基于时间权重序列的GM(1,1)初始条件优化模型

Initial condition optimization of GM(1,1) model based on time weighted sequence

灰色GM(1,1)模型的初始条件对其精度有着重要的影响,为了提高模型的精度,提出一种初始条件的优化方法.首先,综合考虑1-AGO序列中各分量的作用,取所有分量的加权平均作为初始条件,权重由各分量的大小决定;然后,基于时间权重序列,对模拟序列与原始序列的误差平方和进行加权;最后,求解最优问题,确定时间参数,从而建立优化模型.算例表明,所提出的优化模型具有可行性,可以有效地提高模型的精度.

The initial conditions of gray GM（1,1） model have an important influence on the accuracy of the model. In order to improve the accuracy of the grey model, an optimization method of initial condition is proposed. Firstly, the role of each component in the 1-AGO sequence is taken into account. So the weighted average of all components is chosen as the initial condition. Its weight is determined by the size of each component. Then, the error squared sum of the simulation sequence and original sequence is weighted based on the time weight sequence. Finally, the optimal problem is solved and the time parameter is calculated to establish the optimization model. Some examples are given to illustrate that the proposed optimization model is feasible and can improve the accuracy of the grey model effectively.