Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.

Avaliação do desempenho de fundações em edificação no DF com a utilização de técnicas de interação solo-estrutura

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2015.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

Influência de feixes de condutores em linhas de transmissão UAT CA

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2015.

Dimensionamento de uma estrutura de contenção de terras flexível com vários níveis de apoio

O presente trabalho, no âmbito de projeto final de curso de metrado em Engenharia da Construção, teve como objetivo o estudo do comportamento de estruturas de suporte de terras flexíveis multi-apoiadas (com diferentes tipos de apoio) para dois tipos solos homogéneos. Recorreu-se às teorias clássicas, como a de Rankine, desenvolvidas para estruturas de suporte de terras rígidas. Às teorias semi-empíricas de Terzaghi & Peck que culminaram nos diagramas de Terzaghi & Peck. Apesar de os digramas de Terzaghi & Peck serem diagramas de pressões de terras a usar em estruturas de suporte de terras flexíveis, apresentam algumas limitações importantes, como a sua aplicação apenas em solos heterogéneos, com presença ou não de níveis freáticos, e sem fornecer distribuição das pressões de terras na zona passiva (zona enterrada). Como na atualidade os modelos de elementos finitos permitem simular de modo muito mais rigoroso os problemas da engenharia. O presente trabalho esteve focado em analisar um caso prático em diferentes solos e com diferentes tipos de apoios. Será estudado mediante os métodos analíticos usando as teorias clássicas e posteriormente métodos numéricos (com diferentes programas de cálculo). Finalmente serão comparados os resultados obtidos mediante os diferentes métodos usados. As estruturas foram inicialmente pré-dimensionadas usando os métodos clássicos. Assim foram usados os diagramas de pressões de terras de Terzaghi & Peck para a zona ativa (zona em escavação) e a teoria de Rankine para conhecer as pressões de terras na zona enterrada da cortina (parede moldada) e recorrendo ao software Ftool para a obtenção dos parâmetros de dimensionamento de estruturas de suporte de terras objeto de estudo. Posteriormente utilizaram-se os programas de cálculo automático CYPE 2015 k, e o programa de cálculo de elementos finitos PLAXIS Introductory 2010. Estes programas permitem simular o faseamento construtivo do muro. Para estudar a influência de algúns parâmetros no comportamento da Resumo IV cortina o estudo foi realizado com dois solos distintos, um solo argiloso mole e um solo arenoso denso. Assim como para dois tipos de apoios distintos, ancoragens ativas e escoras passivas. Foram analisados diferentes parâmetros na estrutura de suporte; pressões horizontais das terras, deslocamentos horizontais, esforço axial, transverso e momento fletor.

Caracterização analítica e geométrica da metodologia geral de determinação de distribuições de Weibull para o regime eólico e suas aplicações

O regime eólico de uma região pode ser descrito por distribuição de frequências que fornecem informações e características extremamente necessárias para uma possível implantação de sistemas eólicos de captação de energia na região e consequentes aplicações no meio rural em regiões afastadas. Estas características, tais como a velocidade média anual, a variância das velocidades registradas e a densidade da potência eólica média horária, podem ser obtidas pela frequência de ocorrências de determinada velocidade, que por sua vez deve ser estudada através de expressões analíticas. A função analítica mais adequada para distribuições eólicas é a função de densidade de Weibull, que pode ser determinada por métodos numéricos e regressões lineares. O objetivo deste trabalho é caracterizar analítica e geometricamente todos os procedimentos metodológicos necessários para a realização de uma caracterização completa do regime eólico de uma região e suas aplicações na região de Botucatu - SP, visando a determinar o potencial energético para implementação de turbinas eólicas. Assim, foi possível estabelecer teoremas relacionados com a forma de caracterização do regime eólico, estabelecendo a metodologia concisa analiticamente para a definição dos parâmetros eólicos de qualquer região a ser estudada. Para o desenvolvimento desta pesquisa, utilizou-se um anemômetro da CAMPBELL.

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

A novel methodology for simulating contact-line behavior in capillary-driven flows

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Análise comparativa entre simuladores de linha de fluxo e diferenças finitas para um reservatório de petróleo submetido a injeção de água

Water injection is the most widely used method for supplementary recovery in many oil fields due to various reasons, like the fact that water is an effective displacing agent of low viscosity oils, the water injection projects are relatively simple to establish and the water availability at a relatively low cost. For design of water injection projects is necessary to do reservoir studies in order to define the various parameters needed to increase the effectiveness of the method. For this kind of study can be used several mathematical models classified into two general categories: analytical or numerical. The present work aims to do a comparative analysis between the results presented by flow lines simulator and conventional finite differences simulator; both types of simulators are based on numerical methods designed to model light oil reservoirs subjected to water injection. Therefore, it was defined two reservoir models: the first one was a heterogeneous model whose petrophysical properties vary along the reservoir and the other one was created using average petrophysical properties obtained from the first model. Comparisons were done considering that the results of these two models were always in the same operational conditions. Then some rock and fluid parameters have been changed in both models and again the results were compared. From the factorial design, that was done to study the sensitivity analysis of reservoir parameters, a few cases were chosen to study the role of water injection rate and the vertical position of wells perforations in production forecast. It was observed that the results from the two simulators are quite similar in most of the cases; differences were found only in those cases where there was an increase in gas solubility ratio of the model. Thus, it was concluded that in flow simulation of reservoirs analogous of those now studied, mainly when the gas solubility ratio is low, the conventional finite differences simulator may be replaced by flow lines simulator the production forecast is compatible but the computational processing time is lower.

Development of Physics-based Models and Design Optimization of Power Electronic Conversion Systems

The main objective for physics based modeling of the power converter components is to design the whole converter with respect to physical and operational constraints. Therefore, all the elements and components of the energy conversion system are modeled numerically and combined together to achieve the whole system behavioral model. Previously proposed high frequency (HF) models of power converters are based on circuit models that are only related to the parasitic inner parameters of the power devices and the connections between the components. This dissertation aims to obtain appropriate physics-based models for power conversion systems, which not only can represent the steady state behavior of the components, but also can predict their high frequency characteristics. The developed physics-based model would represent the physical device with a high level of accuracy in predicting its operating condition. The proposed physics-based model enables us to accurately develop components such as; effective EMI filters, switching algorithms and circuit topologies [7]. One of the applications of the developed modeling technique is design of new sets of topologies for high-frequency, high efficiency converters for variable speed drives. The main advantage of the modeling method, presented in this dissertation, is the practical design of an inverter for high power applications with the ability to overcome the blocking voltage limitations of available power semiconductor devices. Another advantage is selection of the best matching topology with inherent reduction of switching losses which can be utilized to improve the overall efficiency. The physics-based modeling approach, in this dissertation, makes it possible to design any power electronic conversion system to meet electromagnetic standards and design constraints. This includes physical characteristics such as; decreasing the size and weight of the package, optimized interactions with the neighboring components and higher power density. In addition, the electromagnetic behaviors and signatures can be evaluated including the study of conducted and radiated EMI interactions in addition to the design of attenuation measures and enclosures.

The Influence of Healed Intrablock Rockmass Structure on the Behaviour of Deep Excavations in Complex Rockmasses

Conventional rockmass characterization and analysis methods for geotechnical assessment in mining, civil tunnelling, and other excavations consider only the intact rock properties and the discrete fractures that are present and form blocks within rockmasses. Field logging and classification protocols are based on historically useful but highly simplified design techniques, including direct empirical design and empirical strength assessment for simplified ground reaction and support analysis. As modern underground excavations go deeper and enter into more high stress environments with complex excavation geometries and associated stress paths, healed structures within initially intact rock blocks such as sedimentary nodule boundaries and hydrothermal veins, veinlets and stockwork (termed intrablock structure) are having an increasing influence on rockmass behaviour and should be included in modern geotechnical design. Due to the reliance on geotechnical classification methods which predate computer aided analysis, these complexities are ignored in conventional design. Given the comparatively complex, sophisticated and powerful numerical simulation and analysis techniques now practically available to the geotechnical engineer, this research is driven by the need for enhanced characterization of intrablock structure for application to numerical methods. Intrablock structure governs stress-driven behaviour at depth, gravity driven disintegration for large shallow spans, and controls ultimate fragmentation. This research addresses the characterization of intrablock structure and the understanding of its behaviour at laboratory testing and excavation scales, and presents new methodologies and tools to incorporate intrablock structure into geotechnical design practice. A new field characterization tool, the Composite Geological Strength Index, is used for outcrop or excavation face evaluation and provides direct input to continuum numerical models with implicit rockmass structure. A brittle overbreak estimation tool for complex rockmasses is developed using field observations. New methods to evaluate geometrical and mechanical properties of intrablock structure are developed. Finally, laboratory direct shear testing protocols for interblock structure are critically evaluated and extended to intrablock structure for the purpose of determining input parameters for numerical models with explicit structure.

Confirmação do modelo da estrutura 3D do vale inferior do Tejo a partir de dados de ruído sísmico ambiente

Ao longo de sua história a região do Vale Inferior do Tejo VIT foi abalada por vários sismos consideravelmente destrutivas, tendo alguns deles produzido significativas deformações nas estruturas marítimas localizadas no litoral a sudoeste do território Português; outros, moderados, foram produzidos por fontes locais, como os de 1344, 1531 e 1909. Nos últimos anos, devido à melhoria dos modelos de estrutura 3D e o desenvolvimento dos métodos numéricos, foram elaborados vários estudos de síntese de movimento forte do solo para a região do Baixo Tejo utilizando o método de diferenças finitas. Para confirmar o modelo de velocidades desta bacia usámos medidas de ruído sísmico, aplicámos um método baseado na razão espectral H/V, e, a partir destas curvas, por inversão, obtivemos um modelo de velocidades para a região estudada. Os resultados revelam uma boa concordância entre o modelo obtido e os dados geofísicos e geológicos recolhidos na mesma área._ ABSTRACT: Along his history the Lower Tagus Valley (LTV) area was shaken by several earthquakes. The largest reported had their origin in the southwestern part of Iberia. Other moderate earthquakes were produced by local sources such as the 1344, 1531 and the 1909. ln the last years, due to 3D structural model improvement and development in numerical methods, several studies have successful obtained strong-ground motion synthesis for the LVT region using finite difference method. To confirm the velocity model of the LTV sedimentary basin obtained by geophysical and geological data, we use broad-band microtremor measurements and application of the horizontal to vertical (H/V) spectral ratio method. We have obtained a velocity model for the studied region by inversion of the H/V curve. The results have good agreement geological and geophysical data.

Models for reliability estimation of HVDC cable systems

The work carried out in this thesis aims at: - studying – in both simulative and experimental methods – the effect of electrical transients (i.e., Voltage Polarity Reversals VPRs, Temporary OverVoltages TOVs, and Superimposed Switching Impulses SSIs) on the aging phenomena in HVDC extruded cable insulations. Dielectric spectroscopy, conductivity measurements, Fourier Transform Infra-Red FTIR spectroscopy, and space charge measurements show variation in the insulating properties of the aged Cross-Linked Polyethylene XLPE specimens compared to non-aged ones. Scission in XLPE bonds and formation of aging chemical bonds is also noticed in aged insulations due to possible oxidation reactions. The aged materials show more ability to accumulate space charges compared to non-aged ones. An increase in both DC electrical conductivity and imaginary permittivity has been also noticed. - The development of life-based geometric design of HVDC cables in a detailed parametric analysis of all parameters that affect the design. Furthermore, the effect of both electrical and thermal transients on the design is also investigated. - The intrinsic thermal instability in HVDC cables and the effect of insulation characteristics on the thermal stability using a temperature and field iterative loop (using numerical methods – Finite Difference Method FDM). The dielectric loss coefficient is also calculated for DC cables and found to be less than that in AC cables. This emphasizes that the intrinsic thermal instability is critical in HVDC cables. - Fitting electrical conductivity models to the experimental measurements using both models found in the literature and modified models to find the best fit by considering the synergistic effect between field and temperature coefficients of electrical conductivity.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.