适用于SR-CT技术的新算法

SR-CT(Synchrotron Radiation Computed Tomography)技术中有多种重建算法,其典型算法有滤波反投影算法和迭代算法,这两类算法各有其特点。综合考虑重建结果的质量和重建运算的时间,本文提出了一种新的算法混合算法。通过不同算法重建图像的分析比较,结果表明混合算法包含了前两类算法的优点,而且避免了它们的缺点,是一种行之有效的算法。同时对混合算法中的一些重要参数如初始解系数、迭代步长也进行了详细讨论,并给出了这些参数对重建图像质量的影响关系。     

一种弹性波反演的快速迭代解法

本文研究弹性波反演的数值解法,通过求低频响应值的残差最小和利用有限元及振型分解法计算弹性波正问题的低频响应值,给出了一种弹性波反演的快速迭代解法。该算法允许引入反演参数的约束条件,计算效率很高;尽管一般只能得到弹性波反问题的近似解,但收敛性很好,因此可应用于为其它弹性波反演解法提供较好的初始值。     

基于噪声和残缺投影图像的重建算法研究

滤波反投影法和迭代法是SR-CT重建算法中的两大类算法,松弛迭代法是迭代法中的一种;本文主要研究滤波反投影方法和松弛迭代法.为了研究两种方法的影响因素,讨论了滤波反投影法中滤波函数的选取,分析了松弛迭代法中重要参数,如松弛因子、迭代次数对重建效果的影响,给出了重建效果和这些参数的影响关系;对比了两种方法在处理噪声和残缺...     

基于Wilson-θ和Newmark-β法的非线性动力学方程改进算法

Wilson-θ法和Newmark-β法是非线性动力学方程求解的常用方法。它们的一个基本步骤是,将方程改写为增量平衡的形式,在每一个积分步长内用状态参量修正平衡方程的系数矩阵,其本质是在单个步长内对系统的非线性环节进行了线性化处理。本文基于增量思想分别改进了Wilson-θ法和Newmark-β法,根据即时解给出下一步的猜测解,然后对猜测解进行迭代校正,最终得到收敛的近似解。算例表明,改进算法的精度更高,且收敛准则简单。更为重要的是,本文方法无须对非线性项进行线性化处理,因而计算效率更高,适应范围更广。     

弹塑性问题参数二次规划分析的隐式算法

传统的二次规划算法求解弹塑性问题时一般要经过对问题的线性化,如对屈服条件的一阶近似展开等,这在一定程度上会造成数值解的误差。为此,本文提出一种改进的策略,引入迭代与规划算法相结合的技术对问题进行处理,算法收敛平稳迅速,在大步长荷载增量下使算法的精度大大提高。由于本文的算法属于隐式算法,因而也就弥补了原二次规划算法求解弹塑性问题时只有显式算法的不足,从而达到了对原算法的进一步完善。     

实时ICCP算法重力匹配仿真

利用地球物理场进行辅助匹配导航是组合导航技术研究领域的新方向,该技术为水下潜器无源定位提供新的手段.迭代最近等值线算法作为重要的匹配导航算法之一,但存在实时性不强、搜索速度慢等缺点.考虑到以上两方面缺点,采用固定初始序列长度的方式对算法采样结构进行改善并推导出单点迭代公式,同时采用滑动窗搜索方式缩小搜索范围提高算法速度,最终实现实时ICCP算法设计.基于MATLAB平台下实现了实时ICCP算法重力匹配仿真系统,仿真系统采用0.4′×0.4′重力异常数据库.由仿真结果可以看出,该实时ICCP算法能够实现单点迭代,匹配结果能实时跟踪真实航迹且匹配精度能达到一个重力图网格.     

求解非线性动力系统周期解推广的打靶法

提出一种确定非线性系统周期轨道及周期的改进打靶算法。首先通过改变系统的时间尺度，将非线性系统周期轨道的周期显式地出现在非线性系统的系统方程中，然后对传统打靶法进行改造，将周期也作为一个参数一起参入打靶法的迭代过程，从而能迅速确定出系统的周期轨道及其周期。该方法对初始迭代参数没有苛刻要求，可以用于分析强非线性系统，而且对参数激励系统同样有效，对高维系统也能迅速、准确地求得周期解。文中应用该方法对三维Rǒssler系统和八维非线性柔性转子-轴承系统的周期轨道和周期进行了求解，通过与四阶Runge-Kutta数值积分结果比较，验证了方法的有效性。     

求解病态线性方程的一种精细格式及迭代终止准则

研究了求解病态线性方程组的一种简化精细迭代格式和相应的迭代终止准则。首先将线性病态方程组系数矩阵的逆,归结为一矩阵指数的无穷积分形式;然后选择一个固定步长t,建立前述矩阵指数积分在区间[0,2τ]与[0,τ]上的递推关系,并通过区间倍增的方式逼近无穷积分。算法以2~n指数收敛,经过数十次迭代即可获得高精度解,因此具有极高的效率。在迭代过程中解的精度随着积分区间的增加而迅速提高,但当积分区间达到一定程度后,矩阵自乘过程中的误差积累以及矩阵的病态性,反而会导致精度随着区间的增加迅速下降。故一个可行的迭代终止准则,才使得算法具有实际意义。本文以迭代残差为指标,如果该指标连续n次出现增加,则计算停止。n与问题的病态程度及矩阵规模有关,一般情况下n取2即可,最大不超过10。在算例中,n取为5进行计算,都能使得迭代在解较为精确的次数时停止,证明了准则是有效的。     

Vincent摄动解的收敛上界

本文推证得到了Vincent摄动解与逐次迭代解的一致性,从而由迭代解的收敛性及其收敛上界得到了 Vincent 摄动解的收敛性和收敛上界,同时给出了迭代解的解析特征关系。     

基于体素格尺度不变特征变换的快速点云配准方法

以三维激光雷达为主的多源融合同步定位与建图技术是无人系统室内外无缝定位的研究热点,点云配准是其中重要环节。为了提高点云配准效率,提出一种基于体素格尺度不变特征变换的快速点云配准方法。首先,基于点云体素格提取尺度不变特征变换的特征点,完成初始配准;然后利用随机抽样一致算法剔除边缘匹配点并优化初始变换参数;最后基于优化初始变换参数,采用K维树近邻搜索法,结合最近邻点迭代配准算法完成原始点云数据的快速精确配准。对开源数据集以及实际采集的6个典型场景数据的测试表明,该方法的平均配准时间较传统最近邻点迭代配准算法缩短了78%。实验结果表明了该方法的有效性。     

Comparison of Iterative Methods for Computing the Pressure Field in a Dynamic Network Model

In dynamic network models, the pressure map (the pressure in the pores) must be evaluated at each time step. This calculation involves the solution of a large number of nonlinear algebraic systems of equations and accounts for more than 80 of the total CPU–time. Each nonlinear system requires at least the partial solution of a sequence of linear systems. We present a comparative study of iterative methods for solving these systems, where we apply both standard routines from the public domain package ITPACK 2C and our own routines tailored to the network problem. The conjugate gradient method, preconditioned by symmetric successive overrelaxation, was found to be consistently faster and more robust than the other solvers tested. In particular, it was found to be much superior to the successive overrelaxation technique currently used by many researchers.     

A fast multi-resolution approach to tomographic PIV

Tomographic particle image velocimetry (Tomo-PIV) is a recently developed three-component, three-dimensional anemometric non-intrusive measurement technique, based on an optical tomographic reconstruction applied to simultaneously recorded images of the distribution of light intensity scattered by seeding particles immersed into the flow. Nowadays, the reconstruction process is carried out mainly by iterative algebraic reconstruction techniques, well suited to handle the problem of limited number of views, but computationally intensive and memory demanding. The adoption of the multiplicative algebraic reconstruction technique (MART) has become more and more accepted. In the present work, a novel multi-resolution approach is proposed, relying on the adoption of a coarser grid in the first step of the reconstruction to obtain a fast estimation of a reliable and accurate first guess. A performance assessment, carried out on three-dimensional computer-generated distributions of particles, shows a substantial acceleration of the reconstruction process for all the tested seeding densities with respect to the standard method based on 5 MART iterations; a relevant reduction in the memory storage is also achieved. Furthermore, a slight accuracy improvement is noticed. A modified version, improved by a multiplicative line of sight estimation of the first guess on the compressed configuration, is also tested, exhibiting a further remarkable decrease in both memory storage and computational effort, mostly at the lowest tested seeding densities, while retaining the same performances in terms of accuracy.     

Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions

Tomographic shadowgraphy is an image-based optical technique capable of reconstructing the three dimensional instantaneous spray distributions within a given volume. The method is based on a multiple view imaging setup with inline illumination provided by current-pulsed LEDs, which results in droplet shadows being projected onto multiple sensor planes. Each camera records image pairs with short inter-framing times that allow the trajectories of the individual droplets to be estimated using conventional three-dimensional particle tracking approaches. The observed volume is calibrated with a traversed micro-target. A comparison is made between several photogrammetric and polynomial least-square camera calibration techniques regarding their accuracy in deep volume calibration at magnifications close to unity. A calibration method based on volume calibration from multiple planar homographies at equally spaced z-planes was found to produce the most reliable calibration. The combination of back-projected images at each voxel plane efficiently reproduces the droplet positions in three-dimensional space by line-of-sight (LOS) intensity reconstruction. Further improvement of the reconstruction can be achieved by iterative tomographic reconstruction, namely simultaneous multiplicative algebraic reconstruction technique (SMART). The quality of spray reconstruction is investigated using experimental data from multiple view shadowgraphs of hollow cone and flat fan water sprays. The investigations are further substantiated with simulations using synthetic data.     

Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet

The electrohydrodynamic (EHD) jet is becoming increasingly popular within industrial printing areas based on phenomena induced by electrical potentials. Regardless of the physical observations of unstable ejection phenomena in regions possessing high electric potential, quantitative visualization is still necessary; no report exists exemplifying quantitative visualization. Thus, the size, shape and position of EHD droplets were reconstructed in this study using developed three-dimensional tomography methods. Two computer-synthesized phantoms for the liquid meniscus containing small satellite droplets were generated according to actual images captured by two high-speed cameras. These droplets were made in order to numerically reconstruct droplet behavior. Four three-dimensional tomography methods, such as the algebraic reconstruction technique (ART), the adaptive algebraic reconstruction technique (AART), the simultaneous iterative reconstruction technique (SIRT) and the multiplicative algebraic reconstruction technique (MART), were developed to accurately mimic droplet movement using multiple image views. Four basis functions including the cubic B-spline, cosine, o-Moms and Keys basis functions were adopted in order to improve the performance of the tomographic reconstructions. After completing a comparison of the four tomography results, the MART method in association with the cubic cosine basis function was selected as the means to significantly improve reconstruction accuracy. Additionally, it was the applied method for the reconstruction of the droplet behavior from experimental projections by two cameras.     

Assessment of adaptive and heuristic time stepping for variably saturated flow

The performance of improved initial estimates and ‘heuristic’ and ‘adaptive’ techniques for time step control in the iterative solution of Richards equation is evaluated. The so‐called heuristic technique uses the convergence behaviour of the iterative scheme to estimate the next time step whereas the adaptive technique regulates the time step on the basis of an approximation of the local time truncation error. The sample problems used to assess these various schemes are characterized by nonuniform (in time) boundary conditions, sharp gradients in the infiltration fronts, and discontinuous derivatives in the soil hydraulic properties. It is found that higher order initial solution estimates improve the convergence of the iterative scheme for both the heuristic and adaptive techniques, with greater overall performance gains for the heuristic scheme, as could be expected. It is also found that the heuristic technique outperforms the adaptive method under strongly nonlinear conditions. Previously reported observations suggesting that adaptive techniques perform best when accuracy requirements on the numerical solution are very stringent are confirmed. Overall both heuristic and adaptive techniques have their limitations, and a more general or mixed time stepping strategy combining truncation error and convergence criteria is recommended for complex problems. Copyright © 2006 John Wiley & Sons, Ltd.     

An efficient simultaneous reconstruction technique for tomographic particle image velocimetry

To date, Tomo-PIV has involved the use of the multiplicative algebraic reconstruction technique (MART), where the intensity of each 3D voxel is iteratively corrected to satisfy one recorded projection, or pixel intensity, at a time. This results in reconstruction times of multiple hours for each velocity field and requires considerable computer memory in order to store the associated weighting coefficients and intensity values for each point in the volume. In this paper, a rapid and less memory intensive reconstruction algorithm is presented based on a multiplicative line-of-sight (MLOS) estimation that determines possible particle locations in the volume, followed by simultaneous iterative correction. Reconstructions of simulated images are presented for two simultaneous algorithms (SART and SMART) as well as the now standard MART algorithm, which indicate that the same accuracy as MART can be achieved 5.5 times faster or 77 times faster with 15 times less memory if the processing and storage of the weighting matrix is considered. Application of MLOS-SMART and MART to a turbulent boundary layer at Re _θ = 2200 using a 4 camera Tomo-PIV system with a volume of 1,000 × 1,000 × 160 voxels is discussed. Results indicate improvements in reconstruction speed of 15 times that of MART with precalculated weighting matrix, or 65 times if calculation of the weighting matrix is considered. Furthermore the memory needed to store a large weighting matrix and volume intensity is reduced by almost 40 times in this case.     

截尾Gauss概率密度函数中待定参数的确定

给出一种计算描述标量湍流脉动的截尾Gauss概率密度函数的待定参数的方法. 通过将关于待定参数的代数方程组表示成适于求解的形式，综合应用牛顿法、牛顿下山法和阻尼牛顿法等迭代算法，并恰当地选取待定参数的迭代初值，获得了在标量平均值及其脉动均方值的各种取值条件下待定参数的相应数值.     

Large free vibrations of a beam carrying a moving mass

The focus of this work is to develop a technique to obtain numerical solution over a long range of time for non-linear multi-body dynamic systems undergoing large amplitude motion. The system considered is an idealization of an important class of problems characterized by non-linear interaction between continuously distributed mass and stiffness and lumped mass and stiffness. This characteristic results in some distinctive features in the system response and also poses significant challenges in obtaining a solution.

In this paper, equations of motion are developed for large amplitude motion of a beam carrying a moving spring–mass. The equations of motion are solved using a new approach that uses average acceleration method to reduce non-linear ordinary differential equations to non-linear algebraic equations. The resulting non-linear algebraic equations are solved using an iterative method developed in this paper. Dynamics of the system is investigated using a time-frequency analysis technique.