同时利用x(1)(1)和x(1)(n)为GM(1,1)建模初始条件的预测方法研究

摘要

In order to reestablish the initial value for GM (1,1) model,we proposed a new approach to improve prediction accuracy of GM (1,1) model through optimization of the initial value,which is comprised of the first and the n-th vector as the initialization,and derived from a method of least error summation of square.Then we discussed the parameter which affects the fitting results.By contrasting the improved one to the GM (1,1) about the simulation and prediction,we can conclude that the improved one is superior in prediction and simulation,and it is proved that the optimum one widen its suitable range.%以灰色GM(1,1)模型初始条件的优化为主要研究目的,分别讨论了以x(1)(1)、x(1)(n)为初始条件的GM(1,1)建模机理；提出了同时利用x(1)(1)和x(1)(n)为GM(1,1)模型初始条件的新方法,以x(1)(t)的模拟值与原始数据的1-AGO序列的误差平方和最小为约束条件,推导了初始条件优化后的预测模型公式；对模型预测精度起决定性作用的参数进行分析,给出了初始条件优化后模型的适用范围.经大量的数据模拟和预测,发现初始条件优化后的GM(1,1)模型各项精度指标均优于传统的GM(1,1)模型.