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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。
In this paper, the morphology and characteristics of the gray differential equation and its parameters are studied. The gray of parameters of the gray differential equation is analyzed. A method of using the neural network to whiten the parameters of the gray differential equation is proposed. The parameters of the gray differential equation BP network for whitening, the BP network is a kind of gray neural network because it takes full advantage of the gray parameters of the parameters of the gray differential equation. Based on the research of one-dimensional gray problem and neural network modeling, this paper proposes a method of using neural network to whiten the parameters of gray system - gray neural network GNNM (1,1). Further, the two-dimensional gray problem is studied and the GNNM (1,2) model is established.