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A kind of Static Sensitivity Reanalysis of Structure Based on the Improved epsilon algorithm

Procedia Computer Science 2022年 208卷 650-657页

作者： Kai Ma Bin Wu Jianhang Sun Sengkang Yan School of Mechanical and Aerospace Engineering Jilin University Changchun 13025 P.R. China

This study present a method to calculate first and second order displacement sensitivity based on epsilon algorithm and improved Neumann series. In this paper, analytical expressions of first and second-order sensitivity are derived. They are then decomposed into vectors using the improved Newman series method. Finally, epsilon is used to calculate the result. The method which is suitable for complex structure has the character of fast calculation and high efficiency. The high precision and fast convergence of the proposed method are proved by two numerical examples. The study show that the proposed method has engineering application value.

关键词： Structural reanalysis static sensitivity epsilon algorithm improved neumann series

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Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order

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NUMERICAL algorithmS 2020年第2期83卷 593-627页

作者： Chang, Xiang-Ke He, Yi Hu, Xing-Biao Sun, Jian-Qing Weniger, Ernst Joachim Chinese Acad Sci Acad Math & Syst Sci ICMSEC LSEC POB 2719 Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China Chinese Acad Sci Wuhan Inst Phys & Math Wuhan 430071 Peoples R China Ocean Univ China Sch Math Sci Qingdao 266100 Peoples R China Univ Regensburg Inst Phys & Theoret Chem D-93040 Regensburg Germany

We construct new sequence transformations based on Wynn's epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn's epsilon and rho algorithm and of Osada's generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numerically by applying them to some linearly and logarithmically convergent sequences as well as some divergent series.

关键词： Convergence acceleration algorithm Sequence transformation epsilon algorithm Rho algorithm

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Multi-objective Control Method in Structural Strain Interval Reliability Based on epsilon algorithm

Multi-objective Control Method in Structural Strain Interval...

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3rd International Conference on Civil Engineering and Transportation (ICCET 2013)

作者： Sun Zuozhen Meng Guangwei Ma Kai Jilin Univ Coll Mech Sci & Engn Changchun 130022 Peoples R China

ISBN: (纸本)9783038350057

In this article, a kind of structural strain controlled reliability method was presented. The interval extension of multi-objective control algorithm was applied to control the structural strain reliability. The method has realized the goal of controlling the multiple static interval reliability indexes by the control of the structural interval parameters. In order to accelerate the speed of the structural reanalysis, the epsilon algorithm was used in the process of the structural reanalysis when a wide range of modification happened in the interval parameters. This method can both get a satisfactory accuracy, and improve the speed of the reanalysis. Numerical examples show that the method is effective and feasible.

关键词： epsilon algorithm Interval reliability Multi objective control Neumann series Strain control Static Analysis

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Multi-objective Control Method in Structural Stress Interval Reliability Based on epsilon algorithm

Multi-objective Control Method in Structural Stress Interval...

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3rd International Conference on Mechanical Engineering, Materials and Energy (ICMEME 2013)

作者： Sun Zuozhen Meng Guangwei Li Feng Ma Kai Jilin Univ Coll Mech Sci & Engn Changchun 130022 Peoples R China

ISBN: (纸本)9783037859834

A kind of structural stress reliability control method was presented. In this article, the interval extension of multi-objective control algorithm was applied to control the structural stress reliability. By the control of the structural interval parameters, this method has realized the goal of controlling the multiple static interval reliability indexes. To insure the accuracy of the structural reanalysis, the epsilon algorithm was used in the process of the structural reanalysis when a wide range of modification happened in the interval parameters. This method can both get a satisfactory accuracy, and improve the speed of the reanalysis. The results of the example further proved that the proposed method can be effectively applied in the multi-objective control of the structural stress interval reliability.

关键词： epsilon algorithm Interval reliability Multi objective control Neumann series

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Laplace transform inversion through the theta algorithm for power-system EMT analysis

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ELECTRIC POWER SYSTEMS RESEARCH 2021年 197卷 107342-107342页

作者： Castanon, L. J. Naredo, J. L. Zuluaga, J. R. Banuelos-Cabral, E. Gomez, Pablo Cinvestav Guadalajara Guadalajara Jalisco Mexico Univ Guadalajara CUCEI Guadalajara Jalisco Mexico Western Michigan Univ Kalamazoo MI 49008 USA

Laplace transform analysis of electromagnetic power system transients generally is based on a technique in which the Laplace inversion integral is truncated with a suitable data window. This technique, being referred to as WNLT, is appropriate for most practical cases. Nevertheless, it results inadequate for certain R&D tasks. This paper presents a new technique for numerical Laplace inversion that does not require truncation with a data window;it instead uses Brezinski's theta algorithm to account for the infinite range of the Laplace inversion integral. As opposed to the WNLT, the new technique guarantees consistent and high accuracy levels at low computational costs. Finally, the new technique is applied to the transient analysis of a power-system network. Its results compare favorably well with those from the PSCAD/EMTDC program.

关键词： Electromagnetic transients Frequency-domain Laplace transform Shanks transformation epsilon algorithm Theta algorithm

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Acceleration of the EM algorithm: P-EM versus epsilon algorithm

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2012年第12期56卷 4122-4137页

作者： Berlinet, A. F. Roland, Ch Univ Montpellier 2 Equipe Probabilites & Stat UMR CNRS 5149 Inst Math & Modelisat Montpellier F-34095 Montpellier 5 France

Among recent methods designed for accelerating the EM algorithm without any modification in the structure of EM or in the statistical model, the parabolic acceleration (P-EM) has proved its efficiency. It does not involve any computation of gradient or hessian matrix and can be used as an additional software component of any fixed point algorithm maximizing some objective function. The vector epsilon algorithm was introduced to reach the same goals. Through geometric considerations, the relationships between the outputs of an improved version of P-EM and those of the vector epsilon algorithm are established. This sheds some light on their different behaviours and explains why the parabolic acceleration of EM outperforms its competitor in most numerical experiments. A detailed analysis of its trajectories in a variety of real or simulated data shows the ability of P-EM to choose the most efficient paths to the global maximum of the likelihood. (C) 2012 Elsevier B.V. All rights reserved.

关键词： EM algorithm Fixed point iteration Acceleration Convergence epsilon algorithm

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Defeating divergence

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CHEMTEXTS 2017年第3期3卷 1-6页

作者： Oldham, Keith B. Myland, Jan C. Trent Univ Dept Chem Peterborough ON K9J 7B8 Canada

It is frustrating when a power (or other) series fails to converge, preventing the straightforward calculation of values of a function of interest. Here, the discussion focuses on two algorithms, discovered long ago but not well known, by which the sums of series may be calculated arithmetically, notwithstanding the divergence of the series. A powerful example vindicates both methods.

关键词： Series Sums Convergence Lozenge diagram epsilon algorithm Eta algorithm

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A topological optimization method for flexible multi-body dynamic system using epsilon algorithm

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STRUCTURAL ENGINEERING AND MECHANICS 2011年第5期37卷 475-487页

作者： Yang, Zhi-Jun Chen, Xin Kelly, Robert Guangdong Univ Technol Fac ElectroMech Engn Guangzhou 510006 Guangdong Peoples R China Columbia Univ Dept Mech Engn New York NY 10027 USA

In a flexible multi-body dynamic system the typical topological optimization method for structures cannot be directly applied, as the stiffness varies with position. In this paper, the topological optimization of the flexible multi-body dynamic system is converted into structural optimization using the equivalent static load method. First, the actual boundary conditions of the control system and the approximate stiffness curve of the mechanism are obtained from a flexible multi-body dynamical simulation. Second, the finite element models are built using the absolute nodal coordination for different positions according to the stiffness curve. For efficiency, the static reanalysis method is utilized to solve these finite element equilibrium equations. Specifically, the finite element equilibrium equations of key points in the stiffness curve are fully solved as the initial solution, and the following equilibrium equations are solved using a reanalysis method with an error controlled epsilon algorithm. In order to identify the efficiency of the elements, a non-dimensional measurement is introduced. Finally, an improved evolutional structural optimization (ESO) method is used to solve the optimization problem. The presented method is applied to the optimal design of a die bonder. The numerical results show that the presented method is practical and efficient when optimizing the design of the mechanism.

关键词： topological optimization the flexible multi-body dynamic system die bonder epsilon algorithm

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Convergence Acceleration Techniques for Proposed Numerical Inverse Laplace Transform Method 24

Convergence Acceleration Techniques for Proposed Numerical I...

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24th Telecommunications Forum (TELFOR)

作者： R-Smith, N. Al-Zubaidi Brancik, L. Brno Univ Technol Dept Radio Elect Tech 12 Brno 61600 Czech Republic

ISBN: (纸本)9781509040865

In this paper, novel convergence accelerating techniques are adapted onto the proposed hyperbolic numerical inverse Laplace transform method (hyperbolic-NILT) and analyzed. This Ill NILT method is based on the approximation of the inverse kernel of the Laplace transform Bromwich integral exp(st). It is shown that with the use of the convergence accelerating algorithms onto the essence of the proposed NILT method, an enhancement on the core of the inversion is achieved, with relatively accurate and stable results, while preserving valuable time and memory. The algorithms are tested and their corresponding results are discussed, mainly regarding the accuracy, stability and computational efficiency. The experimental accuracy analysis tests are implemented in the universal MATLAB language with properly chosen Laplace transforms.

关键词： epsilon algorithm Laplace transforms MATLAB numerical accuracy numerical inversion quotient-difference algorithm

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An Accelerating Method of Training Neural Networks Based on Vector epsilon algorithm

An Accelerating Method of Training Neural Networks Based on ...

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Third International Conference on Information and Computing(第三届信息与计算科学国际会议 ICIC 2010)

作者： Lian Lian Jianliang Li Yong Jiang School of Science Nanjing University of Science & Technology Nanjing 210094 P.R. China College of Math & Physics Nanjing University of Information Science & Technology Nanjing 210044P.R.

ISBN: (纸本)9781424470815;9780769540474

This paper studied the accelerating convergence of the vector sequences generated by BP algorithm with vector epsilon algorithm, and presented the conclusion that the algorithms is not only convergent but also accelerated. Finally, we tested them for three classical artificial neural network problems. By numerical experiments, results shown that can reduce CPU time for computation and improve the learning efficiency.

关键词： artificial neural networks BP algorithm epsilon algorithm accelerated convergence numerical analysis

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