灰色问题神经网络建模的白化方法

A PARAMETER WHITENING METHOD FOR NEURAL NETWORK MODELING FOR GRAY PROBLEM

本文对灰微分方程及其参数的形态与特征进行了研究,分析了灰微分方程参数的灰性,提出了用神经网络方法对灰微分方程的参数进行白化的方法,建立了对灰微分方程参数进行白化的BP网络,由于该BP网络充分利用了灰微分方程参数的灰性,因而所建立的BP网络是一种灰色神经网络。本文在对一维灰色问题和神经网络建模进行研究的基础上,提出了一种利用神经网络对灰微分方程参数进行白化的方法——灰色神经网络方法GNNM(1,1)。进一步,对二维灰色问题进行研究并建立了GNNM(1,2)模型。

Gray System, which includes incomplete information on elements , parameters ., structure , relationship or actions, is a system with information that are part definitude and part ambiguity. To solve the gray problem, which has poor information, gray method plays an important role. Neural networks have great excellence in handling complicated artificial intelligence problems. Having worked over both neural networks and gray systems, we found that they could be syncretized. Both of them are function estimators and each has its own strong point. So it is possible to band them together to set up a new method that draws on their merits concurrently from both neural network and gray model. On one hand, less workload and better accuracy can be derived from the combination of gray model and neural network, on the other hand, the error can be directed. The procedure of gray modeling had been studied using gray system theory and method and the shortage of gray modeling had been analyzed. In this paper we put forward a modified gray modeling method and pointed out that this shortage could be overcome by using neural network. Having gone into neural network technology and gray system feature, we found that there is some comparability between neural network and gray system. Consequently, the neural network theory can be combined with the gray system theory. In this paper we discussed such possibility. The modality and features of gray differential equations and the features of differential equation parameters have been researched. The gray attribute of the differential equation parameters also has been analyzed. Base on this, we put forward in this paper a method to whiten the parameters of differential equation using BP neural network Because this BP neural network takes full advantage of the gray attribute of the parameters of differential equation, the BP neural network is a gray neural network (GNNM). Based on studying one dimensional gray problem modeling and neural network modeling, a method of whitening the parameters of gray differential equation using gray neural network-GNNM(1,1) was put forward. Furthermore, we also studied two dimensional gray problem and built GNNM( 1,2).