基于L型线阵的二维分布源参数估计方法

针对二维分布源信号波达方向估计问题,提出了一个新的二维分布源模型及其参数估计方法。将基于角度信号密度函数的一维相干分布源模型扩展至二维,推导了二维分布源的广义阵列方向向量。在L型线阵下,利用广义MUSIC算法,首先估计出俯仰角及其扩散参数,然后利用估计出来的俯仰角及扩散参数对方位角及扩散参数进行估计。仿真实验表明,所提出的二维相干分布源参数估计算法具有良好的定向精度。     

非球面光学零件研磨中安装倾斜误差的影响

针对研磨中工件的安装倾斜误差,提出了导致工件面形误差的分析方法,建立新、原坐标系,应用坐标变换,推导出工件曲线上各点相对理想曲线对应点的误差模型。工件安装倾斜角度不同、形状及精度要求不同导致的面形误差不同,利用模型分析了这几种情况对面形误差的影响,工件面形误差随安装倾斜角度的增大而增大,当安装倾斜角度由0.1°~1°变化时,工件面形负误差由-0.0030mm增大到-0.0448mm,增加了一个数量级;工件面形误差沿着曲面中点向边缘逐渐增大;相同的安装倾斜角度对大陡度曲面的面形误差影响较大。因此,在研磨中等精度要求的工件时,安装倾斜角度不应超过0.1°,陡度参数不应小于100mm。     

基于视觉的内窥镜端部位姿模型分析

针对在假设内窥镜端部固定不变的条件下进行基于光纤光栅传感阵列的内窥镜柔性杆的三维重建存在的问题,提出了基于标志点的内窥镜端部位姿视觉检测模型;利用视觉技术和通过标志点的空间位置信息来获取内窥镜端部位姿的方法,建立了基于主元分析方法及最小二乘法分析标志点位置信息误差对内窥镜端部姿态的影响的方法.模拟分析结果表明,当三个标志点的位置信息误差满足高斯分布且方差在0～3mm之间时,其姿态的最大误差角度为0.59°.通过实验证实了理论计算方法能够有效地利用带有误差的位置信息求解内窥镜端部位姿及误差的大小,为微创手术器具的位姿检测提供了理论和实验基础.     

执行JJG99—90《砝码检定规程》的体会

在新规程的执行中，如何控制级砝码的误差源是1个新课题。同时，大量的原3等砝码如何套级，套什么级合适，也是有待进一步解决的问题。     

时间延迟下双臂空间机器人工作空间轨迹跟踪的改进控制方法

研究了载体姿态受控、位置不受控制情况下, 具有时间延迟的漂浮基双臂空间机器人载体姿态与末端爪手工作空间协调运动的动力学建模与控制问题。利用系统动量守恒关系及Lagrange方法, 建立了漂浮基双臂空间机器人的系统动力学模型及运动Jacobi 关系。以此为基础, 考虑到系统存在时间延迟的复杂情况, 利用Taylor级数展开, 导出了适用于时间延迟情况下控制系统设计的数学模型。利用该模型, 提出了一种双臂空间机器人在时间延迟情况下的改进计算力矩控制方案。而后, 运用Lyapunov 第二类方法, 结合图形分析以及范数的方法证明了该控制系统的稳定性。数值仿真结果证实了该控制方案在系统存在时间延迟的情况下, 仍然可以有效地控制双臂空间机器人, 稳定地追踪工作空间的期望轨迹。     

考虑风切变的风电场尾流模型实验研究

针对当前一维和二维尾流模型只能预测平坦地形风电场内风力机轮毂中心高度平面内的风速分布问题,该文基于Jensen模型,考虑风切变效应和高斯分布特点,提出一种预测复杂风电场内垂直高度平面风速分布的尾流模型。为分析垂直高度平面内尾流分布特点和验证所提出模型的准确性,采用两台不同类型的地基式多普勒激光雷达在河北某风电场进行测风实验。实验数据表明由于风切变效应的影响,垂直高度平面内尾流风速分布呈现非对称分布特点。与此同时,通过对比两个不同下风向位置处实测数据和尾流模型预测风速,结果表明新提出的尾流模型可以很好地预测垂直高度平面风速分布特点,与实测数据吻合度高,符合真实的尾流流场分布。     

结合面静态接触参数的统计模型研究

基于对粗糙表面形貌统计分析的基础上,综合考虑微凸体的完全弹性、弹-塑性和完全塑性三种变形机制,建立了结合面的接触面积、接触载荷及接触刚度的统计模型。该模型揭示了结合面接触参数与材料性能参数及粗糙表面形貌参数之间复杂的非线性关系。在不同的微凸体高度随机分布及塑性指数条件下,对接触参数进行预估和对比研究。结果表明,修正的指数分布对高斯分布有着较好的近似,而简单的指数分布与高斯分布之间的误差较大,且相差1至3个数量级;接触表面间距减小时,接触参数值均呈现增大的趋势;塑性指数增大时,接触载荷和接触刚度都随之增大,而接触面积的变化较小。     

反应扩散方程的奇异摄动问题的最小二乘的有限元方法（英文）

对于一种类型的反应扩散方程的奇异摄动问题,当利用标准能量范数通过有限元方法进行误差计算时,该范数表现为一个弱范数.因为奇异摄动问题的参数使该范数的每个部分有不同的收敛阶,所以范数不稳定.这篇文章中我们引进一个新的强范数,并利用这个新范数在一维空间下构建奇异摄动反应扩散问题的最小二乘有限元方法 (LSFEM)及误差估计,通过数值算例对理论结果进行验证.     

时变工况下行星轮轴承特征分布拟合与智能故障诊断

行星齿轮箱中行星轮轴承运动复杂,振动信号成分多样且呈非线性,时变工况下特征频率随时间变化,人工识别故障特征更为困难。针对该问题,提出基于对抗变分自编码的智能故障诊断模型。获取样本时频图来揭示样本中包含的时变特征;利用模型中的变分自编码器自适应提取时频图特征,为赋予特征显式意义,引入多维独立高斯分布并进行采样,根据类别信息对样本点进行变换,使其服从新的多维独立高斯分布,确保样本点中的每个元素都有自己的专属分布;通过对抗机制,使特征逼近变换后的对应类别的分布样本,且服从新的多维独立高斯分布,从而实现用已知的分布拟合未知的特征分布,同时通过控制分布强化不同类别特征间的差异性,改善特征的模式识别性能;利用优化后的特征对分类器进行训练并识别测试样本特征。模型经行星齿轮箱实验台数据进行了验证。研究表明,该模型能够使提取的特征服从给定的先验分布,通过控制分布强化了不同类别特征间的差异性,提高了特征的聚合性能,有效诊断了行星轮轴承故障,与自编码和变分自编码器相比,表现出一定的优越性。     

大气湍流畸变相位屏的数值模拟方法研究

利用功率谱反演法和Zernike多项式展开法对符合Kolmogonov统计规律的大气湍流畸变波前相位屏进行了数值模拟研究。通过对比模拟相位屏的相位结构函数与理论结果的差异分析模拟相位屏的准确性。结果表明,功率谱反演法产生的相位屏在高空间频率部分与理论相符,在低空间频率部分明显偏离理论值,通过次谐波补偿有效改善低频不足,次谐波级数达到4级足够;Zernike多项式展开法产生的相位屏的低空间频率成分与理论相符,而高空间频率成分不足随着所用Zernike阶数的增加而有所改善,但同时也带来计算量增大的问题。     

Image field distribution model of wavefront aberration and models of distortion and field curvature

The distribution model of wavefront aberrations, which takes on a significant role in the designs and alignments of imaging optical systems without vignetting, is newly presented. This model decomposes the complicated distributions into the characteristic components, which clarifies the alignment criteria. For the actual alignments, only small displacements (decentering, tilt, and surface distance) of rotationally symmetric surfaces in the system are assumed. Then, the model, which regards the aberration distributions of the system as the sum of the contributions of each surface, is extended for the system with surface displacements. As a result of the derivation, it is concluded that the aberration distributions in the rotationally nonsymmetric systems can be expressed as the sum of several folds of rotationally symmetric components. In addition, it is presented that, based on this model, suitable distribution models, even of the arbitrary higher order, can be constructed for any aberration coefficients in various optical systems.     

Aliasing errors due to quadratic nonlinearities on triangular spectral /hp element discretisations

In this paper, consideration is given to how aliasing errors, introduced when evaluating nonlinear products, inexactly affect the solution of Galerkin spectral/hp element polynomial discretisations on triangles. A theoretical discussion is presented of how aliasing errors are introduced by a collocation projection onto a set of quadrature points insufficient for exact integration, and consider interpolation projections to geometrically symmetric ollocation points. The discussion is corroborated by numerica examples that elucidate the key features. The study is first motivated with a review of aliasing errors introduced in one-dimensional spectral-element methods (these results extend naturally to tensor-product quadrilaterals and hexahedra.) Within triangular domains two commonly used expansions are a hierarchical, or modal, expansion based on a rotationally non-symmetric collapsed-coordinate system, and a Lagrange expansion based on a set of rotationally symmetric nodal points. Whilst both expansions span the same polynomial space, the construction of the two bases numerically motivates a different set of collocation points for use in the collocation projection of a nonlinear product. The purpose of this paper is to compare these two collocation projections. The analysis and results show that aliasing errors produced using a collocation projection on the rotationally non-symmetric, collapsed-coordinate system are significantly smaller than those for a collocation projection using the rotationally symmetric nodal points. In the case of the collapsed coordinate projection, if the Gaussian quadrature order employed is less than half the polynomial order of the integrand, then it is possible for the aliasing error to modify the constant mode of the expansion and therefore affect the conservation property of the approximation. However, the use of a collocation projection onto a polynomial expansion associated with a set of rotationally symmetric nodal points within the triangle is always observed to be non-conservative. Nevertheless, the rotationally symmetric collocation will maintain the overall symmetry of the triangular region, which is not typically the case when a collapsed coordinate quadrature projection is used.     

Cumulative Damage Models for System Failure With Application to Carbon Fibers and Composites

To estimate the probability distribution of the tensile strength of materials, specimens tested are typically of a variety of sizes, or “gauge lengths.” Here, a cumulative damage argument is used to develop new models for the strength of a general system that incorporate the size as a variable and are strong competitors to the commonly used Weibull model. These strength distributions can be represented as three-parameter versions of the Birnbaum-Saunders distribution and the inverse Gaussian distribution. Estimation is discussed and illustrations are presented for experimental strength data for carbon fibers and small composite specimens.     

Symmetric metamaterials based on flower-shaped structure

We proposed new models of metamaterials (MMs) based on a flower-shaped structure (FSS), whose “meta-atoms” consist of two flower-shaped metallic parts separated by a dielectric layer. Like the non-symmetric MMs based on cut-wire-pairs or electric ring resonators, the symmetrical FSS demonstrates the negative permeability at GHz frequencies. Employing the results, we designed a symmetric negative-refractive-index MM [a symmetric combined structure (SCS)], which is composed of FSSs and cross continuous wires. The MM properties of the FSS and the SCS are presented numerically and experimentally.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

Spherically symmetric GRIN amplitude formers

Abstract

A new type of spherically symmetric gradient index element is presented. These elements are able to transform an optical field from a point source with a predetermined radiation pattern into an arbitrary amplitude distribution in the target plane. The design method is illustrated with four examples of amplitude formers that produce irradiance distributions that are constant, Gaussian, triangular and ring-shaped.     

Recent epic code developments for high velocity impact: 3D element arrangements and 2D fragment distributions

This paper presents recent developments in the three-dimensional EPIC-3 code and the two-dimensional EPIC-2 code. The EPIC-3 work provides a new symmetric arrangement of tetrahedral elements which is more accurate than the traditional non-symmetric arrangement. The EPIC-2 work provides an algorithm and examples of fragment distributions which occur after impact. Included are numbers of fragments for various sizes, masses, momenta, and kinetic energies.     

Optimal reinforcement of RC columns for biaxial bending

The Reinforcement Sizing Diagram (RSD) approach to determining optimal reinforcement for reinforced concrete beam and column sections subjected to uniaxial bending is extended to the case of biaxial bending. Conventional constraints on the distribution of longitudinal reinforcement are relaxed, leading to an infinite number of reinforcement solutions, from which the optimal solution and a corresponding quasi-optimal pragmatic is determined. First, all possibilities of reinforcement arrangements are considered for a biaxial loading, including symmetric and non-symmetric configurations, subject to the constraint that the reinforcement is located in a single layer near the circumference of the section. This theoretical approach establishes the context for obtaining pragmatic distributions of reinforcement that are more suitable for construction, in which distributions having double symmetry are considered. This contrasts with conventional approaches for the design of column reinforcement, in which a predetermined distribution of longitudinal reinforcement is assumed, even though such a distribution generally is non-optimal in any given design. Column and wall sections that are subjected to uniaxial or biaxial loading may be designed using this method. The solutions are displayed using a biaxial RSD and can be obtained with relatively simple algorithms implemented in widely accessible software programs such as Mathematica^® and Excel^®. Several examples illustrate the method and the savings in reinforcement that can be obtained relative to conventional solutions.     

Fatigue damage assessment for a spectral model of non-Gaussian random loads

In this paper, a new model for random loads–the Laplace driven moving average–is presented. The model is second order, non-Gaussian, and strictly stationary. It shares with its Gaussian counterpart the ability to model any spectrum but has additional flexibility to model the skewness and kurtosis of the marginal distribution. Unlike most other non-Gaussian models proposed in the literature, such as the transformed Gaussian or Volterra series models, the new model is no longer derivable from Gaussian processes. In the paper, a summary of the properties of the new model is given and its upcrossing intensities are evaluated. Then it is used to estimate fatigue damage both from simulations and in terms of an upper bound that is of particular use for narrowband spectra.     

On Abbe's Theory of Image Formation in the Microscope

We consider a new class of bifurcations that may arise in multiphoton processes inside a coherently driven optical cavity involving more than one mode of the radiation field. For a non-saturable, non-linear medium, a single bifurcation point exists where the symmetric solution bifurcates into a number of non-symmetric solutions. The nature of the bifurcation ranges from a simple pitchfork bifurcation, in the case of four-wave mixing, to more complicated phenomena in higher-order processes. A saturable non-linear medium exhibits similar behaviour for low-input intensities; however, as the input intensity is increased the medium saturates, and at a second bifurcation point the symmetric branch regains its stability. The presence of fluctuations assures the accessibility of the symmetric branch. Thus, for example, for a two-photon absorbing medium we have the possibility of optical tristability involving one symmetric solution and two non-symmetric solutions.