ARTICLE pubs.acs.org/IECR
Online near-Infrared Spectroscopy Combined with Alternating Trilinear Decomposition for Process Analysis of Industrial Production and Quality Assurance Jingjing Liu,† Xiang Ma,‡ Yadong Wen,‡ Yi Wang,‡ Wensheng Cai,† and Xueguang Shao†,* † ‡
Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin 300071, People's Republic of China R&D Center, Hongta Group, Yuxi 653100, People's Republic of China ABSTRACT: Process analysis is a great challenge in industry due to the complexity of industrial production. In the present work, an approach was developed based on online near-infrared spectroscopy and alternating trilinear decomposition (ATLD) method for industrial process analysis. The basic idea of the approach is to extract the common information that represents the common property of the batches using ATLD. Using common information, the production process can be monitored by investigating the variation of the common property, and quality assurance can be achieved by discrimination analysis. Taking the tobacco production as an example, the results show that the method is able to capture the intrinsic information of the products and performs well in process analysis and quality assurance.
1. INTRODUCTION Process analysis is critically important in the pharmaceutical,1,2 food,3 chemical, and biochemical industries4,5 as well as other industries. It concerns safety in production and quality assurance for products. However, industrial processes are highly complex and usually influenced by many factors, such as the properties related to the raw materials, the operating conditions, and environment factors. Therefore, great effort has been devoted to developing appropriate analytical methods to analyze and monitor production processes. Multivariate statistical techniques have been used for process analysis. They could extract process information by applying mathematical and statistical methods to the vast volume of data. Typically, they take into account the correlation between the variables and make it easy for the operator to decide whether a production process is normal. Common multivariate statistical techniques used for process analysis include principal component analysis (PCA)68 and partial least-squares (PLS).911 Such methods reduce the number of variables by means of latent variables (LVs) extraction, and these LVs are used for modeling. Recently, several extensions of PCA and PLS used to process analysis have been developed. Nonlinear PCA (NLPCA)1214 was used to deal with the nonlinearity among the process variables. Dynamic PCA1517 and adaptive PCA1820 were proposed to capture the time-variant property and overcome the problem of changing conditions in production processes, respectively. Besides, independent component analysis (ICA),2123 as a useful extension of PCA, was also presented to extract some statistically independent components underlying the process. For improving the process understanding in time or batch direction, process data can be organized into a three-way array. Hence, multiway techniques including multiway PCA (MPCA),24,25 multiway PLS (MPLS),26,27 parallel factor analysis (PARAFAC)2831 and Tucker332 were developed for process analysis. Among these multiway techniques, multiway PCA and multiway PLS are r 2011 American Chemical Society
unfolded methods, which need to unfold the three-way matrix into a two-way matrix. This may lead to a complex computation resulting from a huge unfolded matrix. However, PARAFAC and Tucker3 can directly decompose the three-way matrix according to the original dimensions without any unfolding process. Therefore, they have been recognized as useful tools in process analysis.30 The alternating trilinear decomposition (ATLD)33 is an analytical method for three-way data arrays like PARAFAC. It has gained widespread acceptance among the analytical community.3436 The advantage of the three-way methods is that interested components can be quantified even in the presence of unknown complicated interference, and this property is named as the “second-order advantage”.37 Hence, it is a powerful tool to decompose heavily overlapped peaks into their pure chromatographic, spectral and concentration profiles even in complicated systems. Near infrared (NIR) spectroscopy is a rapid and nondestructive analytical method and could provide direct chemical information related to production process. It has shown great power and gained wide acceptance in process analysis.3840 For a production process, the interested information usually hides in different types of variation, and the variation may vary from batch to batch. In this work, on the basis of the advantage of ATLD that can capture interested information regardless of complicated interference, an approach was proposed for process analysis of industrial production by a combination of online NIR spectroscopy and ATLD. The method can capture common information of the batches in the existence of variation. Using the common information, the variation from batch to batch can be evaluated, and the different properties of the products can be distinguished.
Received: March 17, 2011 Accepted: May 10, 2011 Revised: April 28, 2011 Published: May 10, 2011 7677
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It should be noted that, for obtaining a reliable common spectrum of a product, the reference data must be taken from normal batches. Investigations are needed before the ATLD decomposition. However, the control limits used in this work were estimated by the normal distribution and the weighted χ2 distribution,41 respectively, with 95% significance level. Furthermore, since SPP is a projection value and fluctuates around a mean value, both upper and lower limits are defined. For SPE, however, only the upper limit is used because it is a squared parameter.
Figure 1. Illustration of the ATLD decomposition.
2. ATLD FOR PROCESS ANALYSIS The ATLD algorithm33 is a decomposition method for threeway data arrays. It is based on an alternating least-squares principle, and the iterative procedure is improved by utilizing the MoorePenrose generalized inverse obtained by singular value decomposition. The method exploits the second-order advantage making the calibration possible in the presence of interferences. Supposing a three-way data array X with dimensions I J K, a trilinear model can be expressed as follows: xijk ¼
N
∑ ainbjn ckn þ eijk ði ¼ 1, 2, :::, I; j ¼ 1, 2, :::, J; k n¼1
¼ 1, 2, :::, KÞ
ð1Þ
where xijk is the element of the three-way data array X (I J K). N denotes the number of factors. ain, bjn, and ckn is the element of the I N matrix A, J N matrix B and K N matrix C, respectively. The variable eijk is the residual error element of threeway residual array E (I J K). In process analysis, batch data (NIR spectral data in this work) can be organized into a three-way data array X (I J K), where I, J, and K corresponds to the number of samples in each batch, the number of variables in a spectrum and the number of batches, respectively. The goal of this work is to capture the common information of the batch data and use it for production process analysis. Since the common information hides in variation of different sources, and the variation may be different between batches, ATLD method was, therefore, employed for extracting the common information. In the calculations, the reference batch data, i.e., the NIR spectral data of several normal batches, was first arranged as a three-way data array X (I J K) as illustrated in Figure 1. Then, ATLD method was adopted for extracting the common information hidden in the spectral data. When N = 1, A, B, and C will be the common variance of samples among the batches, the common spectral information among the batches, and the variance between the batches, respectively. The variable B can be defined as the common spectrum of the products that can be used for production process monitoring and discrimination of the products. Therefore, once the common spectrum was obtained, the production process can be monitored by the projection (denoted as SPP) and the residue (denoted as SPE) of the online measured NIR spectrum, which are defined as follows: SPPi ¼ X i B
ð2Þ
ei ¼ Xi X i BBT
ð3Þ
SPEi ¼ ei eTi
ð4Þ
3. ILLUSTRATION AND DISCUSSION 3.1. Experimental Data Description. The measurement was performed on a tobacco production line using an MPA FT-NIR spectrometer (Bruker, Germany). NIR spectra were recorded in the wavenumber range of 400012000 cm1 with the digitization interval of ∼4 cm1. Scan number 32 was used for balancing the spectral quality and scan speed. Three spectra can be measured per minute at the scan number. To reduce the influences of noise and background, wavelet transform (WT)42 was adopted. Although both discrete wavelet transform (DWT) and continuous wavelet transform (CWT) can be used for the purpose, the latter was used for its fastness and convenience.43,44 CWT has been proved a powerful tool for removing the background or baseline from spectral data.43,45 In the calculations, however, different wavelet functions and scale parameters can be used and the result may vary when different setting is used. According to the results of our previous works,4245 Haar wavelets with scale parameter 20 were used. NIR spectra of seven normal batches (Nos. 17) were used as reference data sets, and 100 spectra measured at normal stage of production were selected for each batch. The spectra measured at the beginning and ending stage of a batch were not used because the material is not even. NIR spectra of another nine batches were used as validation sets. Three of them (Nos. 810) were collected from normal batches and the others (Nos. 1116) were collected from “disturbed” batches. Compared with reference data sets, the batch Nos. 1112 and Nos. 1314 were same brand of products but produced one and two months later. Batch Nos. 1516 were the products of different brands. Among the “disturbed” batches, batch Nos. 1114 were designed to evaluate the influence of production time, and batch Nos. 1516 were used to investigate the variation of the materials. Similarly, 100 spectra were selected for each validation batch. Moreover, five brands of products denoted as brand A, B, C, D, and E, respectively, were also used to investigate the discrimination effect of the method. Spectra from two batches of a brand were used, and each brand consists of 200 spectra. 3.2. Process Analysis. In order to investigate the quality of the reference data, an analysis was first performed by using PCA. The first thing is to determine the appropriate number of PCs in PCA model. Due to the similarity of the spectra, the first PC explains more than 90% of the variance. Using one or two PCs would be able to capture the common variability. However, according to our previous works,46,47 the PC number can be very large, e.g., 15, for NIR spectral analysis of real samples, because the difference between the samples may be reflected in the high order PCs explaining small variance. In fact, in the loading plot of high order PCs, e.g., 10 or 15, spectral information is still obvious. Therefore, the first 10 PCs determined by 99.99% contribution were used and the commonly used two statistics, Hotelling T2 statistic48 and Q statistic,41 were calculated. Figure 2(a),(b) show the control 7678
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Figure 2. Control charts of (a) T2, (b) Q, (c) SPP, and (d) SPE of the reference batches.
Figure 3. Control charts of (a) T2, (b) Q, (c) SPP, and (d) SPE of the validation batches.
charts of the two statistics. The control limits were also shown in the figure by red line. It can be seen that, except a few, the T2 and Q values of the products are almost within the control limits. Therefore, the reference batches can be recognized as the normal ones and can be used for building the model. ATLD method was employed to analyze the reference batches. The SPP and SPE charts were shown in Figure 2(c),(d), respectively. It can be seen that the SPP values of all of the products are within the control limits. It indicates that the intrinsic properties of the products are identical in the reference batches. Furthermore, with the control limit at 95% significance level, the SPE values of all the batches are below the control limit. It also suggests that the variance of the products in the reference batches is in control. From the results of the four statistics of the both approaches, the production process of the reference batches is stable. 3.3. Process Monitoring. Figure 3(a)(d) shows the T2, Q, SPP, and SPE values of the nine validation batches. Control limits labeled in Figure 2 are drawn as red lines in the figures, correspondingly. It is clear that, for the batch Nos. 810, which are three normal batches as the reference, almost all of the values are within the control limits, suggesting that all the three batches are as normal as the reference. Such results indicate that the quality (or intrinsic properties reflected by NIR spectra) of the products is consistent with that of the reference batches or there is no significant difference between the three batches and the reference ones. Therefore, both the PCA-based and the ATLD-based method can give a correct monitoring of the production process. As mentioned above, batch Nos. 1112 and 1314 are the same brand of products but the production time is one and two months later, respectively, compared with the reference batches. Therefore, there should be no significant difference between the products of the four batches and the reference batches. However, the T2 and Q values in Figure 3(a),(b) exhibit a large difference from those of the reference batches, and all of the values exceed
the control limits. The results obviously deviate from the actual situation, although there may be some small difference between the products. It is worthy of noting that the difference may be reduced if only one or two PCs are used in computing the T2 values, but there may be a risk of reducing the discrimination ability of the PCA model, because the difference between the samples is generally reflected in the high order PCs as mentioned above. Figure 3(c),(d) shows the SPP and SPE statistics obtained by ATLD method. Different from the results of T2 and Q, no difference is found in the curve of the statistic SPP and obvious variation is found in the SPE chart. This should be an interesting result because the SPP statistic can be known as a parameter which is related to the intrinsic properties of the products, and SPE is a parameter which indicates the difference of a product from the common information. This can be explained by eqs 24. The SPP is calculated by the projection of the NIR spectrum of a product onto the common spectrum. The value is therefore an indication of the similarity of a product with the whole reference products. SPE, however, is the residual of the spectrum of a product after the projection. The value is a reflection of the total difference of a product from the whole products of the reference batches. From this point, the SPP chart shows a stable quality of the products in batch Nos. 1114, but variation can be indicated by an SPE chart. The variation may be the change in moisture, temperature and even the raw materials. It can be seen that the deviation of SPE values for the batch Nos. 1314 (two months difference) is larger than that of batch Nos. 1112 (one month difference). Therefore, ATLD may be a powerful alternative for process analysis or production monitoring. As for batch Nos. 1516, different brands of products were produced. Again, the four statistics of both approaches can be recognize the differences. T2 and Q values in Figure 3(a),(b) exceed the control limits obviously, and large deviation can be found in Figure 3(c),(d) for the SPP and SPE statistics. SPP indicates the difference between the two brands of products in 7679
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SPE chart shown in Figure 4 (d), more clear difference between these brands can be seen. This may help for the discrimination, and also may be useful for analyzing the variation of the production process.
4. CONCLUSIONS An approach for process analysis was presented based on online NIR spectroscopy and ATLD. The approach benefits from the advantage of trilinear decomposition, and, therefore, can be used to extract the common information of the products from different batches even in the presence of the variation. Because the common information represents the intrinsic properties of the products, it was proven to be an efficient tool for production process analysis and discrimination of different products. Compared with the commonly used PCA-based method, ATLD was more powerful to capture the intrinsic information hidden in the NIR spectra of the products, and therefore more useful for industrial process analysis and quality insurance. ’ AUTHOR INFORMATION Corresponding Author
2
Figure 4. Control charts of (a) T , (b) Q, (c) SPP, and (d) SPE of different brands products.
intrinsic properties and SPE shows the variation in production conditions or the materials. 3.4. Discrimination of Different Brands. Discrimination analysis is a powerful tool for distinguish different classes of products. Quality assurance can be achieved by discrimination analysis to analyze the difference between qualified and disqualified products. In this work, discrimination of different brands of tobacco products was examined by using the online NIR spectroscopy and ATLD method. Figure 4 shows the control charts of T2, Q, SPP, and SPE for five brands of tobacco products. In the calculation, all of the 1000 spectra of the 10 batches were used to build the PCA model and extract the common spectrum. Ten PCs were used in computing the T2 and Q. SPP and SPE were calculated as mentioned above. From Figure 4(a),(b), it is difficult to distinguish these brands. The reason maybe that PCA model focuses on retaining as much as the variance of the spectral data. When the model is constructed by using all the spectra, the information of different brands will be included in the PCs. T2 and Q represent, therefore, the distance to the center of the PC spaces and the (squared) residual to the common information. They can be regarded as an equivalence of the distances to the mean spectra. Although the spectra of different batches are different, the distances to the mean are similar to each other. Furthermore, the discrimination ability of the PCA model constructed by using one or two PCs may be further reduced because they capture only the common feature of the spectra. As mentioned above, although most of the variance can be explained by the first one or two PCs, the difference between samples is generally reflected by the high order PCs. However, in the SPP chart shown in Figure 4(c), a clear discrimination of the five brands is achieved, although the difference between B and C is not so large compared with the others. This result indicates that the products with different intrinsic properties can be discriminated by using NIR spectroscopy and the common spectrum extracted by ATLD method. Therefore, the method may provide a useful tool for quality insurance. In the
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’ ACKNOWLEDGMENT This work is supported by National Natural Science Foundation of China (No. 20835002). ’ REFERENCES (1) Vanarase, A. U.; Alcala, M.; JerezRozo, J. I.; Muzzio, F. J.; Romanach, R. J. Real-time monitoring of drug concentration in a continuous powder mixing process using NIR spectroscopy. Chem. Eng. Sci. 2010, 65, 5728–5733. (2) Alcala, M.; Leon, J.; Ropero, J.; Blanco, M.; Romanach, R. J. Analysis of low content drug tablets by transmission near infrared spectroscopy: Selection of calibration ranges according to multivariate detection and quantitation limits of PLS models. J. Pharm. Sci. 2008, 97, 5318–5327. (3) Li Vigni, M.; Durante, C.; Foca, G.; Marchetti, A.; Ulrici, A.; Cocchi, M. Near infrared spectroscopy and multivariate analysis methods for monitoring flour performance in an industrial bread-making process. Anal. Chim. Acta 2009, 642, 69–76. (4) Marengo, E.; Longo, V.; Robotti, E.; Bobba, M.; Gosetti, F.; Zerbinati, O.; Martino, S. D. Development of calibration models for quality control in the production of ethylene/propylene copolymers by FTIR spectroscopy, multivariate statistical tools, and artificial neural networks. J. Appl. Polym. Sci. 2008, 109, 3975–3982. (5) Lee, M. W.; Hong, S. H.; Choi, H.; Kim, J. H.; Lee, D. S.; Park, J. M. Real-time remote monitoring of small-scaled biological wastewater treatment plants by a multivariate statistical process control and neural network-based software sensors. Process Biochem. 2008, 43, 1107–1113. (6) Wold, S.; Esbensen, K.; Geladi, P. Principal component analysis. Chemom. Intell. Lab. Syst. 1987, 2, 37–52. (7) Dunia, R.; Qin, S.; Edgar, T.; McAvoy, T. Identification of faulty sensors using principal component analysis. AIChE J. 1996, 42, 2797–2811. (8) Lu, N.; Gao, F.; Yang, Y.; Wang, F. PCA-based modeling and online monitoring strategy for uneven-length batch processes. Ind. Eng. Chem. Res. 2004, 43, 3343–3352. (9) Kruger, U.; Chen, Q.; Sandoz, D. J.; McFarlane, R. C. Extended PLS approach for enhanced condition monitoring of industrial process. AIChE J. 2001, 47, 2076–2091. 7680
dx.doi.org/10.1021/ie200543v |Ind. Eng. Chem. Res. 2011, 50, 7677–7681
Industrial & Engineering Chemistry Research (10) Zheng, L. L.; Mc Avoy, T. J.; Huang, Y. B.; Chen, G. Application of multivariate statistical analysis in batch processes. Ind. Eng. Chem. Res. 2001, 40, 1641–1649. (11) Reiss, R.; Wojsznis, W.; Wojewodka, R. Partial least squares confidence interval calculation for industrial end-of-batch quality prediction. Chemom. Intell. Lab. Syst. 2010, 100, 75–82. (12) Jia, F.; Martin, E. B.; Morris, A. J. Non-linear principal components analysis for process fault detection. Comput. Chem. Eng. 1998, 22, S851–S854. (13) Choi, S. W.; Lee, C.; Lee, J. M.; Park, J. H.; Lee, I. B. Fault detection and identification of nonlinear processes based on kernel PCA. Chemom. Intell. Lab. Syst. 2005, 75, 55–67. (14) Cui, P.; Li, J.; Wang, G. Improved kernel principal component analysis for fault detection. Expert Syst. Appl. 2008, 34, 1210–1219. (15) Lee, C.; Choi, S. W.; Lee, I. B. Sensor fault identification based on time-lagged PCA in dynamic processes. Chemom. Intell. Lab. Syst. 2004, 70, 165–178. (16) Yao, Y.; Gao, F. R. Batch process monitoring in score space of two-dimensional dynamic principal component analysis (PCA). Ind. Eng. Chem. Res. 2007, 46, 8033–8043. (17) Pollanen, K.; Hakkinen, A.; Reinikainen, S. P.; Rantanen, J.; Minkkinen, P. Dynamic PCA-based MSPC charts for nucleation prediction in batch cooling crystallization processes. Chemom. Intell. Lab. Syst. 2006, 84, 126–133. (18) Rannar, S.; MacGregor, J. F.; Wold, S. Adaptive batch monitoring using hierarchical PCA. Chemom. Intell. Lab. Syst. 1998, 41, 73–81. (19) Choi, S. W.; Martin, E. B.; Julian Morris, A.; Lee, I. B. Adaptive multivariate statistical process control for monitoring time-varying processes. Ind. Eng. Chem. Res. 2006, 45, 3108–3118. (20) Zhao, C. H.; Wang, F. L.; Gao, F. R.; Lu, N. Y.; Jia, M. X. Adaptive monitoring method for batch processes based on phase dissimilarity updating with limited modeling data. Ind. Eng. Chem. Res. 2007, 46, 4943–4953. (21) Yoo, C. K.; Lee, J. M.; Vanrolleghem, P. A.; Lee, I. B. On-line monitoring of batch processes using multiway independent component analysis. Chemom. Intell. Lab. Syst. 2004, 71, 151–163. (22) Zhao, C. H.; Gao, F. G.; Wang, F. L. Nonlinear batch process monitoring using phase-based kernel-independent component analysisprincipal component analysis (KICA-PCA). Ind. Eng. Chem. Res. 2009, 48, 9163–9174. (23) Lee, J. M.; Yoo, C.; Lee, I. B. Statistical process monitoring with independent component analysis. J. Process Control 2004, 14, 467–485. (24) Nomikos, P.; MacGregor, J. F. Monitoring batch processes using multiway principal component analysis. AIChE J. 1994, 40, 1361–1375. (25) Nomikos, P.; MacGregor, J. F. Multivariate SPC charts for monitoring batch processes. Technometrics 1995, 37, 41–59. (26) Nomikos, P.; MacGregor, J. F. Multi-way partial least square in monitoring batch processes. Chemom. Intell. Lab. Syst. 1995, 30, 97–108. (27) Kourti, T. Multivariate dynamic data modeling for analysis and statistical process control of batch processes, start-ups and grade transitions. J. Chemom. 2003, 17, 93–109. (28) Bro, R. PARAFAC. Tutorials and applications. Chemom. Intell. Lab. Syst. 1997, 38, 149–170. (29) Andersen, C. M.; Bro, R. Practical aspects of PARAFAC modeling of fluorescence excitation-emission data. J. Chemom. 2003, 17, 200–215. (30) Matero, S.; Poutiainen, S.; Leskinen, J.; Reinikainen, S. P.; Ketolainen, J.; Jarvinen, K.; Poso, A. Monitoring the wetting phase of fluidized bed granulation process using multi-way methods: The separation of successful from unsuccessful batches. Chemom. Intell. Lab. Syst. 2009, 96, 88–93. (31) Amigo, J. M.; Surribas, A.; Coello, J.; Montesinos, J. L.; Maspoch, S.; Valero, F. On-line parallel factor analysis. A step forward in the monitoring of bioprocesses in real time. Chemom. Intell. Lab. Syst. 2008, 92, 44–52. (32) Kroonenburg, P. M. Three-Mold Principal Component Analysis: Theory and applications; DSWO Press: Leiden, 1983.
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(33) Wu, H. L.; Shibukawa, M.; Oguma., K. An alternating trilinear decomposition algorithm with application to calibration of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons. J. Chemom. 1998, 12, 1–26. (34) Zhang, Y.; Wu, H. L.; Ding, Y. J.; Xia, A. L.; Cui, H.; Yu, R. Q. Simultaneous determination of cortisol and prednisolone in body fluids by using HPLC-DAD coupled with second-order calibration based on alternating trilinear decomposition. J. Chromatogr. B 2006, 840, 116–123. (35) Li, S. F.; Wu, H. L.; Yu, Y. J.; Li, Y. N.; Nie, J. F.; Fu, H. Y.; Yu, R. Q. Quantitative analysis of levodopa, carbidopa and methyldopa in human plasma samples using HPLC-DAD combined with second-order calibration based on alternating trilinear decomposition algorithm. Talanta 2010, 81, 805–812. (36) Escandar, G. M.; Olivieri, A. C.; Faber, N. K. M.; Goicoechea, H. C.; de la Pena, A. M.; Poppi, R. J. Second- and third-order multivariate calibration: data, algorithms and applications. TrAC-Trend Anal. Chem. 2007, 26, 752–765. (37) Booksh, K. S.; Kowalski, B. R. Theory of analytical chemistry. Anal. Chem. 1994, 66, 782A–791A. (38) Li Vigni, M.; Durante, C.; Foca, G.; Marchetti, A.; Ulrici, A.; Cocchia, M. Near infrared spectroscopy and multivariate analysis methods for monitoring flour performance in an industrial breadmaking process. Anal. Chim. Acta 2009, 642, 69–76. (39) Stordrange, L.; Rajalahti, T.; Libnau, F. O. Multiway methods to explore and model NIR data from a batch process. Chemom. Intell. Lab. Syst. 2004, 70, 137–145. (40) Larrechi, M. S.; Callao, M. P. Strategy for introducing NIR spectroscopy and multivariate calibration techniques in industry. TrACTrend Anal. Chem. 2003, 22, 634–640. (41) Nomikos, P.; MacGregor, J. F. Multivariate SPC charts for monitoring batch process. Technometrics 1995, 37, 41–59. (42) Shao, X. G.; Leung, A. K. M.; Chau, F. T. Wavelet: A new trend in chemistry. Acc. Chem. Res. 2003, 36, 276–283. (43) Ma, C. X.; Shao, X. G. Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra. Chem. Inf. Comput. Sci. 2004, 44, 907–911. (44) Shao, X. G.; Shao, L. M.; Zhao, G. W. Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform. Anal. Commun. 1998, 35, 135–137. (45) Shao, X. G.; Ma, C. X. A general approach to derivative calculation using wavelet transform. Chemom. Intell. Lab. Syst. 2003, 69, 157–165. (46) Cai, W. S.; Li, Y. K.; Shao, X. G. A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra. Chemom. Intell. Lab. Syst. 2008, 90, 188–194. (47) Shao, X. G.; Bian, X. H.; Liu, Z. C.; Cai, W. S. An improved boosting partial least squares for near-infrared spectroscopic quantitative analysis. Anal. Chim. Acta 2010, 666, 32–37. (48) Hotelling, H. Multivariate Quality Control-Illustrated by the Air Testing of Sample Bombsights. In Techniques of Statistical Analysis; McGraw-Hill: New York, 1947; 11184.
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