Zugl.: Magdeburg, Univ., Diss., 2009

Pas de résumé / The level set method was introduced by Osher & Sethian (1988) as a general technique to capture moving interfaces. It has been used to study crystal growth, to simulate water and fire for computer graphics applications, to study two-phase flows and in many other fields. The wellknown problem of the level set method is the following: if the flow velocity is not constant, the level set scalar may become strongly distorted. Thus, the numerical integration may suffer from loss of accuracy. In level set methods, this problem is remedied by the reinitialization procedure, i.e. by reconstruction of the level set function in a way to satisfy the eikonal equation. We propose an alternative approach. We modify directly the level set equation by embedding a source term. The exact expression of this term is such that the eikonal equation is automatically satisfied. Furthermore on the interface, this term is equal to zero. In the meantime, the advantage of our approach is this: the exact expression of the source term allows for the possibility of derivation of its local approximate forms, of first-and-higher order accuracy. Compared to the extension velocity method, this may open the simplifications in realization of level set methods. Compared to the standard approach with the reinitialization procedure, this may give the economies in the number of level set re-initializations, and also, due to reduced number of reinitializations, one may expect an improvement in resolution of zero-set level. Hence, the objective of the present dissertation is to describe and to assess this approach in different test cases.

Le soudage hybride arc / laser représente une solution adéquate à l'assemblage de tôles d'acier de forte épaisseur. La présence d'une source laser en amont de la torche MIG permet d'accroître la productivité du procédé tout en assurant une excellente qualité de la soudure. Cependant la phénoménologie complexe de ce procédé multiphysique n'est pas encore totalement maîtrisée, ce qui motive le développement d'outils de simulation numérique. La présente étude s'est déroulée dans le cadre d'un projet multipartenaires "SISHYFE" (ANR Matériaux et Procédés).Dans ce but un modèle éléments finis 3D non stationnaire a été développé. Construit à partir de l'approche level set, il est en mesure de simuler un procédé multi-passes de soudage hybride arc / laser. Il a été développé autour de quatre principaux axes. (1) Une modélisation plus réaliste de l'apport de chaleur a conduit à la définition d'un nouveau modèle basé sur le rayonnement thermique pour décrire la source MIG. (2) Grâce au couplage entre l'intégration de termes source de matière et de chaleur dans les équations de conservation et l'actualisation de l'interface gaz / métal, le modèle proposé est capable de simuler le développement d'un cordon de soudure. (3) L'intégration d'une modélisation des écoulements du bain de fusion dans une approche level set a été évaluée et son impact sur la distribution thermique dans le métal analysé. (4) La simulation de la formation des contraintes pendant et après soudage a été possible grâce à l'adaptation d'un solveur thermomécanique.La modélisation finale a permis de simuler une configuration industrielle de soudage hybride arc / laser multi-passes. Des mesures expérimentales effectuées par les partenaires du projet "SISHYFE" ont été utilisées afin d'évaluer le modèle et d'éprouver sa capacité à reproduire l'expérience. / Hybrid arc / laser welding represents the solution for high thickness steel sheets assembly. The laser heat source added to the MIG torch improves the process productivity while respecting quality standards. Nevertheless, the phenomenology of the process remains complex and not totally understood. This is the thrust for the development of numerical simulation. The present study has been carried out as part of the "SISHYFE" Material and Process ANR project.For that purpose, a new non stationary 3D finite element model has been developed. Based on the level set approach, it allows to simulate a multipass hybrid arc/ laser welding process. The work focused on four research axes. (1) A more representative model of the plasma heat source has been defined, based on thermal radiation. (2) The coupling of a material and a heat source term integrated in the conservation equations and the update of the level set gas / metal interface is able to correctly model the formation of the weld bead. (3) The integration of a fluid flow model within the level set approach has been evaluated and its impact on thermal distribution analyzed. (4) The stress formation during and after the process has been modeled through the adaptation of a thermo-mechanical solver to the previous modeling in a level set framework.In the end, the developed model has shown to be able to simulate an industrial multi-pass hybrid arc / laser welding process. Experimental measurements provided by the project partners have been used to evaluate the model and to assess its abilities to reproduce experimental features.

L’optimisation des transferts de chaleur est un enjeu de recherche important pour améliorer les performances des systèmes énergétiques, notamment des échangeurs de chaleur. Cette optimisation peut s’appuyer sur différents leviers, comme le choix du régime d’écoulement, ou la modification de la géométrie de l’échangeur. C’est sur ce deuxième angle que nous avons travaillé au cours de cette thèse, en proposant une méthode d’optimisation topologique. Le nombre de paramètres impliqués dans cette méthode est important (plusieurs milliers). Une méthode à gradient est donc employée. Le calcul du gradient de la fonction de coût en fonction des paramètres de design est facilité par l’emploi d’une méthode adjointe. Le problème direct est résolu à l’aide de la méthode de Lattice Boltzmann (LBM). L’implémentation aisée des conditions aux limites dans l’algorithme LBM est un bénéfice pour l’optimisation topologique. De plus, la formulation de la LBM est explicite et hautement parallélisable, notamment sur les cartes graphiques (GPU), utilisées au cours de cette thèse. Ensuite le domaine d’optimisation est composé de fluide et de solide. Leur distribution est définie par une fonction Level- Set (LSF). Cette fonction est continue et le contour zéro définit précisément l’interface fluide/solide. La méthode d’optimisation développée a été testée et validée pour différents objectifs (minimisation de la température moyenne, maximisation de l’échange de chaleur) et contraintes (limitation des pertes de charges, porosité fixée). / Heat transfer enhancement is an important research area to improve the efficiency of energy systems, especially for heat exchangers. There are different ways of optimizing such systems as the choice of flow regime or the modification on the fluid channels geometry. This thesis is focused on the latter option with the development of a topology optimization method. The number of design parameters involved in this technique is important (several thousands) so a gradient-based method is employed. The calculation of the cost function gradient with respect to the design variables is done with an adjoint-state method. The forward problem is solved with the Lattice Boltzmann Method (LBM). The simple implementation of the LBM boundary conditions is an interesting feature for topology optimization. The LBM algorithm is also highly parallelizable and GPU cards have been used in this thesis to obtain fast computational times. The efficiency of the LBM is important because the forward problem must be solved at each optimization step. Then, the optimization domain is composed of either solid of fluid elements. This material distribution is defined by a Level-Set Function (LSF). This is a continuous function in which the zero contour defines the fluid/solid interface, allowing an accurate description of both domains. The proposed optimization method has been tested for different objectives (minimization of the mean temperature, maximization of heat transfer rate) and constraints (pressure drops limitation, fixed porosity).

A significant limitation of the conventional level set method in topology optimization is that it can not create new holes in the design domain. Therefore, the topological derivative approach is proposed to overcome this problem. In this part of the thesis, we investigated the use of the topological derivative in combination with the level set method for topology optimization of solid structures. The topological derivative can indicate the appropriate location to create new holes so that the strong dependency of the optimal topology on the initial design can be alleviated. We also develop an approach to evolve the level set function by replacing the gradient item with a Delta function in the standard Hamilton-Jacobi equation. We find that this handling can create new holes in the solid domain, grow a structure from an empty domain, and improve the convergence rate of the optimization process. The success of our approach is demonstrated by several numerical examples. / Following those methods some numerical implementation issues are discussed, and numerical examples of 2D structural topology optimization problems of minimum compliance design are given and combined with a comparative study where the efficiency, convergence and accuracy of the present methods are highlighted. Finally, conclusions are given. / In the second part of this thesis, we implement another variational level set method, the piecewise constant level set (PCLS) method. This method was first proposed by Lie-Lysaker-Tai in the interface problem field for such tasks as image segmentation and denoising problems. In this approach, by defining a piecewise density function over the whole design domain, the sensitivity of the objective function in respect to the design variable, the level set surface, can be explicitly obtained. Thus, the piecewise density function can be viewed as a bridge establishing the relationship between the implicit level set function and the performance function defined on the design domain. This proposed method retains the advantages of the implicit level set representation, such as the capability of the interface to develop sharp corners, break apart and merge together in a flexible manner. Because the PCLS method is implemented by an implicit iteration differential scheme rather than solving the Hamilton-Jacobi equation, it is not only free of the CFL condition and the reinitialization scheme, but it is also easy to implement. These favorable properties lead to a great timesaving advantage over the conventional level set method. Two other meaningful advantages are the natural nucleation property with which the proposed PCLS method need not incorporate any artificial nucleation scheme and the dependence of the initial design is greatly alleviated. / In the third part of this thesis, we apply a parametric scheme by combining the conventional level set method with radial basis functions (RBFs). This method is introduced because the conventional level set function has no analytical form then the entire design domain must be made discrete in an artificial manner using a rectilinear grid for level set processing - often through a distance transform. The classical level set method for structural topology optimization requires a careful choice of an upwind scheme, extension velocity and a reinitialization algorithm. With the versatile tool, RBF, the original problem can be converted to a parametric optimization problem. Therefore, the costly Hamilton-Jacobi PDE solving procedure can be easily replaced by a standard gradient method or another mature conventional optimization method in the parameter space such as MMA, OC, mathematic programming and so on. / Keywords: structural optimization, level set method, topological derivative, radial basis functions, piecewise constant level set method. (Abstract shortened by UMI.) / The concept of structural optimization has been more and more widely accepted in many engineering fields during the past several decades, because the optimization can result in a much more reasonable and economical structure design with even less material consumption. / Wei Peng. / "June 2007." / Adviser: Yu Michael Wang. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0640. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 166-180). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Another interesting area we investigate is topology optimization with geometric control. Our initial research interests in topology optimization with geometric width control were motivated by the challenge of how to get more manufacturable compliant mechanism designs for MEMS devices. Considering MEMS fabrication technologies, say LIGA, it is natural that designs with specified feature width are more preferable with respect to those with free-form geometries. We propose a variational approach to this problem. A novel quadratic energy functional is employed to govern the geometric feature width of the design. This geometry describing functional is added to the performance-describing functionals. In this way both the performance and the geometric width of the design are optimized simultaneously. The preliminary results show that this method is capable of generating strip-like (or beam) designs with specified feature width, which is a highly desirable characteristic and uniquely distinguishes the proposed method. / Compliant mechanisms are involved in many applications both in the macro and in the micro world. But for a long time, the design procedure of compliant mechanisms was rather a handicraft than a technology. The conventional way is made on an ad hoc basis which to a large extent depends on the designers intuition, experience and inspiration. The limitations of such a trial-and-error approach are obvious: it is not always guaranteed to work, especially when the design is very complicated or when topology and multi-material problems are taken into account. The practical design and application of compliant mechanisms are in need of a systematic approach to create conceptual design. Here, we take a level-set-based new approach to solve this problem. / Considering the actual requirements on reliability, we also investigate how to get conceptual designs with distributed compliance, which is the core part of this thesis. We find the intrinsic defects in the widely used spring model and prove that it will inevitably cause designs with both large output displacements and low strain energies. We will show low strain energy does not guarantee high stiffness. To evenly distribute the compliance, we propose a new method considering the "characteristic stiffness" at interested points. In this way, the strength (stiffness) at the output port of the system is involved into the objective function and optimized directly. This new method is applied to some benchmark examples of both structure optimization and compliant mechanism optimization to validate its performance. / In our proposed method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity fields in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady state solution of the partial differential equation. / Our research follows the route from ease to difficulty, reflecting our understanding of the compliant mechanism design problem at different stages. The first problem addressed in this thesis is how to maintain the structural connectivity during the topology optimization process. De facto hinges are known to be a fairly typical phenomenon in topology optimization of compliant mechanisms; they represent highly localized compliance regions. A most adverse side effect caused by de facto hinges is that they are prone to cause a structurally disconnected design, especially to that with a low volume ratio. To solve this problem, a digital topological connectivity scheme is integrated within the level set model, which ensures connectivity while allows topology changes. This is our first step in the research process. / Chen, Shikui. / "January 2007." / Adviser: Michael Yu Wang. / Source: Dissertation Abstracts International, Volume: 68-08, Section: B, page: 5513. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 149-162). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Thesis (M.Sc.). / Written for the School of Computer Science. Title from title page of PDF (viewed 2008/01/15). Includes bibliographical references.

This dissertation presents results for two separate problems, both in the context of variational fracture models. The first problem involved developing and analyzing models of fracture in which we modeled the energy dissipated by crack growth as concentrated on the front of the crack. While many engineering models of fracture are based on a notion of crack front, there had not been a rigorous definition. We present the first work in this area, which includes a natural weak definition of crack front and front speed, a model of fracture whose evolution is described at the crack front, and a relaxation result that shows that these front based dissipations are all effectively equivalent to a Griffith-type dissipation. The second problem involved the computation of stationary points for Mumford-Shah and fracture using a level set method. Our method improves on existing techniques in that it can handle tips in the singular set and can find minimizers that previous techniques are unable to resolve.

Our method can be naturally applied in the application of manga stylization rendering. We propose a novel colorization technique that propagates color over manga regions exhibiting pattern-continuity as well as intensity-continuity. The proposed method works effectively on colorizing black-and-white manga which contains intensive amount of strokes, hatching, halftoning and screening. Once the user scribbles on the drawing, a local, statistical based pattern feature obtained with Gabor wavelet filters is applied to measure the pattern-continuity. The boundary is then propagated by the level set method that monitors the pattern-continuity. Regions with open boundaries or multiple disjointed regions with similar patterns can be sensibly segmented by a single scribble. With the segmented regions, various colorization techniques can be applied to replace colors, colorize with stroke preservation, or even convert pattern to shading. Based on the observation of the manga features, we then propose a framework to generate manga-style backgrounds from real photographs. It frees manga artists from the tedious and time-consuming background production. To mimic how manga artists produce the tidy background, it composes of two major steps, the line drawing and the screen laying. A line importance model is proposed to simplify and embolden lines in a stylish way. During the screen laying, texture analysis is utilized to automatically match the regions in photographs with screens in the database. Two types of screening mechanisms are proposed for matching shading & texture as well as the high-level structures. / Segmentation has always been a crucial and challenging topic in various computer vision and graphics applications. Information from image features can be incorporated into image segmentation techniques to make the process more accurate and robust. This dissertation focuses on encoding these feature information into the image processing procedures, including image segmentation and manga stylization rendering. / The fundamental part of this dissertation includes the discussion on the construction of the speed function, which is important in applying the curve-evolution based image segmentation. We firstly investigate the curvature term in the speed function, and then show how to transform the image segmentation problem into an interface propagating problem. We propose two formulations to enhance the speed function in level set methods, in order to tackle the segmentation problem of tagged MR images. First, a relaxation factor is introduced, aiming at relaxing the boundary condition when the boundary is unclear or blurry. Second, in order to incorporate human visual sensitive information from the image, a simple and general model is introduced to incorporate shape, texture and color features. By further extending this model, we present a unified approach for segmenting and tracking of the high-resolution color anatomical Chinese Visible Human (CVH) data. The underlying relationship of these two applications relies on the proposed variational framework for the speed function. Our proposed method can be used to segment the first slice of the volume data. Then based on the extracted boundary on the first slice, our method can also be adapted to track the boundary of the homogeneous organs among the subsequent serial images. In addition to the promising segmentation results, the tracking procedure requires only a small amount of user intervention. / Qu Yingge. / "July 2007." / Advisers: Heng Pheng Ann; Wong Tien Tsin. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0433. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 107-120). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

The purpose of the thesis was to explore the possibilities of using a Level-Set method to design a time-optimal path planar of a subject to direction-dependent maximum velocities. A promising application for such a planning approach lies in sailboat navigation planning, because of the dynamic ocean waves, current, wind and the characteristics of a sailboat. In the thesis, we developed an IOS application to simulate such scenario as environment properties with wind, static obstacles and the sailboat mapped into direction-dependent velocities in different locations of the environment.  Considering the wind is the main power for the sailboat, a wind speed generation function was created, based on different locations. The Level-Set method is widely used in image processing because of its various advantages, for instance, the ability to deal with topology change and stability. It also can be applied in path planning, in which the process of the Level-Set method can be considered as a continuous wave front propagating with a speed from the start location. A grid-based map was used to represent the environment. While the wave front was crossing the cell on the grid, a time was recorded for every cell, following the negative gradient direction of such crossing time, and then an optimal path could be found. In addition, we used the Narrow Band method to speed up the calculation of processing the level set equation. Finally, this report gives the results of the experiments of static obstacle avoidance, wind effects and smooth path planning.