基于FGCN的针铁矿沉铁过程建模

针铁矿沉铁过程是由多个连续反应器级联，并且包含氧化反应、还原反应以及中和反应等一系列复杂化学反应的复杂过程，具有强非线性、不确定性的特点，难以建立精确的数学模型。提出一种基于模糊灰色认知网络（fuzzy gray cognitive network，FGCN）的针铁矿沉铁过程的建模方法。根据专家经验和历史数据，建立针铁矿沉铁系统的模糊灰色认知网络模型，利用带终端约束的非线性Hebbian学习算法（nonlinear Hebbian learning，NHL）对权值进行学习。在不同程度的不确定性环境下对系统进行分析，结果表明模糊灰色认知网络能够在不确定性高的环境下对复杂工业系统进行有效模拟，收敛到一个灰度为零或者灰度很小的灰数平衡点，利用白化函数得到一个准确的控制输出。

FGCN modeling on iron precipitation process in mineral goethite

Iron precipitation is consisted of several continuous reactors, which involves a series of complex chemical reactions such as oxidation, hydrolysis and neutralization. Owing to its strong nonlinearity and uncertainty, it is difficult to establish an accurate mathematical model of the iron precipitation process. A modeling method based on fuzzy gray cognition network was proposed from expert experience and historical data. The weighted values were studied by nonlinear Hebbian learning algorithm with terminal constraints. The analysis results on system at various extents of uncertainty show that FGCN can effectively simulate complex industrial systems in environment with high uncertainty. The simulated system can be converged to a gray number equilibrium point of very small or zero gray scale and then be solved to obtain an accurate control output by whitening function.