We present a level-set algorithm for topology optimisation and demonstrate its capabilities and advantages in a variety of settings. The algorithm uses discrete element densities so that interpolation schemes are avoided and the boundary of the design is always well defined. A review of the level-set method for topology optimisation, and a description of the mathematical concepts behind the level-set algorithm are given in the introductory chapters. A compact Matlab implementation of the algorithm provides explicit implementation details for the simple example of compliance minimisation with a volume constraint. The remainder of the thesis presents original results obtained using the level-set algorithm. As a new application, we use topology optimisation to maximise fracture resistance. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension. We develop a suitable fracture resistance objective functional, derive its shape derivative and apply the level-set algorithm to simple examples. Topology optimisation methods that involve intermediate density elements are not suitable to solve this problem because the boundary of the design is not well defined. Our results indicate that the algorithm correctly optimises for fracture resistance. As the method is computationally intensive, we suggest simpler objective functionals that could be used as a proxy for fracture resistance. For example, a perimeter penalty could be added to the compliance objective functional in conjunction with a non-linear elasticity law where the Young's modulus in tension is lower than in compression. The level-set method has only recently been applied to fluid flow problems. We utilise the level-set algorithm to minimise energy dissipation in Stokes flows in both two and three dimensions. The discrete element densities allow the no-slip boundary condition to be applied directly. The Stokes equations therefore need only be solved in the fluid region of the design: this results in significant computational savings compared to conventional material distribution approaches. In order to quantify the computational savings the optimisation problems are resolved using an interpolation scheme to simulate the no-slip boundary condition. This significant advantage of the level-set method for fluid flow problems has not been noted by other authors. The algorithm produces results consistent with those obtained by other topology optimisation approaches, and solves large-scale three dimensional problems with modest computational cost. The first examples of three dimensional periodic microstructure design with the level-set method are presented in this thesis. The level-set algorithm is extended to deal with multiple constraints. This is needed so that materials can be designed with symmetry requirements imposed on their effective properties. To demonstrate the capabilities of the approach, unit cells are designed separately to maximise conductivity and bulk modulus with an isotropy requirement. The resulting materials have properties very close to the relevant Hashin-Shtrikman bounds. The algorithm is then applied to multifunctional material design: unit cells are designed to give isotropic materials that have maximum bulk modulus and maximum conductivity. Cross-property bounds indicate the near-optimality of the microstructures obtained. The design space of the problem is extensively explored with different coefficients of the conductivity and bulk modulus in the objective and different volume constraints. We hypothesise the existence of theoretically optimal single-scale microstructures with the topologies of the computationally optimised microstructures we have found. Structures derived from the Schwartz primitive (P) and diamond (D) minimal surfaces have previously been presented as good multifunctional composites. These structures are elastically anisotropic. Although they have similar conductivity, they have stiffness properties inferior to several of the isotropic optimised microstructures.

abstract: Thousands of high-resolution images are generated each day. Segmenting, classifying, and analyzing the contents of these images are the key steps in image understanding. This thesis focuses on image segmentation and classification and its applications in synthetic, texture, natural, biomedical, and industrial images. A robust level-set-based multi-region and texture image segmentation approach is proposed in this thesis to tackle most of the challenges in the existing multi-region segmentation methods, including computational complexity and sensitivity to initialization. Medical image analysis helps in understanding biological processes and disease pathologies. In this thesis, two cell evolution analysis schemes are proposed for cell cluster extraction in order to analyze cell migration, cell proliferation, and cell dispersion in different cancer cell images. The proposed schemes accurately segment both the cell cluster area and the individual cells inside and outside the cell cluster area. The method is currently used by different cell biology labs to study the behavior of cancer cells, which helps in drug discovery. Defects can cause failure to motherboards, processors, and semiconductor units. An automatic defect detection and classification methodology is very desirable in many industrial applications. This helps in producing consistent results, facilitating the processing, speeding up the processing time, and reducing the cost. In this thesis, three defect detection and classification schemes are proposed to automatically detect and classify different defects related to semiconductor unit images. The first proposed defect detection scheme is used to detect and classify the solder balls in the processor sockets as either defective (Non-Wet) or non-defective. The method produces a 96% classification rate and saves 89% of the time used by the operator. The second proposed defect detection scheme is used for detecting and measuring voids inside solder balls of different boards and products. The third proposed defect detection scheme is used to detect different defects in the die area of semiconductor unit images such as cracks, scratches, foreign materials, fingerprints, and stains. The three proposed defect detection schemes give high accuracy and are inexpensive to implement compared to the existing high cost state-of-the-art machines. / Dissertation/Thesis / Ph.D. Electrical Engineering 2010

Dans cette thèse, nous nous intéressons au problème de la segmentation de portraits numériques. Nous appelons portrait numérique la photographie d’une personne avec un cadre allant grossièrement du gros plan au plan poitrine. Le problème abordé dans ce travail est un cas spécifique de la segmentation d’images où il s’agit notamment de définir précisément la frontière de la région « cheveux ». Ce problème est par essence très délicat car les attributs de la région « cheveux » (géométrie, couleur, texture) présentent une grande variabilité à la fois entre les personnes et au sein de la région. Notre cadre applicatif est un système d’« essayage virtuel » de lunettes à destination du grand public, il n’est pas possible de contrôler les conditions de prise de vue comme l’éclairage de la scène ou la résolution des images, ce qui accroît encore la diculté du problème. L’approche proposée pour la segmentation de portraits numériques est une approche du plus grossier au plus fin procédant par étapes successives. Nous formulons le problème comme celui d’une segmentation multi-régions, en introduisant comme « régions secondaires », les régions adjacentes à la région « cheveux » , c.-à-d. les régions « peau » et « fond ». La méthode est fondée sur l’apparence (appearance-based method) et a comme spécificité le fait de déterminer les descripteurs de régions les plus adaptés à partir d’une base d’images d’apprentissage et d’outils statistiques. À la première étape de la méthode, nous utilisons l’information contextuelle d’un portrait numérique — connaissances a priori sur les relations spatiales entre régions— pour obtenir des échantillons des régions « cheveux », « peau » et « fond ». L’intérêt d’une approche fondée sur l’apparence est de pouvoir s’adapter à la fois aux conditions de prises de vue ainsi qu’aux attributs de chaque régions. Au cours de cette étape, nous privilégions les modèles de forme polygonaux couplés aux contours actifs pour assurer la robustesse du modèle. Lors de la seconde étape, à partir des échantillons détectés à l’étape précédente, nous introduisons un descripteur prenant en compte l’information de couleur et de texture. Nous proposons une segmentation grossière par classification en nous appuyant à nouveau sur l’information contextuelle : locale d’une part grâce aux champs de Markov, globale d’autre part grâce à un modèle a priori de segmentation obtenu par apprentissage qui permet de rendre les résultats plus robustes. La troisième étape ane les résultats en définissant la frontière des « cheveux » comme une région de transition. Cette dernière contient les pixels dont l’apparence provient du mélange de contributions de deux régions (« cheveux »et « peau » ou «fond »). Ces deux régions de transition sont post-traitées par un algorithme de «démélange » (digital matting) pour estimer les coecients de transparence entre « cheveux » et « peau », et entre « cheveux » et « fond ». À l’issue de ces trois étapes, nous obtenons une segmentation précise d’un portrait numérique en trois « calques », contenant en chaque pixel l’information de transparence entre les régions « cheveux », « peau » et « fond ». Les résultats obtenus sur une base d’images de portraits numériques ont mis en évidence les bonnes performances de notre méthode. / In this thesis, we are interested in the problem of the segmentation of digital portraits. We call digital portrait the photography of a person with a frame roughly ranging from the close-up to the chest plane. The problem addressed in this work is a specific case of the segmentation of images where it is especially necessary to define precisely the border of the "hair" region. This problem is inherently very delicate because the attributes of the "hair" region (geometry, color, texture) present an important variability between people and within the region. Our application is a system of "virtual fitting" of glasses for the general audience, it is not possible to control the shooting conditions such as stage lighting or image resolution, which increases the difficulty of the problem. The approach proposed for the segmentation of digital portraits is an approach « coarse to fine », proceeding in successive stages. We formulate the problem as a multi-region segmentation, introducing as "secondary regions" regions adjacent to the "hair" region, ie, the "skin" and "background" regions. The method is based on appearance-based method and has as a specificity the determination of the descriptors of regions most adapted from a database of learning and statistical tools. In the first step of the method, we use the contextual information of a Digital portrait - a priori knowledge about the spatial relations between regions - to obtain samples of the regions "hair", "skin" and "background". The value of an appearance-based approach is to be able to adapt to both the shooting conditions and the attributes of each region. During this stage, we prefer polygonal shape models coupled with active contours to ensure the robustness of the model. In the second step, from the samples detected in the previous step, we introduce a descriptor taking into account the color and texture information. We propose a rough segmentation by classification by relying on the contextual information: local on the one hand thanks to the Markov fields, global on the other hand thanks to an a priori model of segmentation obtained by learning which il allow to obtain robust results. The third stage refines the results by defining the border of "hair" as a transition region. This région contains the pixels whose appearance comes from the mixture of contributions of two regions ("hair" and "skin" or "background"). These two transition regions are post-processed by a digital matting algorithm to estimate the coefficients of transparency between "hair" and "skin", and between "hair" and "background". At the end of these three steps, we obtain a precise segmentation of a digital portrait into three "layers", containing in each pixel the information of transparency between the regions "hair", "skin" and "background". The results obtained on the basis of images of digital portraits have highlighted the good performance of our method.

Les méthodes d'optimisation de forme s’industrialisent progressivement, elles permettent la conception automatisée de structures aux propriétés optimales. Elles constituent aussi un outil d'exploration majeur pour la conception de nouveaux matériaux.Dans une première partie nous utilisons ces méthodes afin de générer des matériaux architecturés aux propriétés thermoélastiques effectives cibles et extrêmes. En plus de proposer différentes solutions, nous répertorions les différents mécanismes œuvrant au contrôle des ces propriétés. Dans ce contexte nous proposons aussi de prendre en compte l'influence des interfaces comportant un gradient de propriétés sur les architectures obtenues.Nous étudions ensuite les procédés de fabrication pouvant être utilisés afin de réaliser ces matériaux. Les méthodes de fabrication additive, considérées comme le vecteur d'une prochaine révolution industrielle, constituent une piste que nous considérerons tout particulièrement. Nous proposons plusieurs solutions pour prendre en compte les limitations et les effets collatéraux de ces procédés de fabrication au sein de processus d'optimisation de forme. Nous traitons le problème de la prise en compte des propriétés induites par la méthode de fabrication Fiber Deposition Molding (FDM), à savoir des propriétés anisotropes orientées. Nous proposons ensuite une approche pour traiter le problème des dépôts en porte-à-faux à l'aide d'un critère mécanique.Enfin, nous abordons la prise en compte des non-linéarités géométriques au sein de calculs d'optimisation de forme et discutons de leurs apports ainsi que de leurs limitations. Nous présentons plusieurs applications pour la conception automatisée d'actuateurs non linéaires. / Shape optimization methods are promising methods and are gradually becoming industrialized. They provide the ability to automatically design structures with optimal behavior. They are outstanding tools for exploration and design of new materials.We use these methods to generate architectured multi-phased materials with prescribed thermoelastic properties. We first propose several solutions and we classify them by the mechanisms they rely on in order to control the effective properties. We also propose to evaluate the influence of an interface with a gradient of properties on the obtained architectures.Eventually we focus on the plausible manufacturing solution to produce our architectured materials. In this context, additive manufacturing methods (often considered as the support of an incoming industrial revolution) is our main option. We introduce several strategies to circumvent some limitations and side effects of these manufacturing methods during optimization process. We particularly focus on Fiber Deposition Molding, which induce an important mechanical anisotropy in processed parts. Then we consider the problem of overhangings features in design and propose a way to handle them prior to additive manufacturing using a mechanical criteria.Finally we take into account geometrical non linearities in optimization process. We highlight the pros and cons of this new modeling by presenting several applications of non linear actuators design.

A simulação numérica de escoamento tem se desenvolvido em diferentes aspectos para melhorar sua exatidão e se aproximar cada vez mais da representação de fenômenos reais. O desenvolvimento científico sobre escoamentos turbulentos multifásicos dependem da simulação numérica, onde o custo computacional destas ainda é um fator determinante, principalmente quando se visa resultados mais precisos. Uma das grandes dificuldades é que códigos numéricos de alta ordem, utilizados para simular escoamentos bifásicos, produzem erros de dispersão numérica presentes principalmente na interface, já que nesta posição se apresenta uma descontinuidade nas propriedades físicas dos fluidos envolvidos. O presente trabalho tem o objetivo de propor uma formulação de alta precisão para escoamentos bifásicos. Para isso, realiza-se modificações em um código já existente, denominado Incompact3d que possui a possibilidade de paralelização para até 100:000 núcleos computacionais, utilizando uma decomposição 2D. Entre estas modificações destacam-se a implementação de uma nova formulação do método Level Set, além de pequenas modificações nas equações de Navier-Stokes, como a adição do termo de gravidade, a segregação do termo de difusividade e a adição de um termo referente a força de tensão superficial. Ainda propõem-se uma nova consideração do termo de pressão, que é separado em pressão não hidrostática e pressão hidrostática. Diversos testes de verificação e validação foram realizados, apresentando a capacidade de se realizar simulações numéricas de alta ordem para escoamentos bifásicos. Com esta metodologia, foi identificar características de fenômenos turbulentos bifásicos. / Flow numerical simulation has been developed in di erent ways to improve its results accuracy and have a better approximation to real phenomenon. To scientific development turbulent two-phase flow depends of numerical simulation, where computational cost is an important factor, mainly when accurate results are required. High order two-phase flow codes issue is that they produce numerical dispersion errors that are amplified with the presence of interface, since in its position exist physical proprieties discontinuity. This research main objective is to propose a high precision formulation to two-phase flow. For that, we modified Incompact3d code that has a 2D decomposition making parallelized calculation up to 100:000 computational cores. Some modifications are the implementation of a new Level Set Method formulation; some minor Navier-Stokes equation modifications as the addition of gravity term; the segregation of di usive term; and the addition of surface tension forces. We also proposed a new pressure term consideration where we separate it in hydrostatic and non-hydrostatic pressure. Many verification and validation tests where developed presenting the ability to perform high order numerical simulations for two-phase flows. Also it was possible to identify multiphase turbulent structures in the phenomena simulated.

Nesse trabalho, é investigada a combustão pré-misturada de metano e ar em um queimador poroso radiante com área de seção transversal variável. A estabilidade de chama e a eficiência de radiação neste tipo de queimador são analisadas através de simulação numérica. O problema considerado para análise é de um queimador unidimensional de área variável com perdas de calor por radiação em suas extremidades. A metodologia numérica usada para resolver o conjunto de equações de conservação é o método dos volumes finitos com o sistema de coordenadas cartesianas. Os resultados mostram que, o aumento da área da seção transversal proporciona um aumento na faixa de estabilidade de chama do queimador quando comparado com um de área constante. A eficiência de radiação também é influenciada positivamente pela variação de área, ou seja, um aumento na área da seção de saída do dispositivo resulta em um aumento na eficiência. Também é testada uma modelagem alternativa baseada no método de curvas de nível (level-set method). Nesse modelo as equações das espécies químicas são substituídas pela equação-G, a qual descreve a dinâmica de uma frente de chama infinitamente fina. Os resultados numéricos das simulações bem como as vantagens e as limitações do modelo de curvas de nível são discutidas. Em linhas gerais os resultados do modelo de curvas de nível não foram capazes de reproduzir adequadamente o comportamento obtido com o modelo convencional. / In this work, the premixed combustion of methane and air in a porous radiant burner with a variable cross-sectional area is investigated. The flame stability and the radiant efficiency in this kind of burner are analyzed through numerical simulation. The problem considers a variable area one-dimensional burner with radiation heat losses in its extremities. The numerical method used to solve the set of conservation equations is the finite volume method with the Cartesian coordinate system. The results show that an increase of the cross-sectional area promotes an increase of the flame stability range when compared with a constant area burner. The radiant efficiency is also positively influenced by the area variation, i.e., the increase of the outlet area results in an enhanced efficiency. An alternative modelling based on the level-set method is also tested. In this model the equations of chemical species are replaced by the G-Equation, which describes the dynamics of an infinitely thin flame front. The numerical results of simulations as well as advantages and limitations of the level-set model are discussed. In general the results of the level-set model were not able to reproduce in a suitable way the behavior obtained with the conventional model.

A simulação numérica de escoamento tem se desenvolvido em diferentes aspectos para melhorar sua exatidão e se aproximar cada vez mais da representação de fenômenos reais. O desenvolvimento científico sobre escoamentos turbulentos multifásicos dependem da simulação numérica, onde o custo computacional destas ainda é um fator determinante, principalmente quando se visa resultados mais precisos. Uma das grandes dificuldades é que códigos numéricos de alta ordem, utilizados para simular escoamentos bifásicos, produzem erros de dispersão numérica presentes principalmente na interface, já que nesta posição se apresenta uma descontinuidade nas propriedades físicas dos fluidos envolvidos. O presente trabalho tem o objetivo de propor uma formulação de alta precisão para escoamentos bifásicos. Para isso, realiza-se modificações em um código já existente, denominado Incompact3d que possui a possibilidade de paralelização para até 100:000 núcleos computacionais, utilizando uma decomposição 2D. Entre estas modificações destacam-se a implementação de uma nova formulação do método Level Set, além de pequenas modificações nas equações de Navier-Stokes, como a adição do termo de gravidade, a segregação do termo de difusividade e a adição de um termo referente a força de tensão superficial. Ainda propõem-se uma nova consideração do termo de pressão, que é separado em pressão não hidrostática e pressão hidrostática. Diversos testes de verificação e validação foram realizados, apresentando a capacidade de se realizar simulações numéricas de alta ordem para escoamentos bifásicos. Com esta metodologia, foi identificar características de fenômenos turbulentos bifásicos. / Flow numerical simulation has been developed in di erent ways to improve its results accuracy and have a better approximation to real phenomenon. To scientific development turbulent two-phase flow depends of numerical simulation, where computational cost is an important factor, mainly when accurate results are required. High order two-phase flow codes issue is that they produce numerical dispersion errors that are amplified with the presence of interface, since in its position exist physical proprieties discontinuity. This research main objective is to propose a high precision formulation to two-phase flow. For that, we modified Incompact3d code that has a 2D decomposition making parallelized calculation up to 100:000 computational cores. Some modifications are the implementation of a new Level Set Method formulation; some minor Navier-Stokes equation modifications as the addition of gravity term; the segregation of di usive term; and the addition of surface tension forces. We also proposed a new pressure term consideration where we separate it in hydrostatic and non-hydrostatic pressure. Many verification and validation tests where developed presenting the ability to perform high order numerical simulations for two-phase flows. Also it was possible to identify multiphase turbulent structures in the phenomena simulated.

Nesse trabalho, é investigada a combustão pré-misturada de metano e ar em um queimador poroso radiante com área de seção transversal variável. A estabilidade de chama e a eficiência de radiação neste tipo de queimador são analisadas através de simulação numérica. O problema considerado para análise é de um queimador unidimensional de área variável com perdas de calor por radiação em suas extremidades. A metodologia numérica usada para resolver o conjunto de equações de conservação é o método dos volumes finitos com o sistema de coordenadas cartesianas. Os resultados mostram que, o aumento da área da seção transversal proporciona um aumento na faixa de estabilidade de chama do queimador quando comparado com um de área constante. A eficiência de radiação também é influenciada positivamente pela variação de área, ou seja, um aumento na área da seção de saída do dispositivo resulta em um aumento na eficiência. Também é testada uma modelagem alternativa baseada no método de curvas de nível (level-set method). Nesse modelo as equações das espécies químicas são substituídas pela equação-G, a qual descreve a dinâmica de uma frente de chama infinitamente fina. Os resultados numéricos das simulações bem como as vantagens e as limitações do modelo de curvas de nível são discutidas. Em linhas gerais os resultados do modelo de curvas de nível não foram capazes de reproduzir adequadamente o comportamento obtido com o modelo convencional. / In this work, the premixed combustion of methane and air in a porous radiant burner with a variable cross-sectional area is investigated. The flame stability and the radiant efficiency in this kind of burner are analyzed through numerical simulation. The problem considers a variable area one-dimensional burner with radiation heat losses in its extremities. The numerical method used to solve the set of conservation equations is the finite volume method with the Cartesian coordinate system. The results show that an increase of the cross-sectional area promotes an increase of the flame stability range when compared with a constant area burner. The radiant efficiency is also positively influenced by the area variation, i.e., the increase of the outlet area results in an enhanced efficiency. An alternative modelling based on the level-set method is also tested. In this model the equations of chemical species are replaced by the G-Equation, which describes the dynamics of an infinitely thin flame front. The numerical results of simulations as well as advantages and limitations of the level-set model are discussed. In general the results of the level-set model were not able to reproduce in a suitable way the behavior obtained with the conventional model.

Nesse trabalho, é investigada a combustão pré-misturada de metano e ar em um queimador poroso radiante com área de seção transversal variável. A estabilidade de chama e a eficiência de radiação neste tipo de queimador são analisadas através de simulação numérica. O problema considerado para análise é de um queimador unidimensional de área variável com perdas de calor por radiação em suas extremidades. A metodologia numérica usada para resolver o conjunto de equações de conservação é o método dos volumes finitos com o sistema de coordenadas cartesianas. Os resultados mostram que, o aumento da área da seção transversal proporciona um aumento na faixa de estabilidade de chama do queimador quando comparado com um de área constante. A eficiência de radiação também é influenciada positivamente pela variação de área, ou seja, um aumento na área da seção de saída do dispositivo resulta em um aumento na eficiência. Também é testada uma modelagem alternativa baseada no método de curvas de nível (level-set method). Nesse modelo as equações das espécies químicas são substituídas pela equação-G, a qual descreve a dinâmica de uma frente de chama infinitamente fina. Os resultados numéricos das simulações bem como as vantagens e as limitações do modelo de curvas de nível são discutidas. Em linhas gerais os resultados do modelo de curvas de nível não foram capazes de reproduzir adequadamente o comportamento obtido com o modelo convencional. / In this work, the premixed combustion of methane and air in a porous radiant burner with a variable cross-sectional area is investigated. The flame stability and the radiant efficiency in this kind of burner are analyzed through numerical simulation. The problem considers a variable area one-dimensional burner with radiation heat losses in its extremities. The numerical method used to solve the set of conservation equations is the finite volume method with the Cartesian coordinate system. The results show that an increase of the cross-sectional area promotes an increase of the flame stability range when compared with a constant area burner. The radiant efficiency is also positively influenced by the area variation, i.e., the increase of the outlet area results in an enhanced efficiency. An alternative modelling based on the level-set method is also tested. In this model the equations of chemical species are replaced by the G-Equation, which describes the dynamics of an infinitely thin flame front. The numerical results of simulations as well as advantages and limitations of the level-set model are discussed. In general the results of the level-set model were not able to reproduce in a suitable way the behavior obtained with the conventional model.

This thesis describes a system for dealing with free surface fluid simulations, and the components needed in order to construct such a system. It builds upon recent research, but in a computer graphics context the amount of available literature is limited and difficult to implement. Because of this, the text aims at providing a solid foundation of the mathematics needed, at explaining in greater detail the steps needed to solve the problem, and lastly at improving some aspects of the animation process as it has been described in earlier works. The aim of the system itself is to provide visually plausible renditions of animated fluids in three dimensions in a manner that allows it to be usable in a visual effects production context. The novel features described include a generalized interaction layer providing greater control to artists, a new way of dealing with moving objects that interact with the fluid and a method for adding source and drain capabilities.