Research and application of RBF neural network based on modified Levenberg-Marquardt

Abstract

Radial basis function neural network (RBFNN) has been widely used in industrial process modeling because of its strong approximation ability. However, many existing modeling methods aim at accuracy, but ignore the stability of mode. Therefore, this paper proposes a parameter optimization method of RBF neural network based on modified Levenberg-Marquardt (MLM-RBFNN) to ensure the stability of the network. Firstly, a typical sample mechanism with variance reduction is proposed, which can reduce the error of gradient estimation and use accurate gradient information to guide learning. Secondly, a modified LM optimization algorithm is proposed to optimize the parameters, which not only improve the convergence speed of the network, but also ensure the stability of the model. Finally, a multi-step updating rule based on a typical sample and a single sample is designed, which effectively reduces the sample bias introduced by a single sample. In order to prove the advantages of the MLM-RBFNN method proposed in this paper, experiments are carried out on three benchmark data sets and a practical wastewater treatment process application problem and compared with several existing methods. The results show that the proposed MLM-RBFNN method has good performance in both learning speed and stability.