The Non-linear Function Approximation Based On Wavelet Neural Network

Wavelet analysis is a rising mathematical analysis method. This paper combines theory of wavelet analysis with conventional neural network. Substituting wavelet function for sigmoid function in neural network, to form wavelet neural network.Both wavelet neural network and neural network of feedforward have ability of coherent approximation and L2 approximation. This paper approximates non-linear function with wavelet neural network, whose ability of approximation function is discussed in theory. Wavelet neural network is a combination of wavelet analysis and conventional neural network, so structure of wavelet neural network can be designed with concerned theory of wavelet analysis. To choose wavelet function based on time-frequency region is put forward, time-frequency region composing of all of these wavelet functions can overlay wholly time-frequency region of non-linear function to approximate. In order to make wavelet neural network efficient and minimize structure of network, a novel method optimizing structure of wavelet neural network is advanced. Because it is linear relation between output of network and right of network, method of LS can be directly used to correct right of wavelet neural network. Arithmetic of back propagation withmomentum gene is used to correct right of network and minimize error of approximation.Finally, take example for a non-linear function, method mentioned in this paper is used to design wavelet neural network to approximate this function. The computer simulations confirm the method that is brought out in this paper is useful, and prove that wavelet neural network has not only fast convergence and better precision of approximation, but also good capability of forecasting and escaping error.