武汉工程大学学报2025，Vol.47Issue(6)：647-652,6.DOI:10.19843/j.cnki.CN42-1779/TQ.202406017
一种灰色残差修正模型的算法设计
Algorithm design of a grey residual correction model
摘要
Abstract
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.关键词
GM(1,1)模型/残差/响应函数/灰色预测Key words
GM(1,1)model/residual/response function/grey prediction分类
自科综合引用本文复制引用
何盈杉,肖利芳..一种灰色残差修正模型的算法设计[J].武汉工程大学学报,2025,47(6):647-652,6.基金项目
湖北省教育厅计划项目(B2021083) （B2021083）
武汉工程大学教研资助项目(X2022028) （X2022028）
