基于Excel的连续梁内力有限元数值迭代计算

建立了连续梁的内力计算有限元数值模型,以Excel 软件为计算工具,分别用雅克比迭代法、高斯-赛德尔迭代法、超松弛迭代法和共轭梯度法等4种常用方法对模型进行了迭代计算,并对4种迭代计算方法的收敛速度和效率进行了分析和研究,提出了一种基于Excel的快捷有效的有限元数值计算方法.     

基于GPU的混合精度平方根共轭梯度算法

针对当前基于GPU的数值算法具有双精度数据性能低下的缺陷.提出了一种适于GPU统一计算架构Fermi-CUDA的混合精度平方根共轭梯度算法用以求解稀疏线性方程组.该算法采用单精度内迭代与双精度外迭代结合的方法,以充分利用GPU体系结构下单精度高性能和双精度高精度的优点.整个算法的计算部分完全在GPU端进行,减少了CPU和GPU之间的数据通信.实现了基于GPU的平方根共轭梯度法、Jacobi迭代法和Gauss-Seidel迭代法,分析它们作为内迭代算子对算法收敛性的影响.实验表明,该算法获得了与全双精度数据处理等同的计算精度,比GPU全双精度在浮点性能上提升近一倍,相对于CPU全双精度串行算法,最大加速比达到70以上.     

基于改进共轭梯度法的ERT图像重建

针对电阻层析成像(ERT)图像重建中灵敏度矩阵的病态特性导致共轭梯度法的收敛率低的问题,提出了改进的共轭梯度算法,ERT图像重建前先对数据进行归一化预处理,将解空间映射到Krylov子空间中,再通过共轭梯度法求解低维子空间中的反问题。分别利用共轭梯度法、预处理共轭梯度法和改进共轭梯度法对典型的气水两相流模型做了仿真实验。实验结果表明,改进共轭梯度法能够提高重建图像的质量,并且相对于其他算法,降低了计算时间。     

基于改进牛顿迭代法的手腕偏置型六自由度关节机器人逆解算法

手腕偏置型六自由度关节机器人不满足Pieper法则,无法求得封闭形式的运动学逆解。对比非偏置型机器人结构,提出一种结合非偏置型机器人封闭逆解和改进牛顿迭代法的数值迭代算法。先利用反变换法求得同构型非偏置型机器人的封闭逆解,并将该封闭逆解作为后续迭代搜索的初始值;将偏置型机器人运动学正解的3个位置分量和3个独立姿态分量构造成1个非线性方程组,利用改进牛顿迭代法对该非线性方程组进行迭代搜索,从而求解得到偏置型机器人的数值逆解。大量试验表明,该算法可以满足一般实时控制要求。     

基于改进正则法的ECT图像重建算法

电容层析成像图像重建是一个典型的病态问题,其解是不稳定的。为获得良好的重建效果,需要采用既保证解的稳定性且又能提高重建图像质量的算法。本文提出了一种新的图像重建算法。在分析标准Tikhonov正则法的基础上,针对ECT逆问题的病态性进行改进,并推导出两步图像重建算法：第一步利用标准Tikhonov正则法的计算值获得权矩阵的估计;第二步采用本文所推导的改进Tikhonov正则法获得最终的重建图像。数值实验表明,该算法所获得的图像重建质量得到了明显的提高,且该算法无需迭代,保证了算法实时性。     

电磁层析成像图像重建中的修正共轭梯度算法

通过研究共轭梯度算法,推导出适用于电磁层析成像的修正共轭梯度算法,该方法提高了收敛速度,改善了电磁层析成像重建图像的质量。首先以共轭搜索方向充分下降为充分条件,理论推导出修正共轭梯度算法。然后从相对图像误差、相关系数和收敛曲线几个方面出发,评价了Landweber迭代法、单步Tikhonov正则化方法、共轭梯度法和修正共轭梯度法在电磁层析成像图像重建中的结果,得出结论:修正共轭梯度方法的相对图像误差最小,重建图像和原图像的相关系数最高,收敛情况优于共轭梯度算法。     

大气激光通信光斑图像的快速复原与实时检测

针对大气湍流对激光通信中对信标光的捕获、跟踪与对准(ATP)的影响,提出了基于盲解卷积的快速复原与实时检测算法。采用一维点扩散函数重新构造方位退化模型,取代了原有经典二维退化模型;改进了约束共轭梯度算法中的约束算子,并通过改进的共轭梯度迭代算法求得对原始图像的估计;最后通过连通域计算提取估计结果中的光斑中心位置。采用现场可编程门阵列和数字信号处理器实现所提出的共轭梯度算法并提取光斑中心位置,满足了系统实时性要求。实验表明,所提出的快速复原算法能够实时复原分辨率为200pixel×200piexl,帧频为100 Hz的光斑图像,所提取的信标光光斑中心位置与事后计算结果的误差小于1pixel,能够满足激光通信系统对信标光的实时跟踪要求。     

融合全局逼近与局部精化的协同优化方法

针对标准协同优化方法存在对初始点选取敏感、优化结果易收敛于局部最优解等问题,通过对松弛因子法特点的分析,给出了一种综合应用固定松弛因子和动态松弛因子方法,融合全局逼近与局部精化的改进协同优化方法,并将Kriging近似模型引入到改进的协同优化方法中,减小了迭代计算量,提高了优化效率,可快速精确地收敛到全局最优解处.通过汽车盘式制动器的优化设计,验证了本文方法的有效性与稳定性.     

基于任务的可重构模块机器人构形确定方法

可重构机器人为柔性加工系统提供了更多的选择,但复杂多变的任务、环境以及机器人模块无穷组合,为机器人构形的确定带来了很大的难题。采用遗传算法和迭代算法分两级搜索对机器人构形组合进行优化设计:运用遗传算法对机器人构形进行进化设计,满足工作空间的可达性、环境避障、线性和角度误差、末端操作灵巧度、运动关节的动力学要求、期望模块数目等性能指标要求。运用迭代算法对构形进行运动学逆解求解,计算空间工作点的可达性适应度。根据可装配的模块机器人及模块化思想,建立各个模块的速度、加速度等动力学表达式及相关修正公式,采用补偿迭代法来自动生成动力学方程,计算运动模块驱动性能的适应度。用专家经验对搜索得到适应度较高的构形进行修正,得到满足工作要求的机器人构形。最后给出实例验证。     

基于神经网络的三自由度摇摆台运动学反解

针对传统的数值解法不能满足实时控制算法的要求，研究使用BP网络和径向基函数（RBF）神经网络求解三自由度摇摆台运动学反解的方法。通过离线的迭代算法生成高精度的样本点来训练神经网络，使用动量法、变学习率法和共轭梯度法提高BP网络的收敛速度。使用正交最小二乘法训练的RBF网络具有更小的泛化误差，更适合于实时控制应用。     

最优超松弛因子的一种确定方法及其在裂纹计算中的应用

结合黄金分割法，提出一种最优松弛因子的优选法。该方法区别于常用的直接计算求取的方法和试错法，具有明显的优点。给出的断裂力学应用实例表明计算机确定最优松弛因子的方法是明显有效的。文中给出的松弛因子值可供工程直接应用。     

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.     

Shape identification problems on detecting of defects in a solid body using inverse heat conduction approach

In this paper, a new shape identification method in the inverse heat conduction problem (IHCP) is applied to detect the location and size of defects in a solid body. Different defects are modeled in a solid body as an elliptical geometry whose parameters are estimated with a proposed inverse algorithm. The inverse algorithm consists of direct, inverse analysis, and gradient-based optimization method. The direct analysis is used a finite-element method in an unstructured grid system to solve the direct heat conduction problem. The inverse analysis is based on recording temperatures data on surface of solid body that calculates the objective function. The employed gradient-based optimization method is constructed using the adjoint, sensitivity, and conjugate gradient method (Powell-Beal’s version) that are used to calculate the gradient of objective function, step size, and minimizing the objective function, respectively. The effects of different noisy temperature data, different cavities on some domains, and different type of defects such as poor cure, porosity, and crack are investigated in this work. The results show that this proposed inverse algorithm is more efficient in detection of defects.     

基于改进谱投影梯度算法的X射线发光断层成像

X射线发光断层成像(XLCT)是一种可同时获得解剖结构和功能信息的新型分子影像技术,在早期肿瘤检测与放疗方面具有重要应用潜力,但由于测量信息少,成像模型复杂等原因,其断层重建一直是挑战性难题。本文采用非单调Barzilai-Borwein梯度(NBBG)算法来求解重建问题目标函数。每次迭代中,谱投影梯度方法近似为L1范数约束的最小二乘问题。Barzilai-Borwein梯度法获得相应的更新方向,提高算法的收敛速度。采用非单调性线性搜索策略构建最优步长,保证全局收敛性。通过将Barzilai-Borwein梯度法和非单调性搜索结合,在保证全局收敛的同时,克服了选取精确步长带来较大计算量的缺点。数值仿真实验和物理实验得到的基于NBBG算法的单光原重建位置误差分别为0.68和0.94mm,与分裂增广拉格朗日收缩算法(SALSA)相比,本文方法在重建精度、鲁棒性和重建效率等方面都获得了较优的结果。     

An improved stopping condition guarantee recovery of sparse signal via Subspace Pursuit method

The Subspace Pursuit (SP) algorithm is one of greedy pursuit methods which is used to reconstruct of K-sparse signal. Unlike existing condition produced by Dai and Milenkovic in 2004 that suggests the residual value of current iteration is reduced from the previous iteration, our approach eliminates useless information by reducing the number of iterations used to detect the correct support set. This operation is done by suggesting a new halting condition that can capture the best support set which can give the best representation of the reconstructed signal. The new halting conditions enhanced the SP algorithm to low computational complexity and reconstruction accuracy of the sparse signal.A mathematically proven for two halt condition: noiseless setting, and noisy setting for signal affected by Gaussian noise. An error bound relation also is driven.In this paper, we try also to relax the restricted isometry constant RIC value to narrows the gap between the known bounds and ultimate performance, which it produced by Dai.Simulation results show that the new halting condition can overpass best results produce by earlier iteration and rise time consume. Our new halting condition can catch this earlier iteration and enhanced SP algorithm results.     

Stopping Criterion in Iterative Solution Methods for Reynolds Equations

Iterative solution methods are usually used for solving a variety of Reynolds equations in lubrication analysis due to their simplicity and effectiveness. The objective of this study is to present a robust stopping criterion for iterative methods, by which the iterative process of the methods can be terminated for high execution efficiency without sacrificing the solution accuracy. In this study, the compressible and incompressible fluid Reynolds equations are solved by popular relaxation methods. A very efficient preconditioned conjugate gradient method is also applied in a case for verification. The proposed stopping criterion for iterative methods is based on a coarse-grid truncation error analysis. Three different gridwork groups are required for estimating the truncation errors, which involves only a small amount of additional execution time. In the numerical models examined, the amount of truncation error in a model is insensitive to the gridwork used. It is also found that in a calculation the best prediction of truncation error for terminating the iteration is obtained by using the average fluid film pressure. It is shown that for all the cases tested the proposed stopping criterion can meet the objective stated. The stopping criterion can also be applied when the efficiency of iterative methods is to be compared in solving Reynolds equations.     

基于梯度图的快速POCS超分辨率复原算法研究

随着红外成像相关产业的兴起,红外成像技术具有的隐蔽性好、探测范围广、定位精度高、穿透距离远,以及轻质小巧、低耗可靠等优点备受青睐,已成为当前智能化光电探测发展的主流方向。然而,红外弱小目标的图像细节特征少、信噪比低等特点成为红外图像应用的瓶颈,如何提高红外弱小目标成像效果成为目前的研究热点。POCS算法是目前超分辨率复原中应用非常广泛的一种复原算法,但是该算法运算量大,处理时间较长,同时对图像的边缘细节保留能力较差。针对POCS超分辨率复原算法迭代时间较长,无法满足光电探测系统实时性的问题,提出了基于梯度图的快速POCS超分辨率复原算法(GPOCS)。该算法根据图像的梯度分布对图像中的像素点进行分类,采用不同的迭代系数进行计算。改进算法能够较好的保留边缘信息并抑制噪声,进而在保证超分辨率复原性能的基础上大大缩短了运算时间。实验结果表明:GPOCS算法复原结果在背景处噪声得到一定的抑制,整体复原能力优于传统的POCS复原方法。该算法能够有效地保留边缘细节,同时处理时间小于传统的POCS复原方法,减少了1个数量级已经是接近实时。GPOCS算法能够自适应的选取迭代步长,较好的保留边缘信息并抑制噪声,进而在保证超分辨率复原性能的基础上大大缩短了运算时间,虽然不能满足实时性的要求,但是也已经是接近实时。     

Iterative speed improvement for solving slowly varying total least squares problems

Many problems in signal processing, modal analysis, system identification, etc., give rise to an overdetermined set of linear equations AX ≈ B. Whenever both the observation matrix B and the data matrix A are inaccurate, the total least squares (TLS) method is appropriate for estimating the unknown parameters X. Since the TLS solution is deduced from only one right singular vector or, in general, a basis of the right singular subspace associated with the smallest singular values of the data [A; B], the computational speed can be improved by only calculating those desired base vectors. If a priori information is available (e.g. the TLS solution at a previous time step when slowly varying sets of equations must be solved at each time instant), iterative methods are appropriate to compute those base vectors. It is shown in this paper that inverse iteration is the most efficient iterative technique for solving generic TLS problems of known rank.Two algorithms for subspace inverse iteration are presented. Their convergence properties and applicability in solving TLS problems are analysed. Based on the convergence rate and the operation counts in each iteration step, these iterative algorithms are compared in efficiency with the direct computation methods—classical TLS and partial TLS. In particular, the efficiency of these methods is illustrated in a practical real life problem, namely multiple input estimation of frequency response functions.