1. School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China 2. Taiyuan Iron and Steel Co., Automatic Company, Taiyuan 030003, China 3. Engineering Institute, Air Force Engineering University, Xi’an 710038, China
Abstract：In the present paper, the authors present a new quantitative analysis method of mid-infrared spectrum. The method combines the kernel principal component analysis (KPCA) technique with support vector regress machine (SVR) to createa quantitative analysis model of multi-component gas mixtures. Firstly，the spectra of multi-component gas mixtures samples were mapped nonlinearly into a high-dimensional feature space through the use of Gaussian kernels. And then, PCA technique was employed to compute efficiently the principal components in the high-dimensional feature spaces. After determining the optimal numbers of principal components, the extracted features (principal components) were used as the inputs of SVR to create the quantitative analysis model of seven-component gas mixtures. The prediction RMSE (φ×10－6) of seven-component gases of prediction set samples by use of KPCA-SVR model were respectively 124.37, 72.44, 136.51, 87.29, 153.01, 57.12, and 81.72, ten times less than that by use of SVR model. The elapsed time of modeling and prediction by using KPCA-SVR were respectively 46.59 (s) and 4.94 (s), which was consumedly less than 752.52 (s) and 26.21 (s) by using only SVR. These results show that KPCA has an excellent ability of nonlinear feature extraction. It can make the most of the information of entire spectra range and effectively reduce noise and the dimension of the spectra. The KPCA combined with SVR can improve the model’s analysis precision and cut the elapsed time of modeling and analysis. From our research and experiments, we conclude that KPCA-SVR is an effective new method for infrared spectroscopic quantitative analysis.
郝惠敏1,2,汤晓君1,白鹏1,3,刘君华1,朱长纯1. 基于核主成分分析和支持向量回归机的红外光谱多组分混合气体定量分析[J]. 光谱学与光谱分析, 2008, 28(06): 1286-1289.
HAO Hui-min1,2,TANG Xiao-jun1,BAI Peng1,3,LIU Jun-hua1,ZHU Chang-chun1. Quantitative Analysis of Multi-Component Gas Mixture Based on KPCA and SVR. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2008, 28(06): 1286-1289.
[1] ZHANG Lin, ZHANG Li-ming, LI Yan, et al（张 琳，张黎明，李 燕，等）. Spectroscopy and Spectral Analysis（光谱学与光谱分析）, 2006, 26(4): 620. [2] LI Hong-lei, LIU Xian-yong, ZHOU Fang-jie, et al. Proceedings of the SPIE, 2005, 5640: 692. [3] SUN Xiu-yun, LI Yan, WANG Jun-de（孙秀云，李 燕，王俊德）. Spectroscopy and Spectral Analysis（光谱学与光谱分析）, 2003, 23(4): 739. [4] Evans Wayne F J, Puckrin Eldon, McMaster D. Proceedings of the SPIE, 2002, 4574;44. [5] Bacsik Z, McGregor J, Mink J. Food and Chemical Toxicology, 2007, 45(2): 266. [6] DENG Nai-yang, TIAN Ying-jie（邓乃扬，田英杰）. New Method of Data Mining—Support Vector Machine（数据挖掘中的新方法——支持向量机）. Beijing: Science Press（北京：科学出版社）, 2004. [7] Hoegaerts L, Suykens J A K, Vandewalle J, et al. Neurocomputing, 2005, 63: 293. [8] Vapnik V N. The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995. [9] Vapnik V N. Statistical Learning Theory, New York: Wiley, 1998. [10] Duan Kaibo, Keerthi S Sathiya, Poo Aun Neow. Neurocomputing, 2003, 51: 41. [11] BAI Peng, LIU Jun-hua（白 鹏，刘君华）. Control and Instruments in Chemical Industry（化工自动化及仪表）, 2005, 32(5): 47. [12] LIN Ji-peng, LIU Jun-hua（林继鹏，刘君华）. Journal of Xi’an Jiaotong University（西安交通大学学报）, 2005, 39(6): 586. [13] Kim K L, Franz M O, Schlkopf B. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27: 1351. [14] Rosipal Roman, Girolami Mark, Trejo Leonard J, et al. Neural Computing & Applications, 2001, 10(3): 231. [15] Müller Klaus-Robert, Mika Sebastian, Ratsch Gunnar, et al. IEEE Transactions on Neural Networks, 2001, 12(2): 181. [16] Schlkopf B, Smola A，Müller Klaus-Robert. Neural Computation, 1998, 10(5): 1299. [17] John Shawe-Taylor, Nello Cristianini. Kernel Methods for Pattern Analysis. Cambridge: Cambridge University Press, 2004. 143. [18] Mika Sebastian, Schlkopf Bernhard, Smola Alex, et al. Advances in Neural Information Processing System Ⅱ. Cambridge, MA: MIT Press, 1999. 536. [19] Mika S. Advances in Neural Information Processing System Ⅱ. Cambridge, MA: MIT Press, 1999. 536. [20] Schlkopf B, Smola A. Advances in Kernel Methods-Support Vector Learning. Cambridge, MA: MIT Press, 1999. 327.
