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Li, Xi. "Focused inverse method for LF." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18796.
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Logical frameworks allow us to specify formal systems and prove properties about them. One interesting logical framework is Twelf, a language that uses higher order abstract syntax to encode object languages into the meta language. Currently, uniform proofs have been used for describing proof search in backwards logic programming style. However, there are certain limitations to a backward system, for example, loop-detection mechanisms are required for some of the simplest problems to yield a solution. As a consequence, the search for a more effective proof search algorithm prevails and a forward system is proposed. This thesis will discuss the theoretical foundations for a forward uniform sequent calculus and the implementation of an inverse method prover for Twelf.<br>Les cadres logiques nous permettent de spécifier des systèmes formels et de prouver des propriétés à leur sujet. Un cadre logique intéressant est Twelf, un langage qui emploie la syntaxe abstraite d'ordre supérieur pour encoder des langages objet dans le méta-langage. Actuellement, nous employons des preuves uniformes pour décrire la recherche dans le style de programmation logique arrière. Cependant, il y a certaines limitations à un système arrière: des mécanismes de détection de boucle sont nécessaires pour trouver une solution à certains des problèmes les plus simples. Par conséquent, la recherche d'un algorithme plus efficace de recherche de preuve règne et un système vers l'avant est proposé. Cette thèse discutera les bases théoriques d'un calcul séquent uniforme vers l'avant et l'implantation d'un prouveur à méthode inverse pour Twelf.
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Deolmi, Giulia. "Computational Parabolic Inverse Problems." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.
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This thesis presents a general approach to solve numerically parabolic Inverse Problems, whose underlying mathematical model is discretized using the Finite Element method. The proposed solution is based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problem of pollution rate estimation.<br>In questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo viene descritto per due specici problemi: mentre il primo consiste nella stima della corrosione di una faccia incognita del dominio, il secondo ha come scopo la quanticazione di inquinante immesso in un fiume.
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Lin, Lianshan. "Characterization of material properties using inverse method." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505378.
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The inverse analysis introduced in this dissertation involves detennining an object's properties. In engineering problems, the most important object properties are material or constitutive constants (elastic/plastic). In direct problems, engineers can conveniently look up for the material constants in standard materials handbooks, and use them to pred'ict the structure's responses under the given loads. However, in the cases where the material constants are not available from standard handbooks, or the material properties need to be detennined precisely since a small difference from those listed may have a great influence on the results, inverse methods will need to be used. So far the characterization inverse methods focus mostly on homogeneous isotropic or orthotropic materials. Primarily the characterization concentrated on two important material parameters: Young's Modulus and Poisson's ratio. An experimental-numerical solution of inverse method is brought up, which is verified to be more efficient than previous methods, in the characterization of homogeneous isotropic materials and orthotropic materials. Another important part of this thesis is the inverse method for the characterization of heterogeneous material properties. Applications of this inverse method show its capability in predicting inhomogeneous distribution of material constants. Furthermore, this heterogeneous characterization method can also provide detail localized material information for studies such as trivial initial crack failure evolution, etc.
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QUEIROZ, MARCIO SANTOS DE. "INVERSE DYNAMICS METHOD FOR ROBOT MANIPULATOR CONTROL." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1993. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19548@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>O método da dinâmica inversa para o controle de manipuladores robóticos é apresentado. A ideia básica deste método é cancelar as não linearidades e acoplamentos, que caracterizam o comportamento dinâmico de manipuladores, através de um modelo dinâmico do mesmo (controlador primário). Com isto, o sistema resultante é linear e desaclopado, podendo ser controlado por técnicas de controle linear (controlador secundário). O método é inicialmente desenvolvido considerando o caso ideal do controlador primário (onde o modelo dinâmico é perfeito) e um PD para o controlador secundário.
As implicações de imperfeições no cancelamento das não linearidades e aclopamentos do sistema pelo controlador primário são mostradas. As duas formulações existentes para o controlador primário – computed – torque e feedforward – são descritas. É sugerida uma formulação híbrida para contornar os problemas de implementação das duas formulações. Um enfoque maior é dado às versões simplificadas da formulação computed – torque. Simulações são feitas para melhor esclarecer esta questão.
Em substituição ao PD, é descrito o projeto de um compensador linear robusto a partir do método das fatorações por matrizes própias e estáveis. O projeto é apresentado com análises mais detalhadas de algumas questões e com correções nos erros encontrados, em relação ao projeto existente na literatura. Análises comparativas com o PD são feitas e é explicada a influencia de frequências de amostragem no desempenho e ganhos do controlador PD.<br>The inverse dynamics control of robot manipulators is presented. The main idea of this control method is to cancel the nonlinearities and coupling effects, that describe the dynamic behavior of manipulators, using a dynamic model of the system (primary controller). Since the resulting system is linear and uncoupled, it can be controlled by linear control techniques (secondary controller). The method is initially derived considering the ideal case of the primary controller (where the dynamic model is perfect) and a PD for the secondary controller.
The implications of inexact cancelling of the system nonlinearities and coupling effects by the primary controller are shown. The two existing primary controller formulations – computed-torque and feedforward – are described. A hybrid formulations is suggested to overcome the implementation problems of the two formulations. Special attention is given to the simplified computed-torque schemes, which are subject of controversy in the literature. Simulations are performed to better illustrate this matter.
A robust linear compensator design, based on the stable factorization approach, is described analyses of some questions and with corrections of the detected mistakes, regarding the existing design. Comparative analyses with the PD are done. The effects of sampling rates on the tracking performances and PD gains are explained.
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Butler, Samuel Thomas James. "Inverse Scattering Transform Method for Lattice Equations." Thesis, The University of Sydney, 2012. http://hdl.handle.net/2123/8724.
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The main original contribution of this thesis is the development of a fully discrete inverse scattering transform (IST) method for nonlinear partial difference equations. The equations we solve are nonlinear partial difference equations on a quad-graph, also called lattice equations, which are known to be multidimensionally consistent in N dimensions for arbitrary N. Such equations were discovered by Nijhoff, Quispel and Capel and Adler and later classified by Adler, Bobenko and Suris. The main equation solved by our IST framework is the Q3δ lattice equation. Our approach also solves all of its limiting cases, including H1, known as the lattice potential KdV equation. Our results provide the discrete analogue of the solution of the initial value problem on the real line. We provide a rigorous justification that solves the problem for wide classes of initial data given along initial paths in a multidimensional lattice. Moreover, we show how soliton solutions arise from the IST method and also utilise asymptotics of the eigenfunctions to construct infinitely many conservation laws.
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Skare, Steven Edward. "An Inverse Design Method for Supersonic Airfoils." DigitalCommons@CalPoly, 2012. https://digitalcommons.calpoly.edu/theses/731.
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Airfoil design is one of the most important aspects of aircraft design. Slight changes in airfoil geometry can lead to significant changes in a wide variety of aircraft performance metrics. Inverse design methods offer an efficient alternative to standard direct methods. The key to this design problem is to derive a direct relationship between changes in airfoil geometry and changes in pressure or velocity distributions. This relationship is then used to modify an initial airfoil and its pressure distribution to match a target pressure distribution, which is specified by design parameters. At this point, the engineer now has a final airfoil based off of the design requirements.
This paper attempts to provide a quick and easy inverse design method for a wide variety of supersonic scenarios. This is accomplished by using the class-shape transformation technique to parameterize airfoils during an iterative process. The robustness of the method is demonstrated through several distinct design cases including supersonic airfoils, unique geometries, and a Sears-Haack body.
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Castellet, Llerena Albert. "Solving inverse kinematics problems using an interval method." Doctoral thesis, Universitat Politècnica de Catalunya, 1998. http://hdl.handle.net/10803/5936.
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de la tesi<br/><br/>El principal objectiu d'aquesta tesi és establir una base teòrica que permeti resoldre problemes cinemàtics inversos mitjançant mètodes d'intervals.<br/><br/>La primera part de la tesi desenvolupa i formalitza una nova metodologia per a l'anàlisi de cadenes cinemàtiques espacials. Aquest enfoc es basa en l'estudi de la varietat d'automoviment del mecanisme esfèric ortogonal i en la seva relació amb el mecanisme de n-barres. El principal avantatge respecte a altres mètodes és la seva senzillesa i sobretot la seva generalitat, que permet el mateix tractament del problema per a quelsevol cadena cinemàtica, independentment del nombre d'elements o de la seva geometria.<br/><br/>En la segona part de la tesi s'estudia la utilització de mètodes d'intervals per a la resolució de problemes cinemàtics. En primer lloc s'ha fet un estudi exhaustiu dels mètodes d'intervals ja existents per a la resolució de sistemes d'equacions no lineals. Tot seguit es desenvolupen mètodes ad hoc per al nostre problema i per a les equacions de tancament generals obtingudes en la primera part.<br/><br/>En l'últim capítol es proposa un algoritme per a la resolució del problema cinemàtic invers basat en una combinació de mètodes d'intervals clàssics (mètodes de Newton) i els mètodes específics que s'han desenvolupat (talls directes i propagació d'intervals). L'algoritme està justificat amb detall, així com la seva implementació. Al final es presenten uns quants experiments amb resultats que avalen l'algoritme i es comparen amb altres mètodes.<br/><br/>La resolució del problema cinemàtic invers s'ha basat històricament en dos mètodes principalment: els mètodes d'eliminació i els de continuació. L'alternativa mitjançant un mètode d'intervals que es proposa té diversos avantatges clars respecte als altres mètodes: és general per a qualsevol cadena cinemàtica de llaç simple, troba totes les solucions, evita problemes numèrics i d'arrodoniment i és simple d'implementar. No obstant, encara és més lent que els últims algoritmes basats en mètodes d'eliminació.<br/><br/>Cal destacar que es tracta del primer treball que utilitza mètodes d'intervals per a problemes relacionats amb la robòtica. Els resultats obtinguts permeten avançar que els mètodes d'intervals seran una alternativa als mètodes d'eliminació i continuació per a problemes cinemàtics en el futur.<br>This thesis constitutes an interesting approach to the kinematic analysis of spatial mechanisms. It establishes a theoretical basis for applying interval methods to the resolution of inverse kinematics problems. <br/><br/>A short introduction describes the problem and states the objectives of the work. The previous work is described here concisely, with enough relevant references, but avoiding anything superfluous.<br/><br/>The content of the thesis is divided into two naturally differentiated parts, corresponding to the kinematic analysis and to interval methods respectively.<br/><br/>In the first part, a new general framework for the kinematic analysis of spatial mechanisms is developed. This approach is based on the self-motion manifold of the orthogonal spherical mechanism and the closely related n-bar mechanism, which is used to represent any kinematic loop. This part is very complete and formally structured with rigorous definitions, lemmas, theorems and their proofs.<br/><br/>The second part of the thesis deals with interval methods. The first chapter of this part is devoted to survey the existing interval methods for solving systems of nonlinear equations. Clearness is used here in front of formalism, which makes it easier to get a general idea of the methods. The next chapter constitutes, the second main contribution of the thesis: the development of ad hoc interval methods for inverse kinematic problems. The proposed interval propagation based on spherical geometry is a smart idea, derived directly from a geometric interpretation derived in the first part.<br/><br/>The last chapter proposes a general interval method for solving positional inverse kinematics problems, based on a classic interval Newton method, complemented with the specific cuts of the previous chapter. Some few examples are given, which give all the solutions.<br/><br/>Using interval methods in kinematics is a novel idea and has not been seriously considered before. This thesis is a first important contribution herein, with important and promising results, but leaving still plenty of room for future work. Most probably, it will be a research focus in the near future.
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Hazarika, Neep. "An inverse method for blended wing-body configurations." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/12498.
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Figueiredo, Patric. "Iterative method for solving inverse heat conduction problems." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/14400.
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Kang, Sangwoo. "Direct sampling method in inverse electromagnetic scattering problem." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS417/document.
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Le problème de l'imagerie non itérative dans le cadre de la diffraction électromagnétique inverse utilisant la méthode d'échantillonnage direct (DSM) est considéré. Grâce à une combinaison de l'expression asymptotique du champ proche ou du champ lointain diffracté et de l'hypothèse de petits obstacles, les expressions analytiques de la fonction d'indicateur DSM sont présentées dans diverses configurations telles que des configurations 2D/3D, mono-/multi-configurations statiques, à vue limitée/complète et fréquence unique/ diversité en fréquence. Une fois l'expression analytique obtenue, sa structure est analysée et des améliorations proposées. Notre approche est validée à l’aide de données de simulation, et d’expériences le cas échéant. Premièrement, la structure mathématique du DSM à fréquence fixe en 2D dans divers problèmes de diffusion est établie, permettant une analyse théorique de son efficacité et de ses limites. Pour surmonter les limitations connues, une méthode alternative d'échantillonnage direct (DSMA) est proposée. Puis le cas multi-fréquence est investigué en introduisant et en analysant le DSM multi-fréquence (MDSM) et le DSMA multi-fréquence (MDSMA). Enfin, notre approche est étendue aux problèmes de diffraction électromagnétique inverse 3D pour lesquels le choix de la polarisation du dipôle de test est un paramètre clé. De par notre approche analytique, ce choix peut être effectué sur la base de la polarisation du champ incident<br>The non-iterative imaging problem within the inverse electromagnetic scattering framework using the direct sampling method (DSM) is considered. Thanks to the combination of the asymptotic expression of the scattered near-field or far-field and of the small obstacle hypothesis the analytical expressions of the DSM indicator function are presented in various configurations such as 2D/3D configurations and/or mono-/multi-static configurations and/or limited-/full-view case and/or mono-/multi-frequency case. Once the analytical expression obtained, its structure is analyzed and improvements proposed. Our approach is validated using synthetic data and experimental ones when available. First, the mathematical structure of DSM at a fixed frequency in 2D various scattering problems is established allowing a theoretical analysis of its efficiency and limitations. To overcome the known limitations an alternative direct sampling method (DSMA) is proposed. Next, the multi-frequency case is investigated by introducing and analyzing the multi-frequency DSM (MDSM) and the multi-frequency DSMA (MDSMA).Finally, our approach is extended to 3D inverse electromagnetic scattering problems for which the choice of the polarization of the test dipole is a key parameter. Thanks to our analytical analysis it can be made based on the polarization of the incident field
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Maree, A. J. "The inverse finite element method : sensitivity to measurement setup /." Link to the online version, 2005. http://hdl.handle.net/10019/1088.
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Silieti, Mahmood. "INVERSE BOUNDARY ELEMENT/GENETIC ALGORITHM METHOD FOR RECONSTRUCTION O." Doctoral diss., University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3325.
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A methodology is formulated for the solution of the inverse problem concerned with the reconstruction of multi-dimensional heat fluxes for film cooling applications. The motivation for this study is the characterization of complex thermal conditions in industrial applications such as those encountered in film cooled turbomachinery components. The heat conduction problem in the metal endwall/shroud is solved using the boundary element method (bem), and the inverse problem is solved using a genetic algorithm (ga). Thermal conditions are overspecified at exposed surfaces amenable to measurement, while the temperature and surface heat flux distributions are unknown at the film cooling hole/slot walls. The latter are determined in an iterative process by developing two approaches. The first approach, developed for 2d applications, solves an inverse problem whose objective is to adjust the film cooling hole/slot wall temperatures and heat fluxes until the temperature and heat flux at the measurement surfaces are matched in an overall heat conduction solution. The second approach, developed for 2d and 3d applications, is to distribute a set of singularities (sinks) at the vicinity of the cooling slots/holes surface inside a fictitious extension of the physical domain or along cooling hole centerline with a given initial strength distribution. The inverse problem iteratively alters the strength distribution of the singularities (sinks) until the measuring surfaces heat fluxes are matched. The heat flux distributions are determined in a post-processing stage after the inverse problem is solved. The second approach provides a tremendous advantage in solving the inverse problem, particularly in 3d applications, and it is recommended as the method of choice for this class of problems. It can be noted that the ga reconstructed heat flux distributions are robust, yielding accurate results to both exact and error-laden inputs. In all cases in this study, results from experiments are simulated using a full conjugate heat transfer (cht) finite volume models which incorporate the interactions of the external convection in the hot turbulent gas, internal convection within the cooling plena, and the heat conduction in the metal endwall/shroud region. Extensive numerical investigations are undertaken to demonstrate the significant importance of conjugate heat transfer in film cooling applications and to identify the implications of various turbulence models in the prediction of accurate and more realistic surface temperatures and heat fluxes in the cht simulations. These, in turn, are used to provide numerical inputs to the inverse problem. Single and multiple cooling slots, cylindrical cooling holes, and fan-shaped cooling holes are considered in this study. The turbulence closure is modeled using several two-equation approach, the four-equation turbulence model, as well as five and seven moment reynolds stress models. The predicted results, by the different turbulence models, for the cases of adiabatic and conjugate models, are compared to experimental data reported in the open literature. Results show the significant effects of conjugate heat transfer on the temperature field in the film cooling hole region, and the additional heating up of the cooling jet itself. Moreover, results from the detailed numerical studies presented in this study validate the inverse problem approaches and reveal good agreement between the bem/ga reconstructed heat fluxes and the cht simulated heat fluxes along the inaccessible cooling slot/hole walls<br>Ph.D.<br>Department of Mechanical, Materials and Aerospace Engineering;<br>Engineering and Computer Science<br>Mechanical Engineering
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Mellings, Sharon Christine. "Flaw identification using the inverse dual boundary element method." Thesis, University of Portsmouth, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239881.
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Maree, Abraham Jacobus. "The Inverse Finite Element Method: Sensitivity to Measurement Setup." Thesis, Stellenbosch : University of Stellenbosch, 2005. http://hdl.handle.net/10019.1/2640.
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Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2005.<br>In the inverse finite element method (iFEM), given a finite element model of a structure
and imperfect displacement measurements, the external loads acting on the structure
can be assessed. The basic idea behind iFEM is the optimization of a quadratic cost
function of the difference between the measured and estimated values, with a high cost
corresponding to a high precision of the measurements.
In the present research it is firstly shown how the iFEM theory was broadened to
accommodate for strain measurements through the construction of cost matrices to express
the cost associated with the estimation of the response.
The main focus of the research falls however on the influence that the measurement
set-up has on the quality of the iFEM estimates. Only a limited number of measurements
may be available, therefore it is essential to plan the measurement set-up carefully to
obtain the highest quality of estimates. The number of measurements and the precision
required to obtain a realistic result from an iFEM analysis is also a factor which plays a
role and varies for different types of measurements. A numerical method for systematic
sensitivity study of the measurements set-up without involving the actual measurement
data, is presented.
Two examples consisting of structures with both displacement measurements and
strain measurements being taken, are presented. It illustrates how the sensitivity study
method can be used to plan a more effective measurement set-up.
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Hazanee, Areena. "Boundary element method for solving inverse heat source problems." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/10570/.
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In this thesis, the boundary element method (BEM) is applied for solving inverse source problems for the heat equation. Through the employment of the Green’s formula and fundamental solution, the BEM naturally reduces the dimensionality of the problem by one although domain integrals are still present due to the initial condition and the heat source. We mainly consider the identification of time-dependent source for heat equation with several types of conditions such as non-local, non-classical, periodic, fixed point, time-average and integral which are considered as boundary or overdetermination conditions. Moreover, the more challenging cases of finding the space- and time-dependent heat source functions for additive and multiplicative cases are also considered. Under the above additional conditions a unique solution is known to exist, however, the inverse problems are still ill-posed since small errors in the input measurements result in large errors in the output heat source solution. Then some type of regularisation method is required to stabilise the solution. We utilise regularisation methods such as the Tikhonov regularisation with order zero, one, two, or the truncated singular value decomposition (TSVD) together with various choices of the regularisation parameter. The numerical results obtained from several benchmark test examples are presented in order to verify the efficiency of adopted computational methodology. The retrieved numerical solutions are compared with their analytical solutions, if available, or with the corresponding direct numerical solution, otherwise. Accurate and stable numerical solutions have been obtained throughout for all the inverse heat source problems considered.
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Ross, Christopher Roger. "Direct and inverse scattering by rough surfaces." Thesis, Brunel University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318675.
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Zhang, Wenlong. "Forward and Inverse Problems Under Uncertainty." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE024/document.
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Cette thèse contient deux matières différentes. Dans la première partie, deux cas sont considérés. L'un est le modèle plus lisse de la plaque mince et l'autre est les équations des limites elliptiques avec des données limites incertaines. Dans cette partie, les convergences stochastiques des méthodes des éléments finis sont prouvées pour chaque problème.Dans la deuxième partie, nous fournissons une analyse mathématique du problème inverse linéarisé dans la tomographie d'impédance électrique multifréquence. Nous présentons un cadre mathématique et numérique pour une procédure d'imagerie du tenseur de conductivité électrique anisotrope en utilisant une nouvelle technique appelée Tentomètre de diffusion Magnéto-acoustographie et proposons une approche de contrôle optimale pour reconstruire le facteur de propriété intrinsèque reliant le tenseur de diffusion au tenseur de conductivité électrique anisotrope. Nous démontrons la convergence et la stabilité du type Lipschitz de l'algorithme et présente des exemples numériques pour illustrer sa précision. Le modèle cellulaire pour Electropermécanisme est démontré. Nous étudions les paramètres efficaces dans un modèle d'homogénéisation. Nous démontrons numériquement la sensibilité de ces paramètres efficaces aux paramètres microscopiques critiques régissant l'électropermécanisme<br>This thesis contains two different subjects. In first part, two cases are considered. One is the thin plate spline smoother model and the other one is the elliptic boundary equations with uncertain boundary data. In this part, stochastic convergences of the finite element methods are proved for each problem.In second part, we provide a mathematical analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor using a novel technique called Diffusion Tensor Magneto-acoustography and propose an optimal control approach for reconstructing the cross-property factor relating the diffusion tensor to the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy. The cell model for Electropermeabilization is demonstrated. We study effective parameters in a homogenization model. We demonstrate numerically the sensitivity of these effective parameters to critical microscopic parameters governing electropermeabilization
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Bircan, Ali. "Solution Of Inverse Electrocardiography Problem Using Minimum Relative Entropy Method." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612574/index.pdf.
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The interpretation of heart'<br>s electrical activity is very important in clinical medicine since contraction of cardiac muscles is initiated by the electrical activity of the heart. The electrocardiogram (ECG) is a diagnostic tool that measures and records the electrical activity of the heart. The conventional 12 lead ECG is a clinical tool that provides information about the heart status. However, it has limited information about functionality of heart due to limited number of recordings. A better alternative approach for understanding cardiac electrical activity is the incorporation of body surface potential measurements with torso geometry and the estimation of the equivalent cardiac sources. The problem of the estimating the cardiac sources from the torso potentials and the body geometry is called the inverse problem of electrocardiography. The aim of this thesis is reconstructing accurate high resolution maps of epicardial potential representing the electrical activity of the heart from the body surface measurements. However, accurate estimation of the epicardial potentials is not an easy problem due to ill-posed nature of the inverse problem. In this thesis, the linear inverse ECG problem is solved using different optimization techniques such as Conic Quadratic Programming, multiple constrained convex optimization, Linearly Constrained Tikhonov Regularization and Minimum Relative Entropy (MRE) method. The prior information used in MRE method is the lower and upper bounds of epicardial potentials and a prior expected value of epicardial potentials. The results are compared with Tikhonov Regularization and with the true potentials.
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Rahmati, M. T. "Incompressible Navier-Stokes inverse design method based on unstructured meshes." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1445805/.
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Two inverse methods for turbomachinery blade design are developed. In these inverse design approaches blade shapes are computed for a specified design parameter such as mass-averaged tangential velocity or pressure loading distribution. These inverse methods directly define a geometry needed to obtain these prescribed target design parameters which are related to the performance of turbomachinery blades. The first method is based on the prescription of pressure loading on the blade while the second method is based on the prescription of mass-averaged tangential velocity on the blade. In both methods the blade thickness is also prescribed. These choices of target design prescription allow the designer to control the blade work distribution and the overall flow field effectively. It also prevents the generation of unrealistic blades as the designer directly control the blade thickness. Mesh movement algorithm is an integral part of the current inverse design method as once the blade surface is modified during the design iterations the corresponding unstructured mesh also has to be altered. The mesh movement algorithm is based on a linear tension spring analogy which is a very fast and robust mesh movement method. The capabilities of these design methodologies have been verified for inverse design of two dimensional turbomachinery blades. The flow analysis algorithm is an integral part of the current methodologies. It is based on the incompressible Navier-Stokes flow equations on unstructured meshes. The capability of the flow analysis algorithm is verified for three-dimensional external and internal incompressible flow solutions. Indeed the current method is applied for simulation of flow over marine propeller blades in open water. Also it is applied for the flow analysis of the stator and rotor blades of a low-speed axial turbine.
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Li, Hong. "An inverse reliability method and its applications in engineering design." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0026/NQ38929.pdf.
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Zhong, Ming. "Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems." Thesis, University of Maryland, College Park, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128674.
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<p> We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method <i> successively</i> extracts information from the previous hierarchical residual to the current hierarchical term at a <i>finer</i> hierarchical <i> scale.</i> As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of <i>finitely many</i> hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.</p>
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Shinde, Krushna. "Interval uncertainty method to treat inconsistent measurements in inverse problems." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2594.
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Le problème inverse consiste à trouver les valeurs des paramètres d’un modèle physique à partir d’un ensemble de mesures. Dans les problèmes de génie mécanique, la caractérisation du comportement des matériaux nécessite une méthode inverse pour identifier les paramètres des matériaux. Le problème d’identification déterministe est généralement sensible aux données, et une façon de résoudre ce problème est de prendre en compte les incertitudes dans les données. Bien que plusieurs de ces méthodes existent dans la littérature, la plupart d’entre elles utilisent la minimisation des moindres carrés ou les approches bayésiennes. Cette thèse explore comment les approches d’incertitude non probabiliste (basées sur des intervalles) peuvent aider à obtenir une solution au problème inverse, en particulier lorsque les mesures sont incompatibles les unes avec les autres. Notre approche diffère intrinsèquement de celles mentionnées précédemment. Il ne repose pas sur la minimisation de l’erreur moyenne mais plutôt sur la sélection d’un sous-ensemble de mesures cohérentes. La stratégie d’identification est basée sur la théorie des ensembles développée, qui nous a permis de prendre en compte à la fois les informations préalables sur les paramètres et l’incertitude de mesure sous forme d’ensembles (intervalle ou boîtes) lors du processus d’inversion. Dans cette stratégie, nous avons développé des indicateurs de cohérence des mesures pour caractériser les mesures incohérentes, c’est-à-dire les valeurs aberrantes dans les données. Nous avons appliqué cette stratégie pour identifier les paramètres élastiques d’un matériau isotrope. Le principal avantage de cette stratégie est qu’elle permet d’obtenir un ensemble réalisable de paramètres, mais qu’elle peut également détecter les valeurs aberrantes parmi les mesures bruyantes. La stratégie est ensuite combinée à une modélisation de substitution pour les problèmes d’identification dans des environnements de grande dimension. Nous avons également appliqué notre stratégie pour détecter les dommages dans le matériau<br>The inverse problem consists of finding the parameter values of a physical model given a set of measurements. In mechanical engineering problems, material behavior’s characterization requires an inverse method to identify the material parameters. The deterministic identification problem is generally sensitive to data, and one way to resolve this issue is to consider uncertainties in the data. While several such methods exist in the literature, most of them use least-square minimization or Bayesian approaches. This thesis explores how non-probabilistic uncertainty (interval-based) approaches can help obtain a solution to the inverse problem, particularly when measurements are inconsistent with one another. Our approachintrinsically differs from the previously mentioned ones. It does not rely on minimizing the average error but rather on selecting a subset of consistent measurements. The identification strategy is based on the set theory developed, which allowed us to take into account both prior information about the parameters and measurement uncertainty in the form of sets (interval or boxes) during the inversion process. In this strategy, we developed some indicators of consistency of the measurements to characterize inconsistent measurements, i.e., outliers in the data. We applied this strategy to identify the elastic parameters of an isotropic material. The main advantage of this strategy is that it helps to obtain a feasible set of parameters, but that it can also detect the outliers among noisy measurements. The strategy is subsequently combined with surrogate modeling for identification problems in high dimensional settings. We also applied our strategy to detect damage in the material
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Sztefek, Pavel. "Inverse method for stiffness determination of impact damage in composites." Thesis, Imperial College London, 2009. http://hdl.handle.net/10044/1/5556.
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The limited knowledge of stiffness reductions is a major problem in reliably predicting the post-impact strength of composite structures. This work describes development and application of a non-destructive approach for evaluation of the inplane stiffness of impact damage in composites. The approach combines an inverse method linked to a finite element model and non-contact full-field measurements. The material parameters of impact damage are determined by iteratively matching the finite element model to displacement fields measured optically during post-impact loading. A first order, gradient optimization technique coupled with a modified quadratic algorithm is employed. The method is validated on a reference finite element model with axisymmetric damage containing several concentric zones having different properties, and the influence of measurement noise is examined. The approach is applied to in-house experiments with impacted carbon/epoxy laminates to determine their quasi-isotropic mechanical properties in tension and compression. The resulting stiffness distributions are presented and the corresponding nonlinear behaviour of the damage is described. To examine the effect of the type of damage on the mechanical properties a thorough fractographic analysis of the impacted specimens was undertaken. The tensile stiffness is found to be mainly affected by fibre fracture, while the compressive stiffness is strongly linked to delamination buckling. The approach has further been extended for detection and evaluation of multiple impact damage zones at arbitrary locations as well as for stiffness identification of the damage in orthotropic laminates. The accuracy of both extensions is presented and discussed. Finally, possible future applications of the approach are considered.
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Frassek, Rouven. "Q-operators, Yangian invariance and the quantum inverse scattering method." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2014. http://dx.doi.org/10.18452/17070.
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Inspiriert von den integrablen Strukturen der schwach gekoppelten planaren N=4 Super-Yang-Mills-Theorie studieren wir Q-Operatoren und Yangsche Invarianten. Wir geben eine Übersicht der Quanten-Inverse-Streumethode zusammen mit der Yang-Baxter Gleichung welche zentral für diesen systematischen Zugang zu integrablen Modellen ist. Den Fokus richten wir auf rationale integrable Spinketten und Vertexmodelle. Wir besprechen einige ihrer bekannten Gemeinsamkeiten und wie sie durch Bethe-Ansatz-Methoden mit Hilfe sogenannter Q-Funktionen gelöst werden können. Der Hauptteil basiert auf den ursprünglichen Publikationen des Autors. Zuerst konstruieren wir Q-Operatoren, deren Eigenwerte zu den Q-Funktionen rationaler homogener Spinketten führen. Die Q-Operatoren werden als Spuren gewisser Monodromien von R-Operatoren eingeführt. Unsere Konstruktion erlaubt es uns die Hierarchie der kommutierenden Q-Operatoren und ihre funktionalen Beziehungen herzuleiten. Wir studieren wie der nächste-Nachbarn Hamiltonoperator, sowie höhere lokale Ladungen direkt aus den Q-Operatoren extrahiert werden können. Danach widmen wir uns der Formulierung der Yangschen Invarianzbedingung, wie sie auch im Zusammenhang mit Baumgraphen die bei der Berechnung von Streuamplituden in der N=4 Super-Yang-Mills-Theorie auftreten, innerhalb der RTT-Realisierung. Dies erlaubt es uns den algebraischen Bethe-Ansatz anzuwenden und die dazugehörigen Bethe Gleichungen herzuleiten, welche für die Konstruktion der Eigenzustände die Yangsche Invarianz aufweisen, relevant sind. Die Komponenten dieser Eigenzustände der von uns betrachteten Spinketten können außerdem als Zustandssummen gewisser zweidimensionaler Vertexmodelle angesehen werden. Zudem analysieren wir die Verbindung zwischen den Eigenzuständen und den oben genannten Baumgraphen. Schlussendlich diskutieren wir die von uns vorgelegten Ergebnisse und deren Folgen im Hinblick auf die Erforschung der planaren N=4 Super-Yang-Mills-Theorie.<br>Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method QISM along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author''s original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the functional relations among them. We study how the nearest-neighbor Hamiltonian and in principle also higher local charges can be extracted from the Q-operators directly. Secondly, we formulate the Yangian invariance condition, also studied in relation to scattering amplitudes of N=4 super Yang-Mills theory, in the RTT-realization. We find that Yangian invariants can be interpreted as special eigenvectors of certain inhomogeneous spin chains. This allows us to apply the algebraic Bethe ansatz and derive the corresponding Bethe equations that are relevant to construct the invariants. We examine the connection between the Yangian invariant spin chain eigenstates whose components can be understood as partition functions of certain two-dimensional lattice models and tree-level scattering amplitudes of the four-dimensional gauge theory. Finally, we conclude and discuss some future directions and implications of our studies for planar N=4 super Yang-Mills theory.
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Djedidi, Mouad. "Design of a Fast Antenna Characterization Method Exploiting Echoes." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS348/document.
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Les techniques de mesure de diagramme de rayonnement d’antenne actuelles partagent un paradigme commun qui stipule que l’information utile est exclusivement portée par le signal de test généré. Cela implique un effort mécanique fastidieux en faisant tourner l'antenne sous test ou en déplaçant le système de sondes afin de couvrir des angles de mesure différents jusqu'à ce qu'une caractérisation complète soit effectuée ; une limitation qui est généralement surmontée en utilisant des systèmes multisondes coûteux. En outre, toute réflexion provenant du site de mesure et des équipements de test est considérée comme parasite perturbant le signal de test et est ainsi minimisée.Dans cette thèse, un concept de mesure du diagramme de rayonnement d'antenne remettant en cause ce paradigme commun est présenté comme un moyen d'accélérer le processus de caractérisation en utilisant des systèmes économiques. Le paradigme proposé consiste en la génération d'un ensemble d'échos contrôlées, en utilisant des configurations impliquant des plaques réfléchissantes, qui contribueraient directement à la mesure en couvrant différents angles, et récupérer les informations portées par l'ensemble des signaux générés simultanément. Une diversité fréquentielle est introduite afin de générer un système d'équations équilibré où le vecteur inconnu contenant les valeurs du diagramme de rayonnement est récupéré en inversant un problème matriciel. Par conséquent, une attention considérable est accordée au conditionnement du modèle mathématique afin d'assurer la stabilité et la robustesse du systèmeTrois configurations de différents niveaux de complexité en termes d'échos contrôlés sont étudiées, en mettant l'accent sur la configuration la plus simple impliquant un seul écho contrôlé. Des modèles ont été mis au point, avec des contraintes de conception des configurations proposées en termes de dimensionnement et de bandes passante de fonctionnement, mettant en évidence la viabilité mathématique du concept. Les aspects pratiques ont également été évalués en étudiant la tolérance des modèles développés vis-à-vis des erreurs systématiques, ainsi qu’à l'impact de l’application d'un ensemble d’hypothèses simplificatrices. La faisabilité du concept ainsi que son utilité pour accélérer le processus de caractérisation par rapport aux techniques classiques ont été mises en évidence par des simulations numériques. Ce travail ouvre la porte à l'exploitation des échos, généralement considérés comme perturbateurs, dans un contexte de mesure d’antennes<br>Current antenna radiation pattern measurement techniques share a common paradigm which states that useful information is exclusively carried by the generated test signal. This implies an excessive, time consuming, mechanical effort by rotating the antenna under test or displacing the probe system in order to cover different measurement angles until a complete scan is performed; a limitation that is typically overcome using costly multi-probe systems. Moreover, any reflection from the measurement site and test equipment is considered spurious as it perturbs the test signal and thus is minimized.In this thesis, an antenna radiation pattern measurement concept challenging this common paradigm is introduced as a mean of accelerating the characterization process using cost-efficient systems. The proposed paradigm consists in the generation of a set of controlled echoes, using set-ups involving highly-reflective plates, which would directly contribute to the measurement alongside the line-of-sight signal by covering different measurement angles, and retrieving the ARP information carried by the set of all generated signals concurrently. Frequency diversity is used in order to generate a balanced system of equations where the unknown ARP vector is retrieved by inverting a matrix problem. Consequently, a considerable attention is paid into the conditioning of the mathematical model in order to ensure the system stability and accuracy.Three configurations of different complexity levels in terms of controlled echoes are studied, with focus on the simplest configuration involving a single controlled echo. Models have been developed with design guidelines for the proposed configurations in terms of set-up dimensions and operating frequency bandwidth highlighting the mathematical viability of the concept. Practical issues were also assessed by studying the tolerance of developed models to systematic practical errors, as well as to the impact of an applied set of simplifying assumptions. The feasibility of the concept as well as its usefulness in accelerating the measurement process with respect to classical techniques were highlighted via numerical simulations. This thesis opens the door for exploiting echoes, generally regarded as a nuisance, in an antenna measurements context
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Ismatullah. "Analysis of space-borne antennas by higher-order method of moments and inverse equivalent current methods." kostenfrei, 2010. https://mediatum2.ub.tum.de/node?id=977261.
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Nightingale, Miriam. "Material Characterization of Cardiovascular Biomaterials Using an Inverse Finite Element Method." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36426.
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Being able to accurately model soft tissue behaviour, such as that of heart valvular tissue, is essential for developing effective numerical simulations of in-vivo conditions and determining patient-specific care options. Although several analytical material models, based on strain energy functions, have been successful in predicting soft tissue behaviour, complications arise when these models are implemented into finite element (FE) programs due to the incorporation of a penalty parameter for numerically enforcing material incompressibility. Specifically, material parameters determined through non-FE methods may no longer produce a material behaviour that reflects the experimental behaviour once they are used in an FE analysis. Based on commercial finite element software LS-DYNA, an inverse methodology was developed in MATLAB to simultaneously optimize the material parameters and the penalty parameter for the Guccione strain energy model. The methodology produced accurate predictions of the material behaviour under planar equibiaxial testing for five biomaterials used in heart valve cusp replacements.
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Santos, Luis Carlos de Castro. "A hybrid inverse optimization method for aerodynamic design of lifting surfaces." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/12105.
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Yla-Maihaniemi, Pirre Paivikki. "A novel method for investigating solid-liquid interactions : inverse liquid chromatography." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429885.
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歐陽天祥 and Yeung Tin-cheung Au. "An investigation of the inverse scattering method under certain nonvanishing conditions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1987. http://hub.hku.hk/bib/B31231056.
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Farcas, Adrian. "The dual reciprocity boundary element method for solving some inverse problems." Thesis, University of Leeds, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411306.
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Reeve, Thomas Henry. "The method of fundamental solutions for some direct and inverse problems." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4278/.
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We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require mesh generation or integration over the solution boundary, making it suitable for solving inverse problems, like the BHCP, an ill-posed problem. We extend the MFS proposed in Johansson and Lesnic (2008) for the direct one-dimensional heat equation, and Johansson and Lesnic (2009) for the direct one-phase one-dimensional Stefan problem, with source points placed outside the space domain of interest and in time. Theoretical properties, including linear independence and denseness, the placement of source points, and numerical investigations are included showing that accurate results can be efficiently obtained with small computational cost. Regularization techniques, in particular, Tikhonov regularization, in conjunction with the L-curve criterion, are used to solve the illconditioned systems generated by this method. In Chapters 6 and 8, investigating the linear and nonlinear Stefan problems, the MATLAB toolbox lsqnonlin, which is designed to minimize a sum of squares, is used.
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Brock, Jerry S. "A consistent direct-iterative inverse design method for the Euler equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40033.
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A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This method includes a unique solution algorithm and a design tangency boundary condition which directly relates the target pressure to shape modification. The new design method was evaluated with an upwind, cell-centered finite-volume formulation of the two-dimensional Euler equations. Controlled inverse design tests were conducted with a symmetric channel where the initial and target geometries were known. The geometric design variable was a channel-wall ramp angle, 0, which is nominally five degrees. Target geometries were defined with ramp angle perturbations of J10 = 2 %, 10%, and 20 %. The new design method was demonstrated to accurately predict the target geometries for subsonic, transonic, and supersonic test cases; M=0.30, 0.85, and 2.00. The supersonic
test case efficiently solved the design tests and required very few iterations. A stable and convergent solution process was also demonstrated for the lower speed test cases using an under-relaxed geometry update procedure. The development and demonstration of the consistent direct-iterative method herein represent the important first steps required for a new research area for the advancement of aerodynamic inverse design methods.<br>Ph. D.
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Au, Yeung Tin-cheung. "An investigation of the inverse scattering method under certain nonvanishing conditions /." [Hong Kong : University of Hong Kong], 1987. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12358514.
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Eser, Hülya Tıhmınlıoğlu Funda. "Diffusion And Equilibrium Measurements In Polymer-Solvent Systems By Inverse Gas Chromatography Method/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/kimya/T000451.pdf.
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Li, Xiaobei. "Instrumentation and inverse problem solving for impedance imaging /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5973.
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Borges, Carlos. "A multifrequency method for the solution of the acoustic inverse scattering problem." Digital WPI, 2013. https://digitalcommons.wpi.edu/etd-dissertations/12.
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We are interested in solving the time-harmonic inverse acoustic scattering problem for planar sound-soft obstacles. In this work, we introduce four methods for solving inverse scattering problems. The first method is a variation of the method introduced by Johansson and Sleeman. This method solves the inverse problem when we have the far field pattern given for only one incident wave. It is an iterative method based on a pair of integral equations used to obtain the far field pattern of a known single object. The method proposed in this thesis has a better computational performance than the method of Johansson and Sleeman. The second method we present is a multi-frequency method called the recursive linearization algorithm. This method solves the inverse problem when the far field pattern is given for multiple frequencies. The idea of this method is that from an initial guess, we solve the single frequency inverse problem for the lowest frequency. We use the result obtained as the initial guess to solve the problem for the next highest frequency. We repeat this process until we use the data from all frequencies. To solve the problem at each frequency, we use the first method proposed. To improve the quality of the reconstruction of the shadowed part of the object, we solve the inverse scattering problem of reconstructing an unknown sound-soft obstacle in the presence of known scatterers. We show that depending on the position of the scatterers, we may be able to obtain very accurate reconstructions of the entire unknown object. Next, we introduce a method for solving the inverse problem of reconstructing a convex sound-soft obstacle, given measures of the far field pattern at two frequencies that are not in the resonance region of the object. This method is based on the use of an approximation formula for the far field pattern using geometric optics. We are able to prove that for the reconstruction of the circle of radius $R$ and center at the origin, the size of the interval of convergence of this method is proportional to the inverse of the wavenumber. This procedure is effective at reconstructing the illuminated part of the object; however, it requires an initial guess close to the object for frequencies out of the resonance region. Finally, we propose a globalization technique to obtain a better initial guess to solve the inverse problem at frequencies out of the resonance region. In this technique, given the far field pattern of a convex object at two frequencies out of the resonance region, we use our extrapolation operator to generate synthetic data for low frequencies. We apply the recursive linearization algorithm, using as a single frequency solver the method that is based on geometric optics. We obtain an approximation of the object that can be used as the initial guess to apply the recursive linearization algorithm using the first method introduced as the single frequency solver.
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Helin, Mikael. "Inverse Parameter Estimation using Hamilton-Jacobi Equations." Thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123092.
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Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possible improvementsare given<br>I detta examensarbete återskapas en lösning på ett glest rutnät genom att anpassa en partiell differentialekvation till några givna datapunkter. De partiella differentialekvationer med deras motsvarande syntetiska data som betraktas är värmeledningsekvationen och Dupires ekvation inklusive syntetiska data från Black-Scholes formel. Tillvägagångssättet att anpassa en PDE är att med hjälp av optimal styrning härleda diskreta approximationer på ett system av regulariserade Hamilton karakteristiska ekvationer till vilka olika diskreta stegmetoder och parametrar för släthet undersöks. Med en icke-parametrisk numerisk implementation prövas den härledda metoden och slutligen föreslås möjliga förbättringar till metoden.
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Alqadah, Hatim F. "Space-Frequency Regularization for Qualitative Inverse Scattering." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321967202.
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André, Etienne. "An inverse method for the synthesis of timing parameters in concurrent systems." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2010. http://tel.archives-ouvertes.fr/tel-00595268.
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This thesis proposes a novel approach for the synthesis of delays for timed systems, in particular in the framework oftimed automata, a model for verifying real-time systems. Our approach relies on the following inverse method: given a reference valuation of the parameters, we synthesize a constraint on the parameters, guaranteeing the same timeabstract linear behavior as for the reference valuation. This gives a criterion of robustness to the system. By iterating this inverse method on various points of a bounded parameter domain, we are then able to partition the parametric space into good and bad zones, with respect to a given property one wants to verify. This gives a behavioral cartography of the system. This method extended to probabilistic systems allows to preserve minimum and maximum probabilities of reachability properties. We also present variants of the inverse method for directed weighted graphs and Markov Decision Processes. Several prototypes have been implemented; in particular, IMITATOR II implements the inverse method and the cartography for timed automata. It allowed us to synthesize parameter values for several case studies such as an abstract model of a memory circuit sold by the chipset manufacturer ST-Microelectronics, and various communication protocols.
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Yeh, T. C. Jim, and Jinqi Zhang. "A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose Zone." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1995. http://hdl.handle.net/10150/614185.
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A geostatistical inverse technique utilizing both primary and secondary information is
developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated
hydraulic conductivity and pore -size distribution parameters) in the vadose zone. Measurements of
saturated hydraulic conductivity and pore -size distribution parameters are considered as the primary
information, while measurements of steady -state flow processes (soil -water pressure head and degree
of saturation) are regarded as the secondary information. This inverse approach relies on the classical
linear predictor (cokriging) theory and takes the advantage of the spatial cross- correlation between
soil -water pressure head, degree of saturation, saturated hydraulic conductivity, and pore -size
distribution parameter. Using an approximate perturbation solution for steady, variably saturated
flow under general boundary conditions, the cross- covariances between the primary and secondary
information are derived. The approximate solution is formulated based on a first -order Taylor series
expansion of a discretized finite element equation. The sensitivity matrix in the solution is evaluated
by an adjoint state sensitivity approach for flow in heterogeneous media under variably saturated
conditions. Through several numerical examples, the inverse model demonstrates its ability to
improve the estimates of the spatial distribution of saturated hydraulic conductivity and pore -size
distribution parameters using the secondary information.
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Zhang, Jinqi, and T. C. Jim Yeh. "An Iterative Geostatistical Inverse Method For Steady-Flow In The Vadose Zone." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1996. http://hdl.handle.net/10150/614010.
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An iterative stochastic inverse technique utilizing both primary and secondary
information is developed to estimate conditional means of unsaturated hydraulic conductivity
parameters (saturated hydraulic conductivity and pore -size distribution parameters) in the
vadose zone. Measurements of saturated hydraulic conductivity and pore -size distribution
parameter are considered as the primary information, while measurements of steady -state flow
processes (soil -water pressure head and degree of saturation) are regarded as the secondary
information. This inverse approach is similar to the classical geostatistical approach, which
utilizing a linear estimator that depends on the cross- covariance and covariance functions of
unsaturated hydraulic conductivity parameters and flow processes. The linear estimator is,
however, improved successively by solving the governing flow equation and by updating the
residual covariance and cross- covariance functions, in an iterative manner. Using an
approximate perturbation solution for steady, variably saturated flow under general boundary
conditions, the covariances of secondary information and the cross -covariance between the
primary and secondary information are derived. The approximate solution is formulated based
on a first -order Taylor series expansion of a discretized finite element equation. The
sensitivity matrices in the solution are evaluated by an adjoint state sensitivity approach for
flow in heterogeneous media under variably saturated conditions. As a result, the nonlinear
relationships between unsaturated hydraulic conductivity parameters and flow processes are incorporated in the estimation. Through some numerical examples, the iterative inverse model
demonstrates its ability to improve the estimates of the spatial distribution of saturated
hydraulic conductivity and pore -size distribution parameters compared to the classical
geostatistical inverse approach. In addition, the inconsistency problem existing in classical
geostatistical inverse approach is alleviated. The estimated fields of unsaturated hydraulic
conductivity parameters and flow fields not only retain their observed values at sample
locations, but satisfy the governing flow equation as well.
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De, Villiers Jean Schepers. "Inverse method in seismology." Thesis, 2009. http://hdl.handle.net/10500/3784.
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The problem of fitting a material property of the earth to a certain model by
analysing a returned seismic signal is investigated here. Analysis proceeds with
methods taken from the theory of inverse problems. Seismic wave inversion is tack-
led by minimisation of the objective function with respect to the model parameters.
Absorbing boundary conditions are implemented using an exponentially decaying
ansatz.<br>Physics<br>Ph. D. (Physics)
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Abdel-Khalik, Hany Samy. "Inverse method applied to adaptive core simulation." 2002. http://www.lib.ncsu.edu/theses/available/etd-11042002-114525/unrestricted/etd.pdf.
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Erhard, Klaus. "Point Source Approximation Methods in Inverse Obstacle Reconstruction Problems." Doctoral thesis, 2005. http://hdl.handle.net/11858/00-1735-0000-0006-B402-4.
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"Solving inverse kinematics problems using an interval method." Universitat Politècnica de Catalunya, 1998. http://www.tesisenxarxa.net/TDX-0723102-153600/.
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Picado, de Carvalho Serranho Pedro Miguel. "A Hybrid Method for Inverse Obstacle Scattering Problems." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B38F-0.
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Chang, Mei-Hsia, and 張美霞. "Development and Applications of Inverse Heat Transfer Method." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/02625416116501744718.
Full textAbstract:
博士<br>大同大學<br>機械工程學系(所)<br>93<br>The aim of this thesis is to develop inverse heat transfer methods and apply these methods to optimal design problems in different areas. The inverse heat transfer methods developed in the present thesis include the conjugate-gradient method (CGM), simplified conjugate-gradient method (SCGM), and automatic-filter scheme (AFS). Firstly, the CGM method is modified and categorized into two types: polynomial-function approach and point-by-point approach to extend its feasibility in (1) shape identification for the ice layer within the cylindrical capsules in cold storage system based on the temperature data on the outer surface of these capsules, (2) predictions of inner temperature distribution at the interface between the carbon plate and the membrane electrode assembly of a proton exchange membrane fuel cell (PEMFC), and (3) shape design of slider surfaces to meet the specified load demands.
The CGM is limited in the definition of objective function form. Thus it is not applied to problems with a more general objective function definition. In order to overcome the limitation, the SCGM method is presented by modifying the CGM method. The capability of the SCGM in identifing the boundary of the inner voids in the solid bodies based on the thermal data is tested by several test cases.
In addition, in the thesis a novel inverse heat transfer method is proposed, which incorporates an automatic-filter scheme (AFS) with the CGM method, for identifying shapes, positions, and temperature of heating elements embedded in a rectangular package. The identification is simply based on the upper surface temperature data of the rectangular package. Shapes of the heating elements are visualized by using node-matrix images. In this manner, numerical grid generation is not required and without overwhelming mathematical manipulation, and therefore the form of objective function with this method becomes more flexible.
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Wang, Chun-Jen, and 王俊仁. "Study of optimal fin shape by inverse method." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/86793749140171160903.
Full textAbstract:
碩士<br>逢甲大學<br>機械工程學所<br>96<br>The inverse heat transfer method was adopted in this research to study the optimal three-dimensional fin shape profile of a finned-tube heat exchanger. A modified conjugate gradient method was developed in this research, the method could succeed in obtaining the optimal three-dimensional fin shape profile. The effects of different fin materials and flow velocities were studied with dimensional form;and the effects of different Biot number distributions were also studied with dimensionless form in this research. It is observed by the numerical results that the fin thickness of the optimal fin shape varies with the position on the fin; and the top view profile of the optimal fin shape is not a circularity. It has a sharp fin thickness gradient in the radius direction and in the angle direction on the rear part of the circular tube as well. Regarding the effects of fin materials, the optimal steel fin shape has notch area on the rear part of the circular tube and extended fin surface area on the both sides of the circular tube; but this phenomenon is not observed for aluminum or cooper fins. The fin thickness gradient for the steel fin is the greatest; and which is the least for the cooper fin.The cooper fin has the largest surface area of the optimal fin shape ;and the area for the steel fin is the smallest among the three materials. Regarding the effect of the flow velocity, it is observed that the fin thickness gradient increases and the fin surface area decreases as the flow velocity increases. Especially for steel fin,it has distinct notch area on the rear part of the circular tube, and extended fin surface area on the both sides of the circular tube for higher flow velocity. No matter how Biot number is distributed, the optimal fin thickness is the thickest at the tube surface, thickness decrease gradually along radius direction. As the Biot number increases, the optimal fin thickness at tube increases, the fin thickness gradient is much greater.
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LIN, QIONG-XIAN, and 林瓊仙. "Korteweg-de Vries Equation and Inverse Scattering Method." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/67242767137255095259.
Full textAbstract:
碩士<br>淡江大學<br>數學研究所<br>80<br>1834年J.Scott Russell 在愛丁堡的格拉斯哥運河，觀察到一種奇妙的水波，稱之
為“孤立波”。其後的數十年間，科學家們並未能在流體運動中找出形容此種奇特
現象的運動方程式。
1895年，Korteweg 和de Vries 建立單向運動的淺水波運動方程
ˍ
η 3 ／g 1 2 1 η
─── ＝ ─ ／ ─ ── （ ─η＋ ─αη＋ ─ σ ─── ）
ｔ 2 ＼／ l x 2 3 3 x
即 Korteweg - de Vries 方程，簡稱Kdv 方程。令人感興趣的是這個方程具有孤
立波解，因此我們在理論上證實了孤立波的存在。此後，科學家們則在不同領域中
也導出Kdv 方程。
而這篇文章，我們主要討論的是如何利用散射反演法求解Kdv 方程的初值問題，這
個方法就是將求解非線性方程（Kdv 方程）的初值問題化為求解兩個線性方程的問
題。一個是二階常微分方程的Sturm - Liouville 問題（關於 Schrodinger 方程）
，另一個是線性積分方程（G-L-M 方程）的求解。