非等时距GM(1,1)直接模型及其在材料试验数据处理中的应用

在原始数列等时距处理的基础上,通过用一次累减数列与原始数列构建微分模型,得到了非等时距GM(1,1)直接模型;并给出2个具有不同饱和特征的材料试验数据处理实例.通过这2个实例说明了非等时距GM(1,1)直接模型适合处理呈上升或下降饱和变化趋势、对数据无非负性要求的任意数列,其预测值不需要还原计算,具有适用范围广、预测精度高和简单实用的特点.该模型有效弥补了传统GM(1,1)模型在此类数据处理方面的不足,因此,具有较大的应用推广价值.

Non-equal interval GM (1,1) direct model and its application in processing of materials experimental data

Based on the equidistant processing of the initial data, the non-equal interval GM (1, 1) direct model is established, which is a differential equation consisted of the inverse accumulated generating data list and the initial data list. By applying this modified gray model to process two examples which have different trends of saturation, the prominent characteristics of this modified gray model are shown. The model can be used to process the original data that are negative, non-negative, saturated and non-equal interval; its modeling process is simpler than the traditional GM (1,1) because its forecast data do not have to be reverted to X (0). This modified gray model makes up for the weakness in the existing ways and its forecast accuracy is better. Therefore, it can be widely applied to process the experimental data of materials.