Improvement and application of GM(1, 1) model based on multivariable dynamic optimization

doi:10.23919/JSEE.2020.000024

Abstract

Abstract:

For the classical GM(1, 1) model, the prediction accuracy is not high, and the optimization of the initial and background values is one-sided. In this paper, the Lagrange mean value theorem is used to construct the background value as a variable related to $\boldsymbol k$. At the same time, the initial value is set as a variable, and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error (MRE). Combined with the domestic natural gas annual consumption data, the classical model and the improved GM(1, 1) model are applied to the calculation and error comparison respectively. It proves that the improved model is better than any other models.

Key words: grey prediction, GM(1, 1) model, background value, grey system theory

Yuhong WANG, Jie LU. Improvement and application of GM(1, 1) model based on multivariable dynamic optimization[J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 593-601.

Figures/Tables 7

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Year	Raw data	GM(1,1)		AMGM		FAGM		The proposed model
Year	Raw data	FE	RE	FE	RE	FE	RE	FE	RE
2005	48.2	-	-	-	-	-	-	-	-
2006	59.3	71.49	0.21	63.23	0.06	70.16	0.18	63.94	0.08
2007	73.0	80.19	0.10	72.50	0.01	78.70	0.07	73.16	0.00
2008	84.1	89.94	0.07	83.12	0.01	88.28	0.05	83.73	0.00
2009	92.6	100.89	0.09	95.30	0.03	99.02	0.07	95.81	0.03
2010	111.2	113.17	0.02	109.26	0.02	111.07	0.00	109.63	0.01
2011	137.1	126.94	0.07	125.27	0.08	124.59	0.09	125.45	0.08
2012	150.9	142.38	0.06	143.63	0.05	139.75	0.07	143.55	0.05
2013	171.9	159.71	0.07	164.67	0.04	156.76	0.09	164.26	0.04
2014	188.4	179.14	0.05	188.80	0.01	175.83	0.07	187.96	0.00
2015	197.3	200.94	0.02	216.47	0.09	197.23	0.00	215.09	0.09
2016	205.8	225.40	0.10	248.18	0.21	221.23	0.07	246.12	0.19
MRE		-	0.080	-	0.056	-	0.071	-	0.050

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