针对FTIR光谱分析数据计算量大, 具有相同基团的多组分混合气体交叉灵敏度过高, 以及在线分析过程中基线漂移等问题, 提出了一种改进的TR2-1(Tikhonov 2norm-1norm)正则化特征变量提取法。 该方法借鉴TR1和TR2模型的基本思想, 引入谱线距离和谱线系数绝对值最小化两个约束项来保证所提取特征量的准确度, 消除基线漂移所带来的影响, 并结合上述两种模型建立了不适定问题的最优化求解通式。 该通式有效地克服了经验法和实验法确定正则矩阵和参数所带来的误差。 实验以浓度为0.01%~20%的甲烷、 乙烷、 丙烷、 正丁烷、 异丁烷、 正戊烷和异戊烷气体为例进行了特征光谱选取。 结果表明, 对于浓度为0.2%的甲烷气体, 其预测误差平方和仅为2.6×10-4, 可决系数达到0.959 2, 分析准确度高, 有效增强了TR正则法的实用性。

In the present paper, an improved approach to the TR characteristic spectral selection is presented. For this approach, two ideas of TR1-norm and TR2-norm are used, two constraint items, spectral line distance and minimizing absolute value of coefficient are introduced, and a general formula of ill-posed optimization problem is established. The formula can reduce effectively the errors caused by experienced and experimental method when used in determining the regular matrix and parameter. Finally, the improved approach presented in the paper was used in the analysis of alkane gas mixture, with methane, ethane, propane, n-butane, iso-butane, n-pentane and iso-pentane included. The concentration range is 0.01%~20%. The experimental results show that the predicting error square is only 2.6×10-4, and the coefficient of determination is 0.959 2, which means that preceding accuracy is high, and that the practicability of TR regularization has been enhanced.