Esta tese apresenta os resultados de pesquisa sobre geração de séries sintéticas de radiação solar para estudos energéticos, realizada através do uso de modelos estocásticos e com o propósito de desenvolver método para aplicações práticas no setor elétrico. Para tanto, inicialmente foi levantado o estado da arte do tema, com revisão da literatura de séries temporais e de processos estocásticos, suas particularidades e potencialidades, complementado pela contextualização do uso de cenários no setor elétrico nacional, especialmente na operação e planejamento do sistema hidrotérmico, e por experiências internacionais na modelagem do recurso solar. A modelagem das séries utilizou dados reais de localidades do nordeste brasileiro e foi desenvolvida através do método de Box-Jenkins, realizando-se estudos de alternativas para cada uma de suas etapas. O pré-tratamento dos dados foi avaliado por três estratégias de remoção da tendência das séries e na estimativa dos coeficientes dos modelos foram comparados os métodos de Yule-Walker e dos mínimos quadrados. As análises consideraram quatro opções de modelos autorregressivos e os períodos horário, diário e mensal. O modelo autorregressivo convencional com intervalo mensal, identificado como o mais adequado para aplicação em estudos energéticos, e sua variação periódica foram implementados e avaliados com maior profundidade. Este estudo complementar considerou diferentes ordens de atraso e realizou comparações dos resultados por três métodos de cálculo do erro. O modelo desenvolvido com estrutura autorregressiva periódica de primeira ordem apresentou resultados satisfatórios e significativamente superiores aos dos demais modelos. Por fim, este modelo foi empregado na geração de séries sintéticas, criando 1.000 cenários de radiação solar mensal, posteriormente aplicados em modelo de contrato de venda de energia para avaliação de estratégias de participação em leilões, em análise de riscos de suprimento e em estimativa probabilística da receita esperada por parques geradores. / This thesis presents the results of a research on the generation of solar radiation synthetic sequences for energy studies, carried out through the use of stochastic models and with the purpose of developing a method for practical applications in the electric sector. In order to do so, the state of the art was devised through a review of the literature of time series and stochastic processes, their particularities and potentialities, complemented by the contextualization of the use of scenarios in the national electricity sector, especially in the hydrothermal system operation and planning, and international experiences in modeling the solar resource. The series modeling used real data from localities in the Brazilian Northeast and was developed through the Box-Jenkins method, carrying out alternative studies for each of its stages. The data pretreatment has been evaluated by three strategies for the series trend removal and by the methods of least squares and of Yule-Walker for the estimation of the model coefficients. The analysis considered four options of autoregressive models and hourly, daily and monthly periods. The conventional autoregressive model with monthly interval, identified as the most applications in energy studies, and its periodic variation were implemented and evaluated in greater depth. This complementary study considered different orders of delay and made comparisons of the results for three error calculation methods. The model developed with periodic autoregressive structure of first order presented results that are satisfactory and significantly superior than the other models. Finally, this model was used in the generation of synthetic series, creating 1,000 scenarios of monthly solar radiation, to be later applied in a model of power purchase agreement to evaluate strategies for auctions bidding, analysis of supply risks and probabilistic estimation of the expected revenue of power plants.

Models which describe the performance of physical process are essential for quality prediction, experimental planning, process control and optimization. Engineering models developed based on the underlying physics/mechanics of the process such as analytic models or finite element models are widely used to capture the deterministic trend of the process. However, there usually exists stochastic randomness in the system which may introduce the discrepancy between physics-based model predictions and observations in reality. Alternatively, statistical models can be used to develop models to obtain predictions purely based on the data generated from the process. However, such models tend to perform poorly when predictions are made away from the observed data points. This dissertation contributes to model enhancement research by integrating physics-based model and statistical model to mitigate the individual drawbacks and provide models with better accuracy by combining the strengths of both models. The proposed model enhancement methodologies including the following two streams: (1) data-driven enhancement approach and (2) engineering-driven enhancement approach. Through these efforts, more adequate models are obtained, which leads to better performance in system forecasting, process monitoring and decision optimization. Among different data-driven enhancement approaches, Gaussian Process (GP) model provides a powerful methodology for calibrating a physical model in the presence of model uncertainties. However, if the data contain systematic experimental errors, the GP model can lead to an unnecessarily complex adjustment of the physical model. In Chapter 2, we proposed a novel enhancement procedure, named as "Minimal Adjustment", which brings the physical model closer to the data by making minimal changes to it. This is achieved by approximating the GP model by a linear regression model and then applying a simultaneous variable selection of the model and experimental bias terms. Two real examples and simulations are presented to demonstrate the advantages of the proposed approach. Different from enhancing the model based on data-driven perspective, an alternative approach is to focus on adjusting the model by incorporating the additional domain or engineering knowledge when available. This often leads to models that are very simple and easy to interpret. The concepts of engineering-driven enhancement are carried out through two applications to demonstrate the proposed methodologies. In the first application where polymer composite quality is focused, nanoparticle dispersion has been identified as a crucial factor affecting the mechanical properties. Transmission Electron Microscopy (TEM) images are commonly used to represent nanoparticle dispersion without further quantifications on its characteristics. In Chapter 3, we developed the engineering-driven nonhomogeneous Poisson random field modeling strategy to characterize nanoparticle dispersion status of nanocomposite polymer, which quantitatively represents the nanomaterial quality presented through image data. The model parameters are estimated through the Bayesian MCMC technique to overcome the challenge of limited amount of accessible data due to the time consuming sampling schemes. The second application is to calibrate the engineering-driven force models of laser-assisted micro milling (LAMM) process statistically, which facilitates a systematic understanding and optimization of targeted processes. In Chapter 4, the force prediction interval has been derived by incorporating the variability in the runout parameters as well as the variability in the measured cutting forces. The experimental results indicate that the model predicts the cutting force profile with good accuracy using a 95% confidence interval. To conclude, this dissertation is the research drawing attention to model enhancement, which has considerable impacts on modeling, design, and optimization of various processes and systems. The fundamental methodologies of model enhancement are developed and further applied to various applications. These research activities developed engineering compliant models for adequate system predictions based on observational data with complex variable relationships and uncertainty, which facilitate process planning, monitoring, and real-time control.

This research focuses on fleet management in freight transportation systems. Effective management requires effective planning and control decisions. Plans are often generated using estimates of how the system will evolve in the future; during execution, control decisions need to be made to account for differences between actual realizations and estimates. The benefits of minimum cost plans can be negated by performing costly adjustments during the operational phase. A planning approach that permits effective control during execution is proposed in this dissertation. This approach is inspired by recent work in robust optimization, and is applied to (i) dynamic asset management and (ii) vehicle routing problems. In practice, the fleet management planning is usually decomposed in two parts; the problem of repositioning empty, and the problem of allocating units to customer demands. An alternative integrated dynamic model for asset management problems is proposed. A computational study provides evidence that operating costs and fleet sizes may be significantly reduced with the integrated approach. However, results also illustrate that not considering inherent demand uncertainty generates fragile plans with potential costly control decisions. A planning approach for the empty repositioning problem is proposed that incorporates demand and supply uncertainty using interval around nominal forecasted parameters. The intervals define the uncertainty space for which buffers need to be built into the plan in order to make it a robust plan. Computational evidence suggests that this approach is tractable. The traditional approach to address the Vehicle Routing Problem with Stochastic Demands (VRPSD) is through cost expectation minimization. Although this approach is useful for building routes with low expected cost, it does not directly consider the maximum potential cost that a vehicle might incur when traversing the tour. Our approach aims at minimizing the maximum cost. Computational experiments show that our robust optimization approach generates solutions with expected costs that compare favorably to those obtained with the traditional approach, but also that perform better in worst-case scenarios. We also show how the techniques developed for this problem can be used to address the VRPSD with duration constraints.

Thesis (M.S.)--University of North Carolina Wilmington, 2009. / Title from PDF title page (February 16, 2010) Includes bibliographical references (p. 30)

Στην παρούσα Διδακτορική Διατριβή παρουσιάζονται τρíα νέα στοχαστικά μοντέλα, τα οποία αναπτύχθηκαν με σκοπό την εξομοίωση της διάδοσης των streamers και των leaders, και της επακόλουθης ηλεκτρικής διάσπασης σε διάκενα αέρα μεγαλύτερα από 5cm υπό ατμοσφαιρική πίεση. Η εξομοίωση της διαδικασίας διάσπασης με την χρήση των στοχαστικών μοντέλων, οδήγησε στην εξαγωγή αποτελεσμάτων που αφορούσαν την τάση διάσπασης U50 καθώς και την τυπική απόκλιση σ, όταν τα διάκενα καταπονούνται από συνεχείς και κρουστικές (1,2/50μsec) τάσεις, θετικής πολικότητας. Εξήχθησαν επίσης αποτελέσματα που αφορούσαν τη μέση και στιγμιαία ταχύτητα διάδοσης των streamers μέσα σε διάκενα αέρα μήκους έως 20cm. / At the present PhD Thesis three new stochastic fractal models were introduced. The stochastic models were developed in order to simulate the propagation of streamers and leaders in air gaps, in a wide range of gap distances, under the application of DC and impulse (1,2/50μsec) voltage of positive polarity. Various results, concerning breakdown voltage U50 and standard deviation σ, were obtained. Results concerning mean and instantaneous propagation velocity of streamers (only for gaps up to 20cm), were also obtained.

This study develops new quantitative thermoelastic stress analysis (TSA) techniques for fracture and fatigue damage analysis of composite materials. The first part deals with the thermo-mechanical derivation of two quantitative TSA techniques applied to orthotropic composites with and without a transversely-isotropic surface coating layer. The new TSA test procedures are derived in order to relate the thermal infrared (IR) images with the sum of in-plane strains multiplied by two newly defined material constants that can be experimentally pre-calibrated. Experiments are performed to verify the TSA methods with finite element (FE) numerical results along with available anisotropic elasticity solution. The second part of this study applies the quantitative TSA techniques together with the Lekhnitskii's general anisotropic elasticity solution to calculate mixed-mode stress intensity factors (SIFs) in cracked composite materials. The cracked composite coupons are subjected to off-axis loadings with respect to four different material angles in order to generate mixed-mode SIFs. A least-squares method is used to correlate the sum of in-plane strains from the elasticity solution with the measured TSA test results. The mode-I and mode-II SIFs are determined from eccentrically loaded single-edge-notch tension (ESE(T)) composite specimens. The FE models and virtual crack closure technique (VCCT) are utilized for comparisons. In the third part, a new stochastic model is proposed to generate S-N curves accounting for the variability of the fatigue process. This cumulative damage Markov chain model (MCM) requires a limited number of fatigue tests for calibrating the probability transition matrix (PTM) in the Markov chain model and mean fatigue cycles to failure from experiments. In order to construct the MCM stochastic S-N curve, an iterative procedure is required to predict the mean cycles to failure. Fatigue tests are conducted in this study to demonstrate the MCM method. Twenty-one open-hole S2-glass laminates are fatigue-cycled at two different stress levels. The coupon overall stiffness and surface-ply TSA damage area have been used as two damage metrics. The MCM can satisfactorily describe the overall fatigue damage evolution for a limited number of coupons (less than 6) subjected to a given specific stress level. The stochastic S-N curve can be constructed using at least two sets of fatigue tests under different stress levels. Three available fatigue tests for different E-glass laminates from the literature are also investigated using the proposed MCM approach. The results show the MCM method can provide the stochastic S-N curves for different composite systems and a wide range of fatigue cycles.

Sensor networks are an evolving technology that promise numerous applications. The random and dynamic structure of sensor networks has motivated the suggestion of greedy data-routing algorithms. / In this thesis stochastic models are developed to study the advancement of messages under greedy routing in sensor networks. A model framework that is based on homogeneous spatial Poisson processes is formulated and examined to give a better understanding of the stochastic dependencies arising in the system. The effects of the model assumptions and the inherent dependencies are discussed and analyzed. A simple power-saving sleep scheme is included, and its effects on the local node density are addressed to reveal that it reduces one of the dependencies in the model. / Single hop expressions describing the advancement of messages are derived, and asymptotic expressions for the hop length moments are obtained. Expressions for the distribution of the multihop advancement of messages are derived. These expressions involve high-dimensional integrals, which are evaluated with quasi-Monte Carlo integration methods. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The subsequent results agree extremely well with those obtained via routing simulations. A renewal process model is proposed to model multihop advancements, and is justified under certain assumptions. / The model framework is extended by incorporating a spatially dependent density, which is inversely proportional to the sink distance. The aim of this extension is to demonstrate that an inhomogeneous Poisson process can be used to model a sensor network with spatially dependent node density. Elliptic integrals and asymptotic approximations are used to describe the random behaviour of hops. The final model extension entails including random transmission radii, the effects of which are discussed and analyzed. The thesis is concluded by giving future research tasks and directions.

Sensor networks are an evolving technology that promise numerous applications. The random and dynamic structure of sensor networks has motivated the suggestion of greedy data-routing algorithms. / In this thesis stochastic models are developed to study the advancement of messages under greedy routing in sensor networks. A model framework that is based on homogeneous spatial Poisson processes is formulated and examined to give a better understanding of the stochastic dependencies arising in the system. The effects of the model assumptions and the inherent dependencies are discussed and analyzed. A simple power-saving sleep scheme is included, and its effects on the local node density are addressed to reveal that it reduces one of the dependencies in the model. / Single hop expressions describing the advancement of messages are derived, and asymptotic expressions for the hop length moments are obtained. Expressions for the distribution of the multihop advancement of messages are derived. These expressions involve high-dimensional integrals, which are evaluated with quasi-Monte Carlo integration methods. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The subsequent results agree extremely well with those obtained via routing simulations. A renewal process model is proposed to model multihop advancements, and is justified under certain assumptions. / The model framework is extended by incorporating a spatially dependent density, which is inversely proportional to the sink distance. The aim of this extension is to demonstrate that an inhomogeneous Poisson process can be used to model a sensor network with spatially dependent node density. Elliptic integrals and asymptotic approximations are used to describe the random behaviour of hops. The final model extension entails including random transmission radii, the effects of which are discussed and analyzed. The thesis is concluded by giving future research tasks and directions.

L’établissement correspond à la formation d’une population pérenne dans l’aire d’introduction. Les populations introduites ayant des effectifs faibles, elles sont sujettes à plusieurs mécanismes augmentant leurs risques d’extinction. La structure spatiale de l’aire d’introduction, une mosaïque hétérogène de patchs d’habitat appelée « paysage », peut affecter la persistance de la population introduite. L’objectif de cette thèse est d’étudier l’interaction entre cette structure spatiale et ces mécanismes, ainsi que leur impact sur l’établissement. Les recherches entreprises ont été conduites en utilisant des modèles stochastiques afin de simuler des invasions et faire émerger des prédictions, et en testant expérimentalement ces prédictions grâce à des introductions artificielles de Trichogramma chilonis en microcosmes. Ces travaux ont permis d’identifier un effet fort de la connectivité du site d’introduction, qui peut diminuer les chances d’établissement au niveau local en favorisant l’émigration depuis le site d’introduction, et augmenter les chances d’établissement à un niveau plus large en permettant la colonisation d’autres patchs dans l’aire d’introduction. Au niveau du paysage, nous avons identifié l’impact des hubs, des patchs concentrant les flux de dispersion, qui accroissent fortement la vitesse de colonisation mais diminuent le taux d’établissement. L’établissement était également favorisé par l’agrégation de la ressource et la colonisation par sa dissémination à travers le paysage. La nature stochastique des dynamiques de colonisation est telle qu’il est nécessaire de les prendre en compte pour étudier l’établissement. / Establishment is an important stage of biological invasions, which corresponds to the formation of a persistent population in the introduction area. It is not trivial, as introduced populations are often small, and subject to various specific mechanisms, which increase extinction risks. The spatial structure of the introduction area, which is usually a heterogeneous mosaic of habitat patches called a “landscape”, can interact with those mechanisms and impact the introduced population persistence. This thesis objective is to study the interaction between this spatial structure and those mechanisms, as well as their impact on establishment. On the one hand, we used stochastic models to simulate invasions and formulate predictions. On the other hand, we tested these predictions by performing artificial introductions of Trichogramma chilonis in laboratory microcosms. We were able to identify the impact of the introduction site connectivity, which could decrease establishment probabilities at a local level by increasing the emigration rate from the introduction site, and increase establishment at the landscape level by increasing the colonisation rate of other patches in the introduction area. At the landscape level, we identified the impact of hubs, i.e. patches concentrating dispersal fluxes. They strongly increased colonisation speed, but also decreased establishment. The clustering of resources increased establishment, while its scattering increased colonization. Our results show that introduced population dynamics are highly sensitive to their size. The stochastic nature of colonization dynamics is also necessary to study establishment.

Vários módulos funcionais de células ou bactérias são controlados por meio de genes que se regulam através da codificação de proteínas repressoras ou indutoras. A compreensão destas redes gênicas é um problema em aberto da biologia. Nesta dissertação procuramos aplicar o modelo estocástico de spins e bósons para o caso da rede mais simples, contiduída de dois genes, o primeiro reprimindo o segundo. Apresentamos a solução exata para a distribuição de probabilidades sobre o número das proteínas dos dois genes no estado estacionário, e a probabilidade dependente do tempo sobre o estado do segundo gene (ativado ou desativado). Discutimos também maneiras de generalizar os resultados para redes maiores. / Several functional modules in cells or bacteria are controlled by genes that regulate each other by coding repressive or inducer proteins. The understanding of these genetic networks is still an open problem in biology. In this work we apply the stochastic spin-boson model to the simplest interacting network, made of two genes, the first repressing the second. We present the exact solution for the stationary probability distribution over their both protein numbers, and the temporal evolution of the second genes state (on or off). We also discuss ways of generalizing these results to larger networks.