基于ROLS算法的递归RBF神经网络结构设计

针对递归RBF神经网络结构难以自适应问题，提出一种基于递归正交最小二乘（recursive orthogonal least squares，ROLS）算法的结构设计方法。首先，利用ROLS算法来计算隐含层神经元的独立贡献度和损失函数，以此判断增加或归为不活跃组的神经元，同时调整神经网络的拓扑结构，并且利用奇异值分解（singular value decomposition，SVD）决定最佳的隐含层神经元个数，以此来删除不活跃组中相对不活跃的神经元，有效地解决了递归RBF神经网络结构冗余和难以自适应问题。其次，利用梯度下降算法更新递归RBF神经网络的参数来保证神经网络的精度。最后，通过对Mackey-Glass时间序列预测、非线性系统辨识和污水处理过程中关键水质参数动态建模，证明了该结构设计方法的可行性和有效性。

Structure design for recurrent RBF neural network based on recursive orthogonal least squares

Aiming at the problem of recurrent radial basis function (RRBF) neural network structure which is difficult to be self-adaptive, this paper proposes a structure design method based on recursive orthogonal least square (ROLS) algorithm. Firstly, ROLS algorithm is used to calculate the contribution and the loss function of hidden layer neurons, which determines to increase or be grouped into inactive neurons, and the topology structure of neural network is adjusted accordingly. At the same time, singular value decomposition (SVD) is applied to determine the best number of hidden layer neurons in order to delete the neurons of the inactive group, which effectively solves the problems of RRBF neural network structure which is redundant and hardly self-adaptive. Secondly, the gradient descent algorithm is utilized to update the parameters of RRBF neural network in order to ensure the accuracy of neural network. Finally, several experiments including the Mackey-Glass time series prediction, nonlinear system identification and key water quality parameters dynamic modeling in wastewater treatment process are conducted, and the simulation results prove the feasibility and effectiveness of the structure design method.