Optimal Structure Design for RBFNN Structure

Due to the fact that the conventional radial basis function (RBF) neural network cannot change the structure on-line, a new dynamic structure RBF (D-RBF) neural network is designed in this paper. D-RBF is based on the sensitivity analysis (SA) method to analyze the output values of the hidden nodes for the network output, then the hidden nodes in the RBF neural network can be inserted or pruned. The final structure of D-RBF is not too large or small for the objectives, and the convergence of the dynamic process is investigated in this paper. The grad-descend method for the parameter adjusting ensures the convergence of D-RBF neural network. The structure of the RBF neural network is selforganizing, and the parameters are self-adaptive. In the end, D-RBF is used for the non-linear functions approximation and the non-linear systems modelling. The results show that this proposed D-RBF obtains favorable self-adaptive and approximating ability. Especially, comparisons with the minimal resource allocation networks (MRAN) and the generalized growing and pruning RBF (GGAP-RBF) reveal that the proposed algorithm is more effective in generalization and finally neural network structure.

[1]  Hujun Yin,et al.  Self-organizing mixture networks for probability density estimation , 2001, IEEE Trans. Neural Networks.

[2]  Lajos Hanzo,et al.  Symmetric RBF Classifier for Nonlinear Detection in Multiple-Antenna-Aided Systems , 2008, IEEE Transactions on Neural Networks.

[3]  W. Gujer,et al.  A general model for single-sludge wastewater treatment systems , 1987 .

[4]  Anna Esposito,et al.  Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm , 2000, Neural Networks.

[5]  Héctor Pomares,et al.  Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation , 2003, IEEE Trans. Neural Networks.

[6]  Narasimhan Sundararajan,et al.  A generalized growing and pruning RBF (GGAP-RBF) neural network for function approximation , 2005, IEEE Transactions on Neural Networks.

[7]  Luigi Grippo,et al.  Convergent Decomposition Techniques for Training RBF Neural Networks , 2001, Neural Computation.

[8]  A. Saltelli,et al.  The role of sensitivity analysis in ecological modelling , 2007 .

[9]  De-Shuang Huang,et al.  A Constructive Hybrid Structure Optimization Methodology for Radial Basis Probabilistic Neural Networks , 2008, IEEE Transactions on Neural Networks.

[10]  Stefano Tarantola,et al.  Sensitivity analysis in model calibration: GSA-GLUE approach , 2001 .

[11]  X. X. Wang,et al.  Sparse incremental regression modeling using correlation criterion with boosting search , 2005, IEEE Signal Processing Letters.

[12]  Hak-Keung Lam,et al.  Tuning of the structure and parameters of a neural network using an improved genetic algorithm , 2003, IEEE Trans. Neural Networks.

[13]  Hsuan-Ming Feng,et al.  Self-generation RBFNs using evolutional PSO learning , 2006, Neurocomputing.

[14]  Ioannis Pitas,et al.  Median radial basis function neural network , 1996, IEEE Trans. Neural Networks.

[15]  Bing Lam Luk,et al.  Construction of Tunable Radial Basis Function Networks Using Orthogonal Forward Selection , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Y Lu,et al.  A Sequential Learning Scheme for Function Approximation Using Minimal Radial Basis Function Neural Networks , 1997, Neural Computation.

[17]  Andrea Saltelli,et al.  An effective screening design for sensitivity analysis of large models , 2007, Environ. Model. Softw..

[18]  Marimuthu Palaniswami,et al.  Effects of moving the center's in an RBF network , 2002, IEEE Trans. Neural Networks.

[19]  Stefano Tarantola,et al.  Sensitivity analysis practices: Strategies for model-based inference , 2006, Reliab. Eng. Syst. Saf..

[20]  Lipo Wang,et al.  Data dimensionality reduction with application to simplifying RBF network structure and improving classification performance , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[21]  Zhen Zhu,et al.  Optimized Approximation Algorithm in Neural Networks Without Overfitting , 2008, IEEE Transactions on Neural Networks.