Abstract: The deficiency of the traditional GM(1,1) model for solving the nonlinear problem is pointed out, and an improved model NLCGM(1,1) is proposed by means of gray theory. During establishing the model, the double fitting is introduced both to improve the accuracy of the prediction and to achieve the continuous model. The model has been successfully applied to study the relationship between the capacity factor (k') of 32 polycyclic and monocyclic aromatic hydrocarbons and the composition of mobile phase(φ) in high performance liquid phase chromatography, and good results are obtained. In conclusion, there are three advantages for NLCGM(1,1) model. (1) Capacity factor can be predicted at any composition of mobile phase because the independent variable of the gray model can change continuously. (2) The precision of NLCGM(1,1) is higher than that of the traditional GM(1,1). (3) The traditional GM(1,1) is the special case of NLCGM(1,1). Therefore, the establishment of NLCGM(1,1) broadens the applied range of gray model.

Key words: Gray system, Gray model, Liquid chromatography