Journal of Central South University

, Volume 26, Issue 1, pp 63–74 | Cite as

Modeling of goethite iron precipitation process based on time-delay fuzzy gray cognitive network

  • Ning Chen (陈宁)Email author
  • Jia-qi Zhou (周佳琪)
  • Jun-jie Peng (彭俊洁)
  • Wei-hua Gui (桂卫华)
  • Jia-yang Dai (戴佳阳)


The goethite iron precipitation process consists of several continuous reactors and involves a series of complex chemical reactions, such as oxidation reaction, hydrolysis reaction and neutralization reaction. It is hard to accurately establish a mathematical model of the process featured by strong nonlinearity, uncertainty and time-delay. A modeling method based on time-delay fuzzy gray cognitive network (T-FGCN) for the goethite iron precipitation process was proposed in this paper. On the basis of the process mechanism, experts’ practical experience and historical data, the T-FGCN model of the goethite iron precipitation system was established and the weights were studied by using the nonlinear hebbian learning (NHL) algorithm with terminal constraints. By analyzing the system in uncertain environment of varying degrees, in the environment of high uncertainty, the T-FGCN can accurately simulate industrial systems with large time-delay and uncertainty and the simulated system can converge to steady state with zero gray scale or a small one.

Key words

time-delay fuzzy gray cognitive network (T-FGCN) iron precipitation process nonlinear Hebbian learning 



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、不确定性及大时滞性等特点,难以建立精确的数学模型。 本文提出了一种基于T-FGCN(Time-delay Fuzzy Gray Cognitive Network,T-FGCN)的针铁矿沉铁过 程的建模方法。根据过程机理、专家经验和历史数据,建立针铁矿沉铁系统的T-FGCN 模型,利用带 终端约束的非线性Hebbian 学习算法(Nonlinear Hebbian Learning,NHL)对模型权值进行学习。通过 在不同程度上的不确定性环境下对系统进行分析,结果表明,T-FGCN 建模方法能在不确定性高的环 境下对具有大时滞的工业系统进行较为精确的模拟,系统稳定状态值能收敛到一个灰度为零或者灰度 很小的灰数平衡点。


沉铁过程 模糊灰色认知网络 时滞 非线性Hebbian 学习 


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Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina

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