摘要
为提高传统灰色预测模型GM(1,1)的预测精度,提出了一种灰色残差修正模型REGM(1,1)。首先利用GM(1,1)模型生成的响应函数序列与原始数据累加序列之间的残差,构建残差累加序列,并基于此推导出白化微分方程作为响应函数式。然后利用GM(1,1)模型的响应函数值对残差预测函数值进行修正,得到残差修正序列,最后通过累减还原获得预测结果。2006—2017年美国电力生产指数的实证研究表明,REGM(1,1)模型的平均残差和平均相对误差分别为4.083 9×10^(-4)与3.712 2×10^(-6),平均相对误差相较于GM(1,1)模型降低了99.99%,较傅里叶残差修正模型FGM(1,1)降低了97.93%,预测精度和稳健性显著提升。REGM(1,1)模型通过分析并修正残差累加序列,提升了对未来数据变动的预测能力,在能源管理、经济预测、工业过程优化等领域具有重要应用价值,尤其可为电力系统调度、行业能耗监测等场景的精准预测与决策支持提供新方法。
To enhance the prediction accuracy of the traditional grey prediction model GM(1,1),a grey residual correction model REGM(1,1)was proposed in this paper.First,the residuals between the response function sequence generated by GM(1,1)and the cumulative sequence of the original data were used to construct a residual cumulative sequence,and based on this,the whitening differential equation was derived as the response function formula.Then,the response function values of GM(1,1)were used to adjust the residual prediction function values,yielding a residual-corrected sequence.Final predictions were made through cumulative reduction.Empirical analysis of the U.S.electricity production index from 2006 to 2017 demonstrated that REGM(1,1)achieves average residuals and relative errors of 4.0839×10^(-4) and 3.7122×10^(-6),respectively.Compared with GM(1,1)and the Fourier residual-corrected model FGM(1,1),the average relative errors are reduced by 99.99%,and 97.93%,respectively,confirming significant accuracy and robustness improvements.The REGM(1,1)model can improve the prediction of future data changes by analysing and correcting the residual cumulative series,and holds substantial application value in fields of energy management,economic forecasting,and industrial process optimization,particularly offering a novel methodology for precise prediction and decision-making support in areas of power system dispatching and cross-sector energy consumption monitoring.
作者
何盈杉
肖利芳
HE Yingshan;XIAO Lifang(School of Computer Science and Engineering,Wuhan Institute of Technology,Wuhan 430205,China;Hubei Key Laboratory of Intelligent Robot(Wuhan Institute of Technology),Wuhan 430205,China)
出处
《武汉工程大学学报》
2025年第6期647-652,共6页
Journal of Wuhan Institute of Technology
基金
湖北省教育厅计划项目(B2021083)
武汉工程大学教研资助项目(X2022028)。
