基于estk-Berggren公式的动态固化动力学模型的非线性回归分析

动态自催化固化反应动力学研究中的机理函数基于SB公式,动力学模型需要拟合4个参数:指前因子A、活化能Ea、反应阶数m、n.本文中采用非线性最小二乘回归方法,拟合结果表明4个参数的非线性回归结果不稳定,尤其表现在参数A与m的估计结果上.笔者对造成上述结果的原因进行了分析,指出由于模型参数效应曲率相当大,增加了模型的非线性强度,使得最小二乘回归分析结果不可靠.根据实验数据特征,本文中在不确定机理函数形式前提下,运用Model-free方法,先获得活化能平均意义下的估计值,再进行参数A、m、n的非线性最小二乘回归分析.结果表明减少回归函数参数个数,可极大程度降低模型的非线性强度,从而获得有效的动力学参数估计.

Regression analysis of non-isothermal cure reaction kinetic model based on Sestak-Berggren equation

In chemical kinetic analysis of non-isothermal cure reaction, autocatalytic reaction mechamsm function was based on Sestak-Berggren equation, parameters of regression were pre-exponential factor A, activation energy Ea, reaction order m and n. In this article, we fit rate equation with four parameters by nonlinear regression based on the least squares estimation, regresion result was unreliable, especially the estimator of A and m. This article pointed that nonlinearity of model with large parameter-effects curvature was responsible for the terrible regression result. In the next section, according to characters of experiment data, we estimated Ea firstly with model-free methods, rate equation would only have three parameters, parameter-effects curvature of model was cut short, and with this solution we could get effective estimation of kinetic parameters.