特征值摄动法在利用动响应结构小损伤检测中的应用

目前在使用遗传算法或神经网络方法进行结构动力学损伤检测,需要基于少量的在线测量损伤结构数据和大量的数值仿真数据来实现,其中通过有限元方法来获得仿真数据的巨大计算量是动力学结构损伤检测方法发展中所面临的一个重要问题。本文在建模方面应用近年来提出的调整单元刚度模拟损伤的先进方法,以保证在损伤前后结构自由度数目不变;在此基础上应用特征值摄动法来减少损伤检测中计算量,并通过对复合材料层合板响应信号的小波分析验证了使用一阶矩阵摄动在有效降低计算量的同时,可以获得对损伤检测而言足够准确的响应信号。

Hamilton系统特征值问题的摄动方法及其应用

研究了 Ham ilton系统特征值的摄动问题 ,给出了系统特征值和特征函数的摄动展开式。并基于 H∞ 控制系统的性能指标与相关的 Hamilton微分方程特征值的关系 ,利用特征值摄动方法计算参数摄动控制系统的最优H∞ 性能指标。

不变子空间上特征值的摄动(英文)

本文推广Wielandt—Hoffman定理而得到如下结果:定理1: 设A=X_Adiag(λ_1^((A)),…,λ_n^((A)))X_A^(-1),Q_1∈C^(n×m),T=X_Tdiag万吨(λ_1^((T)),…,λ_m^((T)))X_T^(-1),m≤n。那么,存在1,2,…,n的某个排列π(1),…,π(n)使得:其中,K_2(C)=‖C‖_2‖C^(-1)‖_2,‖‖_2及‖‖_F分别代表矩阵的谱范数和Frobcnius范数,σ_(min)(Q_1)是矩阵Q_1的最小奇异值。

广义复特征值摄动问题的逐步逼近法

以子空间缩聚及正交分解为基础 ,根据复矩阵的奇异值分解定理 ,对广义复特征值摄动问题 ,提出了一种能同时有效地处理孤立复特征值、相重复特征值及相近复特征值 3种不同情况的逐步逼近法。计算实例表明 ,该方法合理可靠 ,通用性好 ,且具有足够的精度。

基于特征根有界摄动分析的高超声速飞行器双通道控制

针对双通道控制高超声速飞行器横侧向欠驱动、强不确定性的特点,研究了适用于工程应用的控制策略,提出一种基于特征根有界摄动分析的反馈控制鲁棒性分析方法。基于线性化近似分析和工程约束需求,给出了双通道飞行器改善荷兰滚模态动态的2种控制策略,分别为极点配置方案和模态解耦方案。提出了特征根灵敏度矩阵和有界摄动矩阵的概念,用于评估闭环系统对参数不确定的鲁棒性。基于闭环六自由度模型在标称及参数拉偏情况下,对2种方案进行了综合分析和仿真验证。仿真结果表明,2种控制方案均可以解决双通道控制问题,所提特征根有界摄动分析方法可准确评估系统的鲁棒性。

变阻力大气摄动问题

本文讨论人造宇宙飞行器的变阻力大气摄动问题，给出摄动的分析解，并与常阻力大气摄动问题进行比较，得到了两个方面的主要结论，一是变阻力大气摄动保留了常阻力大气摄动的基本特征，另一个是变阻力大气摄动的解与帆板的定向有关．

电力系统共振模式下传统特征值灵敏度分析失效问题

特征值灵敏度在电力系统小干扰稳定性分析和控制器设计中应用广泛。基于特征值摄动理论,指出在共振模式和接近共振模式下,传统的特征值1阶、2阶灵敏度计算公式与摄动表达式均可能失效。针对这一问题,提出了一种特征值关于系统参数变化的快速重分析算法,从而可以有效分析系统参数小范围变化时共振模式和接近共振模式特征值的变化情况。IEEE 9节点系统和IEEE 39节点系统的分析结果验证了该算法的有效性。

Reissner-Mindlin板模型的关于板厚一致收敛逼近方法

针对Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｌｉｎ夹支板模型，给出了两个关于板厚一致收敛的稳定混合有限元逼近格式：其一，局部特征值摄动法；其二，残差ｂｕｂｂｌｅ－函数法。

鲁棒极点配置概念在单输入系统控制中的应用

利用矩阵特征值一阶摄动理论解释了鲁棒极点配置的原始目标,指出以特征向量广义夹角加权和最大化为目标的一些方法存在认识偏差,并根据控制问题的特点重新规定了适用于评估闭环稳定性的评判数。在MATLAB环境下编制了可直接使用拉格朗日方程的程序,求出了二级倒立摆稳定位置附近局部线性化模型,以该评判数为基础在GIP-300-VPPA-L型倒立摆上实现了对二级倒立摆的稳定控制。建模程序经适应性修改后可用于对任意可用拉格朗日方程描述的系统进行建模。

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall （QH） effect on a noncommutative phase space （NCPS）. By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.

密集模态的判断准则

用特征向量转角给出了一种密集模态的判别准则。

A direct-variance-analysis method for generalized stochastic eigenvalue problem based on matrix perturbation theory

It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty effects are indispensable during the process of product development.Besides,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best design.Taking uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational costs.Owing to the situations above,matrix perturbation method has been investigated by researchers worldwide recently.However,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational process.This has become the bottleneck of application for matrix perturbation method.In this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation method.In the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have changed.Combining the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure directly.Hence the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being involved.The feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing structure of MA700 commercial aircraft),in which the DVA method also shows superiority in computational efficiency when compared to the Monte-Carlo method.

Modified perturbation method for eigenvalues of structure with interval parameters

In overcoming the drawbacks of traditional interval perturbation method due to the unpredictable effect of ignoring higher order terms,a modified parameter perturbation method is presented to predict the eigenvalue intervals of the uncertain structures with interval parameters.In the proposed method,interval variables are used to quantitatively describe all the uncertain parameters.Different order perturbations in both eigenvalues and eigenvectors are fully considered.By retaining higher order terms,the original dynamic eigenvalue equations are transformed into interval linear equations based on the orthogonality and regularization conditions of eigenvectors.The eigenvalue ranges and corresponding eigenvectors can be approximately predicted by the parameter combinatorial approach.Compared with the Monte Carlo method,two numerical examples are given to demonstrate the accuracy and efficiency of the proposed algorithm to solve both the real eigenvalue problem and complex eigenvalue problem.

Matrix perturbation based approach for sensitivity analysis of eigen-solutions in a microgrid

Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.