基于约束共轭梯度的高能闪光照相图像复原算法

 针对闪光照相系统模糊较大、成像信噪比低的特点,提出了一种基于约束共轭梯度的闪光照相图像复原算法,将闪光照相图像复原问题转化为一个约束优化问题,引入基于非负、中值滤波和偏微分方程的光滑约束条件,并利用约束共轭梯度法迭代求最优解。数值试验表明,该算法能较好再现图像边缘信息,复原出的图像在信噪比和视觉方面都有较大提高。     

三维声波方程逆问题的共轭梯度法求解

考虑一个完整的三维声波方程的逆问题．通过构造一个表面声压偏差平方和形式的目标泛函，把声波方程的逆问题转化为一个控制声学特性参数分布使得目标泛函达到最小伍的优化问题．采用共轭梯度法来求解这个优化问题．通过引入一个对偶函数u（x，t），文中用微扰法求得了目标泛函梯度值的解析表达式，从而克服了以往用共轭梯度法求解偏微分方程控制的优化问题时计算目标活函梯度的困难，大大压缩了共轭梯度法计算目标泛函梯度的时间，而且提高了梯度值的计算精度．还进一步进行了反演声学特性参数三维分布的数值仿真计算．共轭梯度法完整解决了三维声波方程的逆问题．     

管道内壁侵蚀形状识别的无网格法研究

本文使用直接配点无网格法结合共轭梯度法对管道内壁面侵蚀状况进行了反演识别。直接配点无网格法使用节点离散求解区域,采用移动最小二乘近似构造试函数,直接配点法构造线性方程组进行导热正问题求解;反演过程采用共轭梯度法使目标函数最小化,Akima三次样条插值将连续的几何边界反演问题转化为离散点几何位置的反演,并最终将这些离散点拟合成为光滑曲线。文中选择两个典型算例对数值方法进行验证,模拟结果表明使用直接配点无网格法结合共轭梯度法进行管道内壁几何边界识别具有较高精度。     

QL-Born迭代法电磁散射计算

积分方程法是多维电磁响应的数值模拟和反演计算的有效方法之一.在线性化散射电磁场积分方程的基础上,采用迭代Born近似法进行了电导率成像反演.针对迭代Born近似法反演依赖初始模型,而QL近似法无需给定初值的特点,提出了两步法(QL-Born迭代法),用QL近似法计算的结果作为Born迭代法的初始模型,避免人为设置初值,并进行了数值实验.     

基于约束共轭梯度的高能闪光照相3维重建算法

 针对高能闪光照相系统成像信噪比低的特点，提出了3维约束共轭梯度算法，该算法基于3维重建理论来重建方程，利用约束共轭梯度法迭代求图像重建的最优解。数值模拟结果表明：采用3维约束共轭梯度算法能有效改善高能闪光照相重建图像轴线噪声大的问题，是一种具有很高抗噪能力的闪光照相图像重建算法。     

共轭梯度法求解双曲传热多宗量反问题

提出双曲传热反问题热物性参数和边界条件多宗量联合反演的一般数值求解模式,考虑了非均质和分布参数的影响,时域上采用时域精细算法进行离散,建立了便于敏度分析的有限元正演模型.由最小二乘原理建立反演模型,应用共轭梯度法进行求解.探讨了时间步长和测量误差对反演结果的影响,并进行了数值验证.     

基于频域辐射传输模型的光学成像研究

本文以超短脉冲激光照射参与性介质的光学成像为研究背景,分别构建了短脉冲激光在参与性介质内的频域辐射传输正问题模型和根据边界探测所得频域信号重建介质内部光学参数的逆问题模型。在瞬态辐射传输方程的基础上,利用傅里叶变换得到频域辐射传输方程,采用有限体积法求解频域传输方程,模拟超短脉冲激光在二维参与性介质内传输的过程,得到介质边界的出射频域辐射信号。选取共轭梯度法作为反演算法,采用伴随差分模型求解目标函数梯度,重建了二维非均匀参与性介质内不同位置内含物的光学参数分布。结果表明,基于频域辐射传输方程的伴随差分模型能够较为准确地反演多维参与性介质内的光学参数。     

基于L1范数的低场核磁共振T_2谱稀疏反演方法

低场核磁共振技术(LF-NMR)以其无损、非侵入、原位和绿色等优势被广泛应用在食品、农业、能源和化工等行业,尤其是在食品安全监管领域发挥着越来越重要的作用.在油品品质检测中,常规非负奇异值分解(SVD)弛豫(T_2)谱反演方法,只能反映光滑模型的T_2谱,对于稀疏模型的反演结果存在较大差异,从而导致T_2谱反演分辨率低和品质分析不准确的问题.针对这一问题,本文提出基于L1范数最小化约束的T_2谱稀疏反演算法,建立NMR回波曲线的稀疏模型表达式,利用截断牛顿内点法求解L1范数最小化问题,得到稀疏模型的T_2谱反演结果.通过构造光滑模型的T_2谱、以及不同峰值数和信噪比的稀疏模型的T_2谱,对比非负SVD算法和L1稀疏算法的反演效果,得到当信噪比大于20 d B时,L1稀疏算法能精确反演多峰T_2谱,峰值幅度和峰位置均优于非负SVD算法结果.最后通过多组煎炸油样品进行低场核磁共振检测实验和不同信噪比数据的反演结果对比,验证了L1范数稀疏反演算法的准确性和优越性.     

基于差分进化算法的核磁共振T2谱多指数反演

提出了一种基于差分进化(DE)算法的核磁共振弛豫信号多指数反演新方法.将核磁共振T2谱反演问题转化为带非负约束的非线性优化问题,不需要预先给定横向弛豫时间T2分布,直接利用差分进化算法进行反演计算.在测量信号低信噪比的情况下,计算机模拟和实验数据反演鄙表明了该方法在分析处理NMR弛豫信号中的有效性.     

高频地波雷达多站浅海水深与海流反演

针对高频地波雷达浅海观测尝试中面临的参数反演新问题进行了研究.描述了高频地波雷达浅海探测机理,提出了多站高频地波雷达海洋参数反演方法,并推导了利用多站高频地波雷达回波多普勒谱反演浅海水深和矢量流的理论模型.通过三站探测和多站探测的反演数值模拟,表明了多站浅海探测的可行性和反演方法的有效性;通过分析苏北浅滩的三站高频地波雷达观测试验数据,表明了本文反演方法的实用性,这对于利用高频地波雷达进行浅海海洋环境探测的实际工程应用具有广阔的前景.     

具5次强非线性项的波方程新的孤波解

提出一种新的函数变换法，并与直接积分法相结合简便地求出了Lienard方程、广义PC方程以及力学中重要的一类非线性波方程等几类具5次强非线性项的波方程的四类显示精确孤波解.本方法同样适用于求解其他具有更高次非线性项的非线性方程. 关键词： 函数变换法 孤波解 直接积分法 非线性波方程     

Low frequency coupled mode sound propagation over a continental shelf

A two-way integral equation coupled mode method is applied to a continental shelf ocean waveguide proposed for a special session devoted to range-dependent acoustic modeling at the 141st meeting of the Acoustical Society of America. The coupled mode solution includes both sediment trapped and continuum modes. The continuum is approximated by a finite number of leaky modes but neglects the branch cut contribution. Mode coupling matrix elements and the range evolution of the modal amplitudes show the nature of the mode coupling. Transmission loss versus range at 100 Hz predicted by the integral equation approach is compared to the transmission loss predicted by a wide angle parabolic equation method. While there is very good agreement, one observes small differences that can be interpreted as backscattering predicted by the integral equation solution.     

非紧凑低马赫数运动边界散射流动噪声的预测

提出了一种求解非紧凑低马赫数运动边界散射流动诱发噪声的预测方法。该方法首先基于运动坐标系下的连续性方程和动量方程推导得到该坐标系下的波动方程及其积分解,然后在该坐标系下采用边界元方法求解得到非紧凑运动边界表面的声压,最后将求解得到的壁面声压回代到静止或运动坐标系下的积分方程中实现对远场噪声的预测。推导得到的积分方程适用于流体与飞机机身、高速列车车身及旋转叶片等非紧凑结构边界作用诱发噪声的预测。     

Burton-Miller改进型边界方程的多频计算方法

提出了一种采用Burton-Miller改进型边界积分方程进行多频计算的方法。将Burton-Miller方程中的高奇异积分转化为弱奇异积分形式,获得Burton-Miller改进型边界积分方程;将方程中格林函数进行Taylor级数展开,并把波数从方程中分离出来,从而使随波数变化的计算矩阵表示为波数的矩阵级数形式。数值分析表明,本方法不仅保证了解在全波数范围内的唯一性,并且计算频率点数较多时可以节约大量时间,提高计算效率。      

Application of SSOR Preconditioning Technique to Method of Lines for Millimeter Wave Scattering

In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps.     

Analysis of Millimeter Wave Scattering by an Electrically Large Metallic Grating Using Wavelet-Based Algebraic Multigrid Preconditioned CG Method

An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background.     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique

A hybrid finite element–boundary integral–characteristic basis function method (FE-BI-CBFM) is proposed for an efficient simulation of electromagnetic scattering by random discrete particles. Specifically, the finite element method (FEM) is used to obtain the solution of the vector wave equation inside each particle and the boundary integral equation (BIE) using Green's functions is applied on the surfaces of all the particles as a global boundary condition. The coupling system of equations is solved by employing the characteristic basis function method (CBFM) based on the use of macro-basis functions constructed according to the Foldy–Lax multiple scattering equations. Due to the flexibility of FEM, the proposed hybrid technique can easily deal with the problems of multiple scattering by randomly distributed inhomogeneous particles that are often beyond the scope of traditional numerical methods. Some numerical examples are presented to demonstrate the validity and capability of the proposed method.     

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.     

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.