On convergence properties of eigenvalues of space discretized wave equations

A theorem along with proof for the convergence of eigenvalues of spatially discretized wave equations is established in this correspondence by extending earlier work of Mahapatra[3].     

Synthesis of linear stochastic signals in identification problems

Stationary stochastic inputs are generated from linear processes of the autoregressive moving average type. Since the spectral density of such an input process is nonzero everywhere, this belongs to the class of admissible signals satisfying identifiability requirements. A characterization of the optimal signals is obtained in terms of their spectral densities using the results on asymptotic eigenvalue distribution of Toeplitz matrices. These signals belong to the general class of random inputs that can be generated using standard instrumentation consisting of delay lines and a white noise generator.     

Singular perturbation analysis of systems with sustained high frequency oscillations

Using singular perturbation techniques, a system with high frequency oscillations is decomposed into two lower order subsystems, one containing only the slowly varying part and the other containing only the fast oscillatory part. Eigenvalue and state approximations achieved by the subsystems are given. A mass-spring-damper example shows that a stiff spring can be regarded as a perturbation of a rigid rod and an interconnected power system example illustrates the occurrence of coherency and inter-machine oscillations.     

Matrix properties of data from electrical capacitance tomography

Some properties of the matrix of capacitance-data collected by the electrical capacitance tomography (ECT) technique are studied. These data are used to extract information in various industrial process applications and, in particular, about flows in pipelines. The features in the eigenvalue distribution of normalized capacitance matrices for three practical classes of permittivity distributions, namely core flows, annular flows, and stratified flows, are investigated and compared by numerical solution. It is shown that the leading eigenvalue is strongly related to the area ratio of permittivity contrast in the cross-section of the flow, while the next two eigenvalues provide a basis for distinguishing among these three classes of flows. In particular, for core and annular flows, the difference between the second and third eigenvalues is shown to be related to the eccentricity of permittivity profile. Numerical examples are presented to illustrate how the area ratio for some permittivities that do not belong to these classes can be effectively estimated.     

椭圆抛物面的拟合问题

为检测空间一任意放置的椭球抛物面形状天线,可根据由全站仪采集到的设备表面离散点的坐标,求得椭球抛物面体的空间位置和大小。本文讲述了利用附加条件式拟合椭球抛物面以及利用特征值拟合椭球抛物面的方法,从而求得观测坐标系与椭球抛物面主轴坐标系之间的关系,最后得出椭球抛物面在空间的位置、方向和大小,进而分析其不符合量。通过比较分析得出,两种方法拟合出的椭圆抛物面是一致的,利用特征值的方法拟合效果更佳。     

小干扰稳定性分析中按阻尼比递增关键特征子集计算

提出了大规模电力系统小干扰稳定性分析中计算机电振荡模态的一种有效方法。用Jacobi-Davidson方法求取系统状态矩阵按阻尼比递增的特征值子集,抓住了电力系统机电振荡分析问题的本质,避免了大量冗余特征值的计算,大大减少了计算量。另外提出了在Jacobi-Davidson方法中用Arnoldi分解构造初始正交子空间的方法,提高了该方法在迭代初期的计算效率。最后将提出的方法分别在46机和113机系统上进行了试验,结果表明利用所提方法能够有效地求出系统负阻尼和阻尼不足的所有振荡模态,适用于大规模电力系统的机电振荡分析。     

基于最大特征根的相对效率的下界估计

定义了广义线性模型中参数的最小二乘估计（LSE）与最佳线性无偏估计（BLUE）的一种新的相对效率,这种相对效率定义为参数估计量的协方差阵的最大相对特征根之比。给出了当设计矩阵满秩,协方差阵非负定时这种新的相对效率的下界,研究了新的相对效率与广义相关系数之间的关系,由本文的而占可见,当广义线性模型与主成分分析、典型相关分析方法结合应用时,这种相对效率具有很强的实用价值。     

Design of experiments for Quick U-building method for building energy performance measurement

Quick U-building (QUB) is a method for short time measurement of energy performance of buildings, typically one night. It uses the indoor air temperature response to the power delivered to the indoor air by electric heaters. This paper introduces a method for estimating the expected measurement error as a function of the amplitude and the time duration of the input signal based on the decomposition of the time response of a state-space model into a sum of exponentials by using the eigenvalues of the state matrix. It is shown that the buildings have a group of dominant time constants, which gives an exponential response, and many very short and very large time constants, which have a small influence on the response. The analysis of the eigenvalues demonstrates that the QUB experiment may be done in a rather short time as compared with the largest time constant of the building.     

基于卷积神经网络的电力系统小干扰稳定评估

随着电力系统规模的增大,通过传统数值方法计算系统特征值来进行小干扰稳定评估已无法满足实时分析的要求。因此,提出了一种基于深度学习(卷积神经网络)的电力系统小干扰稳定评估方法。该方法以广域测量系统可监测变量作为模型的输入,关键特征值作为输出,对输入数据和输出数据进行相应处理后,利用深层架构对其映射关系进行分析;并针对大系统维数较高、训练速度较慢的问题,采用了离散余弦变换和图形处理器并行技术。算例结果表明,在不考虑控制参数变化的情况下,经过历史数据的离线训练后,该方法能够较准确地计算出系统的关键特征值。     

基于特征值的黑盒子意义下的特殊门限秘密共享方案

摘 要: 基于Shamir(n,t)秘密共享方案,提出一个新的门限秘密共享方案。利用n阶矩阵的特征方程具有重根的特点,实现了不同集合中参与者的秘密共享。同一参与集合所对应的次主密钥是相同的,即特征值是相同的,将同一个特征值所对应的不同特征向量作为子密钥,分发给同一参与集合的参与成员。而且,利用黑盒子,同一集合内部成员可以验证自己手中的子密钥的真实性,从而达到了防欺诈的目的。分析结果表明,本方案是安全的理想秘密共享方案。