NUMERICAL ANALYSIS – THEORY AND APPLICATION Edited by Jan Awrejcewicz Numerical Analysis – Theory and Application Edited by Jan Awrejcewicz Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Ana Nikolic Technical Editor Teodora Smiljanic Cover Designer Jan Hyrat Image Copyright pashabo, 2011. Used under license from Shutterstock.com First published August, 2011 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Numerical Analysis – Theory and Application, Edited by Jan Awrejcewicz p. cm. ISBN 978-953-307-389-7 free online editions of InTech Books and Journals can be found at www.intechopen.com Contents Preface IX Part 1 Theory 1 Chapter 1 Finite Element and Finite Difference Methods for Elliptic and Parabolic Differential Equations 3 Aklilu T. G. Giorges Chapter 2 Data Analysis and Simulations of the Large Data Sets in the Galactic Astronomy 29 Eduardo B. de Amôres Chapter 3 Methods for Blind Estimation of the Variance of Mixed Noise and Their Performance Analysis 49 Sergey Abramov, Victoria Zabrodina, Vladimir Lukin, Benoit Vozel, Kacem Chehdi and Jaakko Astola Chapter 4 A Semi-Analytical Finite Element Approach in Machine Design of Axisymmetric Structures 71 Denis Benasciutti, Francesco De Bona and Mircea Gh. Munteanu Chapter 5 Optimization of the Dynamic Behaviour of Complex Structures Based on a Multimodal Strategy 97 Sébastien Besset and Louis Jézéquel Chapter 6 Numerical Simulation on Ecological Interactions in Time and Space 121 Kornkanok Bunwong Chapter 7 Unscented Filtering Algorithm for Discrete-Time Systems with Uncertain Observations and State-Dependent Noise 139 R. Caballero-Águila, A. Hermoso-Carazo and J. Linares-Pérez Chapter 8 Numerical Validation Methods 155 Ricardo Jauregui and Ferran Silva VI Contents Chapter 9 Edge Enhancement Computed Tomography 175 Cruz Meneses-Fabian, Gustavo Rodriguez-Zurita, and Areli Montes-Pérez Chapter 10 Model Approximation and Simulations of a Class of Nonlinear Propagation Bioprocesses 211 Emil Petre and Dan Selişteanu Chapter 11 Meshfree Methods 231 Saeid Zahiri Part 2 Application 251 Chapter 12 Mechanics of Deepwater Steel Catenary Riser 253 Menglan Duan, Jinghao Chen and Zhigang Li Chapter 13 Robust-Adaptive Flux Observers in Speed Vector Control of Induction Motor Drives 281 Filote Constantin and Ciufudean Calin Chapter 14 Modelling Friction Contacts in Structural Dynamics and its Application to Turbine Bladed Disks 301 Christian Maria Firrone and Stefano Zucca Chapter 15 Modeling and Simulation of Biomechanical Systems - An Orbital Cavity, a Pelvic Bone and Coupled DNA Bases 335 J. Awrejcewicz, J. Mrozowski, S. Młynarska, A. Dąbrowska-Wosiak, B. Zagrodny, S. Banasiak and L.V. Yakushevich Chapter 16 Study Regarding Numerical Simulation of Counter Flow Plate Heat Exchanger 357 Grigore Roxana, Popa Sorin, Hazi Aneta and Hazi Gheorghe Chapter 17 Numerical Modelling and Simulation of Radial-Axial Ring Rolling Process 373 Lianggang Guo and He Yang Chapter 18 Kinetostatics and Dynamics of Redundantly Actuated Planar Parallel Link Mechanisms 395 Takashi Harada Chapter 19 Dynamics and Control for a Novel One-Legged Hopping Robot in Stance Phase 417 Guang-Ping He and Zhi-Yong Geng Chapter 20 Mechanics of Cold Rolling of Thin Strip 439 Z. Y. Jiang Contents VII Chapter 21 Performance Evaluation of Single-Channel Receivers for Wireless Optical Communications by Numerical Simulations 463 M. Castillo-Vázquez, A. Jurado-Navas, J.M. Garrido-Balsells and A. Puerta-Notario Chapter 22 Estimation of Rotational Axis and Attitude Variation of Satellite by Integrated Image Processing 479 Hirohisa Kojima Chapter 23 Coupling Experiment and Nonlinear Numerical Analysis in the Study of Post-Buckling Response of Thin-Walled Airframe Structures 495 Tomasz Kopecki Chapter 24 Numerical Simulation for Vehicle Powertrain Development 519 Federico Millo, Luciano Rolando and Maurizio Andreata Chapter 25 Crash FE Simulation in the Design Process - Theory and Application 541 S. Roth, D. Chamoret, J. Badin, JR. Imbert and S. Gomes Chapter 26 Translational and Rotational Motion Control Considering Width for Autonomous Mobile Robots Using Fuzzy Inference 563 Takafumi Suzuki and Masaki Takahashi Chapter 27 Obstacle Avoidance for Autonomous Mobile Robots Based on Position Prediction Using Fuzzy Inference 577 Takafumi Suzuki and Masaki Takahashi Chapter 28 Numerical Simulation Research and Use of The Steel Sheet Pile Supporting Structure in Vertical Excavation 589 Qingzhi Yan and Xiangzhen Yan Chapter 29 Collision Avoidance Law Using Information Amount 609 Seiya Ueno and Takehiro Higuchi Preface This book focuses on introducing theoretical approaches of numerical analysis as well as applications of various numerical methods to either study or solving numerous physical and engineering problems. Since a large number of pure theoretical research is proposed and a large amount of applications oriented numerical simulation results is given, the book can be useful for both theoretical and applied research aimed at numerical simulations. In addition, in many cases the presented approaches can be applied directly either by theoreticians or engineers. The book consists of two parts devoted to theory and application. Part 1 (Theory) consists of eleven chapters. In chapter 1.1 Aklilu T. G. Giorges illustrates numerical solutions of elliptic and parabolic equations using both finite element and finite difference methods. Author showed how finite element method used discrete elements to obtain the approximate solution of the governing differential equation. Furthermore, author explained how the final system equation was constructed from the discrete element equations and also how finite difference method used points over intervals to define the equation and the combination of all the points to produce the system equation. Chapter 1.2 authored by Eduardo B. De Amôres, summarized the utilization of large data sets in galactic astronomy where most of them covered almost entire area of the sky in several wavelengths. For both the diffuse data were provided by IRAS, DIRBE/COBE, molecular and hydrogen surveys and point sources catalogues were provided by stellar large-scale surveys such as DENIS, 2MASS, SDSS, among others. A brief specification of these surveys and how to access them in the context of Virtual Observatory was introduced. Concerning HI model to describe spiral arms positions from HI data, the results presented allowed to obtain the spiral arm positions based on HI distribution obtaining the spiral arm parameters (r 0, 0, i, ), which reproduced the main observed features in the -v diagrams for HI. Using the Besançon Galaxy Model and the 2MASS data, Dr. Amôres performed a detailed analysis of the tangential directions from near infrared star counts. The aims of chapter 1.3 coauthored by Sergey Abramov et al., were to consider different approaches to robust regression, to compare their performance, to discuss X Preface possible limitations and restrictions, and to give some practical recommendations. The scatter-plot or cluster-center representations were the basis for other operations (curve regression) applied at several application. Secondly, with simulated noise for test images, the studies showed that even the local estimates considered normal could be considerably biased. Furthermore, the weighted methods of LMS regression using cluster centres specified their advantages and what was as well important was a priori information on mixed or signal-dependent noise. The experiments were carried out: those assuming that a model of mixed noise was valid and second ones with simulated noise for i.i.d. noise. Finally, the goal of estimating mixed noise parameters was to use the obtained estimates at later stages of image processing. In chapter 1.4 Denis Benasciutti et al. developed alternative FE methods, which would allow to achieve the solution of complex three-dimensional problems through a combination of several simpler and faster one- and two-dimensional analyses, which usually require reduced computational efforts. Authors focused on mechanical and thermal problems, in which the structure was axisymmetric, but not the load. There are two aspects of this work: first is to provide a theoretical background on the use of semi-analytical FE approach in numerical analysis of axisymmetric structures loaded non-axialsymmetrically. Two original results were obtained: a plane axi-antisimmetric FE model for solving axisymmetric components loaded in torsion, and a semi- analytical approach for the analysis of plane axisymmetric bodies under non- axisymmetric thermal loadings. Authors' second aim was to explain some practical aspects in the application of semi-analytical method to engineering problems. Sébastien Besset and Louis Jézéquel introduced in chapter 1.5 several criteria corresponding to different vibrational propagation paths based on modal motion equations, which allowed for working with small-sized matrices. An optimization criteria founded on a multimodal description of complex structures was proposed. The modal synthesis technique presented was based on the double and triple-modal synthesis. The double modal synthesis operated by introducing generalized boundary coordinates in order to describe substructure connections. The triple modal synthesis consisted of representing the interior points of the fluid by acoustic modes, the describing of the boundary forces between the fluid and each substructure through the use of a set of loaded modes and consisted of describing the boundary forces between each substructure by introducing another set of loaded modes. To sum up, this work was mainly focused on the above mentioned triple modal synthesis method which introduced the acoustic parts of the coupled system using acoustic modes. Chapter 1.6 authored by Kornkanok Bunwong developed the way to approximate higher order quantities and applied them to ecological problems. It was established that the new approach was suitable for a model evolving according to the transition rates affecting additionally by neighbors. The SIS epidemic model, as an example, proved that if continuous time scale is used, then two solutions of the system would be asymptotically stable or unstable depending on parameter values and stable oscillating solutions would never exist. But if discrete time scale was applied, then [...]... As the boundaries of numerical method applications expand to non-traditional fields, there is a greater need for basic understanding of numerical simulation 4 Numerical Analysis – Theory and Application This chapter is intended to give basic insight into FEM and FDM by demonstrating simple examples and working through the solution process Simple one- and two-dimensional elliptic and parabolic equations... weighting functions and , all of the other weighting equations are zero contribution 1 1 2 Fig 5 System of elements shape function and nodes 1 10 Numerical Analysis – Theory and Application The integrals on the right can be evaluated using the linear interpolation functions (Eq 6) characteristics and the finite element equation (Eq 7) The interpolation function 1, at and 0, at Similarly, 1, at and 0, at ... high-end research route for aerospace plasticity technology is presented in terms of our understanding and research experiences on various metal forming processes and an application example is given for the investigation of radial-axial ring rolling technology Furthermore, the authors discussed the involved key FE modelling technologies and reliability of the developed thermo-mechanical coupled 3D-FE... points are used in many numerical simulations, our discussion is limited to simple rectangular elements Our objective is to simply exhibit how two- dimensional elements are applied to define the elements and final system equation 6 Numerical Analysis – Theory and Application Fig 2 Linear shape functions Fig 3 illustrates a linear rectangular element with four nodes The nodes , , , and have at , , , ,,... experimental work is cost prohibitive, well-formed theory with numerical methods may be used to obtain very valuable information In engineering, experimental and numerical solutions are viewed as complimentary to one another in solving problems It is common to use the experimental work to verify the numerical method and then extend the numerical method to solve new design and system The fast growing computational... insulated Assuming the material is isotropic and the elements are square Thus, the elliptic two-dimensional equation (Eq 30) becomes 16 Numerical Analysis – Theory and Application 10 10 (44) 0 For simplicity, we use 4 elements to describe a unit square region The numbering and the boundary conditions are show in Fig 7 For illustrative purposes, we select element 3 and show all contribution for the system... shows one-dimensional linear element The one-dimensional linear element (Fig 1) is defined as a line segment with a length ( ) between two nodes at and The node functional value can be denoted by and When using the linear interpolation (shape), the value varies linearly between and as Finite Element and Finite Difference Methods for Elliptic and Parabolic Differential Equations 5 Fig 1 One-dimensional... Difference Methods for Elliptic and Parabolic Differential Equations Aklilu T G Giorges Georgia Tech Research Institute, Atlanta, GA, USA 1 Introduction With the availability of powerful computers, the application of numerical methods to solve scientific and engineering problems is becoming the normal practice in engineering and scientific communities Well-formed scientific theory with numerical methods may... functions satisfy the conditions: 1 the functions have a value of 1 at their own node and 0 at the other ends, 2 they vary linearly along the two adjacent edges, and 3 the shape functions sum up to one throughout Fig 4 Two-dimensional rectangular linear element shape functions distribution 8 Numerical Analysis – Theory and Application Finite element equation uses the element shape function to define the... kinetostatics (kinematics and static force), and dynamics characteristics of the 3D4M PLM by usage of symbolic mathematical analysis and numerical simulations In short, in this work configurations of the 3D4M PLM on multi drive linear motors are introduced and kinematic equations, forward kinematics and derivative kinematics of the 3D4M PLM are derived Furthermore, singularity and static forces of the . NUMERICAL ANALYSIS – THEORY AND APPLICATION Edited by Jan Awrejcewicz Numerical Analysis – Theory and Application Edited by Jan Awrejcewicz. orders@intechweb.org Numerical Analysis – Theory and Application, Edited by Jan Awrejcewicz p. cm. ISBN 97 8-9 5 3-3 0 7-3 8 9-7 free online editions of InTech Books and Journals can be found. Evaluation of Single-Channel Receivers for Wireless Optical Communications by Numerical Simulations 463 M. Castillo-Vázquez, A. Jurado-Navas, J.M. Garrido-Balsells and A. Puerta-Notario Chapter