An approach was developed which allows for design studies of commercial aircraft using physics-based noise analysis methods while retaining the ability to perform the rapid tradeoff and risk analysis studies needed at the conceptual design stage. A prototype integrated analysis process was created for computing the total aircraft EPNL at the Federal Aviation Regulations Part 36 certification measurement locations using physics-based methods for fan rotor-stator interaction tones and jet mixing noise. The analysis process was then used in combination with design of experiments to create response surface equations (RSEs) for the engine and aircraft performance metrics, geometric constraints and takeoff and landing noise levels. In addition, Monte Carlo analysis was used to assess the expected variability of the metrics under the influence of uncertainty, and to determine how the variability is affected by the choice of engine cycle. Finally, the RSEs were used to conduct a series of proof-of-concept conceptual-level design studies demonstrating the utility of the approach. The study found that a key advantage to using physics-based analysis during conceptual design lies in the ability to assess the benefits of new technologies as a function of the design to which they are applied. The greatest difficulty in implementing the physics-based analysis proved to be the generation of design geometry at a sufficient level of detail for high-fidelity analysis.

Made available in DSpace on 2014-06-11T19:31:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-05-05Bitstream added on 2014-06-13T20:02:21Z : No. of bitstreams: 1 rickli_li_dr_botfca.pdf: 601367 bytes, checksum: abdaa96dc222f7b27de2cdeb6898ad34 (MD5) / Universidade Estadual Paulista (UNESP) / O aumento populacional do planeta tem exigido cada vez mais produtividade na agricultura objetivando suprir suas necessidades alimenticias. Um dos mais importantes fatores que determinam o sucesso ou o fracasso desta producao sao as variaveis climaticas, dentre elas, pode-se citar a precipitacao pluviometrica. A presente pesquisa analisou a eficiencia dos fatores funcionais no processo de simulacao de dados diarios de precipitacao utilizando a distribuicao Gama. Foram utilizadas series climatologicas diarias para as localidades de Piracicaba . SP e Ponta Grossa . PR. Para determinacao dos estimadores dos parametros da distribuicao Gama (ãá e ãâ), foram avaliados os procedimentos baseados no metodo dos momentos, da verossimilhanca e o metodo numerico de Greenwood & Durand. Avaliou-se tres geradores de numeros pseudo-aleatorios congruencias e dois algoritmos computacionais para geracao da variavel aleatorias Gama que foram implementados no simulador Sedac_R. Por meio de procedimentos estatisticos a validacao apontou que a escolha adequada do metodo para estimativa dos parametros da distribuicao Gama e o algoritmo computacional para geracao da variavel aleatoria Gama devem ser levados em consideracao na simulacao de series climaticas de precipitacao. Em relacao ao gerador de numeros pseudo-aleatorios os resultados indicaram... / The increase of people in the planet has required more productivity in the agriculture field in order to supply the food need. One of the most important factors that determine the success or the failures of that productivity are the climatic variables, such as the rain precipitation. This research analyzed the efficiency of the functional factors in the precipitation daily data simulation process, using the Gamma distribution. Daily climatic series related to the Piracicaba - SP and Ponta Grossa - PR cities were used. The procedures based on the Greenwood & Durand numerical, Likelihood and Moment methods were evaluated aiming to determine the approximation of the parameters of the Gamma distribution (á and â). Three congruent pseudorandom generators and two computational algorithms to generate the Gamma random variable implemented in the Sedac_R simulator were evaluated. By way of statistics procedures, the validation indicated that the suitable choose to both the approximation method of the parameters of the Gamma distribution (á and â) and the computational algorithm to generate the Gamma random variable must be taken into consideration in the precipitation climatic series simulation. Related to the numerical pseudo-random generator the results showed that it doesn t interferes in the accuracy of the generated data.

Resumo: O aumento populacional do planeta tem exigido cada vez mais produtividade na agricultura objetivando suprir suas necessidades alimenticias. Um dos mais importantes fatores que determinam o sucesso ou o fracasso desta producao sao as variaveis climaticas, dentre elas, pode-se citar a precipitacao pluviometrica. A presente pesquisa analisou a eficiencia dos fatores funcionais no processo de simulacao de dados diarios de precipitacao utilizando a distribuicao Gama. Foram utilizadas series climatologicas diarias para as localidades de Piracicaba . SP e Ponta Grossa . PR. Para determinacao dos estimadores dos parametros da distribuicao Gama (ãá e ãâ), foram avaliados os procedimentos baseados no metodo dos momentos, da verossimilhanca e o metodo numerico de Greenwood & Durand. Avaliou-se tres geradores de numeros pseudo-aleatorios congruencias e dois algoritmos computacionais para geracao da variavel aleatorias Gama que foram implementados no simulador Sedac_R. Por meio de procedimentos estatisticos a validacao apontou que a escolha adequada do metodo para estimativa dos parametros da distribuicao Gama e o algoritmo computacional para geracao da variavel aleatoria Gama devem ser levados em consideracao na simulacao de series climaticas de precipitacao. Em relacao ao gerador de numeros pseudo-aleatorios os resultados indicaram... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The increase of people in the planet has required more productivity in the agriculture field in order to supply the food need. One of the most important factors that determine the success or the failures of that productivity are the climatic variables, such as the rain precipitation. This research analyzed the efficiency of the functional factors in the precipitation daily data simulation process, using the Gamma distribution. Daily climatic series related to the Piracicaba - SP and Ponta Grossa - PR cities were used. The procedures based on the Greenwood & Durand numerical, Likelihood and Moment methods were evaluated aiming to determine the approximation of the parameters of the Gamma distribution (á and â). Three congruent pseudorandom generators and two computational algorithms to generate the Gamma random variable implemented in the Sedac_R simulator were evaluated. By way of statistics procedures, the validation indicated that the suitable choose to both the approximation method of the parameters of the Gamma distribution (á and â) and the computational algorithm to generate the Gamma random variable must be taken into consideration in the precipitation climatic series simulation. Related to the numerical pseudo-random generator the results showed that it doesn’t interferes in the accuracy of the generated data. / Orientador: Ângelo Catâneo / Coorientador: Jorim Souza Virgens Filho / Banca: Célia Regina Lopes Zimback / Banca: Manoel Henrique Salgado / Banca: Marcelo Giovaneti Canteri / Banca: José Fernando Mantovani Micali / Doutor

[pt] Nesta tese estudamos duas classes de problemas. A primeira delas diz respeito a uma equação completamente não-linear que degenera como uma potência do gradiente. A presença desta interface afeta a elipticidade do sistema e produz redução da regularidade. Combinando técnicas da análise harmônica com métodos da teoria da medida, desenvolvemos uma análise tangencial que produz resultados de regularidade para as soluções em espaços de Sobolev. Como consequência, nossos resultados implicam estimativas em espaços de Hölder para o gradiente das soluções, desconhecidas na literatura no caso de termos de fonte não-limitados. A segunda parte trata de um problema de transmissão livre, governado por operadores completamente não-lineares. Neste caso, obtemos regularidade ótima para as soluções, assim como informações sobre a fronteira livre associada. / [en] This thesis focuses on two classes of problems. Firstly, we examine fully nonlinear equation degenerating as a power of the gradient. The interface along which ellipticity collapses introduces substantial difficulties in the analysis and affects the regularity of the solutions. Through methods in harmonic analysis and measure theory we produce a geometric analysis of the problem, which leads to estimates in Sobolev spaces. Furthermore, our findings set an important open problem in the literature, namely: the H lder-continuity for the gradient of solutions in the presence of unbounded source terms. The second part of the thesis focuses on a free transmission problem driven by fully nonlinear operators. On this topic, our results include the optimal regularity of the solutions and an analysis of the associated free boundary.

Cognitive radio (CR) is often described as a context-intelligent radio, capable of changing the transmit parameters dynamically based on the interaction with the environment it operates. The work in this thesis explores the problem of using received signal strength (RSS) measurements taken by a network of CR nodes to generate an interference map of a given geographical area and estimate the locations of multiple primary transmitters that operate simultaneously in the area. A probabilistic model of the problem is developed, and algorithms to address location estimation challenges are proposed. Three approaches are proposed to solve the localization problem. The first approach is based on estimating the locations from the generated interference map when no information about the propagation model or any of its parameters is present. The second approach is based on approximating the maximum likelihood (ML) estimate of the transmitter locations with the grid search method when the model is known and its parameters are available. The third approach also requires the knowledge of model parameters but it is actually based on generating samples from the joint posterior of the unknown location parameter with Markov chain Monte Carlo (MCMC) methods, as an alternative for the highly computationally complex grid search approach. For RF cartography generation problem, we study global and local interpolation techniques, specifically the Delaunay triangulation based techniques as the use of existing triangulation provides a computationally attractive solution. We present a comparative performance evaluation of these interpolation techniques in terms of RF field strength estimation and emitter localization. Even though the estimates obtained from the generated interference maps are less accurate compared to the ML estimator, the rough estimates are utilized to initialize a more accurate algorithm such as the MCMC technique to reduce the complexity of the algorithm. The complexity issues of ML estimators based on full grid search are also addressed by various types of iterative grid search methods. One challenge to apply the ML estimation algorithm to multiple emitter localization problem is that, it requires a pdf approximation to summands of log-normal random variables for likelihood calculations at each grid location. This inspires our investigations on sum of log-normal approximations studied in literature for selecting the appropriate approximation to our model assumptions. As a final extension of this work, we propose our own approximation based on distribution fitting to a set of simulated data and compare our approach with Fenton-Wilkinson's well-known approximation which is a simple and computational efficient approach that fits a log-normal distribution to sum of log-normals by matching the first and second central moments of random variables. We demonstrate that the location estimation accuracy of the grid search technique obtained with our proposed approximation is higher than the one obtained with Fenton-Wilkinson's in many different case scenarios.

[pt] Neste trabalho examinamos equações completamente não-lineares em dois contextos distintos. A princípio, estudamos jogos de campo médio completamente não-lineares. Aqui, examinamos ganhos de regularidade para as soluções do problema, existência de soluções, resultados de relaxação e aspectos particulares de um example explícito. A segunda metade da tese dedica-se à regularidade ótima das soluções de um modelo completamente não-linear que degenera-se com respeito ao gradiente das soluções. A pergunta fundamental subjacente a ambos os tópicos diz respeito aos efeitos da elipticidade sobre propriedades intrínsecas das soluções de equações não-lineares. Mais precisamente, no caso dos jogos de campo médio, a elipticidade parece magnificada pelos efeitos do acoplamento, enquanto no caso dos problemas degenerados, esta quantidade colapsa em sub-regiões do domínio, dando origem a delicados fenômenos. Nossa análise inclui um breve contexto da inserção do trabalho. / [en] In this thesis, we examine fully nonlinear problems in two distinct contexts. The first part of our work focuses on fully nonlinear mean-field games. In this context, we examine gains of regularity, the existence of solutions, relaxation results, and particular aspects of a one-dimensional problem. The second half of the thesis concerns a (sharp) regularity theory for fully nonlinear equations degenerating with respect to the gradient of the solutions. The fundamental question underlying both topics regards the effects of ellipticity on the intrinsic properties of solutions to nonlinear equations. To be more precise, in the case of mean-field game systems, ellipticity seems to be magnified through the coupling structure. On the other hand, in the degenerate setting, ellipticity collapses, giving rise to intricate regularity phenomena. Our analysis is preceded by some context on both topics.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-01T15:05:14Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Souza_Tese_2015_09_22.pdf: 8187999 bytes, checksum: 664629aed28d692dce410fefbfe793dc (MD5) / Made available in DSpace on 2016-07-01T15:05:14Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Souza_Tese_2015_09_22.pdf: 8187999 bytes, checksum: 664629aed28d692dce410fefbfe793dc (MD5) Previous issue date: 2015-09-22 / Anp / Sob certas hipóteses simplificadoras, o modelo matemático que descreve o escoamento de água e óleo em reservatórios de petróleo pode ser representado por um sistema não linear de Equações Diferenciais Parciais composto por uma equação elíptica de pressão (fluxo) e uma equação hiperbólica de saturação (transporte). Devido a complexidades na modelagem de ambientes deposicionais, nos quais são incluídos camadas inclinadas, canais, falhas e poços inclinados, há uma dificuldade de se construir um modelo que represente adequadamente certas características dos reservatórios, especialmente quando malhas estruturadas são usadas (cartesianas ou corner point). Além disso, a modelagem do escoamento multifásico nessas estruturas geológicas incluem descontinuidades na variável e instabilidades no escoamento, associadas à elevadas razões de mobilidade e efeitos de orientação de malha. Isso representa um grande desafio do ponto de vista numérico. No presente trabalho, uma formulação fundamentada no Método de Volumes Finitos é estudada e proposta para discretizar as equações elíptica de pressão e hiperbólica de saturação. Para resolver a equação de pressão três formulações robustas, com aproximação dos fluxos por múltiplos pontos são estudadas. Essas formulações são abeis para lidar com tensores de permeabilidade completos e malhas poligonais arbitrárias, sendo portanto uma generalização de métodos mais tradicionais com aproximação do fluxo por apenas dois pontos. A discretização da equação de saturação é feita com duas abordagens com característica multidimensional. Em uma abordagem mais convencional, os fluxos numéricos são extrapolados diretamente nas superfícies de controle por uma aproximação de alta resolução no espaço (2ª a 4ª ordem) usando uma estratégia do tipo MUSCL. Uma estratégia baseada na Técnica de Mínimos Quadrados é usada para a reconstrução polinomial. Em uma segunda abordagem, uma variação de uma esquema numérico Verdadeiramente Multidimensional é proposto. Esse esquema diminui o efeito de orientação de malha, especialmente para malhas ortogonais, mesmo embora alguma falta de robustez possa ser observada pra malhas excessivamente distorcidas. Nesse tipo de formulação, os fluxos numéricos são calculados de uma forma multidimensional. Consiste em uma combinação convexa de valores de saturação ou fluxo fracionário, seguindo a orientação do escoamento através do domínio computacional. No entanto, a maioria dos esquemas numéricos achados na literatura tem aproximação apenas de primeira ordem no espaço e requer uma solução implícita de sistemas algébricos locais. Adicionalmente, no presente texto, uma forma modificada desses esquemas “Verdadeiramente” Multidimensionais é proposta em um contexto centrado na célula. Nesse caso, os fluxos numéricos multidimensionais são calculados explicitamente usando aproximações de alta ordem no espaço. Para o esquema proposto, a robustez e o caráter multidimensional também leva em conta a distorção da malha por meio de uma ponderação adaptativa. Essa ponderação regula a característica multidimensional da formulação de acordo com a distorção da malha. Claramente, os efeitos de orientação de malha são reduzidos. A supressão de oscilações espúrias, típicas de aproximações de alta ordem, são obtidas usando, pela primeira vez no contexto de simulação de reservatórios, uma estratégia de limitação multidimensional ou Multidimensional Limiting Process (MLP). Essa estratégia garante soluções monótonas e podem ser usadas em qualquer malha poligonal, sendo naturalmente aplicada em aproximações de ordem arbitrária. Por fim, de modo a garantir soluções convergentes, mesmo para problemas tipicamente não convexos, associados ao modelo de Buckley-Leverett, uma estratégia robusta de correção de entropia é empregada. O desempenho dessas formulações é verificado com a solução de problemas relevantes achados na literatura. / Under certain simplifying assumptions, the problem that describes the fluid flow of oil and water in heterogeneous and anisotropic petroleum reservoir can be described by a system of non-linear partial differential equations that comprises an elliptic pressure equation (flow) and a hyperbolic saturation equation (transport). Due to the modeling of complex depositional environments, including inclined laminated layers, channels, fractures, faults and the geometrical modeling of deviated wells, it is difficult to properly build and handle the Reservoir Characterization Process (RCM), particularly by using structured meshes (cartesian or corner point), which is the current standard in petroleum reservoir simulators. Besides, the multiphase flow in such geological structures includes the proper modeling of water saturation shocks and flow instabilities associated to high mobility ratios and Grid Orientation Effects (GOE), posing a great challenge from a numerical point of view. In this work, a Full Finite Volume Formulation is studied and proposed to discretize both, the elliptic pressure and the hyperbolic saturation equations. To solve the pressure equation, we study and use three robust Multipoint Flux Approximation Methods (MPFA) that are able to deal with full permeability tensors and arbitrary polygonal meshes, making it relatively easy to handle complex geological structures, inclined wells and mesh adaptivity in a natural way. To discretize the saturation equation, two different multidimensional approaches are employed. In a more conventional approach, the numerical fluxes are extrapolated directly on the control surfaces for a higher resolution approximation in space (2nd to 4th order) by a MUSCL (Monotone Upstream Centered Scheme for Conservation Laws) procedure. A least squares based strategy is employed for the polynomial reconstruction. In a second approach, a variation of a “Truly” Multidimensional Finite Volume method is proposed. This scheme diminishes GOE, especially for orthogonal grids, even though some lack of robustness can be observed for extremely distorted meshes. In this type of scheme, the numerical flux is computed in each control surface in a multidimensional way, by a convex combination of the saturation or the fractional flow values, following the approximate wave orientation throughout the computational domain. However, the majority of the schemes found in literature is only first order accurate in space and demand the implicit solution of local conservation problems. In the present text, a Modified Truly Multidimensional Finite Volume Method (MTM-FVM) is proposed in a cell centered context. The truly multidimensional numerical fluxes are explicitly computed using higher order accuracy in space. For the proposed scheme, the robustness and the multidimensional character of the aforementioned MTM-FVM explicitly takes into account the angular distortion of the computational mesh by means of an adaptive weight, that tunes the multidimensional character of the formulation according to the grid distortion, clearly diminishing GOE. The suppression of the spurious oscillations, typical from higher order schemes, is achieved by using for the first time in the context of reservoir simulation a Multidimensional Limiting Process (MLP). The MLP strategy formally guarantees monotone solutions and can be used with any polygonal mesh and arbitrary orders of approximation. Finally, in order to guarantee physically meaningful solutions, a robust “entropy fix” strategy is employed. This produces convergent solutions even for the typical non-convex flux functions that are associated to the Buckley-Leverett problem. The performance of the proposed full finite volume formulation is verified by solving some relevant benchmark problems.

This thesis presents the reader the importance of optimization and probabilistic assessment of structures for civil engineering problems. Chapter 2 further investigates the combination between previously proposed optimization techniques and probabilistic assessment in the form of optimization constraints. Academic software has been developed for the purposes of demonstrating the effectiveness of the suggested methods and their statistical testing. 3th chapter summarizes the results of testing previously described optimization method (called Aimed Multilevel Sampling), including a comparison with other optimization techniques. In the final part of the thesis, described procedures have been demonstrated on the selected optimization and reliability problems. The methods described in text represents engineering approach to optimization problems and aims to introduce a simple and transparent optimization algorithm, which could serve to the practical engineering purposes.

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