一类改进的非等间距灰色模型及应用

An Improved Non-equidistant Grey Model and Its Application

现实中存在着大量近似非齐次指数增长规律的数据序列.根据非等间距灰色模型建模机理,本文构造了一个用非齐次指数序列来拟合原始数据序列的非等间距灰色模型,以原始数据序列的观测值与模拟值的相对误差平方和最小为目标,推导出新模型参数的最小二乘解及其时间响应函数的表达式.最后通过两个实例,将改进模型与经典模型对比,取得了良好的效果,进而验证了所提出模型的有效性和实用性.

There exists a lot of non-homogenous exponential incremental sequence in real life. According to the non-equidistant GM（1,1） modeling mechanism, an improved grey model which uses non-homogenous exponential sequence to fit the original data sequence is proposed. In order to minimize the square sum of relative error between observed values and simulated values, the model＇s parameters are deduced by means of the least square method as well as the time response function. Finally, the improved model is compared with the classical model by two examples, and the results show that the effectiveness and practicality of the new proposed model.