耦合三角函数的灰色GM(1,1,T)模型及其应用

Grey GM(1,1,T)model coupled with trigonometric function and its application

针对小样本序列的周期性波动特征,将三角函数引入灰色预测模型,提出了耦合结构的灰色GM(1,1,T)模型,该模型适用于既存在周期性又具有趋势性的复合型序列.基于最小二乘思想,探讨了模型参数估计的非线性优化问题,利用Levenberg-Marquardt算法进行求解,并给出了初始点选取的经验方法;通过数值实验验证了模型的适用性和参数估计方法的可行性;最后将该模型应用于河南省获嘉县、禹州市、偃师市的农业干旱预测,结果表明2016-2017年河南省土壤含水量呈现出区域性差异,与实际干旱情势比较吻合.

For the periodic fluctuation characteristic of small sample sequences,the trigonometric function is introduced into the grey forecasting model,and a grey GM(1,1,T)model with coupling structure is proposed,which is suitable for compound sequences with trend and periodicity.Based on the least squares theory,the nonlinear optimization problem of model parameter estimation is discussed,which is solved by Levenberg-Marquardt optimization algorithm,and the empirical method of initial point selection is given.The applicability of the model and the effectiveness of the parameter estimation method are verified by numerical experiments.Finally,the GM(1,1,T)model is applied to predict the agricultural drought in Huojia County,Yuzhou City,and Yanshi City of Henan Province.The result shows that there were regional differences in soil water content in Henan Province from 2016 to 2017,which is consistent with the actual drought situation.