Accurate ship-motion prediction is important because it is directly related to the design, control, and economic operation of ships. Many methods are available for studying and predicting ship motions, including time-domain, strip-theory, and system-identification-based predictions. Time-domain and strip-theory predictions suffer from several physical and computational limitations. In this work, we use system-identification techniques to predict ship motions. We establish an identification methodology that can handle general finite-degree-of-freedom (FDOF) models of ship motions. To establish this methodology, we derive the correct form of the equations of motion. This form contains all relevant linear and nonlinear terms. Moreover, it explicitly specifies the dependence of the linear and nonlinear parameters on the forward speed. The energy-formulation approach is utilized to obtain full nonlinear ship-motion equations. The advantages of using this formulation are that self-sustained motions are not allowed and the dependence of the parameters on the forward speed is derived explicitly. The data required for the identification techniques are generated using the Large Amplitude Motions Program (LAMP) developed by the Science Applications International Corporation (SAIC). The ship studied in this work is a Series 60 ship, which is a military cargo ship. LAMP data for different sea states and forward speeds are used to identify and predict the ship motions. For linear parametric identification, we use the Eigensystem Realization Algorithm (ERA) to determine the coefficients in the linearly coupled equations and the effects of the forward speed on these coefficients. For linear nonparametric identification, we present a new analysis technique, namely, the circular-hyperbolic decomposition (CHD), which avoids the leakage effects associated with the discrete Fourier transform (DFT). The CHD is then utilized to determine transfer functions and response amplitude operators (RAOs). For nonlinear parametric identification, we present a methodology that is a combination of perturbation techniques and higher-order spectral moments. We apply this methodology to identify the nonlinear parameters that cause parametric roll resonance. The level of accuracy of the models and the parameter estimates are determined by validations of the predicted ship motions with the LAMP data. / Ph. D.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-22T20:32:01Z No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-23T15:24:03Z (GMT) No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-23T15:24:03Z (GMT). No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-02-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of this work is to investigate the interaction and modal coupling phenomena on the nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and lateral loads. The equations of motion of the cylindrical shell are deduced from their energy functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally, the problem is reduced to a system of nonlinear ordinary differential equations by the application of the standard Galerkin method. The modal expansion that describes the transverse displacement of the shell is obtained by applying perturbation techniques, which identifies the importance of each term in the modal expansion by the power of the perturbation parameter. The Karhunen-Loève method is applied in order to verify the importance of each term in the modal expansion, quantifying the contribution of each of these terms in the total energy of the system. The starting solution used in the perturbation procedure contains two modes of vibration with the same natural frequency and their respective companion modes, yielding a modal expansion able to describe the modal interaction between these two modes. Then, the influence of modal interaction on the nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is studied. From the analysis of the resonance curves, the parametric instability and escape boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the cylindrical shell is possible to identify situations in which the consideration of modal interaction is necessary. / Neste trabalho estudam-se as vibrações não lineares de cascas cilíndricas simplesmente apoiadas sujeitas a um carregamento lateral e a um carregamento axial, ambos harmônicos, com o objetivo de se analisar fenômenos como o acoplamento e a interação modal. As equações de movimento da casca cilíndrica são deduzidas a partir de seus funcionais de energia. O campo de deformações da casca cilíndrica é descrito com base na teoria não linear de Donnell para cascas esbeltas e o problema é reduzido a um sistema de equações diferenciais ordinárias não lineares a partir da aplicação do método de Galerkin. As expansões modais que descrevem o campo de deslocamento transversal da casca são obtidas através da aplicação do método da perturbação, que identifica a importância de cada termo da expansão modal a partir da potência do parâmetro de perturbação. O método de Karhunen-Loève é aplicado a fim de se verificar a importância de cada termo da expansão modal, quantificando a participação de cada um desses termos na energia total do sistema. Utilizam-se, como solução inicial do método da perturbação, dois modos de vibração com frequência natural igual e com seus respectivos companion modes, obtendo-se uma expansão modal capaz de descrever a interação modal entre esses dois modos. Em seguida, analisa-se a influência da interação modal no comportamento não linear da casca cilíndrica submetidas a cargas laterais e axiais harmônicas. A partir da análise das curvas de ressonância, das fronteiras de instabilidade paramétrica, dos diagramas de bifurcação, das bacias de atração e dos planosfase da casca cilíndrica é possível identificar em quais situações de carregamento a consideração da interação modal se faz necessária.

Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.

Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.

Philosophiae Doctor - PhD / Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature. / South Africa

Philosophiae Doctor - PhD / Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Bean. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.

[pt] Esta tese apresenta um estudo sobre métodos semianalíticos para modelagem de guias de ondas com contornos complexos. Os campos eletromagnéticos dentro de meios não homogêneos e anisotrópicos são resolvidos por meio de harmônicos cilíndricos como base para outras abordagens numéricas, como o método de perturbação regular (RPM), o método de perturbação de material em cavidade (CMPM) e o método de casamento de pontos (PMM). As novas soluções semianalíticas que exploramos aqui podem ser empregadas para a análise de comunicação sem fio ao longo de túneis, bem como para a modelagem de sensores realistas de perfilagem durante a perfuração em problemas geofísicos de baixa frequência. Estudamos o potencial do RPM ao combiná-lo com os princípios da transformação óptica (TO) para analisar um guia de onda coaxial excêntrico preenchido com materiais anisotrópicos. Além disso, estendemos o CMPM clássico proposto por Harrington para lidar com meios anisotrópicos para resolver os números de onda de corte dos campos modais no mesmo guia de onda de maneira aproximada, mas numericamente eficiente. Outra solução de perturbação é proposta combinando as correções de baixa ordem do RPM no CMPM para fornecer correções de alta ordem para os números de onda de corte dos modos suportados pelo guia. Uma formulação matemática de um método semianalítico baseado em PMM para resolver guias de onda preenchidos com meios anisotrópicos e com camadas arbitrárias também é apresentada. Uma versão melhorada deste método é introduzida para modelar estruturas guiadas cilíndricas de múltiplas camadas não circulares. Essas soluções baseadas em casamento de pontos representam boas alternativas para abordagens de força bruta, como métodos de elementos finitos e de diferenças finitas. / [en] This thesis presents a study on semi-analytic methods for modeling waveguides with complex-shaped boundaries. The electromagnetic fields inside inhomogeneous and anisotropic media are solved via cylindrical harmonics as a basis for other numerical approaches, including the regular perturbation method (RPM), the cavity-material perturbation method (CMPM), and the point-matching method (PMM). The novel semi-analytic solutions we have explored here can be employed for the analysis of wireless communication along tunnels and boreholes as well as for the modeling of realistic logging-whiledrilling (LWD) sensors and their environments at low-frequency geophysical problems. We studied the potential of the RPM when combining it with the transformation optics (TO) principles to analyze an eccentric coaxial waveguide filled with anisotropic materials. Furthermore, we have extended the classical CMPM proposed by Harrington to handling anisotropic media for solving the cutoff wavenumbers of the modal fields in the same eccentric coaxial waveguide in an approximated but numerically efficient manner. Another perturbation solution is proposed here and combines the low-order corrections from RPM into the CMPM for providing high-order corrections to the cutoff wavenumbers of the modes supported in this guide. A mathematical formulation of a semi-analytic point-matching method for solving more complex anisotropic-filled waveguides with an arbitrary number of layers is also presented. An improved version of this method is introduced for modeling noncircular multi-layered cylindrical guided structures. Such point-matching-based solutions represent good alternatives to brute-force approaches such as finiteelement and finite-difference methods and motivate further investigations. We present a series of validation results showing the accuracy, efficiency, and potential limitations of the explored methods.

Ultrasound acoustic energy transfer (UAET) is an emerging contactless technology that offers the capability to safely and efficiently power sensors and devices while eliminating the need to replace batteries, which is of interest in many applications. It has been proposed to recharge and communicate with implanted medical devices, thereby eliminating the need for invasive and expensive surgery and also to charge sensors inside enclosed metal containers typically found in automobiles, nuclear power plants, space stations, and aircraft engines. In UAET, energy is transferred through the reception of acoustic waves by a piezoelectric receiver that converts the energy of acoustic waves to electrical voltage. It has been shown that UAET outperforms the conventional CET technologies that use electromagnetic waves to transfer energy, including inductive coupling and capacitative coupling. To date, the majority of research on UAET systems has been limited to modeling and proof-of-concept experiments, mostly in the linear regime, i.e., under small levels of acoustic pressure that result in small amplitude longitudinal vibrations and linearized piezoelectricity. Moreover, existing models are based on the "piston-like" deformation assumption of the transmitter and receiver, which is only accurate for thin disks and does not accurately account for radiation effects. The linear models neglect nonlinear effects associated with the nonlinear acoustic wave propagation as well as the receiver's electroelastic nonlinearities on the energy transfer characteristics, which become significant at high source strengths. In this dissertation, we present experimentally-validated analytical and numerical multiphysics modeling approaches aimed at filling a knowledge gap in terms of considering resonant acoustic-piezoelectric structure interactions and nonlinear effects associated with high excitation levels in UAET systems. In particular, we develop a reduced-order model that can accurately account for the radiation effects and validate it by performing experiments on four piezoelectric disks with different aspect ratios. Next, we study the role of individual sources of nonlinearity on the output power characteristics. First, we consider the effects of electroelastic nonlinearities. We show that these nonlinearities can shift the optimum load resistance when the acoustic medium is fluid. Next, we consider the nonlinear wave propagation and note that the shock formation is associated with the dissipation of energy, and as such, shock formation distance is an essential design parameter for high-intensity UAET systems. We then present an analytical approach capable of predicting the shock formation distance and validate it by comparing its prediction with finite element simulations and experimental results published in the literature. Finally, we experimentally investigate the effects of both the nonlinearity sources on the output power characteristics of the UAET system by considering a high intensity focused ultrasound source and a piezoelectric disk receiver. We determine that the system's efficiency decreases, and the maximum voltage output position drifts towards the source as the source strength is increased. / Doctor of Philosophy / Advancements in electronics that underpinned the development of low power sensors and devices have transformed many fields. For instance, it has led to the innovation of implanted medical devices (IMDs) such as pacemakers and neurostimulators that perform life-saving functions. They also find applications in condition monitoring and wireless sensing in nuclear power plants, space stations, automobiles and aircraft engines, where the sensors are enclosed within sealed metal containers, vacuum/pressure vessels or located in a position isolated from the operator by metal walls. In all these applications, it is desired to communicate with and recharge the sensors wirelessly. Such a mechanism can eliminate the need for invasive and expensive surgeries to replace batteries of IMDs and preserve the structural integrity of metal containers by eliminating the need for feed through wires. It has been shown that ultrasound acoustic energy transfer (UAET) outperforms conventional wireless power transfer techniques. However, existing models are based on several assumptions that limit their potential and do not account for effects that become dominant when a higher output power is desired. In this dissertation, we present experimentally validated numerical and theoretical investigations to fill those knowledge gaps. We also provide crucial design recommendations based on our findings for the efficient implementation of UAET technology.

Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-04T20:56:59Z No. of bitstreams: 2 Dissertação - Augusta Finotti Brazão - 2014.pdf: 4325407 bytes, checksum: ed015d93a79ebdcbed577af5e0f9a797 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-02-05T09:48:34Z (GMT) No. of bitstreams: 2 Dissertação - Augusta Finotti Brazão - 2014.pdf: 4325407 bytes, checksum: ed015d93a79ebdcbed577af5e0f9a797 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-02-05T09:48:34Z (GMT). No. of bitstreams: 2 Dissertação - Augusta Finotti Brazão - 2014.pdf: 4325407 bytes, checksum: ed015d93a79ebdcbed577af5e0f9a797 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-04-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present study aims to investigate the influence of uncertainties in physical and geometric parameters to obtain the load parametric instability of cylindrical shell, using the Galerkin method with the stochastic polynomial Hermite-Caos. The nonlinear equations of motion of the cylindrical shell are deduced from their functional power considering the strain field proposed by Donnell´s nonlinear shallow shell theory. The uncertainties are considered as random parameters with probability density function known in the partial differential equation of motion of the cylindrical shell, which it becomes a stochastic partial differential equation due to the presence of randomness. First, the discretization of the stochastic problem is performed using the stochastic Galerkin method together with polynomial Hermite-Chaos, to transform the stochastic partial differential equation into a set of equivalent deterministic partial differential equations, which take into account the randomness of the system. Then, the discretization of the lateral field displacement is made by a perturbation procedure, indicating the nonlinear vibration modes which couple to the linear vibration mode. The set of partial differential equations is transformed into a deterministic system of equations deterministic ordinary second order in time. Uncertainty is considered in one of its parameters: the Young modulus, thickness and amplitude of initial geometric imperfection. Then we analyze the influence of randomness in two parameters simultaneously: the thickness and the Young modulus. Once obtained the system of ordinary differential equations deterministic containing the randomness of the parameters, the integration over discrete time system is made from the Runge- Kutta fourth order to obtain results as the time response, bifurcation diagrams and boundaries of instability which are compared with deterministic analysis, indicating that polynomial Hermite-Chaos is a good numerical tool for predicting the load parametric instability without the need to perform a process of sampling. / O presente trabalho tem como objetivo investigar a influência de incertezas nos parâmetros físicos e geométricos para a determinação da carga de instabilidade paramétrica da casca cilíndrica, utilizando o método de Galerkin Estocástico juntamente com o polinômio de Hermite-Caos. As equações não-lineares de movimento da casca cilíndrica são deduzidas a partir de seus funcionais de energia considerando o campo de deformações proposto pela teoria não linear de Donnell para cascas esbeltas. As incertezas são consideradas como parâmetros aleatórios com função de densidade de probabilidade conhecida na equação diferencial parcial de movimento da casca cilíndrica, que passa a ser uma equação diferencial parcial estocástica devido à presença da aleatoriedade. Primeiramente, faz-se a discretização do problema estocástico utilizando o método de Galerkin Estocástico juntamente com o polinômio de Hermite-Caos, para transformar a equação diferencial parcial estocástica em um conjunto de equações diferenciais parciais determinísticas equivalentes, que levem em consideração a aleatoriedade do sistema. Em seguida, apresenta-se a discretização do campo de deslocamentos laterais através do Método da Perturbação, indicando os modos não-lineares de vibração que se acoplam ao modo linear de vibração, para que o conjunto de equações diferenciais parciais determinísticas seja transformado em um sistema de equações ordinárias determinísticas de segunda ordem no tempo. A incerteza é considerada inicialmente em apenas um de seus parâmetros: no módulo de elasticidade, na espessura e na amplitude da imperfeição geométrica inicial. Em seguida, analisa-se a influência de aleatoriedades em dois parâmetros simultaneamente, sendo eles: a espessura e o módulo de elasticidade. Uma vez obtido o sistema de equações diferenciais ordinárias determinísticas que contêm as aleatoriedades dos parâmetros, a integração ao longo do tempo do sistema discretizado é feita a partir do método de Runge-Kutta de quarta ordem, obtendo-se resultados como resposta no tempo, diagramas de bifurcação e fronteiras de instabilidade, que são comparados com análises determinísticas, indicando que o polinômio de Hermite-Caos é uma boa ferramenta numérica para prever a carga de instabilidade paramétrica sem a necessidade de se realizar um processo de amostragens.

Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.