含时间周期项的离散灰色DGM(1,1,T)模型及其应用

针对系统行为序列的周期性波动特征，将三角函数引入离散灰色预测模型，提出含时间周期项的离散灰色DGM（1，1，T）模型，其还原公式可表示为三角函数和指数函数的耦合形式，从而表明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，将DGM（1，1，T）模型的参数估计转化为非线性优化问题，并提出PSO-LM混合算法进行数值求解；通过数值实验对模型的适用范围和参数估计方法的有效性进行验证；最后将该模型应用于河南省安阳市、洛阳市、许昌市和商丘市的农业干旱预测，结果表明2019年四个地市的土壤湿度将呈现出下降态势.

Discrete grey DGM(1,1,T) model with time periodic term and its application

For the periodic fluctuation characteristic of system behavior sequences, the trigonometric function is introduced into the discrete grey forecasting model, and a discrete grey DGM(1,1,T) model with time periodic term is proposed. The reduction formula of DGM(1,1,T) model can be expressed as the coupling form of trigonometric function and exponential function, which shows that the model is suitable for compound sequences with periodicity and trend. The parameter estimation of DGM(1,1,T) model is transformed into a nonlinear optimization problem based on the least squares theory, and PSO-LM hybrid algorithm is proposed for numerical solution. The applicable range of the model and the validity of the parameter estimation method are verified by numerical experiments. Finally, DGM(1,1,T) model is applied to predict the agricultural drought in Anyang City, Luoyang City, Xuchang City, and Shangqiu City of Henan Province, the result shows that soil moisture in four cities will decrease in 2019.