基于Marquardt和Runge-Kutta算法的发酵过程建模

利用简单的线性模型很难描述发酵这类复杂的非线性动态过程，因此需要利用非线性方法对该类过程进行建模。为此，提出了利用基于Marquardt算法的非线性回归方法和基于四阶Runge-Kutta算法的非线性微分方程求解方法对发酵过程进行建模分析；并进一步利用统计方法分析了该非线性回归方法的有效性。该方法应用于黄酒发酵过程中，实现了黄酒发酵过程模型的求解和模型参数的动态优化。

Fermentation process modeling with Marquardt algorithm and Runge-Kutta algorithm

It is hard to describe complex nonlinear dynamic fermentation process by using a simple linear model. Thus nonlinear modeling is used to examine fermentation progress. To this end, a least-square based algorithm Marquardt algorithm is used to estimate model parameters from experimental data. A model of nonlinear differential equations is solved by Runge-Kutta algorithm. Both Marquardt and fourth Runge-Kutta methods are applied for optimizing parameter values for fermentation model. Regression tests are conducted and results indicate that the model can simulate the rice wine fermentation process with R2] higher than 0.89.