Real-time analysis of ethylene vinyl acetate random copolymers using near infrared spectroscopy during extrusion.
Poly(ethylene vinyl acetate) (EVA) copolymers are random copolymers that are obtained by the copolymerization of ethylene with vinyl acetate under high pressure. The incorporation of vinyl acetate (VA) reduces the crystallinity of the polymers, which in turn improves their flexibility, clarity, and impact strength, and reduces the hardness. Variations in the concentration of vinyl acetate lead to variations in the properties of EVA copolymers, which are used for a variety of applications . Polymers with low concentrations of VA ([less than]20 wt %) are primarily used to make extruded film for flexible packaging. The rubber-like properties of the polymers are used in applications such as bumper pads, flexible toys, etc. Concentrations of VA [greater than]20 wt % are mainly used as hot melt adhesives by further mixing the copolymers with waxes and tackifiers. Thus, the properties of the polymers are largely dependent on the concentration of vinyl acetate in the polymer. For quality control purposes, it is therefore imperative that the VA concentration be monitored.
This paper shall describe the application of near-infrared spectroscopy, fiberoptics, and multivariate analysis in real-time monitoring of composition, during extrusion of EVA random copolymers. The study encompassed ethylene vinyl acetate (EVA) random copolymers, with vinyl acetate (VA, the comonomer) varying in the 0 to 40 wt % range. The effects of different spectral regions and pathlengths on the calibration models were explored. The robustness of the calibration models was tested by using data collected on EVA copolymers from two independent sources. Furthermore, the study also examined the variations in spectra with time, and the robustness of the calibration models in handling these variations. The robustness of the calibration models was also tested by using the models for real-time predictions. Different approaches, analogous to statistical process control charts, were used to study the results of real-time predictions. These approaches facilitated polymer process outlier detection in real-time, even before using the model for predictions.
Figure 1 shows the system for in-line molten polymer analysis. A 3/4-inch Brabender single-screw extruder, with a L/D ratio of 25:1, is used to melt particulate solid polymers. A continuous purge of nitrogen gas in the feed hopper prevents any possible moisture absorption from the ambient atmosphere. Molten polymer from the extruder is pumped through a multifunctional variable pathlength flow cell installed at the exit port of the gear pump. The gear pump is used to ensure a uniform mass flow rate of the molten polymer to the flow cell. This arrangement prevents any perturbations or flow instabilities in the screw region to be propagated to the flow cell. A temperature and pressure control unit regulates the temperature and pressure conditions inside the flow cell.
Figure 2 shows a detailed schematic of the flow cell. This flow cell provides a flow channel of rectangular cross-section that is 20 mm long and 9.5 mm wide. The gear pump head has a circular opening of 3/8-inch diameter. A transition piece provides a smooth transition region between the pump head (circular cross section) and the flow cell (rectangular cross section). This smooth transition region ensures that, from a rheological perspective, the complete flow area is free of dead spaces , where polymer might accumulate and degrade. Double-insertion transmission type fiberoptic probes are used to transmit light through the flowing polymer stream. These probes are mounted into specially designed housings whose internal dimensions match standard industry pressure transducer dimensions. The separation between the probes (i.e., the pathlength) is varied using spacers of different thickness. Ring-shaped spacers are mounted on the neck of the housings. Thus, the thickest spacer makes the housings flush with the walls of the flow channel, and by reducing the thickness of this spacer, the path-length can be varied between 1 and 9.5 mm. Two more ports downstream of the fiberoptic probes are used for temperature and pressure measurement. Finally, a pressure restrictor attached to the flow cell can be used to vary the pressure of the flowing polymer stream.
The fiberoptic probes installed in the flow cell are connected via fiberoptic cables to a Guided Wave Model 260 spectrophotometer . This spectrophotometer comprises a tungsten halogen lamp, a lead sulfide detector, and a holographic diffraction grating. The spectrophotometer is interfaced to a computer for data acquisition. The software package provided by Guided Wave (Scanner & Examiner) is used for data acquisition and manipulation. The details of fiberoptic probes and the mathematical techniques for analysis of spectral data have been described in a previous publication .
I. EXPERIMENTS - EVA COPOLYMERS WITH VARYING VA CONCENTRATION, AND USING 2.5 MM PATHLENGTH
The copolymer samples were obtained from two sources and shall be referred to henceforth as Class I and Class II. Class I comprises 16 samples of EVA copolymers and Class II comprises eight samples of EVA copolymers. The existence of two separate sets of polymer samples provided the advantage of preparing the calibration models on one set of polymer samples and using the second set as an independent test set to validate the precision of the calibration models. The 16 samples of Class I actually comprised nine target concentrations (0, 9, 12, 15, 18, 25, 28, 32, and 36 wt % VA). The eight samples of Class II actually comprised four target concentrations (19, 21, 27, and 35 wt % VA). The actual concentrations of vinyl acetate in the 24 samples has been tabulated in Table 1. The chemical structure of the copolymer is illustrated in Fig. 3. The melting point of the EVA copolymers lies in the 103 to 108 [degrees] C temperature range. Processing temperatures range from 150 to 210 [degrees] C.
The first set of experiments was performed using a fixed optical pathlength of 2.5 mm. This pathlength ensured that the maximum absorbance, over the full range of the spectrum (i.e., from 1200 to 2400 nm), was be less than 1.0 AU. The main reason for working with absorbances in the range 0 to 1 AU is to preserve the linearity of Beer's law. Absorbances greater than 1.0 AU mean that the overall transmittance is less than 10%. The collimated optical beam in the flow cell is [approximately]1.5 mm in diameter. All polymer samples were extruded at a fixed temperature setpoint of 200 [degrees] C. The screw speed (20 rpm) and flow rate (1.2 lb/hr) were kept fixed for all except three of the samples (samples 10, 12, and 13 of Class I). These three samples had a very high melt index and had to be extruded at a higher flow rate (2.4 lb/hr) in order to prevent the polymer flow stream from draining out of the flow cell and forming bubbles in the optical measurement beam. The maximum pressure attained downstream of the gear pump was [approximately]1400 psi. A continuous purge of dry nitrogen gas in the hopper prevented any moisture absorption from the ambient atmosphere. The spectral data for the two sets of polymers were collected on two separate days.
Table 1. Details of the EVA Samples, with Varying VA Concentrations. Class I Class II Sample Sample Number Wt % VA Number Wt % VA 1 0 1 18.72 2 9.08 2 18.82 3 9.11 3 21.01 4 12.12 4 20.90 5 12.04 5 26.70 6 15.18 6 26.87 7 17.91 7 34.80 8 18.06 8 34.95 9 24.89 10 25.22 11 28.49 12 27.84 13 28.59 14 28.37 15 32.05 16 35.57
Results and Discussion
Figure 4 shows the overlaid spectra of polyethylene (PE) and EVA containing 28 wt % VA. The spectrum of pure poly(vinyl acetate) (PVA) has also been overlaid on the spectra in order to determine spectral features that could be attributed to vinyl acetate. The structure of the copolymer [ILLUSTRATION FOR FIGURE 3 OMITTED! shows that although both the comonomers have C - H vibrations, the vibrational overtones and combinations of the C = O stretch, if identifiable and distinct, could be used to quantify the amount of VA present.
A closer look at Fig. 4 shows that there are some changes in two spectral regions: (i) spectral region A, which comprises wavelengths from 1600 to 1950 nm, contains the first overtones of the C - H vibrations [5-7]; and (ii) spectral region B, which comprises wavelengths from 2000 to 2200 nm, contains combination bands [5-7]. These two regions have been enhanced in Figs. 5 and 6, respectively. Spectral region A shows that the incorporation of VA leads to a decrease in the intensity of the polyethylene doublet around 1700 nm. This doublet in polyethylene is probably because of the methylene stretch . With the incorporation of VA in the chain, there is a decrease in the overall methylene content that leads to a decrease in the intensity of the methylene doublet. The presence of VA also leads to subtle changes in the slope of methylene doublet. Furthermore, there is a small peak at [approximately] 1680 nm that evolves with the increase in VA concentration. This peak is also present in the spectrum of pure PVA and is absent in the spectrum of pure PE. Thus, this peak can definitely be assigned to VA and is probably an overtone of the methyl group in VA [7, 8]. The slight variation in the slope of the methylene overtone around 1700 nm is possibly because of the superposition of the VA absorbance in this region.
In the spectrum of pure PVA, there are some distinct peaks around 1900 nm and 2100 nm. The second overtone of the carbonyl band is known to exist around 2140 nm . In the spectra of EVA samples, there is a peak present at [approximately] 2135 nm, which evolves with increase in VA content. Although the intensity of this peak (2135 nm) is much lower than the C - H overtone peaks, it shows the variation in VA content much more clearly, and is free of interference from polyethylene. Our conjecture is that this peak (2135 nm) is probably a combination band of C - H stretch and C = O stretch.
As mentioned earlier, all calibration modeling was performed on one set of polymer samples. Since the number of samples in Class I is higher than in Class II and the samples in Class II lie within the concentration range encompassed by Class I, the samples of Class II were chosen to constitute the independent test set. A three-pronged approach was used to test the robustness of the calibration models: (i) validation of all the calibration models against test sets from Class I; (ii) validation of the lowest-SEP calibration model against an external test set (Class II samples); (iii) validation of the lowest-SEP calibration model by real-time monitoring of VA concentrations in samples from Class II. Please note that SEP stands for standard error of prediction, which is basically the standard deviation between the actual (laboratory values) and predicted (using calibration model) concentrations of the samples in a test set. It must be mentioned that the collection of experimental data on Class I samples, Class II samples, and real-time monitoring experiments were conducted on three separate days. Thus the robustness of the calibration models in handling variations with time was also tested.
Ten spectra corresponding to each of the 16 samples (in Class I) were chosen for data analysis. These spectra were chosen after visual examination to remove any possible outliers. These 160 spectra were divided into two groups comprising 80 spectra each (five spectra for each of the 16 samples), one for calibration and the other for validation. Both of the spectral regions were treated separately for data analysis. Spectral pretreatment consisted of removing baseline offsets by one of two methods: (i) simple 2-pt. baseline correction; and (ii) computation of the first derivative of the spectra. The sloping-baseline corrected data are more useful in qualitative analysis, but sometimes they may not be as accurate as the derivative spectra, which not only provide a very flat baseline but also expose many subtle variations in the spectra. On the other hand, derivative spectra are very noisy and have to be repeatedly smoothed before performing any kind of multivariate analysis. In forming the data sets, the 1615 to 1903 nm wavelength range was used for the first spectral region, while the 2040 to 2160 nm range was used for the second spectral region. From the calibration data (80 spectra), four data sets, two sets each (derivative and baseline corrected data) corresponding to the two spectral regions, were constructed. The four data sets were then used as calibration sets, and the multivariate techniques of partial least squares (PLS) and principal component regression (PCR) were used. Thus, a total of eight calibration models [ILLUSTRATION FOR FIGURE 7A OMITTED! were developed for the four data sets. This kind of extensive calibration modeling was aimed at identifying the best spectral region and also at comparing the performance of common data pretreatment techniques and factor based regression methods. The optimal number of factors was determined using the leave-one-out cross-validation method  and was found to be one factor, in each case. This result explains that there is one prominent source of variation in the data, i.e. the VA content.
From the validation data (80 spectra), just like the calibration data, four data sets were constructed for validation purposes. The predictive ability of each of the eight calibration models, developed above, was tested by using the corresponding validation set for predictions. By using one factor, the standard errors of prediction of the data sets using the corresponding calibration model were computed, and they are tabulated in Table 2 and illustrated in Fig. 7b. As defined earlier, the standard error of prediction represents the standard deviation between the actual and predicted concentrations. Hence, a lower standard error of prediction corresponds to a more accurate calibration model. In the present study, the performance of the [TABULAR DATA FOR TABLE 2 OMITTED] combination region was better than that of the overtone region [ILLUSTRATION FOR FIGURE 7B OMITTED]. In both the regions, the derivative spectra provided better results than the baseline corrected data. This is because 2-pt. baseline-correction does not remove baseline offsets completely. Moreover, the information content of the near infrared spectra is quite complex because of the presence of overlapping absorbances. The derivative spectra help to alleviate this complexity by deconvoluting many subtle variations and overlapping peaks in this region. Also, the results illustrate that the performance of PLS is always fractionally better than PCR. The main reason for this performance is that PLS takes into account the variation in both the absorbance and the property data, while PCR assumes that the property data are proportional to the absorbance data. The advantage of PLS based regression becomes more obvious in situations where the property data has an indirect relationship with the absorbance data. In the present case, even when the absorbance data are directly proportional to the concentration data, it can be seen that PLS slightly outperforms PCR. Thus, it can be concluded that PLS should be the method of choice in all EVA calibrations.
Before proceeding on to the results of external validations, the existence of one optimal factor in EVA calibrations shall be described both qualitatively and quantitatively, using different approaches. The determination of the optimal number of factors in multivariate analysis is a very subjective task, and it requires that the number of factors chosen should be such that there is no underfitting or overfitting, thereby distinguishing between information removal and noise removal, respectively . One way of identifying the ideal number of factors in a calibration model is to compare the residuals and the regenerated spectra, after each factor, to the original spectra. The plot of residuals is also useful in detecting outliers, both in individual samples and variables. Thus a sample or a variable having abnormal values of residuals could be easily identified as an outlier. Figure 8 shows the overlaid derivative plot of all 80 calibration spectra. Figures 9 and 10, respectively, show the regenerated spectra and the spectral residuals, using one factor. Both plots show that the first factor adequately accounts for most of the useful information in the spectra, while random noise constitutes the spectral residuals.
Another approach that was adopted in determining the optimal number of factors was to examine the effect of increasing number of factors on the singular values of the covariance matrix (i.e. [X.sup.T]Y in PLS, where X is the absorbance data matrix and Y is the matrix containing composition data). In the present study, a residual-norm-ratio (RNR - defined as the ratio of the norm of the residual covariance matrix used to determine a particular factor to the norm of the matrix used to extract the first factor, i.e. the original covariance matrix) was determined for each factor that was included in the calibration. The residual-norm-ratio was chosen because it gives a measure of the degree of information still contained in the residual covariance matrix relative to the information contained in the original covariance matrix. Thus, the residual-norm-ratio provides an estimation of the optimal number of principal components required to describe the information content in the original covariance matrix. Furthermore the residual-norm-ratio is easier to plot, because it varies from 0 to 1. Figure 11 shows the variation of the residual-norm-ratio with increasing factors for model 7. The plot illustrates that the residual-norm-ratio of the residual covariance matrix after one factor is close to zero, implying that the original covariance matrix has one principal component. This observation further justifies that the data set has one major factor of variation. This concept would have more utility for complex systems that have more than one factor.
The scores plots were used to interpret the contributions of the first two factors and also to identify clusters of samples that have similar concentrations of VA. Figure 12 shows that the scores of the samples (using model 7) increase with increasing sample number (i.e. increasing VA concentration), implying a positive correlation between the first factor and the VA concentration. Also, the relationships among the samples is effectively modeled by the first factor, where nine separate clusters can be attributed to the nine target concentrations in the sample set. The scores of the samples for the second factor are negligible, thereby justifying once again that the first factor accounts for the main information content in the spectra.
The multivariate analysis of the EVA spectra leads us to conclude that one-factor calibration models on derivative data in the 2040 to 2160 nm wavelength range are the most ideal for correlating the VA content in the copolymers. The robustness of this calibration model (model 7) was tested by validation against the spectral data obtained from Class II samples. Ten spectra corresponding to each of the eight samples were chosen for data analysis. The first derivative data, in the 2040 to 2160 wavelength range were used to construct the data set. It was found that one factor models provided the best results with standard error of prediction (SEP) as low as 0.49 wt %. This test proved two points: (i) the calibration models are robust; and (ii) the optimal number of factors is indeed one. The predictions for VA concentration for both the validation sets (i.e., Class I and Class II) are shown in Fig. 13.
Finally, the ultimate test of the robustness of the calibration model was to use the model for real-time on-line predictions. For real-time predictions, the "Monitor" module of the Guided Wave spectral system software was used. This module acquires spectral data in real-time, preprocesses them as instructed, and then uses an existing model for predictions of the calibrated properties (such as concentration, etc.). Figure 14 shows a block diagram that describes the procedure used for real-time predictions. Three samples of Class II were used for real-time predictions and the calibration model for derivative data in the combination region was used. Each prediction took about 8 s. Thus, even with a slow scanning instrument, where each spectrum takes almost 70 s, the prediction time is drastically lower than the scan time for the full spectrum. The real-time in-line predictions have been illustrated in Fig. 15. It can be seen that almost all the data points lie within the control limits. The control limits were determined by the SEP value of the model for Class II samples (i.e. 0.49 wt %). It has also been illustrated that even by randomly feeding the samples (34.80% VA followed by 20.90% VA, followed by 26.70% VA), the calibration model can adequately account for the variations in VA concentrations. The transition region from one sample concentration to another is smooth, instead of a sudden step change, primarily because the samples were continuously fed into the extruder and the transition region thus corresponds to the residence time of the extruder, gear pump, and flow cell.
In-line monitoring of the VA content in molten EVA copolymers is extremely useful for quality control. This study has demonstrated that NIR spectroscopy, coupled with fiberoptics and chemometric data analysis, is ideal for real-time analysis of VA content in molten EVA copolymers. The robustness of the calibration models was tested by using data from two independent sources, and also during real-time in-line predictions. In each case, the results were very promising for implementation in a polymer manufacturing plant.
In this study, it has been shown that the most precise calibration models for quantification of the VA concentration in EVA copolymers were obtained by using the derivative spectra in the combination region (2000 to 2200 nm). However, it can be seen that the maximum absorbance for the C - H stretch/C = O stretch combination peak is less than 0.14 AU. A major concern at such wavelengths is that there is considerable attenuation in the fibers, as the length of the fibers is increased. In that case, the 2135 nm absorbance peak shall be completely masked by the high baseline. There are two possible ways to circumvent the problem: (i) to use the absorbance data in the C - H overtone region, but at the expense of a higher prediction error; or (ii) to amplify the absorbance of the 2135 nm peak by utilizing the maximum pathlength of the flow cell. The following section shall describe the advantages and pitfalls of the latter alternative.
II. EXPERIMENTS - EVA COPOLYMERS WITH VARYING VA CONCENTRATION, AND USING 9.5 MM PATHLENGTH
As mentioned previously, the low absorbance of the 2135 nm carbonyl combination band in vinyl acetate was a cause for concern in using this peak for monitoring a manufacturing process, where fiber lengths could be very high. In order to amplify the absorbance of this peak, the full pathlength of the flow cell (9.5 mm) was used. At this pathlength, the absorbance of the sample containing maximum amount of vinyl acetate (i.e. 35.57% VA) was less than 1.2 AU. Since all the other samples had absorbances less than 1.0 AU, this pathlength was utilized for the study of EVA samples in the 2000 to 2200 nm wavelength range. In order to ensure consistency, all the other experimental conditions were the same as those used in the first set of experiments. Thus, the temperature setpoint in the flow cell was fixed at 200 [degrees] C, the screw speed was kept constant at 20 rpm and the mass flow rate maintained at 1.2 lb/hr.
However, there was one problem with this higher pathlength. All the EVA samples do not have the same melt index. Their melt index varies in the range from 0.3 to 400 g/10 min. The variable melt index results in variation in the viscosity of the flowing polymer. In the first set of experiments, the main variation in the spectral information was due to the variation in VA content. Other variations, such as slight variations in temperature or variations in downward pressure (due to changes in viscosity of the molten polymer) did not have any major effect on the absorption spectra. In the case of the higher pathlength, the polymers with melt index greater than 10 g/10 min posed a tricky problem. Owing to their low viscosity, they were not able to fully fill up the complete flow path and also they were not able to flush out the preceding viscous polymers. The only way of obtaining the spectra of these polymers was to dismantle and clean the flow cell before running each of these samples. Such a process, however, is not feasible while acquiring data for a calibration model, where it is extremely critical that all the data be acquired without minimal perturbation to the experimental setup. Thus, the only other option was to exclude the high MI samples from these experiments. A closer examination of the samples revealed that five of the 16 Class I samples (25.22%, 27.84%, 28.37%, 28.59%, and 32.05%) had to be excluded. Four of these five samples had low MI counterparts in the sample set. Thus, only one out of the nine target VA concentrations was totally eliminated from the Class I sample set. For the Class II samples, two (19% and 35% concentrations) of the four target concentrations had to be eliminated. The reduction of the number of samples in the Class II set was not a major concern because this sample set was only used for validation purposes.
Results and Discussion
Figure 16 shows an overlaid plot of the eight Class I samples, in the 1200 to 2400 nm wavelength range. The pronounced effect of the increased pathlength is very distinctly noticeable in the spectra. The first overtone C - H peaks in the 1600 to 1850 nm range have very high absorbances, with virtually no light reaching the detector. The 2135 nm C = O combination band is clearly amplified at this pathlength. Once again, it can be noticed that this peak is virtually free of interference from polyethylene, which does not have any absorption in the region. In Fig. 17, the above region has been blown up. It can be noticed that other minor peaks (in the 1900 to 2000 nm range), because of the second overtone of the carbonyl group in vinyl acetate, etc., have also been amplified. Thus, even by visual examination it can be concluded that the 9.5 mm pathlength is more suitable for the analysis of the EVA samples in the 2000 to 2200 nm region. However, it was interesting to compare the performance of the region using the expanded pathlength, vs. the 2.5 mm pathlength, for quantification of the VA content.
In order to avoid redundancy, the quantitative analysis of the above data set was restricted to first derivative data in the 2040 to 2160 nm range. This data set had outperformed the baseline-corrected data by a factor of 2. Also, in this study, only PLS based regression was used for calibration purposes. Ten spectra, each corresponding to each of the 11 samples, were chosen for modeling. The first derivative data for each of the spectra were computed, following which the spectra were smoothed. The data set of 110 spectra was divided into two sets of 55 spectra (five spectra for each sample) each, one for calibration and the other for validation. PLS calibration model of the calibration set yielded that more than 98.5% of the variance was accounted by one factor. The robustness of the calibration model was tested on the Class I validation set. A SEP value of 0.33 wt % was obtained using one factor. This SEP value is slightly lower than the SEP value for the 2.5 mm data set, thereby indicating that the results are comparable and marginally better at this increased pathlength.
The robustness of the calibration model was further verified by tests against external data sets. In this respect, the external set was created by using five spectra each of the four Class II samples. The spectral data were subjected to first derivatives and smoothing. The PLS calibration model, as described above, was used to predict the VA concentration in all the 20 spectra, and the SEP was calculated using one factor. The SEP for this data set was 0.48 wt %, which is almost identical to the SEP value obtained for the Class II samples in the previous study. This result proves that although there is no marked improvement in the prediction results by utilizing the expanded pathlength, the reliability of the NIR results is certainly obvious. Figure 18 shows the scatter plot of predicted vs. actual concentrations for both the calibration and validation sets.
The above results reinforce our initial inference that one-factor calibration models on derivative data in the combination region are the most adequate for quantification of the VA content in EVA copolymers. Furthermore, it must be reiterated that the advantage of a much lower prediction error in the combination region certainly makes the combination region more attractive for plant-wide process control. Also the expanded pathlength of 9.5 mm is certainly more desirable than the 2.5 mm pathlength because it provides a much larger window into the process stream. Also, in some industrial processes, a single-insertion transmission probe with a reflective tip at the far end of the probe, is utilized for data acquisition. The utility of the single-insertion transmission probes over the dual-transmission probes lies in the fact that two transducer ports facing each other may not be present in a process stream, and in such a case, the single-insertion probe can be easily mounted by removing any pressure transducer. However, with a single-insertion transmission probe the effective pathlength is twice the flow path because the optical beam traverses the flow path twice. Thus 2.5 mm and 9.5 mm path-lengths for dual-transmission probes are equivalent to 1.25 mm and 4.75 mm wide flow channels for single-transmission probes, respectively. Thus, for single insertion transmission probes the expanded pathlength would undoubtedly be preferred, in order to avoid any remote possibility of clogging that may occur with a 1.25 mm wide flow channel. Another pertinent reason is that the 9.5 mm pathlength is more adequate for quantification of trace-level additives in EVA copolymers. In that case, the same probe setup could be interchangeably used for both VA and additive quantification, without any perturbation and process shutdown.
Having discussed both the performance and the utility of the expanded pathlength, the real-time monitoring of the Class II EVA copolymers shall be described. As compared to the previous study, a slightly different approach was adopted in this study. In the previous study, the calibration model was utilized for real-time in-line predictions of the VA concentration, but the actual spectra corresponding to each prediction point were not saved. In this case, the actual spectra during real-time monitoring were saved in order to enable diagnostic studies on outliers and scores. These diagnostic studies shall be described following the discussion of the real-time monitoring results.
For real-time monitoring, two samples of Class II, containing 26.87% and 21.01% VA were used, followed by flushing out the extruder with low density polyethylene (LDPE) of MI equal to 1g/10 min. The LDPE was supplied by a third source and is routinely used in the lab for purging the extruder following each set of experiments, and before shutdown. This high-viscosity LDPE helps to flush out the various types of polymer that are used for experimental purposes, some of which crosslink if they are left in the extruder. The upper and lower control limits were fixed as the SEP value of 0.48 wt %, that was obtained by the PLS calibration model for the Class II samples. Since the LDPE was not previously used in any data analysis, its prediction error was not available. However, as a test, the same Class II control limits were used on the LDPE samples, to check their performance. Furthermore, this sample provided another important test to check the robustness of the calibration model, especially considering the facts that the sample had not previously been used in any data analysis and that it was available from an independent source. Figure 19 shows the real-time monitoring results of the three samples. It can be seen that all three samples lie within the control limits, with a very few samples falling out of range. The transition from one sample to another is very smooth, and represents the residence time of the extruder. The performance of the LDPE sample is very promising and proves that the extrusion of the EVA samples could be monitored very effectively within an accuracy of less than 0.5 wt %.
The spectra acquired during real-time predictions were used for diagnostic studies on outliers and scores. According to Kaspar and Ray , the scores values can be used for real-time monitoring, in a way similar to a statistical process control (SPC) chart. One distinct advantage of using scores values, is that the outliers can be easily identified even before the model is utilized for prediction purposes. This procedure thus reduces the computation time involved in calculating the concentrations of the outlier samples, and would trigger off the warning alarms more expeditiously. In the present case, in order to create the scores chart, the scores values corresponding to the actual concentrations and the respective upper and lower control limits had to be calculated. This calculation required back calculation of the scores values using the concentration values and some existing model parameters. The procedure developed for a one-factor model is described in the following equations,
In the prediction step of PLS regression the spectrum of an unknown sample is first scaled (i.e., mean-centered) and then the scores value for the first factor are calculated by projecting the scaled spectrum (x) along the vector containing the loadings weights for the first factor.
Tu = [x.sup.*]W(:, 1) (1)
Here, x is 1 by n (where n is the number of wavelengths), and W (:, 1), which is the first column of the matrix of loadings weights, is of size n by 1. Thus, Tu (the scores vector for an unknown spectral observation) is a number. This Tu is used to calculate the predicted y value ([y.sub.p]) as
[y.sub.p] = [b.sup.*]T[u.sup.*]Q (2)
where b is the regression coefficient corresponding to the regression of the first scores vector of the X (absorbance) calibration matrix on to the first scores vector of the Y (composition) calibration matrix. Q is the vector containing the loadings for the first factor. Since Y has only one variable (the VA concentration), the Q vector has only one entry and is therefore reduced to a number.
Since b and Q are just numbers the back calculation of the Tu values corresponding to the concentrations and the control limits was very straightforward. Each concentration was scaled with respect to the mean of the Y matrix of the calibration set and divided by the product of b and Q.
Tu = [y.sub.p]/([b.sup.*]Q) (3)
An alternative approach for determining the control limits for the scores values (especially when there is more than one factor) , is to determine the scores values for a particular factor, corresponding to both the actual and predicted y values. These scores values can be determined by projecting the actual and predicted y values onto the y loadings vector for the particular factor. The standard deviation of the scores corresponding to actual and predicted y values could then be used as the interval for determining the control limits.
In the present study, the control limits were established for the scores values (Eq 3), and the scores chart was created by computing the scores value for each unknown spectral observation using Eq 1. This scores chart is illustrated in Fig. 20. It can be seen that the scores chart can be easily used to monitor the process and identify perturbations. As seen in both Figs. 19 and 20, there are a few spectral points that fall out of range of the control limits. These points, where the process is upset, are termed as outliers. These outliers could be due to process shifts, bubbles in the flow stream, black particles (a result of degraded polymer) in the flow stream, and particulate matter in the flow stream, such as residual inorganics. As seen in Figs. 19 and 20, two severe outliers have been identified. The spectra corresponding to, these outliers have been shown in Fig. 21. The spikes in the spectra clearly represent the abnormalities in the spectrum, thereby indicating that the samples are out of specifications and corrective measures should be taken for quality control. These outlier samples can be easily identified in the scores chart, even before predictions.
This study has demonstrated that an inherent weakness of the NIR region could be exploited as a strength. The weak absorptions could be magnified by increasing the pathlengths, and thus providing a larger flow channel. Such channels have high flow rates for low pressure drops. However, the method does have its limitations and samples of very high melt index could not fully fill up the flow channel and were not used for data acquisition in the continuous monitoring mode. This situation, however, is rarely encountered in a manufacturing process where there would be sudden change of MI from 0.3 g/10 min to 400 g/10 min.
The study has also demonstrated that a calibration model in the combination region is robust enough to monitor a totally unknown LDPE sample from a new source. The utility of using scores charts for monitoring real-time processes has been successfully demonstrated. It has also been shown that the scores charts could be easily used for real-time outlier detection, without using the model for prediction purposes.
This work was supported through research funding provided by Measurement and Control Engineering Center (MCEC), an NSF/Industry/University cooperative research center at the University of Tennessee, Knoxville. The polymers used in this work were supplied by member companies of MCEC. Special thanks are due to UOP Guided Wave for providing the spectrometer.
AU = Absorbance unit.
MI = Melt index.
NIR = Near infrared.
PCR = Principal component regression.
PLS = Partial least squares.
RNR = Residual-norm-ratio.
SEP = Standard error of prediction.
b = Regression coefficient corresponding to the regression of the first scores vector of the absorbance calibration matrix on to the first scores vector of the composition calibration matrix.
Q = Vector containing the Y loadings for the first factor.
Tu = Scores vector for an unknown spectral observation.
W(:, 1) = Vector containing loading weights for the first factor of absorbance matrix used in calibration.
x = Vector containing spectral values for an unknown sample.
[y.sub.p] = Predicted composition value for the unknown spectrum.
X = Absorbance data matrix (where rows correspond to samples and columns correspond to wavelengths).
Y = Composition matrix (where rows correspond to samples and columns correspond to individual components in each sample).
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|Author:||Khettry, Atul; Hansen, Marion G.|
|Publication:||Polymer Engineering and Science|
|Date:||May 15, 1996|
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