Tang Xiao-Jun, Zhang Lei, Wang Er-Zhen, Li Zhe-Bu, Meng Yong-Peng, Liu Jun-Hua
State Key Laboratory of Electrical Insulation & Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China.
Guang Pu Xue Yu Guang Pu Fen Xi. 2012 Oct;32(10):2730-4.
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 x 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.
本文提出了一种改进的热重（TR）特征光谱选择方法。对于该方法，采用了TR1范数和TR2范数两种思想，引入了谱线距离和系数绝对值最小化两个约束项，并建立了病态优化问题的通用公式。该公式在确定正则矩阵和参数时，能有效减少经验法和实验法所引起的误差。最后，将本文提出的改进方法用于分析包含甲烷、乙烷、丙烷、正丁烷、异丁烷、正戊烷和异戊烷的烷烃气体混合物。浓度范围为0.01% - 20%。实验结果表明，预测误差平方仅为2.6×10⁻⁴，决定系数为0.9592，这意味着预测精度高，且增强了TR正则化的实用性。
