灰色Verhulst-BP网络组合模型在预测中的应用研究

在灰色Verhulst模型和BP神经网络理论的基础上，对两者的结合方式进行了研究，提出了部分数据Verhulst模型组的概念，得到了一种结合灰色Verhulst与BP神经网络的组合预测模型。利用BP神经网络建立部分数据Verhulst模型组与原始数据之间的非线性映射关系，克服了小样本时间序列数据在神经网络训练时的缺陷。实验结果和仿真验证表明，该组合预测模型具有较高的预测精度和良好的稳定性。

Application research of gray Verhulst-BP neural network combined model on prediction

Based on the grey Verhulst model and BP-neural network theory,this paper studies the combination of them,puts forward the partial-data Verhulst model group and proposes a kind of gray Verhulst-BP neural network combined forecasting model.In this paper,BP-neural network is utilized to build up the nonlinear mapping between partial-data Verhulst model group and original data,and the defects of the neural networking training with small sample of time series data are overcome.The experiment results show that the combined forecasting model is valid,high precision and good stability.