Wavelet Neural Network Structure Optimization Method Based on Grey Relational-Sensitivity

Abstract

In view of the wavelet neural network input number to determine the lack of theoretical guidance, the number of hidden layer nodes to determine the defects of difficult, put forward a kind of based on multivariate time series and grey relational sensitivity of the wavelet neural network structure optimization method. This method firstly before the wavelet neural network learning, number of multivariate time series is used to determine the network's input, and then using grey relation in the process of learning sensitivity pruning method to determine the neural network hidden layer node number, to achieve the goal of structural optimization. Through the model simulation results in the short-term wind power prediction, the results show that the method the optimized wavelet neural network to improve the wind power prediction accuracy and verified the effectiveness and feasibility of this structure optimization method, for the determination of wavelet neural network structure provides reference. Introduction Wavelet Neural Network(WNN) is Zhang and Benveniste presented for the first time in 1992 as a kind of wavelet analysis technique was applied to the new neural network model of artificial neural network. It is a good approximation properties of wavelet transform and artificial neural network generalization ability and self-study ability, and the nonlinear approximation properties, which is widely used in signal and image processing, pattern recognition, fault diagnosis and control, etc. This paper presents a grey relational sensitivity based on wavelet neural network structure optimization method. Before the network learning, determine the input the number of the network, the network learning process using grey relational sensitivity pruning method to determine the neural network hidden layer node number, achieve the goal of structural optimization, and the optimized network is applied to wind power prediction. The Wavelet Neural Network Wavelet neural network is the product of combining wavelet analysis and artificial neural network, according to its structure is divided into two categories: the network of loose and tight type. Loose network based on wavelet analysis, as the pre processing means of conventional neural networks for neural network input feature vectors. Compact type is wavelet function instead of conventional neural network hidden layer effect function, respectively using wavelet function coefficient of scale and translation for the instead of the conventional network input layer to hidden layer weights and thresholds. In this paper, nonlinear wavelet function to replace the BP neural network in the Sigmod function as a hidden layer of neural network function, constitute the wavelet neural network, the network structure as shown in figure 1, consists of input layer, hidden layer and output layer, the network nodes are connected by a weight between each layer, the same layer between the nodes are 2nd International Conference on Electrical, Computer Engineering and Electronics (ICECEE 2015) © 2015. The authors Published by Atlantis Press 484 independent of each other, there is no connection to each other. Fig.1 wavelet neural network structure In diagram, wavelet neural network's input layer nodes for m, output layer node number is 1, determined by the actual application situation. Number of hidden layer nodes is n, generally according to empirical formula. j x is the first j a input for the network. Y is the output of the network. ij w is the input node weights between hidden nodes I and j. i w is the hidden node i weights between hidden and output node. θ is the output node threshold. ( ) , i i i a b ψ is the function of the hidden node to the output node I function. i a and i b is the first i a hidden node scale factor and shift factor respectively . The output of wavelet neural network as follows: 1 1 (( ) / ) n m i i ij j i i i j y f w w x b a = =   = − −     ∑ ∑ ψ θ (1) f(•) is the function of the hidden layer to output layer functions, commonly used for the linear function. Wavelet analysis is the precondition of choosing the appropriate wavelet function function, this article selects the wavelet function Morlet which commonly used in engineering, its form is ( ) ( ) ( ) 2 cos 1.75 exp / 2 t t t ψ = − (2) Using the error gradient descent method one by one, from the output layer to input layer to adjust network parameters, after the adjustment parameters are: ( ) 1 ( 1) ( ) N p p p i i i p w k w k d y o η = + = + − ∑ (3) ( ) 1 ( 1) ( ) N p p p k k d y θ θ η = + = + − − ∑ (4) ( ) ( ) 1 ( 1) ( ) ( ) / / N p p p p ij ij i i i i j i p w k w k d y w net b a x a η ψ = ′ + = + − − ∑ (5) j= 1, 2,... , m is the number of input layer nodes. i = 1, 2,... , n is the number of hidden layer nodes. P is sample number. K is the number of iterations. η is Vector . p i o is the output of a hidden node I . 1 i j m p p ij j net w x = =∑ . Determine the Wavelet Neural Network Input Neural network's input generally according to the actual need for sure, has a great deal of subjectivity. Too little and the neural network input, will reduce the network learning accuracy; Too much of the neural network input, will increase the learning time of the network. So in this paper, Outputtt Implied Input 1 x