Tangent Graeffe Iteration

Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running cost. The main ideas from which this algorithm is built are: classical Graeffe iteration and Newton Diagrams, changes of scale (renormalization), and replacement of a difference technique by a differentiation one. The algorithm was implemented successfully and a number of numerical experiments are displayed

Time migration velocity analysis in supergathers

Orientador: Ricardo Caetano Azevedo BilotiTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Na análise de velocidade de migração, o moveout (sobretempo) residual na seção migrada é usado para corrigir o campo de velocidade. Neste trabalho, propomos uma abordagem numérica para descrever o moveout na seção migrada considerando um refletor plano inclinado. A descrição é válida para seções migradas vizinhas e, portanto, várias seções migradas podem ser utilizadas simultaneamente para obter os parâmetros. Esta estratégia proporciona valores mais confiáveis para o fator de correção de velocidade. Através de alguns exemplos sintéticos, validamos e mostramos o bom desempenho da nossa estratégia de ajustar as curvas ou superfícies de moveout numericamente. Além disso, usamos um método de otimização sem derivadas para estimar os parâmetrosAbstract: In migration velocity analysis (MVA), the residual moveout in the image gather is used to correct the velocity field. In this work, we propose a numerical approach to describe the moveout in the image gather considering a dipping reflector. The description is valid for neighbouring image gathers, so that several image gathers can be used simultaneously to obtain the parameters. This strategy provides more reliable values for the velocity correction factor. Through some synthetic examples, we validate and show the good perfomance of our strategy of fitting the moveout curves or surfaces numerically. Also, we use a derivative-free optimization method to estimate the parametersDoutoradoReservatórios e GestãoDoutora em Ciências e Engenharia de PetróleoCAPE

Towards Real Time Optimal Auto-tuning of PID Controllers

The Proportional-Integral-Derivative (PID) controller has been widely used by the process control industry for many years. Design methods for PID Controllers are mature and have been heavily researched and evaluated. For most of its modern history the Ziegler-Nichols methods have been used for tuning PID controllers into desired operating conditions. Recently, automatic tuning methods have been formulated and used to generate stable PID controlled systems. These methods have also been implemented on real time systems. However, the use of optimal methods for auto tuning PID controllers on real time systems has not seen much discussion. In this thesis we explore the applicability of optimal PID design methods from Datta, Ho, and Bhattacharrya, to real time system control. The design method is based on a complete characterization of the set of stabilizing PID parameters for various plant models and a subsequent search over the stabilizing set for the optimal controller. A full implementation of the algorithms is completed on an embedded system with DSP hardware. These implementations are then tested against a large number of examples to determine both accuracy and applicability to real time systems. The major design constraint for application of these algorithms to real time systems is computation time. The faster the optimal result can be computed the more applicable the algorithm is to a real time environment. In order to bring each of these algorithms into a real time system, fast search algorithms were developed to quickly compute the optimal result for the given performance criterion. Three different search methods were developed, compared and analyzed. The first method is a brute force search used as a basis to compare the two additional fast search methods. The two faster search methods prove to be vastly superior in determining the optimal result with the same level of accuracy as brute force search, but in a greatly reduced time. These search methods achieve their superior speeds by reducing the search space without sacrificing accuracy of the results. With these two fast search methods applied to the complete characterization of stabilizing PID controllers, application to real time systems is achieved and demonstrated through examples of various performance criteria

Three-dimensional Green’s function and its derivatives for anisotropic elastic, piezoelectric and magnetoelectroelastic materials

Diese Arbeit behandelt hauptsächlich die Greensche Funktion für lineare allgemein anisotrope Materialien im unendlichen dreidimensionalen Raum, die auch als Fundamentallösung bezeichnet wird. Die detaillierten Herleitungen und die numerischen Auswertungen der expliziten Ausdrücke der Greenschen Funktion bzw. deren ersten und zweiten Ableitung, die auf der Methode der Residuen (RCM), dem Stroh-Formalismus (SFM) sowie der Unified Explicit Expression Method (UEEM) basieren, werden ebenfalls behandelt. Die numerischen Beispiele der drei verschiedenen Methoden werden für die Elastizitätstheorie miteinander verglichen. In nicht-degenerierten Fällen sind alle drei Methoden exakt für einen beliebigen Punkt. Bei nahezu degenerierten Fällen werden sowohl die RCM als auch die SFM instabil, während die UEEM ihre Gültigkeit behält. Ungeachtet dessen ist die SFM etwas stabiler als die RCM. Um deren Instabilität in degenerierten und nahezu degenerierten Fällen zu überwinden, werden in der RCM und der SFM einige Materialkonstanten leicht modifiziert. Trotz der Vorteile der UEEM im Vergleich zu RCM und SFM, ergeben sich Schwierigkeiten bei der Erweiterung auf Mehrfeldmaterialien. Die RCM und die SFM werden auf piezoelektrische Materialien erweitert und miteinander verglichen. Dadurch, dass die SFM bessere Ergebnisse für piezoelektrische Materialien liefert als die RCM, wird sie zusätzlich auf magnetoelektroelastische Materialien erweitert. Darüber hinaus wird die UEEM als Anwendung in einem BEM-Programm implementiert, mit dem sich einfache Elastizitätsprobleme lösen lassen.This thesis mainly deals with the Green’s function for linear generally anisotropic materials in the infinite three-dimensional space, also called the fundamental solution. The detailed derivations and the numerical results of the explicit expressions of the Green’s function and its first and second derivatives based on the residue calculus method (RCM), Stroh formalism method (SFM) and unified explicit expression method (UEEM) are presented. The numerical examples of the three different methods are compared with each other for the anisotropic elasticity. All three methods are accurate for an arbitrary point in non-degenerate cases. For nearly degenerate cases, both the RCM and the SFM become unstable while the UEEM keeps accurate. Moreover, the SFM is more stable than the RCM. To overcome the difficulty in nearly degenerate cases and degenerate cases, some material constants are slightly changed in the RCM and the SFM. Although the UEEM has some advantages compared with the RCM and the SFM, it is difficult to be extended to the multifield coupled materials. The RCM and SFM are extended to the piezoelectric materials and compared with each other. Since the SFM has a better performance than the RCM for the piezoelectric materials, it is extended further to the magnetoelectroelastic materials. The UEEM is implemented into a Boundary Element Method (BEM) as an application. Some demonstrative anisotropic elastic problems are solved by the developed BEM

Modeling and Calibrating the Distributed Camera

Structure-from-Motion (SfM) is a powerful tool for computing 3D reconstructions from images of a scene and has wide applications in computer vision, scene recognition, and augmented and virtual reality. Standard SfM pipelines make strict assumptions about the capturing devices in order to simplify the process for estimating camera geometry and 3D structure. Specifically, most methods require monocular cameras with known focal length calibration. When considering large-scale SfM from internet photo collections, EXIF calibrations cannot be used reliably. Further, the requirement of single camera systems limits the scalability of SfM. This thesis proposes to remove these constraints by instead considering the collection of cameras as a distributed camera that encapsulates the image and geometric information of all cameras simultaneously. First, I provide full generalizations to the relative camera pose and absolute camera pose problems. These generalizations are more expressive and extend the traditional single-camera problems to distributed cameras, forming the basis for a novel hierarchical SfM pipeline that exhibits state-of-the-art performance on large-scale datasets. Second, I describe two efficient methods for estimating camera focal lengths for the distributed camera when calibration is not available. Finally, I show how removing these constraints enables a simpler, more scalable SfM pipeline that is capable of handling uncalibrated cameras at scale

複素減衰の因果的近似法とその巨大地震を受ける長周期構造物への適用

Tohoku University五十子幸樹課