非齐次指数离散灰色预测模型的一个注记及其应用  

A Note on Discrete Grey Prediction Model of Inhomogeneous Exponents and Its Application

作　　者：杨鑫波[1] YANG Xin-bo(College of Mathematics and Big Data,Chongqing University of Education,Chongqing 400065,China)

机构地区：[1]重庆第二师范学院数学与大数据学院,重庆400065

出　　处：《数学的实践与认识》2024年第11期148-160,共13页Mathematics in Practice and Theory

基　　金：重庆市教委科学技术研究项目(KJQN201901601)。

摘　　要：针对非齐次离散灰色模型NDGM(1,1)和三参数离散灰色预测模型TDGM(1,1)的时间响应式均未揭示模拟数据的结构特征.文章在NDGM(1,1)模型基础上,利用数学归纳法重新推导其时间响应式,新的时间响应式和典型实例证明NDGM(1,1)和TDGM(1,1)模型均可对非齐次/齐次指数序列以及线性函数序列进行无偏模拟,且具有良好的实用性和有效性.最后,应用TDGM(1,1)和NDGM(1,1)模型对我国太阳能发电量进行建模,并对预测结果进行比较和分析.本研究对丰富和完善离散型灰色预测模型具有积极意义.The time response functions of the non-homogeneous discrete grey model NDGM(1,1)and the three-parameter discrete grey prediction model TDGM(1,1)do not reveal the structural characteristics of the simulated data.In this paper,based on NDGM(1,1)model,its time response function is re-deduced by Mathematical induction.The new time-response formula and typical examples prove that both NDGM(1,1)and TDGM(1,1)models can simulate non-homogeneous/homogeneous exponential sequences and linear function sequences without bias,and have good practicability and effectiveness.Finally,the TDGM(1,1)and NDGM(1,1)models are applied to model China's solar power generation,and the predicted results are compared and analyzed.This study has positive significance for enriching and improving the discrete grey prediction models.

关 键 词：离散型灰色预测模型 时间响应式 中国太阳能发电量预测 

分 类 号：N941.5[自然科学总论—系统科学]