This D.Sc. thesis proposes new perspectives for modeling drill string torsional dynamics under uncertainties. This work develops a novel stochastic hysteretic (nonreversible) bit-rock interaction model. Firstly, a new nominal interaction model, which depends not only on the bit speed, but also on the bit acceleration is developed. Then, a new stochastic model for the bit-rock interaction, taking into account the inherent fluctuations during the drilling, is also proposed. Furthermore, here a new test-rig is proposed to analyze drill string dynamics and bit-rock interaction, which is able to reproduce stick-slip phenomena while drilling a rock sample using standard masonry bits, as well as to validate bit-rock interaction models. An original strategy for modeling uncertainties globally, based on terms of the nonparametric probabilistic approach, considering a simple torsional model for a drill string, is also proposed herein. This strategy allows to control the dispersion level of each interior and interface DOFs of each drill string substructure independently, which can provide more information to improve the operational safety. / This D.Sc. thesis proposes new perspectives for modeling drill string torsional dynamics under uncertainties. This work develops a novel stochastic hysteretic (nonreversible) bit-rock interaction model. Firstly, a new nominal interaction model, which depends not only on the bit speed, but also on the bit acceleration is developed. Then, a new stochastic model for the bit-rock interaction, taking into account the inherent fluctuations during the drilling, is also proposed. Furthermore, here a new test-rig is proposed to analyze drill string dynamics and bit-rock interaction, which is able to reproduce stick-slip phenomena while drilling a rock sample using standard masonry bits, as well as to validate bit-rock interaction models. An original strategy for modeling uncertainties globally, based on terms of the nonparametric probabilistic approach, considering a simple torsional model for a drill string, is also proposed herein. This strategy allows to control the dispersion level of each interior and interface DOFs of each drill string substructure independently, which can provide more information to improve the operational safety

O estudo das vibrações é importante para prevenir danos em equipamentos ou mesmo evitar catástrofes de grande natureza. Nesse sentido, aproveitar a energia que seria dissipada na vibração e contribuir no controle do sistema representa um grande avanço tecnológico. O termo Energy Harvesting (Colheita de Energia) está relacionado ao contexto do aproveitamento energético, utilizando sistema de conversão para transformação da energia em eletricidade. Através de um dispositivo com viga engastada e massa inercial na extremidade, é possível realizar o estudo de vibração e coleta de energia, ao se considerar uma estrutura piezelétrica acoplada na viga e conectada a um circuito elétrico com resistor. Estruturas inteligentes que atuam na conversão de energia mecânica em elétrica, ou vice-versa, são fundamentais para esse estudo, o que motiva a inclusão dos sensores piezelétricos no projeto de dispositivos estudados e sujeitos a vibrações. Por outro lado, otimizar parâmetros de projeto é fundamental para aumentar a amplitude de vibração e tornar o processo com maior desempenho, tendo em vista maior captação de energia. Ainda, parâmetros otimizados podem estar sujeitos a incertezas do projeto e variações, devido a flutuações ambientais, como temperatura, pressão, propriedades dos materiais, geometria, etc. Por isso, técnicas robustas que tornem os projetos menos sensíveis a variações são interessantes para serem abordadas. Embora métodos de projetos robustos sejam eficientes, poucas pesquisas têm sido feitas na área da dinâmica de vibrações e alguns processos podem demandar tempo computacional dependendo do estudo ou projeto. Este trabalho tem como propósito abordar um método específico de projeto robusto focado em uma metodologia com matrizes chamadas ortogonais. Além disso, o método determinístico via algoritmo de Programação Sequencial Quadrático (SQP) é utilizado. O trabalho consiste numa abordagem para coleta de energia em um modelo de viga engastada, otimizando parâmetros e inserindo incertezas no sistema para análise de robustez e verificação de comprimentos adequados de vigas para os dispositivos. Os resultados mostram um aumento da energia coletada, analisando funções de resposta em frequências para saída de potência, diante de uma entrada de deslocamento no engaste do dispositivo, projetado via otimização determinística, além de aumento de robustez de acordo com certos critérios considerando circuito elétrico com resistência corretamente selecionada. / The study of vibrations is important to prevent damage to equipment or even prevent major catastrophes. In this sense harvesting the energy that would otherwise be dissipated in vibration and contributing to the control of the system represents a great technological advance. The term Energy Harvesting is related to the context of energy use, using a conversion system to transform energy into electricity. Through a device with clamped beam and inertial mass at the end, it is possible to study the vibration and energy harvesting, considering a piezoelectric structure coupled to the beam and connected to a resistance electric circuit. Smart structures that act in the conversion of mechanical energy to electrical energy, or vice versa, are fundamental for this study, which motivates the inclusion of piezoelectric sensors in the design of studied devices and subject to vibrations. On the other hand, optimizing design parameters is fundamental to increase the amplitude of vibration and increase process performance, in view of greater power uptake. Furthermore, optimized parameters may be subject to design uncertainties and variations due to environmental fluctuations such as temperature, pressure, material properties, geometry, etc. Therefore, robust techniques that make designs less sensitive to variations are interesting to be addressed. Although robust design methods are efficient, few researches have been done in the area of vibration dynamics and some processes may require computational time depending on the study or project. This work aims to address a specific method of robust design focused on a methodology with matrices called orthogonal. In addition, the deterministic method using Sequential Quadratic Programming (SQP) algorithm is used. The work consists of an approach to harvest energy in a clamped beam model, optimizing parameters and inserting uncertainties in the system for robustness analysis and verification of adequate beam lengths for the devices. The results show an increase in the harvested energy, analyzing frequency response functions for power output, in the face of a displacement input in the device clamp, designed through deterministic optimization,besides increasing robustness according to certain criteria considering electric circuit with correctly selected resistance.

Dans cette thèse, la conception d’observateurs pour les systèmes singuliers linéaires incertains et leurs applications au contrôle et au diagnostic. En effet, nous avons développé des méthodes de reconstruction d’état et d’estimation de défauts est étudié. Les systèmes algèbro-différentiels ou systèmes singuliers peuvent être considérés comme une généralisation des systèmes dynamiques. Ils constituent un puissant outil de modélisation dans la mesure où ils peuvent décrire des processus régis à la fois par des équations différentielles (dynamiques) et des équations algébriques (statiques). La nouvelle structure d’observateurs utilisée dans cette thèse est nommée l’Observateur Dynamique Généralisé (ODG), elle est plus générale que celle d’Observateurs Proportionnels (OP) et d’Observateurs Proportionnels Intégrals (OPI). Cette structure présente une estimation d’état alternative qui peut être considérée comme plus générale que les OP et les OPI, ceux-ci pouvant être considérés comme des cas particuliers de cette structure. L’approche proposée repose sur la paramétrisation des solutions des équations de Sylvester pour éliminer le biais entre l’erreur d’observation et la paire (entrée état). La thèse est organisée comme suit : Dans l’introduction générale, nous présentons la problématique et les objectifs de la thèse ainsi que les principales contributions. Dans le premier chapitre, nous présentons la classe des systèmes singuliers considérée. Nous faisons des rappels sur l’analyse de stabilité et l’utilisation des outils numériques LMI avec lesquels nous vérifions l’existence de conditions de stabilité. Ensuite, nous présentons les méthodes de reconstruction d’état des systèmes singuliers linéaires à savoir l’ODG, l’OP et l’OPI. Dans le deuxième chapitre, nous présentons en détail la procédure de synthèse d’ODG pour les systèmes singuliers continus avec et sans perturbations. Ensuite, nous faisons une extension aux systèmes singuliers en temps discret avec et sans perturbations. Dans le chapitre 3, nous donnons les conditions d’existence et de stabilité robuste de l’ODG pour les systèmes singuliers à paramètres incertains, où l’incertitude est bornée. Dans le chapitre 4, nous présentons une méthode de synthèse de commande stabilisante par retour d’état basée observateur pour une classe de systèmes singuliers linéaires avec et sans perturbations. Le chapitre 5, est consacré au diagnostic. L’étude que nous avons menée est traitée en deux étapes : La première étape est consacrée à la détection et l’isolation des défauts en utilisant un ODG. Cet observateur génère des résidus qui sont en mesure de représenter seulement la présence d’un défaut, de sorte que nous pouvons localiser des défauts multiples. Enfin, la deuxième étape est consacrée à l’estimation des défauts en utilisant un ODG avec une structure modifiée. Ces approches sont développées pour les systèmes singuliers et pour les systèmes singuliers incertains avec ou sans perturbations. Nous terminerons ce mémoire de thèse par une conclusion générale et quelques perspectives. / In this thesis the observer design for uncertain linear descriptor systems and their applications to control and fault diagnosis is studied. Descriptor systems can be considered as a generalization of dynamical systems. This class of systems include algebraic and differential equations. The observer used in this work has a new structure more general than those presented in the literature. The observer structure proposed has additional degrees of freedom, which provides it robustness in face to variations not considered in the model. The new observer structure used in this thesis, named as generalized dynamic observer (GDO), is designed for different classes of descriptor systems. The asymptotic stability of the observer is proved by Lyapunov analysis through a set of linear matrix inequalities (LMIs). In all cases, the LMI obtained from the Lyapunov analysis is treated by the elimination lemma. The use of the elimination lemma is essential in the development of the stability analysis of the observers, since it allows to obtain the GDO structure. Proportional observers (PO) and proportional-integral observers (PIO) can be considered as particular cases of our observer. The thesis is organized as follows: In the general introduction, the problem formulation is presented, the objectives of the thesis are pointed out, the scope of the investigation and the main contributions are also presented. Chapter 1 introduces descriptor systems as the class of systems considered in this work and presents a review of the state of the art focused on the observers design for these systems. Also we introduce the GDO as an observer with structure more general than that of the PO and the PIO. Chapter 2 develops the GDO for descriptor systems with or without disturbances. Extension of these approaches for discrete-time descriptor systems with or without disturbances are also presented. In Chapter 3, the robust approach of the GDO is treated for parametric uncertain descriptor systems, where the uncertainty is bounded, and for linear parameter varying (LPV) descriptor systems, where the parameters vary inside a polytope. Chapter 4 presents the GDO application to observer-based control with the objective to stabilize descriptor systems that normally are unstable. An extension of this approach to disturbed descriptor systems is also developed. Chapter 5 presents the GDO application to fault diagnosis, which is divided in two parts. The first one is to detect and isolate faults by using a GDO that provides residuals that are able to represent only the presence of one fault, so that we can isolate multiple faults. And the second part is to estimate the faults by using a GDO with a modified structure. These approaches are developed for descriptor systems and for uncertain descriptor systems. The last part is dedicated to general conclusions and some perspectives.

Atualmente é bem conhecido que o uso de dispositivos passivos de dissipação de energia, tais como amortecedores por atrito, reduzem consideravelmente a resposta dinâmica de estruturas. Entretanto, os melhores parâmetros de cada amortecedor e também a melhor posição para instalá-los dentro da estrutura permanecem difíceis de serem estabelecidas. Assim, a otimização de amortecedores é uma área que vem sendo estudada de forma crescente nos últimos anos, tendo grande impacto no projeto ótimo de dispositivos para o controle de vibrações de estruturas, possibilitando obter soluções seguras e ao mesmo tempo econômicas. Contudo, apesar dos amortecedores de vibração por atrito possuírem algumas vantagens em relação a outros dispositivos passivos, poucos trabalhos são encontrados sobre a otimização de seus parâmetros ou sobre a sua melhor posição dentro de uma estrutura, devido à maior dificuldade de se calcular sistemas que envolvem atrito, por este ser não-linear. Entretanto, é interessante se levar em conta as incertezas presentes nas propriedades estruturais e/ou na excitação dinâmica no processo de otimização, o que leva a um problema de otimização sob incerteza, como otimização robusta e otimização baseada em confiabilidade. Assim, nesta Tese é proposta uma metodologia para a otimização simultânea dos parâmetros e das posições de amortecedores de vibração por atrito a serem instalados em edifícios submetidos à excitação sísmica levando em conta as incertezas presentes tanto nas propriedades estruturais quanto no carregamento sísmico, assim como nas forças de atrito dos amortecedores. A fim de ilustrar a metodologia, dois exemplos de aplicação são apresentados, sendo o primeiro sobre otimização robusta e o segundo sobre otimização baseada em confiabilidade. Os resultados mostraram, em ambos os exemplos, que o método proposto obteve sucesso, melhorando consideravelmente o comportamento dinâmico dos edifícios estudados, mesmo para um número limitado de dispositivos instalados. Portanto, acredita-se que a metodologia de otimização desenvolvida constitui uma ferramenta eficaz para o projeto ótimo de amortecedores por atrito. / Nowadays it is well known that the use of passive energy dissipation devices, such as friction dampers, considerably reduces the dynamic response of structures. However, the best parameters of each damper and also the best position to install them within the structure remain difficult to be determined. Thus, optimization of dampers is an area that has been increasingly studied in recent years, having a big impact in the optimal design of devices for the vibration control of structures, allowing to obtain safe and at the same time economic solutions. However, although friction dampers have some advantages over other passive devices, few contributions are found on optimization of their parameters or on their optimal position within a structure. This fact can be explained due to the greater difficulty in determining the response of systems involving friction, because their nonlinear behavior. In addition to the lack of studies on optimization of friction dampers, the few studies found in the literature consider the problem in a deterministic way. However, the uncertainties present in the structural properties and/or in the dynamic excitation can alter the optimal solution. Thus, it is important to take into account these uncertainties in the optimization process, which leads to an optimization problem under uncertainty, such as robust optimization and reliability-based optimization. Thus, in this Thesis, a methodology is proposed for the simultaneous optimization of parameters and positions of friction dampers to be installed in buildings subjected to seismic excitation taking into account uncertainties present in both the structural properties and the seismic load, as well as in the friction forces of the dampers. In order to illustrate the approach, two examples are presented, the first one on robust optimization and the second on reliabilitybased optimization. The results show, in both examples, that the proposed method considerably improves the dynamic behavior of the studied buildings, even for a limited number of installed devices. Therefore, it was shown that the proposed procedure is an effective tool for the optimum design of friction dampers.

The thesis contains three chapters on environmental and natural resource economics and focuses on situations where agents receive private or public information. The first chapter analyses the problem of transboundary fisheries, where harvesting countries behave non-cooperatively. In addition to biological uncertainty, countries may face strategic uncertainty. A country that receives negative assessments about the current level of the fish stock, may become “pessimistic” about the assessment of the other harvesting country, which can ignite “panic-based” overfishing. In such a coordination problem, multiplicity of equilibria is a generic characteristic of the solution. Both strategic uncertainty and equilibrium selection, relatively, have been given less attention in the theoretical literature of common-property natural resources. In this model, in the limit as the harvesting countries observe more and more precise information, rationality ensures the unique “global game” equilibrium, a la Carlsson and van Damme (1993). The improved predictive power of the model helps a potential intergovernmental manager of the stock understand the threshold behaviour of harvesting countries. The global game threshold coincides with the risk-dominance threshold of a precise information model, as if there was no strategic uncertainty, and implies that the countries select the corresponding risk-dominant action for any level of assessment of the stock. Gaining from the risk-dominance equivalence, I derive policy suggestions for the overfishing cost and the property rights in common-property fisheries. The second chapter develops a theoretical framework to examine the role of public information in dynamic self-enforcing international environmental agreements (IEAs) on climate change. The countries choose self-enforcing emission abatement strategies in an infinite-horizon repeated game. In a stochastic model, where the social cost of greenhouse gasses (GHG) is a random variable, a central authority, as an information sender, can control release of information about the unknown state to the countries. In the literature on stochastic IEAs, it is shown that comparison of different scenarios of learning by the countries, depends on ex-ante difference of true social cost of GHG from the prior belief of countries. Here, I try to understand, in a signalling game between the informed sender and the countries, whether the no-learning or imperfect-learning scenarios, can be an equilibrium outcome. It is shown that the equilibrium strategy of the sender, who is constrained to a specific randomisation device and tries to induce an incentive-compatible abatement level which is Pareto superior, leads to full learning of social cost of GHG of symmetric and asymmetric countries. Finally, in the third chapter, I again examine a setting, where a central authority, as an information sender, conducts research on the true social cost of climate change, and releases information to the countries. However, in this chapter, instead of restricting the sender to a specific signalling structure, the sender, who has commitment power, by designing an information mechanism (a set of signals and a probability distribution over them), maximises his payoff, which depends on the mitigation action of countries and the social cost of green-house gases(GHG). The countries, given the information policy (the probability distribution over signals) and the public signal, update their beliefs about the social cost of GHG and take a mitigation action. I derive the optimal information mechanism from the general set of public information mechanisms, in coalition formation games. I show that the coalition size, as a function of beliefs, is an endogenous variable, induced by the information sender. If the sender maximises the expected payoff of either of non-signatories or signatories of the climate treaty, then full revelation is the optimal information policy, while if the sender attempts to reduce the global level of GHG, then optimal information policy leads to imperfect disclosure of the social cost. Furthermore, given any of the specifications of the sender’s payoff, the optimal information policy leads to the socially optimal mitigation and membership outcomes.

O planejamento estratégico de lavra corresponde ao processo para se determinar o \"melhor\" projeto e sequenciamento da lavra, segundo uma estratégia previamente estabelecida. É considerado um elemento chave para o sucesso de um empreendimento de mineração, uma vez que subsidia o processo decisório sobre a sua condução e desenvolvimento. Métodos de planejamento estratégico de lavra convencionais estão baseados em modelos determinísticos, que não são capazes de tomar em consideração a variabilidade intrínseca dos principais elementos que os compõem, consequentemente, podem apresentar resultados bastante distantes da realidade e muitas vezes até comprometer a viabilidade do empreendimento. As incertezas geológicas são consideradas como as principais contribuintes para que projetos de mineração falhem em alcançar as expectativas originalmente projetadas. Este estudo apresenta uma metodologia abrangente, que de forma multi-estagiada, utiliza modelos condicionalmente simulados para quantificar e transferir os riscos associados às propriedades geológicas ao longo do processo de planejamento de lavra. Esta função de transferência integra e incorpora distintos métodos de análises quantitativas, incluindo: Teoria Gráfica; Teoria dos Conjuntos; Realces Flutuantes; e Programação Dinâmica. Seus resultados são finalmente convertidos em atividades de lavra, constituindo um sequenciamento de lavra global, controlado pelos riscos, e adicionalmente refinado a partir de uma interface PERT-GANTT. Logo, análises qualitativas podem também ser consideradas, possibilitando que elementos de flexibilidade e adaptação estratégicas participem deste processo. Os resultados obtidos por esta metodologia, quando comparados aos métodos tradicionais, asseguram um planejamento estratégico de lavra que ao mesmo tempo que maximiza o valor presente líquido, delimitado pelas restrições operacionais e estratégias previamente adotadas, também é capaz de avaliar a sensibilidade do empreendimento às variações dos seus principais componentes, consequentemente, oferecendo maior segurança e correção ao processo decisório a este relacionado. / Strategic mine planning corresponds to the process to determine the best mine design and scheduling according to a previously stablished strategy. It is considered as a key element for the success of a mining venture, once supports the decision process related to it conduct and development. Conventional strategic mine planning methods are based on deterministics models, which are not capable to take into account the intrinsic variability related to it main components. Therefore, it can present results which are fairly distant from the reality and even compromise mine feasibility. Geological uncertainties are considered to be a major contributor to projects which fail to meet expectations. This study presents a comprehensive, multistage, mine planning methodology which utilizes conditional simulated models to address the risks and uncertainties associated with geological properties in order to measure, quantify and assess these factors throughout the mine planning process. This transfer function integrates and encompasses different quantitative analysis methods including graph theory, set theory, floating stopes and dynamic programming. Those are driven by risk measurements and the results are converted into mine activities whose final scheduling can be further refined in a PERT-GANTT interface. This also allows for qualitative analysis being undertaken in the final mine scheduling hence ensuring that operating flexibility and strategic adaptability could be also taken into account. The products obtained from this methodology, when compared with traditional methods, ensure that a strategic mine planning could achieve net present value maximization, constrained by operational elements and a strategy previously adopted, and at the same time it is also capable to evaluate the mine sensitivities according to it main components variation. Hence this methodology will offer and deliver higher safety and correction to the decision process associated to the mine venture.

Les courbes de tarage complexes, qui prennent en entrée la hauteur d'eau et des variables supplémentaires, sont nécessaires pour établir les chroniques de débit des cours d'eau là où la relation hauteur-débit n'est pas univoque. Dans le même cadre bayésien, des méthodes à base hydraulique sont proposées et testées pour construire les courbes de tarage complexes et estimer leurs incertitudes : des modèles hauteur-gradient-débit (SGD) pour résoudre l'hystérésis due aux écoulements transitoires, des modèles hauteur-dénivelée-pente (SFD) pour résoudre le remous variable aux stations à double échelle, le modèle hauteur-période-débit (SPD) pour résoudre les détarages nets dus aux évolutions du lit. Chaque modèle a été appliqué à des stations hydrométriques variées et évalué grâce à des analyses de sensibilité. Pour chacune des trois sources de non-univocité de la relation hauteur-débit, les méthodes bayésiennes proposées fournissent non seulement une analyse d'incertitude quantitative mais aussi des solutions efficaces à des problèmes récurrents que posent les procédures traditionnelles pour les courbes de tarage complexes. / Complex rating curves, with stage and additional variables as inputs are necessary to establish streamflow records at sites where the stage-discharge relation is non-unique. Within the same Bayesian framework, hydraulically-based methods are introduced and tested to develop complex rating curves and estimate their uncertainties: stage-gradient-discharge (SGD) models to address hysteresis due to transient flow, stage-fall-discharge (SFD) models to address variable backwater at twin gauge stations, stage-period-discharge (SPD) model to address net rating changes due to bed evolution. Each model was applied to contrasting hydrometric stations and evaluated through sensitivity analyses. For each of the three sources of non-uniqueness in the stage-discharge relation, the proposed Bayesian methods provide not only quantitative uncertainty analysis but also efficient solutions to recurrent problems with the traditional procedures for complex ratings.

Le lien entre les éléments volatils CO₂-H₂O et la fusion mantellique a depuis maintenant longtemps été illuminé par l’expérimentation. Une large base de données expérimentales existe et souligne l’effet primordial de ces éléments sur l’abaissement des températures de fusion de la péridotite ainsi que sur la composition des liquides magmatiques produits comme une fonction des conditions P – T – fo₂ – composition du système. Néanmoins, la diversité et la complexité de cette base de données peuvent compliquer sa compréhension globale. Dans cette étude, une analyse détaillée de la composition des liquides magmatiques riches en CO₂ et H₂O est réalisée, soulignant notamment une transition non-linéaire et plus ou moins abrupte entre des liquides carbonatitiques et des liquides silicatés. Un modèle thermodynamique est élaboré afin de calculer l’activité de SiO₂ dans les liquides magmatiques riches en CO₂-H₂O (aSiO₂(l)) et coexistant avec un assemblage péridotitique, depuis des termes carbonatitiques jusqu’à des termes basaltiques. L’application de ce modèle dans des conditions de ride océanique prédit la stabilisation des liquides carbonatitiques au démarrage de la fusion redox (liée à la transition graphite/diamant- carbonates) jusqu’à environ 100 km de profondeur, avant d’évoluer plus ou moins abruptement vers des liquides silicatés riche en CO₂. Au niveau des cratons, les kimberlites de Groupe I sont stabilisés en base de lithosphère (~250 km de profondeur), et peuvent être formés à partir d’un plume mantellique. L’épaisseur de cette lithosphère empêche la remontée du plume et la formation des OIB. Afin de décrire plus pleinement les propriétés thermodynamiques du liquide magmatique, un modèle plus complexe (système CMAS-CO₂) est en construction, dont la méthodologie est modifiée par rapport au précédent modèle calculant aSiO₂(l) ; un effort tout particulier est ici mené afin de mieux considérer les incertitudes expérimentales et thermodynamiques. / The link between volatiles (CO₂-H₂O) and mantle melting has so far been illuminated by experiments. A large experimental database exists and emphasizes the importance of volatiles on lowering solidus temperatures of peridotite and modifying the melt composition as a function of P – T – fo₂ – bulk composition. Nevertheless, the diversity and the complexity of this experimental database may complicate its global understanding. In this study, an analysis of CO₂-H₂O-rich melt composition is done, emphasizing the non-linear and more or less abrupt character of the transition between carbonate-rich melts and silicate-rich melts. A thermodynamic model is accomplished to calculate the silica activity in CO₂-H₂O-rich melts coexisting with peridotite assemblage and covering carbonatitic to basaltic terms. Along an oceanic ridge adiabat, the model predicts that carbonatitic melts can be stabilized at the onset of “redox melting” (transition between graphite/diamond-carbonates) to about 100 km depth, before abruptly evolving towards carbonated silicate melts. In cratons, Group I kimberlites are stabilized at the base of the lithosphere (about 250 km depth), and can originate from a mantle plume. The thickness of the lithosphere prevents the plume ascent and the production of OIB. In the aim of describing the melt thermodynamic properties more precisely, a more complex model (system CMAS-CO₂) is under construction, with a modified methodology relative to the previous model of silica activity; a specific effort is here conducted in order to better consider experimental and thermodynamic uncertainties.

Portfolio selection theory, developed by Markowitz (1952), is one of the best known and widely applied methods for allocating funds among possible investment choices, where investment decision making is a trade-off between the expected return and risk of the portfolio. Many portfolio selection models have been developed on the basis of Markowitz's theory. Most of them assume that complete investment information is available and that it can be accurately extracted from the historical data. However, this complete information never exists in reality. There are many kinds of ambiguity and vagueness which cannot be dealt with in the historical data but still need to be considered in portfolio selection. For example, to address the issue of uncertainty caused by estimation errors, the robust counterpart approach of Ben-Tal and Nemirovski (1998) has been employed frequently in recent years. Robustification, however, often leads to a more conservative solution. As a consequence, one of the most common critiques against the robust counterpart approach is the excessively pessimistic character of the robust asset allocation. This thesis attempts to develop new approaches to improve on the respective performances of the robust counterpart approach by incorporating additional investment information sources, so that the optimal portfolio can be more reliable and, at the same time, achieve a greater return.

Cette thèse porte sur l'analyse de sensibilité dans le contexte des études de fiabilité des structures. On considère un modèle numérique déterministe permettant de représenter des phénomènes physiques complexes.L'étude de fiabilité a pour objectif d'estimer la probabilité de défaillance du matériel à partir du modèle numérique et des incertitudes inhérentes aux variables d'entrée de ce modèle. Dans ce type d'étude, il est intéressant de hiérarchiser l'influence des variables d'entrée et de déterminer celles qui influencent le plus la sortie, ce qu'on appelle l'analyse de sensibilité. Ce sujet fait l'objet de nombreux travaux scientifiques mais dans des domaines d'application différents de celui de la fiabilité. Ce travail de thèse a pour but de tester la pertinence des méthodes existantes d'analyse de sensibilité et, le cas échéant, de proposer des solutions originales plus performantes. Plus précisément, une étape bibliographique sur l'analyse de sensibilité puis sur l'estimation de faibles probabilités de défaillance est proposée. Cette étape soulève le besoin de développer des techniques adaptées. Deux méthodes de hiérarchisation de sources d'incertitudes sont explorées. La première est basée sur la construction de modèle de type classifieurs binaires (forêts aléatoires). La seconde est basée sur la distance, à chaque étape d'une méthode de type subset, entre les fonctions de répartition originelle et modifiée. Une méthodologie originale plus globale, basée sur la quantification de l'impact de perturbations des lois d'entrée sur la probabilité de défaillance est ensuite explorée. Les méthodes proposées sont ensuite appliquées sur le cas industriel CWNR, qui motive cette thèse. / This thesis' subject is sensitivity analysis in a structural reliability context. The general framework is the study of a deterministic numerical model that allows to reproduce a complex physical phenomenon. The aim of a reliability study is to estimate the failure probability of the system from the numerical model and the uncertainties of the inputs. In this context, the quantification of the impact of the uncertainty of each input parameter on the output might be of interest. This step is called sensitivity analysis. Many scientific works deal with this topic but not in the reliability scope. This thesis' aim is to test existing sensitivity analysis methods, and to propose more efficient original methods. A bibliographical step on sensitivity analysis on one hand and on the estimation of small failure probabilities on the other hand is first proposed. This step raises the need to develop appropriate techniques. Two variables ranking methods are then explored. The first one proposes to make use of binary classifiers (random forests). The second one measures the departure, at each step of a subset method, between each input original density and the density given the subset reached. A more general and original methodology reflecting the impact of the input density modification on the failure probability is then explored.The proposed methods are then applied on the CWNR case, which motivates this thesis.