非线性Hammerstein本征值问题的非平凡解

运用锥理论和拓扑方法研究一类非线性Hammerstein本征值问题的非平凡解．最后,把抽象结果应用于研究Lidstone本征值问题的非平凡的存在性．     

正交叠层复合材料板弯曲问题辛方法研究

基于变分原理,利用辛对偶方法分析叠层复合材料板弯曲问题。于是在由原变量及其对偶变量组成的辛几何空间内,许多有效的数学物理方法如分离变量法和本征函数展开法等均可直接应用于叠层梁弯曲问题的求解,推导矩形板本征值超越方程和本征向量的解析表达式。通过算例验证理论推导的准确性,结果显示取前几项本征值就可达到较高的精度。     

基于大气电场特征的雷电临近预警方法

针对现有雷电预警技术适用性不强的现状,提出了一种基于大气电场特征的雷电临近预警方法。首先对比了典型雷暴天气与非雷暴天气大气电场的幅值特征;然后采用希尔伯特-黄变换(HHT)提取了二者固有的本征模态分量;最后运用雷电定位系统记录的一次雷暴过程进行预警反演分析。结果表明:结合大气电场幅值及其本征模态分量特征的雷电临近预警方法在不同地区具有很好的运行效果,且命中率约为0. 78、TS评分达到0. 615。该雷电临近预警方法使得在雷暴来临前采取主动性规避措施成为了可能,进一步地提高了雷害防护水平。     

阻燃织物的辐射热防护性能研究

介绍织物的辐射热防护性能 RPP 测试原理。选用 25 种阻燃面料进行测试,分析辐射热源强度与阻燃织物 RPP 值 的关系。借助于 SEM 测试对受热实验后织物微观变化进行表 征,分析实验现象及实验后织物的宏观变化。结果表明：在热流密 度较低的情况下,影响织物辐射热防护性能的主要因素是织物物 理结构参数;本征型阻燃织物的 RPP 值随着热流密度的增加而 减小,非本征型阻燃织物的 RPP 值随着热流密度的增加出现减 小、增加交替现象。热流密度增大时,烧伤时间减小的幅度大于辐 射热流密度增加的幅度,RPP 值总体上呈减小趋势。RPP 值不 宜作为评价织物在宽分布辐射热流量下的辐射热防护性能的唯一 指标。随着辐射热源强度的增加,本征型阻燃织物外观几乎没有 变化,而后整理织物和混纺织物炭化分解逐渐加深。     

一种用CEEMDAN和排列熵去除脉搏信号噪声的方法

为去除脉搏信号中的噪声,提出了一种将自适应噪声完备集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和排列熵(permutation entropy,PE)相结合的方法。首先由HK-2000C脉搏信号传感器采集信号,对采集的脉搏信号用CEEMDAN得到一系列的本征模态分量(intrinsic mode function,IMF);然后计算各个本征模态分量的排列熵值,根据排列熵值选定阈值,确定并处理代表噪声的本征模态分量;最后对处理后的模态分量进行重构,从而消除脉搏信号中的噪声。实验结果表明,与经验模态分解(empirical mode decomposition,EMD)去噪方法和集合经验模态分解(ensemble empirical mode decomposition,EEMD)去噪方法相比,所提方法对脉搏信号去噪的效果更好。     

随机风荷载作用下超大型冷却塔结构屈曲分析

利用屈曲本征方程的形式解推导出随机屈曲本征值满足的概率密度演化方程.以对数风剖面中的10 m高平均风速和地面粗糙度为随机变量,分析了超大型冷却塔的随机屈曲承载力.进而,计算出其均值及标准差.结果表明,随机屈曲承载力的概率密度函数具有一般形式,不易采用常见的概率分布模型拟合.随机屈曲承载力均值与按照均值参数计算的屈曲承载...     

基于EMD_SVD的矿山微震与爆破信号特征提取及分类方法

针对矿山微震与爆破信号难以识别的问题,提出了基于经验模态分解(EMD)和奇异值分解(SVD)的矿山信号特征提取及分类方法。首先对微震与爆破信号进行EMD分解,再借助相关系数和方差贡献率筛选得到主要本征模态分量为IMF1~IMF6,进而利用SVD计算主要本征模态分量构成矩阵的奇异值σ_i(i=1,2,...,6),最后应用支持向量机(SVM)对用沙坝矿微震与爆破信号进行分类。结果表明:微震与爆破信号的奇异值σ_1,σ_2和σ_3差异较大,且σ_1(28)7.5作为识别分界值时准确率达到了88.25%;SVM法识别效果优于BP神经网络法、Bayes法和单一奇异值分界值法,且SVM法准确率达到了93.0%。由此,该方法可为矿山微震与爆破信号特征提取和分类提供一种新方法。     

一种基于解调技术的电机故障诊断方法

本文针对电机故障诊断提出了一种解调方法。首先,对复杂信号进行经验模式分解,得到若干个本征分量,再对包含调制信号的本征分量进行包络解调以提取故障信息。该方法可实现故障信息的有效分离,提高了诊断信号的信噪比,为基于信号分析的故障诊断提供了一种可行的途径。     

基于LPIND的硅基等离子天线

首先介绍了LPIND(Lateral Positive-Intrinsic-Negative Diode)及其在硅基等离子天线方面的应用,并对LPIND进行建模,仿真分析了不同SOI(Silicon On Insulator)埋层材料对LPIND本征区载流子浓度的影响,仿真结果显示,LPIND的自加热效应会降低本征区载流子浓度,通过改变埋层材料,增加埋层的热导率,可以减弱自加热效应。其次给出了LPIND本征区电导率的仿真结果,完成了基于LPIND的半波偶极子天线的设计与仿真,仿真结果显示,本征区电导率和硅衬底厚度会影响天线的回波损耗(S11)。最后总结了降低LPIND静态功耗的有效设计方法。     

基于本征模态修正的POD法在风场重建中的应用

POD法是风工程中常用的风场重建方法,但是在重建过程中,部分重建测点风压时程的方差与风洞试验数据相比会有140%以上的偏差。通过分析某高层建筑风洞试验的刚性模型测压试验数据,首先对结构表面风场进行POD时域分解,然后对主坐标进行频域分析,结果表明前3阶主坐标及其对应的本征模态值对重建风压时程的方差值起到91%以上的作用,其中第1阶主坐标的作用超过58%。最后以试验风压时程的方差值为目标,通过修正第1阶本征模态值,对偏差较大测点的风压场重建进行改进,使重建风场的方差值与实际风场方差值的差距缩小到10%以内。     

Computation of Eigenvectors on Concurrent Processors

Suppose a real symmetric general matrix A is reduced into a real symmetric tridiagonal matrix C by either Householder's method or Givens method. Eigenvalues of the tridiagonal matrix are the eigenvalues of the original matrix since they are similar. After eigenvalues are calculated, the eigenvectors of the original matrix may be obtained by the eigenvectors of the tridiagonal matrix and the transformation matrices used in either Householder's or Givens tridiagonalization methods [1]. In these methods, however, transformation matrices usually are not stored due to memory considerations. Only critical information such as rotation angles in Givens method is saved. Generally, the recovery of all transformation matrices involves more computation than the tridiagonalization procedure. Therefore such a scheme is rarely used. In this paper, a serial eigenvector solution procedure, assuming eigenvalues are known, is first described. This procedure applies Gauss elimination with diagonal pivoting on the characteristic equations. A parallel procedure is then developed by using scattered column decomposition. The efficiency and speedup are given in terms of problem and machine parameters. The efficiency of the parallel algorithm increases as the number of scattered columns assigned to each processor increases, and decreases as communication cost between processors increases.     

Spectral proper transformation of wind pressure fluctuations: application to a square cylinder and a bridge deck

The results of spectral proper transformation (SPT) analyses applied to the pressure fluctuations on a square cylinder and on a bridge box deck are presented in this paper. The main objective of the paper is that of comparing the results obtained using SPT with those obtained through a covariance proper transformation (CPT) analysis, to understand whether additional information is provided by SPT with respect to CPT. The meaning of the frequency dependency of the spectral eigenvalues and eigenvectors is also investigated. It is observed that a correspondence between SPT and CPT modes can be found in some cases, if the phase shift between the components of the SPT complex modes is properly accounted for. It is also found that the frequency variation of the SPT eigenvalues is related to the characteristic frequencies of the different physical phenomena causing the pressure fluctuations.     

State-space methods for calculating concentration dynamics in multizone buildings

This work explores analytic solutions to contaminant transport in multizone systems as a means of solving concentration dynamics more rapidly and providing insight into system behaviour. A general formulation is developed that is consistent with state-space theory. This is used to provide general and specific solutions for the concentration time series. In particular, an analytical expression is presented for the case of constant system parameters and constant input conditions using the eigenvalues and eigenvectors for the case of a diagonalisable state matrix for the multizone system. A method for using this expression to solve concentrations over a series of varying building and input states is developed, with potential for use as a rapid means of calculating concentrations at any time. In principle, this method could be used as a complementary method for solving concentration dynamics within multizone software. Analytical expressions for cumulative exposure for the same case are also presented. The characteristic behaviour of the solutions and their dependence on the eigenvalues and eigenvectors of the state matrix are explored for the steady state case and the decay solution. In particular, the behaviour in the late decay phase is shown to be characterised by a single decay rate, given by the smallest magnitude eigenvalue, and a fixed concentration ratio, given by the associated eigenvector. The independence of the concentration ratio in this phase to the initial conditions is also demonstrated. Two example cases are used to illustrate these and additional features.     

An approach for choosing optimal actively-stretched cablesof cable-strut tensile structures based oneigenvalue of sensitivity matrix

施工时合理选择主动张拉索是控制索杆张力结构预张力偏差的主要措施。以单元的预张力偏差平方和作为评价整体结构预张力偏差的指标,通过对反映单元预张力偏差与索长误差关系的灵敏度矩阵进行谱分解,将该指标表示为索长误差与灵敏度矩阵的特征值和特征向量的解析关系式,理论上解释了选择不同主动张拉索会使灵敏度矩阵特征值发生变化,从而直接影响到对结构预张力偏差的控制效果。由于灵敏度矩阵特征值具有衰减迅速的特点,故采用其一阶特征值和特征向量可有效估计结构的最不利预张力偏差。进一步以灵敏度矩阵的一阶特征值为评价指标,基于遗传算法提出了一种主动张拉索的优选方法。以一实际索杆张力结构为例,进行不同条件下的主动张拉索优选分析,其结果验证了优选方法的有效性。     

利用刚度矩阵法求解多层弹性半空间体的温度应力

从热弹性力学的基本方程出发,采用Hankel 积分变换和Laplace 积分变换等数学手段,首先推导出了单层弹性半空间轴对称体的温度应力问题的刚度矩阵,然后按传统有限元的方法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程组,再对其进行Hankel 和Laplace 积分逆变换就可解出在外荷载和温度联合作用下多层弹性半空间轴对称问题的解析解。由于刚度矩阵的元素中不含有正指数项,计算时不会出现溢出的现象,从而克服了传递矩阵法的缺点。在推导过程中,因不用事先人为的选择应力函数,使得问题的求解更加合理,同时也为进一步研究这类问题如湿度场、动力学等奠定了理论基础。最后,文中还给出了计算实例来证明推导结果的正确性。     

基于哈密顿理论的薄壁结构双向弯曲分析

从能量变分原理出发,由勒让德变换引入对偶变量,导出了薄壁结构双向弯曲问题的哈密顿对偶求解体系,将薄壁结构的控制微分方程转化为哈密顿对偶方程,其系统矩阵具有辛矩阵的特性,可用精细积分法求该体系的高精度数值解。算例计算结果表明,本方法具有较高的精度和适用性,并可方便地用于变截面薄壁结构的计算。     

Reliability analysis using object-oriented constrained optimization

A practical procedure is presented for reliability analysis involving correlated nonnormals. Equivalent normal transformation is performed as in the first order reliability method; the correlation matrix is used as it is without orthogonal transformation. Performance functions appear as simple spreadsheet cell objects but may embody substantial user-created program codes. The multidimensional equivalent dispersion ellipsoid is likewise a single cell object that contains various spreadsheet routines for equivalent normal transformation and matrix operations. The procedure can be viewed as the constrained optimization of the equivalent hyperellipsoid (yielding the reliability index) in the original space, and is automatic and efficient in the ubiquitous spreadsheet platform. Different probability distributions can be selected at ease and conveniently transformed to equivalent normals using a short program code given in the paper. Illustrations are presented using a three-variate simple performance function and various combinations of ten common distributions. This is followed by two relatively complicated examples, namely an asymmetrically loaded beam on Winkler medium, and a complex strut with implicit performance function. The probabilities of failure inferred from reliability indices are compared with Monte Carlo simulations. The simplicity, transparency and flexibilities of the object-oriented constrained optimization approach are demonstrated.     

An Investigation on Optimal Initial Self-Stress Design of Tensegrity Grid Structures

To achieve the optimal feasible force density vector of a given geometry configuration tensegrity grid structure, an efficient procedure is presented for optimal initial self-stress design of tensegrity grid structures by consecutively solving two linear homogeneous systems in conjunction with a minimization problem. The nonlinear constrained optimization algorithm, known as the Interior-Point Method (I-PM), is utilized to obtain the minimal solution, leading to a set of force densities which guarantee the non-degeneracy condition of the force density matrix. The evaluation of the eigenvalues of tangent stiffness matrix is also introduced to check the geometric stability of the tensegrity grid structures. Finally, three numerical examples have been investigated comprehensively to prove the capability of the proposed method in optimal initial self-stress design of tensegrities. Furthermore, division of number of member group has been discussed in detail for the purpose of demonstrating the efficiency of the proposed method in seeking initial force densities of tensegrity grid structures.     

Hermitian Subspace Iteration

The subspace iteration for symmetric real matrices is extended to the partial eigensolutions for Hermitian matrices. Only the lower triangle of the Hermitian matrix in variable band form is required and processed. Efficient and compact fortran subroutines are developed for computing the lowest modes in ascending order of absolute eigenvalues. The method is suitable for incore microcomputer solution of the sparse Hermitian eigenvalue problem.     

Buckling of laminated skew plates

A general high precision triangular plate bending finite element has been extended to the buckling analysis of laminated skew plates. This procedure involves development of the transformation matrix between global and local degrees of freedom for nodes lying on the skew edges and suitable transformation of the element matrices. The accuracy of the present formulation has been verified against literature values. New results are obtained for antisymmetric angle-ply and cross-ply laminated skew plates. In this analysis, the critical buckling loads for different skew angles with various lamination parameters, such as number of layers, fibre orientation angle, different boundary (simply supported, clamped) and loading (uniaxial, biaxial) conditions, have been presented.