Piecewise Direct Standardization Research Articles

Robust calibration model for on-line and off-line prediction of poly(ethylene terephthalate) yarn shrinkage by Raman spectroscopy

In order to transfer a calibration model, techniques such as piecewise direct standardization (PDS) or direct standardization (DS) are used. This implies that the same subset of samples must be measured in both situations. However, when a model is transferred from an off-line application to an on-line application, it is not possible to remeasure the same subset of samples. In this paper, however, a method is presented which can transfer a multivariate calibration model from an off-line application to an on-line application without remeasuring the same subset. For this purpose a calibration model has been calculated with a subset of spectral variables. The variables, which are sensitive to the differences between the off-line and the on-line application, are rejected. The method is compared with the calculation of a hybrid calibration model in which off-line and on-line spectral data are combined into one calibration set. The methods are applied to a calibration model which is used to predict the shrinkage after heat treatment of poly(ethylene terephthalate) (PET) yarns from the Raman spectra measured both off-line and on-line. The Raman spectra of a calibration set have been measured off-line and a smaller set has been measured on-line during the production of PET yarns. It has been found that it is possible to make a universal calibration model for off-line and on-line predictions of PET yarn shrinkage by Raman spectroscopy. Copyright © 1999 John Wiley & Sons, Ltd.

Multivariate standardization techniques on ion-selective sensor arrays

Multivariate standardization techniques [slope/bias (S/B) correction, single wavelength standardization (SWS) and piecewise direct standardization (PDS)] were used to attempt to correct changes over time in multivariate calibration models for potassium and calcium. These models were constructed with ion-selective electrode (ISE) arrays. Multivariate PDS local models which included the correlation between the sensors of the array were better than the other simple techniques. We considered the relationship between the variables (sensors) and, in the PDS treatment, we have indicated their arrangement which is taken from the loadings plot. We used the Kennard–Stone algorithm to select the standardization samples from the original responses of the samples and the partial least squares (PLS) scores of each model. These scores include information about the concentrations. The models and standardizations were validated by predictions on real samples such as natural waters. The best standardization conditions provided unbiased predictions with no loss of precision.

Near-IR Calibration Transfer between Different Temperatures

Calibration transfer between spectra measured at different temperatures was investigated for near-IR spectroscopic determination of NaCl in aqueous solutions. A principal component regression (PCR) calibration model developed at 23.0 C was transferred to 28.5 C by using a piecewise direct standardization (PDS) method. The effect of window symmetry on calibration transfer was investigated. Only two transfer samples were needed in obtaining a good calibration transfer. The standard error of prediction (SEP) was 0.048 M NaCl when the calibration model developed at 23.0 C was used for predictions at 28.5 C without the standardization. The SEP was reduced to 0.008 M through the standardization, which was very close to 0.006 M obtained from a full set recalibration at 28.5 C and 0.007 M obtained from a general calibration model based on the spectra measured at different temperatures between 23.0 and 28.5 C. The calibration transfer from one temperature to another can save a lot of time in remeasuring the calibration samples and redeveloping a new calibration model at a new temperature.

An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra

Orthogonal signal correction (OSC) is a technique for pre-processing of, for example, NIR-spectra before they are subjected to a multivariate calibration. With OSC the X-matrix is corrected by a subtraction of variation that is orthogonal to the calibration Y-matrix. This correction can then be applied to new spectra that are going to be used in predictions. The aim of this study is to investigate if the OSC transform makes the spectra less dependent of instrument variation. This may result in easier calibration model transfer between different instruments without creating or re-analysing the whole calibration sample set. OSC was applied to NIR-spectra that were used in a calibration for the water content in a pharmaceutical product. Partial Least Squares calibrations were then compared to other calibration models with uncorrected spectra, models with spectra subjected to multiplicative signal correction, and a number of other transfer methods. The performance of OSC was on the same level as for piece-wise direct standardisation and spectral offset correction for each individual instrument and PLS-models with both instruments included.

Piecewise Direct Standardization Method Applied to the Simultaneous Determination of Pb(II), Sn(IV) and Cd(II) by Differential Pulse Polarography

A partial least squares (PLS) regression has been used to carry out the simultaneous determination of PbII, SnIV and CdII by differential pulse polarography (DPP) because overlapping peaks exist. But this multivariate regression requires the measurement of a large number of calibration samples, so a standardization procedure, the piecewise direct standardization (PDS) method, has been used in order to reduce the experimental effort that will be necessary in later analysis. The number of calibration samples has been reduced by about 60 %, the results being comparable to those obtained with a full recalibration.

Piecewise Direct Standardization Method Applied to the Simultaneous Determination of Pb(II), Sn(IV) and Cd(II) by Differential Pulse Polarography

Piecewise Direct Standardization Method Applied to the Simultaneous Determination of Pb(II), Sn(IV) and Cd(II) by Differential Pulse Polarography

Improvement of PLS model transferability by robust wavelength selection

Frequently, a calibration model is adapted after being transferred to another instrument by, e.g., direct standardization (DS) or piecewise direct standardization (PDS). For this, a subset from the calibration set should be measured on both instruments. Usually, however, the calibration samples cannot be measured on both instruments. Another approach is to make the model robust with respect to transfer to another instrument during the development of the model, by data preprocessing. In this paper, the robustness of the calibration model is enhanced by using variable selection as data preprocessing. In the case under consideration, variable selection consists in the calculation of a calibration model with a subset of the original wavelengths (of spectroscopic data) that retains its predictive ability when it is transferred to another instrument. Both approaches (variable selection and (P)DS) are applied to the transferability of a PLS model which determines the water content in tablets. To this end, 140 tablets were measured on 2 near-infrared (NIR) reflectance instruments. It has been found that variable selection by simulated annealing (SA) enhances the model's robustness with respect to model transfer and also improves its predictive ability.

Transfer of Calibrations of Near-Infrared Spectra Using Neural Networks

A new approach for multivariate instrument standardization is presented. This approach is based on the use of neural networks (NNs) for modeling spectral differences between two instruments. In contrast to the piecewise direct standardization (PDS) method to which it is compared, the proposed method builds a single transfer model for all spectral windows. The apparently incompatible requirements for a high number of training objects and a low number of standardization samples are addressed by truncating spectra in finite-size windows and assessing a position index to each window. Each spectral window with the corresponding position index constitutes a training object. No prior background correction is required with this method. Both the proposed method and PDS were applied to some real and simulated data sets, and results were evaluated for reconstruction and subsequent calibration. On the studied data sets, the neural network approach was found to perform at least as well as PDS for both reconstruction and calibration.

Modelling the background current with partial least squares regression and transference of the calibration models in the simultaneous determination of Tl and Pb by stripping voltammetry

With the aim of carrying out a calibration transfer for routine analysis, partial least squares (PLS) regression was successfully applied to simultaneously determine thallium and lead by stripping voltammetry when an interfering background current is present. The presence of a significant blank signal that overlaps the thallium peak, together with the overlapping thallium and lead signals were both suitably modelled by this multivariate regression technique. Moreover, once the PLS models are built, the piecewise direct standardization (PDS) method can be used to transfer these models over time in such a way that the number of calibration samples that will be needed in future determinations is reduced from 25 to 9, without a loss of quality in the analyses. The mean of the relative errors (in absolute values) obtained for thallium and lead is below 4.94% and 3.19%, respectively.

Multivariate standardization techniques using UV-Vis data

Three standardization techniques, namely piecewise direct standardization (PDS), single wavelength standardization (SWS) and centering correction (CC) were applied to multivariate models developed using UV-Vis spectra. The data were obtained for the determination of Ca(II) and Mg(II) in natural waters analysed by sequential injection analysis (SIA). Unlike NIR, changes in measuring conditions are mainly reflected by changes in the sensitivity in the spectra. In all the models tested, the prediction errors in the best standardization conditions were less than one half of those in the non-corrected second conditions. Moreover, bias was not detected by the joint interval test. Of all the standardization techniques assayed, PDS gives the lowest mean squared error of prediction, probably due to the inclusion of more variability in the mapping of the spectra. The influential parameters, such as the number of standardization samples or the window size in PDS, were studied. The larger the number of samples in the standardization subsets, the more effective the techniques are, whereas the variation in window size does not greatly affect the calculations.

Calibration transfer from a scanning near-IR spectrophotometer to a FT-near-IR spectrophotometer

A principal component regression calibration model developed on a scanning near-IR spectrophotometer (with a standard cuvette) was transferred to a Fourier transform near-IR spectrophotometer (with a fiber-optic probe) for the determination of NaCl in aqueous solutions by using piecewise direct standardization method. Only two transfer samples were needed in obtaining a good calibration transfer. Standard error of prediction obtainable from the calibration transfer was 0.034 M, compared to 0.012 M produced by the full set recalibration for NaCl in the concentration range of 0–5 M.

Multivariate calibration transfer applied to the routine polarographic determination of copper, lead, cadmium and zinc

The application of calibration transfer methods has been successful in combination with near-infrared spectroscopy or fluorescence spectroscopy for prediction of chemical composition. One of the methods developed that provides accurate performance is the piecewise direct standardization method (PDS), which in this paper is applied to transfer from one day to another the partial least squares (PLS) models built in the polarographic determination of copper, lead, cadmium and zinc. This is an electrochemical example in which interferences have been found, making necessary the use of soft calibration models because of their ability to model this phenomenon, which implies a large number of standard samples for the calibration. Once the PLS models are built, the calibration transfer is carried out to overcome the instrumental change over time in this routine analysis, allowing one to reduce from 28 to 8 the number of calibration standards necessary for later determinations. Standard errors of prediction (SEP) are found similar to those given by the complete recalibration.

Calibration Transfer from Sample Cell to Fiber-Optic Probe

A calibration transfer method, piecewise direct standardization (PDS), was applied to a set of two-component samples measured on the same UV-visible spectrometer with the use of a cuvette cell with a 10-mm pathlength and a fiber-optic probe with a 2-mm pathlength. Piecewise direct standardization proceeds by determining a structured transformation matrix using the spectra of a few samples measured with both devices. This transformation matrix can then be used to transform any spectrum measured on one device to that obtained on another device, thereby making the calibration model transferable between devices. We used the spectra measured in a cuvette as the standard set and transferred the calibration model obtained for these spectra to spectra measured with a 2-mm fiber-optic probe on the same instrument. The total standard error of prediction (SEP) for the fiber-optic probe was 5.84 before the calibration transfer and 1.87 afterwards. Spectra were also processed by taking the Fourier transform prior to the calibration transfer. The 512 data points in each spectrum were compressed to 32 terms, starting with the first term after the dc offset. This processing reduced the background and the noise. As a consequence, in the Fourier domain, the total SEP was 5.69 before the calibration standardization and 0.79 after the calibration standardization. A calibration transfer was also performed between two fiber-optic probes; the total SEP in the spectral domain was 2.16 prior to the transfer and 1.04 after the transfer, whereas in the Fourier domain the SEP was 1.50 prior to the transfer and 0.77 after the transfer.

Standardization of near-infrared spectra in the wavelet domain

A new standardization method based on transferring near-infrared (NIR) spectra in the wavelet domain is proposed. For each NIR spectrum, wavelet transform coefficients are computed, and the transfer step is performed by relating the wavelet transform coefficients of spectra obtained on both instruments with univariate linear models. This method is applied to two different data sets, and its performance is compared with the piecewise direct standardization method. The results obtained with this new method are better than those obtained by PDS, the biggest improvement occurring when very few standardization samples were used to estimate the standardization parameters. Both PDS and wavelet approaches offer advantages only when the spectral differences are local. When spectral differences are global, other methods such as the slope/bias correction function as well.

Appearance of Discontinuities in Spectra Transformed by the Piecewise Direct Instrument Standardization Procedure

Several years ago, we noted that spectra transformed by the piecewise direct standardization (PDS) method may contain discontinuities. Having noticed that the problem was a recurring one, we studied it and recently diagnosed its source. Our investigations suggest that this problem also occurs in applications of window factor analysis, evolving factor analysis, and any other procedure that uses piecewise principal component models. In this work, we report the source of the problem and illustrate it with one example. A procedure is presented for eliminating the problem that is effective in PDS pattern recognition applications. Further work is needed to develop modified algorithms suitable for calibration applications.

Improvement of the piecewise direct standardisation procedure for the transfer of NIR spectra for multivariate calibration

Standardisation of near-infrared spectrometric instruments using the piecewise direct standardisation method is studied. Two important steps of this method, namely the selection of the subset samples and the determination of the local optimal number of principal components, can yield artefacts in the transferred spectra, if they are not carefully performed. Three different algorithms are tested on two different data sets in order to study the subset selection and a method based on the prediction of an independent test sample is proposed in order to detect the artefacts due to bad local rank determinations. Improvements of the standardisation procedures were obtained, particularly when low numbers of standardisation samples were included in the subset.

Standardization of Near-Infrared Spectrometric Instruments

In this paper, two different approaches are studied for the standardization of near-infrared spectrometric instruments. The first is a simple method based on a univariate slope/bias correction of the predicted values. The second approach proposed is the much more sophisticated piecewise direct standardization (PDS) based on a multivariate correction of spectra. Both standardization methods are applied to three different data sets, and the results obtained are compared. In certain cases, the simple slope/bias correction approach yields results at least as good as those obtained by the PDS procedure. In other cases, the complex PDS procedure is required to obtain acceptable results. A diagnostic tool is developed in order to decide whether the simple slope/bias correction approach can be applied instead of PDS.

Direct standardisation in multi wavelength fluorescence spectroscopy

The application of direct standardisation methods by chemometrics has been successful in combination with multi wavelength near-infrared spectroscopy (NIR) for prediction of chemical composition. In this paper the methods of direct standardisation are applied to the analogue case of fluorescence spectroscopy introducing problems due to slit widths, stability of lamp, scanning speed, and pH; measuring at a sensitivity and signal-to-noise ratio of several orders of magnitude better than in NIR spectroscopy. Three different methods of spectrum standardisation have been tested: full spectrum standardisation (FSS), single wavelength standardisation (SWS) and piecewise direct standardisation (PDS). The fluorescence emission spectra stem from transmission measurements of 35 sugar solutions, containing small concentrations of a large number of fluorescent substances such as phenols and amino acids, at four different instrumental configurations. The performances of the algorithms are evaluated by the partial least squares (PLS) prediction errors obtained for two sugar quality parameters, namely colour and amino-nitrogen. It is shown that full spectrum standardisation performs well in the case of amino-nitrogen, while it is necessary to use the SWS or PDS methods to get acceptable colour predictions. The root mean square errors of prediction (RMSEP) obtained in the standardisation of four different instrumental configurations are 0.7–5.6% and 1.1–13.8% higher than the RMSEP values obtained by full recalibration for amino-nitrogen and colour, respectively. As transfer standards sugar samples that are extremely stable are preferred to single chemical standards for standardisation of complex spectra from biological samples. It was not possible to transfer emission spectra of sugar samples measured at pH 7.0 (phosphate buffer) to compare with emission spectra measured in pure water, indicating fundamental chemical changes due to difference in pH.

A multivariate chemometric approach to fluorescence spectroscopy

A multivariate approach to the solution of problems often encountered in the spectrofluorometry of natural samples, utilising information from whole spectra is presented. (a) Piecewise direct standardisation is implemented and employed to transfer emission spectra measured with two different xenon lamps of different ages as if the spectra were measured with the same lamp. (b) It has been shown using a multivariate analysis approach that it is possible to use the raw data points instead of the smoothed data based on an algorithm included in the instrument software by the manufacturer. (c) It is documented that Raman scattering does not hamper the performance of multivariate calibration; on the contrary, in an experiment with sugar samples the concentration prediction errors become about five times lower by including the whole emission spectrum in the analysis instead of using a univariate calibration based on an emission wavelength that only reflects the analyte of interest. (d) An algorithm for variable selection is implemented and employed in the selection of optimal excitation wavelengths. Among 13 emission spectra recorded for a sugar sample at different excitation wavelengths, four of these are chosen that describe 98.51% of the total variance in the original data. (e) Finally the combination of fluorescence spectroscopy and multivariate calibration with conventional chemical data according to the near-infrared black box model is presented. The refined sugar quality parameter, the ash content and the fluorescence emission spectra are correlated by a partial least-squares regression model. Five experiments employing different monochromator slit widths and sugar concentrations are performed, and the best correlation obtained by full cross-validation of the 15 sugar samples is R = 0.98.

Calibration Transfer and Measurement Stability of Near-Infrared Spectrometers

Near-infrared (NIR) spectroscopy has been widely accepted as a quantitative technique in which multivariate calibration plays an important role. The application of NIR to process analysis, however, has been largely limited by a problem identified as calibration transfer, the attempt to transfer a well-established calibration model from one instrument (e.g., located in the central laboratory) to another instrument of the same type (e.g., located on an industrial process). A calibration transfer method called piecewise direct standardization (PDS) is applied to a set of gasoline samples measured on two different NIR spectrometers. On the basis of the measurement of a small set of transfer samples on both instruments, a structured transformation matrix can be determined and applied to transform spectra between two instruments, enabling the transfer of calibration models. The effect of spectrum preprocessing on standardization is studied with the use of a set of gasoline samples. In a separate study, the day-to-day instrument variation as observed from the change in the polystyrene spectrum is related to the prediction of moisture, oil, protein, and starch content in corn samples, and then the possibility of using such generic standards to replace real samples in a transfer set is explored. In all cases, a standard error for prediction comparable to full set cross-validation is obtained through standardization.