Research On Interval Discrete Wavelet Neural Networks

In real world,Datasets we obtained from many production process may be inaccurate,such as scientific experiments or industrial production.It is often complicated while handling such information,we should put the problem,how to describe the uncertain information and module it,into the first place.Granular computing is a new method,which aims to describe imprecise data and fuzzy information.There are many information granulation method,including set theory and interval analysis,they all have good universality,especially in describing imprecise data.On the other hand,interval neural network is an effective method to solve the problem modeling imprecise data,which uses interval number representing imprecise data and uses neural network to module imprecise data.Discrete wavelet transform has a good localization performance both in time and frequency domain,and the idea of analysis and synthesis of discrete wavelet transform is highly similar with three layer neural network.If we combine discrete wavelet transform theory with the interval analysis and neural network,then we can solve the problems of modeling imprecise information and lacking of guidance of setting neural network parameters.The study of interval discrete wavelet neural network structure and learning algorithm have a very important theoretical and practical significance.Based on the interval analysis and discrete wavelet transform theory,I have looked through lots of academic literature and books,and start a further study of structure and learning algorithm based on gradient descent of interval discrete wavelet neural network.Summary of my work in this paper is shown as follows:In this paper,the interval discrete wavelet neural network is divided into three categories.The process of forward calculate and error back propagation learning of the first and second category of interval discrete wavelet neural network with three layer was deduced.The proposed model for interval discrete wavelet neural network takes full advantage of discrete wavelet transform theory to calculate the input layer to hidden layer and hidden layer to output layer weights,and uses the gradient descent algorithm to adjust the weights of the output layer.Through simulation experiments,the advantages of the interval discrete wavelet neural network's network structure and convergence have been proved.Reverse learning is essential to take the method of point value operation in the previous study of interval neural network.But we put forward the idea of using GH-difference to carry out the error back learning process of interval neural network.We proved by experiments that interval derivative can highlight the characteristics of interval neural network of being interval and has good generalization and convergence ability.In the end of the paper,we also put forward the direction of the further research based on the above research results.