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...     

框架结构损伤的检测诊断与评估方法研究

通过构造以损伤参数为未知量的超定非线性方程组,提出了3种改进的框架结构损伤的检测、诊断、评估方法——改进的一阶迭代法、改进的混合迭代法、改进的动静结合法。通过对框架结构损伤识别的数值模拟分析可以得出:在单柱或梁发生20%及以下损伤的情况下,动静结合法、一阶迭代法、混合迭代法均能较好地识别出损伤的位置与程度。在求解40%及以上的损伤或者多处梁柱损伤时,一阶迭代法和混合迭代法分别只经过25次迭代和22次迭代就达到设定的10-8迭代误差而收敛停止计算,均能准确地识别出损伤单元的位置与损伤程度;与一阶迭代法相比,混合迭代算法由于采用了精确度较高的二阶非线性解析解作为迭代修正的初值,因而迭代修正精度更高,收敛性更好;动静结合法由于结合了结构的动态信息和静态信息,识别精度与混合迭代算法接近且减少了运算时间,并且通过提高计算中所使用的模态阶数可大大提高其识别精度。     

SR-CT技术乘型迭代算法的研究

算法为SR-CT(synchrotron radiation computed tomography)技术中的重要组成部分,其中乘型迭代算法为该技术的一种有效算法。本文对乘型迭代算法进行了研究,并对该算法中的一些重要参数,如迭代步长、迭代次数及初始解进行了优化分析,给出了这些参数对重建图像及运算时间的影响关系以及这些参数间的相互影响关系,同时给出了获取较优初始解的方法以及迭代步长和迭代次数的最佳取值范围。     

面向工程全局优化的混沌优化算法研究进展Research advances of chaos optimization algorithms for engineering global optimization

近年来,基于混沌的初值敏感性、伪随机性、遍历性以及自相似分形等非线性动力学特性所发展的混沌优化方法,是一种有潜力的工程全局优化新工具,已广泛应用于科学与工程技术的各学科领域。根据混沌优化方法的发展历程,以算法基本思想和工程应用研究状况为重点,评述了混沌神经网络优化方法、第一类混合混沌优化算法（基于混沌搜索）、第二类混合混沌优化算法（混沌序列代替随机序列）以及混沌分形优化四种主要混沌优化算法。混沌映射最早被引入神经网络,发展了混沌神经网络优化方法,可解决复杂的组合优化等全局优化问题。遗传算法及粒子群等启发式随机算法虽具全局搜索能力,但易出现早熟并陷入局部最优。然后,出现了混沌搜索的概念,研究者将其嵌入启发式算法建立了第一类混合混沌优化算法,可有效克服原启发式算法早熟收敛的缺点。随后,利用混沌映射产生的混沌序列代替启发式算法中的随机参数形成了第二类混合混沌优化算法。混合混沌优化算法有益于实现快速全局收敛和提高计算精度。最后,利用混沌分形特性,从分形理论出发提出一类新颖的混沌分形优化算法,可搜索到优化问题的所有全局最优解。此外,对混沌优化算法研究的几个发展方向进行了展望,诸如加强混沌优化算法的参数设计、处理大规模优化、多目标优化问题以及使用代理模型等。     

结构性软土弹塑性模型的隐式算法实现

对于考虑软土结构性的高度非线性弹塑性本构模型,在采用Newton-CPPM隐式算法对模型进行数值实现的过程中容易出现Jacobian矩阵奇异和不收敛问题。为此,本文提出了两种改进隐式算法。考虑到Newton-CPPM隐式算法是局部收敛性算法,因此引入大范围收敛的同伦延拓算法对Newton-CPPM算法的迭代初值进行改进,形成了同伦-Newton-CPPM算法。考虑到Newton-CPPM隐式算法单个迭代步的计算量过大,因此借鉴显式算法的思想提出一种两阶段迭代算法,第一阶段先求出一致性参数,第二阶段采用类似于显示算法的方法进行回代得出状态变量的值。然后,以考虑软土结构性的SANICLAY模型为例,从弹塑性本构模型的组成和算法的特点两个角度分析了引起Jacobian矩阵奇异和不收敛问题的原因,并且在单单元计算的基础上,对全显式算法、传统隐式算法和两种改进隐式算法在计算收敛性、计算精度和计算效率方面进行了对比。最后,将同伦-Newton-CPPM算法和传统隐式算法用于地基承载力多单元计算中,结果表明该算法能够有效地解决Jacobian矩阵奇异和不收敛问题。      

推进－迭代算法计算效率的研究

本文对求解三维定常超音速动性流场的一次空间推进，在每一个推进站沿伪时间层局部迭代的推进－迭代算法作了进一步的研究．在每一推进站（侧向平面）沿伪时间层局部迭代时，给出了四种不同的隐式迭代方法，即沿侧面两个方向（法向和周向）全用隐式；法向隐式而周向采用Ｇａｕｓｓ－Ｓｉｌｄｌｅ来回扫描迭代；法向隐式而周向显式及以系数矩阵谱半径代替系数矩阵的简化标量隐式算法．用这四种算法模拟了三维球锥黏性绕流，给出了四种不同算法的计算效率和收敛特性比较．     

部分输入未知条件下结构动力复合反演的分解算法

在充分利用部分输入已确知而部分输入未知的激励特性的基础上，提出了结构动力复合反演的分解算法，该算法从源头上消除了迭代过程中参数识别与荷载反演的相互影响，降低了问题的计算规模。对于线性参数系统，该算法不经过任何迭代计算即可一次性完成结构参数识别及荷载反演。将其与松弛法结合，可解决非线性参数系统的识别问题，与文献[4]的方法比较，其收敛速度有显著提高。     

结构可靠度分析FORM迭代算法的混沌控制

利用混沌控制原理对FORM收敛失败进行控制. 理清了全局性和局部性两类混沌反馈 控制各种方法的内在联系，说明稳定转换法和自适应调节法属于全局混沌反馈控制 方法，自适应调节法可视为稳定转换法的特例. 参 数调节混合法不过是松弛牛顿法的另一种表达形式，它们都属于局部混沌反馈控制方法. 阐 明了混沌反馈控制表达式与工程力学收敛控制迭代算法的对应关系. 也揭示了这些迭代算法 收敛控制措施的功效和局限性. 提出了一个以稳定转换法为主联合松弛牛顿法的混 沌反馈控制方法，对可靠度分析FORM迭代算法实现了周期振荡、分岔和混沌控制.     

两种滑动轴承油膜压力计算方法的比较

对常用的两种计算滑动轴承油膜力的方法进行了比较。一种是在迭代求解雷诺方程过程中,如果出现角压力,则用零压力来替代的方法;另一种是根据质量守恒理论（ＪＦ０理论）,由Ｅｌｒｏｄ等人提出的空穴算法。指出用负压力充零的方法代替Ｅｌｒｏｌｄ空穴算法,误差不大,但却可以克服Ｅｌｒｏｄ空穴算法不稳定和振荡的缺点,大大节约计算时间。     

烹饪过程中锅具运动姿态测量方法

提出一种用于跟踪烹饪时锅具运动姿态变化的方法.该方法将MEMS陀螺仪、加速度计以及地磁传感器正交三元组安装于锅具柄部,并将其输出信息经过硬件滤波、软件误差补偿之后利用REQUEST算法进行融合.REQUEST算法与EKF算法相同之处在于均为以四元数为基础的迭代算法,而REQUEST算法由于其不易受锅具线加速度影响的特点而表现出优越性.文末通过仿真和实验对该方法进行了验证,并对REQUEST与EKF两种数据融合算法进行了比较,结果显示,即使在锅具高速运动情况下,由REQUEST算法得到的姿态解算精度仍可在以内,而此时由EKF算法得到的解算误差已达以上.上述结果表明,该文提出的方法对于测量锅具运动姿态而言是适用的.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

Careful numerical simulation and analysis of migration-accumulation of Tanhai Region

Numerical simulation of careful parallel arithmetic of oil resources migration-accumulation of Tanhai Region (three-layer) was done. Careful parallel operator splitting-up implicit iterative scheme, parallel arithmetic program, parallel arithmetic information and alternating-direction mesh subdivision were put forward.Parallel arithmetic and analysis of different CPU combinations were done. This numerical simulation test and the actual conditions are basically coincident. The convergence estimation of the model problem has successfully solved the difficult problem in the fields of permeation fluid mechanics, computational mathematics and petroleum geology.     

Role of Second Phase Powders on Microstructural Evolution During Sintering

The influence of second phase fine powders on solid state sintering was investigated in situ by synchrotron radiation X-ray computed tomography (SR-CT). The evolutions of microstructure during sintering of pure SiO₂ powders and SiO₂ powders mixed with Si₃N₄ powders were observed from reconstructed SR-CT images. Typical sintering parameters, which determine mechanical properties, were extracted from the experimental data, and the effects of the second phase powders were quantitatively analyzed. The experimental results showed that with second phase powders, 1) the specific surface area decreases more efficiently; 2) pore shape evolution is accelerated; 3) sintering necks grow faster and 4) densification process is notably accelerated. It was indicated that the Si₃N₄ fine powders enhanced the sintering of the original SiO₂ powders rather than hindering the process. A qualitative explanation based on the experimental results and existing powder sintering theory is provided.     

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.     

Tomographic particle image velocimetry

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume. The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography. The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV). The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels. The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume. The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure. The study focuses on the accuracy of the light intensity field reconstruction process. The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy. A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras. The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700.     

风沙颗粒运动的数字高速摄影图像的分割算法

为了深入理解多因素驱动下风沙颗粒起动的动态演化规律, 需要准确地获得沙质床面附近沙粒群起跳的方式、速度和运动轨迹. 以连续强激光源为照明的数字高速摄影技术是研究这类问题的有效手段, 但由于风沙运动的高速摄影图像具有运动沙粒和静止床面的对比度小、相邻两帧图像相似性小等特点, 原始图像叠加算法难以有效实现目标与背景的分割. 该文提出了基于相邻的风沙运动图像灰度差值变化原理的图像分割算法. 实例显示,只要选择合适的相邻图像灰度差值阈值和自适应二值化处理方法就能实现图像中运动沙粒与床面分割. 当起跳沙粒浓度较低情况下, 基于MATLAB平台的最小距离匹配的粒子追踪算法(PTV算法)能较为准确地恢复床面附近沙粒的运动轨迹.      

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.     

Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle technique. The convergence of three-step iterative sequences generated by the algorithm is also proved.