用时间序列来判断电力系统中的混沌现象

由于混沌现象对初值、参数等的敏感依赖性,现有的基于电力系统的模型（方程）来研究混沌的方法,会由于建模时方程的形式、参数等误差带来可能的失误。为了弥补这一缺点,文中提出了直接利用对实际系统RS采样得到的时间序列的Lyapunov指数λi分析的方法来判断混沌的存在性。利用矩阵的特征值移动技术可以找到RS的伴随系统RS*,使RS* 的λ*i=λi+k(k为合适的正实数),于是可以利用现有的计算时间序列Lyapunov指数的方法来实现RS的混沌判断。     

On the eigenvalues of a uniform cantilever beam carrying any number of spring–damper–mass systems

The eigenvalues of a uniform cantilever beam carrying any number of spring–damper–mass systems with arbitrary magnitudes and locations were determined by means of the analytical‐and‐numerical‐combined method (ANCM). First of all, each spring–damper–mass system was replaced by a massless effective spring with spring constant k_eff, which is the main point that the ANCM is available for the present problem. Next, the equation of motion for the ‘constrained’ beam (with spring–damper–mass systems attached) was derived by using the natural frequencies and normal mode shapes of the ‘unconstrained’ beam (without carrying any attachments) incorporated with the expansion theorem. Finally, the equation of motion for the ‘constrained’ beam in ‘complex form’ is separated into the real and the imaginary parts. From either part, a set of simultaneous equations were obtained. Since the simultaneous equations are in ‘real form’, the eigenvalues of the ‘constrained’ beam were determined with the conventional numerical methods. To confirm the reliability of the presented theory, all the numerical results obtained from the ANCM were compared with the corresponding ones obtained from the conventional finite element method (FEM) and good agreement was achieved. Because the order of the property matrices for the equation of motion derived by using the ANCM is much lower than that by using the conventional FEM, the storing memory and the CPU time required by the ANCM are much less than those required by the FEM. Besides, the solution of the equation of motion derived from the ANCM can always be obtained with the general personal computers, but that from the FEM can sometimes be obtained only with the computers of workstations or main frames when the total degrees of freedom exceeding a certain limit. Copyright © 1999 John Wiley & Sons, Ltd.     

An asymptotic estimate of the error of eigenvalues in the method of finite elements for the sturm-liouville problem

A scheme of the second order of accuracy for the Sturm—Liouville problem is constructed by the method of finite elements with the use of a special basic system of compact functions. The convergence of the method of finite elements is proved. An exact formula for estimating errors of eigenvalues is obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 28–36, March–Apni, 2000.     

局部化的广义特征值最接近支持向量机

基于广义特征值的最接近支持向量机(Proximal Support Vector Machine via Generalized Eigenvalues,GEPSVM)是一种新的具有与SVM性能相当的两分类方法,通过求解广义特征值来获得两个彼此不平行的拟合两类样本的超平面.其决策是将测试样本归为距其最近的超平面所在的类.然而,该规则在某些情形会导致较差的分类结果.对此,在GEPSVM基础上,通过在类拟合超平面上寻找一个包含了所有训练样本投影的局部凸区域,来决定样本的类别.该局部方法不仅具有较GEPSVM更优的分类性能,同时还衍生出了求解超平面上凸壳的简单且易于核化的新算法.最后在人工和UCI数据集上获得了验证.     

基于MATLAB的磁悬浮系统奇异摄动参数计算

磁悬浮系统的稳定性是磁悬浮列车能否正式投入营运的关键因素。而实际的悬浮系统由于存在小电感奇异摄动参数,使得悬浮系统的动力学模型有相当高的阶数以及病态的数值特性,因此该文采用奇异摄动法处理这类问题。根据奇异摄动理论可知,要使系统稳定,摄动参数必存在一个稳定的上界。该文针对悬浮系统模型复杂和系统变参数的特点,借助MATLAB简化了磁悬浮系统奇异摄动参数稳定上界的计算。结果表明该方法的有效性和可行性,对磁悬浮系统的理论分析和工程研究有一定的参考价值。     

进化策略算法在矩阵特征值求解中的应用

工程实践中多种振动问题的求解常常归纳为求矩阵特征值问题,另外一些稳定性分析问题及相关分析问题也可以转化为求矩阵特征值问题.为了有效求解此类问题,提出了一种新的求解矩阵特征值的进化策略算法,该算法可用于求解任意矩阵的特征值.实验结果表明,这种基于进化策略算法求解矩阵特征值的方法,与传统方法相比,表现出求解精度高,收敛速度快等优点.     

Parallel block tridiagonalization of real symmetric matrices

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which frequently results from applications with strong locality properties, a heuristic parallel algorithm is used to transform it into a block tridiagonal matrix such that the eigenvalue errors remain bounded by some prescribed accuracy tolerance. For a dense matrix without any usable structure, orthogonal transformations are used to reduce it to block tridiagonal form using mostly level 3 BLAS operations. Numerical experiments show that block tridiagonal structure obtained from this algorithm directly affects the computational complexity of the parallel block tridiagonal divide-and-conquer eigensolver. Reduction to block tridiagonal form provides significantly lower execution times, as well as memory traffic and communication cost, over the traditional reduction to tridiagonal form for eigensystem computations.     

Necessary and sufficient conditions for global optimality of eigenvalue optimization problems

The necessary and sufficient conditions for global optimality are derived for an eigenvalue optimization problem. We consider the generalized eigenvalue problem where real symmetric matrices on both sides are linear functions of design variables. In this case, a minimization problem with eigenvalue constraints can be formulated as Semi-Definite Programming (SDP). From the Karush-Kuhn-Tucker conditions of SDP, the necessary and sufficient conditions are derived for arbitrary multiplicity of the lowest eigenvalues for the case where important lower bound constraints are considered for the design variables. Received May 18, 2000     

求一类微分方程特征值上,下界的数值方法

本文首先导出了以y″ λρ(x)y=0的特征值集为其零点集的整函数ω(λ),其中ρ(x)为分段函数(每个小段为线性或零次函数),据此,给出了一个求(ρ(x)y＇)＇ λq(x)y=0的特征值上、下界的数值方法。     

求解平面转子本征问题的因式分解方法

讨论了平面转子的可因式分解性,用因式分解的方法求解了平面转子的本征问题,并计算了均匀强电场下平面转子的能级和波函数。