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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.
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关键词:
- 模糊认知网络 /
- 灰色系统理论 /
- Hebbian学习算法 /
- 终端约束
Abstract: For nonlinear systems with uncertainty, a method of nonlinear system modeling based on fuzzy grey cognitive networks (FGCN) is proposed. By combining fuzzy cognitive networks modeling method and grey system theory, the state value of fuzzy cognitive networks (FCN) node is extended to grey interval. The concept of grey level is introduced to judge the accuracy of the results. This method has the advantages of fuzzy cognitive networks graphical representation and the features of grey system theory that are effective and reliable in the scene of small data, poor information. Moreover, nonlinear Hebbian learning (NHL) with terminal constraint is adopted to identify the system parameters. In the process of weights learning, the algorithm introduces the actual value of the node in the system and increases the difference between measured values and predicted values to amend the weights on the basis of the original update mechanism, then the final value iteration formula is obtained after normalization. The proposed modeling method and the weight learning method are verified in the water tank control system. The algorithm has the advantages of fast convergence rate and accurate study results, and overcomes the traditional shortcoming of nonlinear Hebbian learning, i.e., strong dependence of initial value. Simulation results illustrate the applicability of the FGCN and the algorithm to model uncertain systems.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 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 
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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
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