基于两步正则化Gauss-Newton迭代算法的ECT图像重建

电容层析成像(ECT)技术求解图像重建问题属于非线性问题,并且存在严重的不适定性。为提高图像重建精度,提出了一种基于两步正则化Gauss-Newton迭代算法的ECT图像重建方法。针对标准正则化Gauss-Newton迭代算法在图像重建中存在的不收敛问题,引入了两步迭代方法;改进了正则化矩阵,提高了解估计的精确度;考虑到Gauss-Newton算法对迭代初值的依赖性,加入了同伦算法。最后,进行仿真和静态实验,并与线性反投影(LBP)算法、Landweber算法、Tikhonov正则化算法进行对比。结果表明,该方法可有效提高图像重建精度。

自适应Newton-Thiele有理插值及应用

二元连分式插值是二元有理插值的重要组成部分;文章在前人研究的基础上,对Newton-Thiele有理插值构造过程进行改进。针对Newton-Thiele有理插值在插值过程出现逆差商不存在的情况,传统的解决方法是将相应的Thiele型插值连分式转换为Newton插值多项式,然而该处理方法会导致计算复杂度的增加。借鉴相关文献在一元有理插值上的选点方法,文章给出一种带终止条件的自适应贪婪选点算法,即在给定插值点中根据自适应条件筛选出局部点对函数进行构造,以提高Newton-Thiele有理插值函数构造过程的稳定性,提升运算效率。对非线性函数的插值结果表明:该算法的插值效果较好、误差较小;同时将该算法应用到图像修复中,并与其他相关算法的修复效果进行对比,进一步验证了该算法的有效性。

A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations

In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.

Research on BP Neural Network Algorithm Based on Quasi- Newton Method

With more and more researches about improving BP algorithm, there are more improvement methods. The paper researches two improvement algorithms based on quasi-Newton method, DFP algorithm and L-BFGS algorithm. After fully analyzing the features of quasi- Newton methods, the paper improves BP neural network algorithm. And the adjustment is made for the problems in the improvement process. The paper makes empirical analysis and proves the effectiveness of BP neural network algorithm based on quasi-Newton method. The improved algorithms are compared with the traditional BP algorithm, which indicates that the imoroved BP algorithm is better.

Convergence and stability of the Newton-Like algorithm with estimation error in optimization flow control

The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.

Smoothing Newton Algorithm for Solving Generalized Complementarity Problem

The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.

Optimal Placement and Sizing of Distributed Energy Generation in an Electrical Network Using the Hybrid Algorithm of Bee Colonies and Newton Raphson

Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.

Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a PFunction

By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.

Calculation of Extraction Equilibrium in Multi-Component System by Newton-Raphson Algorithm

Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.

A Distributed Newton Method for Processing Signals Defined on the Large-Scale Networks

In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.

基于Lagrange插值的数字图像相关亚像素位移测量算法

本文旨在通过改进经典Newton-Raphson算法中的插值方法来优化数字图像相关(DIC)亚像素位移测量的计算效率。针对经典Newton-Raphson算法在数字图像相关亚像素位移测量中应用的双三次样条插值算法,特别是在需要计算边界点灰度梯度(即灰度值的一阶导数)时,存在计算量大的问题,本文提出一种基于Lagrange插值的改进算法作为解决方案。Lagrange插值算法在未增加计算节点数的情况下,成功避免了边界点灰度梯度的计算,使插值效率可提高近1/3。应用数值模拟实验和真实刚体平移实验对本文算法的性能进行验证。结果表明,本文算法在保持求解精度的同时,计算测量效率较传统Newton-Raphson算法有了明显提升。单点插值效率平均提升近30%;单点测量效率平均提升近20%。本文首次将Lagrange插值算法应用于数字图像相关的亚像素位移测量中,解决了双三次样条插值算法计算量大的问题,为相关领域提供了一种更为优化的变形测量方法。该研究为DIC亚像素位移测量技术的进一步发展和应用提供了新的思路和参考,有望在实际工程中得到广泛应用,促进相关领域的进步与发展。

基于Newton-Raphson迭代的永磁同步电机MTPA控制算法设计

针对牵引永磁同步电机的最大转矩电流比(MTPA)的控制原理,提出一种基于Newton-Raphson迭代公式的MTPA控制算法,根据转矩指令实时计算最优的d、q轴电流参考值,充分利用了电机的磁阻转矩,以最小的电流输出最大的转矩。Newton-Raphson的迭代次数为10次,最终将迭代误差降到0.01 A以下,对处理器的负担较小。通过MATLAB/Simulink仿真及在中车大连电力牵引研发中心有限公司试验中心进行试验,证明了该MTPA算法的可靠性与有效性,并在系列化标准地铁永磁牵引系统中得以应用。

单调线性权互补问题的新全牛顿步可行内点算法

提出求解单调线性权互补问题(WLCP)的全牛顿步可行内点算法。基于线性优化的连续可微函数,给出中心方程的新等价形式,接着运用牛顿法求解定义中心路径的等价方程组,从而得到单调WLCP的新搜索方向。沿该搜索方向使用全牛顿步,无需进行线搜索。通过适当选取参数,分析了全牛顿步的严格可行性,证得算法是二次收敛的且具有多项式时间迭代复杂度。最后数值实验结果表明算法有效。

基于改进Gauss-Newton的电容层析成像图像重建算法

针对电容层析成像技术中的"软场"效应和病态问题,在分析Gauss-Newton算法基本原理的基础上,提出了一种基于Gauss-Newton新的电容层析成像算法,采用奇异值分解定理对算法的稳定性进行了证明.在此基础上探讨了ECT应用该算法的可行性,算法满足收敛条件且重建图像误差小.仿真和实验结果表明,该算法和LBP、Landweber和共轭梯度算法相比,算法兼备成像质量高、稳定性好等优点,为ECT图像重建算法的研究提供了一个新的思路.

改进的6-DOF并联机器人Newton-Euler动力学模型

本文在 6 - DOF并联机器人运动模型的基础上 ,采用对加速度及作用力正交分解的方法 ,将其 Newton- Euler动力学模型归结为一个简单的、可用于实时计算的模型 .

基于查找表和Newton插值算法的正余弦函数的FPGA实现

正余弦函数在任意次谐波电流的无锁相环ip-iq检测法中有着重要应用。提出了一种基于查找表和Newton插值算法相结合的正余弦函数的实现方法,给出了具体计算公式和RTL级方框图;与查表法和CODIC算法相比,该方法所需时钟周期少(只需120个时钟周期),精度高(可达±1LSB),占用资源少(只需483个LE单元)。在Altera公司的Cyclone系列FPGA器件EP1C6Q240C8上完成了硬件验证,最终应用到某谐波检测ASIC设计中。

基于测深侧扫声呐的DOA估计算法研究

针对测深侧扫声呐进行波达方向(Direction of Arrival,DOA)估计时会受到阵元幅度、相位误差及低信噪比影响的问题,提出一种改进的波束域加权子空间拟合算法。首先,采用总体最小二乘-旋转不变子空间算法进行回波方向预估计;其次,将连续线阵划分为多个子阵,并将各个子阵在预估计方向做加权波束形成;再次,采用加权子空间拟合(Weighted Subspace Fitting,WSF)算法构造代价函数;最后,采用阻尼牛顿法求解得到高精度的DOA估计结果。仿真结果表明,文中所提算法在阵元出现幅度相位误差条件下的角度估计均方误差相对于WSF算法减少了约0.03°。海试数据分析结果表明,文中所提算法的测深点均方误差整体优于WSF算法,其相对测深精度提高了约9.8个百分点。以上分析结果表明,文中所提算法整体优于WSF算法,可以实现在阵元幅度相位误差及低信噪比情况下的高精度DOA估计。

求解非线性回归问题的Newton算法

针对大规模非线性回归问题,提出基于静态储备池的Newton算法.利用储备池搭建高维特征空间,将原始问题转化成与储备池维数相关的线性支持向量回归问题,并应用Newton算法求解.鲁棒损失函数的应用可抑制异常点对预测结果的干扰.通过与SVR(Support Vector Regression)及储备池Tikhonov正则化方法比较,验证了所提方法的快速性、较高的预测精度和较好的鲁棒性.

基于Newton/Gauss-Seidel迭代的DGM隐式方法

在Newton迭代方法的基础上,对高阶精度间断Galerkin有限元方法 (DGM)的时间隐式格式进行了研究.Newton迭代法的优势在于收敛效率高效,并且定常和非定常问题能够统一处理,对于非定常问题无需引入双时间步策略.为了避免大型矩阵的求逆,采用一步Gauss-Seidel迭代和Matrix-free技术消去残值Jacobi矩阵的上、下三角矩阵,从而只需计算和存储对角(块)矩阵.对角(块)矩阵采用数值方法计算.空间离散采用Taylor基,其优势在于对于任意形状的网格,基函数的形式是一致的,有利于在混合网格上推广.利用该方法,数值模拟了Bump绕流和NACA0012翼型绕流.计算结果表明,与显式的Runge-Kutta时间格式相比,隐式格式所需的迭代步数和CPU时间均在很大程度上得到减少,计算效率能够提高1～2个量级.