测量数据点的高精度B样条曲线拟合算法

为提高曲线重构的效率,提出了关键点提取算法,用于三维测量型值点的B样条曲线逼近.根据离散曲率分析提取具有曲率极值的型值点作为初始关键点,再根据初始关键点和型值点的参数值构建的节点矢量,确保最小二乘矩阵满秩,用最小二乘法反算控制顶点.通过Hausdorff距离衡量逼近曲线与型值点间的逼近偏差,设定偏差阈值和多点调整算法,确定新增关键点的位置区间,根据形状指数分析找到新增关键点的精确位置,通过不断迭代找到满足逼近允差要求的最终关键点和控制顶点.实例验证表明,同一逼近允差前提下,新算法在迭代计破算时间、迭代次数及最终所得控制顶点个数等方面优于其他方法.     

无网格法结构拓扑优化模型的GPU并行加速求解及应用

基于无网格法的连续体结构拓扑优化,具有计算精度高、可消除传统拓扑优化中的数值不稳定性等优势,然而无网格法结构拓扑优化模型的求解存在计算耗时长的问题。为此引入GPU(Graphic processing unit,GPU)并行加速技术,开展无网格法结构拓扑优化模型的GPU并行加速求解及应用研究,以缩短拓扑优化模型的求解耗时。基于交叉节点对思想构建了拓扑迭代中刚度矩阵的GPU并行组装流程,结合CUDA(Compute unified device architecture,CUDA)库函数与预处理共轭梯度法实现了离散方程的GPU并行加速计算,且通过提前计算并存储形函数及其导数值以避免重复计算,建立了无网格法拓扑优化模型的GPU并行加速求解算法。通过二维悬臂梁算例验证了算法的正确性,完成了二维曲形支架、三维支撑平台以及多工况固支梁的拓扑优化设计,并分析了GPU并行算法的加速性能。算例结果表明所提GPU并行加速算法的计算结果正确,且极大地提高了无网格法拓扑优化模型的求解效率。     

基于无网格局部Petrov-Galerkin法的曲面修复算法

针对三维残缺数据曲面重构的困难,提出残缺点云或有孔洞网格曲面数据修复的新算法,该方法通过拟合进行曲面重构,大大减小了边界节点误差的影响;同时采用基于板壳理论的无网格法,使孔洞曲面修复更光滑,尤其可以更真实地修补出锻压制造的薄板零件.首先应用移动最小二乘法插值对残缺点云进行边界提取,然后给出逐层节点布置算法,最后应用基于最小势能原理的无网格法进行曲面修复,并将通常无网格法中积分圆域改进为多边形域.编写相应程序,经简单二次曲面缺损网格修补验证算法的有效性,结果分析表明误差很小,曲面修复结果理想.为进一步证明算法实用性,对实际薄壳产品的孔洞进行算法应用,修补效果理想.     

基于偶应力理论的自然单元法研究

理论上偶应力理论较传统连续介质力学理论更精确,在研究具有微结构介质的力学行为时具有优势;在数值方法上,采用non-Sibsonian插值的自然单元法,在计算效率和本质边界条件的施加上较采用移动最小二乘插值的无网格方法具有明显的优势.通过采用基于Voronoi图和Delaunay三角化结构的non-Sibsonian插值方法构造近似位移场向量,实现无网格方法中位移边界条件的直接精确施加;将自然单元法与偶应力理论相结合,运用广义变分原理,推导出基于偶应力理论的无网格自然单元法的离散控制方程,给出基于偶应力理论的自然单元法.并将其应用于薄梁的弯曲问题,数值计算结果验证方法的正确性和有效性.     

基于复合Zernike矩相角估计的图像配准

提出了一种基于复合Zernike矩相角估计的图像配准方法.首先,利用尺度不变检测子Harris-laplace检测图像中的兴趣点作为初始特征点,计算以兴趣点为中心、邻域具有尺度不变性的Zernike矩;提出一种鲁棒的相角估计方法,用于估计两个归一化区域的旋转角度值.然后,利用Zernike矩的幅值和相角信息,通过比较每个兴趣点邻域Zernike矩的相似度提取出初始匹配点.最后,提出一种迭代角度修正算法用于精确估计变换参数,并对输入图像进行几何变换后将两幅图像配准.实验结果表明,该算法可在尺度缩放、任意角度旋转以及噪声等复杂条件下实现图像的高精度配准.当旋转角度误差小于20°时,图像的平均覆盖率达到94.125％,有效降低了误匹配的概率.     

无网格法在形状优化中的应用研究

建立了结构形状优化的数学模型，根据无网格法的离散策略定义了节点位移的设计速度域；引入Lagrange乘子法和罚函数来施加边界条件，借助直接微分法，分别建立了一种离散型的基于无网格Galerkin法的设计灵敏度分析算法；将建立的优化算法结合曲线描述方式对两个工程应用实例进行了形状优化研究，并与基于有限元优化的结果进行了比较，所得结果能够满足工程实际的需求。     

复杂曲面加工检测中的精确定位方法

测量数据的精确定位是实现复杂曲面加工检测的关键,针对其在初始变换估计和最近点计算等方面存在的问题,提出一种快速、精确的定位方法.该方法以曲面的曲率为联系特征,建立起满足角度、距离约束的对应关系,能够实现测量数据的初始定位,从而为后续迭代算法向全局最优收敛提供一个良好的初始变换.进而以Bernstein多项式算术运算为基础,给出一种新的最近点计算方法,能够克服传统方法需要给定初始迭代点的不足.最后利用基于最小二乘的迭代算法完成测量数据定位的精确调整,达到全局最优的目标.试验结果显示,所提出的方法快速、可靠,并且具有良好的定位精度.     

基于多边形分解的质心定位算法

节点定位技术在无线传感器网络的应用中起到很重要的作用。为了能准确定位未知节点,确定未知节点的坐标,提出了一种新的质心定位算法——基于多边形分解的质心定位算法。该算法将锚节点构成的多边形分解成三角形,然后通过未知节点与邻节点交换信息,判断未知节点位于哪个三角形内,计算未知节点所在三角形的质心,最后用三角形三个顶点的RSSI值修正三角形的质心,将其作为未知节点的坐标估计。仿真表明新算法的定位精度比传统的定位算法有很大的提高。     

逆向工程中散乱点云变尺度配准算法研究

针对传统散乱点云配准算法收敛区间与配准精度之间的矛盾,提出一种变尺度点云配准算法.构造一种基于重合点计数点云配准测度函数;对测度函数的高斯平滑过程进行研究,并对尺度参数对测度函数性能的影响规律进行分析;根据测度函数在大尺度参数下平滑但存在极值偏移,在小尺度参数下全局极值位置精确但存在局部极值的特点,提出一种尺度参数可变的散乱点云配准算法;借鉴模拟退火算法的思想,通过对比选定Lundy退化策略作为算法的尺度衰减策略;采用曲率约束进行控制点筛选并利用快速高斯变换进行测度函数值的计算以提高算法效率;利用合成数据和实测数据进行对比试验,结果基于变尺度策略的散乱点云配准算法具有更加广泛的收敛区间和更高的配准精度.     

视觉测量系统的相机校准

提出了一种利用虚拟立体校准模板的有效相机校准技术.通过红外发光二极管按照预定路径在三坐标测量机上移动,构成精确的虚拟立体校准模板.校准过程中考虑了径向畸变和切向畸变.采用二次高斯曲面拟合,精确地提取像点的质心坐标.校准过程包括线性参数估计和基于最大似然估计的非线性校正.首先采用线性方法对部分参数进行初始估计,然后再通过基于最大似然估计的非线性最小化获得所有的参数值.该方法可精确获取图像点坐标和空间点坐标,能够实现快速、有效收敛.实验结果表明,该校准技术能够满足视觉测量系统的要求,也可以满足视觉测量系统对相机参数的特殊要求.     

Stereological analysis of the spatial Poisson–Voronoi tessellation

Stereological model tests and parameter estimators for the spatial Poisson–Voronoi tessellation are discussed. The tests aim to discriminate the Poisson–Voronoi tessellation from more regular or more irregular tessellations. The power of the model tests under some special parametric alternative hypotheses is investigated by simulation. Among the tests considered, the most powerful test is based on the variance of the section cell areas. Various stereological estimators for the model parameter of the spatial Poisson–Voronoi tessellation are compared with respect to their bias and variance by means of a Monte–Carlo study. Formulae are given for variance prediction. An estimator based on vertex counting is found to be the best. Robustness is investigated by applying the estimators to Voronoi tessellations generated by other point process models.     

Voronoi based discrete least squares meshless method for heat conduction simulation in highly irregular geometries

A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM(Voronoi based Discrete Least Squares Meshless) is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares(MLS) shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns(in this particular study, the temperatures at the nodal points) near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method(FEM) when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries and at the same time possesses a high convergence rate which its accuracy is not sensitive to the arrangement of the nodal points. The novelty of this paper is the use of Voronoi concept in determining the weight functions used in the formulation of the MLS type shape functions.     

弹性力学中无网格和有限元耦合的元胞自动机算法

结合有限元和无网格算法的优势,提出了一种元胞自动机算法用以求解二维弹性力学问题。该算法将二维模型离散成一系列节点,这些节点被分成有限元群和无网格群。有限元区域被定义在问题的边界附近,其中的任一节点和其周围相邻点的力学关系通过有限元单元建立;无网格区域定义在远离原理问题边界处,其中的节点之间的关系借用有限元中的位移插值概念建立。无论处于有限元区域还是无网格区域,任何一个节点都被置于元胞自动机的框架下进行处理,即节点的位移通过元胞自动机进行求解。与有限元方法相比,所提出的元胞自动机算法无需采用高斯消去法等传统系统求解器,而是通过元胞自动机的自动演化解决问题。依据该算法,有限元和无网格方法可以实现无缝连接。数值算例验证了该算法的新颖性和正确性。     

特征保持点云数据精简

由于三维扫描设备采集的点云数据庞大,本文提出了一种特征保持的点云精简方法以在减少冗余数据的同时更好地保持原始曲面的几何特征。首先,利用K均值聚类法在空间域对点云全局聚类,对点云构建K-d树并以K-d树的部分节点作为初始化聚类中心。然后,用主成分分析法估计点云法矢和候选特征点,遍历每个聚类,若类中包含特征点则将该类细分为多个子类,细分时将聚类映射到高斯球。最后,基于自适应均值漂移法对高斯球上的数据进行分类,高斯球上的聚类结果对应为空间聚类细分结果,各聚类中心的集合为精简结果。以多个实物模型为例验证了算法的有效性。结果表明,本文方法精简的点云在平坦区域保留少数点,在高曲率区域保留更多的点。相比于非均匀网格、层次聚类、K均值点云精简法,该方法对包含尖锐特征的曲面精简误差最小,更好地保留了原始曲面的几何特征。     

Free vibration and dynamic response analysis by Petrov-Galerkin natural element method

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of twodimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.     

ADAPTIVE RIGID-PLASTIC MESHLESS GALERKIN METHOD AND ITS APPLICATION IN ANALYSIS OF EXTRUSION PROCESSES

Under the hypothesis of the rigid-plastic material,specific efforts are placed on the deve-lopments of the key simulation techniques of the meshless Galerkin method because of the complexity of the deformation process as well as the generality and atomization of the simulation procedures for non-steady state large deformation plastic processes,therefore,an adaptive rigid meshless Galerkin method is developed. The influence domain control method is used in the least square approximation by dynamic evaluation of the magnitude of the influence domain and the effective control of the amount and the positions of the points in the least square approximation in order to improve approxi-mation precision. The amount of the Gauss integration points in the discrete domain is maintained in a considerable magnitude in order to ensure the integration precision in the discrete domain. The length of the frictional boundary of the plastic deformation process may be getting longer when its deforma-tion is getting severe. Thus,the densities of the boundary points of some places get lower. The adap-tive boundary points setting method is employed to improve the approximation precision of the boundary points and enhance the constraint of the boundary condition by adaptive control of boun-dary point density. Some typical extrusion processes are analyzed,detail simulation results such as the deformation field,velocity field,effective strain field,effective strain rate field,the volume loss curve and load-stroke curve are obtained. The effectiveness of the method developed is demonstrated and the precision of the meshless simulation is proved by overall comparison with the results obtained by using the commercial software deform.     

An adaptive procedure based on combining finite elements with meshless methods

This paper presents a new method for combining finite elements with meshless methods, which increases the accuracy of computational solutions in a coarse mesh by adding nodes in the domain of interest. The present method shares the features of the finite element and meshless methods such as (a) the meshless interpolation of the MLS type is employed; (b) integration domains are consistent with support domains; and (c) essential boundary conditions can be applied directly. In the present method, a ground mesh with triangular or quadrilateral elements is constructed to define polygonal support domains, and then additional nodes are placed arbitrarily in a domain without the reconstruction of a mesh. The method is very useful in an adaptive calculation, because nodes can be easily added or removed without any remeshing process. This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho Hyun-Gyu Kim received his B.S. degree from Seoul National University in 1990. He then received M.S. and Ph.D. degrees from KAIST in 1993 and 1998, respectively. Dr. Kim is currently a Professor at the Department of Mechanical Engineering in Seoul National University of Technology, Korea. His research interests include multi-physics coupling analysis, interfacing non-matching meshes, development of special elements, and inverse problems.     

用随机无网格点插值法分析齿轮弯曲疲劳强度的可靠性

用摄动随机无网格点插值法（PSMPIM）分析了齿轮弯曲疲劳强度的可靠性。在无网格点插值法中，所求解问题的域由分布的节点表示；并且利用具有Delta函数性质的多项式进行节点插值，为此，很容易类似有限元法一样处理本质边界条件。同时利用摄动技术，建立了随机结构分析的摄动随机无网格点插值法。并应用随机无网格点插值法分析了齿轮弯曲疲劳强度的可靠性。数值实例表明在随机结构分析与可靠性计算方面随机无网格法具有明显的优势。