doi:

DOI: 10.3724/SP.J.1123.2017.09018

Chinese Journal of Chromatography (色谱) 2018/36:1 PP.59-68

Rapid resolving algorithm of gas chromatographic overlapping peaks based on the asymptotic expansion of integration


Abstract:
A novel algorithm, called asymptotic expansion of integration, is suggested to resolve gas chromatographic overlapping peaks. There are three steps for the algorithm. First, a valley peak or a shoulder peak is separated into two domains, and an integral equation on a subdivision and an algebraic equation on the overlapping peak domain are listed. Secondly, areas needed in two equations, are computed by a numerical integral method, then the integral equation is expended to an algebraic equation by the asymptotic formula of integration. At last, combing two equations with constraint equations of peak heights, we got a nonlinear algebraic set. The equation set can be solved rapidly by Gauss-Seidel iteration, and the maximum number of iterations is not more than 20 times. The simulation and experimental results showed that height and area errors of resolving peaks are quite small, the maximum error of area is less than 6.44%, and that of the height is about 6.80%. Because of the high accuracy and computational efficiency, the algorithm can be used in decomposition of gas chromatographic overlapping peaks and online real-time processing of general chromatographic overlapping peaks.

Key words:integral equation,asymptotic expansion of integration,gas chromatogram,overlapping peaks

ReleaseDate:2018-01-24 14:42:47



[1] Liu H, Pang Z, Fan G. Chromatographia, 2016, 79:1543

[2] Ye G Y, Xu K J. Chinese Journal of Scientific Instrument,2015, 36(2):439叶国阳, 徐科军. 仪器仪表学报, 2015, 36(2):439

[3] Lin B, Lu P. J High Resolut Chromatogr Chromatogr Commun, 1987, 10(8):449

[4] Nikitas P, Pappa Louisi A, Papageorgiou A. J Chromatogr A, 2001, 912:13

[5] Johnsen L G, Amigo J M, Skov T, et al. J Chemometrics, 2014, 28:71

[6] Collantes E R, Duta R, Welsh W J. Anal Chem, 1997, 69(7):1392

[7] O'Halloran R J, Smith D E. Anal Chem, 1978, 50(9):1391

[8] Mohammadpour K, Sohrabi M R, Jourabchi A. Talanta, 2010, 81:1821

[9] Li B Q, Li C P, Huang Q B, et al. Journal of Chinese Mass Spectrometry Society, 2015, 36(3):199李宝强, 李翠萍, 黄启斌, 等. 质谱学报, 2015, 36(3):199

[10] Dubrovkin J. Chemom Intell Lab Syst, 2016, 153:9

[11] Zhu H, Wang G, Yang C, et al. Trans Nonferrous Met Soc China, 2013, 23:2181

[12] Cavanillas S, Serrano N, Díaz Cruz J M, et al. Chemom Intell Lab Syst, 2016, 152:80

[13] Jia Z H, Wang C T, Li H. Chinese Journal of Applied Chemistry, 2013, 30(3):329贾泽慧, 王春涛, 李华. 应用化学, 2013, 30(3):329

[14] Bai Q. Chinese Journal of Chromatography, 2015, 33(11):117白泉. 色谱, 2015, 33(11):117

[15] Miao H, Yu M, Hu S. J Chromatogr A, 1996, 749:5

[16] Cavanillas S, Díaz Cruz J M, Arino C, et al. Anal Chim Acta, 2011, 689:198

[17] Cavanillas S, Serrano N, Díaz Cruz J M, et al. Analyst, 2013, 138:2171

[18] Yan C J.[MS Dissertation]. Tianjin:Tianjin University, 2008:16严彩娟.[硕士学位论文]. 天津:天津大学, 2008:16

[19] Ye G Y.[MS Dissertation]. Hefei:Hefei University of Technology, 2016:15叶国阳.[硕士学位论文]. 合肥:合肥工业大学, 2016:15

[20] Compiling Group of Handbook of Mathematics. Handbook of Mathematics. Beijing:Higher Education Press, 2012:291数学手册编写组. 数学手册. 北京:高等教育出版社, 2012:291