色谱 ›› 2018, Vol. 36 ›› Issue (1): 59-68.DOI: 10.3724/SP.J.1123.2017.09018

• 研究论文 • 上一篇    下一篇

基于积分渐进展开的气相色谱重叠峰快速解析法

柯庆, 高清维, 卢一相   

  1. 安徽大学电气工程与自动化学院, 安徽 合肥 230601
  • 收稿日期:2017-09-08 出版日期:2018-01-08 发布日期:2018-01-22
  • 通讯作者: 高清维,Tel:(0551)63861338,E-mail:qingweigao@ahu.edu.cn.
  • 基金资助:

    国家自然科学基金项目(61370110,61402004).

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

KE Qing, GAO Qingwei, LU Yixiang   

  1. School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China
  • Received:2017-09-08 Online:2018-01-08 Published:2018-01-22
  • Supported by:

    National Natural Science Foundation of China (Nos. 61370110, 61402004).

摘要:

论文提出用积分渐进展开解析气相色谱重叠峰,该方法有3个主要步骤:首先将谷峰或肩峰分成两个积分区域,得到一个子区域的积分方程和一个重叠峰面积的代数方程;然后用数值积分求出这两个方程计算中所需要的峰面积,再用积分渐进公式将积分方程展开成代数方程;最后,将这两个方程与峰高约束方程联立后,得到一个非线性代数方程组,用Gauss-Seidel迭代可以快速求解方程组,方程收敛的最大迭代次数不超过20次。仿真和实验结果表明,解析的峰高和峰面积误差均很小,峰面积最大误差低于6.44%,峰高的最大误差约为6.80%。由于该算法精度高,效率高,所以这个方法可以用于气相色谱重叠峰和一般色谱峰的实时在线解析。

关键词: 积分方程, 积分渐进展开, 气相色谱图, 重叠峰

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

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