Multivariate calibration and instrument standardization for the rapid detection of diethylene glycol in glycerin by Raman spectroscopy

The transfer of a multivariate calibration model for quantitative determination of diethylene glycol (DEG) contaminant in pharmaceutical-grade glycerin between five portable Raman spectrometers was accomplished using piecewise direct standardization (PDS). The calibration set was developed using a multi-range ternary mixture design with successively reduced impurity concentration ranges. It was found that optimal selection of calibration transfer standards using the Kennard-Stone algorithm also required application of the algorithm to multiple successively reduced impurity concentration ranges. Partial least squares (PLS) calibration models were developed using the calibration set measured independently on each of the five spectrometers. The performance of the models was evaluated based on the root mean square error of prediction (RMSEP), calculated using independent validation samples. An F-test showed that no statistical differences in the variances were observed between models developed on different instruments. Direct cross-instrument prediction without standardization was performed between a single primary instrument and each of the four secondary instruments to evaluate the robustness of the primary instrument calibration model. Significant increases in the RMSEP values for the secondary instruments were observed due to instrument variability. Application of piecewise direct standardization using the optimal calibration transfer subset resulted in the lowest values of RMSEP for the secondary instruments. Using the optimal calibration transfer subset, an optimized calibration model was developed using a subset of the original calibration set, resulting in a DEG detection limit of 0.32% across all five instruments.     

Effects of nonlinearities and uncorrelated or correlated errors in realistic simulated data on the prediction abilities of augmented classical least squares and partial least squares

Comparisons of prediction models from the new augmented classical least squares (ACLS) and partial least squares (PLS) multivariate spectral analysis methods were conducted using simulated data containing deviations from the idealized model. The simulated data were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions. Simulated uncorrelated concentration errors, uncorrelated and correlated spectral noise, and nonlinear spectral responses were included to evaluate the methods on situations representative of experimental data. The statistical significance of differences in prediction ability was evaluated using the Wilcoxon signed rank test. The prediction differences were found to be dependent on the type of noise added, the numbers of calibration samples, and the component being predicted. For analyses applied to simulated spectra with noise-free nonlinear response, PLS was shown to be statistically superior to ACLS for most of the cases. With added uncorrelated spectral noise, both methods performed comparably. Using 50 calibration samples with simulated correlated spectral noise, PLS showed an advantage in 3 out of 9 cases, but the advantage dropped to 1 out of 9 cases with 25 calibration samples. For cases with different noise distributions between calibration and validation, ACLS predictions were statistically better than PLS for two of the four components. Also, when experimentally derived correlated spectral error was added, ACLS gave better predictions that were statistically significant in 15 out of 24 cases simulated. On data sets with nonuniform noise, neither method was statistically better, although ACLS usually had smaller standard errors of prediction (SEPs). The varying results emphasize the need to use realistic simulations when making comparisons between various multivariate calibration methods. Even when the differences between the standard error of predictions were statistically significant, in most cases the differences in SEP were small. This study demonstrated that unlike CLS, ACLS is competitive with PLS in modeling nonlinearities in spectra without knowledge of all the component concentrations. This competitiveness is important when maintaining and transferring models for system drift, spectrometer differences, and unmodeled components, since ACLS models can be rapidly updated during prediction when used in conjunction with the prediction augmented classical least squares (PACLS) method, while PLS requires full recalibration.     

Comparison of methods for transfer of calibration models in near-infared spectroscopy: a case study based on correcting path length differences using fiber-optic transmittance probes in in-line near-infrared spectroscopy

This article addresses problems related to transfer of calibration models due to variations in distance between the transmittance fiber-optic probes. The data have been generated using a mixture design and measured at five different probe distances. A number of techniques reported in the literature have been compared. These include multiplicative scatter correction (MSC), path length correction (PLC), finite impulse response (FIR), orthogonal signal correction (OSC), piecewise direct standardization (PDS), and robust calibration. The quality of the predictions was expressed in terms of root mean square error of prediction (RMSEP). Robust calibration gave good calibration transfer results, while the other methods did not give acceptable results.     

Calibration transfer of partial least squares jet fuel property models using a segmented virtual standards slope-bias correction method

Fifteen pure molecular chemicals were used to transfer near-IR partial least squares (PLS) models of jet fuel properties between two dispersive near-IR instruments by a novel calibration transfer, standardization, method. PLS was applied to establish models for quantitative analysis of jet fuels properties. The modeled jet fuel properties include: API gravity; %aromatics; cetane index; density; distillation temperatures for 10%, 20%, 50% and 90% recovered volume; flashpoint; freeze point, %hydrogen content; %saturates; and viscosity. The transfer of the PLS models requires that spectra of only 15 pure chemicals be acquired on the primary and secondary instruments. The spectra of the chemicals are then segmented into distinct spectral regions which are subsequently used to digitally construct spectra of virtual standards which mimic jet fuel spectra in the training set. The resulting virtual standards for the primary and secondary instruments are then predicted using the PLS models, and the prediction values are regressed to provide a simple but effective slope and bias correction for transfer. SVSSB calibration transfer of 7 jet fuels properties shows better performance than PDS, for example, in the case of cetane index Root Mean Square Error of Prediction (RMSEP_c) of SVSSB and PDS corrected secondary instrument relative to primary instrument prediction are 0.19 and 0.27 respectively. SVSSB and PDS show comparable performance of the other 6 jet fuel properties. For example, RMSEP_c of SVSSB and PDS corrected secondary of % hydrogen content of secondary instrument relative to the primary instrument prediction are 0.015 and 0.014 respectively. The Segmented Virtual Standards Slope and Bias Method (SVSSB) performs as well as using real jet fuel standards to generate a slope and bias correction, and also as well as conventional Piecewise Direct Standardization (PDS), while eliminating the need to maintain either the complex fuel standards or the primary instrument.     

Transfer of near-infrared calibration model for determining fiber content in flax: effects of transfer samples and standardization procedure

The transfer of a calibration model for determining fiber content in flax stem was accomplished between two near-infrared spectrometers, which are the same brand but which require a standardization. In this paper, three factors, including transfer sample set, spectral type, and standardization method, were investigated to obtain the best standardization result. Twelve standardization files were produced from two sets of the transfer sample (sealed reference standards and a subset of the prediction set), two types of the transfer sample spectra (raw and preprocessed spectra), and three standardization methods (direct standardization (DS), piecewise direct standardization (PDS), and double window piecewise direct standardization (DWPDS)). The efficacy of the model transfer was evaluated based on the root mean square error of prediction, calculated using the independent prediction samples. Results indicated that the standardization using the sealed reference standards was unacceptable, but the standardization using the prediction subset was adequate. The use of the preprocessed spectra of the transfer samples led to the calibration transfers that were successful, especially for the PDS and the DWPDS correction. Finally, standardization using the prediction subset and their preprocessed spectra with DWPDS correction proved to be the best method for transferring the model.     

Optimization of informative spectral variables for the quantification of EGCG in green tea using Fourier transform near-infrared (FT-NIR) spectroscopy and multivariate calibration

Epigallocatechin-3-gallate (EGCG) is credited with the majority of the health benefits associated with green tea consumption. It has a high economic and medicinal value. The feasibility of using different variable selection approaches in Fourier transform near-infrared (FT-NIR) spectroscopy for a rapid and conclusive quantitative determination of EGCG in green tea was investigated. Graphically oriented multivariate calibration modeling procedures such as interval partial least squares (iPLS), synergy interval partial least squares (siPLS), and genetic algorithm optimization combined with siPLS (siPLS-GA) were applied to select the most efficient spectral variables that provided the lowest prediction error. The performance of the final model was evaluated according to the root mean square error of prediction (RMSEP) and coefficient of determination (R(2)) for the prediction set. Experimental results showed that the siPLS-GA model obtained the best results in comparison to other models. The optimal models were achieved with R(2)(p) = 0.97 and RMSEP = 0.32. The model can be obtained with only 36 variables retained and it provides a robust model with good estimation accuracy. This demonstrates the potential of NIR spectroscopy with multivariate calibration methods to quickly detect the bioactive component in green tea.     

Conductometric simultaneous determination of acetic acid, monochloroacetic acid and trichloroacetic acid using orthogonal signal correction-partial least squares

A simultaneous conductometric titration method for determination of mixtures of acetic acid, monochloroacetic acid and trichloroacetic acid based on the multivariate calibration partial least squares is proposed. It is possible to obtain an adjustable model to relate squared concentration values of the mixtures used in the calibration range by conductance. The effect of orthogonal signal correction (OSC) as a preprocessing technique used to remove the information unrelated to the target variables is studied. The calibration model was build using conductometric titrations data of 16 mixtures of three acids. The concentration matrix was designed by a orthogonal design. The root mean squares error of prediction (RMSEP) for acetic acid, monochloroacetic acid and trichloroacetic acid with and without OSC were 0.08, 0.30 and 0.08, and 0.15, 0.40 and 0.18, respectively. The results obtained by OSC-PLS are better than the PLS and this indicate the successful application of the OSC filter as a good preprocessing method in multivariate calibration methods. The proposed procedure allows the simultaneous determination of these acids, in the synthetic mixtures.     

Temperature-independent near-infrared analysis of lysozyme aqueous solutions

Digital Fourier filtering is used to produce a temperature-insensitive univariate calibration model for measuring lysozyme in aqueous solutions. Absorbance spectra over the 5000-4000 cm-1 spectral range are collected for lysozyme standards maintained at 14 degrees C. These spectra are used to compute the calibration model while a set of spectra collected at temperatures ranging from 4 to 24 degrees C are used to validate the accuracy of this model. The root-mean-square error of prediction (RMSEP) is 0.279 mg/mL over a tested lysozyme concentration range of 0.036-51.6 mg/mL. The detection limit is 0.68 mg/mL. In addition, multivariate calibration models based on partial least-squares regression (PLS) are evaluated and compared to the results from the univariate model. PLS outperforms the univariate model by providing a RMSEP of 0.090 mg/mL. Analysis of variance showed that both calibration methods effectively eliminate the adverse affects created by variations in solution temperature.     

Quantitative measurements of loss on ignition in iron ore using laser-induced breakdown spectroscopy and partial least squares regression analysis

Laser-induced breakdown spectroscopy (LIBS) and partial least squares regression (PLSR) have been applied to perform quantitative measurements of a multiple-species parameter known as loss on ignition (LOI), in a combined set of run-of-mine (ROM) iron ore samples originating from five different iron ore deposits. Global calibration models based on 65 samples and their duplicates from all the deposits with LOI ranging from 0.5 to 10 wt% are shown to be successful for prediction of LOI content in pressed pellets as well as bulk ore samples. A global independent dataset comprising a further 60 samples was used to validate the model resulting in the best validation R(2) of 0.87 and root mean square error of prediction (RMSEP) of 1.1 wt% for bulk samples. A validation R(2) of 0.90 and an RMSEP of 1.0 wt% were demonstrated for pressed pellets. Data preprocessing is shown to improve the quality of the analysis. Spectra normalization options, automatic outlier removal and automatic continuum background correction, which were used to improve the performance of the PLSR method, are discussed in detail.     

Evaluation of infrared-reflection absorption spectroscopy measurement and locally weighted partial least-squares for rapid analysis of residual drug substances in cleaning processes

The usefulness of infrared-reflection absorption spectroscopy (IR-RAS) for the rapid measurement of residual drug substances without sampling was evaluated. In order to realize the highly accurate rapid measurement, locally weighted partial least-squares (LW-PLS) with a new weighting technique was developed. LW-PLS is an adaptive method that builds a calibration model on demand by using a database whenever prediction is required. By adding more weight to samples closer to a query, LW-PLS can achieve higher prediction accuracy than PLS. In this study, a new weighting technique is proposed to further improve the prediction accuracy of LW-PLS. The root-mean-square error of prediction (RMSEP) of the IR-RAS spectra analyzed by LW-PLS with the new weighting technique was compared with that analyzed by PLS and locally weighted regression (LWR). The RMSEP of LW-PLS with the proposed weighting technique was about 36% and 14% smaller than that of PLS and LWR, respectively, when ibuprofen was a residual drug substance. Similarly, LW-PLS with the weighting technique was about 39% and 24% better than PLS and LWR in RMSEP, respectively, when magnesium stearate was a residual excipient. The combination of IR-RAS and LW-PLS with the proposed weighting technique is a very useful rapid measurement technique of the residual drug substances.     

Waveband selection for NIR spectroscopy analysis of soil organic matter based on SG smoothing and MWPLS methods

Savitzky-Golay (SG) smoothing and moving window partial least square (MWPLS) methods were applied to the model optimization and the waveband selection for near-infrared (NIR) spectroscopy analysis of soil organic matter. The optimal single wavelength prediction bias (OSWPB) was used to evaluate the similarity of calibration set and prediction set, and a new division method for calibration set and prediction set was proposed. SG smoothing modes were expanded to 540 kinds. The specific computer algorithm platforms for optimization of SG smoothing mode combined with PLS factor and for MWPLS method with changeable parameters were built up. The optimal waveband for soil organic matter was 1926-2032 nm, the optimal smoothing mode was the 2nd order derivative, 6th degree polynomial, 45 smoothing points, the PLS factor, RMSEP and R_P were 8, 0.260 (%) and 0.877 respectively. The prediction effect was obviously better than that in the whole spectral collecting region. To get stable results, all the optimization processes were based on the average prediction effect on 50 different divisions of calibration set and prediction set.     

Determination of glucose in human aqueous humor using Raman spectroscopy and designed-solution calibration

Glucose concentrations of in vitro human aqueous humor (HAH) samples from cataract patients were determined using 785 nm Raman spectra and partial least squares (PLS) calibration. PLS models were created from spectra of prepared calibration solutions rather than aqueous humor samples. Spectra were obtained with an excitation energy (100 mW for 150 s), which was higher than can be applied in vivo, to decrease the models' contribution to prediction uncertainty. The solutions contained experimentally designed levels of glucose, bicarbonate, lactate, urea, and ascorbate. Multiplicative signal correction of spectra helped compensate for the +/-20% drift in laser power observed at the sample over six noncontiguous days of data collection. Seventeen HAH samples containing 38-775 mg/dL of glucose exhibited a root-mean-square error (RMSEP) of 22 mg/dL, coefficient of determination (r(2)) of 0.989, and bias of 6 mg/dL when predicted from lower energy (30 s) spectra collected contemporaneously with fifty calibration spectra. Similar results were obtained even when spectral data were gathered separately for human aqueous humor samples and calibration samples: 10 HAH samples, calibrated on 25 solutions measured 3.6 weeks earlier, exhibited an RMSEP of 23 mg/dL, r(2) of 0.992, and bias of 9 mg/dL. The results demonstrate progress toward the determination of glucose levels in patient-derived aqueous humor using laboratory-derived "artificial aqueous humor" calibration solutions.     

Spectral variable selection for partial least squares calibration applied to authentication and quantification of extra virgin olive oils using Fourier transform Raman spectroscopy

The limits of quantitative multivariate assays for the analysis of extra virgin olive oil samples from various Greek sites adulterated by sunflower oil have been evaluated based on their Fourier transform (FT) Raman spectra. Different strategies for wavelength selection were tested for calculating optimal partial least squares (PLS) models. Compared to the full spectrum methods previously applied, the optimum standard error of prediction (SEP) for the sunflower oil concentrations in spiked olive oil samples could be significantly reduced. One efficient approach (PMMS, pair-wise minima and maxima selection) used a special variable selection strategy based on a pair-wise consideration of significant respective minima and maxima of PLS regression vectors, calculated for broad spectral intervals and a low number of PLS factors. PMMS provided robust calibration models with a small number of variables. On the other hand, the Tabu search strategy recently published (search process guided by restrictions leading to Tabu list) achieved lower SEP values but at the cost of extensive computing time when searching for a global minimum and less robust calibration models. Robustness was tested by using packages of ten and twenty randomly selected samples within cross-validation for calculating independent prediction values. The best SEP values for a one year's harvest with a total number of 66 Cretian samples were obtained by such spectral variable optimized PLS calibration models using leave-20-out cross-validation (values between 0.5 and 0.7% by weight). For the more complex population of olive oil samples from all over Greece (total number of 92 samples), results were between 0.7 and 0.9% by weight with a cross-validation sample package size of 20. Notably, the calibration method with Tabu variable selection has been shown to be a valid chemometric approach by which a single model can be applied with a low SEP of 1.4% for olive oil samples across three different harvest years.     

Prediction of oil and oleic acid concentrations in individual corn (Zea mays L.) kernels using near-infrared reflectance hyperspectral imaging and multivariate analysis

Due to their heterogeneous structure and variability in form, individual corn (Zea mays L.) kernels present an optical challenge for nondestructive spectroscopic determination of their chemical composition. Increasing demand in agricultural science for knowledge of specific traits in kernels is driving the need to find high-throughput methods of examination. In this study macroscopic near-infrared (NIR) reflectance hyperspectral imaging was used to measure small sets of kernels in the spectroscopic range of 950 nm to 1700 nm. Image analysis and principal component analysis (PCA) were used to determine kernel germ from endosperm regions as well as to define individual kernels as objects out of sets of kernels. Partial least squares (PLS) analysis was used to predict oil or oleic acid concentrations derived from germ or full kernel spectra. The relative precision of the minimum cross-validated root mean square error (RMSECV) and root mean square error of prediction (RMSEP) for oil and oleic acid concentration were compared for two sets of two hundred kernels. An optimal statistical prediction method was determined using a limited set of wavelengths selected by a genetic algorithm. Given these parameters, oil content was predicted with an RMSEP of 0.7% and oleic acid content with an RMSEP of 14% for a given corn kernel.     

A simple method for linearizing nonlinear spectra for calibration

The development and acceptance of spectral calibration methods has been an important success story for the field of chemometrics. This paper contains a new study of a very old calibration method (K-matrix calibration, parallel calibration, or generalized inverse prediction) and partial least squares (PLS), the mainstay of modern chemometrics. We show that with some modest amount of modification, the old method of calibration is comparable, in terms of prediction, to PLS for spectroscopy involving nonlinear spectral responses.     

Quantitative analysis of cotton-polyester textile blends from near-infrared spectra

Quantitative analysis of textile blends and textile fabrics is currently of particular interest in the industrial context. In this frame, this work investigates whether the use of Fourier transform (FT) near-infrared (NIR) spectroscopy and chemometrics is powerful for rapid and accurate quantitative analysis of cotton-polyester content in blend products. As samples of the same composition have many sources of variability that affect NIR spectra, indirect prediction is particularly challenging and a large sample population is required to design robust calibration models. Thus, a total of more than three-hundred cotton-polyester samples were selected covering the range from the 0% to 100% cotton and the corresponding NIR reflectance spectra were measured on raw fabrics. The data set obtained was used to develop multivariate models for quantitative prediction from reference measurements. A successful approach was found to rely on partial least squares (PLS) regression combined with genetic algorithms (GAs) for wavelength selection. It involved evaluating a set of calibration models considering different spectral regions. The results obtained considering 27.5% of the original variables yielded a prediction error (RMSEP) of 2.3 in percent cotton content. It demonstrates that FT-NIR spectroscopy has the potential to be used in the textile industry for the prediction of the composition of cotton-polyester blends. As a further consequence, it was observed that the spectral preprocessing and the complexity of the model are simplified compared to the full-spectrum approach. Also, the relevancy of the spectral intervals retained after variable selection can be discussed.     

Cyclic subspace regression with analysis of wavelength-selection criteria

Common methods of building linear calibration models are principal component regression (PCR), partial least squares (PLS), and least squares (LS). Recently, the method of cyclic subspace regression (CSR) has been presented and shown to provide PCR, PLS, LS and other related intermediate regressions with one algorithm. When forming a linear model with spectral data for quantitative analysis, prediction results can be adversely affected by responses that do not conform well to the linear model proposed. Wavelength selection can be used to eliminate wavelengths where such problem responses occur. It has recently been reported that CSR regression vectors can be formed by summing weighted eigenvectors where weights are determined from the hat matrix, singular values, and eigenvectors characterizing the sample space. Investigation of these weights shows that wavelength selection based on loading vectors can be misleading. Specifically, by using CSR it is shown that a small weight for an eigenvector can annihilate a large peak in a loading vector. In this study, correlograms are used with CSR regression vectors and eigenvector weights as wavelength-selection criteria. It is demonstrated that even though a model generated by LS for a wavelength subset produces substantially reduced prediction errors relative to PCR and PLS, CSR weight plots show that the LS model overfits and should not be used. Simulated situations containing spectral regions with excess noise or nonlinear responses are examined to study the effectiveness of wavelength selection based on the previously listed criteria. Near infrared spectra of gasoline samples with several known properties are also studied.     

Wavelength selection for multivariate calibration using tikhonov regularization

Prediction of sample properties using spectroscopic data with multivariate calibration is often enhanced by wavelength selection. This paper reports on a built-in wavelength selection method in which the estimated regression vector contains zero to near-zero coefficients for undesirable wavelengths. The method is based on Tikhonov regularization with the model 1-norm (TR1) and is applied to simulated and near-infrared (NIR) spectral data. Models are also formed from wavelength subsets determined by the standard method of stepwise regression (SWR). Harmonious (bias/variance tradeoff) and parsimonious considerations are compared with and without wavelength selection for principal component regression (PCR), ridge regression (RR), partial least squares (PLS), and multiple linear regression (MLR). Results show that TR1 models generally contain large baseline regions of near-zero coefficients, thereby essentially achieving built-in wavelength selection. For example, wavelengths with spectral interferences and/or poor signal-to-noise ratios obtain near zero regression coefficients. Results often improve with TR1 models, compared to full wavelength PCR, RR, and PLS models. The SWR subset results are similar to those for the TR1 models using the NIR data and worse with the simulated spectral situations. In general, wavelength selection improves prediction accuracy at a sacrifice to a potential increase in variance and the parsimony remains nearly equivalent compared to full wavelength models. New insights gained from the reported studies provide useful guidelines on when to use full wavelengths or use wavelength selection methods. Specifically, when a small number of large wavelength effects (good sensitivity and selectivity) exist, subset selection by SWR (with caution) and TR1 do well. With a small to moderate number of large to moderate sized wavelength effects, TR1 is better. Lastly, when a large number of small effects are present, full wavelengths with the methods of PCR, RR, or PLS are best.     

Chemometric study of excitation-emission matrix fluorescence data: quantitative analysis of petrol-kerosene mixtures

Products of petroleum crude are multifluorophoric in nature due to the presence of a mixture of a variety polycyclic aromatic hydrocarbons (PAHs). The use of excitation-emission matrix fluorescence (EEMF) spectroscopy for the analysis of such multifluorophoric samples is gaining progressive acceptance. In this work, EEMF spectroscopic data is processed using chemometric multivariate methods to develop a reliable calibration model for the quantitative determination of kerosene fraction present in petrol. The application of the N-way partial least squares regression (N-PLS) method was found to be very efficient for the estimation of kerosene fraction. A very good degree of accuracy of prediction, expressed in terms of root mean square error of prediction (RMSEP), was achieved at a kerosene fraction of 2.05%.     

Determination of the polymorphic forms of bicifadine hydrochloride by differential scanning calorimetry-thermogravimetric analysis, X-ray powder diffraction, attenuated total reflectance-infrared spectroscopy, and attenuated total reflectance-near-infrared spectroscopy

The pharmaceutical compound bicifadine hydrochloride, which has been found to crystallize in two polymorphic forms, has been characterized by thermal analysis, X-ray powder diffraction (XRPD), infrared (IR) spectroscopy, and near-infrared (NIR) spectroscopy. A series of 22 sample mixtures of polymorph 1 and polymorph 2 were prepared and calibration models for the quantitation of these binary mixtures have been developed for each of the XRPD, attenuated total reflectance (ATR)-IR, and ATR-NIR analytical techniques. The quantitative results were obtained using a partial least squares (PLS) algorithm, which predicted the concentration of polymorph 1 from the XRPD spectra with a root mean standard error of prediction (RMSEP) of 4.4%, from the IR spectra with a RMSEP of 3.8%, and from the NIR spectra with a RMSEP of 1.4%. The studies indicate that when analyses are carried out on equivalent sets of spectra, NIR spectroscopy offers significant advantages in quantitative accuracy as a tool for the determination of polymorphs in the solid state and is also more convenient to use than both the ATR-IR and XRPD methods. Density functional theory (DFT) B3LYP calculations and IR spectral simulation have been used to determine the nature of the vibrational modes that are the most sensitive in the analysis.