基于反幂法和扩展卡尔曼滤波的姿态估计算法

针对基于Davenport的四元数法和扩展卡尔曼(extended Kalman filtering,EKF)的姿态估计算法的精度受特征值精度影响的问题,设计一种基于反幂法与EKF算法的姿态估计算法。根据Davenport矩阵K的近似特征值,利用反幂法迭代计算出Davenport矩阵K的特征向量,将其作为EKF的测量值,降低EKF测量值对特征值的敏感度。为验证算法有效性,搭建四旋翼无人机实验平台,实测实验结果表明,该算法能为无人机提供高精度、实时的姿态信息,实现了无人机的稳定飞行。     

Eigenvalues of partitioned matrices "generated" by a matrix with known eigenvalues

A method is shown which allows to compute the eigenvalues of anmn-dimensional square matrixFfrom the eigenvalues of ann-dimensional matrixA, if the m²submatrices ofFare describable by convergent power series ofA. As an illustration, matrices arising in a multivariable feedback control system are considered.     

Eigenvalue tracking due to parameter variation

This note describes an efficient eigenvalue tracking algorithm, which is applicable in many engineering systems where the effect of parameter variation on system stability is to be determined. Starting with the original system eigenvalues, the algorithm uses determinants to compute first-order eigenvalue sensitivities which are used in an iterative method that converges rapidly to the new eigenvalues corresponding to the parameter change. The algorithm tracks all the system eigenvalues starting from a given base case. It is shown to be less costly than repeated eigenvalue evaluation and is illustrated by means of a simple power system example.     

On the evaluation of the eigenvalues of the finite differences laplacian over a hexagon

Fast numerical methods for the evaluation of the eigenvalues of the finite-differences laplacian over a regular hexagon are devised. At first we show how this eigenvalue problem can be splitted into 3 eigenvalue problems, of lower dimension (reduced by a factor of 1/6), for the discrete laplacian over a regular triangle with suitable boundary conditions. Then, expressing explicitely the eigenvalues and the eigenvectors of the discrete laplacian over a triangle in terms of the coefficients of the discrete Fourier transform, we show how to deal efficiently with each subproblem. In particular we show that each step of the shifted inverse power method, for the approximation of the eigenvalues, costs O(n²log n) arithmetic operations in a sequential model of computation, and O(log n) steps with n² processors in a parallel model of computation, where n is the number of the nodes on the edge of the hexagon. Similar estimates hold for the orthogonal iterations (subspaces iterations) method and for Lanczos method. This approach includes the deflation of the eigenvalues of the triangle from those of the hexagon. These results improve the methods given by Bauer and Reiss [1] allowing a higher precision in the approximation of the eigenvalues of the laplacian and reducing the computational cost, either in a sequential or in a parallel model of computation.     

基于加权特征投影的信源数估计方法

考虑到色噪声或低快条件下噪声特征值发散,导致基于特征分解的信源数估计方法得到的信号判据值和噪声判据值区分不明显,提出了一种基于加权特征投影的信源数估计方法;首先,为了使该方法可适用于低信噪比条件,对阵列接收数据的协方差矩阵进行降噪处理,并利用降噪后协方差矩阵所有特征值和特征向量构造了一个用来区分信号和噪声的加权空间矩阵;然后,将降噪后的协方差矩阵在该加权空间矩阵上投影,从而增大了信号判据值与噪声判据值的差异;最后,结合幂函数的缩放性构建了判决函数,进而实现信源数估计;通过理论分析和实验验证,该方法不仅适用于白噪声和色噪声条件,而且在低快拍和低信噪比条件下优势明显,在快拍数为10,信噪比分别为0 dB的白噪声和6 dB的色噪声条件下,该方法的成功检测概率均达到90％以上,同时该算法在信源数较多时效果鲁棒.     

The amended DSeSC power method for polynomial root-finding

Cardinal's matrix version of the Sebastiao e Silva polynomial root-finder rapidly approximates the roots as the eigenvalues of the associated Frobenius matrix. We preserve rapid convergence to the roots but amend the algorithm to allow input polynomials with multiple roots and root clusters. As in Cardinal's algorithm, we repeatedly square the Frobenius matrix in nearly linear arithmetic time per squaring, which yields dramatic speedup versus the recent effective polynomial root-finder based on the application of the inverse power method to the Frobenius matrix.     

一种新的MIMO-OFDM通信系统比特分配方案

从MIMO-OFDM系统模型出发,首先对理想信道传输矩阵进行奇异值分解,在子信道自适应调制设计中应用信道矩阵特征值把空分复用信道转化为并行子信道,将用于多载波自适应比特分配算法应用于MIMO-OFDM系统。然后以实现系统发射功率最小为原则,以降低系统比特分配算法复杂度为目标,提出了一种可变步长的子信道比特分配优化算法。仿真结果表明,这种算法不但可以实现和Campello方法相当的比特分配性能,还可以较大地降低系统的计算复杂度。     

Enhancing SVM performance in intrusion detection using optimal feature subset selection based on genetic principal components

Intrusion detection is very serious issue in these days because the prevention of intrusions depends on detection. Therefore, accurate detection of intrusion is very essential to secure information in computer and network systems of any organization such as private, public, and government. Several intrusion detection approaches are available but the main problem is their performance, which can be enhanced by increasing the detection rates and reducing false positives. This issue of the existing techniques is the focus of research in this paper. The poor performance of such techniques is due to raw dataset which confuse the classifier and results inaccurate detection due to redundant features. The recent approaches used principal component analysis (PCA) for feature subset selection which is based on highest eigenvalues, but the features corresponding to the highest eigenvalues may not have the optimal sensitivity for the classifier due to ignoring many sensitive features. Instead of using traditional approach of selecting features with the highest eigenvalues such as PCA, this research applied a genetic algorithm to search the genetic principal components that offers a subset of features with optimal sensitivity and the highest discriminatory power. The support vector machine (SVM) is used for classification purpose. This research work used the knowledge discovery and data mining cup dataset for experimentation. The performance of this approach was analyzed and compared with existing approaches. The results show that proposed method enhances SVM performance in intrusion detection that outperforms the existing approaches and has the capability to minimize the number of features and maximize the detection rates.     

多机电力系统静态稳定分析的MATLAB方法

给出了多机电力系统静态稳定计算的建摸原理,推导了考虑励磁调节系统动态行为的全系统线性化状态矩阵公式,并设计了基于Matlab语言的运算程序。该程序可以计算系统特征值和每一特征值的机电回路相关比,可以满足多机电力系统低频振荡分析的需要。使用该文方法及其程序与电力科学研究院开发的电力系统分析综合程序（PSASP6．2）分别对EPRI-36节点系统典型算例进行计算比较。二者的全部特征值、机电回路相关比等计算结果完全一致,验证了所述方法正确、有效。     

不规则扁平粒状物表面平整度识别与分选方法的研究

由于不规则扁平粒状物表面为不规则曲面,且体积小,轮廓不规则,通过二维信息对其进行判断存在一定的局限性,而用常规的物理方法和间接测量方法难以满足有效辨析分选所需的环境、标准设定等多项工艺和工程上的要求。为此,本文提出一种自动识别、分选不规则扁平粒状物的方法。该方法通过二维图像进行三维信息重构,然后利用三维信息选择合适的分选特征值,根据特征值进行分选。该方法运用GPU对程序进行加速,可满足不规则扁平粒状物自动化分选的要求。     

基于特征值分解的全极化SAR遥感数据分类研究

应用极化目标特征值分解理论,研究了全极化合成孔径雷达图像的精细分类问题,在H-α-Wishart分类基础上引入平均散射功率,并根据不同地物的散射功率强度信息,给出了一种简单的阈值分割方法,最后利用鄱阳湖地区的Radarsat-2全极化数据进行了实验和分析,结果发现引入平均散射功率信息后的分类类别更多、精度更好。     

A design scheme for incomplete state or output feedback with applications to boiler and power system control

The problem of designing a linear feedback when all state variables are not available is discussed. The design scheme is based on computation of a complete state feedback and a reduction to a specified structure. The reduction is made by approximation of the eigenspace corresponding to a set of dominant eigenvalues. The method consists of successive choices of weightings on this space. The method is applied to the control of a boiler and a three-machine power system. In the power system case the complete state feedback can be replaced by local output feedback without significant decrease in performance.The examples indicate that the proposed method is a realistic design method for multivariable systems.     

基于改善特征值离散度的信源数目估计

相比于传统的信源数目估计方法,基于特征值差值法的信源数目估计具有较小运算量的优点,但是因为在低信噪比时效果差,且在色噪声下效果不稳定等多种缺点一直未能在实际中应用。因此分析了特征值离散度对差值法估计的影响,提出一种基于对数函数拟合改善特征值发散程度的方法,并利用拟合特征值进行差值法进行估计。该算法很大程度上减少了相邻信源特征值之间的差值,使信源特征值和噪声特征值之间的差值更加明显,大大提升了差值法的估计性能,同时保证了较小的运算量。经实验仿真表明,该方法在白噪声和色噪声下都能进行稳定估计,在较低信噪比和低快拍数下依然具有良好估计性能的优点。     

Model reduction by power decomposition and frequency response matching

A mixed method of linear system model reduction, retaining the advantages of the power decomposition method and the frequency response matching method, is proposed. From the viewpoint of energy contributions to the system output, the dynamic modes with dominant energy contributions instead of those with dominant eigenvalues will be preserved. Having determined the denominator of the reduced model, the parameters of the numerator are found by using the frequency response matching technique.     

Statistical MIMO controller performance monitoring. Part I: Data-driven covariance benchmark

In this paper, a data-based covariance benchmark is proposed for control performance monitoring. Within the covariance monitoring scheme, generalized eigenvalue analysis is used to extract the directions with the degraded or improved control performance against the benchmark. It is shown that the generalized eigenvalues and the covariance-based performance index are invariant to scaling of the data. A statistical inference method is further developed for the generalized eigenvalues and the corresponding confidence intervals are derived from asymptotic statistics. This procedure can be used to determine the directions or subspaces with significantly worse or better performance versus the benchmark. The covariance-based performance indices within the isolated worse and better performance subspaces are then derived to assess the performance degradation and improvement. Two simulated examples, a multiloop control and a multivariable MPC system, are provided to illustrate the utility of the proposed approach. Then an industrial wood waste burning power boiler unit is used to demonstrate the effectiveness of the method.     

基于融合邻域寻优与θ-PSO算法的矩阵特征值求解

提出一种融合邻域寻优与θ-PSO算法的矩阵特征值求解新方法,将矩阵特征值的求解问题转化为最优化问题。与需要多次运行程序分别求解不同范围的特征值算法相比,该方法可以一次性求出矩阵的全部特征根。仿真实验表明,该算法编程实现方便,对于不同类型的矩阵均可以应用,求解精度高,收敛速度快,大概在10~15代左右就可以收敛,完全可以满足工程实践运算中对精度和速度的要求。     

A Spectral-Element Method for Transmission Eigenvalue Problems

We develop an efficient spectral-element method for computing the transmission eigenvalues in two-dimensional radially stratified media. Our method is based on a dimension reduction approach which reduces the problem to a sequence of one-dimensional eigenvalue problems that can be efficiently solved by a spectral-element method. We provide an error analysis which shows that the convergence rate of the eigenvalues is twice that of the eigenfunctions in energy norm. We present ample numerical results to show that the method convergences exponentially fast for piecewise stratified media, and is very effective, particularly for computing the few smallest eigenvalues.     

A new digital control strategy for a nuclear boiling water reactor

A method is proposed for the design of constant gain optimal feedback control laws for discrete-time systems which reduce trajectory sensitivity to small system parameter variations and ensure the closed-loop eigenvalues at the prescribed locations. The selected performance index is of standard linear regulator type, modified to include a quadratic sensitivity term. An efficient computational procedure based on direct cost oprimization using gradient type algorithm is also reported. A case study of a Boiling Water Reactor power plant has been presented to illustrate the application of the design procedure.     

A modified stochastic perturbation algorithm for closely-spaced eigenvalues problems based on surrogate model

Aiming at uncertainty propagation and dynamic reanalysis of closely-spaced eigenvalues, with consideration of uncertainties in design variables, a modified stochastic perturbation method is proposed. Concerning quasi-symmetric or partial-symmetric structures that frequently appear, one of their primary features is closely-distributed natural frequencies. For structure with closely-spaced eigenvalues, due to its instability and sensitivity to the changes of design variables and its excessively concentrated adjacent eigenvalues, conventional uncertainty analysis or dynamic reanalysis methods for distinct eigenvalue are no longer available. Initially, the spectral decompositions of stiffness and mass matrices are provided; by transfer technique, the eigen-problem of closely-spaced eigenvalues is converted to that of repeated eigenvalues with two perturbation parts appended; then the perturbed closely-spaced eigenvalue is rewritten as the sum of original closely-spaced eigenvalues’ mean value and surrogate model which approximates the first-order perturbation term by polynomial chaos expansions. According to this method, statistical quantities of perturbed closely-spaced eigenvalues are calculated directly and accurately, which contributes to its uncertainty analysis and dynamic reanalysis. Furthermore, the capability of proposed method in dealing with relatively large uncertainties and complex engineering structure is demonstrated. The accuracy and efficiency of proposed method have been verified sufficiently by numerical examples.     

Decentralized stabilization of large electric power systems

This paper considers the problem of stabilizing the dynamics of a large electric power system, represented by a linear time invariant system of equations, by using several decentralized (or local) state feedback control laws. The stabilization problem is formulated into a functional minimization problem which implicitly controls the closed-loop eigenvalues of the controlled system. The constraint of decentralization is tackled in the minimization algorithm by using the method of feasible directions. To illustrate the application of the algorithm, it is used to stabilize a three machine electric power system.