灰色数模的建立及应用研究(II)——NLCGM(1,1)模型的建立及酚保留行为的预测

Development and Application of Chromatographic Gray Model Establishment of Nonlinear Continuous Gray Model NLCGM(1,1) and Prediction of Retention Behavior of Phenols

考虑到灰色ＧＭ（１，１）模型对于处理某些非线性问题的不足，基于灰色系统理论的建模思想，推导出又一种模型———非线性连续灰色模型ＮＬＣＧＭ（１，１）。由于建模过程中采用了双拟合，不但实现了模型的连续化，而且提高了预测精度。将该模型应用于高效液相色谱中，对５种不同种类的酚保留值随流动相组成变化的关系进行了研究，建立相应的ＮＬＣＧＭ（１，１）模型。经验证，计算值与实验值相吻合，获得了较常规ＣＧＭ（１，１）模型和二次方程更高的精度，平均绝对误差为０．０１６，而常规ＣＧＭ（１，１）模型和二次方程的平均绝对误差分别为０．０３３和０．０５６。

An improved gray model NLCGM(1,1) is proposed. The double fitting is introduced both to improve the accuracy of the prediction and to achieve the continuous model. The capacity factors of different kinds of phenols(Phenol, Methylphenol, Nitrophenol and Dihydroxybenzene) are predicted with mobile phase composition(10%90%) of acetonitrile on Unisil Q C18 column to examine the validity of the model. The results show that NLCGM(1,1) is more accurate than the traditional CGM(1,1) and the quadratic equation. The average absolute deviations of NLCGM(1,1), CGM(1,1) and quadratic equation are 0.016 , 0.033 and 0.056, respectively.