Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T17:29:03Z No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:44:17Z (GMT) No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Made available in DSpace on 2018-01-23T13:44:17Z (GMT). No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) Previous issue date: 2017-09-15 / O presente trabalho propõe uma nova metodologia de Geração de Sinal Sub-Ótimo de Excitação e Estimação Ótima de Parâmetros de sistemas não lineares. É proposto que a avaliação de cada sinal deva considerar, entre outros fatores, a diferença entre os parâmetros reais da planta e os obtidos pela estimação. Entretanto esta métrica não é trivial de ser obtida uma vez que os valores reais são desconhecidos. Para tanto é adotada a hipótese de que, se um sistema real puder ser razoavelmente aproximado por uma caixa branca, é possível utilizar este modelo como referência para indicar o impacto de um sinal sobre a estimação paramétrica. Desta forma, é utilizada uma metodologia de otimização dividida em dois níveis: (i) Nível Interno; para um dado sinal de excitação um método de otimização não linear busca o conjunto ótimo de parâmetros que minimiza o erro entre os sinais de saída do modelos original e do de referência. (ii) No nível externo um método de otimização baseado em meta-heurística é responsável por encontrar o melhor sinal de excitação com base na função custo composta de uma soma ponderada de métricas que consideram o erro entre os sinais de saída do modelo otimizado e do de referência, a diferença quadrática entre seus parâmetros, e o custo em relação ao tempo e espaço necessários para executar o experimento. Portanto, a aplicação da metodologia proposta vem suprir a necessidade de estimar sistemas não lineares apropriadamente, encontrando um conjunto de parâmetros capaz de generalizar o comportamento do sistema real, através de um sinal de excitação que cumpra requisitos práticos do processo. A eficácia da metodologia proposta é analisada em detalhes através de resultados obtidos utilizando sistemas de fluídos, sistemas caóticos e de robótica móvel, tanto sobre rodas quanto subaquática. / The present work proposes a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of nonlinear systems. It is proposed that the evaluation of each signal must to take into account, among other factors, the difference between real system parameters and the obtained by estimation. However, this metric is not trivially obtained once the real parameters values are unknown. To do so it is adopted the hypothesis that, if the system can be fairly approximate by a white box model, it is possible to use this model as a benchmark to indicate the impact of a signal on a parametric estimation. In this way, the method uses an optimization methodology divided into two levels: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the output signals of the original and the benchmark models. (ii) At the outer level, an optimization method based on metaheuristics is responsible for finding the best excitation signal, based on the cost function composed of a weighted sum of metrics, that considers the error between the output signals of the optimized model and the benchmark, the quadratic difference between its parameters, and the cost in relation to the time and space required to execute the experiment. Thus, the application of the proposed methodology comes to supply the need to estimate nonlinear systems appropriately, finding a set of parameters capable of generalizing the behavior of the real system, through an excitation signal that fulfills practical requirements of the process. The proposed methodology is analyzed in detail through results obtained using fluid systems, chaotic systems and mobile robotics, both wheeled and underwater.

No / This paper proposes a hybrid optimization method for optimal allocation of wind turbines (WTs) that combines a fast and elitist multiobjective genetic algorithm (MO-GA) and the market-based optimal power flow (OPF) to jointly minimize the total energy losses and maximize the net present value associated with the WT investment over a planning horizon. The method is conceived for distributed-generator-owning distribution network operators to find the optimal numbers and sizes of WTs among different potential combinations. MO-GA is used to select, among all the candidate buses, the optimal sites and sizes of WTs. A nondominated sorting GA II procedure is used for finding multiple Pareto-optimal solutions in a multiobjective optimization problem, while market-based OPF is used to simulate an electricity market session. The effectiveness of the method is demonstrated with an 84-bus 11.4-kV radial distribution system.

Neste trabalho será apresentado um algoritmo de pontos interiores para a solução do problema de fluxo de carga ótimo (FCO). A abordagem proposta é o método primai dual barreira logarítmica. As restrições de desigualdade do problema de FCO são transformadas em igualdades pelo uso de variáveis de folga, e estas são incorporadas na função objetivo através da função barreira logarítmica. A esparsidade da matriz Lagrangeana é explorada e o processo de fatoração é feito por elementos e não por submatrizes. Resultados numéricos de testes realizados em sistemas de 3, 14, 30 e 118 barras serão apresentados com o objetivo de mostrar a eficiência do método. / In this thesis an interior point algorithm is presented for the solution of the optimal power flow problem (OPF). The approach proposed here is the logarithmic barrier primal-dual method. The inequality constraints of the optimal power flow problem are transformed into equalities by slack variables that are incorporated into the objective function through the logarithmic barrier function. The sparsity of the Lagrangian matrix is explored and the factorization process is carried out by elements rather than submatrices. Numerical tests results obtained with systems of 3, 14, 30 and 118 buses are presented to show the efficiency of the method.

Neste trabalho a família de métodos de pontos interiores barreira logarítmica é desenvolvida para o problema de regressão pela norma Lp e a estrutura matricial resultante é explorada objetivando uma implementação eficiente. Apresentamos alguns conceitos sobre métodos de pontos interiores necessários para o desenvolvimento do método e descrevemos um método de convergência quadrática previamente conhecido. Uma implementação em Matlab dos métodos de pontos interiores desenvolvidos é comparada com uma implementação do método quadrático existente, obtendo desempenho computacional superior. / In this work the family of logarithmic barrier interior point methods is developed for the norm Lp fitting problem and the resultant matrix structure is exploited in order to have an efficient implementation. We introduce some concepts about interior point methods necessary for the development of the method and describe a previously known quadratic convergent problem. An implementation in Matlab of the interior point methods developed is compared with an implementation of the known quadratic method obtaining better computational performance.

The focus of this thesis is formulation and development of a mathematical framework for the solution of the contingency constrained optimal power flow (OPF) based on sequential quadratic programming. The contingency constrained optimal power flow minimizes the total cost of a base case operating state as well as the expected cost of recovery from contingencies such as line or generation outages. The sequential quadratic programming (SCP) OPF formulation has been expanded in order to recognize contingency conditions and the problem is solved as a single entity by an efficient interior point method. The new formulation takes into account the system corrective capabilities in response to contingencies introduced through ramp-rate constraints. Contingency constrained OPF is a very challenging problem, because each contingency considered introduces a new problem as large as the base case problem. By proper system reduction and benefits of constraint relaxation (active set) methods, in which transmission constraints are not introduced until they are violated, the size of the system can be reduced significantly Therefore, restricting our attention to the active set constraint set makes this large problem significantly smaller and computationally feasible.

Mecanismo Flexível é um dispositivo mecânico utilizado para transformar movimento, força ou energia entre as portas de entrada e saída sem a presença de juntas, pinos baseados em uma estrutura em monolítica, em outras palavras, a transformação do movimento é dada pela flexibilidade de sua estrutura. Deste modo a transformação pode ser direcionada em uma direção em específico, amplificando ou reduzindo o deslocamento ou força aplicados. Por este motivo mecanismos flexíveis tem grandes aplicações em micromanipulação e nano posicionamento. A concepção deste tipo de mecanismo é complexa e uma das possibilidades de elaboração deste dispositivo mecânico é através da distribuição de flexibilidade ou rigidez dentro do domínio de projeto utilizando o Método de Otimização Topológica (MOT), que essencialmente combina algoritmos de otimização numéricos como Método de Elementos Finitos (MEF), por exemplo. A grande maioria das classes de mecanismos flexíveis existentes trabalha sob pequenos deslocamentos, na ordem de micro ou nano metros, no entanto, existe uma classe de mecanismos que utiliza o recurso da flambagem não linear para operar com grandes deslocamentos. O procedimento de concepção desta de classe de mecanismo é complexa e ainda se encontra em estagio inicial, necessitando de aprimoramentos que permitam o seu projeto completo via métodos computacionais. Portanto, esta tese foi desenvolvida como objetivo desenvolver uma metodologia computacional para projetar esta classe de mecanismo flexível inovador que emprega a flambagem não linear na sua estrutura como meio para obter sob grandes deslocamentos na porta de saída. A metodologia desenvolvida se baseia no MOT para obter a topologia da estrutura que satisfaça as restrições de projeto. A modelagem do comportamento físico da estrutura utiliza uma formulação variacional não linear do problema elástico, considerando a cinemática não linear com um modelo constitutivo policonvexo. O modelo de material aplicado para obter a topologia da estrutura do mecanismo foi o Solid IsotropicMaterial with Penalization (SIMP) com um algoritmo de otimização numérico baseado no método de ponto interior, onde foi utilizada a implementação do IpOpt em conjunto com a plataforma Python FEniCS de soluções de Equações Diferenciais Parciais (EDPs). São apresentados resultados bidimensionais de mecanismos considerando algumas configurações de geometria, condições de contorno e restrições de flambagem não-linear, como incremento de carga. / The compliant mechanism is a mechanical device used to transform displacement, force or energy between the input and output ports without joints, pins based on a monolithic structure, in other words, the motion transformation is given by the flexibility of its structure. In this way the movement can be defined to a specific axis direction, amplifying or reducing the applied displacement or force. For this reason, the compliant mechanism has significant applications in micromanipulation and nanopositioning system. The design of this type of device is intricate, and one way to achieve such design is trying to distribution flexibility or rigidity within the design domain using the Topology Optimization Method (TOM), which essentially combines numerical optimization algorithms with Finite ElementMethod (FEM), for example. Most models of existing compliant mechanism work under small displacements, in the order of micro or nanometers, nevertheless, there is a class of such mechanisms that uses the nonlinear buckling behavior to operate under large displacements. The design process of this mechanism type is complicated and is still at early stages, requiring improvements that allow a complete design process via computational methods. Therefore, this thesis goal is to develop a computational methodology to create this class of innovative compliant mechanism that employs nonlinear buckling behavior to work under large displacement at the output port. The approach developed is based on TOM to achieve the optimal structure topology that satisfies the design and optimization constraints. The modeling of the elasticity behavior of the structure relies on the nonlinear variational formulation, applying the nonlinear kinematics with a polyconvex constitutive model. The SIMP is employed as a material model to obtain the optimal topology of the mechanismstructure with a numeric optimization algorithm based on the interior point method, where the IpOpt implementation was used with the high-level Python interfaces to FEniCS to solve the partial differential equations (PDEs) problem. Two-dimensional results ofmechanisms are presented considering some geometric, boundary configuration, and including nonlinear buckling as design constraints.

The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of partial differential equations with affine parameter dependence. The critical ingredients of the method are: (i) reduced-basis techniques for dimension reduction in computational requirements; (ii) an "off-line/on-line" computational decomposition for the rapid calculation of outputs of interest and respective sensitivities in the limit of many queries; (iii) a posteriori error bounds for rigorous uncertainty and feasibility control; (iv) Interior Point Methods (IPMs) for efficient solution of the optimization problem; and (v) a trust-region Sequential Quadratic Programming (SQP) interpretation of IPMs for treatment of possibly non-convex costs and constraints. / Singapore-MIT Alliance (SMA)

We report a Hessian-implicit optimization method to quickly solve the charge optimization problem over protein molecules: given a ligand and its complex with a receptor, determine the ligand charge distribution that minimizes the electrostatic free energy of binding. The new optimization couples boundary element method (BEM) and primal-dual interior point method (PDIPM); initial results suggest that the method scales much better than the previous methods. The quadratic objective function is the electrostatic free energy of binding where the Hessian matrix serves as an operator that maps the charge to the potential. The unknowns are the charge values at the charge points, and they are limited by equality and inequality constraints that model physical considerations, i.e. conservation of charge. In the previous approaches, finite-difference method is used to model the Hessian matrix, which requires significant computational effort to remove grid-based inaccuracies. In the novel approach, BEM is used instead, with precorrected FFT (pFFT) acceleration to compute the potential induced by the charges. This part will be explained in detail by Shihhsien Kuo in another talk. Even though the Hessian matrix can be calculated an order faster than the previous approaches, still it is quite expensive to find it explicitly. Instead, the KKT condition is solved by a PDIPM, and a Krylov based iterative solver is used to find the Newton direction at each step. Hence, only Hessian times a vector is necessary, which can be evaluated quickly using pFFT. The new method with proper preconditioning solves a 500 variable problem nearly 10 times faster than the techniques that must find a Hessian matrix explicitly. Furthermore, the algorithm scales nicely due to the robustness in number of IPM iterations to the size of the problem. The significant reduction in cost allows the analysis of much larger molecular system than those could be solved in a reasonable time using the previous methods. / Singapore-MIT Alliance (SMA)

We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a₁,..., am ∈ Rn. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30,000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer. / Singapore-MIT Alliance (SMA)

In this paper we combine ideas from cutting plane and interior point methods in order to solve variational inequality problems efficiently. In particular, we introduce a general framework that incorporates nonlinear as well as linear "smarter" cuts. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence as well as complexity results for this framework. Moreover, in order to devise more practical methods, we consider an affine scaling method as it applies to symmetric, monotone variationalinequality problems and demonstrate its convergence. Finally, in order to further improve the computational efficiency of the methods in this paper, we combine the cutting plane approach with the affine scaling approach.