解线性代数方程组的TCG迭代法

ICCG方法是解线性代数方程组较为理想的方法,但它仅适用于具有正定对称的系数阵。本文介绍的TCG方法便足改造过的ICCG方法,它适用于一般非奇异的非正定对称阵。TCG方法比常用的JLUCG方法,对于非定常问题,可提高效率18%,特别是取用SIP不完全L、U分解作预条件时,可提高效率40%,是计算非正定对称阵较为理想的迭代法之一。本文推导出在消去法不完全L,U分解下的TCG方法,并用数值结果论证出它比ILUCG方法加速收敛的所在。     

一步法设计单色仪凹面全息光栅

凹面全息光栅是光谱分析仪器的核心器件之一,其成像质量直接决定了光谱分析仪器的分辨本领。利用光程函数理论设计凹面全息光栅是一个繁琐的求解非线性方程组的过程,该过程分两步进行,每步需要求解四个非线性方程。分两步求解不但过程麻烦,还不可避免地引入了取舍误差,降低了最优参数的精度。为了解决该问题,本文提出了一种设计单色仪凹面全息光栅的新方法——一步法,该方法不但可以简化求解过程、降低最优参数的误差,还可以方便地控制整体像差的变化趋势。采用有较强全局搜索能力的遗传算法求解该方法中非线性方程的极值问题,并与传统的方法对比验证了该方法的可行性和正确性,结果表明,一步法不但在方法上比两步法简便,其设计结果还优于两步法。     

基于小波变换的新型数字散斑相关方法

通过将小波分析的方法应用到传统的空域相关计算中,提出了基于小波变换的数字散斑相关方法。详细介绍了该方法的原理,并对传统空域相关方法与小波相关方法进行了实验计算比较。实验结果表明,与传统的空域相关方法相比,基于小波变换的数字散斑相关方法大大提高了相关计算的精度,精度由0 05像素提高到了0 01像素以下。最后利用该方法测量了编织结构复合材料板在三点弯曲载荷作用下的位移场。     

融合RANSAC光流跟踪法和特征点匹配法的视觉里程计

为了解决光流跟踪法定位精度不足、误差累积和特征点匹配法耗时久的问题,设计了一种将随机抽样一致性（random sample consensus,RANSAC）光流跟踪法和改进的特征点匹配法结合的视觉里程计。利用RANSAC光流跟踪法对关键帧之间的小规模运动进行估计,RANSAC算法对光流跟踪的误匹配点进行剔除,大大降低了光流跟踪法存在的误匹配;而关键帧之间的运动估计则利用改进的特征点匹配法,以修正光流跟踪法的估计误差;最后利用卡尔曼滤波将RANSAC光流跟踪法和改进的特征点匹配法进行融合。实验结果表明:该文的算法能够克服光流跟踪法精度不足、误差累积的问题,将平均相对误差由15.5%提升到了2.6%;同时也能在一定程度上提高特征点匹配法的速度,将特征点匹配法的平均耗费时间由37.28 ms提升到了21.07 ms。     

基于B样条的拉曼光谱基线校正方法

基线漂移是光谱检测仪器普遍存在的现象,会对光谱信号的特征提取带来十分不利的影响,而基线校正是解决该问题的重要手段,也是拉曼光谱信号预处理的重要组成部分。基线校正的原理一般是通过拟合基线的方法来去除光谱信号中的基线漂移。传统的基线校正方法是利用多项式拟合的方法对拉曼光谱信号的基线进行拟合的,但是该方法容易出现过拟合和欠拟合现象,且拟合阶数难以确定。针对传统方法的缺点进行了改进,利用B样条方法对拉曼光谱信号的基线进行拟合,发挥B样条低阶光滑的优点,能够有效地克服多项式方法的缺陷。在实验中,利用该方法对孔雀石绿、罗丹明B的拉曼光谱信号进行了基线校正,观察并比较该方法和传统方法的校正结果。实验结果表明,该方法能够有效地消除拉曼光谱信号的基线漂移,在基线漂移较小和较大的位置,可以采用相同的拟合阶数,不会出现欠拟合和过拟合的现象,获得了良好的基线校正效果,为进一步分析光谱数据提供准确可靠的信息。     

一种基于连续小波变换的LIBS光谱自动寻峰方法

谱线寻峰在激光诱导击穿光谱(laser-induced breakdown spectroscopy)中是必不可少的步骤,然而噪声和背景的存在,干扰了寻峰的准确性。为了提高LIBS寻峰中重叠峰分辨能力和自适应能力,提出一种适用于LIBS谱图的自动寻峰方法。将基于连续小波变换的脊线寻峰法引入到LIBS中,探讨了连续小波变换中的小波母函数的选择并优化了尺度参数和平移参数,提出一套脊线校正方法对脊线寻峰法进行了改进。实验结果表明,该方法与直接比较法、导数法和脊线寻峰法相比,在重叠峰分辨能力和寻峰精度等方面优势显著,可应用于LIBS数据处理。     

蒙特卡洛模拟漫辐射时两种确定表面发射方向方法的比较

介绍一种有效的确定能束发射方向的方法——切球法.分析传统方法和切球法确定发射方向的原理及实施过程,说明切球法更为方便.采用2种方法对一简单的几何模型的角系数进行蒙特卡洛计算,所得结果与文献中积分结果进行比较,说明了切球法的可行性,计算精度能满足工程要求.同时对2种方法的计算耗时进行比较,切球法可以节省计算时间.将切球法应用到复杂系统中其优越性将会得到更加充分体现.     

基于自适应频率不变响应基阵的宽带信号方位估计

提出一种设计频率不变响应基阵的自适应模拟方法，并将其用于构造波束形成矩阵来实现宽带信号的聚焦。该方法不仅保持了波束域方位估计算法的运算量小、分辨率高等优点，还具有相关信号子空间能解相关源的能力，且对阵形及各阵元的指向性也没有任何限制。仿真结果说明了本文方法的有效性。     

A Biblock Wavelet Zero Tree Coding for Hyperspectral Imagery Data Compression

In this paper, a biblock zero tree compression coding (BBZTC) method, based on wavelet zero tree compression coding (ZTC), is used to exploit redundancy in hyperspectral imagery data. Because of ZTC scanning every wavelet zero tree coefficients with low efficiency, BBZTC method outperforms ZTC in the aspects of high compression ratio, simple real-time implementing, and higher coding/decoding speed, and convenient real-time transmission. The experimental results show that this method can obtain the compression ratio 17～40 times of 224 spectral bands to remove the spectral correlation without any coding by using KLT, and the total compression performance of KLT+BBZTC method is better than the method of KLT and other one dimensional transformation (such as DCT) to remove the spectral correlation. To compare with the total compression ratio of KLT+JPEG method and SFCVQ method, this method reaches 180 at the PSNR of 33.6 db. This method is superior to the present any other method at compression rate.     

能量色散X射线荧光分析中改进型基本参数法研究

能量色散X射线荧光分析方法是目前常用的一种多元素分析方法,但该方法检出限和分析精度,受到分析基体的影响。基本参数法是目前一种常用的分析方法,但在使用过程必须获取净峰面积和基体所有成分,而在实际使用时,尤其在分析低含量样品时,净峰面积计算、基体中“暗物质”影响了测量精度,制约了基本参数法的应用。针对基本参数法的不足,将谱线解析方法与基本参数法融合,将重叠峰剥离过程嵌入基本参数法迭代过程中。在含量计算过程中,采用分析样品特征X射线分支比的理论系数,对重叠峰进行剥离,解决能量色散X射线荧光测量中净峰面积计算和定量分析问题;在计算过程中,对“暗物质”进行均一化处理。通过对标准物质测量分析,结果表明对于Ni,Cu,Zn三个元素改进型基本参数法(改进型FP)测量结果准确度高于影响系数法。     

正则化参数求解方法研究

针对BP神经网络算法训练过程中出现的过拟合问题,提出了利用一阶原点矩,二阶原点矩,方差和极大似然估计概念的推广来计算L2正则化中正则化参数 值的方法。该方法通过对算法数据集[X,Y]中的X矩阵进行运算得到的四个 值,BP神经网络算法训练时通常采用的是贝叶斯正则化方法,贝叶斯正则化方法存在着对先验分布和数据分布依赖等问题,而利用上述概念的推广计算的参数代入L2正则化的方法简便没有应用条件限制。在BP神经网络手写数字识别的实验中,将该方法与贝叶斯正则化方法应用到实验中后的算法识别结果进行比较,正确率提高了1.14-1.50个百分点。因而计算得到的 值应用到L2正则化方法与贝叶斯正则化方法相比更能使得BP神经网络算法的泛化能力强,证明了该算法的有效性。     

A Biblock Wavelet Zero Tree Coding for Hyperspectral Imagery Data Compression

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Improved Faddeev-Jackiw quantization of the electromagnetic field and Lagrange multiplier fields

We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields.The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is given.We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method.Moreover,it is simpler than the usual one if one needs to obtain new secondary constraints.Therefore,the improved Faddeev-Jackiw method is essential.Meanwhile,we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers.     

Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method

The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable and $s$-stage $s$-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method of $s$-stage $2s$-order has been proposed by using undetermined coefficients method and Padéapproximations. The numerical results show that the proposed differential quadrature method is more precise than the traditional differential quadrature method.     

罗替戈汀微球体外释放度的检查方法

分别采用摇床法和流通池法测定罗替戈汀微球的体外释放度,并通过与体内药动学曲线拟合进行选择.结果表明,摇床法和流通池法测定的体外释放度均与体内吸收具有明显相关性,相关系数r分别为0.9937和0.9978,且流通池法可检测到微球存在的较小突释.摇床法和流通池法均可用于罗替戈汀微球的体外释放度检查,流通池法作为一种新型溶出...     

Solving Time-Fractional Advection–Dispersion Equation by Variable Weights Particle Tracking Method

Particle tracking method is an efficient and reliable method to solve time-fractional advection-dispersion equation, which can describe anomalous transport in heterogeneous porous media. However, this method will lead to severe fluctuation or disappearance of solutions if the concentration value is small. A variable weights method is developed to conquer the shortcoming of particle tracking method. Then, one-dimensional and two-dimensional time-fractional advection-dispersion equations are solved by the variable weights particle tracking method. Compared to traditional particle tracking method, the variable weights version may eliminate the fluctuation and improve the accuracy by orders of magnitude without more computational cost.     

Scattering of light by axially symmetric particles: Modification of the point-matching method

The approach based on the separation of the fields into two parts with definite properties and the proper choice of special scalar potentials for each of them is applied to the point-matching method. Earlier, such a procedure carried out within the framework of the method of separation of variables for spheroids allowed us to obtain a solution that is considerably more efficient for strongly prolate and strongly oblate particles than solutions obtained with other versions of this method. It was found that the replacement of the summation over points on the particle surface in the point-matching method by the corresponding integral leads to a faster and more exact algorithm. The applicability of the proposed method is considered in comparison with the related method of extended boundary conditions. For spheroids and Chebyshev particles with a maximum-to-minimum-size ratio exceeding 1.5–2, the efficiency of the point-matching method is not high. For other Chebyshev particles, the point-matching method is undoubtedly preferable to the commonly used method of extended boundary conditions since it allows one to increase the accuracy of calculations by several orders of magnitude. Moreover, whereas the latter method is in principle inapplicable to certain Chebyshev particles, the former lacks this disadvantage.     

荧光寿命的快速傅里叶变换拟合方法

介绍了一种利用快速傅里叶变换算法对稀土掺杂物质的荧光寿命进行数据拟合的方法。稀土掺杂物质可用来制备多种光学传感器,用于温度、pH值等多种参量测量领域。本方法利用快速傅里叶变换(FFT)结果作为基础,从非零项的相位角的正切值得出被测的荧光寿命,具有速度快、误差小、不受本底干扰等一系列优点。以掺铒光纤为例,通过数字仿真将本方法与其它几种传统的拟合方法进行了比较。快速傅里叶变换方法的测量偏差不到Prony方法的50％,为对数似合(log-fit)方法测量偏差的1／6。另外,快速傅里叶变换方法由于不受本底噪声影响,可以不必在信号处理时去掉本底噪声,因而可以明显缩短测量时间。     

路径积分Monte Carlo方法与非线性随机振动

给出了一种求解非线性随机振动问题的新方法-基于路径积分表述的Monte Carlo方法。受白噪声激励的非线性系统的各响应统计值被表成路径积分形式,并采用Monte Carlo方法进行计算。讨论了应用方面的问题,并计算了两个实例。     

点堆中子动力学方程组曲率权重法的解

针对核反应堆安全工程对某些数值计算结果要求较高的精度和正的误差, 以及舰船核反应堆机动性对计算速度的要求, 需要从数学上寻找一种新的数值计算方法, 以满足实际曲线向上凸或向下凹时计算值总是略高于真实值, 且误差不大于欧拉法和改进的欧拉法所得值. 本文研究曲率权重法求解点堆中子动力学方程组, 该方法是在曲率圆法的基础上引入权重的思想来衡量间隔步长上两个曲率对该步长曲率平均值的贡献. 与欧拉法和改进的欧拉法比较, 曲率权重法的计算结果总是能够高于真实值或有正的误差, 且精度和计算速度得到明显提升. 将该方法用于次临界堆阶跃和线性引入反应性时中子密度的求解, 能够快速得到满足计算要求和高精度的数值结果.