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1
Marroquin, J. L. (Jose Luis). "Probabilistic solution of inverse problems." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/15286.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.
Bibliography: p. 195-200.
by Jose Luis Marroquin.
Ph.D.
2
Leathers, Robert A. "Inverse solution methods for optical oceanography /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/7066.
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3
Anagurthi, Kumar. "Analytical solution for inverse heat conduction problem." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1176227397.
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Hebber, Eldad. "Numerical strategies for the solution of inverse problems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0033/NQ27160.pdf.
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5
Hussain, Muhammad Anwar. "Numerical Solution of a Nonlinear Inverse Heat Conduction Problem." Thesis, Linköping University, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-57486.
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The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, ux]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0.
The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense.
The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.
6
Chan, Stephen K. C. "An iterative general inverse kinematics solution with variable damping." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26684.
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Currently, there is much interest in the field of robotics in researching methods of obtaining inverse kinematics solutions for arbitrary manipulators. Simple closed-form inverse kinematics equations can be obtained for a few joint configurations using geometric methods. However, there exist many manipulators which were not originally designed for kinematic control which do not have simple closed-form inverse kinematics equations. An efficient and stable iterative method is investigated in this thesis which solves the general inverse kinematics problem without detailed analysis of the manipulator's structure. The proposed iterative inverse kinematics algorithm combines a calibration procedure to estimate the manipulator's Denavit-Hartenberg parameters with an iterative method using the Jacobian and damped joint corrections. The kinematics control algorithm parameters are selected with a computer graphics simulation of the manipulator. The proposed inverse kinematics algorithm is tested with a simulation of an industrial manipulator arm which does not have a closed-form solution, RSI Robotic Systems International's Kodiak arm, and exhibits stability in all regions of operation and fast convergence over most regions of operation.Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate
7
Aydin, Umit. "Solution Of Inverse Problem Of Electrocardiography Using State Space Models." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611027/index.pdf.
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Heart is a vital organ that pumps blood to whole body. Synchronous contraction of the heart muscles assures that the required blood flow is supplied to organs. But sometimes the synchrony between those muscles is distorted, which results in reduced cardiac output that might lead to severe diseases, and even death. The most common of heart diseases are myocardial infarction and arrhythmias. The contraction of heart muscles is controlled by the electrical activity of the heart, therefore determination of that electrical activity could give us the information regarding the severeness and type of the disease. In order to diagnose heart diseases, classical 12 lead electrocardiogram (ECG) is the standard clinical tool. Although many cardiac diseases could be diagnosed with the 12 lead ECG, measurements from sparse electrode locations limit the interpretations. The main objective of this thesis is to determine the cardiac electrical activity from dense body surface measurements. This problem is called the inverse problem of electrocardiography. The high resolution maps of epicardial potentials could supply the physician the information that could not be obtained with any other method. But the calculation of those epicardial potentials are not easythe problem is severely ill-posed due to the discretization and attenuation within the thorax. To overcome this ill-posedness, the solution should be constrained using prior information on the epicardial potential distributions. In this thesis, spatial and spatio-temporal Bayesian maximum a posteriori estimation (MAP), Tikhonov regularization and Kalman filter and Kalman smoother approaches are used to overcome the ill-posedness that is associated with the inverse problem of ECG. As part of the Kalman filter approach, the state transition matrix (STM) that determines the evolution of epicardial potentials over time is also estimated, both from the true epicardial potentials and previous estimates of the epicardial potentials. An activation time based approach was developed to overcome the computational complexity of the STM estimation problem. Another objective of this thesis is to study the effects of geometric errors to the solutions, and modify the inverse solution algorithms to minimize these effects. Geometric errors are simulated by changing the size and the location of the heart in the mathematical torso model. These errors are modeled as additive Gaussian noise in the inverse problem formulation. Residual-based and expectation maximization methods are implemented to estimate the measurement and process noise variances, as well as the geometric noise.
8
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'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.
9
Yi, Hak-Chae J. "Solution of time-independent inverse problems for linear transport theory /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/10677.
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10
English, Gary E. "Sensitivity of the tomographic inverse solution to acoustic path variability." Thesis, Monterey, California. Naval Postgraduate School, 1992. http://hdl.handle.net/10945/26758.
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As part of the Greenland Sea Project Woods Hole Oceanographic Institution and Scripps Institute of Oceanography deployed six acoustic tomography transceiver moorings to measure variability of the Greenland Sea gyre through a cooling cycle from September 1988 to August 1989. Using a set of Greenland Sea acoustic tomography data provided by Woods Hole Oceanographic Institution this thesis investigated the importance of incorporating acoustic path changes in the construction of the tomographic inverse solution. A comparison of the inverse solutions for changes in sound speed using non-corrected and corrected acoustic multipaths was conducted. Although the two inverse solutions are qualitatively similar, significant quantitative differences exist. These differences indicate that it is necessary to account for changes in the acoustic multipaths for the generation of accurate Greenland Sea acoustic tomography maps. Acoustic Tomograph, Multipath Variability
11
Callahan, Daniel. "Construction and solution of an inverse problem posed by "Piekara’s Chair"." Thesis, Wichita State University, 2008. http://hdl.handle.net/10057/2021.
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The article "Piekara's Chair: Mechanical Model for Atomic Energy Levels" by Zofia Golab-Meyer presents a model of the real-world problem of determining classical energy states suitable for high school or undergraduate college students. This thesis combines this idea with simple geometry to demonstrate how "Piekara's Chair" may be posed and then solved as inverse problems in IR²Thesis (M.S.)--Wichita State University, College of Liberal Arts and Science, Dept. of Mathematics & Statistics
Includes bibliographical references (leaves 46-47)
12
OTERO, JOHNNY ALEXANDER BASTIDAS. "GENETIC ALGORITHMS APPLIED TO THE SOLUTION OF THE BIOMAGNETIC INVERSE PROBLEM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=28372@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Sinais bioelétricos fornecem informações importantes sobre a função fisiológica de muitos organismos vivos. Em magnetismo, denomina-se problema direto aquele em que se determina o campo magnético a partir do conhecimento da fonte de corrente que o gerou. Por outro lado, existem situações em que se deseja determinar a fonte de corrente a partir de valores de campo magnético medidos. Esse tipo de problema é usual em Biomagnetismo e é denominado problema inverso. Por exemplo, com base em medições do campo magnético cardíaco é possível inferir sobre a atividade elétrica, no tecido cardíaco, que foi responsável por sua geração. Este trabalho propõe, apresenta e discute uma nova técnica destinada a resolver o problema biomagnético inverso, por meio de algoritmos genéticos. Objetiva-se estimar a posição, a orientação e a magnitude dos dipolos de corrente equivalentes, responsáveis pela geração de mapas de campos biomagnéticos obtidos experimentalmente por meio de medições realizadas em corações isolados de coelho utilizando um sistema SQUID de 16 canais. O algoritmo busca identificar a distribuição de dipolos que melhor se ajusta aos dados experimentais, objetivando minimizar o erro entre o mapa de campo magnético medido e o obtido por meio das soluções estimadas. O conhecimento dos parâmetros dos dipolos de corrente, em diferentes instantes de tempo, permite a correta interpretação e análise da informação médica obtida a partir dos campos biomagnéticos medidos experimentalmente, auxiliando na definição de diagnósticos e orientação de abordagens terapêuticas.
Bioelectric signals provide important information about the physiological function of many living organisms. In magnetism, the so-called direct problem deals with the determination of the magnetic field associated to well known current sources. On the other hand, there are situations where it is necessary to determine the current source responsible for the generation of a measured magnetic field. This type of problem is common in Biomagnetism and is called inverse problem. For example, based on cardiac magnetic field measurements it is possible to infer the electrical activity in the heart tissue, responsible for its generation. This work proposes, presents and discusses a new technique designed to solve the biomagnetic inverse problem by genetic algorithms. It is intended to estimate the position, orientation and magnitude of the equivalent current dipoles, responsible for the generation of biomagnetic field maps measured with a 16 channel SQUID system. The algorithm attempts to identify the distribution of dipoles that best fits the measured experimental data, aiming at minimizing the error between the experimental magnetic field maps and those obtained by the estimated solutions. The experimental data analyzed in this study were acquired by measurements in isolated rabbit hearts. The knowledge of parameters of current dipoles at different instants of time allows the correct interpretation and analysis of medical information obtained from the experimentally measured biomagnetic fields, providing diagnosis and guiding therapeutic procedures.
13
Hebbur, Venkata Subba Rao Vishwas. "Adjoint based solution and uncertainty quantification techniques for variational inverse problems." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/76665.
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Variational inverse problems integrate computational simulations of physical phenomena with physical measurements in an informational feedback control system. Control parameters of the computational model are optimized such that the simulation results fit the physical measurements.The solution procedure is computationally expensive since it involves running the simulation computer model (the emph{forward model}) and the associated emph {adjoint model} multiple times. In practice, our knowledge of the underlying physics is incomplete and hence the associated computer model is laden with emph {model errors}. Similarly, it is not possible to measure the physical quantities exactly and hence the measurements are associated with emph {data errors}. The errors in data and model adversely affect the inference solutions. This work develops methods to address the challenges posed by the computational costs and by the impact of data and model errors in solving variational inverse problems.
Variational inverse problems of interest here are formulated as optimization problems constrained by partial differential equations (PDEs). The solution process requires multiple evaluations of the constraints, therefore multiple solutions of the associated PDE. To alleviate the computational costs we develop a parallel in time discretization algorithm based on a nonlinear optimization approach. Like in the emph{parareal} approach, the time interval is partitioned into subintervals, and local time integrations are carried out in parallel. Solution continuity equations across interval boundaries are added as constraints. All the computational steps - forward solutions, gradients, and Hessian-vector products - involve only ideally parallel computations and therefore are highly scalable.
This work develops a systematic mathematical framework to compute the impact of data and model errors on the solution to the variational inverse problems. The computational algorithm makes use of first and second order adjoints and provides an a-posteriori error estimate for a quantity of interest defined on the inverse solution (i.e., an aspect of the inverse solution). We illustrate the estimation algorithm on a shallow water model and on the Weather Research and Forecast model.
Presence of outliers in measurement data is common, and this negatively impacts the solution to variational inverse problems. The traditional approach, where the inverse problem is formulated as a minimization problem in $L_2$ norm, is especially sensitive to large data errors. To alleviate the impact of data outliers we propose to use robust norms such as the $L_1$ and Huber norm in data assimilation. This work develops a systematic mathematical framework to perform three and four dimensional variational data assimilation using $L_1$ and Huber norms. The power of this approach is demonstrated by solving data assimilation problems where measurements contain outliers.Ph. D.
14
Callahan, Daniel Behrman Elizabeth. "Construction and solution of an inverse problem posed by "Piekara's Chair"." A link to full text of this thesis in SOAR, 2008. http://hdl.handle.net/10057/2021.
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Thesis (M.S.)--Wichita State University, College of Liberal Arts and Science, Dept. of Mathematics & StatisticsThesis (excluding code) ©Copyright 2008 Daniel Callahanunder the Creative Commons Attribution 3.0 Unported LicenseCode ©Copyright 2008 Daniel Callahan, released under the MIT License:Permission is hereby granted, free of charge, to any person obtaining a copy of thissoftware and associated documentation files (the "Software"), to deal in the Softwarewithout restriction, including without limitation the rights to use, copy, modify, merge,publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons towhom the Software is furnished to do so, subject to the following conditions:The above copyright notice and this permission notice shall be included in all copies orsubstantial portions of the Software.THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIESOF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE ANDNONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHTHOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISINGFROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OROTHER DEALINGS IN THE SOFTWARE. Includes bibliographical references (leaves 46-47).
15
Mein, Stephen James. "Monte Carlo solution to the inverse problem of ultrasonic defect characterisation." Thesis, University of Central Lancashire, 2009. http://clok.uclan.ac.uk/20948/.
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An important problem in the non-destructive testing of materials is the accurate determination of the location, size, shape and orientation of any detected flaws; this is essential for assessing integrity of inspected objects. This thesis presents a novel algorithm wherein recovery of the geometric parameters of flaw captured in pulse-echo ultrasonic inspection data for immersion testing at low angles of incidence is treated as an inverse problem, formulated in terms of directly recovering the underlying physical description of the defect. The forward problem of modelling the ultrasonic echo signals is given by the Impulse Response Method, a frequency independent numerical solution to the acoustic wave equation. To solve the inverse problem, Markov Chain Monte Carlo methodology is employed as an iterative optimisation strategy, minimising a cost function between observations and a projected model. Modelled flaw parameters are updated stochastically such that they converge toward the true values over successive iterations. The advantages of this approach over standard deterministic algorithms are an ability to circumvent local minima in the cost function and a means to incorporate a priori knowledge into the solution space. Results are shown for simulated test data, demonstrating convergence of algorithm is achievable regardless of starting condition, thus illustrating the potential of the method. The proposed method offers the following developments and contributions. The application of Markov Chain Monte Carlo methodology to this particular inverse problem of defect characterisation is unique. Experiments conducted in the latter chapters demonstrate robust convergence of the am proach. The algorithm developed is flexible in its application, in that the formulation allows for various alternate parameterisations of the problem with minimal structural changes. Furthermore the approach is generic in its application, intended to work for standard observation data, collected utilising standard measurement techniques and apparatus.
16
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.
17
Popov, Mikhail. "Analytic and Numerical Methods for the Solution of Electromagnetic Inverse Source Problems." Doctoral thesis, KTH, Electromagnetic Theory, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3134.
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Popov, Mikhail. "Analytical and numerical methods for the solution of electromagnetic inverse source problems /." Stockholm : Tekniska högsk, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3134.
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Guclu, Alperen. "Comparison Of Five Regularization Methods For The Solution Of Inverse Electrocardiography Problem." Master's thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615552/index.pdf.
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Understanding heart&rsquos electrical activity is very important because coronary problems -such as heart attacks, arrhythmia and stroke- are the leading cause of death in the world. Forward and inverse problems of electrocardiography (ECG) are methods that provide detailed information about the electrical activity of the heart. Forward problem of electrocardiography is the estimation of body surface potentials from equivalent cardiac sources. Inverse problem of electrocardiography can be described as estimation of the electrical sources in the heart using the potential measurements obtained from the body surface. Due to spatial smoothing and attenuation that occur within the thorax, inverse ECG problem is ill-posed and the transfer matrix is ill-conditioned. Thus, regularization is needed to find a stable and accurate solution. In this thesis, epicardial potentials used as equivalent cardiac sources to represent electrical activity of the heart and performances of five different regularization methods are compared. These regularization methods are Tikhonov regularization, truncated singular value decomposition, least squares QR factorization, truncated total least squares, and Lanczos truncated total least squares. Results are assessed qualitatively using correlation coefficient (CC) and relative difference measurement star (RDMS) measures. In addition, real and reconstructed surface potential distributions are compared qualitatively. Body surface potential measurements are simulated with different levels of measurement noise. Geometric errors are also included by changing the size and the location of the heart in the mathematical torso model. According to our test results, the performances of the regularization methods in solving the inverse ECG problem depend on the form and amount of the noise.
20
Thomson, Douglas G. "Evaluation of helicopter agility through inverse solution of the equations of motion." Thesis, University of Glasgow, 1987. http://theses.gla.ac.uk/4927/.
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Helicopter agility in nap-of-the-earth flight is widely recognised to be of great importance. Despite this. a general method of quantifying agility does not exist. All previous attempts to quantify agility have been restricted either to flight tests or to simple kinematic modelling - both with obvious disadvantages. A method of quantifying helicopter inherent agility. the agility of the configuration independent of the pilot. utilising inverse solutions of the equations of motion has been developed. A value for the inherent agility of a helicopter is given by studying its performance over a series of standard manoeuvres. The manoeuvres used represent typical tasks undertaken by the configuration under study. The combination of these tasks represent the helicopter's operational role. The helicopter's performance over these standard manoeuvres is found by using an inverse solution of the equations of motion - calculation of the control. and resulting state. time histories needed to fly a given flight path. A six degrees of freedom non-linear mathematical model is used to simulate single main and tail rotor helicopter flight dynamics. The helicopter's performance over each manoeuvre is rated by a quadratic performance function of the state and control variables. The performance function is weighted in such a manner as to penalise undesirably large displacements in the state and control variables of particular importance to that manoeuvre (e.g. large nose down attitude changes in accelerated flight are heavily penalised). An Agility Rating is awarded to a helicopter on the basis of its performance over a wide range of similar manoeuvres. a measure of total inherent agility being a function of the agility ratings for all the manoeuvres relevant to the helicopter's role. The method is illustrated by applying it to two agility studies. Firstly. it is used to show how an optimum tailplane area can be calculated for manoeuvres in the longitudinal plane. Then an "Advanced Rotor Helicopter" is compared with a contemporary battlefield helicopter.
21
Dixit, Surabhi. "An Approach to the Solution of Inverse Problem Using Unsupervised Machine Learning." Thesis, California State University, Long Beach, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10752219.
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The inverse problem is one of the classical problems in Computer Science. There are currently several numerical solutions for this problem based on Linear Algebra. Typically, the forward problem is when we know a model, or a formula, and we compute the values. On the contrary, the inverse problem is when the data is collected with some measuring equipment and then inverted to find the model. It can be described as identifying the cause using its effect. However, there may not exist a unique solution to this problem, but there are approximations to guess what the information might have been. These methods suffer from downsides, because there is not enough data to compute an appropriate solution. This thesis presents a possible approach to the inverse problem using Machine Learning for the Electroencephalography (EEG) dataset and presents an analysis of the results obtained by testing some of the known Unsupervised Learning methods.
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Tsai, Yusheng T. "A strictly convergent, real-time solution for inverse kinematics for robot manipulators /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487267546984588.
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Callahan, Daniel Behrman Elizabeth. "Construction and solution of an inverse problem posed by "Piekara⁰́₉s Chair"." A link to full text of this thesis in SOAR, 2008. http://hdl.handle.net/10057/2021.
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Thesis (M.S.)--Wichita State University, College of Liberal Arts and Science, Dept. of Mathematics & StatisticsThesis (excluding code) ©Copyright 2008 Daniel Callahanunder the Creative Commons Attribution 3.0 Unported LicenseCode ©Copyright 2008 Daniel Callahan, released under the MIT License:Permission is hereby granted, free of charge, to any person obtaining a copy of thissoftware and associated documentation files (the "Software"), to deal in the Softwarewithout restriction, including without limitation the rights to use, copy, modify, merge,publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons towhom the Software is furnished to do so, subject to the following conditions:The above copyright notice and this permission notice shall be included in all copies orsubstantial portions of the Software.THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIESOF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE ANDNONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHTHOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISINGFROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OROTHER DEALINGS IN THE SOFTWARE. Includes bibliographical references (leaves 46-47).
24
Tapdigoglu, Ramiz. "Inverse problems for fractional order differential equations." Thesis, La Rochelle, 2019. http://www.theses.fr/2019LAROS004/document.
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Dans cette thèse, nous nous intéressons à résoudre certains problèmes inverses pour des équations différentielles aux dérivées fractionnaires. Un problème inverse est généralement mal posé. Un problème mal posé est un problème qui ne répond pas à l’un des trois critères de Hadamard pour être bien posé, c’est-à-dire, soit l’existence, l’unicité ou une dépendance continue aux données n'est plus vraie, à savoir, des petits changements dans les données de mesure entraînent des changements indéfiniment importants dans la solution. La plupart des difficultés à résoudre des problèmes mal posés sont causées par l’instabilité de la solution. D’autre part, les équations différentielles fractionnaires deviennent un outil important dans la modélisation de nombreux problèmes de la vie réelle et il y a eu donc un intérêt croissant pour l’étude des problèmes inverses avec des équations différentielles fractionnaires. Le calcul fractionnaire est une branche des mathématiques qui fait référence à l’extension du concept de dérivation classique à la dérivation d’ordre non entier. Calculer une dérivée fractionnaire à un certain moment exige tous les processus précédents avec des propriétés de mémoire. C’est l’avantage principal du calcul fractionnaire d’expliquer les processus associés aux systèmes physiques complexes qui ont une mémoire à long terme et / ou des interactions spatiales à longue distance. De plus, les équations différentielles fractionnaires peuvent nous aider à réduire les erreurs découlant de paramètres négligés dans la modélisation des phénomènes physiquesIn this thesis, we are interested in solving some inverse problems for fractional differential equations. An inverse problem is usually ill-posed. The concept of an ill-posed problem is not new. While there is no universal formal definition for inverse problems, Hadamard [1923] defined a problem as being ill-posed if it violates the criteria of a well-posed problem, that is, either existence, uniqueness or continuous dependence on data is no longer true, i.e., arbitrarily small changes in the measurement data lead to indefinitely large changes in the solution. Most difficulties in solving ill-posed problems are caused by solution instability. Inverse problems come into various types, for example, inverse initial problems where initial data are unknown and inverse source problems where the source term is unknown. These unknown terms are to be determined using extra boundary data. Fractional differential equations, on the other hand, become an important tool in modeling many real-life problems and hence there has been growing interest in studying inverse problems of time fractional differential equations. The Non-Integer Order Calculus, traditionally known as Fractional Calculus is the branch of mathematics that tries to interpolate the classical derivatives and integrals and generalizes them for any orders, not necessarily integer order. The advantages of fractional derivatives are that they have a greater degree of flexibility in the model and provide an excellent instrument for the description of the reality. This is because of the fact that the realistic modeling of a physical phenomenon does not depend only on the instant time, but also on the history of the previous time, i.e., calculating timefractional derivative at some time requires all the previous processes with memory and hereditary properties
25
Qing, Chang, Liu Zhongkan, and Zhang Qishan. "THE RECURSIVE ALGORITHMS FOR GDOP AND POSITIONING SOLUTION IN GPS." International Foundation for Telemetering, 1997. http://hdl.handle.net/10150/609825.
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International Telemetering Conference Proceedings / October 27-30, 1997 / Riviera Hotel and Convention Center, Las Vegas, NevadaThis paper proves theoretically that GDOP decreases as the number of satellites is increased.This paper proposes two recursive algorithms for calculating the GDOP and positioning solution.These algorithms not only can recursively calculate the GDOP and positioning solution, but also is very flexible in obtaining the best four-satellite positioning solution ,the best five-satellite positioning solution and the all visible satellite positioning solution according to given requirements. In the need of the two algorithms,this paper extends the definition of the GDOP to the case in which the number of visible satellites is less than 4.
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Miller, Eric Lawrence. "The application of multiscale and stochastic techniques to the solution of inverse problems." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/11616.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 295-306).
by Eric Lawrence Miller.
Ph.D.
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Alexe, Mihai. "Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/37515.
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Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the
solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients
of a stateâ ofâ theâ art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of fluxâ limited numerical algorithms.Ph. D.
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Holman, Benjamin Robert. "Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/612954.
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In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.
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Meyer, Marcus. "Parameter identification problems for elastic large deformations - Part I: model and solution of the inverse problem." Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901869.
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In this paper we discuss the identification of parameter functions in material models for elastic large deformations. A model of the the forward problem is given, where the displacement of a deformed material is found as the solution of a n onlinear PDE. Here, the crucial point is the definition of the 2nd Piola-Kirchhoff stress tensor by using several material laws including a number of material parameters. In the main part of the paper we consider the identification of such parameters from measured displacements, where the inverse problem is given as an optimal control problem. We introduce a solution of the identification problem with Lagrange and SQP methods. The presented algorithm is applied to linear elastic material with large deformations.
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Mardyanto, Mas Agus. "A solution to an inverse problem of groundwater flow using stochastic finite element method." Thesis, University of Ottawa (Canada), 2004. http://hdl.handle.net/10393/29139.
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In this study, a stochastic finite element method is used to solve an inverse problem in groundwater flow. The adjoint states method combined with cokriging method is used to estimate the distribution of hydraulic conductivities in an area where hydraulic heads and hydraulic conductivities are measured at some locations. This method starts with obtaining the expected hydraulic heads in the entire study domain at different times. Then, the adjoint states at different times are calculated. Using both calculated values as input, the Jacobians that are needed for the development of covariance matrices of hydraulic heads at different times and the cross-covariance matrices between hydraulic heads at different times and hydraulic conductivities in the aquifer are calculated. Using the maximum likelihood estimate method (MLE), which utilizes all covariance and cross-covariance matrices obtained from the previous step, the statistical parameters (mean, variance, and correlation scale) of the model are estimated. Using the statistical parameter values and all observed values of hydraulic heads at different times and all measured hydraulic conductivities, the distribution of hydraulic conductivity in the entire study domain is estimated.
An attempt is made in this thesis to verify the computer program by utilizing two hypothetical problems as verification cases. In some parts of the aquifer, mostly at locations around the observation wells, the resulting hydraulic conductivity distributions have the same pattern with the "true" distribution patterns in both cases of verification. The values of L2-norms calculated by using the "true" and estimated values of log hydraulic conductivity are 0.18 and 0.57 for Case 1 and 2, respectively.
Data from two field problems are analyzed as an application of the computer program. The estimated values of hydraulic conductivity are found to be within the range of the observed values given in the original reports. These applications can be considered as a part of the validation of the method.
Considering the results of both case studies, it appears that the computer program developed in this study can be used with reasonable success to estimate the hydraulic conductivity distribution in real aquifers. As will be explained in the discussion of the results, however, the effect of zonation needs to be investigated further. (Abstract shortened by UMI.)
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Gallegos, Carlos Mario 1973. "Motion based design : solution algorithms to the inverse problem with applications to seismic design." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/46143.
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Benedetti, Manuel. "Multi-résolution techniques based on shape-optimization for the solution of inverse scattering problems." Paris 11, 2008. http://www.theses.fr/2008PA112249.
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La these se focalise sur le developpement et l’analyse de l’integration d’une strategie multi-echelle iterative et de la representation en ensembles de niveaux pour la resolution des problemes de diffraction electromagnetique inverse. L’implementation qui en resulte a pour but d’exploiter de maniere profitable tant la connaissance a priori disponible sur le scenario joue que le contenu informatif des mesures de la diffraction. La formulation du probleme inverse est reduite au cas bidimensionnel de polarisation transverse magnetique quand on traitera d’une ou de plusieurs regions d’interet. Le memoire est organise comme suit. Tout d’abord, la formulation mathematique du probleme de diffraction inverse est decrite et les principales limitations du modele correspondant sont discutes. De maniere plus detaillee, le chapitre 3 se concentre sur l’exploitation de solutions regularisees et d’approximations utiles permettant de surmonter le caractere mal pose du probleme inverse a resoudre. En sus, tant des techniques de minimisation deterministes qu’heuristiques de minimisation sont presentees. Une analyse rapide des techniques de multi-resolution et d’optimisation de forme disponibles est alors donnee. L’architecture de la strategie proposee est presentee dans les chapitres 4 et 5. Afin d’evaluer la capacite de reconstruction, une validation numerique est conduite a partir de donnees synthetiques (simulees) et de donnees acquises en situation controlee de laboratoire (experimentales) et en considerant des objets qui sont de forme simple aussi bien que complexeThe thesis focuses on the development and the analysis of the integration of a multiscale iterative strategy and a level set representation for the solution of electromagnetic inverse scattering problems. The resulting implementation is aimed at suitably exploiting the available a-priori knowledge about the scenario under test and the information content in the scattering measurements. The mathematical formulation of the inverse scattering problem is reduced to the bidimensional transverse-magnetic case when considering one or multiple regions of interest. The thesis is organized as follows. First of all, the mathematical formulation of the inverse scattering problem is described and the main drawbacks of the corresponding model are discussed. More in detail, chapter 3 focuses on the exploitation of regularized solutions and useful approximations in order to overcome the illposedness characterizing the inverse problem to be solved. Moreover, both deterministic and heuristic minimization techniques are presented. Then, the multi-resolution techniques and the shape optimization approaches are analyzed. The architecture of the proposed strategy is presented in chapters 4 and 5. In order to evaluate the reconstruction capabilities, a numerical validation is performed by considering both synthetic and laboratory-controlled data and targets characterized by simple as well as complex shapes
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PABON, MARTIAL. "Synthese en emulsion et microemulsion inverse de polymeres associatifs hydrosolubles : proprietes rheologiques en solution." Université Louis Pasteur (Strasbourg) (1971-2008), 1997. http://www.theses.fr/1997STR13188.
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Dans ce travail, nous avons etendu les procedes de polymerisation radicalaire en emulsion et microemulsion inverse (eau dans huile) a la synthese de polymeres associatifs hydrosolubles. Les monomeres hydrosolubles utilises sont l'acrylamide et l'acrylate de sodium. Les monomeres devant conferer aux polymeres leurs proprietes associatives sont soit hydrophobes (n,n-dihexylacrylamide et n,n-diphenylacrylamide), soit amphiphiles (methacrylates de t-octyl-phenoxy-poly(oxyethylene) avec 1 a 30 motifs oxyethylene). Nous avons montre que la nature de l'amorceur (hydrosoluble ou liposoluble) avait une grande influence sur l'incorporation du monomere hydrophobe ou amphiphile dans le polymere. Les polymeres synthetises avec ces procedes possedent de tres grandes masses molaires (> 5. 10#6) et leur composition varie peu en fonction de la conversion contrairement a ce qui serait observe en phase homogene. Ce dernier point confirme la specificite des procedes de synthese en milieux disperses. L'etude des proprietes rheologiques en solution aqueuse a montre que la nature de l'amorceur etait le parametre essentiel pour la synthese de polymeres associatifs en milieux disperses, celui-ci devant etre localise dans la phase ne contenant pas le monomere amphiphile ou hydrophobe. Les proprietes epaississantes des terpolymeres acrylamide/acrylate de sodium/monomere amphiphile a 10 unites oxyethylene sont optimales pour un taux molaire de monomere amphiphile extremement faible (0,3 %). Des mesures de viscosite sous ecoulement ont permis d'estimer la duree de vie des liaisons hydrophobes intermoleculaires qui est de 10#-#1 s. Des mesures en regime oscillatoire lineaire indiquent que l'introduction d'interactions hydrophobes cause un ralentissement de la reptation des chaines de polymeres, en accord avec les predictions du modele de reptation collante (leibler et al. ).
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De, Villiers Jason Peter. "Correction of radially asymmetric lens distortion with a closed form solution and inverse function." Diss., Pretoria : [s.n.], 2008. http://upetd.up.ac.za/thesis/available/etd-01232009-161525/.
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Lee, Jong-eao John. "The inverse spectral solution, modulation theory and linearized stability analysis of N-phase, quasi-periodic solutions of the nonlinear Schrodinger equation /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu148726601122429.
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Weisz-Patrault, Daniel. "Recherche et utilisation de méthodes analytiques inverses pour des problèmes couplés thermo élastiques." Thesis, Paris Est, 2012. http://www.theses.fr/2012PEST1171/document.
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Ce travail de doctorat porte sur l'utilisation des mathématiques analytiques dans le cadre de méthodes inverses appliquées à l'industrie. Ces travaux tiennent au développement de capteurs inverses en temps réel adaptés au laminage industriel. Le producteur d'acier ArcelorMittal dirige un projet européen, qui vise à montrer la faisabilité de capteurs mesurant les champs (température, contraintes) dans le contact entre le produit et l'outil sans altérer les conditions de ce contact. Les travaux de thèse présentés dans ce mémoire ont été réalisés au sein du laboratoire Navier et financé par l'école des Ponts ParisTech. Cependant un contrat sur trois ans signé avec ArcelorMittal a permis à l'auteur d'être partie prenante de ce projet européen, et ainsi de voir ses recherches concrétisées par une demande industrielle réelle. L'enjeu de cette thèse est double, académique et industriel. Académique en ce sens que les travaux cherchent à recenser et utiliser efficacement les méthodes de résolution analytiques existantes, pour des problèmes inverses en thermoélasticité, dans le cadre d'une métrologie en temps réel. En effet, les solutions analytiques sont souvent exploitées comme des cas purement théoriques, trouvant à bien des égards un certain succès dans la culture de l'ingénieur (comme c'est le cas par exemple du calcul en élasticité linéaire des facteurs d'intensité de contraintes), mais qui par bien des aspects sont reléguées à des cas d'écoles anciens servant au mieux à valider des codes de calculs numériques sur des exemples particulièrement simples. Ces solutions et méthodes de résolution analytiques ne font d'ailleurs guère plus l'objet de recherches en mathématiques pures. Cependant les problématiques propres, liées au caractère inverse des problèmes à traiter, pénalisent les méthodes de résolution numériques, en ce sens que les problèmes inverses sont mal posés, et qu'une stabilisation des algorithmes numériques est nécessaire mais souvent délicate si l'on considère les conditions extrêmes (champs très singuliers) appliquées aux outils industriels de laminage. Par ailleurs la métrologie en temps réel exclut l'utilisation de codes numériques trop coûteux en temps de calcul (méthodes itératives etc...). Ces deux aspects contribuent à renouveler assez largement l'intérêt pour les solutions analytiques. Il convient alors d'en regrouper (dans la mesure du possible) les méthodes les plus efficaces (en termes de précision et de temps de calcul notamment) et les plus adaptées pour la métrologie. Nous verrons notamment différents développements en séries élémentaires permettant non seulement de donner à une suite de points mesurés une forme analytique, mais également de simplifier les équations aux dérivées partielles à résoudre. D'autre part l'enjeu de cette thèse est également industriel, car ces travaux s'inscrivent dans une démarche de développement de capteurs adaptés à la mise en forme de l'acier par laminage. Ainsi l'étude de la robustesse au bruit de mesure, les contraintes technologiques liées à l'insertion des capteurs, les limitations en terme de fréquence d'acquisition et les problématiques de calibrage sont au coeur des développements. Ainsi, l'ensemble des travaux présentés, peut constituer une sorte de réhabilitation des méthodes analytiques, dont la supériorité sur les méthodes numériques (en termes de temps de calcul et parfois aussi de précision) est mise en lumière, dans le contexte précis de la métrologie en temps réel sur des géométries simples. Trois méthodes inverses en deux dimensions, adaptées au laminage industriel, ont été menées à bien (élastique isotherme, thermique et couplage thermoélastique), ainsi qu'une série d'applications expérimentales réalisées sur le laminoir de laboratoire d'ArcelorMittal. Par ailleurs, des extensions en trois dimensions des méthodes inverses élastiques et thermiques sont également détailléesThis thesis is about the use of analytical mathematics within the framework of inverse methods applied to industry. These works are devoted to the development of sensors using real-time inverse methods adapted for rolling process. Steel producer ArcelorMittal leads a European project that aims to demonstrate the feasibility of sensors measuring fields (temperature, stress) in the contact between the product and the tool without altering physical conditions of this contact. The thesis has been funded by l'école des Ponts ParisTech. However, a three-year contract signed with ArcelorMittal has enabled the author to be part of the European project, and thus his research has been motivated by a real industrial demand. The aim of this thesis is twofold, academic and industrial; academic in the sense that these works seek to identify and use efficiently existing analytical methods for inverse problems occurring in thermo-elasticity in the context of real-time metrology. Indeed, analytical solutions are often exploited as purely theoretical cases, finding in many ways some success in engineering (for example in linear elasticity with stress intensity factors), but are most of the time relegated to the validation of numerical codes under simple assumptions. As a matter of fact, there is no research any more in pure mathematics concerning these solutions and analytical methods. However, the specific complications related to the inverse nature of problems under consideration, penalize numerical algorithms because inverse problems are ill-posed and stabilization is needed. But it remains often difficult if we consider the extreme loads (very sharp gradients) applied to industrial tools during rolling. Moreover, the real-time metrology excludes the use of numerical codes too costly in terms of computation time (iterative methods etc...). Both aspects contribute to renew widely interest for analytical solutions. It is then necessary to collect most effective and efficient (in terms of computation time and precision) methods and emphasis the most suitable for metrology. We will see various series expansions, not only to give a sequence of measured points an analytical form, but also to simplify the partial differential equations to solve. On the other hand, the goal of this thesis is also industrial, as these works are part of a process of development of sensors adapted for steel rolling industry. Thus, the robustness to measurement noise, technological constraints related to the local measurement systems (such as limitations in terms of frequency of acquisition) and calibration issues are central in the developments. Thus, the whole work can be a kind of rehabilitation of analytical methods. Their superiority over numerical methods (in terms of computation time and sometime accuracy) is highlighted, in the specific context of metrology in real-time on simple geometries. Three inverse methods in two-dimensions suitable for rolling process were developed successfully (isothermal elastic, thermal and thermoelastic coupling) and a series of experimental tests were made on the laboratory mill of ArcelorMittal. In addition, three-dimensional extensions of elastic and thermal inverse methods are also detailed
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Steward, Jeff. "The solution of a Burgers' equation inverse problem with reduced-order modeling proper orthogonal decomposition." Tallahassee, Florida : Florida State University, 2009. http://etd.lib.fsu.edu/theses/available/etd-07062009-230217.
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Thesis (M.S.)--Florida State University, 2009.Advisor: Ionel M. Navon, Florida State University, College of Arts and Sciences, Dept. of Scientific Computing. Title and description from dissertation home page (viewed on Nov. 17, 2009). Document formatted into pages; contains ix, 67 pages. Includes bibliographical references.
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Yang, Kai. "Dynamics of the energy critical nonlinear Schrödinger equation with inverse square potential." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5685.
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We consider the Cauchy problem for the focusing energy critical NLS with inverse square potential. The energy of the solution, which consists of the kinetic energy and potential energy, is conserved for all time. Due to the focusing nature, solution with arbitrary energy may exhibit various behaviors: it could exist globally and scatter like a free evolution, persist like a solitary wave, blow up at finite time, or even have mixed behaviors. Our goal in this thesis is to fully characterize the solution when the energy is below or at the level of the energy of the ground state solution $W_a$. Our main result contains two parts.
First, we prove that when the energy and kinetic energy of the initial data are less than those of the ground state solution, the solution exists globally and scatters.
Second, we show a rigidity result at the level of ground state solution. We prove that among all solutions with the same energy as the ground state solution, there are only two (up to symmetries) solutions $W_a^+, W_a^-$ that are exponential close to $W_a$ and serve as the threshold of scattering and blow-up. All solutions with the same energy will blow up both forward and backward in time if they go beyond the upper threshold $W_a^+$; all solutions with the same energy will scatter both forward and backward in time if they fall below the lower threshold $W_a^-$.
In the case of NLS with no potential, this type of results was first obtained by Kenig-Merle \cite{R: Kenig focusing} and Duyckaerts-Merle \cite{R: D Merle}. However, as the potential has the same scaling as $\Delta$, one can not expect to extend their results in a simple perturbative way. We develop crucial spectral estimates for the operator $-\Delta+a/|x|^2$, we also rely heavily on the recent understanding of the operator $-\Delta+a/|x|^2$ in \cite{R: Harmonic inverse KMVZZ}.
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Radwan, Samir F. "Numerical solution of the three-dimensional boundary layer equations in the inverse mode using finite differences." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/12029.
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Sanchez, De Lucio Jose Alfonso. "Functional brain connectivity analysis based on the solution of the inverse problem and on covariance analysis." Thesis, University of York, 2015. http://etheses.whiterose.ac.uk/8938/.
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The Linearly Constrained Minimum Variance (LCMV) beamformer is one of the most accepted techniques used to estimate the solution of the inverse problem in functional brain dynamics studies, using magnetoencephalograms (MEG). However, since it is based on the assumption of uncorrelated brain sources, its performance decreases in the presence of correlated brain activity, compromising the accuracy of estimates of brain interactions. This problem has not stopped the use of the beamformer in techniques such as Dynamic Imaging of Coherent Sources (DICS), which estimates the functional brain dynamics in a more direct way than the LCMV, and with less computational cost. In this work it is proposed to use a modified version of the well known Minimum Norm Estimates (MNE) spatial filter to estimate the functional brain dynamics of highly correlated activity. This is achieved by using the filter to estimate the cross-spectral density matrices for the brain activity in the same way that DICS does with the LCMV beamformer. The MNE spatial filter is used as a basis because it is not affected by the presence of correlated brain activity. The results obtained from simulations shown that it is possible to estimate highly correlated brain interactions using the proposed method. However, additional methods and constraints need to be applied because of the distorted and weighted output characteristic of the MNE spatial filter. Methods such as the FOcal Undetermined System Solution (FOCUSS) and Singular Value Decomposition Truncation (SVDT) are used to reduce the distorted output, while the estimation of brain dynamics is limited to cortical surface interactions to avoid weighted solutions.
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Chittabathini, Kumaraswamy. "Investigation of the inverse cascade process in wall-bounded logarithmic flow as a solution of the Euler equation." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/27787.
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Wall-bounded shear flows (WBSF) can be regarded as turbulent, organized coherent structures and occur in many different circumstances. The self-similarity of statistical characteristics of turbulence at different heights in the log layer of WBSF might reflect coherent structures which are also self-similar. McNaughton suggested that these coherent structures are in the form of 'Theodorsen ejection amplifier' (TEA) patterns. The TEA model of the structure of turbulence may be responsible for the formation of the three-dimensional inverse cascade process in log layers over smooth walls. The inverse cascade can serve as an efficient mechanism of energy transfer from small to large scales and enables us to understand the dynamics of large-scale coherent structures in the near-wall region. As far as the author is aware, no previous research has been conducted into the existence of a 3-D inverse cascade in WBSF. The objective of the thesis is to investigate numerically an upscale cascade process that has been hypothesized as a basic element of WBSF, and to examine an inverse cascade of this kind as a valid solution of the Euler equations. Initially, the numerical experiments were performed using the commercial Computational Fluid Dynamics (CFD) FLUENT 6.0 software, to reproduce the 'ejection amplifier' cycle (TEA structure) found by McNaughton and Bluendell (2002). In the numerical experiments, fluid was injected from the wall into the base of an ideal, ffictionless logarithmic flow while an equal volume of fluid was removed by suction along two flanking slots. This arrangement is known to create hairpin vortices in physical experiments. The FLUENT simulation results followed the subsequent formation of a hairpin eddy which induced a second, larger ejection from within its arc. The limited computing resources did not allow the FLUENT simulations to be followed far enough to examine possibility of any subsequent hairpins and ejections, so the feasibility of the TEA cascade was not firmly established. Research-oriented Large-Eddy Simulation (LES) code has been used to examine the inverse cascade process, and to overcome the computational limitations of the FLUENT solver. Several numerical experiments have been done using the LES code. The flow velocity data obtained from the simulations have been used to study the formation and growth of hairpin vortices and ejections, and their regeneration into 'ejection amplifier' structures. A comparison has been made between the CFD FLUENT predictions and initial LES run results so as to validate the LES solver. The results of the initial LES experiment reproduced the formation of the primary hairpin vortex (PHV), but did not reproduce the formation of primary a 'ejection amplifier' cycle. This is because the injection parameters and the spatial resolution were influencing primary hairpin development. The possibility of an upscale cascade of 'ejection amplifier' structure formation has been investigated by changing the injection/suction velocity, size and location in both low and high resolution domains. Fifteen LES simulation runs have been done, in which sets of variables and parameters have been systematically varied. The results obtained from all the LES runs showed that the injected disturbance developed into a primary hairpin vortex. When the slot was near the inflow boundary of the simulation domain, the low resolution runs did not indicate the formation of a primary 'ejection amplifier' cycle from the primary hairpin vortex development. These results suggest that the frequency of hairpin generation decreases with decreasing injection velocity. When the disturbance was injected at the center of the low resolution domain, development of the primary hairpin vortex was not affected by the inflow boundary. However, because of the large injection velocity and large slot the primary hairpin vortex also did not evolve into a primary 'ejection amplifier' cycle. The low resolution simulations done using a small slot with large injection velocity showed that the primary hairpin vortex developed into a primary 'ejection amplifier' cycle, but its development was discontinued because of the small injection. All the high resolution runs that were done using a large slot and a high injection velocity showed the formation of a primary 'ejection amplifier' cycle. The high resolution runs that were done using different injection periods also showed the formation of primary 'ejection amplifier' cycles. However, none of the simulations developed fully into an inverse cascade of ejection amplifier structures. In general, these results suggested that the TEA structure formation depends on the injection parameters (injection velocity, injection size, injection duration and injection location) and resolution. The injected disturbances are able to generate TEA structures, but have not been able to generate upscale cascades of TEA structures in log flow. This suggests that the present LES is not able to establish the 3-D inverse cascade process in wall-bounded log flow.
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Ni, Marcus. "Automated Hybrid Singularity Superposition and Anchored Grid Pattern BEM Algorithm for the Solution of the Inverse Geometric Problem." Master's thesis, University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5827.
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A method for solving the inverse geometrical problem is presented by reconstructing the unknown subsurface cavity geometry using boundary element methods, a genetic algorithm, and Nelder-Mead non-linear simplex optimization. The heat conduction problem is solved utilizing the boundary element method, which calculates the difference between the measured temperature at the exposed surface and the computed temperature under the current update of the unknown subsurface flaws and cavities. In a first step, clusters of singularities are utilized to solve the inverse problem and to identify the location of the centroid(s) of the subsurface cavity(ies)/flaw(s). In a second step, the reconstruction of the estimated cavity(ies)/flaw(s) geometry(ies) is accomplished by utilizing an anchored grid pattern upon which cubic spline knots are restricted to move in the search for unknown geometry. Solution of the inverse problem is achieved using a genetic algorithm accelerated with the Nelder-Mead non-linear simplex. To optimize the cubic spline interpolated geometry, the flux (Neumann) boundary conditions are minimized using a least squares functional. The automated algorithm successfully reconstructs single and multiple subsurface cavities within two dimensional mediums. The solver is also shown to accurately predict cavity geometries with random noise in the boundary condition measurements. Subsurface cavities can be difficult to detect based on their location. By applying different boundary conditions to the same geometry, more information is supplied at the boundary, and the subsurface cavity is easily detected despite its low heat signature effect at the boundaries. Extensions to three-dimensional applications are outlined.M.S.M.E.
Masters
Mechanical and Aerospace Engineering
Engineering and Computer Science
Mechanical Engineering; Thermo-Fluids
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Albrand, Marius. "Etude d'une solution d'évaluation des constantes diélectriques du béton d'ouvrages à risque par une approche problème inverse en électromagnétisme." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30319/document.
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Les travaux de cette thèse concernent l'étude d'une méthode d'évaluation des constantes diélectriques du béton d'ouvrage à risque par une approche problème inverse. Pour cela des mesures radar de type GPR et un modèle électromagnétique de ces mêmes mesures seront utilisés. Les deux premiers chapitres de la thèse présentent les concepts clés, le contexte et un historique des travaux déjà réalisés dans le domaine. Le chapitre 2 propose en outre une adaptation des travaux déjà réalisés à la recherche de gradients de propriétés diélectriques dans le béton en profondeur. Cette recherche préliminaire nous a permis de redéfinir le processus de mesures pour le rendre plus adapté à nos besoins. Ainsi le chapitre 3 présente une campagne de mesure réalisée à l'aide d'un nouveau dispositif radar sur des corps d'épreuve conditionnés de telle sorte que la répartition de la teneur en eau soit maîtrisée. Dans ce chapitre, nous détaillons également un nouveau modèle numérique 3D du dispositif qui nous permet de simuler nos mesures de façon réaliste Ces simulations sont nécessaires à l'expression du problème inverse. à partir de ces mesures, dans le quatrième chapitre, nous définissons tout d'abord le problème inverse, puis en utilisant des mesures sur les corps d'épreuves saturés, pouvant être considérés comme homogènes d'un point de vue diélectrique, nous résolvons ce problème inverse par un algorithme d'optimisation basé sur celui de Levenberg-Marquardt. Les résultats obtenus par notre processus d'inversion sont cohérents avec les valeurs physiques que l'on pouvait attendre et sont indépendants des valeurs données à nos inconnues lors de l'initialisation. Ces résultats correspondent effectivement à un minimum de la fonction coût qui mesure la distance entre mesures et simulations. Nous avons ensuite étudié des stratégies pour diminuer le temps de calcul de notre processus d'inversion. Une première approche consiste à utiliser un modèle simplifié en 2D du dispositif, qui permet d'initialiser l'inversion 3D avec un point plus proche de la solution. Une autre idée consiste à utiliser au mieux les performances d'une machine multiprocesseurs en parallélisant le code 3D. Dans le chapitre 5 nous nous intéressons à des mesures sur des corps d'épreuve en béton dont la teneur en eau est une fonction affine de la profondeur. Dans ces conditions nous avons fait l'hypothèse, en première approche, que les constantes diélectriques suivent aussi ce type de loi. Après avoir redéfini les inconnues de notre problème inverse et adapté l'algorithme, nous montrons que le processus d'inversion fourni des résultats cohérents en ce qui concerne la permittivité diélectrique, mais insatisfaisant pour la conductivité. Après analyse de ces résultats nous avons proposé diverses pistes pour améliorer et valider la méthode d'inversion. Finalement en comparant l'ensemble des résultats, il apparaît que notre méthode d'inversion permet de caractériser des gradients de permittivité, mais pas de conductivité. Cela représente néanmoins une avancée significative pour la mesure de la teneur en eau dans les bétons, facteur principal influençant la constante diélectrique de ce matériau, dans le contexte du contrôle non destructif des ouvrages du génie civilThat thesis aims to propose an assessment method of the concrete electromagnetic properties by using radar measurements in a context of building sustainability, by inverse problem. For that purpose Ground Penetrating Radar (GPR) measurements are used as well as a numerical model of the radar device. The first two chapters of the thesis present the key concepts, the context of the study, as well as the history of the research on that topic in particular in our laboratory. Chapter 2 also expands those early works on the search of electromagnetic properties of concrete in depth. That preliminary work helped us to develop a measurement device that is more fitted to our needs. Chapter 3 presents a measurement campaign that was carried out by using a new measurement device on specially made reinforced concrete slabs whose water content is monitored. In that chapter a 3D model of the device is also described. That model allows us to simulate the measurements very precisely. Those simulations are a critical link on the inverse process. Chapter 4 details the formulation of the inverse problem for the case of concrete slabs saturated with water, which can be therefore considered to have homogeneous electromagnetic properties. The problem is solved by using an optimization algorithm based on Levenberg-Marquardt method. The values obtained by the inverse process are physically acceptable and independent of the values given to the unknowns when initializing the algorithm. Those values are the minimum of the cost function that computes the distance between measured and simulated electromagnetic fields. We then studied some strategies to reduce the computing time of the inverse process. A first approach consists in the use of a 2D simplified model of our device to initialize the 3D inversion with values closer to the searched solution. Another idea is to better take advantage of all the resources of a multiprocessor computer by implementing a parallel version of the 3D code. In chapter 5 we focus on the concrete slab with water content being an affine function of depth. We define the new parameters that represent the unknowns of our problem and we adapt the previous algorithm. Then we show that the inverse process gives satisfying results with regard to the dielectric permittivity only. We suggest some ways to improve the method. Finally we conclude that our method allows to retrieve the permittivity of the concrete, but not its conductivity. Nevertheless that result represents a significant step for the measuring of water content in reinforced concrete in particular when a gradient is present, by using radar measurements
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Pittner, Andreas Verfasser], and Michael [Akademischer Betreuer] [Rethmeier. "A Contribution to the Solution of the Inverse Heat Conduction Problem in Welding Simulation / Andreas Pittner. Betreuer: Michael Rethmeier." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2012. http://d-nb.info/1022885723/34.
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El, Harrouni Khalid. "Coupling BEM, optimization techniques and extended Kalman filtering for the solution of direct and inverse problems of groundwater flow." Thesis, University of Portsmouth, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358819.
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Kotbi, Mohammed. "Etude structurale d'une solution aqueuse de chlorure de lithium LiCl, 6H2O par la méthode de Monte Carlo inverse (RMC)." Lyon 1, 1999. http://www.theses.fr/1999LYO10105.
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Le but de ce travail consiste en une modelisation structurale d'un electrolyte aqueux de type licl-6h 2o presentant la propriete de former un verre en passant par l'etat liquide metastable surfondu quand la temperature diminue. Des resultats experimentaux obtenus par la technique de diffusion de neutrons sont disponibles au departement de physique de materiaux. La methode de simulation utilisee dite de monte carlo inverse (rmc) propose un modele tridimensionnel du systeme au niveau atomique. Son interet est de pouvoir etre appliquee sans que les interactions interatomiques et intermoleculaires ne soient specifiees. En revanche, elle s'appuie sur les donnees experimentales disponibles et certains criteres geometriques locaux. Nous avons d'abord realise une simulation rmc sur l'eau pure a temperature ambiante, pour laquelle les trois fonctions de distribution de paire experimentales sont disponibles. En analysant les correlations angulaires dans notre systeme modele, nous avons deduit que le resultat obtenu pour la molecule d'eau a l'aide de rmc est compatible avec le resultat obtenu par une methode numerique independante aussi basee sur les fonctions de distribution de paire atomique experimentales. Cette etude valide notre modelisation de l'eau pure par la rmc. Nous avons ensuite etudie la structure de licl-6h 2o a l'aide de rmc utilisant quatre fonctions de distribution partielles experimentales, nous avons pu realiser des configurations a trois dimensions compatibles avec ces donnees. A l'aide des fonctions de paire calculees, on a pu determiner les nombres de coordination, les distances de correlation et comparer les etats de l'electrolyte aqueux liquide/verre/surfondu par rapport a l'eau pure a la temperature ambiante. Le calcul des coefficients, dans le developpement de la fonction de distribution moleculaire en harmoniques spheriques generalisees, donne des resultats coherents avec ceux obtenus dans l'etude des correlations radiales de l'electrolyte. Ces analyses de correlations angulaires mettent en evidence l'effet des ions pour les correlations a courte distance et l'effet de temperature sur la structure a moyenne distance de l'electrolyte aqueux a l'etat vitreux. En resume la methode rmc permet d'explorer un certain nombre de caracteristiques structurales de notre systeme, notamment au niveau des correlations de paire radiales et des correlations entre molecules. Des artefacts peuvent etre obtenus et pour y remedier nous devons avoir plus de donnees experimentales ou eventuellement un potentiel d'interaction assez realiste comme contrainte supplementaire dans la simulation rmc.
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Alsoy-akgun, Nagehan. "The Dual Reciprocity Boundary Element Solution Of Helmholtz-type Equations In Fluid Dynamics." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615729/index.pdf.
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In this thesis, the two-dimensional, unsteady, laminar and incompressible fluid flow problems governed by partial differential equations are solved by using dual reciprocity boundary element method (DRBEM). First, the governing equations are transformed to the inhomogeneous modified Helmholtz equations, and then the fundamental solution of modified Helmholtz equation is used for obtaining boundary element method (BEM) formulation. Thus, all the terms in the equation except the modified Helmholtz operator are considered as inhomogeneity. All the inhomogeneity terms are approximated by using suitable radial basis functions, and corresponding particular solutions are derived by using the annihilator method. Transforming time dependent partial differential equations to the form of inhomogeneous modified Helmholtz equations in DRBEM application enables us to use more information from the original governing equation. These are the main original parts of the thesis. In order to obtain modified Helmholtz equation for the time dependent partial differential equations, the time derivatives are approximated at two time levels by using forward finite difference method. This also eliminates the need of another time integration scheme, and diminishes stability problems.
Stream function-vorticity formulations are adopted in physical fluid dynamics problems in DRBEM by using constant elements. First, the procedure is applied to the lid-driven cavity flow and results are obtained for Reynolds number values up to 2000. The natural convection flow is solved for Rayleigh numbers between 10^3 to 10^6 when the energy equation is added to the Navier-Stokes equations. Then, double diffusive mixed convection flow problem defined in three different physical domains is solved by using the same procedure. Results are obtained for various values of Richardson and Reynolds numbers, and buoyancy ratios. Behind these, DRBEM is used for the solution of natural convection flow under a magnetic field by using two different radial basis functions for both vorticity transport and energy equations. The same problem is also solved with differential quadrature method using the form of Poisson type stream function and modified Helmholtz type vorticity and energy equations. DRBEM and DQM results are obtained for the values of Rayleigh and Hartmann numbers up to 10^6 and 300, respectively, and are compared in terms of accuracy and computational cost. Finally, DRBEM is used for the solution of inverse natural convection flow under a magnetic field using the results of direct problem for the missing boundary conditions.
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Dölker, Eva-Maria [Verfasser], Jens [Akademischer Betreuer] Haueisen, Alessandro Gutachter] Formisano, and Daniel [Gutachter] [Baumgarten. "Lorentz force evaluation : novel forward solution and inverse methods / Eva-Maria Dölker ; Gutachter: Alessandro Formisano, Daniel Baumgarten ; Betreuer: Jens Haueisen." Ilmenau : TU Ilmenau, 2020. http://d-nb.info/1207293520/34.
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Uriarte, Sabín Leticia. "Inverse Heat Conduction problem of the Quenching a Rotary Cylinder by Multiple Water Impinging Jets." Thesis, Högskolan i Gävle, Avdelningen för byggnadsteknik, energisystem och miljövetenskap, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-36529.
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The thesis deals with solving the time dependent inverse heat conduction and heat transfer problem of the quenching process of a rotary solid cylinder by multiple impinging water jets. The development of such investigation consists of two parts that complement each other. As is the case of any scientific experiment, first of all, an initial hypothesis will be set to be demonstrated theoretically. The numerical validation is carried out with a series of artificial cooling curve data and sensitivity analyses in the inverse solution. Then, a series of recorded temperature data were implemented into the inverse solution to predict the surface heat transfer during the quenching process.The numerical study consists of the solution of a two-dimensional linear time dependent inverse heat conduction problem based on the Generalized Minimal Residual Method (GMRES). The inverse solution method is based on the solution of an iterative problem, validated by a set of artificial temperature data. Such solution allows the prediction of the surface temperature and heat flux distribution in the quenching process, making use of recorded internal temperatures of the specimen. In order to solve the problem, the Matlab and Comsol Multiphysics programs were used. The GMRES algorithm was written as Matlab code, while the computational domain was defined in Comsol Multiphysics. Moreover, both programs collaborated in the solution of the inverse problem. Once the problem was solved, a sensitivity analysis was carried out in order to study the dependence of the numerical result on various parameters and optimize the inverse solution setup for application of recorded experimental data.The validated inverse solution setup examined by the sensitivity analyses was used on a set of experimental data, allowing the demonstration of the initially proposed hypothesis. This sensitivity analyses were performed consecutively for different key parameters regarding the numerical definition of the problem. The values for the parameters were considered optimal when minimum values for the error of the predicted surface temperature were recorded. In this case, the analyzed parameters were the m-value, mesh cell size, effect of noise, initial quenching temperature and quenching cooling rate. The connection between the experimental and numerical studies is obvious, as the first oneprovides the latter with input data of the inner temperature data of the specimen for the solving of the inverse problem, as is the case of the practical application of the code developed in the present thesis, and the inverse solution is essential in order to predict thesurface temperature and heat flux that are key information in studying quenching systems.
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Candler, S. "A perturbation theory for the inverse scattering transform with application to the solution of the variable depth Korteweg-de Vries equation." Thesis, University of Newcastle Upon Tyne, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355476.
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