加权总体最小二乘平差方法的比较与分析

介绍了求解加权总体最小二乘问题的Schaffrin—Wieser算法和Mahboub算法以及Amiri—Simkooei算法,通过MATLAB软件编程进行数值模拟实验比较了三种方法在近似垂直、近似水平和普通直线拟合中的应用以及在二维坐标转换参数求解中的应用,并分析了三种算法的区别与联系。     

非线性最小二乘问题的一种正则同伦迭代解法

当非线性最小二乘问题的数值迭代解算方法其Jacobian矩阵是秩亏或者严重病态时,诸多方法如高斯-牛顿法、修正高斯-牛顿法等将会失效。本文结合同伦延拓和正则化方法,构造了正则同伦函数min（α‖f（x）-L‖^2＋（1-α）‖x-x0‖^2）来解算Jacobian矩阵是秩亏或者严重病态的非线性最小二乘问题。采用将f（x）线性化的策略,建立了非线性最小二乘问题正则同伦方法迭代公式,对其迭代过程进行了详细的推导,给出了其连续性和收敛性的条件。对两个非线性最小二乘问题和一个非线性秩亏自由网平差实例进行了解算,结果表明本文所提出方法是正确和适用的。     

A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations

A fast finite difference method based on the monotone iterative method and the fast Poisson solver on irregular domains for a 2D nonlinear Poisson–Boltzmann equation is proposed and analyzed in this paper. Each iteration of the monotone method involves the solution of a linear equation in an exterior domain with an arbitrary interior boundary. A fast immersed interface method for generalized Helmholtz equations on exterior irregular domains is used to solve the linear equation. The monotone iterative method leads to a sequence which converges monotonically from either above or below to a unique solution of the problem. This monotone convergence guarantees the existence and uniqueness of a solution as well as the convergence of the finite difference solution to the continuous solution. A comparison of the numerical results against the exact solution in an example indicates that our method is second order accurate. We also compare our results with available data in the literature to validate the numerical method. Our method is efficient in terms of accuracy, speed, and flexibility in dealing with the geometry of the domain     

亮度不均匀低质量图像中压印字符分割方法

字符分割效果,直接影响识别精度.在处理亮度不均匀低质量图像中的压印字符时,由于亮度分布不均匀、目标字符与背景区域对比度较低,传统基于二值化图像的字符分割方法在处理上述情况下的压印字符时,难以确定最优二值化阈值,分割准确率较低.提出基于分割效果评价函数的迭代闭环反馈分割方法,通过建立评价函数对分割效果进行评估,以提高分割...     

布氏硬度自动测量中多圆检测方法

圆检测应用广泛,是布氏硬度自动测量的关键。针对圆检测中存在圆分裂、多个圆、不完整圆的情况,提出一种基于交叉圆合并、凸包点迭代纯化最小二乘拟合的圆检测方法。首先对图像进行纹理增强并二值化,其次提取有效区域的最小外接矩形,并得到圆弧与最小外接矩形的三个切点,得到初始圆,然后合并有交叉的圆。最后求合并圆的轮廓点与其凸包的交集,进行迭代纯化最小二乘拟合,最终得到亚像素级的圆半径值。最后通过实际应用测试,验证了论文方法的有效性。     

On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

In this research article, we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously. These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3. Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3. Using computer algebra system Mathematica, we find the lower bound of the convergence order and verify it theoretically. Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB (R2011b), to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods. Some non-linear models are taken from Physics, Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods. Computational CPU time, and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.     

Iterative reanalysis approximation-assisted moving morphable component-based topology optimization method

An Iterative Reanalysis Approximation- (IRA) assisted Moving Morphable Components- (MMCs) based topology optimization is developed (IRA-MMC) in this study. Compared with other classical topology optimization methods, Finite Element-based solver is replaced with the suggested IRA. In this way, the expensive computational cost can be significantly saved by several nested iterations. In the suggested algorithm, a hybrid optimizer based on Method of Moving Asymptotes approach and Globally Convergent version of Method of Moving Asymptotes is suggested to improve convergence ratio and avoid local optimum. Finally, the proposed approach is evaluated by some classical benchmark problems in topology optimization. The results show significant time saving without compromising accuracy.     

Probabilistic Robust Linear Parameter-varying Control of a Small Helicopter Using Iterative Scenario Approach

In this paper, we present an iterative scenario approach (ISA) to design robust controllers for complex linear parameter-varying (LPV) systems with uncertainties. The robust controller synthesis problem is transformed to a scenario design problem, with the scenarios generated by identically extracting random samples on both uncertainty parameters and scheduling parameters. An iterative scheme based on the maximum volume ellipsoid cutting-plane method is used to solve the problem. Heuristic logic based on relevance ratio ranking is used to prune the redundant constraints, and thus, to improve the numerical stability of the algorithm. And further, a batching technique is presented to remarkably enhance the computational efficiency. The proposed method is applied to design an output-feedback controller for a small helicopter. Multiple uncertain physical parameters are considered, and simulation studies show that the closed-loop performance is quite good in both aspects of model tracking and dynamic decoupling. For robust LPV control problems, the proposed method is more computationally efficient than the popular stochastic ellipsoid methods.