共查询到18条相似文献,搜索用时 93 毫秒
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数字图像中边缘附近的灰度是沿边缘方向和跨边缘方向二维变化的,以前边缘识别的多项式拟合大多采用跨边缘方向的一维拟合.介绍一种采用二维正交多项式进行边缘识别的新方法,由于二维拟合更符合边缘附近小区域内像素灰度二维变化的实际,因此拟合结果优于一维拟合.在进行拟合时,利用正交多项式的正交性将优化方程对角化,避免求逆或解方程,没有多项式拟合优化方程的病态问题,采用高阶多项式拟合可以提高拟合精度.对生成图像的边缘识别结果表明,二维正交多项式拟合识别边缘的精度和稳定性较好.简支梁模型试验表明,采用正交多项式边缘拟合方法检测梁的静变形,图像变形检测精度在0.1像素之内,适当选择图像采集设备和采集范围,点检测精度与传统检测方法的精度相当,边缘检测属线状高密度检测,检测范围远大于传统方法. 相似文献
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多频段拟合的正交多项式方法及其Matlab工具箱 总被引:2,自引:0,他引:2
提出了多频段拟合的Forsythe正交多项式方法。该方法分段截取频率、一次性识别所有模态,在提高识别效率的同时,也提高了识别精度。又提出了移动法建立幂多项式与正交多项式间的转换关系,方便程序设计;归一化频率响应函数、频率向量、以及分母幂多项式系数,进一步提高识别精度。采用了不同类型和难度的2D Frame模型、Antenna模型、GARTEUR飞机模拟以及Richardson的三模态算例进行仿真检验。介绍了基于本算法所发展的多频段Forsythe正交多项式总体拟合Matlab工具箱。 相似文献
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提出了用幂基多项式拟合频响函数的几点技巧。运用幂基多项式和最小二乘法对频响函数拟合的计算公式进行了推导,得到了用于问题求解的线性代数方程组,为改善该方程组系统矩阵的条件数,对频率变量和系数矩阵进行了规范化处理;频率变量被规范化到0=-1的无量纲正实数区域,两个相关矩阵的每列模长被规范为1。然后用奇异值分解的方法求解该方程组,得到拟合频响函数所用的幂基多项式的系数。最后,根据幂基多项式的系数,求出系统的极点和留数,从而识别出系统的模糊态参数,文中给出了一个悬臂梁模拟算例,结果表明本文算法具有较好的计算精度。 相似文献
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主要讨论了多项式正交滤波器和共轭正交滤波器组的构造方法,首先利用Riesz引理和特殊的余弦三角形多项式,给出了一种多项式正交滤波器的构造算法,该算法可以构造出一系列特性各异的紧支撑正交小波基;还给出了由一个矩阵CQFs派生多个新的矩阵CQFs的共轭正交滤波器组算法,包括由低阶矩阵CQFs构造高阶矩阵CQFs。 相似文献
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数据拟合在很多地方都有应用,主要用来处理实验或观测的原始离散数据。通过拟合可以更好的分析和解释数据。在引用前人的算法基础上,采用正交多项式最小二乘法进行曲线拟合,通过实验对算法进行了分析,并给出了C语言实现的代码。 相似文献
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Jen‐Yu Liu 《中国工程学刊》2013,36(3):301-306
Abstract The method of Chebyshev polynomials is introduced to represent approximate solutions of first‐order partial differential equations consisting of two independent variables. A set of linear algebraic equations is obtained by using the properties of Chebyshev polynomials and Kronecker product to analyse first‐order partial differential equations. The coefficient vector of Chebyshev polynomials of the first‐order partial differential equations can be obtained directly from Kronecker product formulas, which are suitable for computer computation. A numerical example for a set of first‐order partial differential equations is solved by a Chebyshev polynomials approximation and the results are satisfactory. 相似文献
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V. V. Zozulya 《先进材料力学与结构力学》2017,24(9):745-760
In this article a higher-order theory for functionally graded beams based on the expansion of the two-dimensional (2D) equations of elasticity for functionally graded materials into Fourier series in terms of Legendre's polynomials is presented. Starting from the 2D equations of elasticity, the stress and strain tensors, displacement, traction, and body force vectors are expanded into Fourier series in terms of Legendre's polynomials in the thickness coordinate. In the same way, the material parameters that describe the functionally graded material properties are also expanded into Fourier series. All equations of the linear elasticity including Hooke's law are transformed into the corresponding equations for the Fourier series expansion coefficients. Then a system of differential equations in terms of the displacements and the boundary conditions for the Fourier series expansion coefficients are obtained. In particular, the first- and second-order approximations of the exact infinite dimensional beam theory are considered in more detail. The obtained boundary-value problems are solved by the finite element method with MATHEMATICA, MATLAB, and COMSOL multiphysics software. Numerical results are presented and discussed. 相似文献
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基于矩量法的移动荷载识别 总被引:4,自引:0,他引:4
从桥梁响应识别桥面移动荷载往往出现逆问题的病态(不适定性)等共性问题。本文基于移动荷载识别理论,借助矩量法求解积分方程理论并采用整域基函数——正交勒让德多项式表达桥面移动荷载,提出了一种移动荷载识别的时域改进算法。两轴车辆多种组合工况下的常载和时变荷载数值仿真研究表明:与时域法比较,改进时域法识别桥面移动荷载时,其识别精度高、抗噪能力强,识别结果不适定性有显著改善。 相似文献
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The current distribution in a parallel set of thin conducting sheets due to an external applied source is investigated. All sheets are placed in one plane. The source, and all excited fields, are time-harmonic. The frequency is low enough to allow for an electro quasi-static approximation (neglecting the displacement current). The conducting sheets are infinitely long and the current is uniform in the longitudinal direction of the sheets. The sheets have a thin rectangular cross-section, so thin that the current can be assumed uniform in the thickness-direction. Hence, the current distribution only depends on the transverse coordinate. Due to the mutual induction between the sheets, the current distribution over the width of the cross-section becomes non-uniform: it accumulates at the edges of the sheets. It is especially this so-called edge-effect, and its dependence on the applied frequency and the distances between the sheets, that is the aim of this investigation. From the Maxwell equations, a set of integral equations for the current distribution in the sheets is derived. These integral equations are solved, as far as possible by analytical means, by writing the current distribution in each sheet as a series of Legendre polynomials. The general method is worked out for N (N 1) sheets, but explicit results are presented for N=1 and 3. It turns out that the edge-effect becomes stronger for increasing frequencies. For this solution, only a very restricted number of Legendre polynomials are needed. 相似文献
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In this paper weakly equilibrated basis functions (EqBFs) are introduced for the development of a boundary point method. This study is the extension of the one in (Int. J. Numer. Methods Engng. 81 (2010) 971–1018) using exponential basis functions (EBFs) which are available just for partial differential equations (PDEs) with constant coefficients. Here the EqBFs are evaluated numerically to solve more general PDEs with non-constant coefficients. The EqBFs are found through weighted residual integrals defined over a fictitious domain embedding the main domain. A series of Chebyshev polynomials are used for the construction of the basis functions. By properly choosing the weight functions as the product of two unidirectional functions, here with Gaussian distribution, the main 2D integrals are written as the product of the simpler 1D ones. The results of the integrals can be stored for further use; however in some particular cases the EqBFs may be stored as a set of library functions. The results may also be found useful for those who are interested in residual-free functions in other numerical methods. For the verification, we discuss on the validity of the solution through an essential and comprehensive test procedure followed by several numerical examples. 相似文献
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É. Savin B. Faverjon 《International journal for numerical methods in engineering》2017,111(12):1192-1200
Because of the complexity of fluid flow solvers, non‐intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for example. The objective function is commonly expressed in terms of moments of these quantities, such as the mean, standard deviation, or even higher‐order moments. Polynomial surrogate models based on polynomial chaos expansions have often been implemented in this respect. The original approach of uncertainty quantification using polynomial chaos is however intrusive. It is based on a Galerkin‐type formulation of the model equations to derive the governing equations for the polynomial expansion coefficients. Third‐order, indeed fourth‐order moments of the polynomials are needed in this analysis. Besides, both intrusive and non‐intrusive approaches call for their computation provided that higher‐order moments of the quantities of interest need to be post‐processed. In most applications, they are evaluated by Gauss quadratures and eventually stored for use throughout the computations. In this paper, analytical formulas are rather considered for the moments of the continuous polynomials of the Askey scheme, so that they can be evaluated by quadrature‐free procedures instead. Matlab© codes have been developed for this purpose and tested by comparisons with Gauss quadratures. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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This paper deals with two questions concerning permutation polynomials in several variables. Lidl and Niederreiter have considered the problem of when a sum of permutation polynomials in disjoint sets of variables is itself a permutation polynomial, and in the case of prime fields have shown that it is necessary and sufficient that at least one summand be a permutation polynomial. They also showed that in the case of non-prime fields this condition is not necessary. In this paper, a necessary and sufficient condition is obtained for the general case which specialises to the previous result for prime fields. The second part extends a criterion of Niederreiter for permutation polynomials over prime fields to any finite field. 相似文献