Computer Vision Techniques for Transcatheter Intervention

Minimally invasive transcatheter technologies have demonstrated substantial promise for the diagnosis and treatment of cardiovascular diseases. For example, TAVI is an alternative to AVR for the treatment of severe aortic stenosis and TAFA is widely used for the treatment and cure of atrial fibrillation. In addition, catheter-based IVUS and OCT imaging of coronary arteries provides important information about the coronary lumen, wall and plaque characteristics. Qualitative and quantitative analysis of these cross-sectional image data will be beneficial for the evaluation and treatment of coronary artery diseases such as atherosclerosis. In all the phases (preoperative, intraoperative, and postoperative) during the transcatheter intervention procedure, computer vision techniques (e.g., image segmentation, motion tracking) have been largely applied in the field to accomplish tasks like annulus measurement, valve selection, catheter placement control, and vessel centerline extraction. This provides beneficial guidance for the clinicians in surgical planning, disease diagnosis, and treatment assessment. In this paper, we present a systematical review on these state-of-the-art methods.We aim to give a comprehensive overview for researchers in the area of computer vision on the subject of transcatheter intervention. Research in medical computing is multi-disciplinary due to its nature, and hence it is important to understand the application domain, clinical background, and imaging modality so that methods and quantitative measurements derived from analyzing the imaging data are appropriate and meaningful. We thus provide an overview on background information of transcatheter intervention procedures, as well as a review of the computer vision techniques and methodologies applied in this area

Accurate 3D shape and displacement measurement using a scanning electron microscope

With the current development of nano-technology, there exists an increasing demand for three-dimensional shape and deformation measurements at this reduced-length scale in the field of materials research. Images acquired by \ud Scanning Electron Microscope (SEM) systems coupled with analysis by Digital Image Correlation (DIC) is an interesting combination for development of a high magnification measurement system. However, a SEM is designed for visualization, not for metrological studies, and the application of DIC to the micro- or nano-scale with such a system faces the challenges of calibrating the imaging system and correcting the spatially-varying and \ud time-varying distortions in order to obtain accurate measurements. Moreover, the SEM provides only a single sensor and recovering 3D information is not possible with the classical stereo-vision approach. But the specimen being mounted on the mobile SEM stage, images can be acquired from multiple viewpoints and 3D reconstruction is possible using the principle of videogrammetry for recovering the unknown rigid-body motions undergone by \ud the specimen.\ud The dissertation emphasizes the new calibration methodology that has been developed because it is a major contribution for the accuracy of 3D shape and deformation measurements at reduced-length scale. It proves that, unlike previous works, image drift and distortion must be taken into account if accurate measurements are to be made with such a system. Necessary background and required theoretical knowledge for the 3D shape measurement using videogrammetry and for in-plane and out-of-plane deformation measurement are presented in details as well. In order to validate our work and demonstrate in particular the obtained measurement accuracy, experimental results resulting from different applications are presented throughout the different chapters. At last, a software gathering different computer vision applications has been developed.\ud Avec le développement actuel des nano-technologies, la demande en matière d'étude du comportement des matériaux à des échelles micro ou nanoscopique ne cesse d'augmenter. Pour la mesure de forme ou de déformations tridimensionnelles à ces échelles de grandeur,l'acquisition d'images à partir d'un Microscope électronique à Balayage (MEB) couplée à l'analyse par corrélation d'images numériques s'est avérée une technique intéressante. \ud Cependant, un MEB est un outil conçu essentiellement pour de la visualisation et son utilisation pour des mesures tridimensionnelles précises pose un certain nombre de difficultés comme par exemple le calibrage du système et la \ud correction des fortes distorsions (spatiales et temporelles) présentes dans les images. De plus, le MEB ne possède qu'un seul capteur et les informations tridimensionnelles souhaitées ne peuvent pas être obtenues par une approche classique de type stéréovision. Cependant, l'échantillon à analyser étant monté sur un support orientable, des images peuvent être acquises sous différents points de vue, ce qui permet une reconstruction tridimensionnelle en utilisant le principe de vidéogrammétrie pour retrouver à partir des seules images les mouvements inconnus du porte-échantillon.\ud La thèse met l'accent sur la nouvelle technique de calibrage et de correction des distorsions développée car c'est une contribution majeure pour la précision de la mesure de forme et de déformations 3D aux échelles de \ud grandeur étudiées. Elle prouve que, contrairement aux travaux précédents, la prise en compte de la dérive temporelle et des distorsions spatiales d'images \ud est indispensable pour obtenir une précision de mesure suffisante. Les principes permettant la mesure de forme par vidéogrammétrie et le calcul de déformations 2D et 3D sont aussi présentés en détails. Enfin, et dans le but de valider nos travaux et démontrer en particulier la précision de mesure obtenue, des résultats expérimentaux issus de différentes applications sont présentés.\ud \ud \u

Graph matching using position coordinates and local features for image analysis

Encontrar las correspondencias entre dos imágenes es un problema crucial en el campo de la visión por ordenador i el reconocimiento de patrones. Es relevante para un amplio rango de propósitos des de aplicaciones de reconocimiento de objetos en las áreas de biometría, análisis de documentos i análisis de formas hasta aplicaciones relacionadas con la geometría desde múltiples puntos de vista tales cómo la recuperación de la pose, estructura desde el movimiento y localización y mapeo. La mayoría de las técnicas existentes enfocan este problema o bien usando características locales en la imagen o bien usando métodos de registro de conjuntos de puntos (o bien una mezcla de ambos). En las primeras, un conjunto disperso de características es primeramente extraído de las imágenes y luego caracterizado en la forma de vectores descriptores usando evidencias locales de la imagen. Las características son asociadas según la similitud entre sus descriptores. En las segundas, los conjuntos de características son considerados cómo conjuntos de puntos los cuales son asociados usando técnicas de optimización no lineal. Estos son procedimientos iterativos que estiman los parámetros de correspondencia y de alineamiento en pasos alternados. Los grafos son representaciones que contemplan relaciones binarias entre las características. Tener en cuenta relaciones binarias al problema de la correspondencia a menudo lleva al llamado problema del emparejamiento de grafos. Existe cierta cantidad de métodos en la literatura destinados a encontrar soluciones aproximadas a diferentes instancias del problema de emparejamiento de grafos, que en la mayoría de casos es del tipo "NP-hard". El cuerpo de trabajo principal de esta tesis está dedicado a formular ambos problemas de asociación de características de imagen y registro de conjunto de puntos como instancias del problema de emparejamiento de grafos. En todos los casos proponemos algoritmos aproximados para solucionar estos problemas y nos comparamos con un número de métodos existentes pertenecientes a diferentes áreas como eliminadores de "outliers", métodos de registro de conjuntos de puntos y otros métodos de emparejamiento de grafos. Los experimentos muestran que en la mayoría de casos los métodos propuestos superan al resto. En ocasiones los métodos propuestos o bien comparten el mejor rendimiento con algún método competidor o bien obtienen resultados ligeramente peores. En estos casos, los métodos propuestos normalmente presentan tiempos computacionales inferiores.Trobar les correspondències entre dues imatges és un problema crucial en el camp de la visió per ordinador i el reconeixement de patrons. És rellevant per un ampli ventall de propòsits des d’aplicacions de reconeixement d’objectes en les àrees de biometria, anàlisi de documents i anàlisi de formes fins aplicacions relacionades amb geometria des de múltiples punts de vista tals com recuperació de pose, estructura des del moviment i localització i mapeig. La majoria de les tècniques existents enfoquen aquest problema o bé usant característiques locals a la imatge o bé usant mètodes de registre de conjunts de punts (o bé una mescla d’ambdós). En les primeres, un conjunt dispers de característiques és primerament extret de les imatges i després caracteritzat en la forma de vectors descriptors usant evidències locals de la imatge. Les característiques son associades segons la similitud entre els seus descriptors. En les segones, els conjunts de característiques son considerats com conjunts de punts els quals son associats usant tècniques d’optimització no lineal. Aquests son procediments iteratius que estimen els paràmetres de correspondència i d’alineament en passos alternats. Els grafs son representacions que contemplen relacions binaries entre les característiques. Tenir en compte relacions binàries al problema de la correspondència sovint porta a l’anomenat problema de l’emparellament de grafs. Existeix certa quantitat de mètodes a la literatura destinats a trobar solucions aproximades a diferents instàncies del problema d’emparellament de grafs, el qual en la majoria de casos és del tipus “NP-hard”. Una part del nostre treball està dedicat a investigar els beneficis de les mesures de ``bins'' creuats per a la comparació de característiques locals de les imatges. La resta està dedicat a formular ambdós problemes d’associació de característiques d’imatge i registre de conjunt de punts com a instàncies del problema d’emparellament de grafs. En tots els casos proposem algoritmes aproximats per solucionar aquests problemes i ens comparem amb un nombre de mètodes existents pertanyents a diferents àrees com eliminadors d’“outliers”, mètodes de registre de conjunts de punts i altres mètodes d’emparellament de grafs. Els experiments mostren que en la majoria de casos els mètodes proposats superen a la resta. En ocasions els mètodes proposats o bé comparteixen el millor rendiment amb algun mètode competidor o bé obtenen resultats lleugerament pitjors. En aquests casos, els mètodes proposats normalment presenten temps computacionals inferiors

Planning and Navigation in Dynamic Environments for Mobile Robots and Micro Aerial Vehicles

Reliable and robust navigation planning and obstacle avoidance is key for the autonomous operation of mobile robots. In contrast to stationary industrial robots that often operate in controlled spaces, planning for mobile robots has to take changing environments and uncertainties into account during plan execution. In this thesis, planning and obstacle avoidance techniques are proposed for a variety of ground and aerial robots. Common to most of the presented approaches is the exploitation of the nature of the underlying problem to achieve short planning times by using multiresolution or hierarchical approaches. Short planning times allow for continuous and fast replanning to take the uncertainty in the environment and robot motion execution into account. The proposed approaches are evaluated in simulation and real-world experiments. The first part of this thesis addresses planning for mobile ground robots. One contribution is an approach to grasp and object removal planning to pick objects from a transport box with a mobile manipulation robot. In a multistage process, infeasible grasps are pruned in offline and online processing steps. Collision-free endeffector trajectories are planned to the remaining grasps until a valid removal trajectory can be found. An object-centric local multiresolution representation accelerates trajectory planning. The mobile manipulation components are evaluated in an integrated mobile bin-picking system. Local multiresolution planning is employed for path planning for humanoid soccer robots as well. The used Nao robot is equipped with only relatively low computing power. A resource-efficient path planner including the anticipated movements of opponents on the field is developed as part of this thesis. In soccer games an important subproblem is to reach a position behind the ball to dribble or kick it towards the goal. By the assumption that the opponents have the same intention, an explicit representation of their movements is possible. This leads to paths that facilitate the robot to reach its target position with a higher probability without being disturbed by the other robot. The evaluation for the planner is performed in a physics-based soccer simulation. The second part of this thesis covers planning and obstacle avoidance for micro aerial vehicles (MAVs), in particular multirotors. To reduce the planning complexity, the planning problem is split into a hierarchy of planners running on different levels of abstraction, i.e., from abstract to detailed environment descriptions and from coarse to fine plans. A complete planning hierarchy for MAVs is presented, from mission planners for multiple application domains to low-level obstacle avoidance. Missions planned on the top layer are executed by means of coupled allocentric and egocentric path planning. Planning is accelerated by global and local multiresolution representations. The planners can take multiple objectives into account in addition to obstacle costs and path length, e.g., sensor constraints. The path planners are supplemented by trajectory optimization to achieve dynamically feasible trajectories that can be executed by the underlying controller at higher velocities. With the initialization techniques presented in this thesis, the convergence of the optimization problem is expedited. Furthermore, frequent reoptimization of the initial trajectory allows for the reaction to changes in the environment without planning and optimizing a complete new trajectory. Fast, reactive obstacle avoidance based on artificial potential fields acts as a safety layer in the presented hierarchy. The obstacle avoidance layer employs egocentric sensor data and can operate at the data acquisition frequency of up to 40 Hz. It can slow-down and stop the MAVs in front of obstacles as well as avoid approaching dynamic obstacles. We evaluate our planning and navigation hierarchy in simulation and with a variety of MAVs in real-world applications, especially outdoor mapping missions, chimney and building inspection, and automated stocktaking.Planung und Navigation in dynamischen Umgebungen für mobile Roboter und Multikopter Zuverlässige und sichere Navigationsplanung und Hindernisvermeidung ist ein wichtiger Baustein für den autonomen Einsatz mobiler Roboter. Im Gegensatz zu klassischen Industrierobotern, die in der Regel in abgetrennten, kontrollierten Bereichen betrieben werden, ist es in der mobilen Robotik unerlässlich, Änderungen in der Umgebung und die Unsicherheit bei der Aktionsausführung zu berücksichtigen. Im Rahmen dieser Dissertation werden Verfahren zur Planung und Hindernisvermeidung für eine Reihe unterschiedlicher Boden- und Flugroboter entwickelt und vorgestellt. Den meisten beschriebenen Ansätzen ist gemein, dass die Struktur der zu lösenden Probleme ausgenutzt wird, um Planungsprozesse zu beschleunigen. Häufig ist es möglich, mit abnehmender Genauigkeit zu planen desto weiter eine Aktion in der Zeit oder im Ort entfernt ist. Dieser Ansatz wird lokale Multiresolution genannt. In anderen Fällen ist eine Zerlegung des Problems in Schichten unterschiedlicher Genauigkeit möglich. Die damit zu erreichende Beschleunigung der Planung ermöglicht ein häufiges Neuplanen und somit die Reaktion auf Änderungen in der Umgebung und Abweichungen bei den ausgeführten Aktionen. Zur Evaluation der vorgestellten Ansätze werden Experimente sowohl in der Simulation als auch mit Robotern durchgeführt. Der erste Teil dieser Dissertation behandelt Planungsmethoden für mobile Bodenroboter. Um Objekte mit einem mobilen Roboter aus einer Transportkiste zu greifen und zur Weiterverarbeitung zu einem Arbeitsplatz zu liefern, wurde ein System zur Planung möglicher Greifposen und hindernisfreier Endeffektorbahnen entwickelt. In einem mehrstufigen Prozess werden mögliche Griffe an bekannten Objekten erst in mehreren Vorverarbeitungsschritten (offline) und anschließend, passend zu den erfassten Objekten, online identifiziert. Zu den verbleibenden möglichen Griffen werden Endeffektorbahnen geplant und, bei Erfolg, ausgeführt. Die Greif- und Bahnplanung wird durch eine objektzentrische lokale Multiresolutionskarte beschleunigt. Die Einzelkomponenten werden in einem prototypischen Gesamtsystem evaluiert. Eine weitere Anwendung für die lokale Multiresolutionsplanung ist die Pfadplanung für humanoide Fußballroboter. Zum Einsatz kommen Nao-Roboter, die nur über eine sehr eingeschränkte Rechenleistung verfügen. Durch die Reduktion der Planungskomplexität mit Hilfe der lokalen Multiresolution, wurde die Entwicklung eines Planers ermöglicht, der zusätzlich zur aktuellen Hindernisfreiheit die Bewegung der Gegenspieler auf dem Feld berücksichtigt. Hierbei liegt der Fokus auf einem wichtigen Teilproblem, dem Erreichen einer guten Schussposition hinter dem Ball. Die Tatsache, dass die Gegenspieler vergleichbare Ziele verfolgen, ermöglicht es, Annahmen über mögliche Laufwege zu treffen. Dadurch ist die Planung von Pfaden möglich, die das Risiko, durch einen Gegenspieler passiv geblockt zu werden, reduzieren, so dass die Schussposition schneller erreicht wird. Dieser Teil der Arbeit wird in einer physikalischen Fußballsimulation evaluiert. Im zweiten Teil dieser Dissertation werden Methoden zur Planung und Hindernisvermeidung von Multikoptern behandelt. Um die Planungskomplexität zu reduzieren, wird das zu lösenden Planungsproblem hierarchisch zerlegt und durch verschiedene Planungsebenen verarbeitet. Dabei haben höhere Planungsebenen eine abstraktere Weltsicht und werden mit niedriger Frequenz ausgeführt, zum Beispiel die Missionsplanung. Niedrigere Ebenen haben eine Weltsicht, die mehr den Sensordaten entspricht und werden mit höherer Frequenz ausgeführt. Die Granularität der resultierenden Pläne verfeinert sich hierbei auf niedrigeren Ebenen. Im Rahmen dieser Dissertation wurde eine komplette Planungshierarchie für Multikopter entwickelt, von Missionsplanern für verschiedene Anwendungsgebiete bis zu schneller Hindernisvermeidung. Pfade zur Ausführung geplanter Missionen werden durch zwei gekoppelte Planungsebenen erstellt, erst allozentrisch, und dann egozentrisch verfeinert. Hierbei werden ebenfalls globale und lokale Multiresolutionsrepräsentationen zur Beschleunigung der Planung eingesetzt. Zusätzlich zur Hindernisfreiheit und Länge der Pfade können auf diesen Planungsebenen weitere Zielfunktionen berücksichtigt werden, wie zum Beispiel die Berücksichtigung von Sensorcharakteristika. Ergänzt werden die Planungsebenen durch die Optimierung von Flugbahnen. Diese Flugbahnen berücksichtigen eine angenäherte Flugdynamik und erlauben damit ein schnelleres Verfolgen der optimierten Pfade. Um eine schnelle Konvergenz des Optimierungsproblems zu erreichen, wurde in dieser Arbeit ein Verfahren zur Initialisierung entwickelt. Des Weiteren kommen Methoden zur schnellen Verfeinerung des Optimierungsergebnisses bei Änderungen im Weltzustand zum Einsatz, diese ermöglichen die Reaktion auf neue Hindernisse oder Abweichungen von der Flugbahn, ohne eine komplette Flugbahn neu zu planen und zu optimieren. Die Sicherheit des durch die Planungs- und Optimierungsebenen erstellten Pfades wird durch eine schnelle, reaktive Hindernisvermeidung gewährleistet. Das Hindernisvermeidungsmodul basiert auf der Methode der künstlichen Potentialfelder. Durch die Verwendung dieser schnellen Methode kombiniert mit der Verwendung von nicht oder nur über kurze Zeiträume aggregierte Sensordaten, ermöglicht die Reaktion auf unbekannte Hindernisse, kurz nachdem diese von den Sensoren wahrgenommen wurden. Dabei kann der Multikopter abgebremst oder gestoppt werden, und sich von nähernden Hindernissen entfernen. Die Komponenten der Planungs- und Hindernisvermeidungshierarchie werden sowohl in der Simulation evaluiert, als auch in integrierten Gesamtsystemen mit verschiedenen Multikoptern in realen Anwendungen. Dies sind insbesondere die Kartierung von Innen- und Außenbereichen, die Inspektion von Gebäuden und Schornsteinen sowie die automatisierte Inventur von Lägern

Optimal manoeuvres and aeroservoelastic co-design of very flexible wings

The single shooting method is applied to the optimal control of very flexible aeroelastic wings and the combined structural and control design (co-design) of geometrically nonlinear beam models in vacuum. As large deflections occur, the dynamical properties of these systems can undergo substantial changes. Efficient actuation strategies require characterising, and possibly exploiting, these phenomena. With this purpose, geometrically-nonlinear models are built using composite beams and an unsteady vortex-lattice aerodynamics description. Optimal control is employed to identify actuations time-histories. Numerical solutions are obtained via single-shooting and sequential quadratic programming upon parametrisation of the control input. The approach is also extended to assess the feasibility of an integrated design strategy for active geometrically-nonlinear structures. Numerical studies are first presented for a very flexible actuated pendulum with large rigid-body motion. The impact of local (B-splines) and global (discrete sines) basis functions is investigated for increasing levels of actuation authority, underlining the importance of the time-frequency resolution of the parametrisation on the convergence properties and outcome quality of the process. Locking between control and structural vibrations around specific design points is found, thus highlighting the limitations of a sequential design approach. Simultaneous designing of control law and structure is seen, instead, to explore more efficiently larger portions of the design space. The lateral manoeuvring of very flexible partially-supported wings is then considered. A flight-dynamics model based on elastified stability derivatives is shown to capture the relevant dynamics either under slow actuation or for stiff wings, and it is hence used as a reference. Embedding the full aeroelastic description into the optimisation framework expands the space of achievable manoeuvres, allowing for quick wing response with low structural vibrations or large lateral forces with minimal lift losses.Open Acces

Sparse Bayesian information filters for localization and mapping

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and Mapping (SLAM) that addresses the problem of scalability in large environments. We describe an estimation-theoretic algorithm that achieves significant gains in computational efficiency while maintaining consistent estimates for the vehicle pose and the map of the environment. We specifically address the feature-based SLAM problem in which the robot represents the environment as a collection of landmarks. The thesis takes a Bayesian approach whereby we maintain a joint posterior over the vehicle pose and feature states, conditioned upon measurement data. We model the distribution as Gaussian and parametrize the posterior in the canonical form, in terms of the information (inverse covariance) matrix. When sparse, this representation is amenable to computationally efficient Bayesian SLAM filtering. However, while a large majority of the elements within the normalized information matrix are very small in magnitude, it is fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability benefits of a sparse parametrization by explicitly pruning these weak links in an effort to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information Filter (SEIF), which has laid much of the groundwork concerning the computational benefits of the sparse canonical form. The thesis performs a detailed analysis of the process by which the SEIF approximates the sparsity of the information matrix and reveals key insights into the consequences of different sparsification strategies. We demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent, suffering from exaggerated confidence estimates. This overconfidence has detrimental effects on important aspects of the SLAM process and affects the higher level goal of producing accurate maps for subsequent localization and path planning. This thesis proposes an alternative scalable filter that maintains sparsity while preserving the consistency of the distribution. We leverage insights into the natural structure of the feature-based canonical parametrization and derive a method that actively maintains an exactly sparse posterior. Our algorithm exploits the structure of the parametrization to achieve gains in efficiency, with a computational cost that scales linearly with the size of the map. Unlike similar techniques that sacrifice consistency for improved scalability, our algorithm performs inference over a posterior that is conservative relative to the nominal Gaussian distribution. Consequently, we preserve the consistency of the pose and map estimates and avoid the effects of an overconfident posterior. We demonstrate our filter alongside the SEIF and the standard EKF both in simulation as well as on two real-world datasets. While we maintain the computational advantages of an exactly sparse representation, the results show convincingly that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the original Gaussian distribution as produced by the EKF, but at much less computational expense. The thesis concludes with an extension of our SLAM filter to a complex underwater environment. We describe a systems-level framework for localization and mapping relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped with a forward-looking sonar. The approach utilizes our filter to fuse measurements of vehicle attitude and motion from onboard sensors with data from sonar images of the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a ship hull

Approximation d’espérances conditionnelles guidée par le problème en optimisation stochastique multi-étapes

RÉSUMÉ: Dans cette thèse, nous considérons d’une façon générale la résolution de problèmes d’optimisation stochastique multi-étapes. Ces derniers apparaissent dans de nombreux domaines d’application tels que la finance, l’énergie, la logistique, le transport, la santé, etc. Ils sont généralement insolubles de façon exacte car ils contiennent des espérances mathématiques qui ne peuvent pas être calculées analytiquement. Il est donc nécessaire de considérer pour cela des méthodes numériques. Nous nous intéressons particulièrement aux méthodes de génération d’arbres de scénarios. Ceux-ci remplacent le processus stochastique sous-jacent au problème afin de ramener ce dernier à une taille raisonnable permettant sa résolution pratique. Numériquement, cela permet de remplacer les opérateurs d’espérance qui apparaissent dans la formulation originale du problème (et qui tiennent compte de toutes les scénarios possibles en les pondérant avec une certaine densité de probabilité), par des sommes finies qui, pour leur part, ne prennent en compte qu’un sous-ensemble de scénarios seulement. Cette approximation permet ensuite à un ordinateur de résoudre le problème discrétisé à l’aide de solveurs classiques d’optimisation. L’arbre de scénarios doit satisfaire un compromis entre la qualité d’approximation, qui voudrait que l’arbre soit le plus grand possible, et la complexité de résolution du problème discrétisé qui, à l’inverse, voudrait qu’il soit le plus petit possible. Alors que ce compromis est relativement facile à satisfaire pour les problèmes à deux étapes, il l’est beaucoup moins pour les problèmes multi-étapes (c.-à-d. à partir de trois étapes). Ceci est dû à la nécessité de considérer des structures d’arbres dont la taille (le nombre de noeuds) croît exponentiellement avec le nombre d’étapes. Dans ce contexte multi-étapes, la recherche d’un compromis satisfaisant entre qualité et complexité a mené la communauté d’optimisation stochastique à développer de nombreuses approches de génération d’arbres de scénarios basées sur des justifications théoriques ou pratiques différentes. Ces justifications portent essentiellement sur la qualité d’approximation du processus stochastique par l’arbre de scénarios. Pour cette raison, ces approches sont dites guidées par la distribution, étant donné qu’elles souhaitent reproduire le mieux possible –suivant leur propre critère de qualité– la distribution du processus stochastique (ou certaines propriétés de celle-ci). Prendre en compte la distribution permet sous certaines conditions assez faibles d’assurer la consistance de la méthode de résolution. Pour cette raison, ces méthodes sont utilisées avec succès dans de nombreux problèmes. Cependant, cette stratégie ne permet pas de tirer profit de la structure même du problème d’optimisation, par exemple la variabilité de sa fonction objectif ou l’influence de ses contraintes, qui joue aussi un rôle important dans la qualité d’approximation. La prise en compte de ces caractéristiques permettrait de construire des arbres de scénarios plus adaptés aux problèmes et ainsi de satisfaire un meilleur compromis entre qualité et complexité. En pratique, cela permettrait de pouvoir résoudre des problèmes avec un plus grand nombre d’étapes.----------ABSTRACT: In this thesis, we consider solution methods for general multistage stochastic optimization problems. Such problems arise in many fields of application, including finance, energy, logistic, transportation, health care, etc. They generally do not have closed-form solutions since they feature mathematical expectations, which cannot be computed exactly in most applications. For this reason, it is necessary to consider solutions through numerical methods. One of them, which is the focus of this thesis, is the scenario-tree generation approach. Its aim is to substitute the underlying stochastic process with a finite subset of scenarios so as to replace the conditional expectations with their finite sum estimators. This reduces the size of the problem, which is then solved using some generic optimization solvers. The generation of scenario trees is subject to a trade-off between the approximation accuracy and the complexity of the resulting discretized problem. The former tends to increase the number of scenarios, whereas the latter tends to decrease it. This trade-off turns out to be fairly easy to satisfy when dealing with two-stage problems. However, it becomes much more difficult when problems are multistage, that is, when they have 3 stages of more. This stems from the fact that multistage problems require specific tree structures whose size (the number of nodes) grow exponentially as the number of stages increases. For this reason, a lot of attention has been drawn on generating scenario trees in the multistage setting. Many methods have been developed based on different theoretical or practical grounds. Most of them can be described as distribution-driven, as they aim at approximating the distribution of the stochastic process (or some features of it), according to their own idea of what a good approximation is. The distribution-driven strategy allows to have consistent scenario-tree estimators under some weak conditions. For this reason, these methods have been successfully applied to many problems. However, it does not allow to capitalize on some specific features of the multistage problem (e.g., the variability of its revenue function or the influence of its constraints), although they play an important role in the scenario-tree approximation quality as well. Taking them into account would lead to more suitable scenario trees that may satisfy a better trade-off between accuracy and complexity. This, in turn, may allow to consider problems with more stages. In this thesis, we introduce a new problem-driven scenario-tree generation approach. It takes into account the whole structure of the optimization problem through its stochastic process, revenue (or cost) function and sets of constraints. This approach is developed in a general setting of multistage problems, hence it is not tied to a particular application or field of applications. The conditions that are introduced along the lines of this thesis about the revenue function, constraints, or probability distribution essentially aims at making sure that the problems is mathematically well-defined

Efficient computational techniques for mistuning analysis of bladed discs:A review

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