高光谱成像技术的油菜叶片氮含量及分布快速检测

应用高光谱成像技术实现了油菜苗-花-角果整个生命期叶片氮含量的快速检测和氮素水平分布的可视化。采集三个生长时期共计420个叶片样本的高光谱图像信息(380～1 030 nm),提取图像中感兴趣区域的平均光谱数据,经过不同光谱预处理后,利用连续投影算法(SPA)选择特征波长,将提取的12个特征波长(467,557,665,686,706,752,874,879,886,900,978和995 nm)作为自变量,叶片氮含量作为因变量,分别建立偏最小二乘法(PLS)和最小二乘-支持向量机(LS-SVM)模型。SPA-PLS和SPA-LS-SVM模型对叶片氮含量的预测相关系数R_P分别为0.807和0.836,预测均方根误差RMSEP分别为0.387和0.358。高光谱图像中的每一个像素点都有对应的光谱反射值,利用结构简单、更易提取回归系数的SPA-PLS模型,快速计算出12个特征波长下高光谱图像中每个像素点对应的氮含量预测值,结合像素点的空间位置生成氮素浓度的叶面分布图。可视化分布图详细且直观的反应出同一叶片内部或不同叶片之间氮含量的差异。结果表明,应用高光谱成像技术分析整个油菜生长期的叶片氮含量及其可视化分布是可行的。     

验证辐射强度与距离平方反比率的实验

利用Nal闪烁谱仪测量了在探测器与放射源间某个距离下对应的计数率.对测量的数据分别利用等精度最小二乘法和未知参数逼近法进行了处理,观察到在某些未知参数下,最小二乘法引起的误差很大,利用未知参数逼近法得到的值能和真实值较好接近,从而验证了辐射强度与距离平方反比率.     

高光谱成像技术的柑橘植株叶片含氮量预测模型

氮素是果树生长发育的一种大量必需元素,及时准确地监控果树的氮营养状况,对果树的合理施肥、增产、优化果实品质以及减缓过量施氮引起的水资源污染具有重要意义。利用高光谱成像技术结合多变量统计学方法,建立了柑橘植株叶片的含氮量预测模型。研究步骤为：高光谱扫描、提取平均光谱曲线、预处理原始光谱数据、采用连续投影法提取特征波段和建立含氮量预测模型。从SG平滑、SNV、MSC、1-Der等11种预处理方法中筛选出的较优预处理方法是SG平滑、Detrending和SG平滑-Detrending。对应这三种最优预处理方法,先采用连续投影法挑选出各自的特征波长,然后将各特征波段下的光谱反射率作为偏最小二乘、多元线性回归和反向传播人工神经网络模型的输入,各自建立三个预测模型。从以上获得的9个预测模型中,得出两个最优模型SG平滑-Detrending-SPA-BPNN(R_p：0.851 3,RMSEP：0.188 1)和Detrending-SPA-BPNN(R_p：0.8609,RMSEP：0.159 5)。结果表明,利用高光谱数据测定柑橘叶片含氮量具有可行性。这为实时、准确地监控柑橘植株生长过程中叶片含氮量的变化以及合理科学的氮肥施加提供了一定的理论基础。     

PLS在基于动态光谱的人体血液中性粒细胞无创测量中的应用

利用动态光谱指端透射法进行了人体血液中性粒细胞百分比无创测量的研究。对21名健康志愿者进行了在体测量,选用偏最小二乘法(PLS)对获取的动态光谱数据和中性粒细胞百分比实测值进行建模分析,建立的定标集的相关系数为0.922,最大相对误差为5.85%,平均相对误差为4.13%;对定标模型的预测能力进行了验证,其中预测集的相关系数为0.912,预测集的相对误差最大为6.74%,平均相对误差为5.07。结果表明：动态光谱法可以有效地克服测量位置及人体成分等对光谱测量的影响,较准确地进行人体血液中性粒细胞百分比的测量,是一种比较好的血液成分无创测量方法,具有较高的临床应用价值。     

矩阵方程AXB+CYD＝E的对称极小范数最小二乘解

对于任意给定的矩阵A∈Rm×n,B∈Rn×s,C∈Rm×k,D∈Rk×s,E∈Rm×s,本文利用矩阵的Kmnecker积和Moore-Penrose广义逆,研究矩阵方程AXB CYD=E的对称极小范数最小二乘解,得到了解的表达式．并由此给出了矩阵方程AXB=C的双对称极小范数最小二乘解的表达式．此外,我们还给出了求矩阵方程AXB=C的双对称极小范数最小二乘解的数值算法和数值例子．     

A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS

Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row rank preservation conditions. According to these conditions, in this paper we show that in general, ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem. We then propose a row block modified Gram-Schmidt algorithm with column pivoting, and show that with appropriately chosen tolerance, this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices, and the computed QR factor R^- contains small roundoff error which is row stable. Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting.     

近红外光谱技术快速鉴别地沟油与食用植物油的研究

地沟油检测是我国食品安全最为关注的话题之一,它给人们的生活健康带来了极大的危害。国内现有的检测手段也仅停留在定性检测水平上,只能确定地沟油的有无,还难以进行定量检测。本实验利用近红外光谱技术与光纤传感技术相结合的新方法对勾兑混合油中地沟油的含量进行了定量分析。将煎炸老油与九三大豆油按照一定的体积比进行勾兑,共计50个样本,采集其近红外透射光谱,分别采用偏最小二乘法(PLS)和BP人工神经网络建立了煎炸老油含量的定量分析模型,校正集决定系数分别为0.908和0.934,验证集决定系数分别为0.961和0.952,均方估计残差(RMSEC)为0.184和0.136,预测均方根误差(RMSEP)都为0.111 6,符合应用要求,同时还结合主成分分析法(PCA)对煎炸老油与食用植物油进行了鉴别,识别准确率为100%。实验研究证明近红外光谱技术不仅可以准确快速的定性分析地沟油, 还能定量的检测地沟油的含量,在油脂的检测方面具有很大的应用前景。     

非线性最小二乘问题的信赖域方法

本文提出一个新的非线性最小二乘的信赖域方法,在该方法中每个信赖域子问题只需要一次求解,而且每次迭代的一维搜索步长因子是给定的,避开一维搜索的环节,大大地提高了算法效率.文中证明了在一定的条件下算法的全局收敛性.     

Analysis of large experimental datasets in electrochemical impedance spectroscopy

An approach for the analysis of large experimental datasets in electrochemical impedance spectroscopy (EIS) has been developed. The approach uses the idea of successive Bayesian estimation and splits the multidimensional EIS datasets into parts with reduced dimensionality. Afterwards, estimation of the parameters of the EIS-models is performed successively, from one part to another, using complex nonlinear least squares (CNLS) method. The results obtained on the previous step are used as a priori values (in the Bayesian form) for the analysis of the next part. To provide high stability of the sequential CNLS minimisation procedure, a new hybrid algorithm has been developed. This algorithm fits the datasets of reduced dimensionality to the selected EIS models, provides high stability of the fitting and allows semi-automatic data analysis on a reasonable timescale. The hybrid algorithm consists of two stages in which different zero-order optimisation strategies are used, reducing both the computational time and the probability to overlook the global optimum. The performance of the developed approach has been evaluated using (i) simulated large EIS dataset which represents a possible output of a scanning electrochemical impedance microscopy experiments, and (ii) experimental dataset, where EIS spectra were acquired as a function of the electrode potential and time. The developed data analysis strategy showed promise and can be further extended to other electroanalytical EIS applications which require multidimensional data analysis.     

Computing the conditioning of the components of a linear least‐squares solution

In this paper, we address the accuracy of the results for the overdetermined full rank linear least‐squares problem. We recall theoretical results obtained in (SIAM J. Matrix Anal. Appl. 2007; 29 (2):413–433) on conditioning of the least‐squares solution and the components of the solution when the matrix perturbations are measured in Frobenius or spectral norms. Then we define computable estimates for these condition numbers and we interpret them in terms of statistical quantities when the regression matrix and the right‐hand side are perturbed. In particular, we show that in the classical linear statistical model, the ratio of the variance of one component of the solution by the variance of the right‐hand side is exactly the condition number of this solution component when only perturbations on the right‐hand side are considered. We explain how to compute the variance–covariance matrix and the least‐squares conditioning using the libraries LAPACK (LAPACK Users' Guide (3rd edn). SIAM: Philadelphia, 1999) and ScaLAPACK (ScaLAPACK Users' Guide. SIAM: Philadelphia, 1997) and we give the corresponding computational cost. Finally we present a small historical numerical example that was used by Laplace (Théorie Analytique des Probabilités. Mme Ve Courcier, 1820; 497–530) for computing the mass of Jupiter and a physical application if the area of space geodesy. Copyright © 2008 John Wiley & Sons, Ltd.