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Dissertations / Theses on the topic 'Jacobian matrix'
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葛彤 and Tong Ge. "Toeplitz Jacobian matrix and nonlinear dynamical systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31234860.
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Ge, Tong. "Toeplitz Jacobian matrix and nonlinear dynamical systems /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18987977.
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Billups, Stephen C. "An augmented Jacobian matrix algorithm for tracking homotopy zero curves." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/90914.
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There are algorithms for finding zeros or fixed points of nonlinear systems of (algebraic) equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. The augmented Jacobian matrix algorithm is part of the software package HOMPACK, and is based on an algorithm developed by W.C. Rheinboldt. The algorithm exists in two forms-one for dense Jacobian matrices, and the other for sparse Jacobian matrices.M.S.
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Bourji, Samih Kassem. "Least-Change Secant Updates of Non-Square Matrices." DigitalCommons@USU, 1987. https://digitalcommons.usu.edu/etd/6989.
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In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry.
All of the updates obtained thus far deal with updating an approximation to an nxn Jacobian matrix. In this thesis we consider extending most of the popular updates to the non-square case. Two applications are immediate: between-step updating of the approximate Jacobian of f(X,t) in a non-autonomous ODE system, and solving nonlinear systems of equations which depend on a parameter, such as occur in continuation methods. Both of these cases require extending the present updates to include the nx(n+l) Jacobian matrix, which is the issue we address here. Our approach is to stay with the least change secant formulation. Computational results for these new updates are also presented to illustrate their convergence behavior.
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KHER, SAMEER. "IMPROVING ANALOG SIMULATION SPEED USING THE SELECTIVE MATRIX UPDATE APPROACH IN A VHDL-AMS SIMULATOR." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1107287248.
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Jones, Jeffrey S. "Analysis of Algorithms for Star Bicoloring and Related Problems." Ohio University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1426770501.
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Korkmaz, Lale. "Static Force Production Analysis in a 3D Musculoskeletal Model of the Cat Hindlimb." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5193.
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To understand control strategies employed by the central nervous system (CNS) control movement or force generation in a limb, a seven degree of freedom cat hindlimb was modeled. In this study, the biomechanical constraints affecting force generation for balance and postural control were investigated. Due to the redundancies at the muscular and joint levels in the musculoskeletal system, even the muscle coordination pattern to statically produce a certain amount of force/torque at the ground is not straightforward.
A 3D musculoskeletal model of the cat hindlimb was created from cat cadaver measurements using Software for Interactive Musculoskeletal Systems (SIMM, Musculographics, Inc.). Six kinematic degrees of freedom and 31 individual hindlimb muscles were modeled. The moment arms of the muscles were extracted from the software model to be used in a linear transformation between muscle activation, and end effector force and moment. The Jacobian matrix that establishes the relationship between joint torques and end effector wrench was calculated. Maximal muscle forces were estimated from the literature. A feasible set of forces that can be generated at the toe was constructed using combination of maximally activated muscle excitations. Because the endpoint torque is typically small in a cat, an optimization algorithm was also performed to maximize the force generation at the end effector while constraining the magnitude of the endpoint torque. The results are compared with the measured force magnitude and direction data from an acute cat hindlimb preparation for different postures. This static model is applicable for understanding muscle coordination during postural responses to small balance perturbations.
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Onur, Omer. "Effect Of Jacobian Evaluation On Direct Solutions Of The Euler Equations." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf.
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A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton’
s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time. In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.
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Meyer, Arnd. "Stable evaluation of the Jacobians for curved triangles." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600629.
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In the adaptive finite element method, the solution of a p.d.e. is approximated
from finer and finer meshes, which are controlled by error estimators. So,
starting from a given coarse mesh, some elements are subdivided a couple of
times. We investigate the question of avoiding instabilities which limit this
process from the fact that nodal coordinates of one element coincide in more
and more leading digits. In a previous paper the stable calculation of the
Jacobian matrices of the element mapping was given for straight line triangles,
quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and
quadratic triangles on curved boundaries.
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Cao, Weiran. "Linear Modeling of DFIGs and VSC-HVDC Systems." Thesis, KTH, Elektrisk energiomvandling, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-177643.
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Recently, with growing application of wind power, the system based on the doubly fedinduction generator (DFIG) has become the one of the most popular concepts. Theproblem of connecting to the grid is also gradually revealed. As an effective solution toconnect offshore wind farm, VSC-HVDC line is the most suitable choice for stabilityreasons. However, there are possibilities that the converter of a VSC-HVDC link canadversely interact with the wind turbine and generate poorly damped sub-synchronousoscillations. Therefore, this master thesis will derive the linear model of a single DFIG aswell as the linear model of several DFIGs connecting to a VSC-HVDC link. For thelinearization method, the Jacobian transfer matrix modeling method will be explainedand adopted. The frequency response and time-domain response comparison betweenthe linear model and the identical system in PSCAD will be presented for validation.Nyligen, med ökande tillämpning av vindkraft, det system som bygger på den dubbeltmatad induktion generator (DFIG) har blivit en av de mest populära begrepp. Problemetmed att ansluta till nätet är också gradvis avslöjas. Som en effektiv lösning för att anslutavindkraftpark är VSC -HVDC linje det lämpligaste valet av stabilitetsskäl. Det finns dockmöjligheter att omvandlaren en VSC-HVDC länk negativt kan interagera medvindturbinen och genererar dåligt dämpade under synkron svängningar. Därför kommerdetta examensarbete härleda den linjära modellen av en enda DFIG liksom den linjäramodellen av flera DFIGs ansluter till en VSC-HVDC -länk. För arise metoden kommerJacobian transfer matrix modelleringsmetodförklaras och antas. Jämförelse mellan denlinjära modellen och identiskt system i PSCAD frekvensgången och tidsdomänensvarkommer att presenteras för godkännande.
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Kang, Yuezhuang. "Computer-aided fixture design verification." Link to electronic thesis, 2002. http://www.wpi.edu/Pubs/ETD/Available/etd-0108102-163543.
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Thesis (M.S.)--Worcester Polytechnic Institute.Keywords: Fixture stiffness matrix; Jacobian matrix; kinetic model; geometric model; fixture design verification; stability analysis; tolerance analysis; tolerance assignment. Includes bibliographical references (p. 92-97).
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Njoroge, Moses M. "On jacobians connected with matrix variate random variables." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61966.
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Goyal, Mini, and University of Lethbridge Faculty of Arts and Science. "Graph coloring in sparse derivative matrix computation." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2005, 2005. http://hdl.handle.net/10133/260.
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There has been extensive research activities in the last couple of years to efficiently determine large sparse Jacobian matrices. It is now well known that the estimation of Jacobian matrices can be posed as a graph coloring problem. Unidirectional coloring by Coleman and More [9] and bidirectional coloring independently proposed by Hossain and Steihaug [23] and Coleman and Verma [12] are techniques that employ graph theoretic ideas. In this thesis we present heuristic and exact bidirectional coloring techniques. For bidirectional heuristic techniques we have implemented variants of largest first ordering, smallest last ordering, and incidence degree ordering schemes followed by the sequential algorithm to determine the Jacobian matrices. A "good" lower bound given by the maximum number of nonzero entries in any row of the Jacobian matrix is readily obtained in an unidirectional determination. However, in a bidirectional determination no such "good" lower bound is known. A significant goal of this thesis is to ascertain the effectiveness of the existing heuristic techniques in terms of the number of matrix-vector products required to determine the Jacobian matrix. For exact bidirectional techniques we have proposed an integer linear program to solve the bidirectional coloring problem. Part of exact bidirectional coloring results were presented at the "Second International Workshop on Cominatorial Scientific Computing (CSC05), Toulouse, France."viii, 83 leaves ; 29 cm.
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Authesserre, Jean-baptiste. "Alignement paramétrique d’images : proposition d’un formalisme unifié et prise en compte du bruit pour le suivi d’objets." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14136/document.
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L’alignement d’images paramétrique a de nombreuses applications pour la réalité augmentée, la compression vidéo ou encore le suivi d’objets. Dans cette thèse, nous nous intéressons notamment aux techniques de recalage d’images (template matching) reposant sur l’optimisation locale d’une fonctionnelle d’erreur. Ces approches ont conduit ces dernières années à de nombreux algorithmes efficaces pour le suivi d’objets. Cependant, les performances de ces algorithmes ont été peu étudiées lorsque les images sont dégradées par un bruit important comme c’est le cas, par exemple, pour des captures réalisées dans des conditions de faible luminosité. Dans cette thèse, nous proposons un nouveau formalisme, appelé formalisme bidirectionnel, qui unifie plusieurs approches de l’état de l’art. Ce formalisme est utilisé dans un premier temps pour porter un éclairage nouveau sur un grand nombre d’approches de la littérature et en particulier sur l’algorithme ESM (Efficient Second-order Minimization). Nous proposons ensuite une étude théorique approfondie de l’influence du bruit sur le processus d’alignement. Cette étude conduit à la définition de deux nouvelles familles d’algorithmes, les approches ACL (Asymmetric Composition on Lie Groups) et BCL (Bidirectional Composition on Lie Groups) qui permettent d’améliorer les performances en présence de niveaux de bruit asymétriques (Rapport Signal sur Bruit différent dans les images). L’ensemble des approches introduites sont validées sur des données synthétiques et sur des données réelles capturées dans des conditions de faible luminositéParametric image alignment is a fundamental task of many vision applications such as object tracking, image mosaicking, video compression and augmented reality. To recover the motion parameters, direct image alignment works by optimizing a pixel-based difference measure between a moving image and a fixed-image called template. In the last decade, many efficient algorithms have been proposed for parametric object tracking. However, those approaches have not been evaluated for aligning images of low SNR (Signal to Noise ratio) such as images captured in low-light conditions. In this thesis, we propose a new formulation of image alignment called Bidirectional Framework for unifying existing state of the art algorithms. First, this framework allows us to produce new insights on existing approaches and in particular on the ESM (Efficient Second-order Minimization) algorithm. Subsequently, we provide a theoretical analysis of image noise on the alignment process. This yields the definition of two new approaches : the ACL (Asymmetric Composition on Lie Groups) algorithm and the BCL (Bidirectional Composition on Lie Groups) algorithm, which outperform existing approaches in presence of images of different SNR. Finally, experiments on synthetic and real images captured under low-light conditions allow to evaluate the new and existing approaches under various noise conditions
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Morales, Usquiano Henry Aldo. "Análisis de sensibilidad para el control de tensión utilizando la matriz jacobiana." Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2012. https://hdl.handle.net/20.500.12672/12132.
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Publicación a texto completo no autorizada por el autorPresenta un análisis para determinar la sensibilidad de tensión de las principales barras del área norte del Sistema Eléctrico Interconectado Nacional (SEIN), el cual tiene una topología radial y presenta una carencia de reserva de generación hidrotérmica, la metodología que se presenta a continuación puede ser útil para realizar de una manera eficiente el control de tensión especialmente en zonas criticas como lo es el área norte del SEIN. Este trabajo esta principalmente dirigido a las personas que se encargan de la operación de sistemas eléctricos de potencia. El tema surge en la necesidad de plantear propuestas de solución a los problemas de tensión en el área norte del SEIN, los cuales se producen actualmente y de manera frecuente debido al crecimiento de la demanda y la falta de planificación de generación adicionándole a esto que el área norte del SEIN es un sistema radial, en el cual un leve déficit de generación en esta área termina produciendo un problema de tensión que si no se controla adecuadamente terminaría en un severo colapso de tensión. En este trabajo, la determinación de las sensibilidades, se realizó mediante el análisis de la matriz Jacobiana, utilizando el método de resolución de flujos de potencia Newton Rhapson. Este análisis nos ayuda a hacer de manera más eficiente el control de potencia activa y reactiva, así como los rechazos de carga manual debido a bajos perfiles de tensión producidos por un déficit de generación. En consecuencia, el planteamiento efectuado en esta tesis constituiría una solución de corto plazo para mejorar y hacer más eficiente el control de tensión en el área norte del SEIN, hasta que se implementen soluciones más robustas de largo plazo.
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Vivo, Pierpaolo. "From Wishart to Jacobi ensembles : statistical properties and applications." Thesis, Brunel University, 2008. http://bura.brunel.ac.uk/handle/2438/2733.
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Sixty years after the works of Wigner and Dyson, Random Matrix Theory still remains a very active and challenging area of research, with countless applications in mathematical physics, statistical mechanics and beyond. In this thesis, we focus on rotationally invariant models where the requirement of independence of matrix elements is dropped. Some classical examples are the Jacobi and Wishart-Laguerre (or chiral) ensembles, which constitute the core of the present work. The Wishart-Laguerre ensemble contains covariance matrices of random data, and represents a very important tool in multivariate data analysis, with recent applications to finance and telecommunications. We will first consider large deviations of the maximum eigenvalue, providing new analytical results for its large N behavior, and then a power-law deformation of the classical Wishart-Laguerre ensemble, with possible applications to covariance matrices of financial data. For the Jacobi matrices, which arise naturally in the quantum conductance problem, we provide analytical formulas for quantities of interest for the experiments.
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Esteve, yague Carlos. "Étude qualitative de trois problèmes paraboliques non-linéaires." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCD033.
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Cette thèse est consacrée à l'étude de trois problèmes paraboliques non linéaires : Premièrement, nous considérons un modèle de systèmes micro-électro-mécaniques (MEMS) avec permittivité diélectrique variable. Le modèle est basé sur une équation parabolique avec non-linéarité singulière, qui décrit la déformation dynamique d'une plaque élastique sous les effets d'un potentiel électrostatique. Nous étudions le phénomène de touchdown, ou quenching. Avec le but de contrôler l'ensemble de touchdown, nous donnons des résultats concernant la localisation du touchdown, en termes du profil de permittivité. Dans la deuxième partie de la thèse, nous étudions une équation de Hamilton-Jacobi avec diffusion dans un domaine borné avec conditions de Dirichlet nulles au bord. On analyse l'explosion du gradient (GBU) qui peut avoir lieu sur le bord du domaine. Dans un article précédent, il a été démontré, pour des domaines très particuliers (domaines localement plats et disques), qu'il est possible de construire des solutions pour lesquelles l'ensemble de GBU est réduit à un seul point. Nous démontrons qu'il est possible de construire ce type de solutions pour une large classe de domaines, où la courbure n'est pas forcement constante près du point de GBU.Dans la dernière partie de la thèse, nous étudions le problème d'évolution associé à la j-ème valeur propre de la matrice Hessienne. On démontre tout d'abord l'existence d'une (unique) solution de viscosité, qui peut être approximée par la fonction valeur d'un jeu à deux joueurs et somme nulle, quand la longueur du pas du jeu tend vers 0.On démontre ensuite la convergence exponentielle des solutions du problème d'évolution vers l'unique solution stationnaire. Finalement, pour des cas particuliers (avec données au bord affines), on démontre que la solution coïncide avec la solution stationnaire en temps finiThis thesis is concerned with the study of three nonlinear parabolic problems : We start with a mathematical model for a micro-electro-mechanical system (MEMS) with variable dielectric permittivity. The model is based on a parabolic equation with singular nonlinearity which describes the dynamic deffection of an elastic plate under the effect of an electrostatic potential. We study the touchdown, or quenching, phenomenon. With the aim of controlling the touchdown set, we give results concerning the touchdownl ocalization in terms of the permittivity profile. In the second part of the thesis, we study a diffusive Hamilton-Jacobi equation in a bounded domain with zero Dirichlet boundary conditions. We analyze the gradient blow-up (GBU) that solutions can exhibit on the boundary of the domain. In a previous work, it was shown that single-point GBU solutions can be constructed in very particular domains, namely, locally fat domains and disks. We prove the existence of this kind ofsolutions for a large family of domains, for which the curvature of the domain may be nonconstant near the GBU point. In the last part of the thesis, we study the evolution problem associated to the j-th eigenvalue of the Hessian matrix. First, we show the existence of a (unique) viscosity solution, which can be approximated by the value function of a two-player zero-sumgame as the step length of the game goes to zero. Then, we show that solutions to this evolution problem converge exponentially fast to the unique stationary solution as t goes to ∞. Finally, we show that in some special cases (for affine boundary data) the solution coincides with the stationary solution in finite time
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Balderrama, Cristina. "Orthogonal polynomials with hermitian matrix argument and associated semigroups." Angers, 2009. http://www.theses.fr/2009ANGE0035.
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Dans ce travail, nous construisons et étudions des familles de polynômes orthogonaux généralisés définis dans l'espace des matrices hermitiennes qui sont associées à une famille de polynômes orthogonaux sur R. Nous considérons plusieurs normalisations pour ces polynômes, et obtenons des formules classiques à partir des formules correspondantes pour des polynômes définis sur R. Nous construisons également des semi-groupes d'opérateurs associés aux polynômes orthogonaux généralisés, et donnons l'expression du générateur infinitésimal de ce semi-groupe ; nous prouvons que ce semi-groupe est markovien dans les cas classiques. En ce qui concerne les expansions d-dimensionnelles de Jacobi nous étudions les notions d'intégrale fractionnelle (potentiel de Riesz), de potentiel de Bessel et de dérivées fractionnelles. Nous donnons une nouvelle décomposition de l'espace L2 associé à la mesure de Jacobi d-dimensionnelle, et obtenons un analogue du théorème du multiplicateur de Meyer dans ce cadre. Nous étudions aussi les espaces de Jacobi-SobolevIn this work we construct and study families of generalized orthogonal polynomials with hermitian matrix argument associated to a family of orthogonal polynomials on R. Different normalizations for these polynomials are considered and we obtain some classical formulas for orthogonal polynomials from the corresponding formulas for the one–dimensional polynomials. We also construct semigroups of operators associated to the generalized orthogonal polynomials and we give an expression of the infinitesimal generator of this semigroup and, in the classical cases, we prove that this semigroup is also Markov. For d–dimensional Jacobi expansions we study the notions of fractional integral (Riesz potentials), Bessel potentials and fractional derivatives. We present a novel decomposition of the L2 space associated with the d–dimensional Jacobi measure and obtain an analogous of Meyer's multiplier theorem in this setting. Sobolev Jacobi spaces are also studied
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Vinícius, Santos Dória André. "Aplicações birracionais em característica arbitrária." Universidade Federal de Pernambuco, 2011. https://repositorio.ufpe.br/handle/123456789/6962.
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Previous issue date: 2011Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Esta tese representa uma sequência natural a trabalhos de vários autores, em que se busca obter resultados novos sobre aplicações birracionais usando técnicas de álgebra comutativa. Uma das lacunas conhecidas é o problema da característica do corpo de base. Habitualmente tratados separadamente, o caso de característica zero e de característica prima, deixam a desejar do ponto de vista da unificação dos resultados gerais. Outro aspecto relevado é o do enunciado de critérios de birracionalidade alternativos ao tradicional cálculo do grau de uma aplicação racional. O principal objetivo deste trabalho é discutir um invariante numérico de birracionalidade válido em característica arbitrária, denominado posto Jacobiano dual. Este invariante depende fortemente da estrutura graduada da álgebra de Rees do ideal de base da aplicação racional, a qual permite uma análise mais precisa do que o tratamento geométrico habitual do gráfico como variedade \blowup
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Dória, André Vinícius Santos. "Aplicações birracionais em característica arbitrária." Universidade Federal de Pernambuco, 2011. https://ri.ufs.br/handle/riufs/1108.
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Esta tese representa uma sequencia natural a trabalhos de vários autores, em que se busca obter resultados novos sobre aplicações birracionais usando técnicas de álgebra comutativa. Uma das lacunas conhecidas é o problema da característica do corpo de base. Habitualmente tratados separadamente, o caso de característica zero e de característica prima, deixam a desejar do ponto de vista da unificação dos resultados gerais. Outro aspecto relevado é o do enunciado de critérios de birracionalidade alternativos ao tradicional cálculo do grau de uma aplicação racional. O principal objetivo deste trabalho é discutir um invariante numérico de birracionalidade válido em característica arbitrária, denominado posto Jacobiano dual. Este invariante depende fortemente da estrutura graduada da álgebra de Rees do ideal de base da aplicação racional, a qual permite uma análise mais precisa do que o tratamento geométrico habitual do gráfico como variedade "b lowup". _________________________________________________________________________________________ ABSTRACT: This thesis stands as a natural sequence to the work of several authors, seeking to obtain new results on birational maps using techniques from commutative algebra. One of the classical problems in the theory of birational maps is the case where the characteristic of the base field is positive. The usual separate treatment of the case of characteristic zero and characteristic prime falls short of unifying general results. Another aspect scarcely dealt with is the statement of a birationality criterion which stands as an alternative to the traditional calculation of the degree of a rational map. The main objective of this work is a numerical invariant of birationality valid in arbitrary characteristic, called the Jacobian dual rank. This invariant depends strongly on the structure of the graded Rees algebra of the base ideal of a rational map, which allows a more precise analysis than the usual geometric treatment of the graph as a "blowup".
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Vasconcelos, de Araújo Kalasas. "A Álgebra de Gauss de uma Álgebra Monomial." Universidade Federal de Pernambuco, 2007. https://repositorio.ufpe.br/handle/123456789/7075.
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Previous issue date: 2007Universidade Federal de Sergipe
A álgebra de Gauss associada à k-subálgebra de um anel polinomial k[t0; : : : ; td] gerado por um número finito de formas de mesmo grau corresponde ao anel de coordenadas homogêneo da imagem de Gauss de uma variedade projetiva uniracional sobre k. Focaremos o caso onde os geradores são monômios. Por caracterizar os menores da matriz jacobiana de um conjunto de monômios como certos n-produtos tornaremos mais concreta a natureza da álgebra de Gauss associada à subálgebra monomial correspondente. A versão reticulada destes n-produtos permite uma abordagem combinatória ao tema. Neste caminho, provaremos resultados já obtidos e estudaremos em detalhes a álgebra de Gauss associada ao conjunto dos monômios livre de quadrados de grau dois
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Harrat, Ayoub. "Problème de moments avec applications et estimations du spectre discret des opérateurs définis par des matrices infinies non bornées THE QUINTIC COMPLEX MOMENT PROBLEM ASYMPTOTIC EXPANSION OF LARGE EIGENVALUES FOR A CLASS OF UNBOUNDED JACOBI MATRICES." Thesis, Littoral, 2020. http://www.theses.fr/2020DUNK0563.
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Dans cette thèse on donne d'abord une solution concrète pour presque tous les scénarios qu'on peut avoir dans le problème de moments complexe quintique et en particulier dans le cas d'une mesure à support minimal. On présente aussi de nombreux exemples pour illustrer chaque cas. La seconde partie présente une approche qui permet de passer du problème de moments tronqué au problème complet à l'aide des idempotents. Il s'agit d'une approche très différente de celle utilisée dans la première partie.Plus précisément, au lieu d'appliquer les méthodes de R. Curto et L. Fialkow où l'objet central est la matrice de moments, on utilise l'approche de F. Vasilescu dont l'objet central est la fonctionnelle de Riesz. Cette fonctionnelle fait associer à chaque monôme tᵅ la valeur γ∝ et elle satisfait trois conditions naturelles dans le cas où la suite (γ∝)∝∈ℕᵈ est donnée par les intégrales de tᵅ par rapport à une mesure. La troisième partie est consacrée à l'asymptotique du spectre pour une classe de matrices hermitiennes tridiagonales infinies. Le but est d'obtenir le comportement asymptotique précis des valeurs propres y associées à partir du comportement asymptotique de ces coefficients. Le résultat est obtenu par une approche nouvelle qui est une adaptation de la théorie de perturbations de Schrieffer-Wolff utilisée en physique de la matière condensée. Cette méthode marche également pour des matrices 'bande', mais le cas des matrices tridiagonales est le plus important pour des applications et encore les expressions explicites des premières corrections dans la formule asymptotique sont plus simples pour les matrices tridiagonalesIn this thesis, we first provide a concrete solution to the, almost all, quintic TCMP (that is, when m = 5). We also study the cardinality of the minimal representing measure. Based on the bi-variate recurrence sequence properties with some Curto-Fialkow's results. Our method intended to be useful for all odd-degree moment problems. Second, we investigate the full moment problem for discrete measures using Vasilescu's idempotent approach based on Λ-multiplicative elements with respect to the associated square positive Riesz functional. We give a sufficient condition for the existence of a discrete integral representation for the associated Riesz functional, which turns to be necessary in bounded shift space case. A particular attention is given to Λ-multiplicative elements, where a total description, for the cases where they are a single point indicator functions, is given. Lastly, We investigate a class of infinite Jacobi matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly. This method works in general for band matrices but Jacobi matrices case still much interesting due to applications and explicit expressions obtained for the first correction terms in the asymptotic formula
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Marchi, Tommaso. "Position and singularity analysis of a class of n-RRR planar parallel robots." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
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Parallel robots with configurable platform are a class of parallel robots in which the end-effector is a closed-loop flexible chain of rigid links. We have developed a 5-RRR planar mechanism that features a flexible 5-bar chain as end-effector. The angles between adjacent sides of this chain can be controlled through the actuated revolute joints attached to the base of the mechanism. This thesis consists in the geometrical design of n-RRR planar parallel robots and in the study of the Direct Kinematics for 4-, 5- and 6-RRR mechanisms using Bilateration, a method that greatly reduces the computational time for the kinematic analysis. The next step is the singularity analysis for the n-RRR robot architectures; finally, in the last part of this thesis we present the results from experimental tests that have been performed on a 5-RRR robot prototype.
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Castelain, Jean-Marie. "Application de la méthode hypercomplexe aux modélisations géométriques et différentielles des robots constitués d'une chaîne cinématique simple." Valenciennes, 1986. https://ged.uphf.fr/nuxeo/site/esupversions/bc4218bf-1a8a-40bb-b433-53644d00e666.
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L'objet de la thèse est l'application de la méthode hypercomplexe a l'étude cinématique d'une classe importante de robots. Apres avoir précise la structure algébrique générale des systèmes hypercomplexes et précise les éléments de l'analyse hypercomplexe nécessaire a l'objet, une étude des mouvements de points et de droites orientées est développée sur base d'un système hypercomplexe particulier: les biquaternions. Dans une seconde partie du mémoire, cette étude est appliquée a l'analyse géométrique des chaines cinématiques élémentaires et ouvertes. L’efficacité de la méthode hypercomplexe est révélée par l'application des modélisations proposées, a la commande de robots industriels
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Adams, Ross Montague. "A study of a class of invariant optimal control problems on the Euclidean group SE(2)." Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1006060.
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The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.
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Labro, Henri. "Application de la dynamique des systèmes a la cinétique chimique." Rouen, 1998. http://www.theses.fr/1998ROUES079.
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Les mécanismes détaillés de cinétique chimique sont difficiles à prendre en compte lorsqu'ils sont inclus dans des codes de calculs simulant des processus de combustion multidimensionnels. Il faut donc avoir recours à des procédés de réduction des systèmes chimiques, sans perdre trop d'informations sur la dynamique globale de ces systèmes. Le nombre des équations différentielles décrivant la cinétique chimique est réduit à l'aide d'un découplage des processus lents et rapides. Deux types de méthodes sont proposés pour simplifier les systèmes chimiques. La première méthode est développée à partir des concepts de la dynamique des systèmes. Une telle approche est basée sur l'estimation des valeurs propres de la matrice jacobienne au voisinage des points fixes. Une analyse de stabilité de tous les points fixes du modelé de Lorenz 9D est ainsi effectuée. Des propriétés de symétrie en sont déduites et une étude des bifurcations est réalisée. Pour un modèle décrivant une réaction chimique, l'obtention de tous les points fixes et l'analyse de stabilité de chacun d'eux permettent d'identifier les variables impliquées dans les processus rapides et celles intervenant dans les phénomènes lents. Des modèles réduits sont élaborés en appliquant des approximations classiques. Deux systèmes de dimensions 4 et 5 issus d'un modèle de Belousov-Zhabotinskii 7D sont alors construits. Mais, la méthode ne peut s'appliquer sur des modèles de combustion car les méthodes de recherche de points fixes échouent. C'est pourquoi, une autre procédure pour simplifier les systèmes chimiques est élaborée. Cette technique consiste à prédire les évolutions du système chimique considéré à l'aide d'une décomposition sur la base des vecteurs propres. Des approximations relatives aux évolutions rapides sont appliquées. Un modèle réduit est ainsi construit.
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Pereira, Hivy Queiroz. "Fluxo de potência trifásico: um estudo comparativo e uma nova metodologia de solução." Universidade Federal de Juiz de Fora (UFJF), 2006. https://repositorio.ufjf.br/jspui/handle/ufjf/3282.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Este trabalho apresenta um estudo comparativo das características de convergência das formulações convencional polar, convencional retangular e injeção de corrente na solução do fluxo de potência trifásico. As metodologias polar e retangular utilizam as equações de potência injetada nas barras expressas em função das coordenadas polares e retangulares da tensão, respectivamente. A formulação de injeção de corrente utiliza as equações de corrente injetada nas barras expressas em termos das coordenadas retangulares da tensão. As equações não lineares referentes a cada um dos métodos são resolvidas através do processo iterativo de Newton-Raphson. Além disto, a manutenção da matriz Jacobiana constante durante o processo iterativo é também investigada. Por outro lado, este trabalho também propõe uma metodologia para a solução do fluxo de potência trifásico sujeito a condições iniciais desfavoráveis. Este método baseia se numa característica particular inerente à formulação de injeção de corrente. O método é simples e rápido, garantindo a convergência do processo iterativo. Os resultados são bastante satisfatórios, demonstrando a eficácia do método proposto em situações nas quais as formulações convencionais de solução do fluxo de potência falham na convergência do processo iterativo.
This work presents a comparative study on convergence characteristics of some three-phase power flow methods, namely, conventional polar, conventional rectangular and current injection formulations. The polar and rectangular methodologies use the injected power equations written in terms of voltage polar and voltage rectangular coordinates, respectively. The current injection method employs the injected current equations expressed in function of voltage rectangular coordinates. The nonlinear equations associated with each method are solved iteratively through Newton-Raphson approach. Moreover, the strategy of keeping the Jacobian matrix constant throughout the iterative process is also investigated. On the other hand, this work also proposes a new methodology for solving threephase power flow problems subjected to poor initial conditions. This method is based on a particular convergence feature inherent in the power flow current injection formulation. It is simple and fast, ensuring the convergence of the iterative process. The results are quite satisfactory and demonstrate the effectiveness of the proposed approach on problems where standard three-phase power flow formulations fail to converge.
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Merelli, Elisa. "Calcolo del Pagerank: una formulazione basata sulla risoluzione di sistemi lineari." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23202/.
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L'obiettivo di questo elaborato è introdurre il problema del calcolo del vettore di PageRank, mostrare come è tradizionalmente risolto e esporre una formulazione alternativa che richiede la risoluzione di sistemi lineari. La trattazione di conclude mostrando i risultati di un'analisi sperimentale volta ad applicare le conoscenze teoriche ad un caso reale.
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Foumouo, Emmanuel. "Problème coulombien à trois corps en champ haute fréquence : application à l'étude de l'ionisation double à deux photons de l'hélium." Université catholique de Louvain, 2008. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-02172008-222015/.
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Ce travail porte sur l’étude théorique de la double ionisation à deux photons de l’atome d’hélium avec comme objectif de comprendre le rôle des corrélations électroniques dans le mécanisme de double éjection. En analysant les distributions en énergie et les distributions angulaires des électrons émis, nous montrons que lors du processus direct, le système initialement dans son état fondamental évolue vers un état hautement corrélé. Les corrélations angulaires forcent les deux électrons à être éjectés dans des directions opposées, le long de l’axe de polarisation. Sous l’effet de "l’écrantage dynamique" c’est-à-dire des corrélations radiales, les deux électrons ont tendance à partager équitablement l’énergie disponible au dessus du seuil de double ionisation. Pour valider ou invalider ce mécanisme, nous proposons de mesurer la distribution des impulsions des ions doublement chargés He++. Tous ces résultats s’obtiennent en résolvant l’équation de Schrödinger dépendante du temps à l’aide d’une méthode spectrale combinée à celle de la matrice de Jacobi. En parallèle, et toujours dans le cas de l’ionisation double à deux photons de l’hélium, nous analysons les effets des corrélations électroniques à l’échelle attoseconde.
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Jha, Vijay. "The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem /." Kingston, Ont., Canada : Queen's University, 1993. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=005385035&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Calisti, Matteo. "Misure di Hausdorff e formula dell'area in R^n." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17037/.
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La misura di Lebesgue permette di misurare il volume degli oggetti n-dimensionali di R^n, ma tutti quelli di dimensione inferiore s come le superfici sono sottoinsiemi di R^n di misura di Lebesgue nulla. Non potendo definire una nozione, ad esempio, di "area" attraverso suddivisioni successive come per la lunghezza di una curva si ricorre alla teoria della misura definendo la misura di Hausdorff s-dimensionale. Viene dapprima esposta la teoria della misura nella sua generalità, con alcune proprietà delle misure astratte e della sigma-algebra di Borel, una loro classificazione e alcuni teoremi di ricoprimento (in particolare quello di Vitali) a cui si farà ricorso dopo. Successivamente vengono introdotte la premisura e misura di Hausdorff H^s, alcune sue prime proprietà e la dimensione di Hausdorff dim_H. Viene studiato il comportamento di H^s e dim_H sotto l'effetto di funzioni lipschitziane e bilipschitziane con studio della dimensione di Hausdorff dell'insieme di Cantor e un breve accenno ai frattali e la loro relazione con le funzioni bilipschitziane. Un tema centrale per poter introdurre la formula di area è la simmetrizzazione di Steiner: ne vengono dimostrate le proprietà principali e attraverso di essa si dimostra la disuguaglianza isodiametrica e l'uguaglianza tra le misure di Hausdorff e di Lebesgue, quando s=n. Infine si dimostra la formula dell'area dapprima per insiemi piatti e poi per insiemi parametrizzabili e nell'Appendice si giustifica l'utilizzo della costante di normalizzazione nella definizione di H^s.
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Pasca, Bogdan Mihai. "Calcul flottant haute performance sur circuits reconfigurables." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00654121.
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De plus en plus de constructeurs proposent des accélérateurs de calculs à base de circuits reconfigurables FPGA, cette technologie présentant bien plus de souplesse que le microprocesseur. Valoriser cette flexibilité dans le domaine de l'accélération de calcul flottant en utilisant les langages de description de circuits classiques (VHDL ou Verilog) reste toutefois très difficile, voire impossible parfois. Cette thèse a contribué au développement du logiciel FloPoCo, qui offre aux utilisateurs familiers avec VHDL un cadre C++ de description d'opérateurs arithmétiques génériques adapté au calcul reconfigurable. Ce cadre distingue explicitement la fonctionnalité combinatoire d'un opérateur, et la problématique de son pipeline pour une précision, une fréquence et un FPGA cible donnés. Afin de pouvoir utiliser FloPoCo pour concevoir des opérateurs haute performance en virgule flottante, il a fallu d'abord concevoir des blocs de bases optimisés. Nous avons d'abord développé des additionneurs pipelinés autour des lignes de propagation de retenue rapides, puis, à l'aide de techniques de pavages, nous avons conçu de gros multiplieurs, possiblement tronqués, utilisant des petits multiplieurs. L'évaluation de fonctions élémentaires en flottant implique souvent l'évaluation en virgule fixe d'une fonction. Nous présentons un opérateur générique de FloPoCo qui prend en entrée l'expression de la fonction à évaluer, avec ses précisions d'entrée et de sortie, et construit un évaluateur polynomial optimisé de cette fonction. Ce bloc de base a permis de développer des opérateurs en virgule flottante pour la racine carrée et l'exponentielle qui améliorent considérablement l'état de l'art. Nous avons aussi travaillé sur des techniques de compilation avancée pour adapter l'exécution d'un code C aux pipelines flexibles de nos opérateurs. FloPoCo a pu ainsi être utilisé pour implanter sur FPGA des applications complètes.
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Vestin, Albin, and Gustav Strandberg. "Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms." Thesis, Linköpings universitet, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160020.
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Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms.
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Tai, Chi-yuan, and 戴啓原. "A Reinforcement Learning Approach to Timing Varying Image Jacobian Matrix." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/uj9h2d.
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碩士國立中山大學
電機工程學系研究所
107
The behavior of traditional image-based visual servoing method is unsatisfactory when current camera pose is very different from the desired, especially the rotational error along or around the optical axis. During the movement, it might encounter the singular point of image Jacobian matrix, causing the robot arm to lose control, or to leave the feature points out of FOV, resulting servoing failure. Therefore, this thesis propose a reinforcement learning approach to time varying image Jacobian matrix. It is implemented by Q-learning, because Q-learning is easy to realize and model-free. This thesis discretize image plane into state space according to the location of feature points, and the action space is composed of the linear combination of image Jacobian matrix. Then, according to current state, learning agent choose an action by ε-greedy policy. The agent finally get a reward by environment, and use it to update the policy. The agent will learn a policy approximate to the best solution through fully interaction with the environment. In order to verify the method proposed in this paper, a six-axis robot arm and a single-lens camera are used to form a visual servoing system. The method proposed in this thesis is verified by comparing the result with visual servo system using fixed image Jacobian matrix in the Webots simulation software and real world environment, respectively.
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施志玄. "Determining the reachable workspace of parallel manipulators using jacobian matrix." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/03408158935209613313.
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碩士國立臺灣科技大學
機械工程系
91
The existing methods to find the reachable workspace of a parallel manipulator either use searching approach or solve about 20 nonlinear equations. In this thesis an efficient method is proposed in which the boundaries of workspace can be determined by solving 4 nonlinear equations. Furthermore, the proposed method is applicable to many different types of parallel designs. The possible boundaries of workspace are generated by configurations in which 4 out of the 6 serial chains reach extreme positions, which means a total of 15 combinations have to be checked before we start to plot the workspace. This thesis first develops the necessary and conditions for the workspace boundaries using Jacobean matrix. The conditions significantly facilitate the searching process for the right combination to generate workspace boundaries. The reachable workspace of parallel manipulator can be efficiently determined with the conditions and the proposed method.
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Hsu, Yu-Lun, and 許育綸. "The Estimation of Image Jacobian Matrix for Image-based Uncalibrated Visual Servoing." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/51734124412821656514.
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碩士國立交通大學
電機與控制工程系所
97
This thesis proposes an image-based visual servo system, which can estimate and update Image Jacobian Matrix to control a robot arm without camera calibration. There are two parts in the visual servo system. The first one is image feature extraction. We apply the Mean-Shift algorithm in order to improve the performance of feature tracking. Mean-Shift algorithm, which takes the color distribution as a model, is based on the similarity measure function to decide a tracking candidate. This algorithm works well in a real-time and complicated environment. The second part is the control of a manipulator to track visual objects. An easy-to-implement algorithm is proposed to find the relationship between the camera and the manipulator. It can be carried out easily as compared with other methods. We use the camera and the manipulator emulator to simulate the system effectively. In the implementation, we use only one computer to develop all the software, including the communication to the manipulator and the processing of two cameras' images to solve the local and the global Image Jacobian matrices. Ball-hitting experiments such as the juggling task are presented to analyze the real-time performance of the proposed algorithms.
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Xiong, Xin. "Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation." Thesis, 2014. http://hdl.handle.net/10012/8197.
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This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear
vector maps using automatic differentiation (AD). Specifically, we propose the use of
two directed edge separator methods, the weighted minimum separator and natural order separator methods, to exploit the structure of the computational graph of the nonlinear system.This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments.
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Li, Jian. "Design of 3-DOF parallel manipulators for micro-motion applications." Thesis, 2009. http://hdl.handle.net/10155/68.
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This thesis presents two unique micro-motion parallel kinematic manipulators (PKM):
a three degrees of freedom (3-DOF) micro-motion manipulator and a 3-DOF micro-motion
manipulator with actuation redundancy. The 3-DOF micro-motion manipulator has three
linear-motion driving units, and the 3-DOF micro-motion manipulator with redundancy has
four of these units.
For both designs, the linear motion driving units are identical, and both machines
have a passive link in the center of the structure. The purpose of this passive link is to
restrain the movement of the manipulator and to improve the stiffness of the structure. As a
result, both structures support 3-DOF, including one translation on the Z-axis and two
rotations around the X and Y axes. The manipulator with redundancy is designed to prevent
singularity and to improve stiffness.
In this thesis, the inverse kinematic, Jacobian matrix and stiffness analyses have been
conducted, followed by the design optimization for structures. Finally, the FEA (Finite
Element Analysis) and dynamic analysis have also been performed.
There are many practical applications for micro-motion parallel manipulators. The
typical applications include micro-machine assembly, biological cell operation, and microsurgery
.UOIT
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Khazenifard, Amirhosein. "Improved measure of orbital stability of rhythmic motions." Thesis, 2017. https://dspace.library.uvic.ca//handle/1828/8822.
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Rhythmic motion is ubiquitous in nature and technology. Various motions of organisms like the heart beating and walking require stable periodic execution. The stability of the rhythmic execution of human movement can be altered by neurological or orthopedic impairment. In robotics, successful development of legged robots heavily depends on the stability of the controlled limit-cycle. An accurate measure of the stability of rhythmic execution is critical to the diagnosis of several performed tasks like walking in human locomotion. Floquet multipliers have been widely used to assess the stability of a periodic motion. The conventional approach to extract the Floquet multipliers from actual data depends on the least squares method. We devise a new way to measure the Floquet multipliers with reduced bias and estimate orbital stability more accurately. We show that the conventional measure of the orbital stability has bias in the presence of noise, which is inevitable in every experiment and observation. Compared with previous method, the new method substantially reduces the bias, providing acceptable estimate of the orbital stability with fewer cycles even with different noise distributions or higher or lower noise levels. The new method can provide an unbiased estimate of orbital stability within a reasonably small number of cycles. This is important for experiments with human subjects or clinical evaluation of patients that require effective assessment of locomotor stability in planning rehabilitation programs.Graduate
2018-11-22
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Pereira, André Filipe Gomes. "On the Constitutive Parameters Identification of Metal Sheets: Bulge, Shear and Tensile Tests." Doctoral thesis, 2019. http://hdl.handle.net/10316/87395.
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Tese de Doutoramento em Engenharia Mecânica, no ramo de Produções Tecnológicas, apresentada ao Departamento de Engenharia Mecânica da Faculdade de Ciências e Tecnologia da Universidade de CoimbraA modelação do comportamento plástico de chapas metálicas é um aspeto importante a ter em conta na utilização apropriada da análise por elementos finitos para otimização e desenvolvimento de processos de conformação. A utilização de novas ligas na indústria também tem estimulado o desenvolvimento de novos modelos constitutivos e, consequentemente, o interesse renovado pela identificação de parâmetros. Este trabalho pretende contribuir para o desenvolvimento de estratégias clássicas e inversas de identificação dos parâmetros do modelo constitutivo (critério de plasticidade e leis de encruamento), fazendo uso de ensaios mecânicos simples (tração, corte e o ensaio hidráulico de expansão biaxial), mas evitando as simplificações normalmente utilizadas na análise clássica dos seus resultados. As estratégias de identificação inversa são geralmente entendidas como problemas de otimização, cujo objetivo é minimizar a diferença entre resultados numéricos e experimentais. No método de atualização do modelo de elementos finitos, esta minimização é geralmente realizada com algoritmos de otimização baseados na determinação do gradiente, o que envolve o cálculo da matriz de sensibilidade. Esta matriz é tipicamente avaliada usando diferenças finitas, que podem ser computacionalmente dispendiosas. Neste trabalho, propõe-se uma abordagem analítica alternativa para o cálculo eficiente da matriz de sensibilidade, aplicável na identificação dos parâmetros das leis de encruamento isotrópico e cinemático. Esta abordagem analítica apoia-se na observação empírica de sensibilidades idênticas dos resultados numéricos, pressão vs. altura de polo e tensão de escoamento vs. altura de polo, às variações dos parâmetros do encruamento, durante o ensaio hidráulico de expansão biaxial. Posteriormente, a abordagem foi testada em estratégias inversas, que recorrem ao ensaio hidráulico de expansão biaxial, ao ensaio de tração biaxial num provete cruciforme e ao ensaio de corte com inversão de trajetória, e os resultados das identificações foram comparados com os obtidos com diferenças finitas. A estratégia proposta provou ser uma alternativa precisa e expedita.
O ensaio hidráulico de expansão biaxial é uma importante ferramenta de caracterização mecânica, devido à possibilidade de avaliar a resposta do material numa trajetória de deformação biaxial, até grandes níveis de deformação plástica. A determinação da curva tensão biaxial vs. deformação é geralmente realizada com recurso à teoria da membrana e assumindo um estado de tensão equibiaxial no polo do provete, o que pode introduzir erros significativos na determinação da curva tensão biaxial vs. deformação, de materiais proeminentemente anisotrópicos. Para superar esta simplificação e facilitar o procedimento experimental, propõe-se uma estratégia inversa para identificar os parâmetros de leis de encruamento isotrópico. A estratégia recorre ao método de Levenberg-Marquardt para minimizar de forma sequencial a diferença entre as curvas numéricas e experimentais de pressão vs. altura de polo do ensaio hidráulico de expansão biaxial, em matrizes circular e elíptica. Os resultados da identificação são comparados com os obtidos pela teoria da membrana em materiais fictícios, e o procedimento inverso é posteriormente aplicado a casos experimentais. Para materiais anisotrópicos, a metodologia proposta representa uma clara melhoria em comparação com a teoria da membrana, permitindo a determinação precisa dos parâmetros da lei de encruamento isotrópico, independentemente do critério de plasticidade que melhor descreve o comportamento anisotrópico do material. Os ensaios de corte são um modo conveniente de caracterizar o comportamento mecânico de chapas metálicas para grandes deformações e possibilitam a inversão da direção de carregamento para identificar os parâmetros do encruamento cinemático. A análise tradicional dos resultados do ensaio de corte negligencia o aparecimento de componentes normais durante o ensaio, apesar destas poderem ter magnitudes semelhantes à da componente de corte. No presente trabalho, recorre-se a simulações numéricas do ensaio de corte para estudar o impacto da anisotropia do material, da geometria do provete, das condições de fronteira e da direção de carregamento, nas componentes normais. Com base nestes resultados, é proposta uma abordagem analítica para prever essas componentes durante o ensaio de corte. As componentes normais previstas estão em conformidade com as avaliadas numericamente, e o seu uso permite a correta determinação da curva de tensão vs. deformação equivalente do ensaio de corte.
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Afzal, Mohammad. "On efficient and adaptive modelling of friction damping in bladed disks." Doctoral thesis, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-202978.
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This work focuses on efficient modelling and adaptive control of friction damping in bladed disks. To efficiently simulate the friction contact, a full-3D time-discrete contact model is reformulated and an analytical expression for the Jacobian matrix is derived that reduces the computation time drastically with respect to the classical finite difference method. The developed numerical solver is applied on bladed disks with shroud contact and the advantage of full-3D contact model compared to a quasi-3D contact model is presented. The developed numerical solver is also applied on bladed disks with strip damper and multiple friction contacts and obtained results are discussed. Furthermore, presence of higher harmonics in the nonlinear contact forces is analyzed and their effect on the excitation of the different nodal diameters of the bladed disk are systematically presented. The main parameters that influence the effectiveness of friction damping in bladed disks are engine excitation order, contact stiffnesses, friction coefficient, relative motion at the friction interface and the normal contact load. Due to variation in these parameters during operation, the obtained friction damping in practice may differ from the optimum value. Therefore, to control the normal load adaptively that will lead to an optimum damping in the system despite these variations, use of magnetostrictive actuator is proposed. The magnetostrictive material that develops an internal strain under the influence of an external magnetic field is employed to increase and decrease the normal contact load. A linearized model of the magnetostrictive actuator is used to characterize the magnetoelastic behavior of the actuator. A nonlinear static contact analysis of the bladed disk reveals that a change of normal load more than 700 N can be achieved using a reasonable size of the actuator. This will give a very good control on friction damping once applied in practice.QC 20170310
TurboPower
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Chang, Tian-Tsair, and 張天財. "On the Numerical Construction of a Jacobi Matrix." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/54422755042942493348.
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碩士國立政治大學
應用數學系
87
In this thesis seven methods LMGS、ITQR、imITQR、CB、HH、TLS and TLD developed in the past are applied to construct a Jacobi matrix. We use the known eige- envalues and the first components of eigenvctors of a Jacobi matrix to execute thes- e algorithms and list the numerical results and compare the accuracy of the computed Jacobi matrix.
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Wong, Peng-Jie, and 翁鵬絜. "Some inverse problems with mixed spectral data for the Jacobi matrix and the Green's matrix." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/06354506467991107655.
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碩士國立清華大學
數學系
100
Applying the factorization of some related matrix functions, we investigate some inverse problems with mixed spectral data for Jacobi matrices and Stieltjes strings. Besides, we prove a discrete analogue of Borg's theorem for the Green's matrix. We also study the first eigenvalue, and the ratio of the first two eigenvalues of the Stieltjes string equation. With certain restrictions on the class of density sequences $p$, we determine the shapes of the extremal density sequence for the first eigenvalue, and the minimum for the ratio of the first two eigenvalues.
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Tsou, Tsai-Jung, and 鄒采蓉. "Some eigenvalue problems related to the Stieltjes string and the Jacobi matrix." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/92010065561199531601.
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碩士國立清華大學
數學系
101
With the help of methods developed for the Jacobi continued fraction and the Stieltjes continued fraction, we investigate some inverse spectral problems related to the Jacobi matrix equation and the Stieltjes string equation, which may be viewed respectively as the discrete analogues of the potential equation and the string equation studied in the classical theory of Sturm-Liouville equations. We prove, among others, a Dirichlet-Neumann-isospectral theorem for Stieltjes string equations, we find a necessary and sufficient condition for the transformability of a Jacobi matrix equation into a Stieltjes string equation and provide a transformation method. We investigate a theory of Jacobi matricial couples which is related to the two spectra Borg's theorem in the theory of Sturm-Liouville equations. We also consider some inverse spectral problems related to persymmetric Jacobi matrices and even Stieltjes strings with prescribed eigenvalues.
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Pei, Yuk Kong, and 費毓港. "On some eigenvalue problems of Jacobi matrices and selfadjoint second order linear differential systems with Jacobi matrix- valued coefficients." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/41007336024216030664.
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