Neural Network Modeling Research Based On Wavelet Theory And Swarm Intelligence

Wavelet network is a new kind of neural network, it is the combination of the mathematical wavelet theory and the powerful artificial intelligent algorithm of neural network. The fusion of these two both embodies the theoretical wavelet its practical application and help to adds to the diversity of the family of neural network. In this thesis all the efforts are made to perfectly reconcile wavelet and neural network, the application of wavelet here in the realm of artificial network is strictly according to the rules of wavelet theories. Nevertheless many of the qualities of wavelet serves neural network vary well: Orthogonality and compact support of mother wavelet functions make it a wonderful alternative for the nodes of neural network, wavelet decomposition provide new schemes for the structure of artificial network, also the Multiresolution representation of wavelet also help to the problem of Multiobjective optimization.Another issue of this thesis lies in the corporation between Swarm intelligence-Particle Swarm Optimization and Wavelet Network. Particle Swarm Optimization has been proved to be highly efficient optimization algorithm, however the other side of this effort always leads to prematurely convergence which is the reason of inviting wavelet network here.The way of combination of wavelet theories and artificial network is first introduced and discussed and then the prospect of its modification is probed into and approached in every possible way. The second and third chapters are mainly for the discussion of the development of Fixed Grid Wavelet Network along with Adaptive Wavelet Network and the problem of how to better the learning and approximation abilities. The training methods of Fixed Grid Wavelet Network include Orthogonal Least Square, QR Decomposition and support vector machine. The Singular Value Decomposition method is introduced here to compete with The QR Decomposition, so is the PRESS statistic used here for the Classical Orthogonal method. These two are destined for the better capture of the characteristics of the system and the reduction of the structure of the network. Also the Particle Swarm Optimization is incorporated into the training process of Adaptive Wavelet Network to speed the reaching of optimal point. In the last chapter, again the Particle Swarm Optimization is adopted this time for the training of Multiobjective Optimization formed by the wavelet theory of Muliresolution representation.