Multivariate calibration in TXRF analysis of water

The aim of this paper is the application of multivariate linear calibration for quantitative determination of elements (K, Cd, Co, Hg, As, Pb, Ni, and Al) in water by using Total Reflection X‐ray Fluorescence Analysis with partial least squares (PLS) as a regression method to improve a result of common univariate method. In purpose of elimination of matrix effects in X‐ray fluorescence analysis, experimental design was applied. As a set of standard samples for multivariate calibration, a five‐level eight‐factor calibration design of 25 samples was chosen, ensuring mutual orthogonality of factors. For model's validation, the independent test set of 15 samples was examined. The collection of spectra and quantitative measurements was carried out on S2 PICOFOX. The PLS regression was performed by using software package STATISTICA. Quality indicators of multivariate calibration as slope (b) and intercept (a) of calibration, correlation coefficient (r), determination coefficient (R²), root mean square errors of calibration and of prediction, standard errors of calibration and of prediction, biases of calibration, and biases of prediction were calculated. These results were compared with the univariate model, and as a result, the multivariate calibration method exceeds the univariate one. The obtained results could be applied in a laboratory for an analysis of water solutions in the concentration range 0.05–2.00 mg/L. In many real situations, when analytical chemist deals with multi‐element mixtures, multivariate calibration approach combined with orthogonal design for multivariate calibration set could be successfully used to improve a conventional univariate calibration.     

Multivariate Versus Classical Univariate Calibration Methods for Spectrofluorimetric Data: Application to Simultaneous Determination of Olmesartan Medoxamil and Amlodipine Besylate in their Combined Dosage Form

Olmesartan medoxamil (OLM, an angiotensin II receptor blocker) and amlodipine besylate (AML, a dihydropyridine calcium channel blocker), are co-formulated in a single-dose combination for the treatment of hypertensive patients whose blood pressure is not adequately controlled on either component monotherapy. In this work, four multivariate and two univariate calibration methods were applied for simultaneous spectrofluorimetric determination of OLM and AML in their combined pharmaceutical tablets in all ratios approved by FDA. The four multivariate methods are partial least squares (PLS), genetic algorithm PLS (GA-PLS), principal component ANN (PC-ANN) and GA-ANN. The two proposed univariate calibration methods are, direct spectrofluorimetric method for OLM and isoabsorpitive method for determination of total concentration of OLM and AML and hence AML by subtraction. The results showed the superiority of multivariate calibration methods over univariate ones for the analysis of the binary mixture. The optimum assay conditions were established and the proposed multivariate calibration methods were successfully applied for the assay of the two drugs in validation set and combined pharmaceutical tablets with excellent recoveries. No interference was observed from common pharmaceutical additives. The results were favorably compared with those obtained by a reference spectrophotometric method.     

利用近红外光谱法分析玉米籽粒脂肪酸含量的研究

采用傅里叶近红外漫反射光谱技术,结合偏最小二乘法,以294份中选的普通和高油玉米自交系以及高油玉米重组自交系为样品建立了玉米籽粒四种主要脂肪酸(软脂酸、硬脂酸、油酸和亚油酸)含量和含油量的近红外光谱(NIRS)校正模型。其中,油酸、亚油酸和含油量的校正模型质量较高,交叉验证决定系数分别为0.89,0.88和0.91,外部验证决定系数分别为0.86,0.84和0.92,相对分析误差(RSP(C))均大于2.5。软脂酸和硬脂酸的校正模型不够精确,交叉验证决定系数和外部验证决定系数均小于0.80,相对分析误差(RSP(C))均小于2.5。通过实际预测进一步验证了油酸、亚油酸和含油量NIRS模型的准确性和可靠性。这些模型可应用于玉米籽粒脂肪酸含量及油分含量大批量快速测定,对玉米油分的品质育种具有重要意义。     

Megavariate analysis of environmental QSAR data. Part I – A basic framework founded on principal component analysis (PCA), partial least squares (PLS), and statistical molecular design (SMD)

This paper introduces principal component analysis (PCA), partial least squares projections to latent structures (PLS), and statistical molecular design (SMD) as useful tools in deriving multi- and megavariate quantitative structure-activity relationship (QSAR) models. Two QSAR data sets from the fields of environmental toxicology and environmental chemistry are worked out in detail, showing the benefits of PCA, PLS and SMD. PCA is useful when overviewing a data set and exploring relationships among compounds and relationships among variables. PLS is the regression extension of PCA and is used for establishing QSARs. SMD is essential for selecting informative training and test sets of compounds for QSAR calibration and validation.     

基于高光谱成像的苹果多品质参数同时检测

利用高光谱空间散射曲线的3个洛伦兹拟合参数对苹果的品质(硬度、可溶性固溶物含量)进行同时检测。采用偏最小二乘,逐步多元线性回归和BP神经网络3种方法,对归一化处理和未归一化处理的3个洛伦兹参数组合分别建立苹果品质的预测模型。结果表明:采用偏最小二乘法对未归一化处理参数的组合建立硬度的预测模型其预测结果最好,校正组相关系数Rc=0.93,校正标准差SEC=0.56,验证组相关系数Rv=0.84,验证标准差SEV=0.94。采用偏最小二乘法对归一化处理参数的组合建立可溶性固形物的预测模型其预测结果最好,Rc=0.95,SEC=0.29,Rv=0.83,SEV=0.63。研究结果表明:利用高光谱空间散射曲线的多拟合参数组合可以同时检测苹果的多品质参数。     

新鲜苹果汁可溶性固形物含量的傅里叶变换近红外光谱检测

用傅里叶变换近红外(FTNIR)光谱透射方式对新鲜苹果汁溶性固形物含量(SSC)进行了快速定量分析。实验共测定了60个果汁样品的SSC,并采集了样品的近红外光谱数据。42个样品用来建模,剩下的18个用来验证模型的性能。对实验室测得的SSC与FTNIR光谱数据进行相关性分析,以TQ 6.2.1定量分析软件中集成的主成分回归法(PCR)和偏最小二乘回归法(PLS)建立了检测模型。该研究对比了不同光谱范围内建立的检测模型的性能。根据预测平方根误差(RMSEP)和相关系数(r2)进行不同模型的预测性能,最好的新鲜苹果汁SSC预测模型的RMSEP＝0.603 0Brix,r2＝0.997。结果表明FT-NIR可以作为一种可靠、准确、快速的无损检测方法来评价新鲜果汁的可溶性固形物含量。     

Analyzing the performance of statistical models for estimating leaf nitrogen concentration of Phragmites australis based on leaf spectral reflectance

Abstract

Nitrogen is an essential nutrient for plant growth and development. Rapid and nondestructive monitoring of nitrogen nutrition in plants using hyperspectral remote sensing is important for accurate diagnosis and quality evaluation of plant growth status. The sensitive bands of leaf nitrogen concentration varied in different plants. However, most of the current studies are concentrated on crops, and only a few studies focused on wetland plants. This study investigated the accuracy of the most common univariate, stepwise multiple linear regression, and partial least squares regression models for predicting leaf nitrogen content in a wetland plant reed (Phragmites australis) by testing the accuracy of all the models through leave-one-out cross validation coefficient of determination, root mean square error and relative error. It found that: (i) sensitive bands responding to leaf nitrogen concentration were concentrated in the green and red regions of visible light; (ii) for univariate regression models, the quadratic polynomial model based on the difference spectral index composed of 665?nm and 680?nm had the highest predictive accuracy (the validation coefficient of determination was 0.7535); (iii) for multivariate regression models, the stepwise multiple linear regression models had superior predictive accuracy to the partial least squares regression models, and the stepwise multiple linear regression model with first derivative reflectance was optimal for predicting leaf nitrogen concentration (the validation coefficient of determination was 0.7746, the validation root mean square error was 0.2925, and the validation relative error was 0.0804). The findings provide a scientific basis for rapid estimation and monitoring of leaf nitrogen concentration in P. australis in a nondestructive manner.     

Ultrasonic concentration measurement of aqueous solutions using PLS regression

This work demonstrates the use of a multivariate statistical technique called partial least squares (PLS) to extract material related data by analyzing spectra of ultrasonic pulses. We show how PLS can be used to estimate the concentration of sodium chloride in an aqueous solution. The paper describes the use of PLS and discusses pre-processing of ultrasonic data, the PLS algorithm as well as model validation. The measured concentrations are compared to reference values. The influence of disturbances and parameter changes is highlighted. The proposed method is easily adaptable to similar applications and permits a cost-saving implementation using existing and approved hardware.     

激光诱导击穿光谱联合UVE变量优选检测大豆油中的铬含量

利用激光诱导击穿光谱(LIBS)技术对大豆油中的重金属Cr进行检测研究。以松木木片对重金属Cr进行富集,采用AvaSpec双通道高精度光谱仪在206.28~481.77 nm波段范围内采集松木木片样本的LIBS光谱,利用无信息变量消除(UVE)方法筛选与重金属Cr相关的波长变量,应用偏最小二乘(PLS)回归建立大豆油中重金属Cr的定标模型,并与单变量及全波段PLS定标模型进行比较。结果表明,相比单变量及全波段PLS定标模型,UVE-PLS定标模型的性能更优,其相关系数、校正均方根误差、交互验证均方根误差及预测均方根误差分别为0.990,0.045,0.050及0.054 mg·g-1。经UVE变量筛选后,UVE-PLS定标模型所用的波长变量数仅为全波段PLS的2%。由此可见,UVE是一种有效的波长变量筛选方法,能有效筛选出与重金属Cr相关的波长变量。     

The use of combined trace element XRF and EDXRD data as a histopathology tool using a multivariate analysis approach in characterizing breast tissue

The concentrations of K, Fe, Cu and Zn were measured in 77 breast tissue samples (38 classified as normal and 39 classified as diseased) using x‐ray fluorescence (XRF) techniques. The coherent scattering profiles were also measured using energy‐dispersive x‐ray diffraction (EDXRD), from which the proportions of adipose and fibrous tissue in the samples were estimated. The data from 30 normal samples and 30 diseased samples were used as a training set to construct two calibration models, one using a partial least‐squares (PLS) regression and one using a principal component analysis (PCA) for a soft independent modelling of class analogy (SIMCA) technique. The data from the remaining samples, eight normal and nine diseased, were presented to each model and predictions were made of the tissue characteristics. Three data groups were tested, XRF, EDXRD and a combination of both. The XRF data alone proved to be most unreliable indicator of disease state with both types of analysis. The EDXRD data were an improvement, but with both methods of modelling the ability to predict the tissue type most accurately was by using a combination of the data. Copyright © 2004 John Wiley & Sons, Ltd.     

Multivariate calibrations for the SR‐TXRF determination of trace concentrations of lead and arsenic in the presence of bromine

A synchrotron radiation source and total reflection x‐ray fluorescence (SR‐TXRF) spectrometry were used for the determination of lead and arsenic in aqueous samples. To overcome the serious spectral interference between the two species and the overlap of another interfering element (bromine), a partial least‐squares regression (PLSR) method was used. The calibration models PLSR2 and PLSR1 were based on the x‐ray fluorescence emission signals (9.550–13.663 keV) for a set of 26 different mixtures containing the elements of interest, lead and arsenic, as well as bromine. The results obtained by PLSR1 and PLSR2 were compared with those obtained by the conventional univariate methodology. In the latter case, the areas of the secondary emission lines (Lβ for lead and Kβ for arsenic) were used to elaborate the analytical curves. The capacity of all optimized models was verified using five synthetic samples (external validation). Subsequently the best model was used to determine lead and arsenic recovery capacities when these metals are retained on two ion‐exchange resins (Dowex 50‐X8 and Dowex 1‐X8). The best multivariate model (PLSR1) allowed the determination of lead and arsenic with root mean square errors of prediction (RMSEPs) of 0.03 and 0.24 mg l^?1, respectively. The reduction of this parameter, with respect to the values obtained by conventional univariate methodology (0.26–0.03 mg l^?1 for lead and 0.30–0.24 mg l^?1 for arsenic), indicates that the proposed multivariate methodology really overcomes the problems associated with spectral interferences and minimizes the influence of an interfering agent (bromine). Copyright © 2005 John Wiley & Sons, Ltd.     

Probing the sulfur content in gasoline quantitatively with terahertz time-domain spectroscopy

Terahertz time-domain spectroscopy(THz-TDS)was used for the quantitative detection of sulfur content in gasoline.Models of chemo metrics methods and partial least squares(PLS)were built to measure THz-TDS and the sulfur content.All of the samples were divided into two parts.One part was used for calibration and the other one for validation.In order to evaluate the quality of the models,the correlation coefficient(R)and root-mean-square errors(RMSE)of calibration and validation models were calculated.The value of R and RMSE were close to 1 and 0 within acceptable levels,respectively,indicating that the combination of THz-TDS and PLS is a potential method for further quantitative detection.     

傅里叶近红外光谱的雪青梨酸度偏最小二乘法定量分析

利用近红外漫反射光谱测定法获取了完整雪青梨的近红外光谱(12 500～4 000 cm-1), 采用多元校正算法偏最小二乘法(PLS)方法,选取不同的波段范围对漫反射光谱进行有效信息提取和分析,得出了不同因子数时PLS方法进行酸度分析的结果及其因子数与交互有效检验标准偏差(RMSECV)关系,确定了最佳回归的因子数和用于定量分析的最佳波段范围。实验结果表明: 校正模型的预测精度在5 452～12 285 cm-1波段范围内,最佳主因子数为7时,雪青梨总酸的预测精度最好,其预测集的相关系数达到了0.79, 预测标准偏差为0.018 6。     

Determination of the Al content in aluminum‐modified SiO2 stationary phases using X‐ray scattering spectroscopy

This paper describes the determination of aluminum in the presence of silica using a method based on X‐ray scattering spectrometry coupled with chemometric tools (principal component analysis and partial least squares) that treat samples according to their Al concentrations. Samples were prepared by mixing Al and Si oxides. X‐ray spectra of all samples, including pure oxides of aluminum and silicon, were submitted to the chemometric tools. Principal component analysis results show that it is possible to classify three subgroups of Al (low, medium and high Al content), whereas partial least squares 1 was used to construct calibration and cross‐validation models for Al in the presence of Si. The method is simple, fast, does not require sample dissolution prior to analysis, is of low cost and can be applied as a routine procedure. The method was used to quantify Al in some chromatographic stationary phases covered with a layer of Al₂O₃. Good correlations with low errors were obtained. Copyright © 2013 John Wiley & Sons, Ltd.     

不同年份和产地美味牛肝菌的红外光谱鉴别研究

采用傅里叶变换红外光谱技术结合多元统计分析建立快速鉴别不同年份、不同产地美味牛肝菌的方法。采集2011年一2014年云南26个不同地区152个美味牛肝菌样品的红外光谱,使用正交信号校正(orthogonal signal correction,OSC)、微波压缩(wavelet compression)方法对原始光谱进行优化处理,OSCW校正前后的光谱数据进行偏最小二乘判别分析(partial least squares discriminant analysis,PLS-DA),比较光谱预处理前后PLS-DA的分类效果。将152个美味牛肝菌随机分为训练集(120个)和验证集(32个),建立OS--CW校正前后的PLS分类预测模型。结果显示,经OSCW处理后的PLS-DA分类效果明显优于处理前的结果,主成分得分图能准确区分不同年份、不同产地美味牛肝菌样品,表明OSCW处理能有效滤除光谱中的噪音及与因变量无关的干扰信息,提高光谱分析的准确性和计算速率。OSCW处理前PLS模型训练集的R~2和RMSEE分别为0.790 1和21.246 5,验证集的R~2和RMSEP分别为0.922 5和14.429 2;OSCW预处理后训练集的R~2和RMSEE分别为0.852 3和17.238 1,验证集的R~2和RMSEP分别为0.845 4和20.87,表明OSCW预处理提高了训练集的预测效果,但OSCW-PLS出现了过拟合现象降低验证集的预测能力,因此,OSCW不适宜与PLS结合建立模型。OSCW结合PLS-DA能滤除光谱中大量的干扰信息,准确区分不同年份、不同产地美味牛肝菌样品,为野生食用菌的鉴别分类提供可靠依据。     

基于LIBS技术的钢铁合金中元素多变量定量分析方法研究

针对钢铁合金样品元素组成相对复杂,基体效应较严重的问题,利用激光诱导击穿(LIBS)光谱技术对钢铁合金中的元素进行了定量分析。以Nd∶YAG脉冲激光器基频1 064 nm波长激光作为激发光源,采用中阶梯光栅光谱仪和ICCD分光探测钢铁合金样品的LIBS光谱。通过优化实验确定最佳探测延时为1.5 μs,最佳探测门宽为2 μs,激光聚焦点位置在实验样品靶面以下1.5 mm。采用单变量定量分析、多变量线性回归和偏最小二乘(PLS)三种方法分析钢铁合金中Cr元素和Ni元素的含量。结果表明,采用单变量定标方法定标曲线相关系数不高,对待测样的预测误差相对较大,难以有效地定量分析基体元素复杂的钢铁合金中金属元素的含量;采用多变量线性回归分析方法能有效提高定量分析的精度;采用PLS方法得到的Cr和Ni元素的拟合曲线相关系数r分别为0.981和0.995,对两个待测样品中Cr元素和Ni元素的预测相对误差在6.4%和7.1%以内,分析结果优于多变量线性回归方法。可见,采用多变量校正的PLS方法能更有效地校正基体效应对定量分析的影响,提高定量分析的精度。     

实测甘草冠层光谱定量估算甘草酸和甘草苷含量

甘草酸(GA)和甘草苷(LQ)是甘草的两个主要的活性成分, 常用作评估甘草的质量主要指标。首次尝试应用实测甘草冠层的可见-短波红外(Vis-SWIR)高光谱数据定量估算甘草中的GA和LQ含量,利用高效液相色谱方法(HPLC)分别测定甘草中GA和LQ含量作为参考值,通过结合一阶导数预处理和运用Wilk’lambda 逐步回归法选择特征波长等光谱预处理方法,在选择9个最优波段基础上建立偏最小二乘(PLS)回归预测模型,甘草GA和LQ的回归精度R2分别为0.953和0.932,校正集的均方根误差(RMSEC)分别为0.31和0.22, 预测精度R2分别为0.875和0.883,验证集的均方根误差(RMSEP)分别为0.39和0.27。结果显示,用光谱预测模型获得甘草GA和LQ含量预测与HPLC方法获得的甘草GA和LQ含量实测之间具有较高的相关性,说明Vis-SWIR技术从遥感数据中来确定GA和LQ含量的可行性。为野外利用外机载和/或星载高光谱传感器对甘草质量遥感监测提供理论依据。     

多信息融合的冬小麦地上鲜生物量检测研究

将小麦冠层光谱与小麦冠层图像或者侧面图像进行多信息融合,对冬小麦地上鲜生物量进行预测,提高了冬小麦地上鲜生物量无损检测精度,试验获取苗期93个样本的冠层光谱和冠层图像,中后期(拔节期、抽穗期、开花期、灌浆期)200个样本的冠层光谱和侧面图像。将光谱反射率作为光谱特征参数,并通过图像处理提取小麦覆盖度作为图像特征参数,建立苗期和中后期基于光谱特征参数和图像特征参数的地上生物量检测模型,将冠层光谱反射率和小麦覆盖度作为多信息融合的输入,利用多元回归分析(MRA)和偏最小二乘法(PLS)建立地上鲜生物量预测模型并进行验证。结果表明,在苗期和中后期,将光谱信息和图像信息融合,采用PLS所建立的预测模型与单独的图像模型和光谱模型相比精度最高。苗期基于信息融合所建立的PLS模型验证集R2为0.881,其RMSE为0.015 kg;中后期基于信息融合所建立的PLS模型验证集R2为0.791,RMSE为0.059 kg。由此可见,相比单一的光谱模型和图像模型,图像信息和光谱信息融合之后,充分提高了光谱信息和图像信息的利用率,使模型的精度得以提高。     

遗传算法结合偏最小二乘法无损评价西洋梨糖度

基于遗传算法的波段选择法在组合优化问题上具有很大的搜索优势,适应性很广。文章将该方法应用于西洋梨糖度近红外光谱分析中,探讨数据优化筛选的可行性。光谱经多元散射校正或标准归一化处理后进行波段选择,选择结果与样品中被测成分有关, 4个品种洋梨的最佳个体染色体编码有一定共性。分别建立了四种洋梨的GA-PLS模型和全谱模型,早红考密斯、五九香、凯斯凯德和康佛伦斯的GA-PLS建模数据点分别从1 557减少到了434,496,310和496。GA-PLS/Fr-PLS模型的预测标准偏差分别为0.428/0.518,0.696/0.694,0.425/0.421和0.567/0.633, 其中早红考密斯和康佛伦斯GA-PLS模型的预测精度明显优于全谱模型,而五九香和凯斯凯德的GA-PLS模型与全谱模型相近。结果表明,遗传算法用于PLS建立西洋梨糖度校正模型前的数据优化筛选是可行的, 有效提高测量精度, 减少建模变量。