应用非线性Galerkin方法求解微梁的动态响应

分析在电场力驱动下微共振器的非线性动力学特性．取前3阶模态,利用非线性Galerkin方法得到单自由度的降阶模型．用多尺度法计算降阶模型的动态响应,并得出了稳态响应的幅频特性曲线,与利用传统Galerkin方法直接取1阶模态所得的结果比较．以数值积分法求解3自由度模型得到的微共振器动力学响应为参考标准,验证了非线性Galerkin方法与传统Galerkin方法相比具有较高的精度．     

挠性结构广义特征值问题的简化处理

本文讨论了挠性飞行器混合坐标动力学模型广义特征值问题的简化计算方法,导出了由三阶行列式计算整体广义特征值和三阶线性代数方程计算整体广义特征向量的公式,所得结果可使得处理高维广义特征值问题大为简化,并可为挠性结构模型降阶提供方便,文中还给出了两个数值例子。     

概率二维主分量分析

二维主分量分析是一种直接面向图像矩阵表达方式的特征抽取与降维方法. 提出了一个基于二维主分量分析的概率模型. 首先, 通过对此产生式概率模型参数的最大似然估计得到主分量(矢量); 然后, 考虑到缺失数据问题, 利用期望最大化算法迭代估计模型参数和主分量. 混合概率二维主分量分析模型在人脸聚类问题上的应用表明概率二维主分量分析模型能作为图像矩阵的密度估计工具. 含有缺失值的人脸图像重构实验阐述了此模型及迭代算法的有效性.     

中心刚体-柔性梁刚柔耦合动力学模型降阶研究

有限单元法被广泛的采用来描述柔性体的弹性变形,然而有限元节点坐标数目庞大,将会给动力学方程求解带来巨大的计算负担.如何降低柔性体的自由度,是当前柔性多体系统动力学研究的一个重要命题.本文以中心刚体-柔性梁系统为例,采用Krylov方法和模态方法进行降价.然后分别采用有限元全模型、Krylov降阶模型和模态降阶模型,对中心刚体-柔性梁进行刚-柔耦合动力学仿真.仿真结果表明,与采用模态降阶方法相比,采用Krylov模型降阶方法只需要较低的自由度,就可以得到与采用有限元方法完全一致的结果.说明Krylov模型降阶方法能够有效的用于柔性多体系统的模型降价研究.     

利用特征值和特征向量降低状态模型的阶

高阶系统的降阶是十分重要的问题。本文介绍了一种实用方法,即利用状态矩阵的特征值和特征向量在总响应中所起的作用,来简化状态模型。文中较详细地说明了思路,并给出了算法、程序以及一个9阶锅炉模型的简化实例。     

用于故障检测的集成核主分量分析

针对复杂环境下的多变量工业过程在线故障检测问题, 提出基于集成核主分量分析的解决方法. 该方法首先求出样本映射后的无限维空间的多组近似基, 将主分量分析问题特征向量的解空间限定在近似基张成空间求解; 然后集成特征向量和特征值, 并计算Hotelling ??2 统计量和平方预报误差; 最后据此判断检测结果. 该方法对Tennessee Eastman 过程故障检测样本进行测试, 并与其他两种方法进行对比. 测试结果表明了所提出方法的有效性.

     

大系统模型简化的一种新的时域最优逼近法

从大系统及其降阶模型的单位脉冲响应矩阵近似相等出发,推导了大系统及其降阶模型 的特征值应该遵守的关系式.利用该关系式可以改进大系统模型简化的时域最优逼近法,将 泛函求极值的问题转化为参数优化的问题,有可能使问题的解决简单化.本文提出了两种算 法:1)保留主特征值的最优逼近;2)修改特征值的最优逼近.附有数字实例.     

非线性映射与特征提取：KMSE模型与核主分量分析技术

分析表明,KMSE模型准则中正则项的使用相当于引入了一个与核矩阵特征值直接相关的项以度量模型的泛化性能.根据矩阵特征值知识,可知核主分量分析实际上为KMSE模型应用过程中的一个中间步骤.此时,KMSE的作用表现为将样本在特征空间中的主分量映射为指示其类别的计算输出值.KMSE模型可看作是在特征空间的主分量分析基础上进一步实施特征变换的过程.本文全面阐述了KMSE模型与KFDA,LS-SVM,核主分量分析以及Bayesian判别函数间的理论关系.此外,通过分类实验测试了KMSE、核主分量分析与本文方法的性能.     

基于光流的动态手势识别

手势识别是人机交互中的重要组成部分，文章针对基于光流PCA（主分量分析）和DTW（动态时间规整）进行命令手势识别。利用块相关算法计算光流，并通过主分量分析得到降维的投影系数，以及手掌区域的质心作为混合特征向量。针对该混合特征向量定义了新的加权距离测度，并用DTW对手势进行匹配。针对9个手势训练和识别，识别率达到92％。     

Log-Gabor小波和分数阶多项式KPCA的火焰图像状态识别

目的 为了进一步提高锅炉燃烧火焰图像状态识别的性能,提出了一种基于Log-Gabor小波和分数阶多项式核主成分分析(KPCA)的火焰图像状态识别方法。方法 首先利用Log-Gabor滤波器组对火焰图像进行滤波,提取滤波后图像的均值和标准差,并构成纹理特征向量。然后使用分数阶KPCA方法对纹理特征向量进行降维,并将降维后的纹理特征向量输入支持向量机进行分类。结果 本文与基于Log-Gabor小波特征提取以及2种基于Gabor小波特征提取的方法相比,本文方法的分类识别正确率更高,分类精度为76%。同时,第1主分量方差比重与核函数参数d之间满足递增关系。本文方法能够准确地提取火焰图像纹理特征。结论 本文提出一种对锅炉燃烧火焰图像进行状态识别的方法,对提取的火焰图像纹理特征向量进行降维并进行分类,可以获得较高的分类精度。实验结果表明,本文方法分类精度较高,运行时间较短,具有良好的实时性。     

Higher order eigensensitivity analysis of damped systems with repeated eigenvalues

A simplified method for the computation of first-, second- and higher-order derivatives of eigenvalues and eigenvectors associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation. The algebraic equation which is developed can be used to compute derivatives of eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space, it is numerically stable and very efficient compared to previous methods. To verify the efficiency of the proposed method, the finite element model of the cantilever beam and a mechanical system in the case of a non-proportionally damped system are considered.     

一种求解复Hermite矩阵特征值的方法

介绍几种求解矩阵特征值和特征向量的经典算法及各自优缺点,通过理论推导,提出了一种性能稳健的方法,可以求解信号处理中常见的复Hermite阵.将对复Hermite矩阵求特征值和特征向量的问题转化为求解实对称阵的特征值和特征向量,而实对称阵的求解采用一种改进的三对角Householder法.最后把结果与Matlab仿真结果比较,可以看出该方法有很高的精确度.     

Generalized eigenvalue problems: Lanczos algorithm with a recursive partitioning method

In this paper, the computation of the smallest eigenvalues and the corresponding eigenvectors of the generalized eigenvalue problem using Lanczos algorithm with a recursive partitioning method as well as the Sturm sequence-bisection method have been discussed. We have also presented the comparison of the numerical results and the CPU-time between the above two methodologies. Our comparative study indicates that the Lanczos with a recursive partitioning method takes relatively less computing time than that of the Sturm sequence-bisection method.     

GA-fisher: A new LDA-based face recognition algorithm with selection of principal components.

This paper addresses the dimension reduction problem in Fisherface for face recognition. When the number of training samples is less than the image dimension (total number of pixels), the within-class scatter matrix (Sw) in Linear Discriminant Analysis (LDA) is singular, and Principal Component Analysis (PCA) is suggested to employ in Fisherface for dimension reduction of Sw so that it becomes nonsingular. The popular method is to select the largest nonzero eigenvalues and the corresponding eigenvectors for LDA. To attenuate the illumination effect, some researchers suggested removing the three eigenvectors with the largest eigenvalues and the performance is improved. However, as far as we know, there is no systematic way to determine which eigenvalues should be used. Along this line, this paper proposes a theorem to interpret why PCA can be used in LDA and an automatic and systematic method to select the eigenvectors to be used in LDA using a Genetic Algorithm (GA). A GA-PCA is then developed. It is found that some small eigenvectors should also be used as part of the basis for dimension reduction. Using the GA-PCA to reduce the dimension, a GA-Fisher method is designed and developed. Comparing with the traditional Fisherface method, the proposed GA-Fisher offers two additional advantages. First, optimal bases for dimensionality reduction are derived from GA-PCA. Second, the computational efficiency of LDA is improved by adding a whitening procedure after dimension reduction. The Face Recognition Technology (FERET) and Carnegie Mellon University Pose, Illumination, and Expression (CMU PIE) databases are used for evaluation. Experimental results show that almost 5 % improvement compared with Fisherface can be obtained, and the results are encouraging.     

求解矩阵特征值和特征向量的PSO算法

提出一种基于粒子群优化算法的求解方法,将线性方程组的求解转化为无约束优化问题加以解决,采用粒子群优化算法求解矩阵特征值和特征向量。仿真实验结果表明,该方法求解精度高、收敛速度快,能够在10代左右收敛,可以有效获得任意矩阵的特征值和特征向量。     

PD Controller for Manipulator with Kinetic Energy Term

A kinetic energy approach to PD control in joint space of a manipulator in terms of the eigenfactor quasi-coordinate velocity (EQV) vector is considered in this paper. The modified PD controller which contains quantities resulting from decomposition of a manipulator mass matrix is proposed. The obtained equations of motion are based on the eigenvalues and eigenvectors of the mass matrix (Junkins, J. L. and Schaub, H. [7]. It is shown that utilizing the EQV vector one can determine directly the kinetic energy of the manipulator and at the same time realize PD control in its joint space. This energy-based strategy gives an interesting insight into position control. The controller presented here was tested in simulation on a 3 d.o.f. direct drive arm manipulator and via experiment on a 2 d.o.f. manipulator. The results confirmed that one can directly determine the kinetic energy for the total manipulator as well for its each joint. Additionally, time response of the system under EQV controller is faster than for the classical controller if mechanical coupling are strong.     

Partial solution of large symmetric generalized eigenvalue problems by nonlinear optimization of a modified Rayleigh quotient

A method is presented to solve numerically the lowest (or highest) eigenvalues and eigenvectors of the symmetric generalized eigenvalue problem. The technique proposed is iterative, does not transform the original matrices and yields eigencharacteristics in sequence, even for repeated eigenvalues. It is based on a nonlinear optimization of an unconstrained penalty function obtained from a generalization of the Rayleigh quotient. In addition, when the normality constraint is imposed, the eigenvectors are obtained by a sequence of solutions to linear equations, all with the same matrix. Examples demonstrate the validity of the method.     

A practical algorithm for the efficient computation of eigenvector sensitivities

Derivatives of eigenvalues and eigenvectors have become increasingly important in the development of modern numerical methods for areas such as structural design optimization, dynamic system identification and dynamic control, and the development of effective and efficient methods for the calculation of such derivatives has remained to be an active research area for several decades. In this paper, a practical algorithm has been developed for efficiently computing eigenvector derivatives of generalized symmetric eigenvalue problems. For eigenvector derivative of a separate mode, the computation only requires the knowledge of eigenvalue and eigenvector of the mode itself and an inverse of system matrix accounts for most computation cost involved. In the case of two close modes, the modal information of both modes is required and the eigenvector derivatives can be accurately determined simultaneously at minor additional computational cost. Further, the proposed method has been extended to the case of practical structural design where structural modifications are made locally and the eigenderivatives of the modes concerned before are still of interest. By combining the proposed algorithm together with the proposed inverse iteration technique and singular value decomposition theory, eigenproperties and their derivatives can be very efficiently computed. Numerical results from a practical finite element model have demonstrated the practicality of the proposed method. The proposed method can be easily incorporated into commercial finite element packages to improve the computational efficiency of eigenderivatives needed for practical applications.     

Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations

The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many contexts, for example in electronic structure calculations. If a significant portion of the eigensystem is required then typically direct eigensolvers are used. The central three steps are: reduce the matrix to tridiagonal form, compute the eigenpairs of the tridiagonal matrix, and transform the eigenvectors back. To better utilize memory hierarchies, the reduction may be effected in two stages: full to banded, and banded to tridiagonal. Then the back transformation of the eigenvectors also involves two stages. For large problems, the eigensystem calculations can be the computational bottleneck, in particular with large numbers of processors. In this paper we discuss variants of the tridiagonal-to-banded back transformation, improving the parallel efficiency for large numbers of processors as well as the per-processor utilization. We also modify the divide-and-conquer algorithm for symmetric tridiagonal matrices such that it can compute a subset of the eigenpairs at reduced cost. The effectiveness of our modifications is demonstrated with numerical experiments.