基于模糊认知网络的改进非线性Hebbian算法
Improved nonlinear Hebbian learning algorithm based on fuzzy cognitive networks model

针对难以用机理模型准确描述的非线性系统, 研究基于模糊认知网络(fuzzy cognitive networks, FCN)的非线性 系统建模和参数辨识问题. 首先, 建立非线性系统的具有数值推理和模糊信息表达的模糊认知网络模型, 利用包含节 点、权值和反馈的有向图表示系统. 其次, 由于模型的精确性取决于权值参数, 提出了一种带终端约束的非线性Hebbian 学习算法(nonlinear Hebbian learning, NHL). 该算法在权值的学习过程中引入了FCN模型中节点的系统实际值, 在原更 新机制的基础上, 增加了包含反馈值与预测值差值的修正项, 然后归一化得到最终权值迭代公式. 该算法具有收敛速度 快、学习结果精准等优点, 解决了传统非线性Hebbian算法对初始值依赖性强的缺点. 最后将所提出的方法运用到水箱 控制系统, 仿真结果说明了基于FCN的非线性Hebbian学习算法的有效性.
Modeling and parameter identification problems based on fuzzy cognitive networks (FCN) is studied for a kind of nonlinear systems which is difficult to accurately modelled by the mechanism. First, fuzzy cognitive networks with numerical reasoning and fuzzy information expression is established. The FCN model can express the system utilizing the directed graph containing nodes, weights, and feedback. Second, due to the precision of the model depends on the weight parameter, a nonlinear Hebbian learning algorithm with terminal constraints is proposed. The algorithm introduces the actual feedback value of system to the process of weight training. Based on the old update mechanism, a correction term with difference between the feedback value and predictive value is increased, then normalized to the final weight iteration formula. This algorithm has the advantages of fast convergence rate, high accuracy. The nonlinear Hebbian algorithm solves the shortcomings of traditional nonlinear Hebbian learning algorithm that initial value is strongly depended. Finally, the proposed method is applied to water tank control system. The simulation results illustrate the nonlinear Hebbian learning algorithm based on FCN is effective.