The Establishment Of The Grey Neural Network Model And Its Application On The Problem Of Complex Nonlinear Prediction

The grey neural network model is a model that nearly integrates the grey system method with the neural networks method by a valid path in order to solve the complicated indeterminate problems.The grey system is a system of the incomplete and indeterminate information and the grey problem is the problem of the incomplete information in construction, character, parameter, etc. But the neural network has many advantages, for example, the parallel calculation, the distributed information memory, the admitting-error ability, the self-adapt learning function, etc. So the neural network show the very superior position in handling complicated artificial problem. From studying the grey system and the neural network, we have discovered that they can estimate the function. Each of the two kinds of methods has its own strong point. If we put two kinds of methods together, we can establish the grey neural network model. When we solve the grey problem, the calculating quantity of this model is less than that of the neural network and under the few samples condition it still can attain the higher precision. And compared with the neural network method, the grey neural network model has the higher precision and can control the error.The basic theory of establishing the grey neural network model is according to the tenet that we set up the grey system model, and then we can constitute a differential equation with the primitive sequence. Because of appearing empty aggregates in the time zone (the time zone do not include the information), we only establish the indeterminate grey differential equation according to the approximate condition of the differential equation. But the grey differential equation almost cannot be applied to the practical problems, so we should turn the gery differential equation into the white differential equation. For this reason, in order to ascertain the grey parameters included the grey differential equation we construct a BP neural network including these grey parameters, namely we mapping the function responding to the time on the grey differential equation into the BP neural network. Then, we train the BP network with the simples that distilled from the known data in the grey system. When the BP network attains the convergence, we can distill the certain parameters of the grey differential equation, so we can find a determinate grey differential equation under a certain precision and establish the continuous model. According to the theory we have described. The important base of establishing the grey neural network includes the theory of grey system and the neural network, and the emphasis are the theory of establishing the grey system model and the back propagation (BP) network. In this paper, GNNM (1,1) that is the grey neural network model of first order is improved and perfected. Make use of the parameters attained by least squares estimation in the grey differential equation:and then find the original weight value and the original threshold value that they are very closed to the exact value. So we can overcome the randomicity and indeterminacy about the original value in the BP network, reduce the times of network training, improve the network convergence speed and the precision of output value, and avoid appearing the local minimum value. And the momentum items are added when the weight values are modified each time, the form of the momentum item is as follows: At the same time, the method of reducing learning velocity is taken, form is: These ways may avoid fluctuate during the network convergence proceeding, the reason of generating fluctuate is owing to the immoderate large or small learning velocity, so the convergence speed is improved and the number of training time is reduced. -1 LA LB LC LDFigure...