小波变换和DGM(2,1)模型在昆明市人口预测中的应用  

Application of Wavelet Transform and DGM (2,1) Model in Population Prediction of Kunming City

作　　者：宋国鹏 张述清 朱大明[1] 阮理念[1] SONG Guopeng;ZHANG Shuqing;ZHU Daming;RUAN Linian(School of Land and Resources Engineering,Kunming University of Science and Technology,Kunming 650093,China;Yunnan Institute of Land and Resources Planning and Design,Kunming 650216,China)

机构地区：[1]昆明理工大学国土资源工程学院,云南昆明650093 [2]云南省国土资源规划设计研究院,云南昆明650216

出　　处：《贵州大学学报（自然科学版）》2022年第2期59-65,共7页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(41761081)。

摘　　要：对于昆明市人口呈不均匀的增长趋势,传统的灰色预测方法并不能取得很好的预测效果。将小波变换与DGM(2,1)模型相结合,利用小波变换去除原始序列中的噪声,将非光滑的原始序列转化为相对光滑的新序列,然后通过DGM(2,1)模型对新序列进行预测,可以得到较为满意的预测效果。以2006—2014年的昆明市人口数据为基础,预测2015—2019年5年昆明市人口数据,并和传统GM(1,1)模型、DGM(2,1)模型进行对比。结果表明:小波DGM(2,1)模型的平均绝对百分比误差为0.15%,DGM(2,1)模型为0.79%,GM(1,1)模型为0.96%,小波DGM(2,1)模型精度高于DGM(2,1)模型和GM(1,1)模型;小波DGM(2,1)模型的均方根误差与平均绝对误差都低于GM(1,1)模型和DGM(2,1)模型。由此,以2006—2019年昆明市人口数据作为原始序列样本,用小波DGM(2,1)模型预测2025、2035年人口为723.07万人、766.56万人。For the uneven growth trend of Kunming population,the traditional grey prediction method can not achieve good prediction results.The method of combining wavelet transform with DGM(2,1)model can get a satisfactory prediction result.The noise in the original sequence is removed by wavelet transform,and the non-smooth original sequence is transformed into a relatively smooth new sequence.Then the new sequence of removing noise by wavelet transform is predicted by DGM(2,1)model.Based on the population data of Kunming from 2006 to 2014,the population data of Kunming from 2015 to 2019 are predicted and compared with grey GM(1,1)model and DGM(2,1)model.The results show that the average absolute percentage error of wavelet DGM(2,1)model is 0.15%,DGM(2,1)model is 0.79%,GM(1,1)model is 0.96%,the accuracy of wavelet DGM(2,1)model is higher than that of DGM(2,1)model and GM(1,1)model;The root mean square error and average absolute error of the wavelet DGM(2,1)model are lower than those of the grey GM(1,1)model and DGM(2,1)model.Taking the population of Kunming from 2006 to 2019 as the original sequence sample,the wavelet DGM(2,1)model is used to predict the population of 7.2307 million and 7.6656 million in 2025 and 2035.

关 键 词：小波变换 DGM(2 1) 预测 人口增长 

分 类 号：N941.5[自然科学总论—系统科学] C924.24[社会学—人口学]