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模糊灰色认知网络的建模方法及应用

陈宁 彭俊洁 王磊 郭宇骞 桂卫华

陈宁, 彭俊洁, 王磊, 郭宇骞, 桂卫华. 模糊灰色认知网络的建模方法及应用. 自动化学报, 2018, 44(7): 1227-1236. doi: 10.16383/j.aas.2017.c160578
引用本文: 陈宁, 彭俊洁, 王磊, 郭宇骞, 桂卫华. 模糊灰色认知网络的建模方法及应用. 自动化学报, 2018, 44(7): 1227-1236. doi: 10.16383/j.aas.2017.c160578
CHEN Ning, PENG Jun-Jie, WANG Lei, GUO Yu-Qian, GUI Wei-Hua. Fuzzy Grey Cognitive Networks Modeling and Its Application. ACTA AUTOMATICA SINICA, 2018, 44(7): 1227-1236. doi: 10.16383/j.aas.2017.c160578
Citation: CHEN Ning, PENG Jun-Jie, WANG Lei, GUO Yu-Qian, GUI Wei-Hua. Fuzzy Grey Cognitive Networks Modeling and Its Application. ACTA AUTOMATICA SINICA, 2018, 44(7): 1227-1236. doi: 10.16383/j.aas.2017.c160578

模糊灰色认知网络的建模方法及应用

doi: 10.16383/j.aas.2017.c160578
基金项目: 

湖南省自然科学基金项目 2017JJ2329

国家自然科学基金 61673399

详细信息
    作者简介:

    彭俊洁 中南大学博士生.主要研究方向为非线性系统的建模与控制和模糊认知网络建模方法研究.E-mail:yuzoudiyi@126.com

    王磊  中南大学硕士.主要研究方向为非线性系统的建模与控制.E-mail:122548287@qq.com

    郭宇骞  中南大学教授.主要研究方向为非线性控制系统, 混杂控制系统, 逻辑演化网络.E-mail:gyuqian@csu.edu.cn

    桂卫华 中国工程院院士, 中南大学教授.主要研究方向为复杂工业过程建模与优化控制, 分散鲁棒控制及故障诊断.E-mail:gwh@csu.edu.cn

    通讯作者:

    陈宁 中南大学教授.主要研究方向为复杂系统建模与控制、模糊认知网络建模方法研究.本文通信作者.E-mail:ningchen@csu.edu.cn

Fuzzy Grey Cognitive Networks Modeling and Its Application

Funds: 

Natural Science Foundation of Hunan Province 2017JJ2329

National Natural Science Foundation of China 61673399

More Information
    Author Bio:

    Ph. D. candidate at Central South University. His research interest covers modeling and control of nonlinear systems, and fuzzy cognitive networks

    Master student at Central South University. Her research interest covers modeling and control of nonlinear systems

    Professor at Central South University. His research interest covers nonlinear control systems, hybrid control systems and logic networks

    Academician of Chinese Academy of Engineering, professor at Central South University. His research interest covers modeling and optimal control of complex industrial process, distributed robust control, and fault diagnoses

    Corresponding author: CHEN Ning Professor at Central South University. Her research interest covers modeling and control of complex systems, and fuzzy cognitive networks. Corresponding author of this paper
  • 摘要: 针对具有不确定性非线性系统的机理模型难以建立的问题,提出了基于模糊灰色认知网络(Fuzzy grey cognitive networks,FGCN)的非线性系统建模方法.该方法将模糊认知网络和灰色系统理论相结合,把模糊认知网络的节点状态值和权值扩展为灰色区间,引入灰度来评判可靠性.采用一种带终端约束的非线性Hebbian学习算法(Nonlinear hebbian learning,NHL)辨识FGCN的模型参数,引入了与FGCN模型中节点的系统实际测量值对应的灰数值,在更新机制中增加了包含系统测量值与预测值之差的修正项,对权值进行有监督的修正.利用水箱控制系统进行的仿真实验结果表明,本文提出的建模方法能解决对数据存在不确定性或缺失的复杂系统建模的难题,所建的模型能做出接近人类智能的控制决策,所采用的权值学习方法具有收敛速度快、学习结果精准等优点,并克服了传统非线性Hebbian算法对初始值依赖性强的缺点,对不确定性系统的建模具有广泛适用性.
    1)  本文责任编委 刘艳军
  • 图  1  基于FGCN带终端约束的非线性Hebbian算法流程图

    Fig.  1  Flowchart of NHL with terminal constraints based on FGCN

    图  2  水箱控制过程

    Fig.  2  The control process of tanks

    图  3  水箱控制过程的FGCN模型

    Fig.  3  FGCN model of the tank control process

    图  4  NHL学习的FGCN仿真结果

    Fig.  4  FGCN simulation results trained by NHL

    图  5  带终端约束的NHL学习的FGCN仿真结果

    Fig.  5  FGCN simulation results trained by NHL with terminal constraints

    表  1  NHL算法学习的仿真结果

    Table  1  Simulation results trained by NHL

    概念节点 FGCN模型(灰度为零) FGCN模型(灰度不为零)
    灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$ 灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$
    1 [0.728, 0.728] 0 0.728 [0.7279, 0.7280] 0.0001 0.72795
    2 [0.6663, 0.6663] 0 0.6663 [0.6662, 0.6663] 0.0001 0.66625
    3 [0.7523, 0.7523] 0 0.7523 [0.7522, 0.7523] 0.0001 0.75225
    4 [0.6608, 0.6608] 0 0.6608 [0.6608, 0.6609] 0.0001 0.66085
    5 [0.799, 0.799] 0 0.799 [0.7989, 0.7991] 0.0002 0.799
    6 [0.835, 0.835] 0 0.835 [0.8349, 0.8351] 0.0002 0.835
    7 [0.7826, 0.7826] 0 0.7826 [0.7826. 0.7827] 0.0001 0.75265
    8 [0.6399, 0.6399] 0 0.6399 [0.6397, 0.6399] 0.0002 0.6398
    下载: 导出CSV

    表  2  带终端约束非线性Hebbian算法学习仿真结果

    Table  2  Simulation results trained by NHL with terminal constraints

    概念节点 FGCN模型(灰度为零) FGCN模型(灰度不为零)
    灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$ 灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$
    1 [0.73, 0.73] 0 0.73 [0.7300, 0.7301] 0 0.73005
    2 [0.67, 0.67] 0 0.67 [0.6700, 0.6701] 0.0001 0.67005
    3 [0.75, 0.75] 0 0.75 [0.7500, 0.7500] 0.0001 0.75005
    4 [0.66, 0.66] 0 0.66 [0.6599, 0.6600] 0.0001 0.65995
    5 [0.80, 0.80] 0 0.8 [0.8000, 0.8001] 0.0001 0.80005
    6 [0.8304, 0.8304] 0 0.8304 [0.8304, 0.8305] 0.0001 0.83045
    7 [0.7799, 0.7799] 0 0.7799 [0.7798, 0.7799] 0.0001 0.77985
    8 [0.6290, 0.6290] 0 0.629 [0.6290, 0.6291] 0.0001 0.62905
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-08-06
  • 录用日期:  2017-06-22
  • 刊出日期:  2018-07-20

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