求解实对称矩阵区间特征值问题的直接优化法

提出了一种用于对称区间矩阵特征值问题求解的直接优化法。将区间矩阵中为区间量的各元素作为优化设计变量,将区间量的分布区间作为相应的设计变量的边界约束,运用约束优化法求出区间矩 最大特征值和最小特征值,从而获得区间矩阵特征值问题的解。本文提出的直接优化法适用于对称区间矩阵的标准特征值问题和广义特征值问题。文中给出的两个计算实例显示了该法的有效性。     

基于区间参数的水电机组振动传导研究

在建立的伞式混流式水轮发电机组振动完善模型的基础上,引入各参数的区间性,结合区间算法和随机摄动理论,推导了水电机组各传导路径的传导力及传导率的上、下限和均值的计算表达式,建立了具有区间参数的水电机组-厂房耦合系统的振动传导分析方法。通过算例,分析了结构参数不确定性对传导率的影响,验证了模型和方法的合理性与可行性。该方法能够反映参数不确定时振动传导路径传递率的范围及敏感性等问题,为全面分析水电机组振动传递特性提供理论基础和数据支撑。     

特征值问题迭代伽略金法与Rayleigh商加速

该文讨论特征值问题非协调有限元和混合有限元的加速计算方法。基于迭代伽略金法和Rayleigh商加速技巧,我们建立了特征值问题Wilson非协调有限元和Ciarlet-Raviart混合有限元的加速计算方案。这些新方案把在细网格上解一个特征值问题简化为在粗网格上解一个特征值问题和在细网格上解一个线性方程。文中证明了新方案的计算结果仍然保持了渐近最优精度阶,并用数值实验验证了理论结果。     

Rayleigh波作用下地下结构地震反应影响分析

采用基于时域粘弹性人工边界的Rayleigh波输入方法,进行了土-地下结构相互作用体系在Rayleigh波作用下的动力时程反应分析,对Rayleigh波作用下地下结构的地震反应特性进行研究。重点讨论了地下结构材料强度、结构厚度以及土层刚度等因素对Rayleigh波作用下地下结构地震反应的影响。结果表明Rayleigh波对浅埋地下结构的地震动力反应影响显著,将使结构产生较大的内力与变形,在地下结构抗震设计尤其是浅埋地下结构的抗震设计时应予以足够的重视。     

基于特征值分解的随机子空间算法研究

针对基于数据驱动的随机子空间法计算效率低下的问题,提出一种基于特征值分解的随机子空间算法,该方法通过对ＣＨ矩阵的特征值分解得到扩展可观测矩阵Ｔｍｉ,进而识别出系统模态参数。相比于传统算法,该算法免去了对Ｈａｎｋｌ矩阵的ＱＲ分解及投影矩阵的ＳＶＤ运算,从而大大节省了内存和计算时间。通过一个７自由度的数值仿真和重庆朝天门大桥模型的实例分析证明该方法在保持计算精度的情况下大幅度地提升了计算效率。     

用有限元亏量校正求特征值下界

对解2阶椭圆特征值问题的线性有限元法,本文考虑了一种计算简单的有限元亏量校正方案。基于插值校正和Rayleigh商给出了新的校正特征值。理论分析表明该校正特征值或者达到二次元的精度阶或者当网格直径充分小时下逼近准确特征值,并用数值实验验证了理论结果。     

区间参数结构动力特征值分析的仿射算法

将不确定结构系统中的区间参数用仿射型来表示,对获得的广义区间特征值方程的求解方法进行了研究,提出了一种改进的仿射算法。此方法考虑到广义特征值方程中各区间元素的相关性,通过独立的区间参数在子区间上转为仿射型,将特征值方程的求解转化为相应的确定性问题,再利用常规的仿射算法,搜索方程解中的最大最小值来确定各阶特征值边界。先用数学算例对所提改进的仿射算法的有效性进行了验证,随后将其应用于工程算例的特征值区间分析中,并与其它算法进行了比较。结果表明该算法是合理可行的,有较高的准确性。     

重力对具有表面层的半空间中Rayleigh波的影响

重力对具有表面层的半空间中Rayleigh波具有重要的影响,假设表面层和半空间均为均匀各向同性介质,首先利用考虑重力作用的运动方程得出了重力影响下具有表面层的半空间中Rayleigh波的弥散方程。该方程经退化后得出了不受重力作用时的弥散方程,且与忽略重力时得到的方程完全一致。然后利用数值方法得到了重力影响下的Rayleigh波弥散曲线,分析了泊松比和表面层的厚度的影响,结果表明泊松比和表面层的厚度对弥散曲线具有明显影响。     

广义特征值问题求解的改进Ｒｉｔｚ向量法

从提高算法的稳定性和计算效率入手,采取迭代及防止漏根、多根的措施,对传统的Ｒｉｔｚ向量法进行改进,提出改进的Ｒｉｔｚ向量法。此算法仅需生成ｒ维的Ｋｒｙｌｏｖ空间,大大降低投影矩阵阶数,减少投影矩阵特征值计算时间。引入重正交方案和模态比较法,并给出Ｒｉｔｚ向量块宽ｑ与生成步数ｒ的建议取值。最后通过四参数的谱变换法,不     

时滞微分方程特征值的近似求解方法

通过将时滞微分方程变换为积分方程后并进行离散,得到相应的差分方程,从理论上建立了差分方程的系统矩阵的特征值与原线性时滞微分系统的特征值之间的关系,从而得到了一种求解时滞微分方程特征值的新方法。作为算例,计算了时滞的Logistic方程的前10阶特征值。误差分析表明,提出的近似方法不但简单,并且有很高的精度。     

Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters

This paper proposes a fuzzy interval perturbation method (FIPM) and a modified fuzzy interval perturbation method (MFIPM) for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions. Interval variables are used to quantify the non‐probabilistic uncertainty with limited information, whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions. The level‐cut method is introduced to decompose the fuzzy parameters into interval variables. FIPM approximates the interval matrix inverse by the first‐order Neumann series, while MFIPM improves the accuracy by considering higher‐order terms of the Neumann series. The membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem. Three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters, pure interval parameters, and pure fuzzy parameters, respectively. Copyright © 2015 John Wiley & Sons, Ltd.     

一种针对未知参数系统的实时混沌化方法

针对未知参数系统,本文提出一种基于频谱优化和时延反馈控制的实时混沌化方法。首先,基于系统稳态响应构造频谱性能指标,量化系统稳态行为（周期或混沌等）;然后,随着时间进程的推进,按照直接寻优算法（Hooke-Jeeves 方法）实时调整反馈控制器的时延,直至算法收敛。当性能指标达到最小值时,系统进入最佳混沌状态。数值算例验证了本方法的有效性。本方法最大优点在于无需知道系统参数,仅基于系统响应状态便可实施混沌化控制,易于实现工程化应用。     

Interval static displacement analysis for structures with interval parameters

In this paper, a new method to solve the uncertain static displacement problem of structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even if an optimum scheme is adopted when there are many uncertain parameters. With the interval mathematics, the interval finite element equation is developed. Based on the perturbation and the interval extension, the upper and lower bounds of the static displacements are obtained, in which the sharp bounds are guaranteed by the interval calculation operators. Two numerical examples, a box cantilever beam and an automobile frame, are given to illustrate the validity of the present method. Copyright © 2001 John Wiley & Sons, Ltd.     

An interval random perturbation method for structural‐acoustic system with hybrid uncertain parameters

An interval random model is introduced for the response analysis of structural‐acoustic systems that lack sufficient information to construct the precise probability distributions of uncertain parameters. In the interval random model, the uncertain parameters are treated as random variables, whereas some distribution parameters of random variables with limited information are expressed as interval variables instead of precise values. On the basis of the interval random model, the interval random structural‐acoustic finite element equation is constructed, and an interval random perturbation method for solving this interval random equation is proposed. In the proposed method, the interval random matrix and vector are expanded by the first‐order Taylor series, and the response vector of the structural‐acoustic system is calculated by the matrix perturbation method. According to the linear monotonicity of the response vector, the lower and upper bounds of the response vector are calculated by the vertex method. On the basis of the lower and upper bounds, the intervals of expectation and standard variance of the response vector are obtained by the random interval moment method. The numerical results on a shell structural‐acoustic model and an automobile passenger compartment with flexible front panel demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Technique of checking missed eigenvalues for eigenproblem with damping matrix

In the case of the non‐proportionally damped system such as the soil–structure interaction system, the structural control system and composite structures, the eigenproblem with the damping matrix should be necessarily performed to obtain the exact dynamic response. However, most of the eigenvalue analysis methods such as the subspace iteration method and the Lanczos method may miss some eigenvalues in the required ones. Therefore, the eigenvalue analysis method must include a technique to check the missed eigenvalues to become the practical tools. In the case of the undamped or proportionally damped system the missed eigenvalues can easily be checked by using the well‐known Sturm sequence property, while in the case of the non‐proportionally damped system a checking technique has not been developed yet. In this paper, a technique of checking the missed eigenvalues for the eigenproblem with the damping matrix is proposed by applying the argument principle. To verify the effectiveness of the proposed method, two numerical examples are considered. Copyright © 2001 John Wiley & Sons, Ltd.     

主动约束层阻尼圆柱壳动力学分析的新传递矩阵法

基于作者最近导出的被动约束层阻尼(PCLD)圆柱壳的一阶整合矩阵微分方程,结合压电材料本构关系和比例微分负增益反馈控制策略(PD),建立了一种求解主动约束层阻尼(ACLD)圆柱壳动力学问题的新传递矩阵方法。提出的ACLD圆柱壳的一阶矩阵微分方程,采用了简化的机电耦合模型。通过对ACLD圆柱壳自由振动及其在地震激励作用下的动力学响应分析,表明ACLD圆柱壳的阻尼特性和减振效果相对于PCLD圆柱壳具有明显优势,并且发现采用周向分块敷设ACLD,且施加与结构变形中的占优模态相匹配的控制电压分布方式对地震激励的抑制效果更好。     

Derivatives of complex eigenvectors with distinct and repeated eigenvalues

In this paper, we investigate the computation of the first‐order derivatives of complex eigenvectors for general non‐defective eigensystems. A new normalization condition is proposed, with which we can compute unique first‐order derivatives of arbitrary differentiable eigenvectors of systems with distinct and repeated eigenvalues. We also present an efficient algorithm to compute the particular solutions to the governing equations of the first‐order derivatives of eigenvectors. Finally, numerical examples are included to demonstrate the validity of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

基于高维随机矩阵特征值之差的滚动轴承状态异常检测算法

针对滚动轴承异常检测准确性差、精度低及数据维度灾难造成检测困难等问题,提出一种基于随机矩阵特征值之差指标的滚动轴承状态异常检测算法.运用平移时间窗对不同时刻的轴承信息锁定,并通过分段、随机化、扩增和维度重构等方法构造出高维随机特征矩阵;利用随机矩阵理论对高维数据良好的处理能力,给出了滚动轴承特征值之差指标的构造方法及动...     

一种基于振型正交化的元素型模型修正方法

在振型正交化的一阶增量摄动格式基础上,综合元素型方法的灵活特点与矩阵型方法的公式简洁的优点,提出了内部元素联系矩阵这一概念,保持了刚度矩阵和质量矩阵的物理特性和内部元素的关联性的同时,有效的降低了求解增量方程组的欠定性,而且仅用前几阶试验频率和振型就能有效的修改系统的动力特性。最后分别用前两阶和前三阶试验频率及振型修正一个楼板结构和一个平面框架结构,表明了本方法的有效性和鲁棒性