摘要
初始序列的光滑度与级比偏差是影响GM(1,1)模型预测精度的重要因素,为了提高模型的预测精度,文章提出了初始序列基于指数函数与正切函数组合优化的GM(1,1)模型,通过理论证明了该种函数变换方式的光滑度大于指数函数变换光滑度且减小了级比偏差,并利用遗传算法智能搜索出变换函数中的核心参数,计算变换后的初始序列。以我国1990—2002年的客运量序列作为初始序列,基于指数函数与正切函数组合优化的GM(1,1)模型平均相对误差相较于基于指数函数变换、正切函数变换、正切函数与幂函数组合变换、反余弦函数变换的GM(1,1)模型预测平均相对误差最高可分别降低1.62%、0.07%、0.05%与0.03%。
The smoothness and class ratio dispersion of the initial sequence is an important factor affecting the prediction accuracy of GM(1,1)model.In order to improve the prediction accuracy of the model,this paper presents a GM(1,1)model of initial sequence optimization based on the combination of exponential function and tangent function.Firstly,the paper theoretically proves that the smoothness of the transformation is greater than that of the exponential function,with the class ratio dispersion reduced,and then uses the genetic algorithm to search out the core parameters of the transformation function and calculate the initial sequence after transformation.Finally,taking China's passenger transport volume from 1990 to 2002 as the initial sequence,the paper makes verification whose results show that the average relative error of GM(1,1)model based on the combination of exponential function and tangent function can be reduced by 1.62%,0.07%,0.05%and 0.03%,respectively,compared with GM(1,1)models based on exponential function transformation,tangent function transformation,combined transformation of tangent function and power function and inverse cosine function transformation.
作者
包旭
张山华
陈锦文
王珂
Bao Xu;Zhang Shanhua;Chen Jinwen;Wang Ke(Jiangsu Key Laboratory of Traffic and Transportation Security,Huai’an Jiangsu 223003,China;College of Transportation Science&Engineering,Nanjing Tech University,Nanjing 210000,China;Navigation Institute,Jimei University,Xiamen Fujian 361021,China)
出处
《统计与决策》
CSSCI
北大核心
2020年第10期45-50,共6页
Statistics & Decision
基金
国家自然科学基金资助项目(51308246)
住建部科技资助项目(2014-K5-013)
大学生创新创业训练计划项目(201811049052X)。
关键词
GM(1
1)模型
初始序列
光滑度
级比偏差
遗传算法
GM(1
1)model
initiation sequence
smoothness
class ratio dispersion
genetic algorithm
