建模序列数乘变换下的DDGM(1,1)模型参数特性
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摘要
为进一步揭示DDGM(1,1)模型在建模序列经数乘变换后的参数变化规律,文章采用参数包技术分析了该模型参数在系统特征序列经数乘变换前后的量化关系及该变换对其建模精度的影响程度。结果表明,DDGM(1,1)模型的建模精度与系统特征序列的数乘变换无关。利用数乘变换可在不改变该模型精度的前提下简化其建模程序。
In order to further reveal the parameter variation rule of DDGM(1,1) model after the scalar multiplication transformation of modeling sequence, this paper uses the parameter package technique to analyze the quantitative relationship of the model parameters before and after the scalar multiplication transformation of the system characteristic series, and the degree of the influence of the transformation on modeling accuracy. The results show that the modeling accuracy of the DDGM(1,1) model is independent of the scalar multiplication transformation of the system characteristic sequence, and that the transformation of scalar multiplication can be used to simplify the modeling program without changing the precision of the model.
In order to further reveal the parameter variation rule of DDGM(1,1) model after the scalar multiplication transformation of modeling sequence, this paper uses the parameter package technique to analyze the quantitative relationship of the model parameters before and after the scalar multiplication transformation of the system characteristic series, and the degree of the influence of the transformation on modeling accuracy. The results show that the modeling accuracy of the DDGM(1,1) model is independent of the scalar multiplication transformation of the system characteristic sequence, and that the transformation of scalar multiplication can be used to simplify the modeling program without changing the precision of the model.
引文
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[2]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002.
[3]Cui J,Ma H Y,Yuan C Q,et al.Novel Grey Verhulst Model and Its Prediction Accuracy[J].The Journal of Grey System,2015,27(2).
[4]Fariborz Rahimnia,Mahdi Moghadasian,Ebrahim Mashreghi.Application of Grey Theory Approach to Evaluation of Organizational Vision[J].Grey Systems:Theory and Application,2011,1(1).
[5]Hsieh C H,Liu C H,Hsiung K C,et al.Grey Temporal Error Concealment[J].Grey Systems:Theory and Application,2011,1(2).
[6]Wang Y H,Tang J R,Cao W B.Grey Prediction Model-based Food Security Early Warning Prediction[J].Grey Systems:Theory and Application,2011,2(1).
[7]Lin Y,Liu S F.A Systemic Analysis With Data[J].International Journal of General Systems,2000,29(6).
[8]Xiao X P,Deng J L.Parameter Characteristics of GM(0,N)Model Under Multiple Transformation[J].Systems Engineering and Electronic,2000,22(10).
[9]谢乃明,刘思峰.离散灰色模型的仿射特性研究[J].控制与决策,2008,23(2).
[10]Cui J,Liu S F,Zeng B,et al.A Novel Grey Forecasting Model and Its Optimization[J].Applied Mathematical Modelling,2013,37(6).
[11]Li X C.On Parameter in Grey Model GM(1,1)[J].The Joural of Grey System,1998,10(2).
[12]崔杰,刘思峰,曾波,谢乃明.灰色Verhulst预测模型的数乘特性[J].控制与决策,2013,28(4).
[13]熊萍萍,党耀国等.灰色Verhulst模型的参数特征研究[J].长春理工大学学报(自然科学版),2012,35(1).
[14]崔杰,刘思峰,赵磊.新型灰色Verhulst预测模型的参数特性[J].控制与决策,2015,30(11).
[15]谢乃明,刘思峰.离散GM(1,1)模型与灰色预测模型建模机理[J].系统工程理论与实践,2005,25(1).
[16]曾波,刘思峰.近似非齐次指数序列的DGM(1,1)直接建模法[J].系统工程理论与实践,2011,31(2).