A self-adaptive grey forecasting model and its application

doi:10.23919/JSEE.2022.000061

Abstract

Abstract:

GM(1,1) models have been widely used in various fields due to their high performance in time series prediction.However, some hypotheses of the existing GM(1,1) model family may reduce their prediction performance in some cases. To solve this problem, this paper proposes a self-adaptive GM(1,1) model, termed as SAGM(1,1) model, which aims to solve the defects of the existing GM (1,1) model family by deleting their modeling hypothesis. Moreover, a novel multi-parameter simultaneous optimization scheme based on firefly algorithm is proposed, the proposed multi-parameter optimization scheme adopts machine learning ideas, takes all adjustable parameters of SAGM(1,1) model as input variables, and trains it with firefly algorithm. And Sobol’ sensitivity indices are applied to study global sensitivity of SAGM(1,1) model parameters, which provides an important reference for model parameter calibration. Finally, forecasting capability of SAGM(1,1) model is illustrated by Anhui electricity consumption dataset. Results show that prediction accuracy of SAGM(1,1) model is significantly better than other models, and it is shown that the proposed approach enhances the prediction performance of GM(1,1) model significantly.

Key words: grey forecasting model, GM(1,1) model, firefly algorithm, Sobol’ sensitivity indices, electricity consumption prediction

Xiaozhong TANG, Naiming XIE. A self-adaptive grey forecasting model and its application[J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 665-673.

Figures/Tables 6

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Parameter	First-order sensitivity	Total-order sensitivity
Background-value coefficient $ \varepsilon $	?0.000 04	0.000 19
Accumulation order number γ	0.012 97	0.057 77
Dynamic weighting parameter $ \lambda $	0.424 82	0.444 35
Time input parameter $ {t}_{0} $	0.495 36	0.664 77

Parameter	Value
$ {\beta }_{0} $	1
$ \mathrm{\alpha } $	0.01
$ \mathrm{\gamma } $	1
Population size (maximum)	100
Number of iterations (maximum)	100

Year	Actual data	GM(1,1)	DGM(1,1)	GM(1,1,x⁽¹⁾(n))	NSGM(1,1) λ = 0.149 1 t_o = 10.055 4	FGM(1,1) γ = 0.873 5	SAGM(1,1) ? = 0.589 5 γ = 0.956 5 λ = 0.269 8 t_o = 7.599 0
2010	1 077.92	－	－	－	－	－	－
2011	1 221.19	1 258.263 6	1 259.136 2	1 258.594 0	1 246.088 4	1 213.424 5	1 248.598 0
2012	1 361.10	1 353.556 3	1 354.467 2	1 353.908 0	1 340.459 4	1 348.057 2	1 360.954 5
2013	1 528.07	1 456.065 8	1 457.015 9	1 456.440 1	1 441.977 4	1 470.820 2	1 472.185 8
2014	1 585.18	1 566.338 7	1 567.328 7	1 566.737 1	1 551.183 8	1 589.519 0	1 586.707 7
2015	1 639.79	1 684.963 0	1 685.993 4	1 685.387 0	1 668.660 8	1 707.817 9	1 706.481 9
2016	1 794.98	1 812.571 1	1 813.642 4	1 813.022 2	1 795.034 8	1 827.773 4	1 832.732 3
2017	1 921.48	1 949.843 4	1 950.955 9	1 950.323 4	1 930.979 5	1 950.716 4	1 966.396 9
2018	2 135.07	2 097.511 8	2 098.665 6	2 098.022 4	2 077.219 9	2 077.609 6	2 108.294 0
MAPE/%		2.057 6	2.058 4	2.058 1	2.037 7	1.975 3	1.971 3
RMSE		37.973 8	37.961 2	37.965 2	41.659 4	40.906 1	37.503 4
MAE		33.018 6	33.028 8	33.024 9	32.737 9	33.739 4	32.637 8
2019	2 300.68	2 256.363 7	2 257.558 7	2 256.906 8	2 234.535 5	2 209.214 7	2 259.195 3
MAPE/%		1.926 2	1.874 3	1.902 6	2.875	3.9756	1.803 1
RMSE		44.316 3	43.121 3	43.773 2	66.144 5	91.465 3	41.484 7
MAE		44.316 3	43.121 3	43.773 2	66.144 5	91.465 3	41.484 7

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