基于响应面的概率集群优化方法

面对实际应用中的大规模优化问题,基于响应面估计的概率集群优化方法以设计变量的概率分布作为优化对象,而非直接对设计变量值进行优化,可适应连续、离散及混合的设计变量类型。采用响应面构建概率集群评估函数的近似模型,并采用置信区间方法在迭代优化过程中不断更新响应曲面以确保近似精度。实验结果表明算法对解决复杂优化问题有效。     

基于空间网格表面距离的插值曲面

主要讨论基于空间网格表面距离的插值曲面.定义了一种空间网格表面距离,基于空间网格表 面距离,给出了两种定义在空间网格上的插值曲面：基于网格表面距离的径向基函数插值曲 面和基于网格表面距离的Kriging插值曲面,讨论了曲面的无穷阶光滑性,给出了一种计算网 格表面距离的折线跟踪算法.作为整体曲面,此类插值曲面与网格表面形状较为相符,比较适 合于局部插值与参数估计,如梯度、法方向的估计等计算.     

一种基于Bezier插值曲面的图像放大方法

章提出了一种利用Ｂｅｚｉｅｒ插值曲面进行图像放大的方法,该方法是为数字图像的第一个色彩分量构造一个分块双三次Ｂｅｚｉｅｒ插值Ｃ＾１曲面的 图像放大等价于以不同的采样速度地该曲面进行采样的过程,实验结果表明,该方法可以大大改善放大图像的效果。     

基于改进朴素贝叶斯的区间不确定性数据分类方法

基于Parzen窗的朴素贝叶斯在区间不确定性数据分类中存在计算复杂度高、空间需求大的不足。针对该问题,提出一种改进的区间不确定性数据分类方法IU-PNBC。首先采用Parzen窗估计区间样本的类条件概率密度函数(CCPDF);然后通过代数插值得到类条件概率密度函数的近似函数;最后利用近似代数插值函数计算样本的后验概率, 并用于预测。通过人工生成的仿真数据和UCI标准数据集验证了算法假设的合理性以及插值点数对IU-PNBC算法分类精度的影响。实验结果表明,当插值点数大于15时,IU-PNBC算法的分类精度趋于稳定,且插值点数越多,算法分类精度越高;该算法可以避免原Parzen窗估计对训练样本的依赖, 并有效降低计算复杂度;同时由于该算法具有远低于基于Parzen窗的朴素贝叶斯的运行时间和空间需求, 因此适合解决数据量较大的区间不确定性数据分类问题。     

插值细分曲面三角剖分研究

把三维参数化曲面的离散化算法应用到三角网格表示的离散曲面上。用一种可生成C1阶连续曲面的插值分割技术——改进蝶形算法，重新构造极限面。用推进波前法在物理空间直接离散化，所以不需要进行参数化。     

一种精度可控的CAD网格模型及轻量化算法的研究

针对现有三维CAD系统中,CAD网格模型显示精度固定,难以动态调整以及细分后网格数量过多等瓶颈问题,在原始模型基础上,结合CAD模型中边、面等几何与拓扑信息,提出了一种精度可控的三维CAD网格模型.根据该模型的结构特点,采用曲面内部插值与边界曲线插值相结合的轻量化分类细分算法来实现模型精度调整,并有效控制细分后的网格数量,可满足三维CAD系统对模型精度可控、减少网格数量的需要.     

基于薄板样条插值算法的巨幅影像分块并行处理

薄板样条函数是空间插值中的一种重要方法。对于巨幅影像数据使用薄板样条函数进行空间插值时,可能会出现运行时间太长,以及计算机内存空间不足或程序运行无响应的问题。针对这些问题,根据薄板样条函数光滑、连续的特点,基于GDAL开源函数库,提出对巨幅影像数据的分块读取,在块内利用并行技术求解线性方程组,确定薄板样条函数,最后进行空间插值的方法。结果表明,该方法可以有效的解决这些问题。     

基于空间多边形三角剖分的曲面分割求交算法

针对传统曲面分割求交方法存在的平面片的选取、遗漏部分交线段以及交线间断 的问题,提出一种基于空间多边形三角剖分的曲面分割求交算法。以等深度分割方法为基础, 避免了交线不连续的问题,当分割达到一定层次时以空间多边形近似曲面片,并对空间多边形 进行三角剖分,以三角形对的交线近似空间多边形之间的交线,进而以空间多边形的交线近似 曲面片的交线,最终得到相交曲面之间的交线。利用曲面片轮廓构造出的空间多边形更加接近 曲面片的真实形状,提高了逼近精度,同时对空间多边形进行三角剖分,提高了求交精度,进 而降低了丢失交线的可能性。实验验证了该算法比传统的分割法更加精确。     

细分曲面求交裁剪算法研究

基于细分曲面的参数化表示,研究了细分曲面的精确求交、裁剪算法。首先对控制网格建立局部坐标系,将细分曲面表示为一系列小的面片,并对每个控制顶点赋予参数值。然后用改进的轮廓删除法细分控制网格,在关联曲面间进行相交性检测,得到近似交点及其参数值,再用迭代法求得精确解。根据用户指定的裁剪区域确定交线的走向,将被裁剪曲面的控制网格面分为保留面、裁剪面和删除面,设置每个裁剪面的裁剪域,从而实现细分曲面的精确裁剪。算例表明,该文的方法简单、有效。     

基于Delaunay三角网的克里金并行算法优化

当采样点数据量较大时, 可以采用Delaunay三角剖分建立三角网来使用局部邻域采样点进行克里金插值. 但是该算法需要对每个插值点拟合半变异函数, 插值点规模大时造成巨大开销. 为此, 本文提出了一种以三角形为单位拟合半变异函数的克里金插值方法, 采用CPU-GPU负载均衡将部分计算优化, 充分考虑不均匀样本对克里金插值效果的影响. 结果表明, 本文算法能够保证不均匀样本集的插值效果, 提升了计算性能且能够保证较高的精度.     

Analysis of gene expression programming for approximation in engineering design

To reduce the computational cost of implementing computer-based simulations and analyses in engineering design, a variety of metamodeling techniques have been developed and used for the construction of metamodels. Metamodels, also called approximation models and surrogate models, can be used to make a replacement of the expensive simulation codes for design and optimization. In this paper, gene expression programming (GEP) algorithm in the evolutionary computing area is investigated as an alternative metamodeling technique to provide the approximation of a design space. The approximation performance of GEP is tested on some low-dimensional mathematical and engineering problems. A comparative study is conducted on GEP and three common metamodeling techniques in engineering design (i.e., response surface methodology (RSM), kriging and radial basis functions (RBF)) for the approximation of the low-dimensional design space. Multiple evaluation criteria are considered in the comparison: accuracy, robustness, transparency and efficiency. Two different sample sizes are adopted: small and large. Comparative results indicate that GEP can achieve the most accurate and robust approximation of a low-dimensional design space for small sample sets. For large sample sets, GEP also presents good prediction accuracy and high robustness. Moreover, the transparency of GEP is the best since it can provide clear function relationships and factor contributions by means of compact expressions. As a novel metamodeling technique, GEP shows great promise for metamodeling applications in a low-dimensional design space, especially when only a few sample points are selected and used for training.     

New formulation of minimum-bias central composite experimental design and Gauss quadrature

Response surface methods provide a powerful tool for constructing approximations to complex response functions. Statistical design of experiments is usually used to select optimal points that minimize the error in the resulting response surface approximation. Traditionally, data points are selected using minimum-variance designs, for example the D-optimal design, which may result in large bias errors for low-order approximation. Minimum-bias criteria have been developed for selecting data points to minimize the bias error of a response surface approximation. The present work developed a minimum-bias counterpart to the popular minimum-variance central composite designs. In addition, a new formulation of the minimum-bias design that assigns unequal weights to the design points, based on Gauss quadrature, is explored. Example problems are evaluated and the results obtained from D-optimal, the traditional minimum-bias, and the new Gauss-quadrature-based minimum-bias designs are compared. It is shown that the Gauss-quadrature-based minimum-bias design criterion results in the most accurate approximations and provides analytical solutions to a wider range of approximation domains than the traditional minimum-bias design. Response surface approximations based on minimum-bias central composite designs are more accurate than those constructed from traditional central composite design. Moreover, it is shown that using weights in regression has little influence on the accuracy of the response surface approximation in Gauss-quadrature minimum-bias designs.     

支持向量回归与常用近似模型的非线性预测性能比较研究

为降低计算成本和提高优化效率,工程实践中广泛应用近似模型拟合或预测非线性系统响应是研究的前沿与热点。引入支持向量回归方法,通过典型数值案例对比分析其与多项式响应面、kriging和径向基函数的非线性预测性能。利用箱线图直观的证明支持向量回归的非线性预测性能明显优于多项式响应面、kriging和径向基函数,且支持向量回归的预测精度对DOE的依赖性最弱,体现出良好的稳健性能,进一步验证了支持向量回归适用于非线性系统响应的近似建模。     

土地覆被遥感产品真实性检验方法对比

真实性检验是保障土地覆被遥感产品生产质量,支持土地覆被遥感产品应用的重要环节.土地覆被遥感产品真实性检验实践总与理论存在一些差异,其主要体现在用于检验的参考数据样本数量和空间分布两个方面,而这种差异对检验结果的影响还不十分清楚.以中国陆地范围为实验区域,GlobeLand30作为全样本参考数据,ESA CCI-LC作为...     

Curved shell elements for heat conduction with p-approximation in the shell thickness direction

A finite element formulation is presented for the curved shell elements for heat conduction where the element temperature approximation in the shell thickness direction can be of an arbitrary polynomial order p. This is accomplished by introducing additional nodal variables in the element approximation corresponding to the complete Lagrange interpolating polynomials in the shell thickness direction. This family of elements has the important hierarchical property, i.e. the element properties corresponding to an approximation order p are a subset of the element properties corresponding to an approximation order p + 1. The formulation also enforces continuity or smoothness of temperature across the inter-element boundaries, i.e. C⁰ continuity is guaranteed.

The curved shell geometry is constructed using the co-ordinates of the nodes lying on the middle surface of the shell and the nodal point normals to the middle surface. The element temperature field is defined in terms of hierarchical element approximation functions, nodal temperatures and the derivatives of the nodal temperatures in the element thickness direction corresponding to the complete Lagrange interpolating polynomials. The weak formulation (or the quadratic functional) of the three-dimensional Fourier heat conduction equation is constructed in the Cartesian co-ordinate space. The element properties of the curved shell elements are then derived using the weak formulation (or the quadratic functional) and the hierarchical element approximation. The element matrices and the equivalent heat vectors (resulting from distributed heat flux, convective boundaries and internal heat generation) are all of hierarchical nature. The element formulation permits any desired order of temperature distribution through the shell thickness.

A number of numerical examples are presented to demonstrate the superiority, efficiency and accuracy of the present formulation and the results are also compared with the analytical solutions. For the first three examples, the h-approximation results are also presented for comparison purposes.     

CNC系统中NURBS曲线插补及相关算法研究

为提高计算机数字控制（CNC）系统的轮廓控制精度,需解决系统控制软件样条直接输出的问题。基于Taylor公式得到了非均匀有理B样条（NURBS）曲线上两个相邻插补点参数间的递推关系。对于NURBS曲线插补过程中需要频繁计算的B样条基函数及其任意阶导数提出了一种分块矩阵连乘积形式的统一计算方法。应用数值计算方法解决了插补过程中曲线长度等的相关计算问题。实例运算表明所提出的方法可以应用到实际CNC系统中。     

基于WEKA的序列最小化算法的改进研究

数据挖掘算法中的支持向量机算法,在通过若干学者的改进研究后,有一种改进算法即序列最小化算法主要应用于小样本数据集的分类,且分类效果较好,但在训练大规模数据集时,用时长、所需存储空间大,挖掘效率低。针对这一缺陷,通过改变存储策略改进该算法,在WEKA这个软件平台下,在保证分类正确率的前提下,缩短了训练时间,缩减了大量的存储空间,大大地提高了算法的效率,使其更加适应大规模数据集的训练。     

协同训练算法在滚动轴承故障诊断中的应用

针对单个分类器方法在滚动轴承故障诊断中精度较低、故障样本标记稀缺、特征空间维度高等问题，提出一种将协同训练与集成学习相结合的Co-Forest轴承故障诊断算法。Co-Forest是半监督学习中的协同训练算法，包含多个基分类器，通过投票实现协同训练中的置信度估算。从滚动轴承的振动信号中提取时域、频域特征指标。利用少量带标签和大量未标记样本重复地训练基分类器。集成基分类器，实现对滚动轴承故障的诊断。实验结果表明，与同类型的协同训练算法（Co-Training、Tri-Training）相比，Co-Forest算法在轴承故障诊断中具有更高的正确率，与当前针对特征向量高维、标记样本稀缺问题的ISS-LPP算法，SS-LLTSA算法相比，Co-Forest算法在保持很高诊断正确率的情况下，不需要降维、参数设置简单，具有一定的实际应用价值。     

An adaptive method for smooth surface approximation to scattered 3D points

The construction of a surface from arbitrarily scattered data is an important problem in many applications. When there are a large number of data points, the surface representations generated by interpolation methods may be inefficient in both storage and computational requirements. This paper describes an adaptive method for smooth surface approximation from scattered 3D points. The approximating surface is represented by a piecewise cubic triangular Bézier surface possessing C¹ continuity. The method begins with a rough surface interpolating only boundary points and, in the successive steps, refines it by adding the maximum error point at a time among the remaining internal points until the desired approximation accuracy is reached. Our method is simple in concept and efficient in computational time, yet realizes efficient data reduction. Some experimental results are given to show that surface representations constructed by our method are compact and faithful to the original data points.     

一种相似性学习算法及其在人脸识别中的应用

传统的支持向量机相似性学习算法在构造样本对时,会考虑所有的原始训练样本,致使样本对空间和原样本空间呈平方关系,而过多的训练样本对会降低训练速度。为此,提出一种改进的支持向量机相似性学习算法,并应用到人脸识别中。引入二元样本对方法构造样本对,采用K近邻算法减少不相似样本对的生成,从而加快支持向量机的训练速度,同时使用随机降维方法来降低人脸数据的维数。实验结果表明,与基于差空间样本对和差绝对值样本对的算法相比,该算法可获得更高的识别率。