[pt] Elementos de paredes finas com seções transversais abertas têm sido amplamente empregados em aplicações de engenharia. Embora as aplicações convencionais e os códigos de projeto se concentrem predominantemente em elementos de aço, observa-se um interesse crescente no uso de materiais alternativos, especialmente compósitos. Entre estes, polímeros reforçados com fibra (FRP) têm sido cada vez mais empregados devido às suas propriedades benéficas. No entanto, a natureza ortotrópica das colunas FRP, produzidas através de pultrusão, apresenta um desafio, uma vez que as prescrições convencionais de projeto para estruturas de aço não podem ser aplicadas diretamente. Assim, mais pesquisas são essenciais para fornecer normas de projeto confiáveis para membros estruturais em FRP. Entre as geometrias tradicionais de seção aberta, seções cantoneira têm sido comumente empregadas. Apesar de sua simplicidade geométrica, colunas com seção cantoneira apresentam uma flambagem estrutural e um comportamento dinâmico complexos, que decorre do fato de tais colunas apresentarem diferentes modos de deformação, função de suas propriedades geométricas e materiais, incluindo interação modal, principalmente entre os modos de flexão e torção. Este trabalho se concentra na investigação das características de flambagem e vibração de colunas pultrudadas FRP com seção cantoneira, abrangendo seções de abas iguais e desiguais, e abrangendo colunas curtas a longas. Para isso, são desenvolvidos modelos de dimensão reduzida (ROMs) baseados na teoria clássica não linear de placas (CPT) proposta por von Kármán. A seção cantoneira é modelada como duas placas, com restrições de continuidade imposta na ligação entre ambas. Utilizando o software GBTul, é conduzida uma investigação abrangente da participação modal nos modos de flambagem e vibração. Com base nesta análise, o campo de deslocamentos de cada placa para todos os ROMs é aproximado por funções de interpolação derivadas analiticamente, que são usadas para discretizar o sistema contínuo com base no método de Ritz. Pela aplicação do princípio de Hamilton, os problemas de autovalor e equações não lineares de movimento são derivados. São realizadas análises paramétricas dimensionais e adimensionais, com cargas críticas e frequências de vibração comparadas favoravelmente com os resultados do GBTul. Caminhos pós-flambagem são explorados resolvendo-se os sistemas de equações de equilíbrio não lineares para cada ROM. A influência dos parâmetros geométricos e materiais na rigidez pós-flambagem é investigada, juntamente com a sensibilidade às imperfeições geométricas iniciais. Finalmente, a estabilidade de colunas sob carregamento axial harmônico é avaliada resolvendo-se numericamente as equações não lineares de movimento usando-se o método Runge-Kutta de quarta ordem. As regiões de instabilidade paramétrica são determinadas em função da frequência e magnitude da força de excitação harmônica, considerando a influência do material, do amortecimento e da geometria da seção transversal. Os diagramas de bifurcação são obtidos empregando-se o método da força bruta e técnicas de continuação, esclarecendo as bifurcações associadas aos limites de instabilidade paramétrica. A evolução das bacias de atração de soluções coexistentes é investigada, proporcionando uma avaliação da integridade dinâmica. Os resultados demonstram que a coluna pode perder estabilidade sob níveis de carga bem abaixo da carga estática de flambagem e, portanto, os projetistas devem ter cautela ao trabalhar com essas estruturas sujeitas a cargas axiais variáveis no tempo. / [en] Thin-walled elements with open cross sections have been widely employed in engineering applications. While conventional applications and design codes predominantly focus on steel members, a growing interest has emerged in exploring alternative materials, particularly composites. Among these, fiber reinforced polymer (FRP) has witnessed increased application owing to its advantageous properties. However, the orthotropic nature of FRP columns, produced through pultrusion, presents a challenge as conventional design prescriptions for structural steel cannot be directly applied. Thus, further research is essential to derive reliable design rules for FRP members. In the realm of traditional open section geometries, angle sections have been commonly employed. Despite their geometric simplicity, angles exhibit a complex structural buckling and dynamic behaviour which arises from the fact that such columns may undergo different deformation modes, according to their geometric and material properties, with modal interaction observed, particularly between flexural and torsional modes. This work focuses on investigating the buckling and vibration characteristics of pultruded FRP angle sections, encompassing both equal and unequal-leg sections, and spanning short to long columns. For this, reduced order models (ROMs) are developed based on the classical von Kármán nonlinear plate theory (CPT). The angle section is modelled as two plates, with continuity constraints considered at the common boundary. Utilizing GBTul software, a comprehensive investigation of modal participation in linear buckling and vibration modes is conducted. Based on this analysis, the plate displacement field for each ROM is approximated by suitable analytically derived interpolating functions, which are used to discretize the continuous system on the basis of the Ritz energy method. By application of Hamilton s principle, the eigenvalue problems and nonlinear equations of motion are derived. Parametric dimensional and nondimensional analyses are carried out, with critical loads and vibration frequencies compared favorably with GBTul results. Post-buckling paths are explored by solving the systems of nonlinear equilibrium equations for each ROM. The influence of geometric and material parameters on post-buckling stiffness is investigated, along with the sensitivity to initial geometrical imperfections. Finally, the stability of the columns under harmonic axial loading is assessed by numerically solving the nonlinear equations of motion using the fourth-order Runge-Kutta method. Parametric instability regions are determined as a function of the frequency and magnitude of the harmonic excitation force, considering the influence of material, damping, and cross-sectional geometry. Bifurcation diagrams are obtained employing the brute force method and continuation techniques, clarifying the bifurcations associated to the parametric instability boundaries. The evolution of basins of attraction of coexisting solutions is investigated, providing an evaluation of dynamic integrity. The results demonstrate that the column may lose stability at load levels well below the static buckling loads and, therefore, designers must exercise caution when working with these structures subjected to time-varying axial loads.

Simulations and modeling of large-scale systems are vital to understanding real world phenomena. However, even advanced numerical models can only approximate the true physics. The discrepancy between model results and nature can be attributed to different sources of uncertainty including the parameters of the model, input data, or some missing physics that is not included in the model due to a lack of knowledge or high computational costs. Uncertainty reduction approaches seek to improve the model accuracy by decreasing the overall uncertainties in models. Aiming to contribute to this area, this study explores uncertainty quantification and reduction approaches for complex physical problems. This study proposes several novel probabilistic and statistical approaches for identifying the sources of uncertainty, modeling the errors, and reducing uncertainty to improve the model predictions for large-scale simulations. We explore different computational models. The first class of models studied herein are inherently stochastic, and numerical approximations suffer from stability and accuracy issues. The second class of models are partial differential equations, which capture the laws of mathematical physics; however, they only approximate a more complex reality, and have uncertainties due to missing dynamics which is not captured by the models. The third class are low-fidelity models, which are fast approximations of very expensive high-fidelity models. The reduced-order models have uncertainty due to loss of information in the dimension reduction process. We also consider uncertainty analysis in the data assimilation framework, specifically for ensemble based methods where the effect of sampling errors is alleviated by localization. Finally, we study the uncertainty in numerical weather prediction models coming from approximate descriptions of physical processes. / Ph. D. / Computational models are used to understand the behavior of the natural phenomenon. Models are used to approximate the evolution of the true phenomenon or reality in time. We obtain more accurate forecast for the future by combining the model approximation together with the observation from reality. Weather forecast models, oceanography, geoscience, etc. are some examples of the forecasting models. However, models can only approximate the true reality to some extent and model approximation of reality is not perfect due to several sources of error or uncertainty. The noise in measurements or in observations from nature, the uncertainty in some model components, some missing components in models, the interaction between different components of the model, all cause model forecast to be different from reality. The aim of this study is to explore the techniques and approaches of modeling the error and uncertainty of computational models, provide solution and remedies to reduce the error of model forecast and ultimately improve the model forecast. Taking the discrepancy or error between model forecast and reality in time and mining that error provide valuable information about the origin of uncertainty in models as well as the hidden dynamics that is not considered in the model. Statistical and machine learning based solutions are proposed in this study to identify the source of uncertainty, capturing the uncertainty and using that information to reduce the error and enhancing the model forecast. We studied the error modeling, error or uncertainty quantification and reduction techniques in several frameworks from chemical models to weather forecast models. In each of the models, we tried to provide proper solution to detect the origin of uncertainty, model the error and reduce the uncertainty to improve the model forecast.

Many companies have a large collection of different model variants and results. Hexagon's (formerly MSC Software) software Odyssee helps to find out what information is contained in this data. New calculations can sometimes be avoided because the results for new parameter combinations can be predicted from the existing calculations. This is particularly interesting for non-linear or large models with long run times. The software also helps when setting up new DOEs and offers a variety of options for statistical displays. In the lecture, the number-based and image-based methods are compared. / Viele Firmen können auf eine große Sammlung vorhandener Rechnungen für verschiedene Modellvarianten zurückgreifen. Die Software Odyssee von Hexagon (früher MSC Software) hilft herauszufinden, welche Informationen in diesen Daten stecken. Neue Rechnungen kann man sich teilweise ersparen, weil die Ergebnisse für neue Parameterkombinationen aus den vorhandenen Rechnungen vorhergesagt werden können. Dies ist besonders interessant für nichtlineare oder große Modelle mit langer Rechenzeit. Die Software hilft auch beim Aufsetzen neuer DOEs und bietet vielfältige Möglichkeiten für statistische Darstellungen. In dem Vortrag werden die zahlenbasierte und bildbasierte Methode gegenübergestellt.

Cette thèse porte sur le développement d’une approche pratique de modélisation/simulation des systèmes solaires combinés Photovoltaïques/Thermiques PV/T. Il s’agit d’une approche basée sur un modèle d’ordre réduit en représentation d’état (ORRE). En effet, les systèmes solaires thermiques, électriques et combinés intégrés aux bâtiments possèdent des spécificités permettant de s’affranchir des méthodes numériques classiques (mécanique des fluides numérique et thermique numérique). Ces méthodes sont réputées dans le domaine de l’aérodynamique, de l’aéraulique…etc. Par contre, dans le domaine du mix-énergétique tels que celui considéré dans ce mémoire, l’application directe de ce modèle peut conduire à des dépassements des capacités mémoire ou des temps de calcul exorbitants. Une alternative est de développer des méthodes adaptées au problème physique considéré, en traitant l’aspect multi-physique toute en restant dans une taille de données raisonnable et du temps de calcul réduit. La méthodologie de modélisation consiste à réduire les dimensions des équations qui régissent le problème. En se basant sur la symétrie du système, puis en découpant le système en zones de contrôle basées sur une valeur moyenne gouvernée par les nombres adimensionnels de Biot (Bi) et de Fourier (Fo). Les résultats obtenus en fonctionnement dynamique pourront nous fournir des paramètres de sorties, plus particulièrement, les rendements électrique, thermique et la puissance de circulation du fluide caloporteur. L’avantage de l’approche proposée réside dans la simplification du modèle résultant, qui est représenté par un seul système d’équations algébriques en représentation d’état regroupant tous les éléments physiques du système en fonctionnement dynamique (conditions aux limites variables dans le temps). Ce modèle regroupe la variable fondamentale qui est la température, et les deux types de contrôle et de conception. De plus, le modèle d’ORRE est intégrable dans le fonctionnement en temps réel des systèmes PV/T intégrés aux bâtiments (PV/T-Bât) afin d’accompagner leurs régulation et gestion des flux mise en jeu. Le modèle ainsi proposé a fait l’objet d’une validation où les résultats numériques ont été comparés aux résultats expérimentaux. En effet, quatre configurations ont été étudiées et évoquées dans une approche linéaire. Les résultats obtenus montrent une cohérence tolérable entre les résultats expérimentaux, et numériques. Cette cohérence a été évaluée en termes d’incertitude entre les résultats du modèle et le cas étudié expérimentalement. Le cas d’un système non-linéaire a été également abordé. En effet, rares sont les travaux qui ont été publiés mettant en valeur les phénomènes non-linéaires dans les systèmes complexes PV/T-Bât, Ainsi, on a développé avec la même stratégie, des modèles bilinéaires qui modélise le mieux possible le comportement thermique dans les systèmes PV/T-Bât. Une étude d’optimisation du système multi-physique en introduisant une étude paramétrique est menée en terme afin d’étudier la sensibilité des paramètres sur le rendement énergétique. Cependant, les études d’optimisation paramétriques restent limitées et insuffisantes à cause de la résolution mono-objectif du problème d’optimisation, alors que notre système manifeste un comportement combiné et multi-physique de nature contradictoire. Pour ce faire, une optimisation multi-objectifs est introduite avec trois fonctions objectif en employant l’algorithme génétique NSGA-II. L’originalité de notre méthode est d’employer l’algorithme en régime dynamique afin de choisir la conception du système la plus optimale. Les résultats trouvés peuvent contribuer à améliorer la conception des systèmes PV/T-Bât et l’optimisation de leur fonctionnement / This thesis consists to develop a simplified model approach for Photovoltaic / Thermal (PV / T) combined solar system based on state-space reduced order model. The building integrated solar systems are getting high attention in these last decencies, as well as the performance increasing which require high numerical methods to improve the design and reducing the costs. In one hand, the CFD methods are useful tool to predict the energy (mechanical and thermal) of combined PV/T systems, but it requires an expensive computing capacities and exorbitant calculation times, On the other hand, the PV/T systems can generate both the electrical and thermal flows, and requires an easily and performant optimization model. An alternative is to develop methods that are adapted to the physical problem under consideration, treating the multi-physics aspect while remaining in a reasonable data size and reduced computing time. The first part of the current thesis consists to develop a mathematical model which consists of reducing the dimensions of the governed equations. Based on the symmetry of the geometry, the system is subdivided into control areas which governed by the dimensionless Biot (Bi) and Fourier (Fo) numbers. The obtained results in dynamic mode can provide output key parameters, more particularly the electrical and thermal efficiencies and the dissipated hydrodynamic power. The advantage of this approach lies in the simplification of the resulting model, which is represented by a single state-space representation that groups all the physical elements of the system into dynamic mode, i.e. in continuous variation of the boundary condition. This model groups the fundamental variable, which is the temperature, and two type parameters, which are the control parameters and the design parameters. In addition, the reduced order model can be integrated into real-time operation of building-integrated PV / T (BIPV/T) systems in order to support their regulation and management of intervening flows. In order to validate the use of our model, it is necessary to test it for several cases of Building Integrated PV/T systems (BIPV/T). For this, four major configurations were studied and discussed in a linear approach; the found results show a good agreement with experimental works. A second level has been developed as part of our thesis work, which is the non-linearity in combined PV / T and BIPV/T systems; in particular, bilinear models have been developed with the same strategy which best models the thermal behavior in BIPV/T systems. The second issue, related to Multi-physics aspect. Furthermore, in order to evaluate the sensitivity of the parameters, a parametric optimization has been made with dimensionless numbers. However, parametric optimization studies remain limited and insufficient because of the single-objective resolution of the optimization problem, whereas our system manifests a mixed and multi-physics behavior with contradictory nature. To do this, a multi-objective optimization is introduced with three objective functions using the NSGA-II genetic algorithm. The originality of our method is to use the algorithm in dynamic mode in order to choose the design of the optimal system. The found results can contribute to the design of BIPV/T systems and optimize their operation

Dans le domaine automobile, les modules électroniques de puissance des produits mécatroniques voient leur puissance sans cesse s'accroître, tout en étant confinés dans des volumes de plus en plus réduits. Au cours de leur fonctionnement, les composants semi-conducteurs et leur assemblage subissent ainsi des contraintes électro-thermo-mécaniques sévères, susceptibles d'entraîner leur destruction et de provoquer la défaillance du produit. L'étude de la fiabilité et le calcul de la durée de vie de tels produits dépendent des températures de jonction calculées au niveau des puces des composants de puissances. De surcroît, le contexte d'applications embarquées requiert de maîtriser, outre les paramètres électriques et mécaniques, les paramètres thermiques tels que les températures de jonctions et les puissances dissipées au niveau des composants, qu'il est nécessaire de réguler et contrôler en temps réel afin d'assurer le bon fonctionnement du produit. L'objectif de cette thèse est ainsi de proposer une méthode d'identification de modèles réduits dans le but d'estimer le comportement thermique des modules électroniques de puissance, en se fondant uniquement sur les données d'entrées et les résultats issus d'une simulation numérique d'un modèle détaillé du système étudié. Dans cette thèse, une nouvelle méthode d'identification, nommée « Kernel Identification Method », est développée. Cette méthode a été validée sur une application industrielle traitant d'un problème thermique couplé solide/fluide dont le comportement est essentiellement régi par de la convection forcée. Une étude exploratoire portant sur l'identification de problèmes non linéaires où la convection naturelle joue le rôle dominant est ensuite proposée. A cet effet, deux méthodes d’identification non-paramétrique sont proposées : (i) une première méthode basée sur l’extension de la méthode Kernel Identification Method ; et (ii) une deuxième méthode basée sur la variante dite « Unscented » du filtre de Kalman. / In automotive applications, the thermal dissipation of power electronics modules in mechatronic products is constantly increasing, whereas these products are confined in increasingly reduced volumes. During their operation, the semiconductor components and their environment are then submitted to severe electro-thermo-mechanical stresses that could cause their damage and lead to the product failure. The reliability and lifetime prevision of such products depend on the temperature junction located at the chip of power components. Furthermore, in order to ensure the safe operation of embedded applications, it is essential to perform a real-time control of thermal parameters such as the junction temperatures and power dissipated on the power components, in addition to the electrical and mechanical parameters. The objective of this thesis is to develop an identification method aimed at producing reduced thermal models to estimate the thermal behaviour of power electronic modules. Designed in a non-intrusive framework, this method post-processes the input data and the results produced by the numerical simulation of a detailed of the system under study. In this thesis, a new identification method, called "Kernel Identification Method" is developed. It has been validated on an industrial application dealing with a thermally coupled solid / fluid problem mainly governed by forced convection. An exploratory study of nonlinear problems identification where the natural convection plays the dominant role is then proposed. To this end, two identification methods of nonparametric nature are proposed: (i) a method based on the extension of the Kernel Identification Method; and (ii) a second method based on the "unscented" variant of the Kalman filter.

Le contrôle d'écoulements turbulents est un enjeu majeur en aérodynamique. Cependant, la présence d'un grand nombre de degrés de libertés et d'une dynamique complexe rend délicat la modélisation dynamique de ces écoulements qui est pourtant nécessaire à la conception d'un contrôle efficace. Au cours de cette thèse, différentes directions ont été suivies afin de développer des modèles réduits dans des configurations réalistes d'écoulements et d'utiliser ces modèles pour le contrôle.Premièrement, la décomposition en modes dynamiques (DMD), et certaines de ses variantes, ont été exploitées en tant que base réduite afin d'extraire au mieux le comportement dynamique de l'écoulement. Par la suite, nous nous sommes intéressés à l'assimilation de données 4D-Var qui permet de combiner des informations inhomogènes provenant d'un modèle dynamique, d'observations et de connaissances a priori du système. Nous avons ainsi élaboré des modèles réduits POD et DMD d'un écoulement turbulent autour d'un cylindre à partir de données expérimentales PIV. Finalement, nous avons considéré le contrôle d'écoulement dans un contexte d'interaction fluide/structure. Après avoir montré que les mouvements de solides immergés dans le fluide pouvaient être représentés comme une contrainte supplémentaire dans le modèle réduit, nous avons stabilisé un écoulement de sillage de cylindre par oscillation verticale. / Control of turbulent flows is still today a challenge in aerodynamics. Indeed, the presence of a high number of active degrees of freedom and of a complex dynamics leads to the need of strong modelling efforts for an efficient control design. During this PhD, various directions have been followed in order to develop reduced-order models of flows in realistic situations and to use it for control. First, dynamic mode decomposition (DMD), and some of its variants, have been exploited as reduced basis for extracting at best the dynamical behaviour of the flow. Thereafter, we were interested in 4D-variational data assimilation which combines inhomogeneous informations coming from a dynamical model, observations and an a priori knowledge of the system. POD and DMD reduced-order models of a turbulent cylinder wake flow have been successfully derived using data assimilation of PIV measurements. Finally, we considered flow control in a fluid-structure interaction context. After showing that the immersed body motion can be represented as an additional constraint in the reduced-order model, we stabilized a cylinder wake flow by vertical oscillations.

O objetivo deste estudo é apresentar uma revisão sobre técnicas de redução da ordem de modelos dinâmicos lineares e invariantes no tempo. Com a implementação de tais técnicas, o autor mostra que é possível reproduzir as principais características da resposta de um modelo de alta ordem através de um modelo de ordem reduzida com menor número de graus de liberdade. Uma metodologia para redução da ordem de modelos de sistemas dinâmicos foi apresentada. Os processos envolvidos nesta metodologia foram descritos, os quais são: técnicas para realizar projeções do sistema em diferentes bases, selecionar os graus de liberdade que são bons candidatos a eliminação, eliminar graus de liberdade do modelo completo e implementar correções na resposta do modelo reduzido. Foram apresentadas maneiras de quantificar as similitudes entre as respostas dos modelos completo e reduzido através de métricas de representatividade. Para implementar e estudar as técnicas de redução apresentadas, o autor elaborou dois modelos para estudo de caso: um modelo para estudo da dinâmica vertical de um veículo de passeio e outro modelo para estudo da dinâmica longitudinal de um trem. Diferentes técnicas de redução foram implementadas a partir dos dois modelos para estudo de caso e os resultados foram comparados através das métricas de representatividade. O critério proposto pelo autor para quantificar desempenho de um modelo reduzido foi utilizado para determinar de maneira objetiva o modelo reduzido mais adequado para cada aplicação. Como contribuição neste trabalho, o autor propôs uma definição de desempenho de um modelo reduzido e um método para quantificar o mesmo, além de duas novas métricas para mensurar a capacidade do modelo reduzido em reproduzir os máximos sobre-sinais e tempos de acomodação do modelo completo. / The objective of this work is to present a revision about model order reduction techniques applied to linear, time invariant dynamic systems. With the implementation of these techniques, the author shows that it is possible to reproduce the main characteristics of the response of a high order dynamic system using a reduced order model with fewer degrees of freedom. A model order reduction methodology was presented. The processes which are involved in this methodology were described, which are: techniques for projection onto different basis, selection of the most suitable degrees of freedom to be reduced, elimination of degrees of freedom from the high order model, implementation of corrections at the reduced model response. The author showed ways to quantify the similarities between the responses of the complete and reduced models using representativeness metrics. In order to implement and study the presented model order reduction techniques, the author developed two case study models: one model to study the vertical dynamics of a passenger car and another model to study the longitudinal dynamics of a train. Different model order reduction techniques were implemented and its results were compared using representativeness metrics and the performance of the reduced models. The criteria proposed by the author to quantify the performance of a reduced order model was used to objectively determine the most suitable reduced order model for each application. The author proposed, as contribution at this work, a definition of the reduced order model performance, a method to quantify its performance and two new metrics to measure the capacity of the reduced model to reproduce the overshoots and settling times of the complete model.

[pt] Este trabalho apresenta um método para calcular a resistência à fadiga de uma torre de perfuração considerando a elevação da superfície do mar, a dinâmica da plataforma na qual a torre está instalada e a dinâmica da própria torre. Modelos de ordem reduzida são utilizados para obter a elevação da superfície do mar e a dinâmica torre, e as incertezas nos parâmetros dos componentes do sistema podem ser incluídas na análise também. As análises podem ser feitas para vários estados de mar, conforme sua distribuição de probabilidade, e nenhuma hipótese sobre a distribuição de probabilidade precisa ser feita inicialmente. O histograma de distribuição de ciclos de tensão para toda vida útil do equipamento é obtido usando um procedimento de contagem de ciclos Rainflow. Os resultados e as incertezas nos mesmos são discutidos. / [en] This work presents a method for evaluation of the fatigue resistance of a drilling tower considering the sea surface elevation, the dynamics of the platform on which the tower is installed and the dynamics of the tower itself. Reduced order models are used for obtaining the sea surface elevation and the dynamics of the tower, and the uncertainties on the parameters of the components of the system can be included in the analysis as well. The analysis can be done for several sea states, according its probability distribution, and no assumption about the probability distribution of the stress ranges has to be made previously. The histogram for the distribution of stress ranges for the entire working life of the equipment is obtained using a Rainflow technique. The results and the uncertainties on them are discussed.

La stabilisation inertielle de ligne de visée est essentiellement un problème de rejet de perturbations : il faut rendre la ligne de visée de la caméra embarquée dans le viseur insensible aux mouvements du porteur. Les méthodes de commande robuste du type H-infini sont bien adaptées à la résolution de ce type de problème, et plus particulièrement l’approche Loop-Shaping qui repose sur des concepts de réglage de l’automatique fréquentielle classique. Cependant, les correcteurs obtenus via cette approche sont généralement d’ordre élevé et donc difficilement implémentables sur le calculateur embarqué du viseur.Dans cette thèse, nous avons proposé des méthodologies de synthèse de correcteurs robustes d’ordre réduit et/ou de structure fixée. Pour cela, nos travaux ont été axés sur :- L’optimisation pour la synthèse H-infini à ordre et/ou structure fixée. Tout d’abord nous avons exploré les possibilités offertes par l’optimisation sous contraintes LMI (Linear Matrix Inequalities). Celles-ci se sont avérées limitées, bien que de nombreux algorithmes aient été proposés dans ce cadre depuis le début des années 90. Ensuite, nous avons opté pour l’optimisation non lisse. En effet des outils numériques récemment développés rendent accessible cette approche, et leur efficacité s’est avéré indéniable.- L’adaptation au cadre particulier du critère H-infini Loop-Shaping.La structure particulière de ce critère de synthèse a été exploitée afin de mieux prendre en compte les pondérations, et d’améliorer la réduction d’ordre du correcteur final. Enfin, une approche basée uniquement sur le réglage graphique d’un gabarit de gain fréquentiel en boucle ouverte est proposée. Ces différentes méthodologies sont illustrées, tout au long de la thèse, sur un viseur dont le modèle a été identifié à partir de mesures expérimentales. / Inertial line of sight stabilization is a disturbance rejection problem: the goal is to hold steady in the inertial space, the line of sight of a camera, which is carried on a mobile vehicle. H-infinity robust control techniques are well suited for this type of problem, in particular the Loop-Shaping approach which relies on classical frequency domain concepts. However, this approach results in high order controllers which are hardly implementable on the real time embedded electronic unit of the sight system.In this thesis, fixed order and fixed structure controller design methodologies are proposed. This development follows two main axis: - Fixed order H-infinity Optimization. First, fixed order controllers have been investigated through the LMI (Linear Matrix Inequalities) optimization framework. However the numerical efficiency of this approach is still limited, despite the large amount of research in this area since the 90’s. Then, we used recently developed and more efficient tools that recast the fixed order H-infinity synthesis problem as a nonsmooth optimization problem.- Adaptation to the H-infinity Loop-Shaping frameworkWe adapted the 4 block H-infinity criterion in order to include the weighting filters in the fixed order controller optimization, which enhance the final controller order reduction. Then, we proposed a fixed order controller design approach, based only on graphically tuning a target open loop frequency gain.

Cette recherche se focalise sur les problèmes d’instabilités de combustion hautes fréquences dans les moteurs fusées. Ces instabilités sont connues pour avoir des effets néfastes et peuvent, dans certains cas, causer la destruction du système propulsif. Pour éviter l’apparition de ces instabilités, il est important de connaître les mécanismes qui entretiennent ces phénomènes dynamiques et de comprendre le couplage complexe entre l’injection, la combustion et la résonnance acoustique du système. Ce travail comprend trois parties.La première partie traite de la simulation numérique de jets non-réactifs et réactifs soumis à différentes conditions de modulation afin de comprendre les interactions entre les jets, les flammes et leur environnement. Les calculs numériques de jets ronds non-réactifs ainsi que des flammes plus complexes formées par des injecteurs coaxiaux dans des conditions transcritiques ont été effectuées avec des simulations aux grandes échelles (SGE), adaptées aux conditions gaz réels à l’aide du solveur AVBP-RG. Les jets ronds ont été soumis à des fluctuations de vitesse transverse. Il a été trouvé que pour toutes les amplitudes et fréquences de modulation, le jet est déformé et oscille dans la direction transverse. Ce comportement peut être représenté par un modèle. Les flammes coaxiales ont été soumises à une modulation de débit et de pression. La modulation induit des variations du dégagement de chaleur global. Un modèle mathématique reliant les paramètres modulés au dégagement de chaleur est proposé.La seconde partie contient les travaux expérimentaux. Dans ce cadre, un nouveau banc expérimental a été développé pour l’étude de cavités couplées pressurisées (NPCC). Le couplage entre le plénum (ou dôme) et la chambre a été étudié. Un modèle reliant les fluctuations de pression et de vitesse en sortie des injecteurs a été développé et comparés aux données d’essais. Le banc NPCC a aussi été utilisé pour acquérir plus de connaissances sur le niveau d’amortissement. Les coefficients d’amortissement ont été déterminés.La dernière partie de ce document traite du développement d’un modèle ordre réduit qui représente des mécanismes qui entretiennent et amortissent les instabilités de combustion hautes fréquences. Cette description dynamique a été incorporée dans un code de stabilité haute fréquence (STAHF). Ce code a été utilisé pour étudier un moteur à ergols liquides d’une puissance de 87 MW (le banc BKD du DLR en Allemagne) qui présente des instabilités hautes fréquences. Après le recalage de certains paramètres de contrôle, STAHF a été capable de retrouver des résultats obtenus d’essais au DLR. / This research concerns some of the issues raised by high frequency combustion instabilities in rocket engines. These instabilities are known to have detrimental effects leading, in some cases, to the destruction of the propulsion system. To avoid the appearance of such instabilities it is important to gain an understanding of the processes driving such dynamical phenomena. One has to consider the complex coupling between injection, combustion and the acoustic resonances of the system. The present work contributes to this objective by developing three items.The first deals with numerical simulations of non-reactive and reactive jets submitted to different modulation conditions to understand the interaction between jets, flames and their environment. Numerical simulations of non-reactive round jets as well as more complex flames formed by coaxial injectors operating under transcritical conditions were carried out using large eddy simulation (LES) adapted to real gas situations by making use of the AVBP-RG flow solver. Round jets were submitted to transverse velocity fluctuations. It has been found that for all amplitudes and frequencies of modulation, the modulated jet is deformed and oscillates. This behavior can be represented by a model. The coaxial flames were submitted to mass flow rate and pressure modulation. For these cases it has been found that the modulation induces variations of the global heat release rate. A mathematical relationship between the modulated parameters and the heat release rate has been proposed.The second item includes experimental investigations. For this purpose a New Pressurized Coupled Cavities (NPCC) laboratory test rig has been developed. The possible coupling between the plenum and the thrust chamber was studied. A model, linking pressure and velocity fluctuations between the plenum and the thrust chamber, has been developed. The laboratory test rig was also used to gather some knowledge on the levels of damping and the damping coefficients could be determined.The last item of this document deals with the development of a reduced order dynamical model which includes some of the driving and damping mechanisms of high frequency combustion instabilities. This dynamical description was implemented in a high frequency stability code (STAHF). This code was used to examine a 87 MW liquid rocket engine (BKD operated at DLR, Germany) exhibiting high frequency oscillations. After the adjustment of some control parameters, STAHF was able to retrieve some the features observed in experiments carried out at DLR.