HBF神经网络的一种结构自适应在线学习算法  

A Structural Adaptive Online Learning Algorithm for Hyper Basis Function Neural Network

作　　者：武晨 谷松原 房圣超 WU Chen;GU Song-yuan;FANG Sheng-chao(China Academy of Electronics and Information Technology,Beijing 100141,China)

机构地区：[1]中国电子科学研究院,北京100141

出　　处：《中国电子科学研究院学报》2021年第5期486-495,共10页Journal of China Academy of Electronics and Information Technology

基　　金：基础加强计划重点基础研究资助项目(2020-JCJQ-ZD-081)。

摘　　要：超级基(HBF)神经网络是高斯RBF神经网络的泛化形式,针对该神经网络文中提出了一种可增加或删除隐含层节点的结构自适应在线学习算法。对于隐含层节点的增加,提出了输入隶属度的概念,并同时考虑网络对输入的映射能力和网络输出偏差给出了隐含层节点增加规则;对于隐含层节点的删除,文中采用归一化的思想计算每个隐含层节点对网络输出的贡献度,并将贡献度小于阈值的隐含层节点从网络中删除。在线学习过程中,仅需调整隐含层节点的HBF激活函数的宽度和隐含层与输出层之间的连接权值,HBF激活函数的宽度通过所提出的简单运算进行调整,而连接权值的调整采用递归最小二乘法调整。为验证所提出学习算法的有效性,将HBF神经网络分别应用于非线性函数逼近和动态系统在线预测,数值分析结果说明该结构自适应在线学习算法使HBF神经网络不仅具有较高的逼近精度和预测精度,而且具有简洁的网络拓扑结构。Hyper basis function(HBF)neural network is a generalization of Gaussian radial function neural network.In this paper,a structural adaptive online learning algorithm is presented for this neural network,which can adjust the network structure adaptively by adding or removing hidden-layer nodes.For adding hidden-layer node,the concept of input membership is proposed,and the criteria for adding a hidden-layer node consider the mapping ability of the network to the input and the deviation of the network output simultaneously.For removing hidden-layer node,this paper calculates the contribution of each hidden-layer node to the network output using the normalization method,and the hidden-layer node whose contribution is less than the threshold is removed from the network.During the learning,the widths of HBFs and the connection weights should be adjusted.The widths of HBFs are adjusted using simple arithmetical operation proposed in this paper,and the adjustment of the weights is accomplished by the recursive least squares.In order to verify the effectiveness of the proposed learning algorithm,the HBF neural network is applied to nonlinear function approximation and dynamic system online prediction respectively.The numerical analysis shows that the proposed learning algorithm makes the HBF neural network not only have high approximation accuracy and prediction accuracy but also have compact network topology structure.

关 键 词：超级基神经网络 结构自适应 在线学习 输入隶属度 归一化方法 递归最小二乘法 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]