Computing the frequency response of linear systems with parametric perturbation

The problem of computing the frequency response of linear systems with parametric perturbation is addressed. Under the assumption that the coefficients of the system transfer function depend on the perturbation parameters in a linear manner, we provide results for plotting the frequency response of the perturbed transfer function. These results are useful in determining the H∞ norm, gain margin and phase margin and in improving the diagonal dominance of multi-input multi-out-put uncertain systems. An illustrative example is provided to demonstrate the results.     

权回归扰动模型的影响分析

针对线性加权回归模型，从统计诊断的角度分析了协方差阵扰动的影响度量和回归系数的估计效率，并给出了2种效率的下界。     

An application of modified reductive perturbation method to long water waves

In this work, we extended the application of “the modified reductive perturbation method” to long water waves and obtained the governing equations as the KdV hierarchy. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameter c₁so as to remove the possible secularities that might occur. The present method is seen to be fairly simple as compared to the renormalization method [Kodama, Y., & Taniuti, T. (1977). Higher order approximation in reductive perturbation method 1. Weakly dispersive system. Journal of Physics Society of Japan, 45, 298–310] and the multiple scale expansion method [Kraenkel, R. A., Manna, M. A., & Pereira, J. G. (1995). The Korteweg–deVries hierarchy and long water waves. Journal of Mathematics Physics, 36, 307–320].     

Arc perturbation theory of magnetic deflection

A perturbation theory is presented for deflection angles larger than 45°. Several parameters that previously had to be treated perturbatively are handled exactly. The theory can be used for a systematic study of front‐of‐screen errors in slim CRTs. First‐order results are presented and applied to a field configuration with a strongly varying dipole strength.     

Natural Frequencies of Stable Griffith Cracks

A quasi-statically growing stable crack, if perturbed from its equilibrium position, will accelerate back towards it. Within quasi-static, ideal, Griffith fracture theory, vibrations of the crack and the structure have characteristic natural frequencies. We explore this feature of Griffith fracture theory in two simple geometries: a crack between a bar and a substrate, and a crack in a double-cantilever beam (DCB) specimen. For small perturbations about the stable quasi-static configuration, the dynamic equations of motion reduce to simple eigenvalue problems, leading to exact expressions for natural frequencies and mode shapes. An interesting feature of the mode shapes is that they correspond to force-free or moment-free conditions at the crack tip. Using an extended form of Hamilton's principle, we have developed a variable-length finite element technique to calculate natural frequencies and mode shapes of deformations perturbed from the stable equilibrium state. Its accuracy is demonstrated by application to the two problems analyzed previously. The possibility of crack tip oscillations in real brittle materials with irreversibility in crack tip decohesion is discussed in light of Rice's generalization of the Griffith theory.     

On the sensitivity of the ESPRIT algorithm to non-identical subarrays

ESPRIT (estimation of signal parameters via rotational invariance techniques) is a recently introduced algorithm for narrowband direction-of-arrival (DOA) estimation. Its principal advantage is that the DOA parameter estimates are obtained directly, without knowledge (and hence storage) of the array manifold and without computation or search of some spectral measure. This advantage is achieved by constraining the sensor array to be composed of two identical, translationally invariant subarrays. In this paper, we analyse the sensitivity of ESPRIT to the assumption that the subarrays are identical. The analysis is applicable to a wide variety of array errors, including non-identical angle-dependent and angle-independent gain and phase perturbations, errors in the locations of the subarray elements, and mutual coupling effects. A representative simulation example will be presented to validate the analysis and compare the performance degradation of ESPRIT with that of the MUSIC algorithm.     

由自由振动响应识别非线性系统参数的一种方法

本文提出了一种由自由振动响应识别非线性系统参数的方法,即首先用直接摄动法求出系统自由振动的近似解作为数学模型,然后用最小二乘法来识别系统的物理参数.此方法具有精度高、应用方便的特点.     

基于摄动法的多股簧冲击载荷改进模型

在多股簧冲击载荷原有模型的基础上引入非线性刚度,建立冲击载荷改进模型;基于强非线性振动求解原理提出一种改进多尺度法,并推导了该模型的非线性响应摄动解;结合冲击试验数据对两种模型进行比较。结果表明,改进模型体现了多股簧刚度非线性及振动频率非线性特性,提高了试验数据拟合精度,对描述多股簧动态运动规律更精确,尤其对受冲击载荷及大振幅工况下的多股簧非线性特性研究具有重要意义。该研究也为课题组正在研究的多股簧动态响应特性提供理论基础。     

基于摄动理论的动态弹道偏差阈值修正方法

基于摄动落点偏差预测的弹道修正方法具有落点偏差计算精度高,弹上计算量小等优点。研究了基于该理论在二维弹道修正应用中相关的系列问题。基于多元函数的泰勒级数展开理论,推导了完整的摄动落点偏差预测理论模型。基于摄动偏差理论提出了一种修正步长自适应的射角诸元快速求解方法,一般循环解算弹道模型不超过3次即可得到落点误差不超过1 m的射角诸元。基于不同弹道位置上平均弹道误差,给出了偏导数求解中弹道偏差设置方法。提出了一种动态弹道偏差阈值修正方法,选用该方法进行弹道修正,平均弹道修正次数减少29.1%,而弹丸落点CEP增大不明显。     

基于P—M谱的二维各向异性分层海面电磁散射研究

为了得到基于P-M谱的二维各向异性分层海面电磁散射特性,以便为海洋遥感、海上目标检测与识别等领域的应用提供理论依据,采用微扰法研究了平面波入射分层介质粗糙面的电磁散射特性,结合海面P-M谱推导出了平面波入射时的散射系数计算公式,通过数值计算获得了HH极化下中间介质的介电常数和厚度、摩擦风速、风区范围、观察方向与逆风方向之间夹角和入射波频率对双站散射系数的影响,得到了分层海面电磁散射系数的基本特征、分区特征和随频率变化的特征。