A self-adaptive grey forecasting model and its application

doi:10.23919/JSEE.2022.000061

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (3): 665-673.doi: 10.23919/JSEE.2022.000061

收稿日期:2021-02-15 出版日期:2022-06-18 发布日期:2022-06-24

A self-adaptive grey forecasting model and its application

Xiaozhong TANG^1,²(), Naiming XIE^1,*()

¹ College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
² Department of Industry and Finance, Huangshan Vocational and Technical College, Huangshan 245000, China

Received:2021-02-15 Online:2022-06-18 Published:2022-06-24
Contact: Naiming XIE E-mail:tangxz1985@163.com;xienaiming@nuaa.edu.cn
About author:|TANG Xiaozhong was born in 1985. He received his B.S. degree from Huangshan University in 2008, and M.S. degree from Shenyang University of Technology in 2012. Now, he is an associate professor at Huang shan Vocational and Technical College. He has been pursuing his Ph.D. degree in Nanjing University of Aeronautics and Astronautics since 2018. His research interests include grey system theory and prediction modeling algorithm. E-mail: tangxz1985@163.com||XIE Naiming was born in 1981. He received his B.S., M.S., and Ph.D. degrees in grey systems theory from Nanjing University of Aeronautics and Astronautics (NUAA). Now he is a professor in the College of Economics and Management of NUAA and an associate editor of Grey Systems: Theory and Application. His research interests include Grey Systems theory, production scheduling, and control. E-mail: xienaiming@nuaa.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (72171116;71671090), the Fundamental Research Funds for the Central Universities (NP2020022), the Key Research Projects of Humanities and Social Sciences in Anhui Education Department (SK2021A1018), and Qinglan Project for Excellent Youth or Middle-aged Academic Leaders in Jiangsu Province, China

摘要/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

. [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 665-673.

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.

图/表 6

参考文献 49

1	DENG J L Control problems of grey systems. Systems and Control Letters, 1982, 1 (5): 288- 294. doi: 10.1016/S0167-6911(82)80025-X
2	LIU S F, YANG Y J, FORREST J. Grey data analysis: methods, models and applications. Berlin: Springer, 2016.
3	XIE N M, WANG R Z A historic review of grey forecasting models. Journal of Grey System, 2017, 29 (4): 1- 29.
4	TANG X Z, XIE N M Research on the evaluation of tourism development potential of tea intangible cultural heritage based on grey clustering. Grey Systems: Theory and Application, 2019, 9 (3): 295- 304.
5	XIE N M, LIU S F Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model. Journal of Systems Engineering and Electronics, 2015, 26 (1): 96- 102. doi: 10.1109/JSEE.2015.00013
6	HSU L C Using improved grey forecasting models to forecast the output of opto-electronics industry. Expert Systems with Applications, 2011, 38 (11): 13879- 13885.
7	TAN G J The grey forecasting method of life test data of electronic equipments. Systems Engineering and Electronics, 2001, 23 (9): 102- 104.
8	OU S L Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm. Computers and Electronics in Agriculture, 2012, 85, 33- 39. doi: 10.1016/j.compag.2012.03.007
9	XIE N M, PEARMAN A D Forecasting energy consumption in China following instigation of an energy-saving policy. Natural Hazards, 2014, 74 (2): 639- 659. doi: 10.1007/s11069-014-1200-x
10	XIE N M, YUAN C Q, YANG Y J Forecasting China’s energy demand and self-sufficiency rate by grey forecasting model and Markov model. International Journal of Electrical Power and Energy Systems, 2015, 66, 1- 8. doi: 10.1016/j.ijepes.2014.10.028
11	WANG Y H, LU J Improvement and application of GM(1, 1) model based on multivariable dynamic optimization. Journal of Systems Engineering and Electronics, 2020, 31 (3): 593- 601. doi: 10.23919/JSEE.2020.000024
12	TANG X Z, XIE N M, HU A Q. Forecasting annual foreign tourist arrivals to China by incorporating firefly algorithm into fractional non-homogenous discrete grey model. Kybernetes, 2021. DOI:10.1108/K-11-2020-0787.
13	SUN X, SUN W S, WANG J Z, et al Using a Grey-Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tourism Management, 2016, 52, 369- 379. doi: 10.1016/j.tourman.2015.07.005
14	HU Y C, JIANG P, LEE P Forecasting tourism demand by incorporating neural networks into Grey-Markov models. The Journal of the Operational Research Society, 2019, 70 (1): 12- 20. doi: 10.1080/01605682.2017.1418150
15	ZHOU W, HE J M Generalized GM(1, 1) model and its application in forecasting of fuel production. Applied Mathematical Modelling, 2013, 37 (9): 6234- 6243. doi: 10.1016/j.apm.2013.01.002
16	XIAO X P, DUAN H M, WEN J H A novel car-following inertia gray model and its application in forecasting short-term traffic flow. Applied Mathematical Modelling, 2020, 87, 546- 570.
17	DANG Y G, LIU S F, CHEN K J The GM models that x(n) be taken as initial value . Kybernetes, 2004, 33 (2): 247- 254. doi: 10.1108/03684920410514175
18	WANG Y H, DANG Y G, LI Y Q, et al An approach to increase prediction precision of GM(1, 1) model based on optimization of the initial condition. Expert Systems with Applications, 2010, 37 (8): 5640- 5644. doi: 10.1016/j.eswa.2010.02.048
19	XIONG P P, DANG Y G, YAO T X, et al Optimal modeling and forecasting of the energy consumption and production in China. Energy, 2014, 77, 623- 634. doi: 10.1016/j.energy.2014.09.056
20	DING S A novel self-adapting intelligent grey model for forecasting China’s natural-gas demand. Energy, 2018, 162, 393- 407. doi: 10.1016/j.energy.2018.08.040
21	ZHU X Y, DANG Y G, DING S Using a self-adaptive grey fractional weighted model to forecast Jiangsu ’s electricity consumption in China. Energy, 2020, 190, 116417. doi: 10.1016/j.energy.2019.116417
22	ZENG B, LI C Improved multi-variable grey forecasting model with a dynamic background-value coefficient and its application. Computers & Industrial Engineering, 2018, 118, 278- 290.
23	ZENG X Y, YAN S L, HE F L, et al Multi-variable grey model based on dynamic background algorithm for forecasting the interval sequence. Applied Mathematical Modeling, 2020, 80, 99- 114. doi: 10.1016/j.apm.2019.11.032
24	LIN Y H, LEE P C, CHANG T P Adaptive and high-precision grey forecasting model. Expert Systems with Applications, 2009, 36 (6): 9658- 9662. doi: 10.1016/j.eswa.2008.12.009
25	MA X, WU W Q, ZHANG Y Y Improved GM(1, 1) model based on Simpson formula and its applications. Journal of Grey System, 2019, 31 (4): 33- 46.
26	WU L F, LIU S F, YAO L G, et al Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation, 2013, 18 (7): 1775- 1785. doi: 10.1016/j.cnsns.2012.11.017
27	WU L F, LIU S F, CUI W, et al Non-homogenous discrete grey model with fractional-order accumulation. Neural Computing and Applications, 2014, 25 (5): 1215- 1221. doi: 10.1007/s00521-014-1605-1
28	MAO S H, GAO M Y, XIAO X P, et al A novel fractional grey system model and its application. Applied Mathematical Modelling, 2016, 40, 5063- 5076. doi: 10.1016/j.apm.2015.12.014
29	MA X, XIE M, WU W Q, et al The novel fractional discrete multivariate grey system model and its applications. Applied Mathematical Modelling, 2019, 70, 402- 424. doi: 10.1016/j.apm.2019.01.039
30	TSAUR R Forecasting analysis by using fuzzy grey regression model for solving limited time series data. Soft Computing, 2008, 12 (11): 1105- 1113. doi: 10.1007/s00500-008-0278-z
31	JIA Z, ZHOU Z F, ZHANG H J, et al Forecast of coal consumption in Gansu province based on Grey-Markov chain model. Energy, 2020, 199, 117444. doi: 10.1016/j.energy.2020.117444
32	HSU Y T, LIU M C, YEH J, et al Forecasting the turning time of stock market based on Markov-Fourier grey model. Expert Systems with Applications, 2009, 36 (4): 8597- 8603. doi: 10.1016/j.eswa.2008.10.075
33	HU Y C Forecasting tourism demand using fractional grey prediction models with Fourier series. Annals of Operations Research, 2021, 300 (2): 467- 491. doi: 10.1007/s10479-020-03670-0
34	FAN C, JIAO Y J, GUO Y F, et al Forecasting the Chinese grain yield using hybrid ARIMA and error-corrected grey model base on the wavelet transform. Journal of Grey System, 2019, 31 (4): 97- 110.
35	YAO T, WANG Z H Crude oil price prediction based on LSTM network and GM (1, 1) model. Grey Systems: Theory and Application, 2020, 11 (1): 80- 94. doi: 10.1108/GS-03-2020-0031
36	MOONCHAI S, CHUTSAGULPROM N Short-term forecasting of renewable energy consumption: augmentation of a modified grey model with a Kalman filter. Applied Soft Computing, 2020, 87, 105994. doi: 10.1016/j.asoc.2019.105994
37	LI K W, LIU L, ZHAI J N, et al The improved grey model based on particle swarm optimization algorithm for time series prediction. Engineering Applications of Artificial Intelligence, 2016, 55, 285- 291. doi: 10.1016/j.engappai.2016.07.005
38	YANG X S. Nature-inspired metaheuristic algorithms. Cambridge: Luniver Press, 2008.
39	XIAO L Y, SHAO W, LIANG T L, et al A combined model based on multiple seasonal patterns and modified firefly algorithm for electrical load forecasting. Applied Energy, 2016, 167, 135- 153. doi: 10.1016/j.apenergy.2016.01.050
40	IBRAHIM I A, KHATIB T A novel hybrid model for hourly global solar radiation prediction using random forests technique and firefly algorithm. Energy Conversion and Management, 2017, 138, 413- 425. doi: 10.1016/j.enconman.2017.02.006
41	SOBOL’I M. Sensitivity analysis for non-linear mathematical models. Mathematical Modelling and Computational Experiment, 1993, 1(4): 407–414.
42	ZHANG X Y, TRAME M N, LESKO L J, et al Sobol sensitivity analysis: a tool to guide the development and evaluation of systems pharmacology models. CPT Pharmacometrics & Systems Pharmacology, 2015, 4, 69- 79.
43	NARIMAN N A, HUSSAIN R R, MOHAMMAD I I, et al. Global sensitivity analysis of certain and uncertain factors for a circular tunnel under seismic action. Frontiers of Structural and Civil Engineering, 2019, 13: 1289−1300.
44	XIE N M, LIU S F Discrete grey forecasting model and its optimization. Applied Mathematical Modelling, 2009, 33 (2): 1173- 1186. doi: 10.1016/j.apm.2008.01.011
45	Anhui Statistical Bureau, NBS Survey Office in Anhui. Anhui Statistical Yearbook-2013. Beijing: China Statistics Press,2013. (in Chinese)
46	Anhui Statistical Bureau, NBS Survey Office in Anhui. Anhui Statistical Yearbook-2015. Beijing: China Statistics Press,2015. (in Chinese)
47	Anhui Statistical Bureau, NBS Survey Office in Anhui. Anhui Statistical Yearbook-2017. Beijing: China Statistics Press,2017. (in Chinese)
48	Anhui Statistical Bureau, NBS Survey Office in Anhui. Anhui Statistical Yearbook-2019. Beijing: China Statistics Press,2019. (in Chinese)
49	Anhui Statistical Bureau, NBS Survey Office in Anhui. Anhui Statistical Yearbook-2020. Beijing: China Statistics Press,2020. (in Chinese)

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

A self-adaptive grey forecasting model and its application

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