O objetivo desse trabalho foi investigar o modelo matemático para baterias de chumbo-ácido, usada em aplicações veiculares, mais adequado para a condição de descarga, que ocorre durante o teste de Cold Crank, e propor uma metodologia para identificar os parâmetros da bateria, a partir de ensaios experimentais. A simulação do teste de Cold Crank foi a motivação para o início da pesquisa. Dentre os diversos modelos pesquisados, foram selecionados aqueles que representam a dinâmica da bateria durante a descarga e que são baseados em circuitos elétricos. O modelo de Jackey foi escolhido, por possuir um circuito equivalente com adequada complexidade para o objetivo estudado. Após algumas simplificações e usando a 1ª Lei de Kirchhoff, definiu-se a equação da bateria, que calcula a tensão nos terminais para um dado valor de corrente de descarga constante. Adotaram-se ainda algumas leis de formação propostas por Jackey e uma forma alternativa para a descrição de R1. Alguns parâmetros da equação da bateria foram calculados usando a curva de tensão em aberto (OCV) em função do estado de carga (SOC), a equação da variação do estado de carga em função do tempo (SOC(t)) e o circuito simplificado para o instante inicial. Para os demais parâmetros, uma metodologia de resolução foi apresentada e implementada em ambiente MatLab®. Através da utilização de curvas de descarga experimentais e com o auxílio dos algoritmos de otimização genético e de busca local, os parâmetros desconhecidos foram estimados de forma a minimizar o erro entre os valores calculados e os valores experimentais. Por fim, foi apresentada a variação dos parâmetros em função da corrente de descarga. Com o uso das curvas que aproximam essa variação, alguns exemplos foram gerados para mostrar que os valores calculados continuam coerentes, tanto em forma quanto em escala, quando comparados com valores experimentais para outros níveis de corrente. Dessa forma, o objetivo do trabalho foi alcançado uma vez que a metodologia aplicada apresentou bons resultados mesmo com o número limitado de curvas de descarga experimentais. / The aim of this study was to investigate the most suitable lead-acid battery model, used in vehicular application, to the discharge condition which occurs during a Cold Crank test, and to propose a methodology to identify the battery parameters from experimental tests. The Cold Crank simulation was the motivation for this research. Among the various studied models, were selected those that describe the battery dynamic during a discharge process and that are based on electrical circuits. Jackey model was chosen because it has an equivalent circuit with suitable complexity to the aim. After some simplifications and using 1st Kirchhoffs Law, the battery equation was defined, which calculates the terminal voltage for a given constant discharge current. Also, it was adopted some laws proposed by Jackey and an alternative way to describe R1. Some parameters from battery equation were defined using the open circuit voltage (OCV) as function of state of charge (SOC), the equation of SOC variation as function of time and simplified circuit for the initial time. For the others parameters, a solving methodology was introduced and implemented in Matlab® environment. Usage of experimental discharge curves and with the help of genetic and local search algorithms, the unknown parameters were estimated in order to minimize the error between calculated and experimental values. Finally, it was presented the parameters variation as function of discharge current. With the use of curves that approximate this variation, some examples were generated to show that the calculated values remain consistent in both shape and range when compared to experimental values for others current levels. In this way, the aim was reached since methodology produced good results even with limited number of experimental discharge curves.

Este trabalho inicia descrevendo as principais teorias de laminação que têm sido empregadas nos últimos anos na determinação das condições ideais para operação de laminadores a frio. Estas condições ideais estão ligadas a um conjunto de referências dos controladores do sistema, visando a máxima produtividade do laminador e a melhor qualidade da chapa laminada. As principais contribuições desta tese são: (i) proposta de um novo procedimento não iterativo para a determinação inicial de referências para redução em cada cadeira de um laminador de tiras a frio, originado do algoritmo iterativo do fator beta, introduzido por R. M. Guo; (ii) em seguida, é feito uso do modelo de Bland e Ford para cálculo de força e torque de laminação, utilizando o esquema de reduções sugerido pelo algoritmo de inicialização. A partir deste ponto, emprega-se o algoritmo de otimização de Nelder e Mead. A contribuição da tese para esta fase de otimização consiste na proposta da função objetivo a ser minimizada. Esta função objetivo leva em conta os principais atributos de qualidade e produtividade do laminador, ou seja, espessura, planicidade e utilização de toda a potência disponível, igualmente distribuída por todas as cadeiras; (iii) finalmente, visando garantir máxima precisão para as previsões do modelo, é proposto um algoritmo de otimização para ser utilizado em um esquema de adaptação, tendo em vista as dificuldades de se estimar duas importantes variáveis do processo de laminação: o coeficiente de atrito e o limite de escoamento. São também apresentados resultados obtidos à partir de um laminador tandem de 4 cadeiras, industrial, no qual foram implantados alguns dos métodos propostos. / This work begins describing the main rolling theories which have been employed during the recent years, in order to achieve the ideal conditions for the operation of tandem cold rolling mills. These optimum conditions are connected to a set of references used by the main systems regulators, aiming at getting the best quality of the strip and the maximum productivity of the mill. The main contributions of this thesis are: (i) proposal of a new non-iterative procedure to initial reduction calculation for each stand of a tandem cold mill, based on the iterative beta factor algorithm introduced by R.M. Guo; (ii) Use of Bland and Ford model for roll force and roll torque calculation, starting from the initial reduction schedule proposed by the non-iterative initialization algorithm and optimized by the Nelder and Mead method. The contribution of this thesis for this optimization phase consists in its proposal for an objective function to be minimized. This objective function takes into consideration the main product quality and process productivity attributes, i.e., thickness, flatness and the use of maximum available power, evenly distributed among all stands; (iii) finally, aiming at ensuring maximum precision for the model predictions, it is proposed an optimization algorithm to be used by an adaptation strategy, considering the difficulties to estimates two main rolling mill process variables: friction and yield stress coeficientes. Results extracted from an industrial four stand tandem cold mill, on which some of the proposal theories were implemented, are presented and discussed.

O objetivo desse trabalho foi investigar o modelo matemático para baterias de chumbo-ácido, usada em aplicações veiculares, mais adequado para a condição de descarga, que ocorre durante o teste de Cold Crank, e propor uma metodologia para identificar os parâmetros da bateria, a partir de ensaios experimentais. A simulação do teste de Cold Crank foi a motivação para o início da pesquisa. Dentre os diversos modelos pesquisados, foram selecionados aqueles que representam a dinâmica da bateria durante a descarga e que são baseados em circuitos elétricos. O modelo de Jackey foi escolhido, por possuir um circuito equivalente com adequada complexidade para o objetivo estudado. Após algumas simplificações e usando a 1ª Lei de Kirchhoff, definiu-se a equação da bateria, que calcula a tensão nos terminais para um dado valor de corrente de descarga constante. Adotaram-se ainda algumas leis de formação propostas por Jackey e uma forma alternativa para a descrição de R1. Alguns parâmetros da equação da bateria foram calculados usando a curva de tensão em aberto (OCV) em função do estado de carga (SOC), a equação da variação do estado de carga em função do tempo (SOC(t)) e o circuito simplificado para o instante inicial. Para os demais parâmetros, uma metodologia de resolução foi apresentada e implementada em ambiente MatLab®. Através da utilização de curvas de descarga experimentais e com o auxílio dos algoritmos de otimização genético e de busca local, os parâmetros desconhecidos foram estimados de forma a minimizar o erro entre os valores calculados e os valores experimentais. Por fim, foi apresentada a variação dos parâmetros em função da corrente de descarga. Com o uso das curvas que aproximam essa variação, alguns exemplos foram gerados para mostrar que os valores calculados continuam coerentes, tanto em forma quanto em escala, quando comparados com valores experimentais para outros níveis de corrente. Dessa forma, o objetivo do trabalho foi alcançado uma vez que a metodologia aplicada apresentou bons resultados mesmo com o número limitado de curvas de descarga experimentais. / The aim of this study was to investigate the most suitable lead-acid battery model, used in vehicular application, to the discharge condition which occurs during a Cold Crank test, and to propose a methodology to identify the battery parameters from experimental tests. The Cold Crank simulation was the motivation for this research. Among the various studied models, were selected those that describe the battery dynamic during a discharge process and that are based on electrical circuits. Jackey model was chosen because it has an equivalent circuit with suitable complexity to the aim. After some simplifications and using 1st Kirchhoffs Law, the battery equation was defined, which calculates the terminal voltage for a given constant discharge current. Also, it was adopted some laws proposed by Jackey and an alternative way to describe R1. Some parameters from battery equation were defined using the open circuit voltage (OCV) as function of state of charge (SOC), the equation of SOC variation as function of time and simplified circuit for the initial time. For the others parameters, a solving methodology was introduced and implemented in Matlab® environment. Usage of experimental discharge curves and with the help of genetic and local search algorithms, the unknown parameters were estimated in order to minimize the error between calculated and experimental values. Finally, it was presented the parameters variation as function of discharge current. With the use of curves that approximate this variation, some examples were generated to show that the calculated values remain consistent in both shape and range when compared to experimental values for others current levels. In this way, the aim was reached since methodology produced good results even with limited number of experimental discharge curves.

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed. / Singapore-MIT Alliance (SMA)

We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the quasi-Newton method. Although the zeroth-order algorithms have the property of strict monotone decrease in both primal and dual objective values, they may not converge. We give an illustrative example as well as an algebraic proof to show that the zeroth-order algorithms do not converge to an optimal solution in some cases. The second-order algorithms use the gradients and Hessians of the barrier functions. Tuncel has shown that all second-order algorithms have a polynomial iteration bound. The second-order algorithms have a range of primal-dual scaling matrices to be chosen. We give a method to construct such a primal-dual scaling matrix. We then analyze a new centrality measure. This centrality measure appeared in both first- and second-order algorithms. We compare the neighbourhood defined by this centrality measure with other known neighbourhoods. We then analyze how this centrality measure changes in the next iteration in terms of the step length and some other information of the current iteration.

We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the quasi-Newton method. Although the zeroth-order algorithms have the property of strict monotone decrease in both primal and dual objective values, they may not converge. We give an illustrative example as well as an algebraic proof to show that the zeroth-order algorithms do not converge to an optimal solution in some cases. The second-order algorithms use the gradients and Hessians of the barrier functions. Tuncel has shown that all second-order algorithms have a polynomial iteration bound. The second-order algorithms have a range of primal-dual scaling matrices to be chosen. We give a method to construct such a primal-dual scaling matrix. We then analyze a new centrality measure. This centrality measure appeared in both first- and second-order algorithms. We compare the neighbourhood defined by this centrality measure with other known neighbourhoods. We then analyze how this centrality measure changes in the next iteration in terms of the step length and some other information of the current iteration.

Quality of municipal water is sustained by addition of disinfectant, generally chlorine, to the water distribution network. Because of health problems, chlorine concentration in the network is limited between maximum and minimum limits. Cancerogenic disinfectant by-products start to occur at high concentrations so it is desired to have minimum amount of chlorine without violating the limit. In addition to the health issues, minimum injection amount is favorable concerning cost. Hence, an optimization model is necessary which covers all of these considerations. However, there are uncertain factors as chlorine is reactive and decays both over time and space. Thus, probabilistic approach is necessary to obtain reliable and realistic results from the model. In this study, a linear programming model is developed for the chance constrained optimization of the water distribution network. The objective is to obtain minimum amount of injection mass subjected to maintaining more uniformly distributed chlorine concentrations within the limits while considering the randomness of chlorine concentration by probability distributions. Network hydraulics and chlorine concentration computations are done by the network simulation software, EPANET.

Sparse approximation is an important class of optimization problem in signal and image processing applications. This thesis presents an analog solution to this problem, based on the Locally Competitive Algorithm (LCA). A Hopfield-Network-like analog system, operating on sub-threshold currents is proposed as a solution. The results of the circuit components' implementation on the RASP2.8a chip, a Field Programmable Analog Array, are presented.

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ABSTRACT DESIGN OF WATER DISTRIBUTION SYSTEM BY OPTIMIZATION USING RELIABILITY CONSIDERATIONS Akdogan, Tevfik Department of Civil Engineering Supervisor : Assoc. Prof. Dr. Nuri Merzi April 2005, 91 pages In spite of a wide research, design of water distribution networks are not realized using optimization techniques. One reason for this fact is, design of water distribution networks is evaluated, mostly, as a least-cost optimization problem where pipe diameters being the only decision variables. The other motivation for preferring the traditional modeling practice is that, existing optimization algorithms are not presented to the user as friendly as it should be. In fact, water distribution systems are very complex systems such that it is not easy to obtain least-cost design systems considering other constraints such as reliability, in addition to classical constraints related to hydraulic feasibility, satisfaction of nodal demands and requirement of nodal pressures. This study presents a user-friendly package concerning the design of water distribution networks by optimization using reliability considerations / this works employs the algorithm proposed by Goulter and Coals (1986). At the end, a skeletonized network design is offered / various costs are estimated in regard to the degree of reliability.