中文摘要：

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。

英文摘要：

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.