Ce manuscrit présente des contributions aux méthodes de propagation et d’analyse d’incertitude pour des applications en Mécanique des Fluides Numérique. Dans un premier temps, deux schémas numériques innovantes sont présentées: une approche de type ”Collocation”, et une autre qui est basée sur une représentation de type ”Volumes Finis” dans l’espace stochastique. Dans les deux, l’élément clé est donné par l’introduction d’une représentation de type ”Multirésolution” dans l’espace stochastique. L’objectif est à la fois de réduire le nombre de dimensions et d’appliquer un algorithme d’adaptation de maillage qui puisse être utilisé dans l’espace couplé physique/stochastique pour des problèmes non-stationnaires. Pour finir, une stratégie d’optimisation robuste est proposée, qui est basée sur une analyse de décompositionde la variance et des moments statistiques d’ordre plus élevé. Dans ce cas, l’objectif est de traiter des problèmes avec un grand nombre d’incertitudes. / In this manuscript, three main contributions are illustrated concerning the propagation and the analysis of uncertainty for computational fluid dynamics (CFD) applications. First, two novel numerical schemes are proposed : one based on a collocation approach, and the other one based on a finite volume like representation in the stochastic space. In both the approaches, the key element is the introduction of anon-linear multiresolution representation in the stochastic space. The aim is twofold : reducing the dimensionality of the discrete solution and applying a time-dependent refinement/coarsening procedure in the combined physical/stochastic space. Finally, an innovative strategy, based on variance-based analysis, is proposed for handling problems with a moderate large number of uncertainties in the context of the robust design optimization. Aiming to make more robust this novel optimization strategies, the common ANOVA-like approach is also extended to high-order central moments (up to fourth order). The new approach is more robust, with respect to the original variance-based one, since the analysis relies on new sensitivity indexes associated to a more complete statistic description.

Dans un modèle qui peut s'avérer complexe et fortement non linéaire, les paramètres d'entrée, parfois en très grand nombre, peuvent être à l'origine d'une importante variabilité de la sortie. L'analyse de sensibilité globale est une approche stochastique permettant de repérer les principales sources d'incertitude du modèle, c'est-à-dire d'identifier et de hiérarchiser les variables d'entrée les plus influentes. De cette manière, il est possible de réduire la dimension d'un problème, et de diminuer l'incertitude des entrées. Les indices de Sobol, dont la construction repose sur une décomposition de la variance globale du modèle, sont des mesures très fréquemment utilisées pour atteindre de tels objectifs. Néanmoins, ces indices se basent sur la décomposition fonctionnelle de la sortie, aussi connue soue le nom de décomposition de Hoeffding. Mais cette décomposition n'est unique que si les variables d'entrée sont supposées indépendantes. Dans cette thèse, nous nous intéressons à l'extension des indices de Sobol pour des modèles à variables d'entrée dépendantes. Dans un premier temps, nous proposons une généralisation de la décomposition de Hoeffding au cas où la forme de la distribution des entrées est plus générale qu'une distribution produit. De cette décomposition généralisée aux contraintes d'orthogonalité spécifiques, il en découle la construction d'indices de sensibilité généralisés capable de mesurer la variabilité d'un ou plusieurs facteurs corrélés dans le modèle. Dans un second temps, nous proposons deux méthodes d'estimation de ces indices. La première est adaptée à des modèles à entrées dépendantes par paires. Elle repose sur la résolution numérique d'un système linéaire fonctionnel qui met en jeu des opérateurs de projection. La seconde méthode, qui peut s'appliquer à des modèles beaucoup plus généraux, repose sur la construction récursive d'un système de fonctions qui satisfont les contraintes d'orthogonalité liées à la décomposition généralisée. En parallèle, nous mettons en pratique ces différentes méthodes sur différents cas tests. / A mathematical model aims at characterizing a complex system or process that is too expensive to experiment. However, in this model, often strongly non linear, input parameters can be affected by a large uncertainty including errors of measurement of lack of information. Global sensitivity analysis is a stochastic approach whose objective is to identify and to rank the input variables that drive the uncertainty of the model output. Through this analysis, it is then possible to reduce the model dimension and the variation in the output of the model. To reach this objective, the Sobol indices are commonly used. Based on the functional ANOVA decomposition of the output, also called Hoeffding decomposition, they stand on the assumption that the incomes are independent. Our contribution is on the extension of Sobol indices for models with non independent inputs. In one hand, we propose a generalized functional decomposition, where its components is subject to specific orthogonal constraints. This decomposition leads to the definition of generalized sensitivity indices able to quantify the dependent inputs' contribution to the model variability. On the other hand, we propose two numerical methods to estimate these constructed indices. The first one is well-fitted to models with independent pairs of dependent input variables. The method is performed by solving linear system involving suitable projection operators. The second method can be applied to more general models. It relies on the recursive construction of functional systems satisfying the orthogonality properties of summands of the generalized decomposition. In parallel, we illustrate the two methods on numerical examples to test the efficiency of the techniques.

As metodologias normalmente utilizadas para otimizar as dimensões de uma usina hidroelétrica, incluindo os métodos empregados pelo Setor Elétrico Brasileiro, baseiam-se em análises do tipo custo/benefício. Os custos provêm de gastos diretos com a construção da usina e os benefícios correspondem a receitas proporcionadas pela venda de energia. Para avaliar os benefícios, são realizadas simulações da operação da usina e a energia produzida é valorizada economicamente. Esta necessidade das simulações da operação faz com que o problema de dimensionamento não possua uma função analítica explícita para determinar os benefícios energéticos, o que dificulta a implementação de métodos tradicionais de otimização. O objetivo deste trabalho é justamente desenvolver e implementar uma metodologia de dimensionamento que permita que o processo de busca pelas dimensões ótimas seja automático. Para tanto, acoplam-se um modelo de otimização evolutiva e um modelo de simulação da operação de sistemas hidroelétricos. Adicionalmente, o modelo proposto também deve ser flexível, permitindo que as regras de operação do sistema hidroelétrico, o conjunto de vazões afluentes, a forma de valorização da energia gerada e uma série de outros fatores sejam tratados como parâmetros do modelo. Os resultados encontrados indicam que, sob o ponto de vista computacional, o modelo proposto é automático, flexível e eficiente. Além disso, as várias análises de sensibilidade realizadas atestam a consistência da metodologia proposta e permitem avaliar a forma como os diferentes parâmetros do modelo influenciam as próprias dimensões da usina sob dimensionamento. A partir destas análises, sugerem-se algumas medidas de regulamentação e planejamento para que as dimensões de novas usinas não sejam determinadas a partir de sinalizações imprecisas de parâmetros que influenciam de forma decisiva suas dimensões ótimas. / The methods normally applied to optimally size a hydropower plant, including the ones used by the Brazilian Power Industry, are based on cost/benefit analysis. The costs are due to direct expenses with the hydropower plant construction and the benefits correspond to incomes from selling energy. The benefits are evaluated throughout computing simulations of the hydropower plant operation, followed by the assignment of an economical value to the energy produced by it. The need for computing simulations turns out a non-analytical objective function for the sizing problem, what makes the use of traditional optimization tools very hard. The objective of this work is just to develop and implement a sizing method that automatically performs the search for the optimal sizes of a hydropower plant. The proposed method combines an evolutionary optimization technique and a simulation model for the operation of hydropower systems. Additionally, the proposed model is also flexible in the sense that the operation rules for the hydroelectric system simulation, the set of water inflows, the way the energy is valued and some other factors that may influence the results are treated as parameters. The results show that, from the computing point of view, the proposed method is automatic, flexible and efficient. Furthermore, the sensitivity analyses performed validate the method consistency and establish relationships among the different parameters and the way they affect the optimal features of the new hydropower plant. Based on the results of such analyses, some regulation and planning measures are suggested in order to avoid sizing hydropower plants with mistaken parameters that can substantially change its optimal features.

Submitted by Paulo Henrique Peres Verdi (pauloh_verdi@hotmail.com) on 2018-04-21T15:54:25Z No. of bitstreams: 1 Dissertação - FGV - Paulo Henrique Peres Verdi - FINAL.pdf: 1875588 bytes, checksum: ca0b7e99ed960b3d7a1dfa1875d49ad2 (MD5) / Approved for entry into archive by Mayara Costa de Sousa (mayara.sousa@fgv.br) on 2018-04-25T22:15:03Z (GMT) No. of bitstreams: 1 Dissertação - FGV - Paulo Henrique Peres Verdi - FINAL.pdf: 1875588 bytes, checksum: ca0b7e99ed960b3d7a1dfa1875d49ad2 (MD5) / Approved for entry into archive by Suzane Guimarães (suzane.guimaraes@fgv.br) on 2018-04-26T12:51:21Z (GMT) No. of bitstreams: 1 Dissertação - FGV - Paulo Henrique Peres Verdi - FINAL.pdf: 1875588 bytes, checksum: ca0b7e99ed960b3d7a1dfa1875d49ad2 (MD5) / Made available in DSpace on 2018-04-26T12:51:22Z (GMT). No. of bitstreams: 1 Dissertação - FGV - Paulo Henrique Peres Verdi - FINAL.pdf: 1875588 bytes, checksum: ca0b7e99ed960b3d7a1dfa1875d49ad2 (MD5) Previous issue date: 2018-03-26 / There is much talk about the low productivity of Brazilian cattle ranching and the enormous extent of degraded pastures that the country has, including regions of sandy soils with less agricultural potential. Public and private institutions invest in research to find alternatives on how to increase productivity and mitigate the environmental impacts caused by cattle production. The objective of this study is to analyze the economic viability of pasture recovery systems in sandy soils, considering the model of production in degraded pastures, the production model with the São Mateus integrated system, and a model considering pasture renovation and maintenance with fertilizers and correctives. From the main models, alternative scenarios have been created modifying the main variables to understand under which condition a system is economically attractive or not. The results indicate that the São Mateus integrated system is the most profitable in the proposed scenario, followed by the production model in degraded pastures. The model considering renovation of pastures on sandy soils with fertilization and maintenance of fertility resulted to be economically unfeasible. / Muito se fala sobre a baixa produtividade da pecuária de corte brasileira e a enorme extensão de pastagens degradadas que o país possui, inclusive em regiões de solos arenosos com menor potencial agropecuário. Instituições públicas e privadas investem em pesquisa para buscar alternativas de como incrementar a produtividade e mitigar os impactos ambientais causados pela produção de bovinos. O objetivo deste trabalho é analisar a viabilidade econômica de sistemas de recuperação de pastagens em solos arenosos, considerando o modelo de continuidade de produção em pastagens degradadas, o modelo de produção com o sistema iLP (integração lavoura-pecuária) São Mateus, e um modelo considerando reforma e manutenção de pastagens com fertilizantes e corretivos. A partir dos modelos principais, foram criados cenários alternativos modificando as principais variáveis para entender sob qual condição um sistema é ou não atrativo economicamente. Os resultados indicam que o sistema iLP São Mateus é o mais rentável no cenário proposto, seguido do modelo de produção em pastos degradados. A reforma de pastagens em solos arenosos com adubação e manutenção da fertilidade se mostrou economicamente inviável.

L’objectif de la thèse est d’effectuer l’analyse de sensibilité paramétrique du logiciel Phast de modélisation de la dispersion atmosphérique de gaz toxiques et/ou inflammables. La technique a consisté à coupler Phast et l’outil d’analyse de sensibilité SimLab, ce qui permet d’exécuter automatiquement un grand nombre de simulations en faisant varier l’ensemble des paramètres du modèle de façon simultanée. La méthode d’analyse de sensibilité globale choisie, E-FAST, est basée sur l’analyse de la variance des sorties du modèle pour le calcul des indices de sensibilité. Nous avons étudié des scénarios de rejet continus pour six produits différents (monoxyde d’azote, ammoniac, chlore, azote, n-hexane et fluorure d’hydrogène), sélectionnés pour couvrir une large gamme de caractéristiques physiques et de conditions de stockage. L’analyse du modèle de dispersion de Phast, Unified Dispersion Model, a été séparée en deux étapes : étape de « screening » avec pour but de comparer l’influence de l’ensemble des paramètres puis étude de l’influence globale des paramètres de modélisation, autres que les paramètres météo et du terme source, sur une plage large de valeurs. Pour chaque produit, nous avons décomposé les scénarios de base en sous-scénarios correspondant à des conditions de rejet différentes. Ce travail a notamment permis de classifier les paramètres du modèle selon leur degré d’influence sur la variabilité de différentes sorties et d’effectuer une analyse comparative par produit indiquant, pour des conditions de rejet données, quels paramètres sont les plus influents sur les sorties. Une étude complémentaire a consisté à effectuer une analyse de sensibilité locale de ces paramètres autour de leur valeur par défaut. / We have undertaken a parametric sensitivity analysis of the Phast software tool’s models for atmospheric dispersion of toxic and/or inflammable gases. We have coupled Phast with the sensitivity analysis tool SimLab, and have automated the execution of a large number of simulations while varying simultaneously selected model parameters. The global sensitivity analysis method used, E-FAST, is based on analysis of the variance of model outputs, and allows us to estimate sensitivity indices. We have studied continuous release scenarios for six different products (nitric oxide, ammonia, chlorine, nitrogen, n-hexane and hydrogen fluoride), which were chosen to cover a wide range of physical characteristics and storage conditions. Our analysis of Phast’s Unified Dispersion Model comprises two phases: a screening phase which allows the sensitivity of a wide range of parameters to be compared, followed by a phase focusing on the sensitivity of internal model parameters (excluding weather and source term variables), over a wide input range. For each product, we have broken down base-case scenarios into a number of sub-scenarios corresponding to different release conditions. This work has allowed us to rank model parameters according to their influence on the variability of a number of model outputs. It also includes a per-product comparative analysis indicating, for each release condition studied, which parameters have the most influence on the outputs. In the final part of the work, we have analyzed the local sensitivity of these parameters in a narrow range around their default values.

This diploma thesis based on a result of the European Union's intention to increase the share of electricity produced from renewable energy sources in the total production, Slovak Republic currently subsidises building gasifier power plants (high efficiency combined production) to produce electricity and thermal energy from the biomass. Therefore, this thesis aims to build a financial plan of gasifier, which will be used for the evaluation of the investment from the point of view of an investor. Valuation depends mainly on the economic benefits of the project with regards to the assessment of business environment. The work contains a sensitivity analysis to determine what impact on the value of the cash flows will make a percentage change in one variable.

Neste trabalho é proposta a determinação do ponto de Máximo Carregamento (PMC) em sistemas elétricos de potência por meio do método da Função Lagrangiana Barreira Modificada (FLBM), uma variante do método de Pontos Interiores (PI). Também por meio do método da FLBM, busca-se determinar qual é a barra, para cada sistema, que apresenta a maior sensibilidade em relação ao fator de carregamento, ou seja, qual seria a primeira barra que deveria sofrer corte de carga a fim de aumentar a margem de carregamento do sistema e, assim, evitar o colapso de tensão. Para comprovação dos resultados obtidos por meio do método da FLBM utiliza-se a técnica de Análise de Sensibilidade (AS). A formulação do problema tem como restrições de igualdade as equações de balanço de potência do sistema elétrico e como restrições de desigualdade os limites de tensões nas barras, assim como os limites de geração de potência reativa nas barras com controle da referida potência. Estudos de casos foram realizados em um sistema de 3 barras e nos sistemas IEEE 14, 57, 118 e 300 barras; tais estudos demonstraram a robustez e a eficiência dos algoritmos propostos. / This work proposes the determination of the Maximum Loading Point (MLP) in electric power system via Lagrangian Modified Barrier Function (LMBF) method, a variant of Interior Point (IP). The LMBF method is also used to determine which bus, for each system, has the highest sensitivity of load factor, i.e., which bus would be the first to have load shedding in order to increase the loading margin system and thus prevent voltage collapse. To validate this approach, the Sensitivity Analysis (SA) technique was used for the confirmation of the results obtained by the LMBF method. The formulation of the problem considered the equations of power balance of the electrical system equality constraints, and the buses voltage magnitude limits, as well as the limits of reactive power control at the buses of that power inequality constraints. Case studies were conducted in a system of 3 buses and IEEE systems 14, 57, 118 and 300 buses, demonstrating the robustness and efficiency of the proposed algorithms.

Forests are a valuable resource for humans providing a range of products and services such as construction timber, paper and fuel wood, recreation, as well as living quarters for indigenous populations and habitats for many animal and bird species. Most recent international political agreements such as the Kyoto Protocol emphasise the role of forests as a major sink for atmospheric carbon dioxide mitigation. However, forest areas are rapidly decreasing world wide. Thus, it is vital that efficient strategies and tools are developed to encourage sustainable ecosystem management. These tools must be based on known ecological principles (such as tree physiological and soil nutrient cycle processes), capable of supplying fast and accurate temporal and spatial predictions of the effects of management on both timber production and carbon sequestration. This thesis had two main objectives. The first was to investigate the environmental factors affecting growth and carbon sequestration of Scots pine (Pinus sylvestris L.) across Scotland, by developing a knowledge base through a statistical analysis of old and novel field datasets. Furthermore, the process-based ecosystem model 3-PGN was developed, by coupling the existing models 3-PG and ICBM. 3-PGN calibrated using a Bayesian approach based on Monte Carlo Markov Chain simulations and it was validated for plantation stands. Sensitivity and uncertainty analyses provided an understanding of the internal feedbacks of the model. Further simulations gave a detailed eco-physiological interpretation of the environmental factors affecting Scots pine growth and it provided an assessment of carbon sequestration under the scenario of sustainable, normal production and its effects from the environment. Finally, the study investigated the spatial and temporal patterns of timber production and carbon sequestration by using the spatial version of the model and applying advanced spatial analyses techniques. The second objective was to help close the gap between environmental research and forest management, by setting a strategic framework for a process-based tool for sustainable ecosystem management. The thesis demonstrated the procedures for a site classification scheme based on modelling results and a yield table validation procedure, which can provide a way forward in supporting policies for forest management and ensuring their continued existence in the face of the present and future challenges.

Le transport routier est au cœur des enjeux environnementaux actuels. Les véhicules électriques hybrides (VEH) sont une alternative intéressante, notamment en milieu urbain. Cependant, la conception de tels systèmes est complexe car la chaîne de traction (composants et architecture), la mission et la gestion énergétique du véhicule sont intimement liées.Les travaux de V. Reinbold ont permis de mettre au point une méthodologie de dimensionnement de VEH. Les composants sont optimisés conjointement avec la gestion énergétique sur un cycle de fonctionnement afin de minimiser la consommation de carburant du véhicule. Une attention particulière est portée à la conception fine de la machine électrique via un modèle électromagnétique adapté à l’optimisation.Dans la suite de ces travaux, nous approfondissons plusieurs aspects du dimensionnement des VEH. Tout d’abord, nous introduisons la possibilité de gérer des paramètres discrets de la machine, comme le nombre de paires de pôles. Dans un second temps, nous développons un modèle thermique de la machine prenant notamment en compte les échanges autour des têtes de bobine. Ce modèle analytique par réseau de résistances thermiques est intégré puis utilisé dans le processus de dimensionnement par optimisation. Il a été préalablement validé via un modèle par éléments finis. Des méthodes d’analyse d’incertitude et de sensibilité sont appliquées afin de quantifier l’influence de certains paramètres thermiques. Enfin, nous appliquons la méthodologie de dimensionnement par optimisation à une architecture série/parallèle, intégrant deux machines électriques. / Road transportation has a huge impact on the environment. Hybrid electric vehicles (HEV) are an interesting alternative, especially for urban uses. However, HEV are complex systems to design because of the strong interaction between the component sizing, the energy management and the driving cycle.V. Reinbold previously developed a sizing methodology for HEV. The components and the energy management are simultaneously optimized to reduce the fuel consumption of the vehicle over a driving cycle. A specific electromagnetic model is used during the optimization process to describe accurately the electrical machine.As a continuation, we introduce firstly the possibility to deal with discrete variables such as the pole number of the electrical machine. Then, we develop a thermal model of the machine considering the convection exchanges around the end-windings. This analytical lumped parameter thermal network is used during the optimization process after being validated thanks to a finite element model. Uncertainty and sensitivity analysis are used to check the influence of some of the thermal parameters. Finally, the sizing methodology is applied to a series/parallel HEV including two electrical machines.

Feeder reconfiguration is performed by changing the open/close status of two types of switches: normally open tie switches and normally closed sectionalizing switches. A whole feeder or part of a feeder may be served from another feeder by closing a tie switch linking the two while an appropriate sectionalizing switch must be opened to maintain the radial structure of the system. Feeder reconfiguration is mainly aiming to reduce the system overall power losses and improve voltage profile. In this dissertation, several approaches have been proposed to reconfigure the radial distribution networks including the potential impact of integrating Distributed Energy Resources (DER) into the grid. These approaches provide a Fast-Genetic Algorithm “FGA” in which the size and convergence speed is improved compared to the conventional genetic algorithm. The size of the population matrix is also smaller because of the simple way of constructing the meshed network. Additionally, FGA deals with integer variable instead of a binary one, which makes FGA a unique method. The number of the mesh/loop is based on the number of tie switches in a particular network. The validity of the proposed FGA is investigated by comparing the obtained results with the one obtained from the most recent approaches. The second the approach is the implementation of the Differential Evolution (DE) algorithm. DE is a population-based method using three operators including crossover, mutation, and selection. It differs from GA in that genetic algorithms rely on crossover while DE relies on mutation. Mutation is based on the differences between randomly sampled pairs of solutions in the population. DE has three advantages: the ability to find the global optimal result regardless of the initial values, fast convergence, and requirement of a few control parameters. DE is a well-known and straightforward population-based probabilistic approach for comprehensive optimization. In distribution systems, if a utility company has the right to control the location and size of distributed generations, then the location and size of DGs may be determined based on some optimization methods. This research provides a promising approach to finding the optimal size and location of the planned DER units using the proposed DE algorithm. DGs location is obtained using the sensitivity of power losses with respect to real power injection at each bus. Then the most sensitive bus is selected for installing the DG unit. Because the integration of the DG adds positive real power injections, the optimal location is the one with the most negative sensitivity in order to get the largest power loss reduction. Finally, after the location is specified, the proposed Differential Evolution Algorithm (DEA) is used to obtain the optimal size of the DG unit. Only the feasible solutions that satisfy all the constraints are considered. The objective of installing DG units to the distribution network is to reduce the system losses and enhance the network voltage profile. Nowadays, these renewable DGs are required to equip with reactive power devices (such as static VAR compensators, capacitor banks, etc.), to provide reactive power as well as to control the voltage at their terminal bus. DGs have various technical benefits such as voltage profile improvement, relief in feeder loading, power loss minimization, stability improvement, and voltage deviation mitigation. The distributed generation may not achieve its full potential of benefits if placed at any random location in the system. It is necessary to investigate and determine the optimum location and size of the DG. Most distribution networks are radial in nature with limited short-circuit capacity. Therefore, there is a limit to which power can be injected into the distribution network without compromising the power quality and the system stability. This research is aiming to investigate this by applying DG technologies to the grid and keeping the system voltage within a defined boundary [0.95 - 1.05 p.u]. The requirements specified in IEEE Standard 1547 are considered. This research considers four objectives related to minimization of the system power loss, minimization of the deviations of the nodes voltage, minimization of branch current constraint violation, and minimization of feeder’s currents imbalance. The research formulates the problem as a multi-objective problem. The effectiveness of the proposed methods is demonstrated on different revised IEEE test systems including 16 and 33-bus radial distribution system.