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Towards criteria for selecting approximation functions in the Dual Reciprocity Method

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2000年第7-8期24卷 519-529页

作者： Partridge, PW Univ Brasilia Dept Engn Civil FT BR-70910900 Brasilia DF Brazil

Since the publication of a book about the Dual Reciprocity Method in 1992 there has been much research into the development of approximation functions employed with this method, and many new functions have been proposed. Given this wealth of new functions, it is important for engineers to be able to identify an adequate function for a given problem. Unfortunately, most authors, in proposing functions for use in DRM compare results principally with the r function used in the book mentioned above, and which is now considered to be that which has the worst performance. In view of this six examples are solved here using a wide range of functions and the results obtained with each function compared with the aim of establishing some guidelines for selecting the function. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： dual reciprocity approximation functions comparative error linear and quadratic elements

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Hybrid approximation functions in the dual reciprocity boundary element method

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COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING 1997年第2期13卷 83-94页

作者： Partridge, PW Sensale, B UNIV REPUBLICA FAC INGNINST ESTRUCT & TRANSPORTESMONTEVIDEOURUGUAY

The dual reciprocity boundary element method traditionally uses the linear radial basis function r for interpolation. Recently, however, the use of the r function has been questioned both in relation to accuracy and in relation to the number and position of internal nodes required to obtain satisfactory solutions. Much research has been done in an attempt to fix criteria for choosing which approximation function should be used. One of the alternatives recently suggested is the augmented thin plate spline function, which consists of a thin plate spline function, r(2) log(r), augmented with the first three terms of a Pascal triangle expansion. In this paper families of similar functions are obtained by augmenting radial basis functions with appropriate global expansions: these functions will be called hybrid approximate functions. It will be shown that using an appropriate hybrid function accurate results can be obtained for many body forces or pseudo body forces in elasticity without the need for internal nodes. (C) 1997 by John Wiley & Sons, Ltd.

关键词： boundary elements dual reciprocity body forces approximation functions elasticity hybrid functions

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DUAL RECIPROCITY BEM - LOCAL VERSUS GLOBAL approximation functions FOR DIFFUSION, CONVECTION AND OTHER PROBLEMS

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 1994年第4期14卷 349-356页

作者： PARTRIDGE, PW Departamento de Engenharia Civil Universidade de Brasilia 70910 Brasilia DF Brazil

The use of the global approximation functions (elements of Rascals' triangle, sine expansions and others) in the dual reciprocity boundary element method is compared to the better known local radial basis functions for convection, diffusion and other problems in which the volume integrals considered contain first and second derivatives of the problem variables, time derivatives and sums and products of functions, including nonlinear terms. It will be shown that whilst it is possible to obtain accurate solutions to the problems considered using the global functions, a successful solution to a given problem depends very much on the function chosen, as well as other factors.

关键词： BOUNDARY ELEMENT METHOD DUAL RECIPROCITY approximation functions

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Parametric characterization of approximation functions for the axial and lateral force between electromagnets and spherical permanent magnets

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MEASUREMENT 2022年 202卷

作者： Perez-San Lazaro, Rafael Fuentes-Aguilar, Rita Q. Chairez, Isaac Tecnol Monterrey Sch Engn & Sci Zapopan Jalisco Mexico Tecnol Monterrey Inst Adv Mat Sustainable Mfg Zapopan Jalisco Mexico Inst Politecn Nacl Unidad Profes Interdisciplinaria Biotecnol Mexico City DF Mexico

The interaction between magnetic objects has been widely explored due to their range of applications, which usually involves complex calculations regarding magnetic forces. This paper presents approximation functions to describe the force generated between cylindrical electromagnets and spherical permanent magnets. These functions consider the electrical current that passes through the electromagnets, and the geometry of the devices to associate their relationship through parametric adjustments. A nonlinear least mean square parameter estimation method yields electromagnetic functions in axial and lateral directions in the relative configuration of the magnetic devices. An own developed measurement device is used to get the experimental data that leads to the functions characterization. The functions are developed considering a piecewise approximation depending on the relative distance between the electrical and permanent magnets. The modeling strategy leads to an accurate and precise representation of the force between the magnetic devices, as the correlation index and relative errors indicate.

关键词： Electromagnets Permanent magnets Electromagnetic functions approximation functions Parametric characterization

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HYBRID approximation functions IN THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD

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International Journal for Numerical Methods in Biomedical Engineering 1999年第2期13卷

作者： PAUL W. PARTRIDGE BERARDI SENSALE Departamento de Engenharia Civil Universidade de Brasília 70910-900 Brasília DF Brazil Instituto de Estructuras y Transportes Facultad de Ingenieria Universidad de la Republica Montevideo Uruguay

The dual reciprocity boundary element method traditionally uses the linear radial basis function r for interpolation. Recently, however, the use of the r function has been questioned both in relation to accuracy and in relation to the number and position of internal nodes required to obtain satisfactory solutions. Much research has been done in an attempt to fix criteria for choosing which approximation function should be used. One of the alternatives recently suggested is the augmented thin plate spline function, which consists of a thin plate spline function, r 2 log( r ), augmented with the first three terms of a Pascal triangle expansion. In this paper families of similar functions are obtained by augmenting radial basis functions with appropriate global expansions: these functions will be called hybrid approximate functions. It will be shown that using an appropriate hybrid function accurate results can be obtained for many body forces or pseudo body forces in elasticity without the need for internal nodes.© 1997 John Wiley & Sons, Ltd.

关键词： boundary elements dual reciprocity body forces approximation functions elasticity hybrid functions

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High output dynamic range exponential function synthesizer

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MICROELECTRONICS JOURNAL 2017年 63卷 123-130页

作者： Popa, Cosmin Radu Fac Elect Telecommun & Informat Technol Bucharest Romania

The paper presents two original high-accuracy exponential function synthesizers with wide output dynamic ranges. The improved accuracies of the proposed computational structures are obtained using new superior-order approximation functions. In order to additionally improve the circuits' output dynamic ranges, an original method based on proper variable changing will be used and implemented. As a result of the new proposed design methods, the performances of the exponential structures are only slightly affected by technological errors. The best original proposed architecture of the exponential synthesizer has an output dynamic range of 100 dB, for an approximation error smaller than +/- 1 dB. The exponential circuits are designed for implementing in 0.18 mu m CMOS technology and they present a low-voltage low-power operation - the minimal supply voltage is about 0.7 V, while the power consumption is smaller than 2 mu W. The chip area is about 4.5 mu m(2) for an implementation in 0.18 mu m CMOS technology of the best proposed exponential circuit.

关键词： Exponential function Analog signal processing Low-voltage low-power circuits approximation functions Variable changing Current-mode operation

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The analysis of laminated plates using distinct advanced discretization meshless techniques

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COMPOSITE STRUCTURES 2016年 143卷 165-179页

作者： Belinha, J. Araujo, A. L. Ferreira, A. J. M. Dinis, L. M. J. S. Jorge, R. M. Natal Univ Porto Inst Mech Engn & Ind Management Rua Dr Roberto Frias S-N P-4200465 Oporto Portugal Univ Porto Dept Mech Engn Fac Engn Rua Dr Roberto Frias S-N P-4200465 Oporto Portugal Univ Lisbon Inst Super Tecn Dept Mech Engn Rua Rovisco Pais 1 P-1049001 Lisbon Portugal

Composite laminated plates are structural elements with a high strength/weight ratio, being very popular in the aeronautic industry. This work analyses such structural elements using the finite element method, an approximation meshless method (the element free Galerkin method) and three interpolation meshless methods (the radial point interpolation method, the natural neighbor radial point interpolation method and the natural radial element method). Here, the displacement field of the plate is defined by an equivalent single layer theory - the first-order shear deformation theory (FSDT). Thus, a brief theoretical description of the advanced meshless techniques extended to the analysis of composite plates, considering a weak-form approach combined with the FSDT, is presented. In the end, several composite laminates are analyzed and the results obtained with the distinct numerical approaches are compared and discussed. The results show that meshless methods are capable to efficiently analyze composite laminated plates submitted to static loads under linear elastic regimes. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Meshless methods Interpolation functions approximation functions Laminated plate First-order shear deformation theory

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Low-voltage CMOS current-mode exponential circuit with 70 dB output dynamic range

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MICROELECTRONICS JOURNAL 2013年第12期44卷 1348-1357页

作者： Popa, Cosmin Radu Fac Elect Telecommun & Informat Technol Bucharest Romania

The paper proposes new accurate exponential circuits, having a multitude of practical applications in analog signal processing. The original method for obtaining the exponential function is based on the utilization of new superior-order approximation functions. The accuracy of the proposed structures is excellent and the output dynamic range is strongly extended as a result of the fourth-order approximation and of the independence of implemented function on technological errors and on temperature variations (the best original proposed architecture of the exponential generator has an output dynamic range of 70 dB for an approximation error smaller than +/- 1 dB). The exponential circuits are designed for implementing in 0.18 mu m CMOS technology, having a low-voltage operation (a minimal supply voltage of 1 V). The power consumptions of the proposed exponential circuits are smaller than 0.08 mW, for a supply voltage of I V. As application of the new exponential circuit, a dB-linear VGA circuit with high output dynamic range will be presented. The new computational structures have the possibility of generating any continuous mathematical function, presenting also an increased modularity and controllability and reduced design costs per implemented function. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Exponential function Analog signal processing Low-voltage circuits approximation functions Current-mode VGA circuit

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SOME PROCEDURES FOR FUNCTION approximation BASED ON THE USE OF SAMPLE DATA AND THEIR APPLICATION IN HEURISTIC METHODS FOR SOLVING PRACTICAL PROBLEMS

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PATTERN RECOGNITION 1979年第2期11卷 77-83页

作者： BRAILOVSKY, V Pr. Vernadskogo 99-1-128 Moscow 117526 U.S.S.R

Let f(x) be a member of a set of functions over a probability space. Samples of f(x) are 2-tuples (xi,f(xi) where xi is a sample of the random variable X and f(xi) is a sample of f(x) at x = xi. Some procedures and analysis are presented for the approximation of such functions by systems of orthonormal functions. The approximations are based on the data samples. The analysis includes the case of error in the measurement of f(xi). The properties of the expected square error in the approximation are examined for a number of different estimators for the coefficients in the expansion and these well-behaved and easily analyzed estimators are compared to those obtained using the method of least squares. The effectiveness of different sets of basis functions, those involved in the Karhunen-Loeve expansion and others, can be compared and an approach is suggested to adaptive basis selection in order to select that basis which is most efficient in approximating the particular function under examination. The connection between results and applications are discussed in the introduction and conclusion.

关键词： Functional approximation approximation functions Canonical function system Sample data approximation

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A Newton-like algorithm for L₂-gain optimal control of an electro-hydraulic servo-system 22

A Newton-like algorithm for <i>L</i><sub>2</sub>-gain optima...

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22nd Mediterranean Conference on Control and Automation (MED)

作者： Milic, Vladimir Kasac, Josip Situm, Zeljko Univ Zagreb Fac Mech Engn & Naval Architecture HR-10000 Zagreb Croatia

ISBN: (纸本)9781479959013

This paper is concerned with L-2-gain optimal control approach for rotary electro-hydraulic servo-system. The electro-hydraulic dynamics with respect to hydraulic motor velocity, with input voltage to the servo valve as control input and load torque as disturbance input, is formulated. The mathematical model results in input-affine nonlinear system. A numerical algorithm based on Newton method to solve a finite-horizon minimax problem for L-2-gain minimisation of electro-hydraulic system is presented. The feedback control and disturbance variables are formulated as linear combination of approximation functions. The proposed algorithm, which has recursive matrix structure, directly finds approximations of the feedback control and the "worst case" disturbance variables. Developed controller has been tested experimentally in the laboratory model of an electro-hydraulic servo system.

关键词： Newton method electrohydraulic control equipment feedback matrix algebra minimax techniques nonlinear systems optimal control servomechanisms torque torque control Newton-like algorithm approximation functions electrohydraulic dynamics feedback control finite horizon minimax problem hydraulic motor velocity input-affine nonlinear system laboratory model load torque mathematical model numerical algorithm recursive matrix structure rotary electrohydraulic servo system servo valve worst case disturbance variables approximation methods Heuristic algorithms Induction motors Mathematical model Servomotors Torque Valves

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