基于变权优化背景值改进的GM(1,1)灰色预测模型及其应用  

Improved GM(1,1)Grey Prediction Model Based on Background Value of Variable Weight Optimization and Its Application

作　　者：张丽洁 沙秀艳 尹传存 段钧陶 张欣怡 李紫桐 姜福蕾 ZHANG Li-jie;SHA Xiu-yan;YIN Chuan-cun;DUAN Jun-tao;ZHANG Xin-yi;LI Zi-tong;JIANG Fu-lei(School of Statistics, Qufu Normal University, Jining 273165, China)

机构地区：[1]曲阜师范大学统计学院,山东济宁273165

出　　处：《计算机与现代化》2021年第1期1-6,27,共7页Computer and Modernization

基　　金：国家自然科学基金资助项目(11171179,11571198);全国统计科学研究项目(2019LY47);山东省大学生创新创业训练计划项目(S201910446069)。

摘　　要：针对传统的GM(1,1)灰色预测模型背景值采用均等权值导致预测精度不高的缺点,本文提出一种变权优化选择背景值方法。首先将黄金分割搜索和抛物线插值法相结合确定改进GM(1,1)模型的背景值;然后将改进后的背景值代入灰色预测代数递推方程,从而代替传统的GM(1,1)模型中的白化方程;最后选取指数数列进行模拟并结合某高校教师人数的实际统计数据进行仿真实验。结果表明,改进的GM(1,1)模型减少了平均相对误差,提高了预测精度,具有一定的应用价值。In view of the disadvantage that the traditional GM(1,1)grey prediction model adopts equal weight in the background value,which results in low prediction accuracy,this paper proposes a variable weight optimization method for selecting background value.Firstly,the golden section search and parabolic interpolation method are combined to determine the background value of the improved GM(1,1)model.Then the improved background value is brought into the grey prediction algebraic recursive equation,replacing the whitening equation in the traditional GM(1,1)grey prediction model.Finally,we select the exponential sequence to simulate,and carry out a simulation experiment based on the actual statistical data of the number of teachers in a university.The results show that the improved GM(1,1)model reduces the average relative error,improves the prediction accuracy and has certain application value.

关 键 词：灰色预测 黄金分割 抛物线插值法 变权优化 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]