A computer program for searching the best model for describing different experimental systems

An algorithm for searching the best polynomial analytical function for describing different experimental systems is presented. It is based

1. (1)on the generation of all possible analytical functions of a given order, with a given number of terms and with a given number of independent variables, and

2. (2)on the calculation of the parameters of all selected functions using the linear regression method.

To show the ability of the program two different examples are given:

1. (1) searching the best univariate polynomial model, and

2. (2) modelling of the stability of a two-component mixture as a function of three factors.

A method for calibration and validation subset partitioning

This paper proposes a new method to divide a pool of samples into calibration and validation subsets for multivariate modelling. The proposed method is of value for analytical applications involving complex matrices, in which the composition variability of real samples cannot be easily reproduced by optimized experimental designs. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. The proposed technique is illustrated in a case study involving the prediction of three quality parameters (specific mass and distillation temperatures at which 10 and 90% of the sample has evaporated) of diesel by NIR spectrometry and PLS modelling. For comparison, PLS models are also constructed by full cross-validation, as well as by using the Kennard-Stone and random sampling methods for calibration and validation subset partitioning. The obtained models are compared in terms of prediction performance by employing an independent set of samples not used for calibration or validation. The results of F-tests at 95% confidence level reveal that the proposed technique may be an advantageous alternative to the other three strategies.     

Multivariate monitoring of soybean oil ethanolysis by FTIR

In this work, an analytical procedure was developed to monitor the ethanolysis of degummed soybean oil (DSO) using Fourier-transformed mid-infrared spectroscopy (FTIR) and methods of multivariate analysis such as principal component analysis (PCA) and partial least squares regression (PLS). The triglycerides (reagents) and ethyl esters (products) involved in ethanolysis were shown to have similar FTIR spectra. However, when the FTIR spectra derived from seven standard mixtures of triolein and ethyl oleate were treated by PCA at the region that represents the CO stretching vibration of ester groups (1700-1800 cm⁻¹), only two principal components (PC) were shown to capture 99.95% of the total spectral variance (92.37% for the former and 7.58% for the latter PC). This observation supported the development of a multivariate calibration model that was based on the PLS regression of the FTIR data. The prevision capability of this model was measured against 40 reaction aliquots whose ester content was previously determined by size exclusion chromatography. Only small discrepancies were observed when the two experimental data sets were treated by linear regression (R²=0.9837) and these deviations were attributed to the occurrence of non-modeled transient species in the reaction mixture (reaction intermediates), particularly at short reaction times. Therefore, the FTIR/PLS model was shown to be a fast and accurate method to predict reaction yields and to follow the in situ kinetics of soybean oil ethanolysis.     

Simultaneous kinetic spectrophotometric determination of cyanide and thiocyanate using the partial least squares (PLS) regression

The partial least squares (PLS-1) calibration model based on spectrophotometric measurement, for the simultaneous determination of CN⁻ and SCN⁻ ions is described. The method is based on the difference in the rate of the reaction between CN⁻ and SCN⁻ ions with chloramine-T in a pH 4.0 buffer solution and at 30 °C. The produced cyanogen chloride (CNCl) reacts with pyridine and the product condenses with barbituric acid and forms a final colored product. The absorption kinetic profiles of the solutions were monitored by measuring absorbance at 578 nm in the time range 20-180 s after initiation of the reaction with 2 s intervals. The experimental calibration matrix for partial least squares (PLS-1) calibration was designed with 31 samples. The cross-validation method was used for selecting the number of factors. The results showed that simultaneous determination could be performed in the range 10.0-900.0 and 50.0-1200.0 ng mL⁻¹ for CN⁻ and SCN⁻ ions, respectively. The proposed method was successfully applied to the simultaneous determination of cyanide and thiocyanate in water samples.     

一种用于中药纯化过程的近红外光谱分析新方法

针对中药大孔吸附树脂纯化过程缺乏在线检测分析手段等问题，提出基于光纤 近红外透射光谱的过程分析新方法．以黄连提取物为例，采用HPLC分析测定值作参 比，用偏最小二乘算法建立了近红外透射光谱校正模型，并成功地用于预测黄连生 物碱在大孔树脂纯化过程中的洗脱曲线．本方法实时、快速，可同时测定洗脱物中 盐酸小檗碱、盐酸巴马亭、盐酸药相碱和黄连总生物碱的浓度．预测精度满足工业 过程分析要求，为提高中药质量分析水平提供了新的途径．     

Determination of ethanol in fuel ethanol and beverages by Fourier transform (FT)-near infrared and FT-Raman spectrometries

Fourier transform-near infrared (FT-NIR) and FT-Raman spectrometries have been used to design partial least squares (PLS) calibration models for the determination of the ethanol content of ethanol fuel and alcoholic beverages. In the FT-NIR measurements the spectra were obtained using air as reference, and the spectral region for PLS modeling were selected based on the spectral distribution of the relative standard deviation in concentration. In the FT-Raman measurements hexachloro-1,3-butadiene (HCBD) has been used as an external standard. In the PLS/FT-NIR modeling for ethanol fuel analysis 50 ethanol fuel standards (84.9-100% (w/w)) were used (25 in the calibration, 25 in the validation). In the PLS/FT-Raman modeling 25 standards were used (13 in the calibration, 12 in the validation). The PLS/FT-NIR and FT-Raman models for beverage analysis made use of 24 standards (0-100% (v/v)). Twelve of them contained sugars (1-5% (w/w)), one-half was used in the calibration and the other half in the validation. Different spectral pre-processing were used in the PLS modeling, depending on the type of sample investigated. In the ethanol fuel analysis the FT-NIR pre-processing was a 17 points smoothed first derivative and for beverages no spectral pre-processing was used. The FT-Raman spectra were pre-processed by vector normalization in the ethanol fuel analysis and by a second derivative (17 points smoothing) in the beverage analysis. The PLS models were used in the analysis of real ethanol fuel and beverage samples. A t-test has shown that the FT-NIR model has an accuracy equivalent to that of the reference method (ASTM D4052) in the analysis of ethanol fuel, while in the analysis of beverages, the FT-Raman model presents an accuracy equivalent to the reference method. The limits of detection for NIR and Raman calibration models were 0.05 and 0.2% (w/w), respectively. It has also been shown that both techniques, present better results than gas chromatography (GC) in evaluating the ethanol content of beverages.     

Durbin-Watson statistic as a morphological estimator of information content

The present work proposes a new approach for the evaluation of the information content in latent variables, and therefore, for the determination of the regression model dimensionality. Several examples are provided, using simulated, real-world, and reference datasets. The results showed that the application of the Durbin-Watson (DW) criterion could be used for the determination of the number of latent variables. Moreover, the method is straightforward in its implementation and could help in the understanding of model behaviour, particularly in complex datasets. A comparison is made with cross-validation techniques for the case of reference datasets, showing the potential of the Durbin-Watson criterion in the characterisation of the regression model. The advantages and disadvantages of this procedure (compared to cross-validation) are discussed. The properties of the information content of the regression vectors (loadings p, w and b vectors) are shown as well as how to use them for the current purpose.