LARGE MOTION VISUALIZATION AND ESTIMATION FOR FLAPPING WING SYSTEMS

Studies of fluid-structure interactions associated with flexible structures such as flapping wings require the capture and quantification of large motions of bodies that may be opaque. Motion capture of a free flying insect is considered by using three synchronized high-speed cameras. A solid finite element representation is used as a reference body and successive snapshots in time of the displacement fields are reconstructed via an optimization procedure. An objective function is formulated, and various shape difference definitions are considered. The proposed methodology is first studied for a synthetic case of a flexible cantilever structure undergoing large deformations, and then applied to a Manduca Sexta (hawkmoth) in free flight. The three-dimensional motions of this flapping system are reconstructed from image date collected by using three cameras. The complete deformation geometry of this system is analyzed. Finally, a computational investigation is carried out to understand the flow physics and aerodynamic performance by prescribing the body and wing motions in a fluid-body code. This thesis work contains one of the first set of such motion visualization and deformation analyses carried out for a hawkmoth in free flight. The tools and procedures used in this work are widely applicable to the studies of other flying animals with flexible wings as well as synthetic systems with flexible body elements.

Conversor de energia das ondas em energia elétrica com dispositivo de coluna de água oscilante: simulação numérica e estudo geométrico

Os oceanos representam um dos maiores recursos naturais, possuindo expressivo potencial energético, podendo suprir parte da demanda energética mundial. Nas últimas décadas, alguns dispositivos destinados à conversão da energia das ondas dos oceanos em energia elétrica têm sido estudados. No presente trabalho, o princípio de funcionamento do conversor do tipo Coluna de Água Oscilante, do inglês Oscillating Water Colum, (OWC) foi analisado numericamente. As ondas incidentes na câmara hidro-pneumática da OWC, causam um movimento alternado da coluna de água no interior da câmara, o qual produz um fluxo alternado de ar que passa pela chaminé. O ar passa e aciona uma turbina a qual transmite energia para um gerador elétrico. O objetivo do presente estudo foi investigar a influência de diferentes formas geométricas da câmara sobre o fluxo resultante de ar que passa pela turbina, que influencia no desempenho do dispositivo. Para isso, geometrias diferentes para o conversor foram analisadas empregando modelos computacionais 2D e 3D. Um modelo computacional desenvolvido nos softwares GAMBIT e FLUENT foi utilizado, em que o conversor OWC foi acoplado a um tanque de ondas. O método Volume of Fluid (VOF) e a teoria de 2ª ordem Stokes foram utilizados para gerar ondas regulares, permitindo uma interação mais realista entre o conversor, água, ar e OWC. O Método dos Volumes Finitos (MVF) foi utilizado para a discretização das equações governantes. Neste trabalho o Contructal Design (baseado na Teoria Constructal) foi aplicado pela primeira vez em estudos numéricos tridimensionais de OWC para fim de encontrar uma geometria que mais favorece o desempenho do dispositivo. A função objetivo foi a maximização da vazão mássica de ar que passa através da chaminé do dispositivo OWC, analisado através do método mínimos quadrados, do inglês Root Mean Square (RMS). Os resultados indicaram que a forma geométrica da câmara influencia na transformação da energia das ondas em energia elétrica. As geometrias das câmaras analisadas que apresentaram maior área da face de incidência das ondas (sendo altura constante), apresentaram também maior desempenho do conversor OWC. A melhor geometria, entre os casos desse estudo, ofereceu um ganho no desempenho do dispositivo em torno de 30% maior.

O problema de alocação de berços: um estudo das heurísticas simulated annealing e algoritmo genético

Este trabalho apresenta um estudo de caso das heurísticas Simulated Annealing e Algoritmo Genético para um problema de grande relevância encontrado no sistema portuário, o Problema de Alocação em Berços. Esse problema aborda a programação e a alocação de navios às áreas de atracação ao longo de um cais. A modelagem utilizada nesta pesquisa é apresentada por Mauri (2008) [28] que trata do problema como uma Problema de Roteamento de Veículos com Múltiplas Garagens e sem Janelas de Tempo. Foi desenvolvido um ambiente apropriado para testes de simulação, onde o cenário de análise foi constituido a partir de situações reais encontradas na programação de navios de um terminal de contêineres. Os testes computacionais realizados mostram a performance das heurísticas em relação a função objetivo e o tempo computacional, a m de avaliar qual das técnicas apresenta melhores resultados.

Simulation Optimization of the Crossdock Door Assignmnet Problem

The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold solution; simulation and optimization of the simulation model - simulation optimization. The novel aspect of our solution approach is that we intend to use simulation to derive a more realistic objective function and use Memetic algorithms to find an optimal solution. The main advantage of using Memetic algorithms is that it combines a local search with Genetic Algorithms. The Crossdock Door Assignment Problem is a new domain application to Memetic Algorithms and it is yet unknown how it will perform.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Modelo para distribuição de recursos nos municípios brasileiros baseado na lei de diretrizes orçamentárias, análise multicritério e programação linear

The municipal management in any country of the globe requires planning and allocation of resources evenly. In Brazil, the Law of Budgetary Guidelines (LDO) guides municipal managers toward that balance. This research develops a model that seeks to find the balance of the allocation of public resources in Brazilian municipalities, considering the LDO as a parameter. For this using statistical techniques and multicriteria analysis as a first step in order to define allocation strategies, based on the technical aspects arising from the municipal manager. In a second step, presented in linear programming based optimization where the objective function is derived from the preference of the results of the manager and his staff. The statistical representation is presented to support multicriteria development in the definition of replacement rates through time series. The multicriteria analysis was structured by defining the criteria, alternatives and the application of UTASTAR methods to calculate replacement rates. After these initial settings, an application of linear programming was developed to find the optimal allocation of enforcement resources of the municipal budget. Data from the budget of a municipality in southwestern Paraná were studied in the application of the model and analysis of results.

Simulation Optimization of the Crossdock Door Assignmnet Problem

The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold solution; simulation and optimization of the simulation model - simulation optimization. The novel aspect of our solution approach is that we intend to use simulation to derive a more realistic objective function and use Memetic algorithms to find an optimal solution. The main advantage of using Memetic algorithms is that it combines a local search with Genetic Algorithms. The Crossdock Door Assignment Problem is a new domain application to Memetic Algorithms and it is yet unknown how it will perform.

Risk management for mathematical optimization under uncertainty

We present a general multistage stochastic mixed 0-1 problem where the uncertainty appears everywhere in the objective function, constraints matrix and right-hand-side. The uncertainty is represented by a scenario tree that can be a symmetric or a nonsymmetric one. The stochastic model is converted in a mixed 0-1 Deterministic Equivalent Model in compact representation. Due to the difficulty of the problem, the solution offered by the stochastic model has been traditionally obtained by optimizing the objective function expected value (i.e., mean) over the scenarios, usually, along a time horizon. This approach (so named risk neutral) has the inconvenience of providing a solution that ignores the variance of the objective value of the scenarios and, so, the occurrence of scenarios with an objective value below the expected one. Alternatively, we present several approaches for risk averse management, namely, a scenario immunization strategy, the optimization of the well known Value-at-Risk (VaR) and several variants of the Conditional Value-at-Risk strategies, the optimization of the expected mean minus the weighted probability of having a "bad" scenario to occur for the given solution provided by the model, the optimization of the objective function expected value subject to stochastic dominance constraints (SDC) for a set of profiles given by the pairs of threshold objective values and either bounds on the probability of not reaching the thresholds or the expected shortfall over them, and the optimization of a mixture of the VaR and SDC strategies.

Train scheduling and rolling stock assignment in high speed trains

The Train Timetabling Problem (TTP) has been widely studied for freight and passenger rail systems. A lesser effort has been devoted to the study of high-speed rail systems. A modeling issue that has to be addressed is to model departure time choice of passengers on railway services. Passengers who use these systems attempt to travel at predetermined hours due to their daily life necessities (e.g., commuter trips). We incorporate all these features into TTP focusing on high-speed railway systems. We propose a Rail Scheduling and Rolling Stock (RSch-RS) model for timetable planning of high-speed railway systems. This model is composed of two essential elements: i) an infrastructure model for representing the railway network: it includes capacity constraints of the rail network and the Rolling-Stock constraints; and ii) a demand model that defines how the passengers choose the departure time. The resulting model is a mixed-integer programming model which objective function attempts to maximize the profit for the rail operator

Two near-optimal layouts for trusslike bridge structures bearing uniform weight between supports

Although the primary objective on designing a structure is to support the external loads, the achievement of an optimal layout that reduces all costs associated with the structure is an aspect of increasing interest. The problem of finding the optimal layout for bridgelike structures subjected to a uniform load is considered. The problem is formulated following a theory on economy of frame structures, using the stress volume as the objective function and including the selection of appropriate values for statically indeterminate reactions. It is solved in a function space of finite dimension instead of using a general variational approach, obtaining near-optimal solutions. The results obtained with this profitable strategy are very close to the best layouts known to date, with differences of less than 2% for the stress volume, but with a simpler layout that can be recognized in some real bridges. This strategy could be a guide to preliminary design of bridges subject to a wide class of costs.

Robustness in facility location

Facility location concerns the placement of facilities, for various objectives, by use of mathematical models and solution procedures. Almost all facility location models that can be found in literature are based on minimizing costs or maximizing cover, to cover as much demand as possible. These models are quite efficient for finding an optimal location for a new facility for a particular data set, which is considered to be constant and known in advance. In a real world situation, input data like demand and travelling costs are not fixed, nor known in advance. This uncertainty and uncontrollability can lead to unacceptable losses or even bankruptcy. A way of dealing with these factors is robustness modelling. A robust facility location model aims to locate a facility that stays within predefined limits for all expectable circumstances as good as possible. The deviation robustness concept is used as basis to develop a new competitive deviation robustness model. The competition is modelled with a Huff based model, which calculates the market share of the new facility. Robustness in this model is defined as the ability of a facility location to capture a minimum market share, despite variations in demand. A test case is developed by which algorithms can be tested on their ability to solve robust facility location models. Four stochastic optimization algorithms are considered from which Simulated Annealing turned out to be the most appropriate. The test case is slightly modified for a competitive market situation. With the Simulated Annealing algorithm, the developed competitive deviation model is solved, for three considered norms of deviation. At the end, also a grid search is performed to illustrate the landscape of the objective function of the competitive deviation model. The model appears to be multimodal and seems to be challenging for further research.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

An adaptive neighborhood search algorithm for optimizing stochastic mining complexes

Les métaheuristiques sont très utilisées dans le domaine de l'optimisation discrète. Elles permettent d’obtenir une solution de bonne qualité en un temps raisonnable, pour des problèmes qui sont de grande taille, complexes, et difficiles à résoudre. Souvent, les métaheuristiques ont beaucoup de paramètres que l’utilisateur doit ajuster manuellement pour un problème donné. L'objectif d'une métaheuristique adaptative est de permettre l'ajustement automatique de certains paramètres par la méthode, en se basant sur l’instance à résoudre. La métaheuristique adaptative, en utilisant les connaissances préalables dans la compréhension du problème, des notions de l'apprentissage machine et des domaines associés, crée une méthode plus générale et automatique pour résoudre des problèmes. L’optimisation globale des complexes miniers vise à établir les mouvements des matériaux dans les mines et les flux de traitement afin de maximiser la valeur économique du système. Souvent, en raison du grand nombre de variables entières dans le modèle, de la présence de contraintes complexes et de contraintes non-linéaires, il devient prohibitif de résoudre ces modèles en utilisant les optimiseurs disponibles dans l’industrie. Par conséquent, les métaheuristiques sont souvent utilisées pour l’optimisation de complexes miniers. Ce mémoire améliore un procédé de recuit simulé développé par Goodfellow & Dimitrakopoulos (2016) pour l’optimisation stochastique des complexes miniers stochastiques. La méthode développée par les auteurs nécessite beaucoup de paramètres pour fonctionner. Un de ceux-ci est de savoir comment la méthode de recuit simulé cherche dans le voisinage local de solutions. Ce mémoire implémente une méthode adaptative de recherche dans le voisinage pour améliorer la qualité d'une solution. Les résultats numériques montrent une augmentation jusqu'à 10% de la valeur de la fonction économique.

An adaptive neighborhood search algorithm for optimizing stochastic mining complexes

Les métaheuristiques sont très utilisées dans le domaine de l'optimisation discrète. Elles permettent d’obtenir une solution de bonne qualité en un temps raisonnable, pour des problèmes qui sont de grande taille, complexes, et difficiles à résoudre. Souvent, les métaheuristiques ont beaucoup de paramètres que l’utilisateur doit ajuster manuellement pour un problème donné. L'objectif d'une métaheuristique adaptative est de permettre l'ajustement automatique de certains paramètres par la méthode, en se basant sur l’instance à résoudre. La métaheuristique adaptative, en utilisant les connaissances préalables dans la compréhension du problème, des notions de l'apprentissage machine et des domaines associés, crée une méthode plus générale et automatique pour résoudre des problèmes. L’optimisation globale des complexes miniers vise à établir les mouvements des matériaux dans les mines et les flux de traitement afin de maximiser la valeur économique du système. Souvent, en raison du grand nombre de variables entières dans le modèle, de la présence de contraintes complexes et de contraintes non-linéaires, il devient prohibitif de résoudre ces modèles en utilisant les optimiseurs disponibles dans l’industrie. Par conséquent, les métaheuristiques sont souvent utilisées pour l’optimisation de complexes miniers. Ce mémoire améliore un procédé de recuit simulé développé par Goodfellow & Dimitrakopoulos (2016) pour l’optimisation stochastique des complexes miniers stochastiques. La méthode développée par les auteurs nécessite beaucoup de paramètres pour fonctionner. Un de ceux-ci est de savoir comment la méthode de recuit simulé cherche dans le voisinage local de solutions. Ce mémoire implémente une méthode adaptative de recherche dans le voisinage pour améliorer la qualité d'une solution. Les résultats numériques montrent une augmentation jusqu'à 10% de la valeur de la fonction économique.