A Novel Radial Basis Function Neural Network with High Generalization Performance for Nonlinear Process Modelling

A radial basis function neural network (RBFNN), with a strong function approximation ability, was proven to be an effective tool for nonlinear process modeling. However, in many instances, the sample set is limited and the model evaluation error is fixed, which makes it very difficult to construct an optimal network structure to ensure the generalization ability of the established nonlinear process model. To solve this problem, a novel RBFNN with a high generation performance (RBFNN-GP), is proposed in this paper. The proposed RBFNN-GP consists of three contributions. First, a local generalization error bound, introducing the sample mean and variance, is developed to acquire a small error bound to reduce the range of error. Second, the self-organizing structure method, based on a generalization error bound and network sensitivity, is established to obtain a suitable number of neurons to improve the generalization ability. Third, the convergence of this proposed RBFNN-GP is proved theoretically in the case of structure fixation and structure adjustment. Finally, the performance of the proposed RBFNN-GP is compared with some popular algorithms, using two numerical simulations and a practical application. The comparison results verified the effectiveness of RBFNN-GP.

Download Full-text

Radial Basis Function network learning using localized generalization error bound

Information Sciences ◽

10.1016/j.ins.2009.06.001 ◽

2009 ◽

Vol 179 (19) ◽

pp. 3199-3217 ◽

Cited By ~ 37

Author(s):

Daniel S. Yeung ◽

Patrick P.K. Chan ◽

Wing W.Y. Ng

Keyword(s):

Radial Basis Function ◽

Error Bound ◽

Basis Function ◽

Radial Basis Function Network ◽

Generalization Error ◽

Network Learning ◽

Radial Basis ◽

Generalization Error Bound ◽

Function Network ◽

Localized Generalization Error

Download Full-text

Human Activity Recognition Using Radial Basis Function Neural Network Trained via a Minimization of Localized Generalization Error

Ubiquitous Computing and Ambient Intelligence - Lecture Notes in Computer Science ◽

10.1007/978-3-319-67585-5_50 ◽

2017 ◽

pp. 498-507 ◽

Cited By ~ 3

Author(s):

Shuai Zhang ◽

Wing W. Y. Ng ◽

Jianjun Zhang ◽

Chris D. Nugent

Keyword(s):

Neural Network ◽

Radial Basis Function ◽

Activity Recognition ◽

Human Activity ◽

Basis Function ◽

Human Activity Recognition ◽

Generalization Error ◽

Radial Basis ◽

Localized Generalization Error

Download Full-text

Equipment Maintenance Support Effectiveness Evaluation Based on Improved Generative Adversarial Network and Radial Basis Function Network

Complexity ◽

10.1155/2021/1332242 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Zhen Li ◽

Jianping Hao ◽

Cuijuan Gao

Keyword(s):

Neural Network ◽

Radial Basis Function ◽

Basis Function ◽

Effectiveness Evaluation ◽

Generative Adversarial Network ◽

Generalization Ability ◽

Rbf Network ◽

Adversarial Network ◽

Radial Basis ◽

Network Evaluation

Due to the lack of maintenance support samples, maintenance support effectiveness evaluation based on the deep neural network often faces the problem of small sample overfitting and low generalization ability. In this paper, a neural network evaluation model based on an improved generative adversarial network (GAN) and radial basis function (RBF) network is proposed to amplify maintenance support samples. It adds category constraint based on category probability vector reordering function to GAN loss function, avoids the simplification of generated sample categories, and enhances the quality of generated samples. It also designs a parameter initialization method based on parameter components equidistant variation for RBF network, which enhances the response of correct feature information and reduces the risk of training overfitting. The comparison results show that the mean square error (MSE) of the improved GAN-RBF model is 5.921 × 10 − 4 , which is approximately 1/2 of the RBF model, 1/3 of the Elman model, and 1/5 of the BP model, while its complexity remains at a reasonable level. Compared with traditional neural network evaluation methods, the improved GAN-RBF model has higher evaluation accuracy, better solves the problem of poor generalization ability caused by insufficient training samples, and can be more effectively applied to maintenance support effectiveness evaluation. At the same time, it also provides a good reference for evaluation research in other fields.

Download Full-text