Dissertations / Theses on the topic 'Inverse linear model'

Dans un monde industriel marqué par un contexte économique difficile, les entreprises se doivent d’étudier toutes les possibilités de réduction de coûts et d’optimisation de leur chaîne logistique. Un des champs récents d’optimisation développé dans la littérature concerne le concept de logistique inverse. Cette logistique représente la gestion des flux traversant une chaîne logistique dans le sens inverse des flux traditionnels. On y retrouve des activités liées au recyclage, à la réparation ou encore à la réutilisation de produits. Au sein de la Chaire Supply Chain, nous nous sommes donc intéressés à l’optimisation de la gestion de ces flux de retours, avec les contenants réutilisables comme objet d’étude intéressant pour nos différents partenaires. Dans ce sens, après avoir passé en revue la littérature sur le concept général de la logistique inverse, nous développons un ensemble de modèles recouvrant les combinaisons mono ou multi niveaux, mono ou multi périodes et mono ou multi contenants afin d’optimiser ces retours au sein de chaînes logistiques déjà définies. Ces modèles sont par la suite appliqués, soit fictivement pour un des modèles mono-période résolu grâce à une heuristique de décomposition développée pour des réseaux logistiques de grande taille, soit réellement chez nos partenaires pour les modèles multi-périodes résolus de façon exacte. Le but de ces applications étant d’utiliser ces modèles théoriques dans un contexte réel d’entreprise et d’en dégager les possibles bénéfices économiques mais également environnementaux grâce à la prise en compte des émissions liées au transport et au cycle de vie de ces contenants
In an industrial world touched by a complicated economic environment, companies need to explore all opportunities for cost reduction and supply chain optimization. A recent optimization field developed in the literature concerns the concept of reverse logistics. This concept deals with the flows management through a supply chain in the opposite direction to the traditional one. It includes activities related to recycling, repair or products reuse. In partnership with the industrial of the “Chaire Supply Chain”, we are interested in optimizing these reverse flows by focusing more particularly on reusable containers. For that, we propose a literature review on the general concept of reverse logistics and develop a set of models covering combinations between single and multi-levels, single and multi-periods and single and multi-containers problems in order to optimize this type of returns within already defined supply chains. These models are then applied, either in a fictive way for a single-period one solved by a decomposition heuristic proposed for large logistics networks, or in a real way for multi-period models solved exactly and applied to our partners problematic. The purpose of these applications is to use these theoretical models in a real business in order to identify economic benefits but also environmental ones by taking into account emissions from these containers transportation and manufacturing

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the "classical" approach and the "inverse" regression approach. Both of these models are static models and are used to estimate "exact" measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe the measurement. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM framework is used to capture the time-varying parameters that may be changing or drifting over time. Dynamic based approaches to the linear, nonlinear, and multivariate calibration problem are presented in this dissertation. Simulation studies are conducted where the dynamic models are compared to some well known "static'" calibration approaches in the literature from both the frequentist and Bayesian perspectives. Applications to microwave radiometry are given.

Depuis plusieurs années, les évolutions considérables survenues au niveau des moyens de calcul à disposition ont entraîné de nouvelles pratiques de simulation des structures mécaniques. Parmi ces nouvelles pratiques celle qui motive ces travaux de thèse est le paradigme Dynamic Data Driven Application Systems (DDDAS). L’idée fondatrice de cette approche est de mettre en place un dialogue entre un système physique et son modèle numérique. L’objectif est alors de (i) permettre un recalage du modèle numérique à l’aide de mesures faites sur le système physique ; (ii) contrôler l’évolution du système physique à l’aide de la prédiction faite par la simulation numérique. La difficulté majeure est de réaliser ce dialogue en temps réel. Ces travaux de thèse se focalisent sur l’étape de recalage de modèle du paradigme DDDAS. La problématique est alors de développer des méthodes et outils de résolution de problèmes inverses prenant en compte diverses contraintes à savoir : (i) une robustesse vis-à-vis des données corrompues ; (ii) une généricité permettant de considérer une grande variété de problèmes et de modèles mécaniques ; (iii) un temps de calcul réduit afin de tendre vers un recalage de modèle en temps réel. Le point de départ de ces travaux est l’Erreur en Relation de Comportement modifiée, approche énergétique dédiée à la résolution des problèmes inverses en mécanique, s’étant notamment illustrée par sa grande robustesse vis-à-vis des bruits de mesure. Dans un premier temps, afin de garantir un processus d’identification rapide, nous avons couplé l’Erreur en Relation de Comportement modifiée avec la réduction de modèle PGD dans le cadre de modèle linéaire, permettant ainsi de mettre en place un processus d’identification rapide et automatique. Ensuite, dans le but d’être appliquée au paradigme DDDAS, nous avons développé une démarche d’identification reposant sur un processus d’assimilation de données (le filtre de Kalman) et utilisant l’Erreur en Relation de Comportement modifiée comme opérateur d’observation toujours dans le cadre de problèmes linéaires. Nous avons ensuite étendu cette méthode d’assimilation de données à la problématique de l’identification de champs de paramètres en introduisant une séparation des discrétisations spatiales et des outils provenant de l’adaptation de maillage. Nous avons ensuite abordé la problématique des modèles mécaniques non-linéaires, au travers de modèles d’endommagement et de visco-plasticité. Pour cela nous avons dans un premier temps reformulé et étendu le concept d’Erreur en Relation de Comportement modifiée à ce cadre non-linéaire matériau et nous avons mis en place un processus de résolution dédié, s’inspirant de la méthode LaTIn. Pour finir nous avons introduit cette reformulation de l’Erreur en Relation de Comportement modifiée au sein de la méthode d’assimilation de données développée précédemment afin de traiter le recalage dynamique de modèles non-linéaires
For several years, the considerable changes that have occurredin computing tools have led to new practices in the simulation of mechanical structures. Among them, the motivation for this work is the Dynamic Data Driven Application Systems paradigm (DDDAS). The founding idea of this approach is to establish a dialogue between a physical system and its numericalmodel. The objective is then to (i) allow a calibration of the numerical model by means of measurements performed on the physical system; (ii) control the evolution of the physical system using theprediction given by numerical simulation. The major difficulty is to realize this dialogue in real time. This work focuses on the model updating step of the DDDAS paradigm. The problem is then to develop methods and tools to solve inverse problems taking into account various constraints, namely: (i) robustness with respect to corrupted data; (ii) genericity for considering a wide variety of problems and mechanical models; (iii) a reduced computation time in order to tend towards a real-time model updating.The starting point of this work is the modified Constitutive Relation Error, an energetic approach dedicated to the solution of inverse problems in mechanics, notably illustrated by its robustness with respect to measurement noises. First, in order to guarantee a fast identification process, we have coupled the modified Constitutive Relation Error with the PGD model reduction in the linear model framework, thus enabling a fast and automatic identification process. Then, in order to be applied to the DDDAS paradigm, we have developed an identification method based on a data assimilation process (the Kalman filter) and using the modified Constitutive Relation Error as an observer alwayswithin the framework of linear problems. We have then extended this data assimilation approach to the problem of the identification of parameter fields by introducing a separation of the spatial discretizations and by introducing tools resulting from the mesh adaptation framework. We have then addressed the problem of non-linear mechanical models, through damage and visco-plasticitymodels. To this end, we have first recast and extended the concept of the modified Constitutive Relation Error to this nonlinear material framework and we have implemented a dedicated resolution process, based on the LaTIn method. Finally, we have introduced this reformulation of the modified Constitutive Relation Error in the previously data assimilation method in order to process the model updating of nonlinear models

This thesis summarizes latest findings about municipal solid waste (MSW) modelling. These are used to solve multivariable version of inverse prediction problem. It is not possible to solve such problem analytically, so heuristic framework using regression models and data reconciliation was developed. As a side product, models for MSW modelling using PCA (Principal Component Analysis) and LM (Linear Model) were created. These were compared with heuristic model called RF (Random Forest). Both of these models were also used for per capita MSW modelling. Theoretical parts about generalized linear models, data reconciliation and nonlinear programming are also included.

Une image observee est modelisee comme la convolution d'un noyau de flou du a la turbulence atmospherique par une image originale, a laquelle est ajoutee un bruit d'acquisition. L'objectif de notre etude est la mise en uvre d'une methode de restauration dont la complexite numerique est independante de la taille du noyau de perturbation. Nous proposons une methode de restauration en deux etapes: la premiere etant un filtrage de moindres carres faiblement regularise, la seconde un filtrage markovien. Nous etudions les methodes de deconvolution de moindres carres en proposant une technique de comparaison adaptee a ces methodes. Elles sont lineaires et l'image restauree par celles-ci peut etre separee en un terme de signal et un terme de bruit. L'etude du compromis realise entre ces deux termes permet de comparer les methodes de restauration de moindres carres. Le filtrage de tikhonov-miller apparait comme la methode la plus performante. Nous developpons alors une methode en deux etapes constituee par un filtrage de tikhonov-miller suivit d'un filtrage markovien. La premiere etape deconvolue l'image observee et la deuxieme filtre le bruit de deconvolution. Cette methode en deux etapes est une methode de restauration non lineaire dont la complexite est independante de la taille du noyau de perturbation. Nous comparons les images obtenues avec cette methode en deux etapes avec celles obtenues lorsque le filtrage markovien est remplace par un filtrage de diffusion. Nous adaptons la technique en deux etapes au cas de la deconvolution multi-images. La premiere etape devient une deconvolution par la methode de la pseudo-inverse multi-images, la seconde reste inchangee. Le nombre d'images observees necessaires ainsi que les hyper-parametres de la modelisation markovienne sont determines automatiquement. La methode multi-images permet alors d'obtenir des images restaurees de qualite independante du rapport signal a bruit des images observees

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In this dissertation it is reported the results of a comprehensive comparative study involving six local models applied to the task of learning the inverse kinematics of three redundant robotic arm (planar, PUMA 560 and Motoman HP6). The evaluated algorithms are the following ones: radial basis functions network (RBFN), local model network (LMN), SOMbased local linear mapping (LLM), local linear mapping over k-winners (K-SOM), local weighted regression (LWR) and counter propagation (CP). Each algorithm is evaluated with respect to its accuracy in estimating the joint angles given the cartesian coordinates which comprise end-effector trajectories within the robot workspace. A comprehensive evaluation of the performances of the aforementioned algorithms is carried out based on correlation analysis of the residuals. Finally, hypothesis testing procedures are also executed in order to verifying if there are significant differences in performance among the best algorithms.
Nesta dissertaÃÃo sÃo reportados os resultados de um amplo estudo comparativo envolvendo seis modelos locais aplicados à tarefa de aproximaÃÃo do modelo cinemÃtico inverso de 3 robÃs manipuladores (planar, PUMA 560 e Motoman HP6). Os modelos avaliados sÃo os seguintes: rede de funÃÃes de base radial (RBFN), rede de modelos locais (LMN), mapeamento linear local baseado em SOM (LLM), mapeamento linear local usando K vencedores (KSOM), regressÃo local ponderada (LWR) e rede counterpropagation (CP). Estes algoritmos sÃo avaliados quanto à acurÃcia na estimaÃÃo dos Ãngulos das juntas dos robÃs manipuladores em experimentos envolvendo a geraÃÃo de vÃrios tipos de trajetÃrias no espaÃo de trabalho dos referidos robÃs. Uma avaliaÃÃo abrangente do desempenho de cada algoritmo à feita com base na anÃlise dos resÃduos e testes de hipÃteses sÃo realizados para verificar a semelhanÃa estatistica entre os desempenhos dos melhores algoritmos.

La méiofaune joue un rôle important dans le fonctionnement des habitats benthiques à substrat meuble (ex. flux de matière) en relation avec sa production élevée, sa position trophique intermédiaire et les importants transferts d’énergie vers les niveaux trophiques supérieurs qui y sont lié. Les relations trophiques et les flux de matière organique liés à la méiofaune restent néanmoins mal connus ou peu pris en compte. Afin de mieux appréhender le rôle de la méiofaune, la structure des communautés et les relations trophiques entre les sources de nourriture et ces consommateurs ont été déterminées dans cinq habitats à substrat meuble (i.e., vasière nue, herbier, zone à sables) de la baie de Marennes-Oléron, France, et de la baie de Sylt-Rømø, Allemagne, en tenant compte des variations temporelles. Le peuplement de méiofaune s’est trouvé être dominé par les nématodes et les copépodes benthiques. Les biomasses de microphytobenthos et de matière organique du sédiment sont apparues comme étant deux facteurs structurants pour les communautés. L’utilisation combinée de différents traceurs de la matière (i.e., isotopes stables, acides gras) a démontré que le microphytobenthos et les bactéries étaient les ressources trophiques majeures de la méiofaune dans les cinq habitats étudiés. Les mesures réalisées sur la structure des communautés et les données issues des traceurs de la matière ont été implémentées dans des modèles de réseaux trophiques. Dans tous les habitats, ces modèles ont mis en évidence que le flux de carbone dominant était issu du microphytobenthos, ceci démontrant les très faibles changements de comportements alimentaires malgré les importantes différences de sources trophiques en termes de disponibilité et de production des sources de nourriture entre ces différents habitats. Tous les groupes trophiques de nématodes, à l’exception des déposivores sélectifs, étaient particulièrement sélectifs et s’alimentaient majoritairement à partir de microphytobenthos, ceci étant à l’origine d’une forte production et d’un court temps de renouvellement de la méiofaune. En conclusion, cette thèse démontre le rôle important de la méiofaune dans les habitats à substrat meuble ainsi que l’importance de la relation trophique entre le microphytobenthos et la méiofaune dans le fonctionnement de ces réseaux trophiques
Meiofauna play an important role in ecosystem processes in soft-bottom benthic habitats, e.g. food web dynamics, related to their highproduction, their intermediate trophic position and the energy they transfer towards higher trophic levels. The trophic linkages and flows of organic matter related to the meiofauna remain poorly known or taken into account. To better assess the role of meiofauna, the community structure and trophic relationships between food sources and meiofauna were determined in five intertidal soft-bottom habitats (i.e., mudflat, seagrass bed, sandflat) of the Marennes-Oléron Bay, France, and the Sylt-Rømø Bight, Germany, taking temporal variations into account. Meiofauna communities were dominated by nematodes and benthic copepods. Biomass of microphytobenthos and of sediment organic matter were two of the major drivers of community structure. The combination of trophic markers (i.e., stable isotopes, fatty acids) demonstrated that microphytobenthos and bacteria were the major food sources of meiofauna in the five habitats. Information from community structure assessments and trophic marker analyses were implemented in food web models. In all habitats, these models demonstrated that the main flow of carbon to meiofauna originated from microphytobenthos, highlighting negligible changes in meiofauna feeding behavior besides the large differences in availability and productivity of food sources between these habitats. All trophic groups of nematodes, except for selective deposit feeding nematodes, were highly selective and mainly fed on microphytobenthos, resulting in a high production and a short turn-over time of meiofauna. In conclusion, this thesis demonstrated the important role of meiofauna in soft-bottom habitats as well as the importance of the trophic pathway from microphytobenthos to meiofauna in the functioning of these food webs

L'etude porte sur la resolution de problemes de moindres carres non lineaires rencontres dans le domaine des ecoulements oceaniques a grande echelle. L'originalite de ce travail reside dans l'approche qui est faite par la methode du controle optimal plutot que par une technique statistique. Cette methode consiste a minimiser une fonctionnelle correspondant au probleme de moindre carre etudie, le minimum de cette optimisation etant une solution du probleme. Lors des applications numeriques, le gradient de cette fonctionnelle n'est pas calcule par differences finies mais a l'aide du modele adjoint. La premiere etude de cette these concerne l'estimation des conditions initiales manquantes de modeles oceaniques tels que ceux de saint-venant, stokes et boussinesq a l'aide de donnees partielles sur l'etat du systeme. Cette etude theorique faite essentiellement en lineaire est suivie d'une application reelle, l'initialisation d'un modele shallow water non lineaire avec des donnees d'altimetrie du satellite geosat. La troisieme etude traite de l'initialisation d'un modele non lineaire de boussinesq quasi stationnaire avec des donnees de temperature et de salinite uniquement. Cette etude theorique est suivie d'une experience numerique d'initialisation d'un modele operationnel de simulation oceanique tridimensionnelle a l'aide de donnees in situ de temperature et de climatologie de temperature et de salinite. Les resultats theoriques partiels ainsi que les experiences numeriques montrent que la methode s'applique de maniere satisfaisante et qu'elle pourra etre utilisee de maniere operationnelle ainsi qu'en mode recherche pour ameliorer notre vision de l'ocean et parfaire sa description

Linear time-invariant models are widely used in the control community. They often serve as approximations of nonlinear systems. For control purposes linear approximations are often good enough since feedback control systems are inherently robust to model errors. In this thesis some of the possibilities for linear time-varying modeling are studied. In the thesis it is shown that the balanced truncation procedure can be applied to reduce the order of linear time-varying systems. Many of the attractive properties of balanced truncation for time-invariant systems can be generalized into the time-varying framework. For example, it is shown that a truncated input-output stable system will be input-output stable, and computable simple worst-case error bounds are derived. The method is illustrated with model reduction of a nonlinear diesel exhaust catalyst model. It is also shown that linear time-periodic models can be used for analysis of systems with power converters. Power converters produce harmonics in the power grids and give frequency coupling that cannot be modeled with standard time-invariant linear models. With time-periodic models we can visualize the coupling and also use all the available tools for linear time-varying systems, such as balanced truncation. The method is illustrated on inverter locomotives.
QC 20120208

"This project utilized generalized estimating equations and general linear modeling to model learning curves for sonographer performance in emergency ultrasonography. Performance was measured in two ways: image quality (interpretable vs. possible hindrance in interpretation) and agreement of findings between the sonographer and an expert reviewing sonographer. Records from 109 sonographers were split into two data sets-- training (n=50) and testing (n=59)--to conduct exploratory analysis and fit the final models for analysis, respectively. We determined that the number of scans of a particular exam type required for a sonographer to obtain quality images on that exam type with a predicted probability of 0.9 is highly dependent upon the person conducting the review, the indication of the scan (educational or medical), and the outcome of the scan (whether there is a pathology positive finding). Constructing family-wise 95% confidence intervals for each exam type demonstrated a large amount of variation for the number of scans required both between exam types and within exam types. It was determined that a sonographer's experience with a particular exam type is not a significant predictor of future agreement on that exam type and thus no estimates were made based on the agreement learning curves. In addition, we concluded based on a type III analysis that when already considering exam type related experience, the consideration of experience on other exam types does not significantly impact the learning curve for quality. However, the learning curve for agreement is significantly impacted by the additional consideration of experience on other exam types."

Nous avons d’abord étudié les rôles de la variabilité interne (telle que l’IPO) et des forçages externes dans le refroidissement régional dans la zone d’upwelling du Pérou-Chili et les mécanismes associés. Les résultats montrent que l’expansion de la cellule de Hadley dans l’hémisphère Sud en réponse aux forçages anthropiques est un résultat robuste dans nos grands ensembles d’attribution du modèle IPSL-CM5A et les observations et est responsable de l’intensification de l’upwelling depuis les années 80s. Celle-ci se traduit par une intensification des alizés et de l’upwelling le long des côtes Chiliennes et un approfondissement de la couche de mélange qui s’oppose régionalement au signal de réchauffement climatique dans le Pacifique Sud-Est. La fenêtre d’observation instrumentale restreinte limite néanmoins notre compréhension du rôle de la dynamique naturelle dans les changements observés. Nous proposons dans la seconde partie une méthode d’assimilation de données dans le modèle de l’IPSL permettant de reconstruire la variabilité naturelle passée. Ce type de méthode est confronté à un problème de dégénérescence associé à la résolution d’un problème de grande dimension avec un nombre de particules restreint. Pour lever ce verrou un filtre particulaire avec ré-échantillonnage est proposé, utilisant un émulateur statistique du modèle de l’IPSL (LIM) comme modèle d’intégration. La validation de cette nouvelle méthode baptisée SIR-LIM permet aujourd’hui d’envisager la reconstruction de la variabilité climatique des siècles passés par l’assimilation d’observations et de proxys dans les modèles de classe CMIP tout en préservant la cohérence physique le long de la simulation
Using large ensembles of IPSLCM5A model simulations, we first investigate the roles of internal variability (and in particular the IPO) and external forcing in driving recent Peru-Chile regional cooling. The simulations reproduce the relative cooling, in response to an externally-forced southerly wind anomaly, which strengthens the upwelling off Chile in recent decades. This southerly wind anomaly results from the expansion of the Southern Hemisphere Hadley Cell in response to increasing greenhouse gases and stratospheric ozone depletion since ~1980. An oceanic heat budget confirms that the wind-forced upwelling dominates the cooling near the coast while a wind-forced deepening of the mixed layer drives the offshore cooling, irrespectively of the IPO phase, hence indicating the preeminent role of external forcing. Constraining the climate sensitivity from observations remains however fraught with uncertainties due to the limited instrumental window of observation. In a second part, a data assimilation method is developed to reconstruct past natural variability relying on a particles filter using CMIP-class climate models. Such method is confronted with a problem of degeneracy associated with the resolution of a large problem with a limited number of particles. This issue has been resolved using a statistical emulator of the IPSL model (LIM) as an integration model in a particle filter with resampling. The validation of this new method, called SIR-LIM, allows the reconstruction of the climate variability of the past centuries by assimilating observations and proxy records into a CMIP-class coupled model while preserving the physical coherence along the simulation

The aim of the thesis was to study the Energy Models of Linear Axes with Ball Screws and Servo Drives, to analyze the individual parts of the axis with respect to losses, the methodology of calculating the losses on the electrical part and the mechanical part of the drive and creating a complex algorithm that calculates the energy consumed for the specified motion. The thesis is divided into a theoretical and practical part, where the theoretical part is divided into the treatise on the electrical part of the axis and its losses and the part that deals with the mechanical part and its losses. The calculation is divided into the basic verification algorithm and the calculation on the given example. Each calculation is calculated for both linear acceleration and S-curve acceleration. For both types of acceleration, the result of energy and its course over time is also the waveforms of position, velocity, acceleration, angular acceleration, moments, powers, power, speed and currents over time.

O estudo da estabilidade e desempenho em sistemas de controle é um tópico relevante na teoria de sistemas. Quando são assumidas incertezas no modelo da planta, existe uma maior dificuldade para garantir um nível de desempenho adequado do sistema dinâmico e a estabilidade pode ser comprometida. Neste trabalho são utilizados um regulador linear quadrático robusto e um filtro de Kalman robusto combinados em uma única formulação para tratar de sistemas dinâmicos incertos em tempo real. O caso de estudo selecionado é o pêndulo invertido. Seus principais desafios de controle encontrados na literatura: estabilização, seguimento e levantamento-captura, serão considerados. Os algoritmos utilizados são motivados pelo fato de que problemas estocásticos podem ser resolvidos por meio de argumentos determinísticos, baseados nos conceitos de função penalidade e mínimos quadrados regularizados. Desta forma, é possível a obtenção do melhor desempenho em contrapartida à máxima influência de incerteza admissível. A análise de desempenho do controlador robusto é realizada por meio de ensaios práticos incluindo incertezas na planta, ruído nos sensores e distúrbios no sinal de controle do pêndulo.
The study of stability and performance in control systems is a relevant topic in systems theory. When uncertainties are considered in the model of the plant, there is a greater difficulty in ensuring an appropriate performance level of the dynamic system, plus, the stability could be compromised as well. In this dissertation a robust linear quadratic regulator and a robust Kalman filter are used in a unified manner to deal with uncertain dynamic systems in real time. The selected case study is the inverted pendulum. Its main control challenges found in the literature will be considered: stabilization, tracking and catching swing-up. The used algorithms are motivated by the fact that stochastic problems can be solved through deterministic arguments based on the concepts of penalty function and regularized least-squares. Thus, it is possible to obtain an optimal performance for the maximum acceptable uncertainty. The performance analysis of the robust control is carried out by practical experiments including uncertainties in the plant, noise in the sensors and disturbance in the pendulum control signal.

En los últimos años la Logística Inversa se ha hecho relevante no solo para el mundo académico sino también para el empresarial. Las empresas dan cada día más importancia a esta área, debido a los factores medioambientales y a los beneficios derivados del mejoramiento de su proceso de devoluciones. Así mismo, para tener unos procesos de Logística Inversa eficientes y exitosos, es necesaria la colaboración entre los miembros de la cadena de suministro. Esta tesis se concentra en ambos aspectos, Colaboración y Logística Inversa.
El propósito de esta tesis es doble; primero, analizar los problemas que sufren hoy en día las empresas en esta área, partiendo de una perspectiva general, y posteriormente analizando la industria editorial española. En segundo lugar, nosotros proponemos cuatro modelos matemáticos concernientes a los problemas de planificación que presentan las empresas cuando incorporan las devoluciones, y finalmente proponemos unas metodologías para solucionarlos.
During last years Reverse Logistics has become a relevant topic not only for academics but also for the business world. Companies are giving each day more and more importance to this field, because the environmental issues and the benefits that the company can obtain by the improvement of their return's processes. To obtain a successful and efficient Reverse Logistics processes there exist the need to collaborate along the supply chain. This thesis focuses on both of these two topics, Collaboration and Reverse Logistics.
The aim of this thesis is twofold; first, we try to understand the returns processes' problems that companies are facing today from the management point of view, from a general perspective and afterwards on the editorial industry. Secondly, we propose some mathematical models and solution methods related to real planning problems faced by the companies when the returns are incorporated.

La compréhension et la prédiction du comportement vibro-acoustique des systèmes légers bois du bâtiment constitue un enjeu scientifique d'actualité. En 2015 une étude montrait encore que presque la moitié de ces systèmes constructifs n'offrait pas satisfaction. Un modèle prédictif à l'échelle du bâtiment, en cours de normalisation, permet de prendre en compte la performance individuelle des différents systèmes séparatifs pour remonter à un niveau de performance globale. La difficulté scientifique réside alors dans l'évaluation de la performance individuelle associée à chaque conception admissible, dans un vaste ensemble de systèmes techniquement réalisables. Dans cette recherche, une méthodologie est proposée pour la construction de modèles numériques capables de prendre en compte, aux basses fréquences, la complexité et la diversité des systèmes bois constitués de multiples plaques, poutres, cavités acoustiques et matériaux poroélastiques. En accord avec les procédures d'évaluation normalisées, des modèles déterministes pour les excitations mécaniques du système sont construits. Une approche probabiliste est alors développée en réponse à la problématique des incertitudes liées à la construction légère. Ainsi, en résolvant un problème stochastique inverse utilisant des données expérimentales pour identifier les hyperparamètres de modèles probabilistes développés, il est possible de quantifier la propagation des incertitudes du système à la performance prédite en conditions de laboratoire. Par suite, des configurations optimales, robustes aux incertitudes, sont recherchées. Du fait de la nature combinatoire du problème d'optimisation, un algorithme génétique, particulièrement adapté à un espace de recherche discret ainsi qu'à l'optimisation multi-objectif, est mis en oeuvre. Dans les cas traités, les configurations optimales tendent vers une maximisation de la rigidité structurelle
Being able to understand and predict the vibroacoustic behavior of lightweight wood-based building systems contitute a serious scientific concern. In 2015, acoustic comfort investigation claims that unsatisfactions are expressed with respect to around 50% of such constructions. In particular, low frequency discomfort is target of criticism. A methodology was proposed, currently running through standardisation process, which translates the individual performance of the building systems into a global building performance index. The challenge consequently lies in the prediction of the individual performances in regard to the wide spread of wood based designs. In this research, a methodology is introduced for the construction of computational models able to handle the complexity and diversity of the systems, constituted of multiple boards, stiffeners, cavities and poroelastic media. Structural excitations of the system are constructed according to standard evaluation procedures. Then, a probabilistic approach is undertaken in order to take into account the uncertainty problematic, inherent to lightweight wood based constructions. In particular, stochastic inverse problems are constructed to identify, from experimental measurements, hyperparameters associated with ad hoc probabilistic models. Eventually, uncertainty quantification can be performed in regard to predicted performance in laboratory conditions. Following, robust optimal designs are sought in the presence of uncertainties. No continuous mapping from the search space of the configurations to the space of the fitness functions representative of the objective performance exists and derivatives cannot be defined. By way of consequence, the class of the evolutionnary algorithm, suited to discrete search spaces as well as multi-objective optimisation, is chosen. Considered optimisation problems displayed preferential directions of the genetic algorithm towards stiffest admissible designs

Les données manquantes sont fréquentes dans les études médicales. Dans les modèles de régression, les réponses manquantes limitent notre capacité à faire des inférences sur les effets des covariables décrivant la distribution de la totalité des réponses prévues sur laquelle porte l'intérêt médical. Outre la perte de précision, toute inférence statistique requière qu'une hypothèse sur le mécanisme de manquement soit vérifiée. Rubin (1976, Biometrika, 63:581-592) a appelé le mécanisme de manquement MAR (pour les sigles en anglais de « manquant au hasard ») si la probabilité qu'une réponse soit manquante ne dépend pas des réponses manquantes conditionnellement aux données observées, et MNAR (pour les sigles en anglais de « manquant non au hasard ») autrement. Cette distinction a des implications importantes pour la modélisation, mais en général il n'est pas possible de déterminer si le mécanisme de manquement est MAR ou MNAR à partir des données disponibles. Par conséquent, il est indispensable d'effectuer des analyses de sensibilité pour évaluer la robustesse des inférences aux hypothèses de manquement.Pour les données multivariées incomplètes, c'est-à-dire, lorsque l'intérêt porte sur un vecteur de réponses dont certaines composantes peuvent être manquantes, plusieurs méthodes de modélisation sous l'hypothèse MAR et, dans une moindre mesure, sous l'hypothèse MNAR ont été proposées. En revanche, le développement de méthodes pour effectuer des analyses de sensibilité est un domaine actif de recherche. Le premier objectif de cette thèse était de développer une méthode d'analyse de sensibilité pour les données longitudinales continues avec des sorties d'étude, c'est-à-dire, pour les réponses continues, ordonnées dans le temps, qui sont complètement observées pour chaque individu jusqu'à la fin de l'étude ou jusqu'à ce qu'il sorte définitivement de l'étude. Dans l'approche proposée, on évalue les inférences obtenues à partir d'une famille de modèles MNAR dits « de mélange de profils », indexés par un paramètre qui quantifie le départ par rapport à l'hypothèse MAR. La méthode a été motivée par un essai clinique étudiant un traitement pour le trouble du maintien du sommeil, durant lequel 22% des individus sont sortis de l'étude avant la fin.Le second objectif était de développer des méthodes pour la modélisation de risques concurrents avec des causes d'évènement manquantes en s'appuyant sur la théorie existante pour les données multivariées incomplètes. Les risques concurrents apparaissent comme une extension du modèle standard de l'analyse de survie où l'on distingue le type d'évènement ou la cause l'ayant entrainé. Les méthodes pour modéliser le risque cause-spécifique et la fonction d'incidence cumulée supposent en général que la cause d'évènement est connue pour tous les individus, ce qui n'est pas toujours le cas. Certains auteurs ont proposé des méthodes de régression gérant les causes manquantes sous l'hypothèse MAR, notamment pour la modélisation semi-paramétrique du risque. Mais d'autres modèles n'ont pas été considérés, de même que la modélisation sous MNAR et les analyses de sensibilité. Nous proposons des estimateurs pondérés et une approche par imputation multiple pour la modélisation semi-paramétrique de l'incidence cumulée sous l'hypothèse MAR. En outre, nous étudions une approche par maximum de vraisemblance pour la modélisation paramétrique du risque et de l'incidence sous MAR. Enfin, nous considérons des modèles de mélange de profils dans le contexte des analyses de sensibilité. Un essai clinique étudiant un traitement pour le cancer du sein de stade II avec 23% des causes de décès manquantes sert à illustrer les méthodes proposées
Missing data are a common occurrence in medical studies. In regression modeling, missing outcomes limit our capability to draw inferences about the covariate effects of medical interest, which are those describing the distribution of the entire set of planned outcomes. In addition to losing precision, the validity of any method used to draw inferences from the observed data will require that some assumption about the mechanism leading to missing outcomes holds. Rubin (1976, Biometrika, 63:581-592) called the missingness mechanism MAR (for “missing at random”) if the probability of an outcome being missing does not depend on missing outcomes when conditioning on the observed data, and MNAR (for “missing not at random”) otherwise. This distinction has important implications regarding the modeling requirements to draw valid inferences from the available data, but generally it is not possible to assess from these data whether the missingness mechanism is MAR or MNAR. Hence, sensitivity analyses should be routinely performed to assess the robustness of inferences to assumptions about the missingness mechanism. In the field of incomplete multivariate data, in which the outcomes are gathered in a vector for which some components may be missing, MAR methods are widely available and increasingly used, and several MNAR modeling strategies have also been proposed. On the other hand, although some sensitivity analysis methodology has been developed, this is still an active area of research. The first aim of this dissertation was to develop a sensitivity analysis approach for continuous longitudinal data with drop-outs, that is, continuous outcomes that are ordered in time and completely observed for each individual up to a certain time-point, at which the individual drops-out so that all the subsequent outcomes are missing. The proposed approach consists in assessing the inferences obtained across a family of MNAR pattern-mixture models indexed by a so-called sensitivity parameter that quantifies the departure from MAR. The approach was prompted by a randomized clinical trial investigating the benefits of a treatment for sleep-maintenance insomnia, from which 22% of the individuals had dropped-out before the study end. The second aim was to build on the existing theory for incomplete multivariate data to develop methods for competing risks data with missing causes of failure. The competing risks model is an extension of the standard survival analysis model in which failures from different causes are distinguished. Strategies for modeling competing risks functionals, such as the cause-specific hazards (CSH) and the cumulative incidence function (CIF), generally assume that the cause of failure is known for all patients, but this is not always the case. Some methods for regression with missing causes under the MAR assumption have already been proposed, especially for semi-parametric modeling of the CSH. But other useful models have received little attention, and MNAR modeling and sensitivity analysis approaches have never been considered in this setting. We propose a general framework for semi-parametric regression modeling of the CIF under MAR using inverse probability weighting and multiple imputation ideas. Also under MAR, we propose a direct likelihood approach for parametric regression modeling of the CSH and the CIF. Furthermore, we consider MNAR pattern-mixture models in the context of sensitivity analyses. In the competing risks literature, a starting point for methodological developments for handling missing causes was a stage II breast cancer randomized clinical trial in which 23% of the deceased women had missing cause of death. We use these data to illustrate the practical value of the proposed approaches

In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning.

Computation of parameters often includes as a part solution of linear system of equations Ax = b. The corresponding pseudoinverse solution depends on the properties of the matrix A and vector b. The singular value decomposition of A can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution x. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of A into account

This thesis describes the process of rebuilding an experimental model of a single pendulum on a cart into the double pendulum on a cart. The control algorithm in MATLAB/Simulink environment for stabilization of the pendulum in the inverse position is designed. For this purpose, LQR state feedback control was implemented. Also method for swinging the pendulum into inverse position from stable state (swing-up) was designed. Feedforward method was utilised for swing-up control. In the thesis, functionality of these algorithms is shown.

Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia
Neste trabalho investigamos o modelo matemático para a reconstrução das propriedades mecânicas de um meio elástico. Com esse objectivo, nós desenvolvemos o modelo matemático para as deformações mecânicas assumindo que os parâmetros que definem as propriedades mecânicas de o meio são conhecidos. O modelo é baseado em equações de elasticidade linear em tempo harmónico. A solução numérica é obtida usando a discretização de elementos finitos em um domínio tridimensional. O desempenho do método é ilustrado com exemplos numéricos. O modelo matemático para resolver este problema direto é a base computacional para abordar o problema inverso que consiste em determinar o conjunto de parâmetros que caracterizam as propriedades mecânicas de um meio conhecendo o campo de deslocamentos para uma dada excitação. Nós consideramos diferentes métodos de otimização para resolver o problema inverso e discutimos o seu desempenho. Nós exibimos vários resultados computacionais que ilustram seu comportamento em termos de precisão e eficiência. O estudo descrito nesta tese foi desenvolvido no âmbito de um projecto mais amplo com o objectivo do desenvolvimento de uma nova técnica de imagiologia que permite mapear in vivo as propriedades mecânicas da retina por Elastografia de Coerência Óptica, que é uma técnica de elastografia baseada na Tomografia de Coerência Óptica. O objectivo final é a descoberta de biomarcadores baseados nas propriedades mecânicas da retina que permitam a deteção precoce, anterior às manifestações clínicas, de processos neurodegenerativos.
In this work we investigate a mathematical model to reconstruct the mechanical properties of an elastic medium. To this end, we develop of a mathematical model for the mechanical deformation assuming that the parameters that define the mechanical properties of the medium are known. The model is based on time-harmonic equations of linear elasticity. The numerical solution is obtained using a finite element discretization in a three-dimentional domain. The performance of the method is illustrated with numerical examples. The mathematical model for solving this direct problem is the computational basis to address the inverse problem which consists of determining the set of parameters that characterize the mechanical properties of the medium knowing the displacement fields for a given excitation. We consider different optimization methods to solve the inverse problem and discuss their performance. We report several computational results which illustrate their behavior in terms of accuracy and efficiency.The study reported in this thesis was developed in the scope of a broader project with the objective of developing a new imaging technique that allows to map in vivo the mechanical properties of the retina by Optical Coherence Elastography, which is an elastography technique based on Optical Coherence Tomography. The final goal is the discovery of biomarkers based on the mechanical properties of the retina that allow the early detection, before clinical manifestations, of neurodegenerative processes.
Universidade de Coimbra - "Optical Coherence Elastography forimaging of the mechanical properties of the retina" PTDC/EMD-EMD/32162/2017

Inverse problems arise in many fields. They are usually ill-posed since they often violate one or more of Hadmard's three conditions for well-posedness: existence, uniqueness and stability. In this thesis, we propose a new method for computing approximate solutions in certain linear inverse problems. We consider linear inverse problems based on integral equations of the first kind. Analysis of Picard's condition reveals that such equations may lead to ill-posed problems which may have no solution satisfying the observed data exactly and stably, but may have infinitely many solutions satisfying the data approximately. To get a unique and stable solution to this kind of inverse problem, we use Tikhonov's Regularization Method. To obtain the best possible approximation to the true model, we should use any and all available information regarding the true model, although we can not expect to get sufficient data. For example, it is standard practice to use the positivity of the model in inverting magnetic and IP data, and to use special weighting functions in solving magnetic problems. The key feature of the present work is a method that exploits the correlation between different model parameters in inverting the geophysical data. To keep different parameters in suitable confidence regions, a new methodology, Combined Inversion, is developed. In combined inversion, different kinds of data are inverted simultaneously. The objective functional imposing the correlation requirement may be neither convex nor quadratic, so corresponding algorithm and code are developed. When the objective functional is not quadratic, we use an iterative method to solve it and approximate the functional with its second order Taylor approximation in each iteration. When the objective functional is not convex, it may have more than one local minimum. To get the minimum which well approximates the true model we should begin with a good initial model. In our case we produce the initial model by solving the combined problem with no correlation requirement. We introduce our method in the context of two practical geophysical inverse problems: the magnetic problem and the Induced Polarization (IP) problem. As we expect, regularization smooths the inverted models, so some model characteristics are lost in the recovered models. Our numerical examples confirm the smoothing effects of the regularization operators. Since magnetic susceptibility and chargeability are negatively correlated, we introduce a nonquadratic, nonconvex "correlation function", whose sub-level sets define confidence regions for the vector of susceptibility and chargeability. Then we require our recovered models to be in the confidence region. The recovered models from combined inversion method are significantly better than those from independent inversion. This method should be useful in practical prospecting when several kinds of data are available and there is some correlation among the parameters. This is the case in mining industry where several kinds of geophysical data are usually measured at the same time and the different parameters producing the data are known to be correlated. If we approximate the correlation with, a reasonable functional, we may reconstruct models satisfying the corresponding correlation.

by Wong Kwok Keung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.
Includes bibliographical references (leaves 50-52).
Chapter 1. --- Introduction --- p.1
Chapter 2. --- Taguchi's methodology in design of experiments --- p.3
Chapter 2.1 --- System design
Chapter 2.2 --- Parameter design
Chapter 2.3 --- Tolerance design
Chapter 3. --- Inverse Gaussian distribution --- p.8
Chapter 3.1 --- Genesis
Chapter 3.2 --- Probability density function
Chapter 3.3 --- Estimation of parameters
Chapter 3.4 --- Applications
Chapter 4. --- Iterative procedures and Derivation of the GLIM 4 macros --- p.21
Chapter 4.1 --- Generalized linear models with varying dispersion
Chapter 4.2 --- Mean and dispersion models for inverse Gaussian distribution
Chapter 4.3 --- Devising the GLIM 4 macro
Chapter 4.4 --- Model fitting
Chapter 5. --- Simulation Study --- p.34
Chapter 5.1 --- Generating random variates from the inverse Gaussian distribution
Chapter 5.2 --- Simulation model
Chapter 5.3 --- Results
Chapter 5.4 --- Discussion
Appendix --- p.46
References --- p.50

碩士
國立臺灣科技大學
電機工程系
100
Linear inverted pendulum model (LPIM) is usually used to generate real-time bipedal locomotion of a humanoid robot because of considering lower computational loads. LIPM uses the operational height of center of mass (CoM) of a biped robot as a primary parameter to generate locomotion trajectory. However, the operational height of CoM is hardly determined because of complicated mechanical structures of biped humanoid robots. Improper operational CoM height setting would induce locomotion stability problems. In addition, extra masses applied on the robot will also alter the operational CoM height setting. Therefore, self-adjustment of the operational CoM height is necessary to the study of bipedal locomotion stability. In this study, a gyro sensor is placed at the center of hips to measure the variation of angular velocities of the robot’s hip plane. The angular velocities in a cycle are further used to define the cycle-based gyro stability index (CBGSI). In addition to evaluate the stability of bipedal locomotion, the CBGSI is also capable of realizing a closed-loop proportional controller to automatically adjust the operational CoM height setting to improve the stability of bipedal locomotion. Finally, a 19-degrees-of-freedom biped humanoid robot with 52 cm in height is developed in this study to evaluate the performance of the proposed operational CoM height adjustment approach based on an omni-locomotion controller.

碩士
國立臺灣科技大學
電機工程系
102
This study presents a field programmable gate array (FPGA) based hardware/software co-design approach to implement a biped locomotion controller for an adult-size humanoid robot. The proposed hardware/software co-design approach is capable of flexibly arranging hardware and software components and modules in systems according to their characteristics to achieve specific application purposes when compared to dedicated microcontroller based solutions. For the software components, this study uses the NIOS II-based system on a programmable chip (SoPC) technique to generate joint angles with respect to reachable parametric locomotion commands. The software components developed in this work are composed of linear inverted pendulum model (LIPM) based center of mass (CoM) trajectory planning, cycloid trajectory planning for the swing foot and inverse kinematics. The main hardware module in this system is a 1 Mbps high speed serial communication module, and it is used to control the smart servo motors used for actuating joint movements of a humanoid robot. To validate the feasibility the proposed FPGA-based biped locomotion controller, this study employs the FIRA HuroCup marathon game as a test environment. The vision system is implemented with a PC-based system. The image processing and recognition approaches are responsible for recognizing the distance and heading angle to the line segment appeared in front of the robot. The distance and heading angle to the line segment information is further used to determine parametric locomotion commands. Finally, the generated parametric locomotion command is transmitted to the FPGA-based biped locomotion controller to control the robot to autonomously follow a specific marathon track.

碩士
國立成功大學
機械工程學系碩博士班
94
The aim of this paper is to apply Model Predictive Control (MPC) to the Parallel-type Double Inverted Pendulum (PDIP). Control of the PDIP is more difficult among the inverted pendulum family. Because the different lengths of the two pendulums give them distinct natural frequencies and the stoke length is limited. Besides, friction is not homogenously distributed on the track. Please bear in mind that one cannot achieve good performance if only state feedback is used. Therefore, we proposed a cascade structure where the inner loop was formed via state feedback and MPC directed the outer loop to enhance position control of the linear motor. In this work, a positive feedback control combined with energy-based control is adopted to swing up the PDIP sequentially, and then is switched to balance control. From simulation and experimental results, the proposed control scheme was successfully applied to the PDIP. Compared with conventional state feedback control, position errors could be reduced by MPC, which overcome the requirement of precise friction model needed in state feedback applications.

碩士
國立成功大學
電機工程學系
103
Design of a teen-sized humanoid robot David Junior and its stable gait pattern generation are proposed in this thesis. First, the system architecture and the design concept of enhanced mechanism are introduced. Second, the Linear Inverted Pendulum Model (LIPM) theory is used for gait pattern generation. Conventional LIPM is assumed that the mass of legs should be much less than the mass of the upper body, the mass of legs is neglected to simplify the model. However, it causes the conflict between LIPM and real models of most current humanoid robots. Hence, this thesis proposes an improved LIPM, and the mass of legs can be included in the model. Therefore, the improved LIPM is more suitable for real situation and application. Third, a training process is utilized to learn a suitable pose of supporting sole, which seriously affects the stability of gait pattern, for stable walking. Finally, acceleration feedback is adopted to overcome the uncertainty factors such as uneven terrain and environment disturbance which cause unstable phenomenon. This real-time closed-loop control increases the robustness of gait pattern. Experimental results demonstrate that the walking speed of David Junior with improved LIPM can achieve 17.4cm/s, and it is 2.4 times faster than previous generation adult-sized robot. Furthermore, David Junior won the all-round championship in Adult-sized HuroCup category of 2014 FIRA RoboWorld Cup.

Multilevel inverters play a major role in the modern day medium and high power energy conversion processes. The classic two level voltage source inverter generates PWM pole voltage output having two levels with strong fundamental component and harmonics centered around the switching frequency and its multiples. With higher switching frequency, its components can be easily filtered and results in better Total harmonic distortion (THD) output voltage and current. But with higher switching frequency, switching loss of power devices increases and electromagnetic interferences also increases. Also in two level inverter, pole voltage switches between zero and DC bus volt-age Vdc. This switching results in high dv=dt and causes EMI and increased stress on the motor winding insulation. The attractive features of multilevel inverters compared to a two level inverter are reduced switching frequency, reduced switching loss, improved volt-age and current THD, reduced dv=dt, etc. Because of these reasons, multilevel invertersultilevelinvertersplayamajorroleinthemoderndaymediumandhighpower find application in electric motor drives, transmission and distribution of power, transportation, traction, distributed generation, renewable energy systems like photo voltaic, hydel power, energy management, power quality, electric vehicle applications, etc. AC motor driven applications are consuming the significant part of the generated electrical energy (more than 60%) around the world. The multilevel inverters are ideal for such applications, since the switching frequency of the devices can be kept low with lower out-put voltage dv=dt. Also by using multilevel inverters, the common mode voltage (CMV) switching can be made zero and associated motor bearing failure can be mitigated. For multilevel inverter topologies, as the number of level increases, the power circuit becomes more complex by the increase in the number of DC power supplies, capacitors, switching devices and associated control circuitry. The main focus of development in multilevel inverter for medium and high power applications is to obtain an optimized number of voltage levels with reduced number of switching devices, capacitors and DC power sources. In this thesis, a new hybrid seven level inverter topology with a single DC supply is proposed with reduced switch count. The inverter is realized by cascading two three level flying capacitor inverters with a half bridge module. Compared to the conventional seven level inverter topologies, the proposed inverter topology uses lesser number of semiconductor devices, capacitors and DC power supplies for its operation. For this topology, capacitor voltage balancing is possible for entire modulation range irrespective of the load power factor. Also capacitor voltage can be controlled over a switching cycle and this result in lowering the capacitor sizing for the proposed topology. A simple hysteresis band based capacitor voltage balancing scheme is implemented for the inverter topology. For a voltage source inverter fed induction motor drive system, the inverter pole voltage is the sum of motor phase voltage and common mode voltage. In induction motors, there exists a parasitic capacitance between stator winding and stator iron, and between stator winding and rotor iron. Common mode voltage with significant magnitude and high frequency switching causes leakage current through these parasitic capacitances and motor bearings. This leakage current can cause ash over of bearing lubricant and corrosion of ball bearings, resulting in an early mechanical failure of the drive system. In this thesis, analysis of extending the linear modulation range of a general n-level inverter by allowing reduced magnitude of common mode voltage (CMV) switching (only Vdc/18) is presented. A new hybrid seven level inverter topology, with a single DC supply and with reduced common mode voltage (CMV) switching is presented in this thesis for the first time. Inverter is operated with zero CMV for modulation index less than 86% and is operated with a CMV magnitude of Vdc/18 to extend the linear modulation range up to 96%. Experimental results are presented for zero CMV operation and for reduced common voltage operation to extend the linear modulation range. A capacitor voltage balancing algorithm is designed utilizing the pole voltage redundancies of the inverter, which works for every sampling instant to correct the capacitor voltage irrespective of load power factor and modulation index. The capacitor voltage balancing algorithm is tested for different modulation indices and for various transient conditions, to validate the proposed topology. In recent years, model predictive control (MPC) using the system model has proved to be a good choice for the control of power converter and motor drive applications. MPC predicts system behavior using a system model and current system state. For cascaded multilevel inverter topologies with a single DC supply, closed loop capacitor voltage control is necessary for proper operation. This thesis presents zero and reduced common mode voltage (CMV) operation of a hybrid cascaded multilevel inverter with predictive capacitor voltage control. For the presented inverter topology, there are redundant switching states for each inverter voltage levels. By using these switching state redundancies, for every sampling instant, a cost function is evaluated based on the predicted capacitor voltages for each phase. The switching state which minimizes cost function is treated as the best and is switched for that sampling instant. The inverter operates with zero CMV for a modulation index upto 86%. For modulation indices from 86% to 96% the inverter can operate with reduced CMV magnitude ( Vdc/18) and reduced CMV switching frequency using the new space-vector PWM (SVPWM) presented herein. As a result, the linear modulation range is increased to 96% as compared to 86% for zero CMV operation. Simulation and experimental results are presented for the inverter topology for various steady state and transient operating conditions by running an induction motor drive with open loop V/f control scheme. The operation of a two level inverter in the over-modulation region (maximum peak phase fundamental output of inverter is greater than 0:577Vdc) results in lower order harmonics in the inverter output voltage. This lower order harmonics (mainly 5th, 7th, 11th, and 13th) causes electromagnetic torque ripple in motor drive applications. Also these harmonics causes extra losses and adversely affects the efficiency of the drive system. Also inverter control becomes non linear and special control algorithms are required for inverter operation in the over modulation region. In conventional schemes, maximum fundamental output voltage possible is 0:637Vdc. In that case inverter is operated in a square wave mode, also called six-step mode. This operation results in high dv=dt for the inverter output voltage. With multilevel inverters also, the inverter operation with peak phase fundamental output voltage above 0:577Vdc results in lower order harmonics in the inverter output voltage and results in electromagnetic torque pulsation. In this thesis, a new space vector PWM (SVPWM) method to extend the linear modulation range of a cascaded five level inverter topology with a single DC supply is presented. Using this method, the inverter can be controlled linearly and the peak phase fundamental output voltage of the inverter can be increased from 0:577Vdc to 0:637Vdc without increasing the DC bus voltage and without exceeding the induction motor voltage rating. This new technique makes use of cascaded inverter pole voltage redundancy and property of the space vector structure for its operation. Using this, the induction motor drive can be operated till the full speed range (0 Hz to 50 Hz) with the elimination of lower order harmonics in the phase voltage and phase current. The ve level topology presented in this thesis is realized by cascading a two level inverter and two full bridge modules with floating capacitors. The inverter topology and its operation for extending the modulation range is analyzed extensively. Simulation and experimental results for both steady state and dynamic operating conditions are presented. Zero common mode voltage (CMV) operation of multilevel inverters results in reduced DC bus utilization and reduced linear modulation range. In this thesis two reduced CMV SVPWM schemes are presented to extend the linear modulation range by allowing reduced CMV switching. But using these SVPWM schemes the peak phase fundamental output voltage possible is only 0:55Vdc in the linear region. In this thesis, a method to extend the linear modulation range of a CMV eliminated hybrid cascaded multilevel inverter with a single DC supply is presented. Using this method peak fundamental voltage can be increased from 0 to 0:637Vdc with zero CMV switching inside the linear modulation range. Also inverter can be controlled linearly for the entire modulation range. Also, various PWM switching sequences are analyzed in this thesis and the PWM sequence which gives minimum current ripple is used for the zero CMV operation of the inverter. The inverter topology with single DC supply is realized by cascading a two level inverter with two floating capacitor fed full bridge modules. Simulation and experimental results for steady state and dynamic operating conditions are presented to validate the proposed method. A three phase, 400 V, 3.7 kW, 50 Hz, two-pole induction motor drive with the open-loop V/f control scheme is implemented in the hardware for testing proposed inverter topology and proposed SVPWM algorithms experimentally. The semiconductor switches that were used to realize the power circuit for the experiment were 75 A, 1200 V IGBT half-bridge modules (SKM-75GB-12T4). Optoisolated gate drivers with de-saturation protection (M57962L) were used to drive the IGBTs. For the speed control and PWM timing computation, TMS320F28335 DSP is used as the main controller and Xilinx SPARTAN-3 XC3S200 FPGA as the PWM signal generator with dead time of 2.5 s. Level shifted carrier-based PWM algorithm is implemented for the normal inverter operation and zero CMV operation. From the PWM algorithm, information about the pole voltage levels to be switched can be obtained for each phase. In the sampling period, for capacitor voltage balancing of each phase, the DSP selects a switching state using the capacitor voltage information, current direction and pole voltage data for each phase. This switching state information along with the PWM timing data is sent to an FPGA module. The FPGA module generates the gating signals with a dead time of 2.5 s for the gate driver module for all the three phases by processing the switching state information and PWM signals for the given sampling period. For fundamental frequencies above 10Hz, synchronous PWM technique was used for testing the inverter topology. For modulation frequencies 10Hz and below, a constant switching frequency of 900 Hz was used. Various steady state and transient operation results are provided to validate the proposed inverter topology and the zero and reduced CMV operation schemes and extending the linear modulation scheme presented in this thesis. With the advantages like reduced switch count, single DC supply requirement, zero and reduced CMV operation, extension of linear modulation range, linear control of induction motor over the entire modulation range with zero CMV, lesser dv=dt stresses on devices and motor phase windings, lower switching frequency, inherent capacitor balancing, the proposed inverter power circuit topologies, and the SVPWM methods can be considered as good choice for medium voltage, high power motor drive applications.

Multilevel inverters play a major role in the modern day medium and high power energy conversion processes. The classic two level voltage source inverter generates PWM pole voltage output having two levels with strong fundamental component and harmonics centered around the switching frequency and its multiples. With higher switching frequency, its components can be easily filtered and results in better Total harmonic distortion (THD) output voltage and current. But with higher switching frequency, switching loss of power devices increases and electromagnetic interferences also increases. Also in two level inverter, pole voltage switches between zero and DC bus volt-age Vdc. This switching results in high dv=dt and causes EMI and increased stress on the motor winding insulation. The attractive features of multilevel inverters compared to a two level inverter are reduced switching frequency, reduced switching loss, improved volt-age and current THD, reduced dv=dt, etc. Because of these reasons, multilevel invertersultilevelinvertersplayamajorroleinthemoderndaymediumandhighpower find application in electric motor drives, transmission and distribution of power, transportation, traction, distributed generation, renewable energy systems like photo voltaic, hydel power, energy management, power quality, electric vehicle applications, etc. AC motor driven applications are consuming the significant part of the generated electrical energy (more than 60%) around the world. The multilevel inverters are ideal for such applications, since the switching frequency of the devices can be kept low with lower out-put voltage dv=dt. Also by using multilevel inverters, the common mode voltage (CMV) switching can be made zero and associated motor bearing failure can be mitigated. For multilevel inverter topologies, as the number of level increases, the power circuit becomes more complex by the increase in the number of DC power supplies, capacitors, switching devices and associated control circuitry. The main focus of development in multilevel inverter for medium and high power applications is to obtain an optimized number of voltage levels with reduced number of switching devices, capacitors and DC power sources. In this thesis, a new hybrid seven level inverter topology with a single DC supply is proposed with reduced switch count. The inverter is realized by cascading two three level flying capacitor inverters with a half bridge module. Compared to the conventional seven level inverter topologies, the proposed inverter topology uses lesser number of semiconductor devices, capacitors and DC power supplies for its operation. For this topology, capacitor voltage balancing is possible for entire modulation range irrespective of the load power factor. Also capacitor voltage can be controlled over a switching cycle and this result in lowering the capacitor sizing for the proposed topology. A simple hysteresis band based capacitor voltage balancing scheme is implemented for the inverter topology. For a voltage source inverter fed induction motor drive system, the inverter pole voltage is the sum of motor phase voltage and common mode voltage. In induction motors, there exists a parasitic capacitance between stator winding and stator iron, and between stator winding and rotor iron. Common mode voltage with significant magnitude and high frequency switching causes leakage current through these parasitic capacitances and motor bearings. This leakage current can cause ash over of bearing lubricant and corrosion of ball bearings, resulting in an early mechanical failure of the drive system. In this thesis, analysis of extending the linear modulation range of a general n-level inverter by allowing reduced magnitude of common mode voltage (CMV) switching (only Vdc/18) is presented. A new hybrid seven level inverter topology, with a single DC supply and with reduced common mode voltage (CMV) switching is presented in this thesis for the first time. Inverter is operated with zero CMV for modulation index less than 86% and is operated with a CMV magnitude of Vdc/18 to extend the linear modulation range up to 96%. Experimental results are presented for zero CMV operation and for reduced common voltage operation to extend the linear modulation range. A capacitor voltage balancing algorithm is designed utilizing the pole voltage redundancies of the inverter, which works for every sampling instant to correct the capacitor voltage irrespective of load power factor and modulation index. The capacitor voltage balancing algorithm is tested for different modulation indices and for various transient conditions, to validate the proposed topology. In recent years, model predictive control (MPC) using the system model has proved to be a good choice for the control of power converter and motor drive applications. MPC predicts system behavior using a system model and current system state. For cascaded multilevel inverter topologies with a single DC supply, closed loop capacitor voltage control is necessary for proper operation. This thesis presents zero and reduced common mode voltage (CMV) operation of a hybrid cascaded multilevel inverter with predictive capacitor voltage control. For the presented inverter topology, there are redundant switching states for each inverter voltage levels. By using these switching state redundancies, for every sampling instant, a cost function is evaluated based on the predicted capacitor voltages for each phase. The switching state which minimizes cost function is treated as the best and is switched for that sampling instant. The inverter operates with zero CMV for a modulation index upto 86%. For modulation indices from 86% to 96% the inverter can operate with reduced CMV magnitude ( Vdc/18) and reduced CMV switching frequency using the new space-vector PWM (SVPWM) presented herein. As a result, the linear modulation range is increased to 96% as compared to 86% for zero CMV operation. Simulation and experimental results are presented for the inverter topology for various steady state and transient operating conditions by running an induction motor drive with open loop V/f control scheme. The operation of a two level inverter in the over-modulation region (maximum peak phase fundamental output of inverter is greater than 0:577Vdc) results in lower order harmonics in the inverter output voltage. This lower order harmonics (mainly 5th, 7th, 11th, and 13th) causes electromagnetic torque ripple in motor drive applications. Also these harmonics causes extra losses and adversely affects the efficiency of the drive system. Also inverter control becomes non linear and special control algorithms are required for inverter operation in the over modulation region. In conventional schemes, maximum fundamental output voltage possible is 0:637Vdc. In that case inverter is operated in a square wave mode, also called six-step mode. This operation results in high dv=dt for the inverter output voltage. With multilevel inverters also, the inverter operation with peak phase fundamental output voltage above 0:577Vdc results in lower order harmonics in the inverter output voltage and results in electromagnetic torque pulsation. In this thesis, a new space vector PWM (SVPWM) method to extend the linear modulation range of a cascaded five level inverter topology with a single DC supply is presented. Using this method, the inverter can be controlled linearly and the peak phase fundamental output voltage of the inverter can be increased from 0:577Vdc to 0:637Vdc without increasing the DC bus voltage and without exceeding the induction motor voltage rating. This new technique makes use of cascaded inverter pole voltage redundancy and property of the space vector structure for its operation. Using this, the induction motor drive can be operated till the full speed range (0 Hz to 50 Hz) with the elimination of lower order harmonics in the phase voltage and phase current. The ve level topology presented in this thesis is realized by cascading a two level inverter and two full bridge modules with floating capacitors. The inverter topology and its operation for extending the modulation range is analyzed extensively. Simulation and experimental results for both steady state and dynamic operating conditions are presented. Zero common mode voltage (CMV) operation of multilevel inverters results in reduced DC bus utilization and reduced linear modulation range. In this thesis two reduced CMV SVPWM schemes are presented to extend the linear modulation range by allowing reduced CMV switching. But using these SVPWM schemes the peak phase fundamental output voltage possible is only 0:55Vdc in the linear region. In this thesis, a method to extend the linear modulation range of a CMV eliminated hybrid cascaded multilevel inverter with a single DC supply is presented. Using this method peak fundamental voltage can be increased from 0 to 0:637Vdc with zero CMV switching inside the linear modulation range. Also inverter can be controlled linearly for the entire modulation range. Also, various PWM switching sequences are analyzed in this thesis and the PWM sequence which gives minimum current ripple is used for the zero CMV operation of the inverter. The inverter topology with single DC supply is realized by cascading a two level inverter with two floating capacitor fed full bridge modules. Simulation and experimental results for steady state and dynamic operating conditions are presented to validate the proposed method. A three phase, 400 V, 3.7 kW, 50 Hz, two-pole induction motor drive with the open-loop V/f control scheme is implemented in the hardware for testing proposed inverter topology and proposed SVPWM algorithms experimentally. The semiconductor switches that were used to realize the power circuit for the experiment were 75 A, 1200 V IGBT half-bridge modules (SKM-75GB-12T4). Optoisolated gate drivers with de-saturation protection (M57962L) were used to drive the IGBTs. For the speed control and PWM timing computation, TMS320F28335 DSP is used as the main controller and Xilinx SPARTAN-3 XC3S200 FPGA as the PWM signal generator with dead time of 2.5 s. Level shifted carrier-based PWM algorithm is implemented for the normal inverter operation and zero CMV operation. From the PWM algorithm, information about the pole voltage levels to be switched can be obtained for each phase. In the sampling period, for capacitor voltage balancing of each phase, the DSP selects a switching state using the capacitor voltage information, current direction and pole voltage data for each phase. This switching state information along with the PWM timing data is sent to an FPGA module. The FPGA module generates the gating signals with a dead time of 2.5 s for the gate driver module for all the three phases by processing the switching state information and PWM signals for the given sampling period. For fundamental frequencies above 10Hz, synchronous PWM technique was used for testing the inverter topology. For modulation frequencies 10Hz and below, a constant switching frequency of 900 Hz was used. Various steady state and transient operation results are provided to validate the proposed inverter topology and the zero and reduced CMV operation schemes and extending the linear modulation scheme presented in this thesis. With the advantages like reduced switch count, single DC supply requirement, zero and reduced CMV operation, extension of linear modulation range, linear control of induction motor over the entire modulation range with zero CMV, lesser dv=dt stresses on devices and motor phase windings, lower switching frequency, inherent capacitor balancing, the proposed inverter power circuit topologies, and the SVPWM methods can be considered as good choice for medium voltage, high power motor drive applications.

An important research area in computer vision is parameter estimation. Given a mathematical model and a sample of image measurement data, key parameters are sought to encapsulate geometric properties of a relevant entity. An optimisation problem is often formulated in order to find these parameters. This thesis presents an elaboration of fundamental numerical algorithms for estimating parameters of multi-objective models of importance in computer vision applications. The work examines ways to solve unconstrained and constrained minimisation problems from the view points of theory, computational methods, and numerical performance. The research starts by considering a particular form of multi-equation constraint function that characterises a wide class of unconstrained optimisation tasks. Increasingly sophisticated cost functions are developed within a consistent framework, ultimately resulting in the creation of a new iterative estimation method. The scheme operates in a maximum likelihood setting and yields near-optimal estimate of the parameters. Salient features of themethod are that it has simple update rules and exhibits fast convergence. Then, to accommodate models with functional dependencies, two variant of this initial algorithm are proposed. These methods are improved again by reshaping the objective function in a way that presents the original estimation problem in a reduced form. This procedure leads to a novel algorithm with enhanced stability and convergence properties. To extend the capacity of these schemes to deal with constrained optimisation problems, several a posteriori correction techniques are proposed to impose the so-called ancillary constraints. This work culminates by giving two methods which can tackle ill-conditioned constrained functions. The combination of the previous unconstrained methods with these post-hoc correction schemes provides an array of powerful constrained algorithms. The practicality and performance of themethods are evaluated on two specific applications. One is planar homography matrix computation and the other trifocal tensor estimation. In the case of fitting a homography to image data, only the unconstrained algorithms are necessary. For the problem of estimating a trifocal tensor, significant work is done first on expressing sets of usable constraints, especially the ancillary constraints which are critical to ensure that the computed object conforms to the underlying geometry. Evidently here, the post-correction schemes must be incorporated in the computational mechanism. For both of these example problems, the performance of the unconstrained and constrained algorithms is compared to existing methods. Experiments reveal that the new methods perform with high accuracy to match a state-of-the-art technique but surpass it in execution speed.
Thesis (Ph.D.) - University of Adelaide, School of Mathemtical Sciences, Discipline of Pure Mathematics, 2008

This thesis introduces a multilinear algebraic framework for computer graphics, computer vision, and machine learning, particularly for the fundamental purposes of image synthesis, analysis, and recognition. Natural images result from the multifactor interaction between the imaging process, the scene illumination, and the scene geometry. We assert that a principled mathematical approach to disentangling and explicitly representing these causal factors, which are essential to image formation, is through numerical multilinear algebra, the algebra of higher-order tensors. Our new image modeling framework is based on(i) a multilinear generalization of principal components analysis (PCA), (ii) a novel multilinear generalization of independent components analysis (ICA), and (iii) a multilinear projection for use in recognition that maps images to the multiple causal factor spaces associated with their formation. Multilinear PCA employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the M-mode SVD, while our multilinear ICA method involves an analogous M-mode ICA algorithm. As applications of our tensor framework, we tackle important problems in computer graphics, computer vision, and pattern recognition; in particular, (i) image-based rendering, specifically introducing the multilinear synthesis of images of textured surfaces under varying view and illumination conditions, a new technique that we call ``TensorTextures'', as well as (ii) the multilinear analysis and recognition of facial images under variable face shape, view, and illumination conditions, a new technique that we call ``TensorFaces''. In developing these applications, we introduce a multilinear image-based rendering algorithm and a multilinear appearance-based recognition algorithm. As a final, non-image-based application of our framework, we consider the analysis, synthesis and recognition of human motion data using multilinear methods, introducing a new technique that we call ``Human Motion Signatures''.