基于最小二乘法的优化GM(1,1)模型及应用  

Optimized GM(1,1)model and application based on least square method

作　　者：陈传玺[1] 陈慧敏 宋韶君 CHEN Chuanxi;CHEN Huimin;SONG Shaojun(Beijing Institute of Economics and Management,Beijing 100102)

机构地区：[1]北京经济管理职业学院,北京100102

出　　处：《自动化与仪器仪表》2024年第8期23-27,共5页Automation & Instrumentation

摘　　要：为了更准确地捕捉和预测经济动态,特别是城市交通领域的发展趋势。以经典的GM(1,1)模型为基础,利用最小二乘法重构样本数据和背景值权重,提出了一种基于最小二乘法的优化GM(1,1)模型,并将该模型应用于城市交通指标“私人汽车拥有量”的数据拟合和预测中,拟合值的平均相对误差由1.73%减小到0.4%,预测值的平均相对误差由9.94%减小到3.85%。结果表明,在满足灰色建模准指数条件的前提下,新模型算法能够达到拟合序列在最小二乘意义下的最优状态,可为相关领域的研究和应用提供一定的技术支持。In order to more accurately capture and predict economic trends,especially in the field of urban transportation,this paper is based on the classic GM(1,1)model,uses the least squares method to reconstruct sample data and background value weights,optimizes and innovates the GM(1,1)model,and proposes an optimized GM(1,1)model based on the least squares method,and applies the model to the data fitting and prediction of the urban transportation indicator“private car ownership”.It can be seen from the specific example that the average relative error of the fitted value is reduced from 1.73%to 0.4%,and the average relative error of the predicted value is reduced from 9.94%to 3.85%.The results show that,under the premise of meeting the quasi exponential conditions of grey modeling,the new model algorithm can achieve the optimal state of the fitting sequence in the least squares sense,which can provide certain technical support for research and application in related fields.

关 键 词：GM(1 1)模型 最小二乘法 私人汽车拥有量 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]