Robustness we will compare the reliability of methods in in normal use. Accuracy of the calculation will be determined by comparing the maximum deformation structures. Comparison will be made with examples from practice.
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Shirabayashi, Wesley Vagner Ines. "Estrategias de segunda ordem para problemas de complementaridade." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306537.
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Orientadores: Sandra Augusta Santos, Roberto AndreaniTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho reformulamos o problema de complementaridade não linear generalizado (GNCP) em cones poliedrais como um sistema não linear com restrição de não negatividade em algumas variáveis, e trabalhamos na resolução de tal reformulação por meio de estratégias de pontos interiores. Em particular, definimos dois algoritmos e provamos a convergência local de tais algoritmos sob hipóteses usuais. O primeiro algoritmo é baseado no método de Newton, e o segundo, no método tensorial de Chebyshev. O algoritmo baseado no método de Chebyshev pode ser visto como um método do tipo preditor-corretor. Tal algoritmo, quando aplicado a problemas em que as funções envolvidas são afins, e com escolhas adequadas dos parâmetros, torna-se o bem conhecido algoritmo preditor-corretor de Mehrotra. Também apresentamos resultados numéricos que ilustram a competitividade de ambas as propostas.
Abstract: In this work we reformulate the generalized nonlinear complementarity problem (GNCP) in polyhedral cones as a nonlinear system with nonnegativity in some variables and propose the resolution of such reformulation through interior-point methods. In particular we define two algorithms and prove the local convergence of these algorithms under standard assumptions. The first algorithm is based on Newton's method and the second, on the Chebyshev's tensorial method. The algorithm based on Chebyshev's method may be considered a predictor-corrector one. Such algorithm, when applied to problems for which the functions are affine, and the parameters are properly chosen, turns into the well-known Mehrotra's predictor corrector algorithm. We also present numerical results that illustrate the competitiveness of both proposals.
Doutorado
Otimização
Doutor em Matemática Aplicada
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Begiato, Rodolfo Gotardi 1980. "Métodos híbridos e livres de derivadas para resolução de sistemas não lineares." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305946.
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Orientadores: Márcia Aparecida Gomes Ruggiero, Sandra Augusta SantosTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: O objetivo desta tese é tratar da resolução de sistemas não lineares de grande porte, em que as funções são continuamente diferenciáveis, por meio de uma abordagem híbrida que utiliza um método iterativo com duas fases. A primeira fase consiste de versões sem derivadas do método do ponto fixo empregando parâmetros espectrais para determinar o tamanho do passo da direção residual. A segunda fase é constituída pelo método de Newton inexato em uma abordagem matrix-free, em que é acoplado o método GMRES para resolver o sistema linear que determina a nova direção de busca. O método híbrido combina ordenadamente as duas fases de forma que a segunda é acionada somente em caso de falha na primeira e, em ambas, uma condição de decréscimo não-monótono deve ser verificada para aceitação de novos pontos. Desenvolvemos ainda um segundo método, em que uma terceira fase de busca direta é acionada em situações em que o excesso de buscas lineares faz com que o tamanho de passo na direção do método de Newton inexato torne-se demasiadamente pequeno. São estabelecidos os resultados de convergência dos métodos propostos. O desempenho computacional é avaliado em uma série de testes numéricos com problemas tradicionalmente encontrados na literatura. Tanto a análise teórica quanto a numérica evidenciam a viabilidade das abordagens apresentadas neste trabalho
Abstract: This thesis handles large-scale nonlinear systems for which all the involved functions are continuously differentiable. They are solved by means of a hybrid approach based on an iterative method with two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists of a matrix-free inexact Newton method that employs the GMRES to solve the linear system that computes the search direction. The proposed hybrid method neatly combines the two phases in such a way that the second is called only in case the first one fails. To accept new points in both phases, a nonmonotone decrease condition upon a merit function has to be verified. A second method is developed as well, with a third phase based on direct search, that should act whenever too many line searches have excessively decreased the steplenght along the inexact- Newton direction. Convergence results for the proposed methods are established. The computational performance is assessed in a set of numerical experiments with problems from the literature. Both the theoretical and the experimental analysis corroborate the feasibility of the proposed strategies
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Fantini, Jay A. "CONVERSION FROM ENGINEERING UNITS TO TELEMETRY COUNTS ON DRYDEN FLIGHT SIMULATORS." International Foundation for Telemetering, 1998. http://hdl.handle.net/10150/609226.
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International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, CaliforniaDryden 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.
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Andreussi, Tommaso. "A variational treatment of hydrodynamic and magnetohydrodynamic flows." Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85792.
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In order to describe stationary plasma flows in thrusters based on plasma propulsion, an ideal,
axial symmetric, single-fluid motion is assumed. The conservation laws of conductive fluids
and the Maxwell’s equations lead to a second order differential equation for the magnetic flux
function ψ, i.e. the generalized Grad Shafranov (GS) equation, and to two implicit constraints
relating ψ to the plasma density and the azimuthal velocity. This set of three equations, one
differential and two algebraic, is then expressed using a variational approach and the solution is
obtained in a straightforward manner from the extremum of the appropriate Lagrangian functional.
The numerical approach is based on Ritz’s method, which has the advantage of producing
analytic (though approximate) solutions. Both non-conductive fluids, where the acceleration
can only be obtained exploiting the internal energy of the flow (thermodynamic process), and
conductive fluids, where the electromagnetic forces play a fundamental role, are considered.
In order to apply this approach to the acceleration processes in nozzle-like configurations, an
open-boundary geometry is investigated and specific attention is paid to a physical definition
of boundary conditions. Hydrodynamic shocks are taken into account and it is shown that
the appropriate jump conditions follow implicitly from a natural extension of the Lagrangian
variational principle. A comparison test with an explicit solution permits an estimate of the
approximate results.
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Brown, Nathan L. "An evaluation of transfer capability limitations and solutions for South Mississippi Electric Power Association." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-03252002-094046.
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Nyzen, Ronald A. "Spherically-actuated platform manipulator with passive prismatic joints." Ohio : Ohio University, 2002. http://www.ohiolink.edu/etd/view.cgi?ohiou1174930163.
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von, Dewall Johannes, and Markus Johansson-Näslund. "Hållfasthetssimulering av hydrauliska högtryckskopplingar." Thesis, Högskolan i Skövde, Institutionen för ingenjörsvetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:his:diva-15915.
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Hydrauliska högtryckskopplingar av typen FEM ½” studeras med avsikten att fastställa en effektiv beräkningsmetodik som kan användas till att prediktera kopplingarnas hållfasthet. Metodiken utgörs av finita element analyser (FEA), och valideras av experimentella trycktester utförda på kopplingstypen FEM ½”. Genom FEA kan kopplingarnas hållfasthetsbeteende och maximala belastningskapacitet studeras virtuellt, vilket minskar behovet av experimentella tester och medför potential för optimering av produkterna. Arbetet utförs på Parker Hannifin AB i Skövde. Experimentella tester utförs på 20 stycken kopplingspar av typen FEM ½” för att utöka förståelsen av kopplingarnas beteende under brottsförloppet och för att prediktera trycket som medför haveri. Testernas genomförande och struktur baseras på metodiken Design of Experiments (DOE). Kritiska komponenter identifieras utifrån experimentets resultat, vilka sedan studeras närmare via FEA. Analyserna valideras utifrån standarder som kopplingarna ska efterfölja, och mätdata insamlad under de experimentella testerna. Från de experimentella testerna är det komponenterna: kulhållaren, styrningen och nippelhuset som upptar belastning i störst utsträckning. Vid haveri framgår två brottmoder som vanliga, att kulhållaren slits isär samt att styrningen brister, båda fallen uppkommer vid approximativt samma tryck. FE-analyserna för styrningen och kulhållaren visar god överensstämmelse med experimentella resultat. Deformationerna skiljer sig dock mellan analyserna och de experimentella testerna, var nippelhusets analyser uppvisar störst avvikelser. FE-modellerna uppvisar god potential för att prediktera samt utvärdera kopplingarnas mekaniska beteende under tryckbelastning. Analyserna är dock helt beroende av ingående data, var saknaden av en verklig materialmodell medför avvikelser från experimentella resultat. Förhållandet framgår tydligt av nippelhuset, vars relaterade härdningsegenskaper saknas.Hydraulic FEM ½" high pressure couplings are studied with the purpose of establishing an effective methodology that can be used to predict the strength of the couplings. The methodology consists of finite element analyzes (FEA) and is validated by experimental pressure tests, performed on the FEM ½” couplings pairs. Using FEA, the couplings solid mechanical behavior and maximum load ability can be viewed virtual, reducing the need for experimental tests and gives the potential for optimized products. The work is performed at Parker Hannifin AB in Skovde. Experimental tests are performed on 20 FEM ½” couplings pairs, to understand the solid mechanical behavior of the couplings until failure occurs, and to predict the maximum pressure that can be applied. The experimental structure and performance is based on the method Design of Experiments (DOE). Critical components are identified based on the results from the experimental tests, which are then studied more closely through FEA. The analysis are validated based on the applied material model, and data collected during the experimental tests. From the experimental tests it is shown that the components: ball cage, guide and plug housing are the components in which failure occur. In case of failure, two failure modes appear as common, that the ball cage is worn apart and that the guide burst, both types of failure modes occur at a similar pressure. The analysis for the guide and ball cage corresponds with the experimental outcomes. Differences occurs however when looked at the deformations, in which the plug housing shows the largest deviation when compared to the experimental results. The usage of FE-models appears to be appropriate for predicting and evaluating the mechanical strengths of the couplings during pressure loads. The analysis are however entirely dependent on the input data, where an incorrect material model generates incorrect results. The relationship is shown for the plug housing, which lack the mechanical properties related to curing processes.
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Valeš, Jan. "Počítačová simulace kolapsu budovy zplastizováním kloubů." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2012. http://www.nusl.cz/ntk/nusl-225731.
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The aim of the thesis is to create an analytical 2D model of a multi-storey building and its consequent loading until the point of collapse which occures due to formation of plastic hinges. The first part is going to present a linear analysis of the problem; it focuses on location and level of load when the plastic hinges are formed. Then a nonlinaer analysis is going to be performed by RFEM programme using postcritical analysis and dynamic relaxation. Differences between the results of mentioned types and methods of analysis are going to be compared and an impact of variables is going to be evaluated .
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Munnae, Jomkwun. "Uncalibrated robotic visual servo tracking for large residual problems." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37219.
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In visually guided control of a robot, a large residual problem occurs when the robot configuration is not in the neighborhood of the target acquisition configuration. Most existing uncalibrated visual servoing algorithms use quasi-Gauss-Newton methods which are effective for small residual problems. The solution used in this study switches between a full quasi-Newton method for large residual case and the quasi-Gauss-Newton methods for the small case. Visual servoing to handle large residual problems for tracking a moving target has not previously appeared in the literature.
For large residual problems various Hessian approximations are introduced including an approximation of the entire Hessian matrix, the dynamic BFGS (DBFGS) algorithm, and two distinct approximations of the residual term, the modified BFGS (MBFGS) algorithm and the dynamic full Newton method with BFGS (DFN-BFGS) algorithm. Due to the fact that the quasi-Gauss-Newton method has the advantage of fast convergence, the quasi-Gauss-Newton step is used as the iteration is sufficiently near the desired solution. A switching algorithm combines a full quasi-Newton method and a quasi-Gauss-Newton method. Switching occurs if the image error norm is less than the switching criterion, which is heuristically selected.
An adaptive forgetting factor called the dynamic adaptive forgetting factor (DAFF) is presented. The DAFF method is a heuristic scheme to determine the forgetting factor value based on the image error norm. Compared to other existing adaptive forgetting factor schemes, the DAFF method yields the best performance for both convergence time and the RMS error.
Simulation results verify validity of the proposed switching algorithms with the DAFF method for large residual problems. The switching MBFGS algorithm with the DAFF method significantly improves tracking performance in the presence of noise. This work is the first successfully developed model independent, vision-guided control for large residual with capability to stably track a moving target with a robot.
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Liu, Qi. "CIRCE a new software to predict the steady state equilibrium of chemical reactions." Thesis, Compiègne, 2018. http://www.theses.fr/2018COMP2455/document.
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L'objectif de cette thèse est de développer un nouveau code pour prédire l'équilibre final d'un processus chimique complexe impliquant beaucoup de produits, plusieurs phases et plusieurs processus chimiques. Des méthodes numériques ont été développées au cours des dernières décennies pour prédire les équilibres chimiques finaux en utilisant le principe de minimisation de l'enthalpie libre du système. La plupart des méthodes utilisent la méthode des « multiplicateurs de Lagrange » et résolvent les équations en employant une approximation du problème de Lagrange et en utilisant un algorithme de convergence pas à pas de type Newton-Raphson. Les équations mathématiques correspondantes restent cependant fortement non linéaires, de sorte que la résolution, notamment de systèmes multiphasiques, peut être très aléatoire. Une méthode alternative de recherche du minimum de l’énergie de Gibbs (MCGE) est développée dans ce travail, basée sur une technique de Monte-Carlo associée à une technique de Pivot de Gauss pour sélectionner des vecteurs composition satisfaisant la conservation des atomes. L'enthalpie libre est calculée pour chaque vecteur et le minimum est recherché de manière très simple. Cette méthode ne présente a priori pas de limite d’application (y compris pour las mélanges multiphasiques) et l’équation permettant de calculer l’énergie de Gibbs n’a pas à être discrétisée. Il est en outre montré que la précision des prédictions dépend assez significativement des valeurs thermodynamiques d’entrée telles l'énergie de formation des produits et les paramètres d'interaction moléculaire. La valeur absolue de ces paramètres n'a pas autant d’importance que la précision de leur évolution en fonction des paramètres du process (pression, température, ...). Ainsi, une méthode d'estimation cohérente est requise. Pour cela, la théorie de la « contribution de groupe » est utilisée (ceux de UNIFAC) et a été étendue en dehors du domaine d'interaction moléculaire traditionnel, par exemple pour prédire l'énergie de formation d’enthalpie libre, la chaleur spécifique... Enfin, l'influence du choix de la liste finale des produits est discutée. On montre que la prédictibilité dépend du choix initial de la liste de produits et notamment de son exhaustivité. Une technique basée sur le travail de Brignole et Gani est proposée pour engendrer automatiquement la liste des produits stable possibles. Ces techniques ont été programmées dans un nouveau code : CIRCE. Les travaux de Brignole et de Gani sont mis en œuvre sur la base de la composition atomique des réactifs pour prédire toutes les molécules « réalisables ». La théorie de la « contribution du groupe » est mise en œuvre pour le calcul des propriétés de paramètres thermodynamiques. La méthode MCGE est enfin utilisée pour trouver le minimum absolu de la fonction d'enthalpie libre. Le code semble plus polyvalent que les codes traditionnels (CEA, ASPEN, ...) mais il est plus coûteux en termes de temps de calcul. Il peut aussi être plus prédictif. Des exemples de génie des procédés illustrent l'étendue des applications potentielles en génie chimiqueThe objective of this work is to develop a new code to predict the final equilibrium of a complex chemical process with many species/reactions and several phases. Numerical methods were developed in the last decades to predict final chemical equilibria using the principle of minimizing the Gibbs free energy of the system. Most of them use the “Lagrange Multipliers” method and solve the resulting system of equations under the form of an approximate step by step convergence technique. Notwithstanding the potential complexity of the thermodynamic formulation of the “Gibbs problem,” the resulting mathematical formulation is always strongly non-linear so that solving multiphase systems may be very tricky and having the difficult to reach the absolute minimum. An alternative resolution method (MCGE) is developed in this work based on a Monte Carlo technique associated to a Gaussian elimination method to map the composition domain while satisfying the atom balance. The Gibbs energy is calculated at each point of the composition domain and the absolute minimum can be deduced very simply. In theory, the technique is not limited, the Gibbs function needs not be discretised and multiphase problem can be handled easily. It is further shown that the accuracy of the predictions depends to a significant extent on the “coherence” of the input thermodynamic data such the formation Gibbs energy of the species and molecular interaction parameters. The absolute value of such parameters does not matter as much as their evolution as function of the process parameters (pressure, temperature, …). So, a self-consistent estimation method is required. To achieve this, the group contribution theory is used (UNIFAC descriptors) and extended somewhat outside the traditional molecular interaction domain, for instance to predict the Gibbs energy of formation of the species, the specific heat capacity… Lastly the influence of the choice of the final list of products is discussed. It is shown that the relevancy of the prediction depends to a large extent on this initial choice. A first technique is proposed, based on Brignole and Gani‘s work, to avoid omitting species and another one to select, in this list, the products likely to appear given the process conditions. These techniques were programmed in a new code name CIRCE. Brignole and Gani-‘s method is implemented on the basis of the atomic composition of the reactants to predict all “realisable” molecules. The extended group contribution theory is implemented to calculate the thermodynamic parameters. The MCGE method is used to find the absolute minimum of the Gibbs energy function. The code seems to be more versatile than the traditional ones (CEA, ASPEN…) but more expensive in calculation costs. It can also be more predictive. Examples are shown illustrating the breadth of potential applications in chemical engineering
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Sampaio, Maria do Socorro Martins. "Análise não linear geométrica de cascas laminadas reforçadas com fibras." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-14032014-153137/.
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Em geral, as formulações disponíveis na literatura para a análise de cascas laminadas reforçadas com fibras substituem o meio original heterogêneo por um homogêneo equivalente, que dificulta a identificação das tensões fibra-matriz, ou requerem que a malha de elementos finitos seja disposta de modo que os nós dos elementos finitos de fibra coincidam com os nós dos elementos finitos de casca, que é uma exigência bastante restritiva e que aumenta o número de graus de liberdade do sistema de equações resultante. Neste sentido, o objetivo geral desta tese consiste em desenvolver uma formulação para a inclusão de fibras longas e curtas aleatórias nas diversas lâminas de cascas laminadas anisotrópicas com não linearidade geométrica utilizando o método dos elementos finitos sem aumentar o número de graus de liberdade do sistema de equações resultante e sem a necessidade de coincidência de nós na discretização das fibras e da matriz. Nesta formulação, o elemento finito triangular de casca laminada utilizado para discretizar a matriz possui dez nós e sete graus de liberdade por nó, sendo três translações, três componentes do vetor generalizado e a taxa de variação linear da deformação ao longo da espessura. As fibras curvas, curtas aleatórias ou longas, são introduzidas, em qualquer camada do laminado, por meio de relações cinemáticas que garantem sua aderência à matriz sem a introdução de novos graus de liberdade no sistema de equações resultante. Para discretizá-las são utilizados elementos finitos unidimensionais de ordem qualquer com três graus de liberdade por nó e que consideram consistentemente a não linearidade geométrica. Todas as grandezas envolvidas são escritas em relação à configuração inicial do corpo, caracterizando a descrição Lagrangeana total ou material do movimento. Para modelar o comportamento do material adota-se a Lei Constitutiva de Saint-Venant-Kirchhoff que relaciona de forma linear o tensor de tensões de Piolla-Kirchhoff de segunda espécie e o tensor de deformações de Green-Lagrange. O equilíbrio é encontrado a partir do Princípio da Mínima Energia Potencial Total e o sistema não linear de equações resultante é resolvido utilizando-se o procedimento iterativo de Newton-Raphson. As ações externas podem ser introduzidas ao sistema de forma total ou incremental e a contribuição das fibras para a energia do sistema é adicionada na matriz global do problema. Os exemplos numéricos testados validam e demonstram as potencialidades da formulação proposta.In general, the Finite Element (FE) formulations available in the literature for the analysis of fibre reinforced laminated shells replace the original heterogeneous medium by an equivalent homogeneous one, which makes difficult the identification of fiber-matrix stress distribution, or require that the finite element mesh is arranged in a way that the fibre finite element nodes coincide with the shell finite element ones, which is a very restrictive requirement and increases the number of degrees of freedom of the resulting system of equations. In this sense, the objective of this thesis is to develop a formulation for the inclusion of long and random short fibres in any layer of FE laminated anisotropic shells developing large displacement and rotations without increasing the number of degrees of freedom and the necessity of matching nodes in the discretization of the fibre and the matrix. In this formulation, the triangular laminated shell finite element used to discretize the matrix has ten nodes and seven degrees of freedom per node, that are, three translations, three components of a generalized vector and the linear rate of strain variation along the thickness. The curved fibres, long or random short, are introduced in any layer of the laminate shell by means of kinematic relation to ensure its adherence to the matrix without introducing new degrees of freedom in the resulting system of equations. To discretize them, any order one-dimensional finite elements with three degrees of freedom per node are used. These fibres elements are consistently considered by Geometric nonlinearity. All involved variables are written with respect to the initial configuration of the body, characterizing the Total Lagrangian description. To model the behavior of the material we use the Saint-VenantKirchhoff Constitutive Law that relates linearly the second Piolla-Kirchhoff stress tensor and Green-Lagrange strain tensor. The equilibrium is achieved from the Principle of Minimum Potential Energy and the non-linear system of equations is solved by the Newton-Raphson iterative procedure. External loads may be introduced to the system by one or various steps and the contribution of fibres to the energy of the system is added to the global matrix of the problem. The numerical examples validate and demonstrate the potential of the proposed formulation.
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Jakel, Roland. "Das neue Kontaktmodell in Mechanica WF 4.0 mit Reibung : Theoretische Grundlagen und Anwendungsbeispiele." Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200900787.
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Der Vortrag stellt das neue, unendlich reibungsbehaftete Kontaktmodell der FEM-Berechnungssoftware Pro/ENGINEER Mechanica in der Version Wildfire 4.0 von PTC vor. Dabei werden sowohl die Grundlagen des reibungsfreien Kontaktes als auch die Theorie des unendlich reibungsbehafteten Kontaktmodells behandelt sowie die Grundlagen der zur numerischen Lösung in der Software verwendeten Penalty- und Newton-Raphson-Methode erläutert.
Als Anwendungsbeispiel für das reibungsfreie Kontaktmodell wird ein Zylinderrollenlager vollständig mit sämtlichen Wälzkontakten für verschiedene Lager- und Einbauspiele berechnet, die Ergebnisse umfassend dargestellt sowie eine analytische Gegenrechnung nach der Hertzschen Theorie ausgeführt, die sehr gute Übereinstimmung mit der numerischen Simulation zeigt. Für das reibungsbehaftete Kontaktmodell wird exemplarisch eine geschrumpfte Welle-Nabe-Verbindung unter Torsion berechnet. Diese wird einer analytischen Lösung sowie verschiedenen 2D-Idealisierungen (ebener Spannungszustand, ebener Dehnungszustand, 2D-Axialsymmetrie) gegenübergestellt.
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Despret, Pierre. "Simulation numérique de la solidification avec réduction de modèle PGD appliquée à la fonderie." Thesis, Compiègne, 2015. http://www.theses.fr/2015COMP2226/document.
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La thèse CIFRE s'est déroulée dans un contexte de métallurgie industrielle et de simulation numérique. La modélisation de la solidification, via l'équation de la chaleur et avec des méthodes de réduction de modèle, était un objectif majeur. L'entreprise Montupet, spécialisée dans la fonderie d'aluminium, est le porteur du projet et financeur de la thèse. L'université de Technologie de Compiègne (UTC) a réalisé l'accompagnement académique. La méthode PGD “Proper General Decomposition”, basée sur une séparation de variables, est l'objet de nombreuses recherches. Nous avons proposé, concernant des propriétés matériaux non-linéaires, une discrétisation spatio-temporelle des matrices matériaux. Avec une formulation en température, sans chaleur latente, les gains sont élevés. L'introduction de la chaleur latente réduit fortement les gains. Nous formulons l'hypothèse que la difficulté de convergence de la méthode PGD dans le cas de la solidification repose sur une formulation en température inadaptée. Nous décidons d'opter une formulation en enthalpie. Il s'avère que cette formulation offre des perspectives encourageantes, mais nécessite encore beaucoup de développements. En parallèle de ces développements, un séjour de 5 mois aux États-Unis a été réalisé afin d'obtenir une meilleure caractérisation de la fraction solide. La recherche s'est portée sur l'évolution de la fraction solide en fonction de la vitesse de refroidissement. Sous réserve de mesures complémentaires, les essais ont mis en évidence une modification de la courbe de fraction solide en fonction de la vitesse de refroidissement, notamment un agrandissement de l'intervalle de solidificationThe PhD Thesis was carried out in a metallurgy and numerical simulation environment. The main topic was to model solidification, thought heat equation formulation and reduced order model PGD resolution. Montupet, specialized in aluminium alloys foundry hold and financed the project, the Université de Technologie de Compiègne did the acadernic supervising. The PGD method "Proper General Decomposition" is a hot topic based on variable separation. We proposed, regarding the non-linear materials, a space-time discretization of material matrix. With a temperature formulation, without latent heat, gains are high. With latent heat, gains fall drastically. We proposed the hypothesis that temperature could be an inadapted formulation. We decided to use the enthalpy formulation. This formulation offers good perspectives but needs more developments. During the thesis, five months were spent in the USA to get a better caracterisation of the solid fraction, particularly its variation in function of the cooling rate. Under reservation, the samples show a modification of solid fraction curves and particularly a change of solidification interval in function of cooling rate
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Zanella, Filippo. "A Consensus Approach to Distributed Convex Optimization in Multi-Agent Systems." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3423080.
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In this thesis we address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where a network of agents, each endowed with local private convex cost and subject to communication constraints, wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proven, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We consider both a scalar and a multidimensional scenario of the Synchronous Newton-Raphson Consensus, proposing some alternative strategies which trade-off communication and computational requirements with convergence speed. We provide analytical proofs of convergence and we show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers, the Distributed Subgradient Method and Distributed Control Method.
Moreover, we consider the convergence rates of the Synchronous Newton-Raphson Consensus and the Gradient Descent Consensus under the simplificative assumption of quadratic local cost functions. We derive sufficient conditions which guarantee the convergence of the algorithms. From these conditions we then obtain closed form expressions that can be used to tune the parameters for maximizing the rate of convergence. Despite these formulas have been derived under quadratic local cost functions assumptions, they can be used as rules-of-thumb for tuning the parameters of the algorithms.
Finally, we propose an asynchronous version of the Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. Again, we analytically prove that under some assumptions it shows either local or global convergence properties. Through numerical simulations we corroborate these results and we compare the performance of the Asynchronous Newton-Raphson Consensus with other distributed optimization methods.In questa tesi viene affrontato il problema dell'ottimizzazione distribuita non vincolata di funzioni convesse. Lo scenario è costituito da una rete di agenti interconnessi, ognuno dei quali è dotato di una funzione costo locale convessa ed è soggetto a vincoli di comunicazione. Ogni agente vuole collaborare per calcolare il minimo della somma dei costi locali. Viene proposta una soluzione che combina algoritmi di average consensus con concetti di separazione delle scale temporali, propri della teoria del controllo non lineare. Tale strategia, denotata come Newton-Raphson Consensus, si dimostra convergere globalmente al minimo richiesto, sotto opportune ipotesi. Intuitivamente, l'algoritmo permette agli agenti di calcolare in maniera distribuita e di aggiornare sequenzialmente una direzione approssimata alla Newton-Raphson, tramite specifici rapporti di average consensus. Viene proposta una versione sincrona del Newton-Raphson Consensus, validata sia per funzioni scalari che vettoriali, proponendo nel secondo caso alcune strategie alternative volte a bilanciare le prestazioni, in termini di requisiti computazionali e di comunicazione, con una adeguata velocità di convergenza. Vengono presentate prove analitiche di convergenza e simulazioni numeriche che evidenziano come la velocità di convergenza del Synchronous Newton-Raphson Consensus è comparabile con strategie di ottimizzazione alternative quali l'Alternating Direction Method of Multipliers, il Distributed Subgradient Method e il Distributed Control Method. La trattazione si completa con l'analisi della velocità di convergenza del Synchronous Newton-Raphson Consensus, comparata con quella di un Gradient Descent Consensus, sotto l'ipotesi semplificativa di funzioni costo quadratiche. Vengono derivate condizioni sufficienti che garantiscono la convergenza di tali algoritmi. Da queste condizioni si ottengono espressioni in forma chiusa che possono essere utilizzate per regolare i parametri che caratterizzano gli algoritmi e per massimizzare la velocità di convergenza. Si evidenzia che nonostante queste formule siano derivate assumendo funzioni di costo (locali) quadratiche, esse possono essere usate come metodologie di riferimento per la regolazione dei parametri degli algoritmi in situazioni generali. Infine, viene proposta una versione asincrona del Newton-Raphson Consensus. Oltre ad avere una ridotta complessità computazionale e minimi requisiti di comunicazione, questa tecnica richiede poca coordinazione tra gli agenti e si mantiene valida in topologie tempo-varianti. Ancora una volta, viene dimostrato analiticamente, sotto opportune ipotesi, che l'Asynchronous Newton-Raphson Consensus ha proprietà di convergenza locali o globali. Mediante simulazioni numeriche vengono corroborati tali risultati e vengono confrontate le prestazioni di tale algoritmo con altri metodi di ottimizzazione distribuita quali l'Asynchronous Fast Newton-Raphson Consensus, l'Asynchronous Distributed Subgradient Method, l'Asynchronous Alternating Direction Method of Multipliers e il Pairwise Equalizing Method.
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Nascimento, Demilson Antonio do. "Métodos para Encontrar Raízes Exatas e Aproximadas de Funções Polinomiais até o 4º Grau." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/8060.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In several scienti c character problems, it is common to come across us with the need to obtain an approximate solution to nd roots of functions. At this point, this paper aims to conduct a study about some methods used to obtain an approximate solution of the functions of roots. The survey was made by means of a literature review, focusing on Numerical Methods Bisection, False Position, Fixed Point, Newton-Raphson and Secant. In order to illustrate the operation and application of these methods, numerical test problems taken from the literature were performed by implementing these. For each test performed were analyzed parameters that in uence each method and the convergence situation for the approximate solution of the analyzed problems. Although these methods do not always make available exact roots, they can be calculated with the precision that the problem needs. At this point, it is evident the importance of studying methods for nding such equations roots. Thus, the work is justi ed on the need to discuss the problems facing the nding roots of polynomial functions in the literature. In addition, this paper describes a comparison between the methods studied by applying mathematical problems. All this research material becomes adept and e ective for students and professionals from all areas that make use of them, or perhaps wish to extract it for enrichment of several sources of study.
Em diversos problemas de caráter cientí co, é comum depararmo-nos com a necessidade de obter uma solução aproximada para encontrar raízes de funções. Nesse ponto, este trabalho objetiva realizar um estudo acerca de alguns métodos utilizados para a obtenção de uma solução aproximada das raízes de funções. A pesquisa realizada deu-se por meio de uma revisão bibliográ ca, enfocando os Métodos Numéricos da Bisseção, Falsa Posição, Ponto Fixo, Newton-Raphson, Secante e Muller. Com o intuito de ilustrar o funcionamento e aplicação desses métodos, foram realizados testes numéricos de problemas extraídos da literatura por meio da implementação destes. Para cada teste realizado foram analisados os parâmetros que in uenciam cada método e a situação de convergência para a solução aproximada dos problemas analisados. Embora esses métodos, nem sempre, disponibilizem raízes exatas, estas poderão ser calculadas com a precisão que o problema necessite. Nesse ponto, ca evidente a importância de estudar métodos para encontrar tais raízes de equações. Diante disso, o trabalho se justi ca na necessidade de se discutir os problemas voltados a encontrar raízes de funções polinomiais, existentes na literatura. Além disso, o presente trabalho descreve um comparativo entre os métodos estudados mediante aplicação de problemas matemáticos. Todo esse material de pesquisa torna-se hábil e e caz para os estudantes e pro ssionais de todas as áreas que dele faça uso, ou, porventura, pretendam extraí-lo para enriquecimento de fontes diversas de estudo.
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Dai, Min. "Control of power converters for distributed generation applications." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124329850.
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Liu, Miao-Yi, and 劉妙宜. "Linkage map construction with dominant and missing markers by Newton-Raphson method." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/91178764064911960396.
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碩士國立臺灣大學
農藝學研究所
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The purpose of this study is to construct the linkage map with dominant and missing markers. A correct and accurate gene linkage map is vital for mapping and analysing quantitative trait loci (QTL). If the gene linkage map is unknown for a sequence of markers in the genome, we have to firstly divide the markers in the sequence into linkage groups, and then determine the most likely order of markers and the distances between neighboring markers within a linkage group. This is done by maximum likelihood (ML) method. When markers within a linkage group are fully observed, using the multilocus likelihood function to simultaneously estimate the recombination frequencies for all markers is equivalent to using two point analysis to independently estimate recombination frequency for each pair of markers. However, when some markers are partially observed or missing, the only way to calculate the recombination frequencies of markers is to simultaneously estimate the recombination frequencies according to the information of all markers within a linkage group by multilocos likelihood function. Usually, the multilocus likelihood function is too complicated to have a closed form solution and we can only use numerical analysis methods such as Newton-Raphson or EM algorithms to derive an approximate solution by iteration. The EM algorithm does not use the second order derivatives of likelihood function, so the convergence rate is slower and is unable to calculate the asymptotic covariance matrix of ML estimates. This study simulated the backcross data and F2 intercross data, using the Newton-Raphson method to simultaneously calculate the ML estimates of the recombination frequencies of all markers within a linkage group. The Newton-Raphson method can get not only ML estimates but also the asymptotic covariance matrix of ML estimates, the latter enables us to evaluate the plausibility of our statistical inference based on ML estimates, and then applying Haldane’s mapping function to transform the estimated recombination frequencies into genetic distances. We found the calculated distances are similar to what we originally assigned. The asymptotic covariance matrix showed that the standard errors are pretty small. In addition, the results of ML estimates by the Newton-Raphson method are identical to those of the EM algorithm.
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Chen, Yan-Wen, and 陳衍文. "An optimum research on the suspension of the bicycle based on Newton-Raphson method." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/k537f2.
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碩士國立虎尾科技大學
機械與機電工程研究所
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The framework, suspension system etc. of Diamond-type bicycle is analyzed in this thesis. The riding comfort and safety of framework is the most important issue. Pro-ENGINEER is adopted to construct the solid model, ANSYS is adopted in the static and modal analysis and ADAMS is used in the dynamic analysis of the bike. This thesis uses CAE analysis to study the structural strength of vehicle frames and the vibration pattern on rough roads, and obtain simulated dynamics diagram. It also uses Newton-Raphson method to obtain the optimal values for the stiffness of the spring as well as the damping coefficient. Finally, the tested result of the structural analysis shows that the frame is safe. The dynamic analysis using ADAMS and Newton-Raphson method got the optimum spring stiffness 16.934N/mm and damping coefficient 1.0766N-s/mm of the front fork of the suspension system. The suspension system had been proved to get the best comfort index for the riders in this experiment.
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WU, YUAN-DING, and 吳元丁. "Image reconstruction based on the electrical impedance tomography by the application of Newton-Raphson method." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/14438850443007132137.
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Zhou, Xiaoliang. "Studies of Extensions of HRM-SDT for Constructed Responses." Thesis, 2019. https://doi.org/10.7916/d8-s55z-sv06.
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This research examines an ordered perception rater model, an extension of the equal perception signal detection theory (SDT) latent class rater model. The expectation-maximization algorithm and the Newton-Raphson algorithm are used to estimate parameters. Four simulation studies are conducted to answer three research questions.
Simulation studies 1 and 2 fit correct models to the data. Simulation study 1 generates one hundred data sets from the equal perception rater model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the equal perception model. Parameter recovery is excellent for fully-crossed design and reasonable for BIB design, and all rater effects are detected. Simulation study 2 generates one hundred simulated data sets from the ordered perception model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the ordered perception rater model. Although parameter recovery is biased for some parameters in the BIB design, all rater effects are recovered.
Simulation studies 3 and 4 fit wrong models to the data. Simulation study 3 fits equal perception models to the fully-crossed and BIB ordered perception data sets generated in simulation study 2. All rater effects are revealed, although rater effects are distorted to some extent in the BIB design. Simulation study 4 fits ordered perception models to the fully-crossed and BIB equal perception data sets generated in study 1. All rater effects are recovered.
Using essay scores from a large-scale language test, an empirical study is conducted. Both the equal and the ordered perception models are fitted. Information criteria favor the equal perception model.
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陳新得. "Applications of the network diakoptics algorithm and the fast newton-raphson method for multiobjective power dispatch." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/36853640313914900196.
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Naik, P. "Power system contingency ranking using Newton Raphson load flow method and its prediction using soft computing techniques." Thesis, 2014. http://ethesis.nitrkl.ac.in/6134/1/E-69.pdf.
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The most important requirement and need of proper operation of power system is maintenance of the system security. Power system security assessment helps in monitoring and in giving up to date analysis regarding currents, bus voltages, power flows, status of circuit breaker, etc. This system assessment has been done in offline mode in which the system conditions are determined using ac power flows. The use of AC power flows is it gives information of power flows in terms of MW and MVAR , line over loadings and voltage limit violation with accurate values. Contingency selection or contingency screening is a process in which probable and potential critical contingencies are identified for which it requires consideration of each line or generator outage. . Contingency ranking is a procedure of contingency analysis in which contingencies are arranged in descending order, sorted out by the severity of contingency. Overall severity index (OPI) is calculated for determining the ranking of contingency. Overall performance index is the summation of two performance index , one of the performance index determines line overloading and other performance index determines bus voltage drop limit violation and are known as active power performance index and voltage performance index respectively. Here in this proposed work the contingency ranking has been done with IEEE 5 bus and 14 bus system. But the system parameters are dynamic in nature, keeps on changing and may affect the system parameters that are why there is need of soft computing techniques for the prediction purpose. Fuzzy logic approach has also been used. Two model of Artificial Neural Network namely, Multi Layer Feed Forward Neural Network (MFNN) and Radial Basis Function Network (RBFNN) have been considered. With these soft computing techniques the prediction method helps in obtaining the OPI with greater accuracy.
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Sun, Jingyan. "The mathematics behind speciated isotope dilution mass spectrometry." 2007. http://etd1.library.duq.edu/theses/available/etd-10022006-164607/.
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