当近红外光谱信息远大于样本量时, 对光谱信息进行自动变量选择进而建立光谱与样品含量的稀疏线性模型重要且具有挑战性。 利用近红外光谱, 将变量选择方法Elastic Net用于聚苯醚生产过程中微量成分邻甲酚的测量, 建立近红外光谱与邻甲酚含量之间的定量校正模型, 并将其模型预测效果与Lasso方法进行对比。 在变量数目远远大于样本量的情形下, Lasso方法虽可实现变量选择, 但由于对系数的过度压缩, 使得模型的预测精度受到影响, 而Elastic Net通过增加L2惩罚项避免了过多删失数据, 可以提高模型预测精度。 为了验证Elastic Net方法的模型性能指标, 用复相关系数R2和调整的复相关系数R2a来评价模型的可解释性, 利用平均相对预测误差MRPE(mean relative prediction error)和预测相关系数Rp来评价模型的预测精度。 Lasso方法建立的模型性能指标为: R2=0.94, R2a=0.93, MRPE=4.51％, Rp=0.96; Elastic Net方法的性能指标为: R2=0.97, R2a=1, MRPE=3.25％, Rp=0.98。 结果表明, Elastic Net所建立模型的性能指标优于Lasso方法, 可以得到可解释性较强和预测精度较高的稀疏线性模型。

It is important and challenging to select the variable for the spectral information automatically and establish a sparse linear model between the spectrum and the sample content under the circumstance that the near-infrared spectral information is much larger than the sample size. In this paper, Elastic Net was used for the measurement of o-cresol in the polyphenylene ether by utilizing the near infrared spectroscopy and a quantitative calibration model between near infrared spectroscopy and o-cresol content was established. Then, the model prediction effect is compared with the Lasso method. In the case where the number of variables is much larger than that of the samples. Although Lasso method can achieve variable selection, the prediction accuracy of the model is affected due to excessive compression to variable coefficients. Elastic Net avoids excessive censorship by increasing L2 penalty, which can improve model prediction accuracy. In order to verifymodel performance indicators ofElastic Net method, we use the complex correlation coefficient R2 and the adjusted complex correlation coefficient R2a to evaluate the interpretability of the model, meanwhile, the prediction accuracy of the model is evaluated by using the mean relative prediction error MRPE and the prediction correlation coefficient Rp. Lasso method to establish the model performance indicators are: R2=0.94, R2a=0.93, MRPE=4.51％, Rp=0.96; Elastic Net method performance indicators are: R2=0.97, R2a=1, MRPE=3.25％, Rp=0.98. From the result we could draw the conclusion that Elastic Net’s model is better than Lasso method. A sparse linear model with higher interpretability and high prediction accuracy can be obtained by the Elastic Net regression.