近似非齐次指数数据的灰色建模方法与模型

传统GM(1,1)建模是用齐次的指数序列来拟合原始数据,对近似非齐次指数序列进行建模时会有较大的偏差,而现实中存在大量的近似非齐次指数的数据序列.根据传统灰色GM(1,1)建模机制,提出了一个用非齐次指数序列来拟合原始数据的灰色模型,给出了模型参数的最小二乘解,并给出了模型时间响应函数的表达式. 最后,通过实验验证了新模型的拟合和预测精度实验结果显示,新模型比传统GM(1,1)模型具有更好的拟合和预测精度.

Methods and model of grey modeling for approximation non-homogenous exponential data

When the traditional GM(1,1) modeling is using homogeneous index series to fit the original data on the approximation of non-homogeneous index series modeling, there will be a large deviation. However, There exists a large number of data are the approximation of non-homogenous index series. According to the traditional grey GM(1,1) modeling mechanism, proposed a grey model using non-homogenous index series to fit the original data, and gives out the model parameters least-square solutions as well as the time response function. Finally, the new model is verified by the experiment. Experiments shows that the new model has more approximating and forecasting accuracy than the traditional GM(1,1) model.