关键词: 自动微分, 非线性拟合, 黏度模型, 汉森矩阵

Abstract: The key problem in evaluating the parameters of the 7-parameter Cross-WLF viscosity model of polymer materials with nonlinear fitting method is how exactly to calculate the gradient vector f2(x) and the Hessian matrix?? f2(x). Numerical method loses its efficiency here and singularity problem arises due to the significant difference of the parameters in magnitude. In order to overcome this problem，automatic differentiation method was adopted in this paper to calculate? f2(x) and? f2(x). Its differentiation accuracy is up to that of analytical method when neglecting the truncation error. Further more，this method is of high stability and benefits much to the final result of the fitting program. Test case shows the RMS error between the fitting viscosity and the experimental viscosity is less than 1×10－5.

Key words: automatic differentiation, nonlinear fitting, viscosity model, Hessian matrix