The application of an optimized fractional order accumulated grey model with variable parameters in the total energy consumption of Jiangsu Province and the consumption level of Chinese residents

Dewang Li; Meilan Qiu; Jianming Jiang; Shuiping Yang; Dewang Li; Meilan Qiu; Jianming Jiang; Shuiping Yang

doi:10.3934/era.2022042

Electronic Research Archive

2022, Volume 30, Issue 3: 798-812. doi: 10.3934/era.2022042

Previous Article Next Article

Research article Special Issues

The application of an optimized fractional order accumulated grey model with variable parameters in the total energy consumption of Jiangsu Province and the consumption level of Chinese residents

1.
School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China
2.
School of Mathematics and Statistics, Baise University, Baise 533000, China

Academic Editor: Jingzhi Li

Received: 31 December 2021 Revised: 09 February 2022 Accepted: 16 February 2022 Published: 01 March 2022

Fractional order imply the idea of "in between", the grey model generated by fractional accumulation has better prediction and adaptability than that generated by first-order accumulation. General grey model of the differential equation of the left is a cumulative function derivative of time, in order to improve the adaptability of the model and prediction ability, general fractional order differential equation model is presented. In this paper, on the basis of the derivation of time $ t $ extensions to the derivation of $ {t^u} $, added a variable coefficient, and through the integral differential equation and tectonic background value. We establish an optimized fractional order cumulative grey model with variable parameters, i.e., optimized fractional order accumulated grey model (FOGM (1, 1)). By using the Particle swarm optimization (PSO) algorithm, we search for the order and variable parameters of the optimal fractional order. Then we apply the proposed model to predict the total energy consumption of Jiangsu province and the consumption level of Chinese residents. The results indicate that the proposed model has high fitting and prediction accuracy compared to other classical grey prediction models, such as grey model (GM (1, 1)), non-homogeneous grey model (NGM (1, 1)) and fractional order accumulated grey model (FGM (1, 1)). It also validates that the proposed model is a practical and promising model for forecasting the energy consumption as well as the consumption level of Chinese residents.
- FOGM (1, 1) model,
- variable parameter,
- PSO algorithm,
- prediction accuracy
Citation: Dewang Li, Meilan Qiu, Jianming Jiang, Shuiping Yang. The application of an optimized fractional order accumulated grey model with variable parameters in the total energy consumption of Jiangsu Province and the consumption level of Chinese residents[J]. Electronic Research Archive, 2022, 30(3): 798-812. doi: 10.3934/era.2022042

Related Papers:

Abstract

Fractional order imply the idea of "in between", the grey model generated by fractional accumulation has better prediction and adaptability than that generated by first-order accumulation. General grey model of the differential equation of the left is a cumulative function derivative of time, in order to improve the adaptability of the model and prediction ability, general fractional order differential equation model is presented. In this paper, on the basis of the derivation of time $ t $ extensions to the derivation of $ {t^u} $, added a variable coefficient, and through the integral differential equation and tectonic background value. We establish an optimized fractional order cumulative grey model with variable parameters, i.e., optimized fractional order accumulated grey model (FOGM (1, 1)). By using the Particle swarm optimization (PSO) algorithm, we search for the order and variable parameters of the optimal fractional order. Then we apply the proposed model to predict the total energy consumption of Jiangsu province and the consumption level of Chinese residents. The results indicate that the proposed model has high fitting and prediction accuracy compared to other classical grey prediction models, such as grey model (GM (1, 1)), non-homogeneous grey model (NGM (1, 1)) and fractional order accumulated grey model (FGM (1, 1)). It also validates that the proposed model is a practical and promising model for forecasting the energy consumption as well as the consumption level of Chinese residents.

References

[1]	K. C. Ho, K. Marie, Y. J. Song, Sequence-to-sequence deep learning model for building energy consumption prediction with dynamic simulation modeling, J. Build. Eng., 43 (2021), 102577. https://doi.org/10.1016/J.JOBE.2021.102577 doi: 10.1016/J.JOBE.2021.102577
[2]	R. Liu, Z. H. Wang, H. H. Chen, J. Yang, Research on energy consumption prediction based on machine learning, IOP Conf. Ser.: Earth Environ. Sci., 791 (2021), 012100. https://doi.org/10.1088/1755-1315/791/1/012100 doi: 10.1088/1755-1315/791/1/012100
[3]	N. M. M. Bendaoud, N. Farah, S. Ben Ahmed, Applying load profiles propagation to machine learning based electrical energy forecasting, Electr. Power Syst. Res., 203 (2022), 107635. https://doi.org/10.1016/J.EPSR.2021.107635 doi: 10.1016/J.EPSR.2021.107635
[4]	J. Feng, J. Yang, Y. Li, H. Wang, H. Ji, W. Yang, et al., Load forecasting of electric vehicle charging station based on grey theory and neural network, Energy Rep., 7 (2021), 487-492. https://doi.org/10.1016/J.EGYR.2021.08.015 doi: 10.1016/J.EGYR.2021.08.015
[5]	S. Ding, Z. Tao, H. H. Zhang, Y. Li, Forecasting nuclear energy consumption in China and America: An optimized structure-adaptative grey model, Energy, 239 (2022), 121928. https://doi.org/10.1016/J.ENERGY.2021.121928 doi: 10.1016/J.ENERGY.2021.121928
[6]	M. Y. Gao, H. L. Yang, Q. Z. Xiao, G. Mark, A novel method for carbon emission forecasting based on Gompertz's law and fractional grey model: Evidence from American industrial sector, Renewable Energy, 181 (2022), 803-819. https://doi.org/10.1016/J.RENENE.2021.09.072 doi: 10.1016/J.RENENE.2021.09.072
[7]	W. J. Zhou, J. Pan, H. H. Tao, S. Ding, L. Chen, X. Zhao, A novel grey seasonal model based on cycle accumulation generation for forecasting energy consumption in China, Comput. Ind. Eng., 163 (2022), 107725. https://doi.org/10.1016/J.CIE.2021.107725 doi: 10.1016/J.CIE.2021.107725
[8]	P. Xiong, K. Li, H. Shu, J. Wang, Forecast of natural gas consumption in the Asia-Pacific region using a fractional-order incomplete gamma grey model, Energy, 237 (2021), 121533. https://doi.org/10.1016/J.ENERGY.2021.121533 doi: 10.1016/J.ENERGY.2021.121533
[9]	H. F. Xiang, Grey correlation analysis and forecast of residents' income and consumption structure, Acad. J. Bus. Manage. 2 (2020), 6-14. https://doi.org/10.25236/AJBM.2020.020302 doi: 10.25236/AJBM.2020.020302
[10]	X. Yan, M. Y. Wu, Study of Shanghai residents tourism consumption structure based on the tourism engel coefficient, Bus. Manage. Res., 2 (2013), 136-148. https://doi.org/10.5430/ bmr.v2n4p136 doi: 10.5430/bmr.v2n4p136
[11]	J. L. Deng, Control problem of grey systems, Syst. Control Lett., 1 (1982), 288-294. https://doi.org/10.1016/S0167-6911(82)80025-X doi: 10.1016/S0167-6911(82)80025-X
[12]	F. P. Zhang, X. K. Liu, K. Wang, Prediction of postgraduate education scale in China based on grey model, Math. Pract. Theory, 49 (2019), 318-323. https://doi.org/CNKI:SUN:SSJS.0.2019-15-037
[13]	R. X. Suo, X. Y. Wang, J. Shen, Prediction of Chinese coal demand based on dynamic unbiased grey markov model, Math. Pract. Theory, 49 (2019), 179-186. https://doi.org/CNKI:SUN:SSJS. 0.2019-13-019
[14]	B. Wu, M. Xin, Z. D. Bo, Y. Wang, W. Cai, Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model, Renewable Energy, 140 (2019), 70-87. https://doi.org/10.1016/j.renene.2019.03.006 doi: 10.1016/j.renene.2019.03.006
[15]	J. L. Deng, Grey exponential law for accumulative generation, J. huazhong Univ. Sci. Technol., 15 (1987), 7-12. https://doi.org/10.13245/j.hust.1987.05.002 doi: 10.13245/j.hust.1987.05.002
[16]	Z. Yang, P. Ren, Y. G. Dang, Grey opposite-direction accumulated generating and optimization of GOM (1, 1) model, Syst. Eng.-Theory Pact., 29 (2009), 162-166. https://doi.org/CNKI:SUN:XTLL.0.2009-08-022
[17]	W. Y. Qian, Y. G. Dang, Y. M. Wang, GM (1, 1) Model Based on Weighting Accumulated Generating Operation and Its Application, Math. Pract. Theory, 39 (2009), 49--53. https://doi.org/CNKI:SUN:SSJS.0.2009-15-008
[18]	W. J. Zhou, H. R. Zhang, Y. G. Dang, Z. X. Wang, New information priority accumulation grey discrete model and its application, Chin. Manage. Sci., 25 (2017), 140-148. https://doi.org/10.16381/j.cnki.issn1003-207x.2017.08.015 doi: 10.16381/j.cnki.issn1003-207x.2017.08.015
[19]	L Wu, S Liu, L Yao, S Yan, D Liu, Grey system model with the fractional order accumulation, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), 1775-1785. https://doi.org/10.1016/j.cnsns.2012.11.017
[20]	N. M. Xie, S. F. Liu, Discrete grey forecasting model and its optimization, Appl. Math. Modell., 33 (2009), 1173-1186. https://doi.org/10.1016/j.apm.2008.01.011 doi: 10.1016/j.apm.2008.01.011
[21]	J. Cui, S. F. Liu, B. Zeng, N. M. Xie, A novel grey forecasting model and its optimization, Appl. Math. Modell., 37 (2013), 4399-4406. https://doi.org/10.1016/j.apm.2012.09.052 doi: 10.1016/j.apm.2012.09.052
[22]	Y. S. Chen, H. L. Chen, S. P. Chen, Forecasting of foreign exchange rates of Taiwan's major trading partners by novel nonlinear Grey Bernoulli model NGBM (1, 1), Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 1194-1204. https://doi.org/10.1016/j.cnsns.2006.08.008 doi: 10.1016/j.cnsns.2006.08.008
[23]	X. Liu, N. Xie, A nonlinear grey forecasting model with double shape parameters and its application, Appl. Math. Comput. 360 (2009), 203-212. https://doi.org/10.1016/j.amc. 2019.05.012 doi: 10.1016/j.amc.2019.05.012
[24]	W. A. Meng, W. A. Wei, L. F. Wu, Application of a new grey multivariate forecasting model in the forecasting of energy consumption in 7 regions of China, Energy, 243 (2022), 123024. https://doi.org/10.1016/j.energy.2021.123024 doi: 10.1016/j.energy.2021.123024
[25]	B. Zeng, H. Li, Prediction of coalbed methane production in China based on an optimized grey system model, Energy Fuels, 35 (2021), 4333-4344. https://doi.org/10.1021/acs.energyfuels.0c04195 doi: 10.1021/acs.energyfuels.0c04195
[26]	J. Kennedy, R. Eberhart, Particle swarm optimization, in Icnn95-international Conference on Neural Networks IEEE, 1995.
[27]	Y. N. Yang, Y. Liu, C. Wen, H. Li, J. F. Wang, Efficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model, Electron. Res. Arch., 30 (2022), 440-458. https://doi.org/10.3934/era.2022023 doi: 10.3934/era.2022023

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)