Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

In this paper,the least square fitting method with the cubic B-spline basis hmctioas is derived to reduce the influence of statistical fluctuations in the gamma ray spectra.The derived procedure is simple and automatic.The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.     

最小二乘B样条函数在火箭发动机数据处理中的应用

在固体火箭发动机地面试验数据处理中,通过应用最小二乘三次B样条函数拟合的方法,进行野值辨识和修复。文中阐述了实际应用中的步骤及应注意的几点问题。为避免常规的控制序列中含有野值而影响数据辨识的问题,提出差别选取控制点循环过滤的方法,实现精度更高的野值辨识。进而采用门限判别方法,实现野值的修复。通过实测数据处理的应用表明,该算法对单个和成片野值的辨识度都很高,适用于火箭发动机地面试验数据处理。     

D-u关系的最小绝对值线性拟合法

 采用最小绝对值方法对几类物质的冲击波速度D与波后粒子速度u的关系进行了直线拟合,并将其与常用的最小二乘法拟合的结果进行了比较。结果显示：对于实验数据分散性较小的密实材料（金属、离子晶体、氧化物等）,两种方法拟合的线性系数一致;而对于实验数据分散性较大的一些疏松材料（包括液体等）,两种方法拟合的线性系数有差异。对所有物质,最小绝对值法拟合的平均绝对误差比最小二乘法拟合的要小,因而最小绝对值法较最小二乘法有更高的准确性。同时讨论了导致这两种拟合差异的因素。     

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

基于Matllab的约束最小二乘法拟合磁滞回线

由实验测得的磁滞回线数据的是一系列离散、带噪声的值。通过约束最小二乘方法对曲线进行分段拟合,使曲线的畸变程度得到了改善,准确地表达磁滞回线的特性,为磁材料的定量分析述提供了基础。     

Vibrational transition spectra of H2＋ in a strong magnetic field

Vibrational transition spectra of H2+ in an ultra-strong magnetic field are determined. The validity of Born-Oppenheimer approximation is analyzed based on one-center method and B-spline basis sets. It is shown that Born-Oppenheimer approximation is reliable for the investigation on the ground state and low excited states of H2+ subjected to the strong magnetic field. Furthermore, it is found that the vibrational transition spectra from 1σ g , 1π u , and 1δ g states lie in infrared, visible, and ultraviolet ranges with increasing magnetic field strength.     

最小二乘法在单缝衍射测波长中的应用

针对单缝夫琅禾费衍射实验,提出了用最小二乘法对测量到的衍射图像相对光强分布进行二次曲线拟合,并由拟合得到的数学表达式确定衍射条纹的精确位置．通过用最小二乘法与非最小二乘法对同一测量数据的处理结果进行比较,结论表明,用最小二乘法处理数据,可明显提高单缝夫琅禾费衍射方法测量光波波长的精度。     

用B样条函数方法研究碱金属原子里德堡态在静电场中的性质

由原子的模型势出发,利用B样条函数方法研究了钾和铯原子的里德堡态在静电场中Stark态能级反交叉位置以及微波场中钾原子的多光子共振吸收谱.研究表明我们的结果与实验和其他理论结果符合得很好.     

Data point selection for weighted least square fitting of cavity decay time constant

For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting(NLSF) method and the linear regression of the sum(LRS) method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.     

Implementation and comparative study of random sequences for nonlinear least square data fitting

A numerical study of nonlinear least square data fitting using random numbers from the congruential generator and several quasi-random generators is presented. The results indicate that at least up to five dimensions some of the quasi-random sequences yield better accuracy than the congruential pseudo-random sequence. Some recommendations for selecting the generators of quasi-random sequences are also given.     

Application of radial basis functions to evolution equations arising in image segmentation

In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.     

基于径向基函数神经网络的荧光光谱技术在菌种识别中的应用

对嗜酸乳杆菌、变异链球菌和保加利亚乳杆菌这三种菌的荧光光谱进行研究,发现在紫外光的激励下,益生菌溶液发出荧光.在最佳激发波长290　nm的激励下,荧光峰值在300—650　nm范围内.采用小波变换对测得的150组光谱数据进行压缩,压缩后每组数据由原来的1341个点减少为168个点,既保留了原图谱的特征,又提高了神经网络的处理速度.径向基函数神经网络方法对压缩后的数据进行研究,对每种菌的40组实验数据进行训练,在此基础上对30组未知数据进行识别.结果表明经过训练之后,径向基函数神经网络能够准确预测未知菌种. 关键词： 荧光光谱 径向基函数神经网络 数据压缩     

基于径向基函数神经网络的荧光光谱技术在菌种识别中的应用

对嗜酸乳杆菌、变异链球菌和保加利亚乳杆菌这三种菌的荧光光谱进行研究,发现在紫外光的激励下,益生菌溶液发出荧光.在最佳激发波长290　nm的激励下,荧光峰值在300—650　nm范围内.采用小波变换对测得的150组光谱数据进行压缩,压缩后每组数据由原来的1341个点减少为168个点,既保留了原图谱的特征,又提高了神经网络的处理速度.径向基函数神经网络方法对压缩后的数据进行研究,对每种菌的40组实验数据进行训练,在此基础上对30组未知数据进行识别.结果表明经过训练之后,径向基函数神经网络能够准确预测未知菌种.     

基于变量选择的偏最小二乘回归法和田间行走式近红外光谱进行土壤碳含量测定研究

针对田间状态下通过行走式设备获取的近红外反射光谱数据,存在干扰因素多,数据获取环境复杂多变,比实验室条件下建立土壤碳预测模型更加困难的情况,研究了通过变量选择来提高模型质量的效果及有效性。从独立检验数据集来分析,与采用所有变量所建模型的预测精度相比,进行变量选择后的预测精度,均有不同程度的提高,说明在建立土壤碳预测模型时,进行光谱变量选择,是有益和必要的。基于无信息变量消除法(UVE)和无信息变量消除-连续投影法(UVE-SPA)进行变量选择所建模型的预测精度较高,而SPA和遗传算法-偏最小二乘法(GA-PLS)的效果较差;对于协同区间最小二乘法而言,分割的区间数、参与建模子区间数的变化,会对所建模型的预测精度产生影响,选择合适的区间分割数和子区间组合,可以获得与UVE和UVE-SPA相当的效果,但其不足是需要大量的运算来进行最优子区间组合的选择。     

基于RANSAC的空间圆拟合算法及其在机械手运动检测中的应用

为了实现对水下机械手运动范围的检测,研发了一套多目立体视觉测量系统。通过测量机械手末端空间运动轨迹,利用空间圆拟合算法可计算出被测关节的实际运动范围。对其中的核心算法空间圆拟合进行了研究。首先空间圆可看作是由一个平面与球体相交而成,其圆心必定在球体上任意两点连线的中垂面上,可基于空间向量的拟合方法推导出中垂面的方程,与拟合的空间平面联立即可求出空间圆方程,进而利用拟合出来的空间圆的圆心坐标求出圆半径。然后对实际测量过程中的错误跟踪点进行了分析,如果在空间圆拟合的过程中对错误跟踪点不加以去除,则会带来错误的拟合结果,从而会大大影响测量结果的正确性。最后提出了基于RANSAC(Random Sample Consensus)的空间圆拟合算法,它可以从一组包含错误点的测量数据集中通过迭代方式有效剔除粗大误差点,从而估计出数学模型的参数和正确的拟合结果。仿真测试及实际测量实验的结果表明,当粗大误差点所占总测量点数的比例小于20%时,所提出的算法可有效地剔除所有粗大误差点,很好地解决了机械手运动范围检测系统在实际工程应用中所遇到的问题。     

Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

The maximum entropy (MaxEnt) principle is a versatile tool for statistical inference of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdf’s. It maximizes Shannon entropy, satisfying the moment constraints. Thus, the MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m>5–10)$(m>5''–''10)$ due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. Classic MaxEnt algorithms overcome these difficulties by using orthogonal polynomials, which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper, we employ an idea based on different principles, using Fup_n${\mathit{Fup}}_n$ basis functions with compact support, which can exactly describe algebraic polynomials, but only if the Fup order-n   is greater than or equal to the polynomial’s order. Our algorithm solves the CMP with respect to the moments of only low order Fup₂${\mathit{Fup}}_2$ basis functions, finding a Fup₂${\mathit{Fup}}_2$ optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup₂${\mathit{Fup}}_2$ basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Only consequences are an iterative scheme of the algorithm where power moments are a sum of Fup₂${\mathit{Fup}}_2$ and residual moments and an inexact entropy upper bound. However, due to small residual moments, the algorithm converges very quickly as demonstrated on two continuous pdf examples – the beta distribution and a bi-modal pdf, and two discontinuous pdf examples – the step and double Dirac pdf. Finally, these pdf examples present that Fup MaxEnt algorithm yields smaller entropy value than classic MaxEnt algorithm, but differences are very small for all practical engineering purposes.     

Rapid determination of flavonoids in green tea by synchronous fluorescence spectra coupled with chemometrics

Flavonoids are one of the most important antioxidant compounds of tea. It is necessary to determine flavonoid concentration of tea infusions and to understand how the storage condition and tea brewing processing impact on flavonoid content. The aim of this study is to analyze flavonoids’ properties and predict flavonoid concentration using synchronous fluorescence spectra coupled with chemometrics. Different wavelength intervals were measured to develop an optimal model. Successive projection algorithms and interval partial least square regression were applied to extract informative wavelengths. The optimal interval partial least square regression model was obtained with the determination coefficient of calibration of 0.95, determination coefficient of cross-validation of 0.90.     

光点定位中的曲面拟合迭代算法

在光电检测系统中,需要对光点信号的位置实现亚像素定位。光纤从一端照明,由光纤另一端出射光点,由面阵CCD摄像机获取光点的灰度分布。基于最小二乘法,采用高斯曲面拟合算法拟合其分布,用高斯拟合函数的极值点作为光点的定位点。实验结果表明,采用多次迭代算法可以提高定位精度;拟合算法的稳定性(标准差)为0.7μm.高斯曲面拟合算法具有重复精度高、稳定性好的特点。     

基于偏最小二乘回归的荧光粉涂覆型白光LED的光谱预测研究

为了更便捷高效地对荧光粉涂覆型白光LED的发光光谱进行预测,利用GaN蓝光LED芯片与杭州萤鹤光电材料有限公司的YH-S525M绿色荧光粉和YH-C640E红色荧光粉进行实验样品的制备。分别测量其单色荧光光谱,测得蓝光芯片的发射峰波长为453 nm,选用的红色和绿色荧光粉的发射峰波长分别为631和526 nm。制备红色和绿色荧光粉通过AB胶混合并涂覆于蓝光芯片上的LED实验样品,红粉/绿粉质量比设置为1∶3,1.2∶3,1.4∶3,1.6∶3,1.8∶3,2∶3,红粉混胶后的浓度为7%,9%,11%,13%,15%,17%。每组质量比和混胶浓度条件下的样品制备3~5份,利用杭州远方色谱有限公司的HAAS-2000高精度快速光谱辐射计测试样品的发光光谱,并进行蓝峰归一化处理得到共36组光谱数据。将白光光谱视为蓝色,绿色和红色三种单色荧光光谱的线性叠加,蓝色和红色峰项直接选用对应的发射谱,而绿色峰项选用两个高斯线型方程拟合,系数均由强度决定。通过循环搜索算法,分别计算36组实验条件下的模型参数最优值,对拟合结果进行优度检验,R2的范围为99.33%~99.88%。然后运用偏最小二乘回归方法建立荧光粉质量比和浓度与模型参数间的回归方程,最终得到一种能够精确预测两种荧光粉混合涂覆的白光LED发光光谱的新方法。用一组新制备的样品测得的光谱功率分布进行预测效果检验,得到的预测光谱相对于实测光谱的拟合优度为99.62%,证明该方法的预测效果良好。该研究建立的预测模型从该类型的白光LED的发光机理出发,分析发光时两种荧光粉之间的相互作用,并引入绿色荧光谱线的展宽效应,更加简单有效地建立起两种荧光粉的质量比和混胶浓度与白光光谱间的数学关系。该方法具有更好的普适性,为荧光粉涂覆型LED的光源参数优化提供了一种新的思路。     

净信号预处理结合径向基偏最小二乘回归在血糖无创检测中的应用

为了提高人体血糖近红外光谱定量分析模型的预测精度,结合净信号预处理(NAP)算法和径向基偏最小二乘(RBFPLS)回归建立了一种适合于人体血糖测量的非线性建模方法NAP-RBFPLS。本文首先利用NAP对近红外光谱进行预处理来有效地提取原始光谱中仅与葡萄糖信号相关的光谱信息,从而有效地减弱了人体血液中水、白蛋白、血红蛋白、脂肪等成分的吸收干扰以及人体体温的变化、测量仪器本身的漂移、测量环境的变化和测量条件的变化引起的干扰因素与血糖变化的偶然相关问题;然后把净信号预处理后的近红外光谱数据通过RBFPLS建立了非线性定量分析模型来解决由于人体强散射引起的血糖浓度与近红外光谱之间的非线性关系,并与偏最小二乘(PLS)、基于净信号预处理的偏最小二乘(NAP-PLS)和RBFPLS这三种建模方法建立的定量分析模型进行了对比分析。实验结果表明,这两种方法相结合建立的非线性校正模型对预测集的预测精度有了很大的提高,这将对人体血糖浓度无创检测技术的研究具有实际应用价值。