Equilibrium conditions of a tensegrity structure

This paper characterizes the necessary and sufficient conditions for tensegrity equilibria. Static models of tensegrity structures are reduced to linear algebra problems, after first characterizing the problem in a vector space where direction cosines are not needed. This is possible by describing the components of all member vectors. While our approach enlarges (by a factor of 3) the vector space required to describe the problem, the advantage of enlarging the vector space makes the mathematical structure of the problem amenable to linear algebra treatment. Using the linear algebraic techniques, many variables are eliminated from the final existence equations.     

Hybrid Parallel Linear System Solvers

This paper presents a new approach to the solution of nonsymmetric linear systems that uses hybrid techniques based on both direct and iterative methods. An implicitly preconditioned modified system is obtained by applying projections onto block rows of the original system. Our technique provides the flexibility of using either direct or iterative methods for the solution of the preconditioned system. The resulting algorithms are robust, and can be implemented with high efficiency on a variety of parallel architectures. The algorithms are used to solve linear systems arising from the discretization of convection-diffusion equations as well as those systems that arise from the simulation of particulate flows. Experiments are presented to illustrate the robustness and parallel efficiency of these methods.     

混凝土细观力学分析程序中的快速算法与并行算法设计

针对一套混凝土细观力学分析程序,在分析其计算方法与计算效率的不足之后,提出了采用稀疏矩阵与稀疏向量技术来高效实现有限元刚度矩阵装配过程的算法,并采用双门槛不完全Cholesky分解预条件技术与CG法相结合来高效地求解稀疏线性方程组。之后,从整体上提出了一个将有限单元分布与未知量分布有机结合的并行算法设计方案,并分别针对刚度矩阵装配、双门槛不完全Cholesky分解、稀疏矩阵与稠密向量相乘、稀疏向量相加等核心算法,进行了相应的并行算法设计。最后,在由每节点2 CPU的8个Intel Xeon节点采用千兆以太网连成的机群上,针对两个混凝土数值试样进行了数值实验,第一个试样含44117个网格点与53200个有限单元,第二个试样含71013个网格点与78800个有限单元;对第一个试样,原串行程序进行全程567次加载计算需要984.83小时约41天,采用文中串行算法后,模拟时间减少到22531秒约6.26小时,采用并行算法在16个CPU上的模拟时间进一步降为3860秒约1.07小时。对第二个试样,原串行程序进行全程94次加载计算需要467.19小时约19.5天,采用文中串行算法后,模拟时间减少到11453秒约3.18小时,采用并行算法在16个CPU上的模拟时间进一步降为1704秒约28.4分钟。串行算法的改进与并行算法的设计大大缩短了计算时间,对加快混凝土力学性能的分析研究具有重要意义。     

A technical review on navigation systems of agricultural autonomous off-road vehicles

With the predicted increase in world population to over 10 billion, by the year 2050, growth in agricultural output needs to be continued. Considering this, autonomous vehicles application in precision agriculture is one of the main issues to be regarded noteworthy to improve the efficiency. In this research many papers on autonomous farm vehicles are reviewed from navigation systems viewpoint. All navigation systems are categorized in six classes: dead reckoning, image processing, statistical based developed algorithms, fuzzy logic control, neural network and genetic algorithm, and Kalman filter based. Researches in many agricultural operations from water monitoring to aerial crop scouting revealed that the centimeter level accuracy in all techniques is available and the velocity range for evaluated autonomous vehicles almost is smaller than 1 m/s. Finally it would be concluded although many developments in agricultural automation using different techniques and algorithms are obtained especially in recent years, more works are required to acquire farmer’s consensus about autonomous vehicles. Additionally some issues such as safety, economy, implement standardization and technical service support in the entire world are merit to consideration.     

Numerical simulation of nonholonomic rigid-body systems

The paper proposes computer algebra system (CAS) algorithms for computer-assisted derivation of the equations of motion for systems of rigid bodies with holonomic and nonholonomic constraints that are linear with respect to the generalized velocities. The main advantages of using the D’Alembert-Lagrange principle for the CSA-based derivation of the equations of motion for nonholonomic systems of rigid bodies are demonstrated. Among them are universality, algorithmizability, computational efficiency, and simplicity of deriving equations for holonomic and nonholonomic systems in terms of generalized coordinates or pseudo-velocities __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 106–115, September 2006.     

Measurement data handling in identification of mechanical systems

Integration algorithms for data handling in identification of linear stationary systems from sampled transient data are proposed. The problem of identification from several simultaneously measured phase coordinates is detailed. The identification procedure is generalized to the case of irregularly sampled data. The efficiency of the algorithms is demonstrated by examples     

Iterative methods for stabilized mixed velocity–pressure finite elements

This paper is concerned with iterative techniques for the solution of the linear system of equations arising from a finite element approximation of an elliptic partial differential equation by a mixed method. Three types of iterative algorithms are investigated. Applications to the Stokes equations are discussed and the results of numerical experiments given.     

Function of region

The purpose of this paper is to extend points function and interval functions theoretics to an arbitrary region. For this, the new theory, the contraction of a region, and the retraction of a region; the extension of a region, and the kernel-preserving extension of a region are established by the author. Starting from these concepts, the new definitions of a region function is given. And a kernel (i.e. fixed point) of a region function is connected with a stable centre of defining region of such a region function. Thereby, the region theoretics and algorithms are established.In applications, to find a stable centre of a region, the author has utilized the measure theoretics of matrice defined by Hartfiel⁽⁷⁾ and other authors. The measure problems of coefficient matrice of system of equations of linear algebra associated with some region are discussed.     

基于哈密顿动力系统新变分原理的保辛算法之三：数值算例

文献[1,2]给出了四种不同类型的求解哈密顿动力系统的数值方法,并证明了它们的保辛特性。本文将讨论这四类算法的具体数值性能,包括算法的线性稳定性,精度和效率等。     

求解非线性方程组的混合遗传算法

非线性方程组的求解是数值计算领域中最困难的问题。大多数的数值求解算法例如牛顿法的收敛性和性能特征在很大程度上依赖于初始点。但是对于很多非线性方程组,选择好的初始点是一件非常困难的事情。本文结合遗传算法和经典算法的优点,提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了遗传算法的群体搜索和全局收敛性,有效地克服了经典算法的初始点敏感问题;同时在遗传算法中引入经典算法(Powell法、拟牛顿迭代法)作局部搜索,克服了遗传算法收敛速度慢和精度差的缺点。选择了几个典型非线性方程组,从收敛可靠性、计算成本和适用性等指标分析对比了不同算法。计算结果表明所设计的混合遗传算法有着可靠的收敛性和较高的收敛速度和精度,是求解非线性方程组的一种成功算法。     

Brief review on application of nonlinear dynamics in image encryption

Chaos-based cryptology has become one of the most common design techniques to design new encryption algorithms in the last two decades. However, many proposals have been observed to be weak against simple known attacks. However, security of proposals cannot be proved. An analysis roadmap is needed for the security analysis of new proposals. This study aims to address this shortcoming. Analysis and test results show that many chaos-based image encryption algorithms previously published in the nonlinear dynamics are actually not as secure as they are expressed although these algorithms do pass several statistical and randomness tests. A checklist has been proposed to solve these problems. The applications of the proposed checklist have been shown for different algorithms. The proposed checklist is thought to be a good starting point for researchers who are considering to work in chaos-based cryptography.     

An adaptive genetic algorithm for solving bilevel linear programming problem

Bilevel linear programming,which consists of the objective functions of the upper level and lower level,is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem.Of all the algorithms,the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming.In this paper,we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation.In addition,some techniques are adopted not only to deal with the difficulty that most of the chromosomes may be infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm.The performance of this proposed algorithm is illustrated by the examples from references.     

Solutions of matrix equations in problems of mechanics and control

The paper considers algorithms for solving linear matrix equations related to problems of mechanics and control, namely, the Lyapunov and Sylvester matrix equations and Riccati-type nonlinear matrix equations. These algorithms are capable of solving both linear equations and linear matrix inequalities. Algorithms based on the Bass relations are used to solve Riccati-type nonlinear matrix equations in so-called special cases where some eigenvalues of the matrix pencil are on a unit circle. These algorithms are compared with those of other authors by way of examples. It is shown that the algorithms can be implemented in symbolic computing routings, which allows solving these equations with high accuracy     

On Taylor weak statement finite element methods for computational fluid dynamics

A Taylor series augmentation of a weak statement (a ‘Taylor weak statement’ or ‘Taylor-Galerkin’ method) is used to systematically reduce the dispersion error in a finite element approximation of the one-dimensional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi-implicit linear, quadratic and cubic basis one-dimensional finite element methods and of several comparative finite difference/finite volume algorithms. The finite element methods analysed include both Galerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for verification problems in one and two dimensions and are compared with finite volume solutions. The improved finite element algorithms have sufficient phase accuracy to achieve highly accurate linear transient solutions with little or no artificial diffusion.     

Review of Computational Aeroacoustics Algorithms

This paper presents a review of recent advancements in computational methodology for aeroacoustics problems. High-order finite difference methods for computation of linear and nonlinear acoustic waves are the primary focus of the review. Schemes for numerical simulation of linear waves include explicit optimized and DRP finite-difference operators, compact schemes, wavenumber extended upwind schemes and leapfrog-like algorithms. Both spatial approximations and time-integration techniques, which include low-dissipation low-dispersion Adams-Bashforth and Runge-Kutta (RK) methods, are examined. Wave propagation properties are analysed in the wavenumber and frequency space. Different approaches to eliminate short-wave spurious numerical waves are also reviewed. Methods for simulating nonlinear acoustic phenomena include essentially non-oscillatory (ENO) schemes, numerical adaptive filtering for high-order explicit and compact finite-difference operators, MacCormack and adaptive compact nonlinear algorithms. A literature survey of other CAA methods is provided in the introductory part.     

On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.     

Méthode de Le Verrier–Souriau et équations différentielles linéaires

A crucial step of algorithms allowing the study of discrete mechanical system vibrations is the determination of eigenmodes and eigenvalues. The accuracy of the results is of great importance because the stability study of the system depends on them. Eigenvalues can be found with a very good precision, however the eigenmodes determination is awkward: their direction could present significant instabilities. We proposed a method which avoids the necessity of doing eigenmodes research and so the attendant instabilities. It is based on Le Verrier–Souriau algorithm usually reserved for the resolution of linear algebraic systems.     

Globally convergent homotopy algorithms for nonlinear systems of equations

Probability-one homotopy methods are a class of algorithms for solving nonlinear systems of equations that are accurate, robust, and converge from an arbitrary starting point almost surely. These new globally convergent homotopy techniques have been successfully applied to solve Brouwer fixed point problems, polynomial systems of equations, constrained and unconstrained optimization problems, discretizations of nonlinear two-point boundary value problems based on shooting, finite differences, collocation, and finite elements, and finite difference, collocation, and Galerkin approximations to nonlinear partial differential equations. This paper introduces, in a tutorial fashion, the theory of globally convergent homotopy algorithms, deseribes some computer algorithms and mathematical software, and presents several nontrivial engineering applications.This work was supported in part by DOE Grant DE-FG05-88ER25068, NASA Grant NAG-1-1079, and AFOSR Grant 89-0497.     

单步辛算法的相位误差分析及修正

若一个算法的幅值误差和相位误差都不累加，则该算法就是最理想的算法， 但这样的算法难以构造. 辛几何算法解决了幅值误差的累加问题，但相位误差累加问题仍然 存在. 给出了单步隐式辛算法相位误差的精确估计公式，提出了简单而实用的修正方法. 以 Euler中点隐式辛差分格式为例，针对几个线性动力学系统，对相位误差进行了数值分析和 修正.     

Duality between plane trusses and grillages

In the paper, projective plane duality, that is, a point-to-line, line-to-point, incidence-to-incidence correspondence between plane trusses and grillages of simple connection is treated. By means of linear algebra it is proved that the rank of the equilibrium matrix of plane trusses and grillages does not change under projective transformations and polarities: consequently the number of infinitesimal inextensional mechanisms and the number of independent states of self-stress are preserved under these transformations. The results obtained are also applied to structures with unilateral constraints, and by using several examples it is shown that plane tensegrity trusses have projective dual counterparts among grillages which can be physically modelled with popsicle sticks by weaving.