Abstract: The traditional gray GM（1, 1） model is established for the approximation of homogeneous exponent sequence. In order to expand the applied range of gray forecasting models, the DNGM（1, 1） model is present for approximation non-homogeneous exponent sequence. The properties of this model are discussed, and it is proved that the DNGM（1, 1） model not only has coincidence of white non-homogeneous exponent law, but also has uniformity of linear transformation. The forecast accuracy of this model may be affected by the initial value conditions, the improvement DNGM（1, 1） model is obtained by parameters optimal. The data simulation and application example show that this model has higher precision than the traditional GM（1, 1） model.

Key words: gray forecast model, DNGM（1, 1） model, parameters optimal

摘要： 传统的灰色GM（1，1）预测模型是针对近似齐次指数序列建立的预测模型。为了拓广灰色预测模型的适用范围，建立了近似非齐次指数序列的灰色DNGM（1，1）预测模型。研究了这种灰色预测模型的性质，证明了这种模型都具有线性不变性，也能够完全拟合非齐次指数序列。考虑到初值条件对灰色模型的影响，对该模型进行了参数优化。数据仿真和实例分析表明，灰色DNGM（1，1）预测模型具有较高的预测精度。

关键词: 灰色预测模型, DNGM（1, 1）模型, 参数优化