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.

Machine learning is a major source of interesting optimization problems of current interest. These problems tend to be challenging because of their enormous scale, which makes it difficult to apply traditional optimization algorithms. We explore three avenues to designing algorithms suited to handling these challenges, with a view toward large-scale ML tasks. The first is to develop better general methods for unconstrained minimization. The second is to tailor methods to the features of modern systems, namely the availability of distributed computing. The third is to use specialized algorithms to exploit specific problem structure. Chapters 2 and 3 focus on improving quasi-Newton methods, a mainstay of unconstrained optimization. In Chapter 2, we analyze an extension of quasi-Newton methods wherein we use block updates, which add curvature information to the Hessian approximation on a higher-dimensional subspace. This defines a family of methods, Block BFGS, that form a spectrum between the classical BFGS method and Newton's method, in terms of the amount of curvature information used. We show that by adding a correction step, the Block BFGS method inherits the convergence guarantees of BFGS for deterministic problems, most notably a Q-superlinear convergence rate for strongly convex problems. To explore the tradeoff between reduced iterations and greater work per iteration of block methods, we present a set of numerical experiments. In Chapter 3, we focus on the problem of step size determination. To obviate the need for line searches, and for pre-computing fixed step sizes, we derive an analytic step size, which we call curvature-adaptive, for self-concordant functions. This adaptive step size allows us to generalize the damped Newton method of Nesterov to other iterative methods, including gradient descent and quasi-Newton methods. We provide simple proofs of convergence, including superlinear convergence for adaptive BFGS, allowing us to obtain superlinear convergence without line searches. In Chapter 4, we move from general algorithms to hardware-influenced algorithms. We consider a form of distributed stochastic gradient descent that we call Leader SGD, which is inspired by the Elastic Averaging SGD method. These methods are intended for distributed settings where communication between machines may be expensive, making it important to set their consensus mechanism. We show that LSGD avoids an issue with spurious stationary points that affects EASGD, and provide a convergence analysis of LSGD. In the stochastic strongly convex setting, LSGD converges at the rate O(1/k) with diminishing step sizes, matching other distributed methods. We also analyze the impact of varying communication delays, stochasticity in the selection of the leader points, and under what conditions LSGD may produce better search directions than the gradient alone. In Chapter 5, we switch again to focus on algorithms to exploit problem structure. Specifically, we consider problems where variables satisfy multiaffine constraints, which motivates us to apply the Alternating Direction Method of Multipliers (ADMM). Problems that can be formulated with such a structure include representation learning (e.g with dictionaries) and deep learning. We show that ADMM can be applied directly to multiaffine problems. By extending the theory of nonconvex ADMM, we prove that ADMM is convergent on multiaffine problems satisfying certain assumptions, and more broadly, analyze the theoretical properties of ADMM for general problems, investigating the effect of different types of structure.

<p>Finite element modeling of the structural response of hollow concrete block walls subject to out-of-plane loading has become more common given the availability of computers and general-purpose finite element software packages. In order to develop appropriate models of full-scale walls with and without openings, a parametric study was conducted on simple wall elements to assess different modeling techniques. Two approaches were employed in the study, homogeneous models and heterogeneous models. The linear elastic analysis was carried out to quantify the effects of the modeling techniques for hollow blocks on the structural response of the assembly, specifically for out-of-plane bending. Three structural elements with varying span/thickness ratios were considered, a horizontal spanning strip, a vertical spanning strip and a rectangular wall panel supported on four edges. The values computed using homogeneous and heterogeneous finite element models were found to differ significantly depending on the configuration and span/thickness ratio of the wall.</p><p>Further study was carried out through discrete modeling approach to generate a three-dimensional heterogeneous model to investigate nonlinear behaviour of full-scale walls under out-of-plane loading. The Composite Interface Model, established based on multi-surface plasticity, which is capable of describing both tension and shear failure mechanisms, has been incorporated into the analysis to capture adequately the inelastic behaviour of unit-mortar interface.An effective solution procedure was achieved by implementing the Newton-Raphson method, constrained with the arc-length control method and enhanced by line search algorithm. The proposed model was evaluated using experimental results for ten full-size walls reported in the literature. The comparative analysis has indicated very good agreement between the numerical and experimental results in predicting the cracking and ultimate load values as well as the corresponding crack pattern. / Thesis / Master of Applied Science (MASc)

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2016-11-29T11:25:36Z No. of bitstreams: 1 Paulo Cesar Alves.pdf: 3064049 bytes, checksum: bbbbb8cfdb6249b85002761ac406c6dd (MD5) / Made available in DSpace on 2016-11-29T11:25:36Z (GMT). No. of bitstreams: 1 Paulo Cesar Alves.pdf: 3064049 bytes, checksum: bbbbb8cfdb6249b85002761ac406c6dd (MD5) Previous issue date: 2016-09-12 / 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

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.

Thesis (M.S.)--Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Mathematics. / Typescript. Includes bibliographical references (leaves 114-119). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66358.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-08-01T12:22:33Z No. of bitstreams: 2 Dissertação - Janio Cesar Alencar dos Santos - 2018.pdf: 1167560 bytes, checksum: cba31dafa5c96d61d508fb8034159563 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-08-01T13:39:27Z (GMT) No. of bitstreams: 2 Dissertação - Janio Cesar Alencar dos Santos - 2018.pdf: 1167560 bytes, checksum: cba31dafa5c96d61d508fb8034159563 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-08-01T13:39:27Z (GMT). No. of bitstreams: 2 Dissertação - Janio Cesar Alencar dos Santos - 2018.pdf: 1167560 bytes, checksum: cba31dafa5c96d61d508fb8034159563 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-06-28 / 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.

Orientadores: Carlos Alberto de Castro Junior, Luiz Carlos Pereira da Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-04T14:18:50Z (GMT). No. of bitstreams: 1 Meireles_EduardoDavid_M.pdf: 1486956 bytes, checksum: 1e441015d6ae62bfd66ac90c0c7635dd (MD5) Previous issue date: 2005 / 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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