Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-17T13:13:41Z No. of bitstreams: 2 Dissertação - Layane Rodrigues de Souza Queiroz - 2017.pdf: 8629970 bytes, checksum: af72c48499b0b9a9f4f284f02a016ae0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-17T13:14:07Z (GMT) No. of bitstreams: 2 Dissertação - Layane Rodrigues de Souza Queiroz - 2017.pdf: 8629970 bytes, checksum: af72c48499b0b9a9f4f284f02a016ae0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-11-17T13:14:07Z (GMT). No. of bitstreams: 2 Dissertação - Layane Rodrigues de Souza Queiroz - 2017.pdf: 8629970 bytes, checksum: af72c48499b0b9a9f4f284f02a016ae0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-09-15 / Mechanical systems may suffer with uncertainties that can appear from non-precise data and due the dynamic nature of the problem. Different methods have been used to deal with uncertainty propagation, such as the Latin Hypercube sampling and Polynomial Chaos. Latin hypercube allows to obtain the solution of the random process, from sampling using some probability distribution, over the process domain data. In its turn, the polynomial chaos expansion allows to separate the stochastic components from the deterministic ones of the random solution by using orthogonal polynomials in conformity with the probability distribution of the random variables representing uncertainties. In this work, we apply the Latin hypercube and the polynomial chaos in the quantification of uncertainties. In the beginning some simple mechanical systems were considered, for the purpose to validate the methodology and, then, we studied the effects of uncertainties on a rotor supported by hydrodynamic bearings. / Sistemas mecânicos estão sujeitos a incertezas que surgem a partir da imprecisão dos dados ou da natureza dinâmica do problema. Diferentes métodos têm sido utilizados para lidar com a propagação de incertezas, entre eles o Hipercubo Latino e o Caos Polinomial. O hipercubo latino permite obter a resposta do processo aleatório, a partir da amostragem por alguma destruição de probabilidade, sobre pontos do domínio do processo. Por sua vez, a expansão em caos polinomial permite separar as componentes estocásticas e determinísticas da resposta do processo aleatório a partir do uso de polinômios ortogonais condizentes com a distribuição de probabilidade das variáveis aleatórias que representam as incertezas. Neste trabalho, utiliza-se hipercubo latino e o caos polinomial para a quantificação de incertezas. Inicialmente foram considerados sistemas mecânicos mais simples, como forma de validação da metodologia e, em seguida, faz-se um estudo do efeito de incertezas em um rotor com mancais hidrodinâmicos.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-13T11:17:18Z No. of bitstreams: 2 Dissertação - Michael Dowglas de Gois Silva - 2016.pdf: 9167389 bytes, checksum: e1d3f6cb2f3408867017625b852da695 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-13T11:17:59Z (GMT) No. of bitstreams: 2 Dissertação - Michael Dowglas de Gois Silva - 2016.pdf: 9167389 bytes, checksum: e1d3f6cb2f3408867017625b852da695 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-13T11:17:59Z (GMT). No. of bitstreams: 2 Dissertação - Michael Dowglas de Gois Silva - 2016.pdf: 9167389 bytes, checksum: e1d3f6cb2f3408867017625b852da695 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-07-25 / In the present paper several configurations of static and dynamic equilibrium in the non-linear oscillations are studied through a simple structural system, given by a rigid bar-spring model with a degree of freedom, that depending on its parameters, can represent in a simplified way several structural elements such as portico, column, arch, shells and plaques, among others. Therefore, a bibliographical research about the instability regarding the static and dynamic equilibrium, the analysis of bifurcations, the phase plane and the basin of attraction of discrete models was made. The purpose of this study is to situate the problem, in order to evaluate in this dissertation, the influence of the uncertainties of the geometric parameters on the nonlinear vibrations and the stability of mechanical systems susceptible to buckling by comparing deterministic and nondeterministic responses. Legendre-Chaos polynomial is used to obtain the stochastic responses of the model studied. The equations of the system are deduced from their energy functionalities using the principle of stationary potential energy allowing the analysis of different bifurcation mechanisms from the chosen parameters. Two particularities are studied, the systems that present symmetrical bifurcation of the Butterfly type and the systems that present asymmetric Swallowtail bifurcation, in both cases the bifurcations present an initial unstable post critical path. For the systematic study of the nonlinear equilibrium equations, we used the symbolic algebra software, MAPLE, and computational codes written in the C language, allowing us to obtain the post-critical paths and the integration of the equilibrium equations for the analysis of the time responses, phase planes, attraction basins, and integrity factors. / No presente trabalho são estudadas diversas configurações de equilíbrio estático e dinâmico nas oscilações não lineares por meio de um sistema estrutural simples, dado por um modelo barra rígida-mola com um grau de liberdade, que dependendo de seus parâmetros, pode representar de maneira simplificada vários elementos estruturais tais como pórtico, coluna, arco, cascas e placas, dentre outros. Para isso fez-se um levantamento bibliográfico sobre a instabilidade no que diz respeito ao equilíbrio estático e dinâmico, à análise de bifurcações, ao plano fase e a bacia de atração de modelos discretos. A finalidade desse estudo é situar o problema, para poder avaliar nesta dissertação, a influência das incertezas dos parâmetros geométricos nas vibrações não lineares e na estabilidade de sistemas mecânicos sujeitos a flambagem comparando respostas determinísticas e não determinísticas. Para obter as respostas estocásticas do modelo estudado utiliza-se o polinômio de Legendre-Caos. As equações do sistema são deduzidas a partir de seus funcionais de energia usando o princípio da energia potencial estacionária permitindo a partir dos parâmetros escolhidos a análise de diferentes mecanismos de bifurcação. São estudadas duas particularidades, os sistemas que apresentam bifurcação simétrica do tipo Butterfly e os sistemas que apresentam bifurcação assimétrica Swallowtail, em ambos os casos as bifurcações apresentam um caminho pós-crítico inicial instável. Para o estudo sistemático das equações não lineares de equilíbrio foi utilizado o software de álgebra simbólica, MAPLE, e códigos computacionais escritos na linguagem C, permitindo a obtenção dos caminhos pós-críticos e a integração das equações de equilíbrio para a análise das respostas no tempo, dos planos fase, das bacias de atração e dos fatores de integridade.

Processos aleatórios de corrosão e fadiga reduzem lentamente a resistência de estruturas e componentes estruturais, provocando um aumento gradual nas probabilidades de falha. A gestão do risco de falha de componentes sujeitos a corrosão e/ou fadiga é feita através de políticas de inspeção, manutenção e substituição, atividades que implicam em custos, mas visam manter a confiabilidade em níveis aceitáveis, enquanto o componente permanecer em operação. Aparentemente, os objetivos economia e segurança competem entre si, no entanto, a redução de recursos para inspeção e manutenção pode levar a maiores e crescentes probabilidades de falha, implicando em maiores custos esperados de falha, ou seja, maior risco. A otimização de risco estrutural é uma formulação que permite equacionar este problema, através do chamado custo esperado total. Nesta Tese, a otimização de risco é utilizada no intuito de encontrar políticas ótimas de inspeção e manutenção, isto é, quantidades de recursos a serem alocadas nestas atividades que levem ao menor custo esperado total possível. Os processos de corrosão e fadiga são representados através de modelos em polinômios de caos, construídos de maneira inédita, com base em dados experimentais ou observados da literatura. Com base nestes modelos, os problemas de otimização de risco envolvendo processos de fadiga e corrosão são resolvidos para diferentes configurações de custos de falha e de inspeções. Verifica-se que as políticas ótimas de inspeção, manutenção e substituição podem ser bastante diferentes para configurações de custo distintas, e que a determinação destas políticas é bastante desafiadora, devido, dentre outros fatores, à grande quantidade de mínimos locais do problema de otimização em questão, causadas por descontinuidades e oscilações da função custo esperado total. / Random corrosion and fatigue processes reduce slowly but gradually the resistance of structures and mechanical components, leading to gradual increase in failure probabilities. Risk management for mechanical components subject to corrosion and fatigue is made by means of policies of inspection, maintenance and substitution. These activities imply costs, but are made to maintain the reliability at acceptable levels, while the component remains in operation. Apparently, economy and safety are competing objectives; however, reduction in inspection and maintenance spending may lead to larger failure probabilities, increasing expected costs of failure (risk). Risk optimization allows one to solve this problem, by means of the so-called total expected cost. In this Thesis, risk optimization is used in order to find the best inspection and maintenance policy, i.e., the proper amount of resources to allocate to such activities in order to obtain minimum total expected cost. Corrosion and fatigue are modeled by means of polynomial chaos expansions, using a novel approach developed herein and experimental or observed data obtained from the literature. These models are employed within two risk optimization problems, solved for different failure and inspection cost configurations. Results show that the optimal policies of inspection, maintenance and replacements can be very different, for different cost configurations, and that the solution of the associated risk optimization problems is a very challenging task, due to the large number of local minima, caused by discontinuities and fluctuations in the total expected costs.

One of the major tasks in electronic circuit design is the ability to predict the performance of general circuits in the presence of uncertainty in key design parameters. In the mathematical literature, such a task is referred to as uncertainty quantification. Uncertainty about the key design parameters arises mainly from the difficulty of controlling the physical or geometrical features of the underlying design, especially at the nanometer level. With the constant trend to scale down the process feature size, uncertainty quantification becomes crucial in shortening the design time. To achieve the uncertainty quantification, this thesis presents a new approach based on the concept of generalized Polynomial Chaos (gPC) to perform variability analysis of general nonlinear circuits. The proposed approach is built upon a decoupling formulation of the Galerkin projection (GP) technique, where the large matrix is transformed into a block-diagonal whose diagonal blocks can be factorized independently. The proposed methodology provides a general framework for decoupling the GP formulation based on a general system of orthogonal polynomials. Moreover, it provides a new insight into the error level that is caused by the decoupling procedure, enabling an assessment of the performance of a wide variety of orthogonal polynomials. For example, it is shown that, for the same order, the Chebyshev polynomials outperforms other commonly used gPC polynomials.

Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms defined through the formulation of Manning’s n coefficients. This thesis considers the Bayesian inference problem of the Manning’s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part if the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning’s n coefficient and a 2-D parameterized Manning’s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an inflation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK filter, we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning’s n coefficient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to different OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the contexts of their algorithms, and make recommendation for fully realistic application.

In dieser Arbeit wird für Strukturen, die im makroskopischen aufgrund unterschiedlicher Materialeigenschaften oder komplexer Geometrien eine hohe Netzfeinheit für Finite-Elemente-Berechnungen benötigen, eine neue Möglichkeit zur Berechnung effektiver Materialkennwerte vorgestellt. Durch einen modalen Ansatz, bei dem, je nach Struktur analytisch oder numerisch, mit Hilfe der modalen Kennwerte die Formänderungsenergie eines repräsentativen Volumens der Originalstruktur mit der Formänderungsenergie eines äquivalenten homogen Vergleichsvolumens verglichen wird, können effektive Materialkennwerte ermittelt und daran anschließend eine Finite-Elemente-Berechnung mit einem im Vergleich zum Originalmodell sehr viel gröberen Netz durchgeführt werden, was eine enorme Zeiteinsparung mit sich bringt. Weiterhin enthält die vorgestellte Methode die Möglichkeit, unsichere Eingabeparameter wie Geometrieabmessungen oder Materialkennwerte mit Hilfe der polynomialen Chaos Expansion zu approximieren, um Möglichkeiten zur Aussage bzgl. der daraus resultierenden Verteilungen modaler Kenngrößen auf eine schnelle und effektive Weise zu gewinnen.

Fractional diffusion equations have played an increasingly important role in ex- plaining long-range interactions, nonlocal dynamics and anomalous diffusion, pro- viding effective means of describing the memory and hereditary properties of such processes. This dissertation explores the uncertainty propagation in space fractional diffusion equations in one and multiple dimensions with variable diffusivity and order parameters. This is achieved by:(i) deploying accurate numerical schemes of the forward problem, and (ii) employing uncertainty quantifications tools that accelerate the inverse problem. We begin by focusing on parameter calibration of a variable- diffusivity fractional diffusion model. A random, spatially-varying diffusivity field is considered together with an uncertain but spatially homogeneous fractional operator order. Polynomial chaos (PC) techniques are used to express the dependence of the stochastic solution on these random variables. A non-intrusive methodology is used, and a deterministic finite-difference solver of the fractional diffusion model is utilized for this purpose. The surrogates are first used to assess the sensitivity of quantities of interest (QoIs) to uncertain inputs and to examine their statistics. In particular, the analysis indicates that the fractional order has a dominant effect on the variance of the QoIs considered. The PC surrogates are further exploited to calibrate the uncertain parameters using a Bayesian methodology. In the broad range of parameters addressed, the analysis shows that the uncertain parameters having a significant impact on the variance of the solution can be reliably inferred, even from limited observations. Next, we address the numerical challenges when multidimensional space-fractional diffusion equations have spatially varying diffusivity and fractional order. Significant computational challenges arise due to the kernel singularity in the fractional integral operator as well as the resulting dense discretized operators. Hence, we present a singularity-aware discretization scheme that regularizes the singular integrals through a singularity subtraction technique adapted to the spatial variability of diffusivity and fractional order. This regularization strategy is conveniently formulated as a sparse matrix correction that is added to the dense operator, and is applicable to different formulations of fractional diffusion equations. Numerical results show that the singularity treatment is robust, substantially reduces discretization errors, and attains the first-order convergence rate allowed by the regularity of the solutions. In the last part, we explore the application of a Bayesian formalism to detect an anomaly in a fractional medium. Specifically, a computational method is presented for inferring the location and properties of an inclusion inside a two-dimensional domain. The anomaly is assumed to have known shape, but unknown diffusivity and fractional order parameters, and is assumed to be embedded in a fractional medium of known fractional properties. To detect the presence of the anomaly, the medium is forced using a collection of localized sources, and its response is measured at the source locations. To this end, the singularity-aware finite-difference scheme is applied. A non-intrusive regression approach is used to explore the dependence of the computed signals on the properties of the anomaly, and the resulting surrogates are first exploited to characterize the variability of the response, and then used to accelerate the Bayesian inference of the anomaly. In the regime of parameters considered, the computational results indicate that robust estimates of the location and fractional properties of the anomaly can be obtained, and that these estimates become sharper when high contrast ratios prevail between the anomaly and the surrounding matrix.

No description available.

Modeling and simulations of large-scale systems are used extensively to not only better understand a natural phenomenon, but also to predict future events. Accurate model results are critical for design optimization and policy making. They can be used effectively to reduce the impact of a natural disaster or even prevent it from happening. In reality, model predictions are often affected by uncertainties in input data and model parameters, and by incomplete knowledge of the underlying physics. A deterministic simulation assumes one set of input conditions, and generates one result without considering uncertainties. It is of great interest to include uncertainty information in the simulation. By ``Uncertainty Quantification,'' we denote the ensemble of techniques used to model probabilistically the uncertainty in model inputs, to propagate it through the system, and to represent the resulting uncertainty in the model result. This added information provides a confidence level about the model forecast. For example, in environmental modeling, the model forecast, together with the quantified uncertainty information, can assist the policy makers in interpreting the simulation results and in making decisions accordingly. Another important goal in modeling and simulation is to improve the model accuracy and to increase the model prediction power. By merging real observation data into the dynamic system through the data assimilation (DA) technique, the overall uncertainty in the model is reduced. With the expansion of human knowledge and the development of modeling tools, simulation size and complexity are growing rapidly. This poses great challenges to uncertainty analysis techniques. Many conventional uncertainty quantification algorithms, such as the straightforward Monte Carlo method, become impractical for large-scale simulations. New algorithms need to be developed in order to quantify and reduce uncertainties in large-scale simulations. This research explores novel uncertainty quantification and reduction techniques that are suitable for large-scale simulations. In the uncertainty quantification part, the non-sampling polynomial chaos (PC) method is investigated. An efficient implementation is proposed to reduce the high computational cost for the linear algebra involved in the PC Galerkin approach applied to stiff systems. A collocation least-squares method is proposed to compute the PC coefficients more efficiently. A novel uncertainty apportionment strategy is proposed to attribute the uncertainty in model results to different uncertainty sources. The apportionment results provide guidance for uncertainty reduction efforts. The uncertainty quantification and source apportionment techniques are implemented in the 3-D Sulfur Transport Eulerian Model (STEM-III) predicting pollute concentrations in the northeast region of the United States. Numerical results confirm the efficacy of the proposed techniques for large-scale systems and the potential impact for environmental protection policy making. ``Uncertainty Reduction'' describes the range of systematic techniques used to fuse information from multiple sources in order to increase the confidence one has in model results. Two DA techniques are widely used in current practice: the ensemble Kalman filter (EnKF) and the four-dimensional variational (4D-Var) approach. Each method has its advantages and disadvantages. By exploring the error reduction directions generated in the 4D-Var optimization process, we propose a hybrid approach to construct the error covariance matrix and to improve the static background error covariance matrix used in current 4D-Var practice. The updated covariance matrix between assimilation windows effectively reduces the root mean square error (RMSE) in the solution. The success of the hybrid covariance updates motivates the hybridization of EnKF and 4D-Var to further reduce uncertainties in the simulation results. Numerical tests show that the hybrid method improves the model accuracy and increases the model prediction quality. / Ph. D.

In this study we investigate the propagation of uncertainties in the input forces through a mechanical system. The system of interest was a wheel loader, but the methodology developed can be applied to any multibody systems. The modeling technique implemented focused on efficiently modeling stochastic systems for which the equations of motion are not available. The analysis targeted the reaction forces in joints of interest. The modeling approach developed in this thesis builds a foundation for determining the uncertainties in a Caterpillar 980G II wheel loader. The study begins with constructing a simple multibody deterministic system. This simple mechanism is modeled using differential algebraic equations in Matlab. Next, the model is compared with the CAD model constructed in ProMechanica. The stochastic model of the simple mechanism is then developed using a Monte Carlo approach and a Linear/Quadratic transformation method. The Collocation Method was developed for the simple case study for both Matlab and ProMechanica models. Thus, after the Collocation Method was validated on the simple case study, the method was applied to the full 980G II wheel loader in the CAD model in ProMechanica. This study developed and implemented an efficient computational method to propagate computational method to propagate uncertainties through "black-box" models of mechanical systems. The method was also proved to be reliable and easier to implement than traditional methods. / Master of Science