Abstract
Under the background of a green, low carbon economy, it is significant to accurately estimate the future CO2 emissions of countries with significant CO2 emissions for developing the world’s green economy. A new Nonlinear Grey Bernoulli and BP neural network combined model (BP-ONGBM (1,1) model) have been proposed to study the CO2 emissions of China, the USA, the European Union, India and Japan. Firstly, the Particle Swarm Optimization (PSO) algorithm is optimized using the Artificial Fish Swarm Algorithm (AFSA). Then, the background value of the ONGBM (1,1) model is dynamically optimized. Based on the linearization of the model, the time response function is derived. Then, the ONGBM (1,1) model is combined with the BP neural network model. An improved PSO algorithm determines the combined weight and the background value coefficient. Finally, according to the observation data from 2010 to 2021 in the Emissions Database for Global Atmospheric Research 2022, the model is established to calculate the CO2 emissions of the selected countries from 2022 to 2026 and compared with the prediction results provided by multiple competitive models. The empirical application shows that the proposed BP-ONGBM (1,1) model is significantly better than other competitive models.
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References
Akay D, Atak M (2007) Grey prediction with rolling mechanism for electricity demand forecasting of Turkey. Energy 32(9):1670–1675. https://doi.org/10.1016/j.energy.2006.11.014
Chen CI (2008) Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos, Solitons Fractals 37(1):278–287. https://doi.org/10.1016/j.chaos.2006.08.024
Chen CI, Chen HL, Chen SP (2008) 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(6):1194–1204. https://doi.org/10.1016/j.cnsns.2006.08.008
Chen YY, Chen GW, Chiou AH, Chen SH (2017) Forecasting nonlinear time series using an adaptive nonlinear grey Bernoulli model: cases of energy consumption. J Grey Syst 29(4):75–93
Chen K, Laghrouche S, Djerdir A (2019) Degradation prediction of proton exchange membrane fuel cell based on grey neural network model and particle swarm optimization. Energy Convers Manage 195:810–818. https://doi.org/10.1016/j.enconman.2019.05.045
Chen L, Ding Y, Liu B, Wu S, Wang Y, Pan H (2022) Remaining useful life prediction of lithium-ion battery using a novel particle filter framework with grey neural network. Energy. https://doi.org/10.1016/j.energy.2021.122581
Deng JL (1989) Introduction to grey system theory. J Grey Syst 1(1):1–24
Ding S (2019) A novel discrete grey multivariable model and its application in forecasting the output value of China’s high-tech industries. Comput Ind Eng 127:749–760. https://doi.org/10.1016/j.cie.2018.11.016
Ding S, Xu N, Ye J, Zhou W, Zhang X (2020) Estimating Chinese energy-related CO2 emissions by employing a novel discrete grey prediction model. J Clean Prod 259:120793. https://doi.org/10.1016/j.jclepro.2020.120793
Ding Y, Chen Z, Zhang H, Wang X, Guo Y (2022) A short-term wind power prediction model based on CEEMD and WOA-KELM. Renew Energy 189:188–198. https://doi.org/10.1016/j.renene.2022.02.108
Eberhart R, & Kennedy, J (1995, October) A new optimizer using particle swarm theory. In MHS’95. In: Proceedings of the sixth international symposium on micro machine and human science (pp 39–43). IEEE. doi:https://doi.org/10.1109/MHS.1995.494215
Entezari A, Bahari M, Aslani A, Ghahremani S, Pourfayaz F (2021) Systematic analysis and multi-objective optimization of integrated power generation cycle for a thermal power plant using Genetic algorithm. Energy Convers Manag 241:114309. https://doi.org/10.1016/j.enconman.2021.114309
He Z, Liu T, Liu H (2022) Improved particle swarm optimization algorithms for aerodynamic shape optimization of high-speed train. Adv Eng Softw 173:103242. https://doi.org/10.1016/j.advengsoft.2022.103242
He J, Mao S, Ng AK (2023) Neural computing for grey Richards differential equation to forecast traffic parameters with various time granularity. Neurocomputing. https://doi.org/10.1016/j.neucom.2023.126394
Hsu LC (2010) A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Syst Appl 37(6):4318–4323. https://doi.org/10.1016/j.eswa.2009.11.068
Hsu CC, Chen CY (2003) Applications of improved grey prediction model for power demand forecasting. Energy Convers Manage 44(14):2241–2249. https://doi.org/10.1016/S0140-6701(03)92466-0
Huang H, Tao Z, Liu J, Cheng J, Chen H (2021) Exploiting fractional accumulation and background value optimization in multivariate interval grey prediction model and its application. Eng Appl Artif Intell 104:104360. https://doi.org/10.1016/j.engappai.2021.104360
International Energy Agency (IEA), 2022. Global Energy Review: CO2 Emissions in 2021. https://www.iea.org/data-and-statistics/data-product/global-energy-review-co2-emissions-in-2021.
Kong L, Ma X (2018) Comparison study on the nonlinear parameter optimization of nonlinear grey Bernoulli model (NGBM (1, 1)) between intelligent optimizers. Grey Syst: Theory Appl. https://doi.org/10.1108/GS-01-2018-0005
Li Z, Nguyen TT, Chen S, Truong TK (2015) A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems. Appl Soft Comput 35:525–540. https://doi.org/10.1016/j.asoc.2015.06.036
Li M, Chen H, Shi X, Liu S, Zhang M, Lu S (2019) A multi-information fusion “triple variables with iteration” inertia weight PSO algorithm and its application. Appl Soft Comput 84:105677. https://doi.org/10.1016/j.asoc.2019.105677
Li J, Han P, Ren X, Hu J, Chen L, Shang S (2021a) Sequence labeling with meta-learning. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/tkde.2021.311846932
Li J, Shang S, Chen L (2021b) Domain generalization for named entity boundary detection via metalearning. IEEE Trans Neural Netw Learn Syst 32(9):3819–3830. https://doi.org/10.1109/tnnls.2020.3015912
Li N, Wang J, Wu L, Bentley Y (2021c) Predicting monthly natural gas production in China using a novel grey seasonal model with particle swarm optimization. Energy 215:119118. https://doi.org/10.1016/j.energy.2020.119118
Li X, Zhang Z, Xu D, Wu C, Li J, Zheng Y (2021d) A prediction method for animal-derived drug resistance trend using a grey-BP neural network combination model. Antibiotics (basel). https://doi.org/10.3390/antibiotics10060692
Li J, Chiu B, Feng S, Wang H (2022) Few-shot named entity recognition via meta-learning. IEEE Trans Knowl Data Eng 34(9):4245–4256. https://doi.org/10.1109/tkde.2020.3038670
Liu X, Moreno B, García AS (2016a) A grey neural network and input–output combined forecasting model. Primary energy consumption forecasts in Spanish economic sectors. Energy 115:1042–1054. https://doi.org/10.1016/j.energy.2016.09.017
Liu S, Yang Y, Xie N, Forrest J (2016b) New progress of grey system theory in the new millennium. Grey Syst: Theory Appl. https://doi.org/10.1108/GS-09-2015-0054
Ma X, Hu YS, Liu ZB (2017) A novel kernel regularized nonhomogeneous grey model and its applications. Commun Nonlinear Sci Numer Simul 48:51–62. https://doi.org/10.1016/j.cnsns.2016.12.017
Pao HT, Fu HC, Yu HC (2013) Forecasting Russian renewable, nuclear, and total energy consumption using improved nonlinear grey Bernoulli model. Int J Comput Sci Issues (IJCSI) 10(1):689
Pourpanah F, Wang R, Lim CP, Wang XZ, Yazdani D (2023) A review of artificial fish swarm algorithms: recent advances and applications. Artif Intell Rev 56(3):1867–1903. https://doi.org/10.1007/s10462-022-10214-4
Şahin U (2020) Projections of Turkey’s electricity generation and installed capacity from total renewable and hydro energy using fractional nonlinear grey Bernoulli model and its reduced forms. Sustain Prod Consum 23:52–62. https://doi.org/10.1016/j.spc.2020.04.004
Wang ZX, Li Q (2019) Modelling the nonlinear relationship between CO2 emissions and economic growth using a PSO algorithm-based grey Verhulst model. J Clean Prod 207:214–224. https://doi.org/10.1016/j.jclepro.2018.10.010
Wang ZX, Hipel KW, Wang Q, He SW (2011) An optimized NGBM (1, 1) model for forecasting the qualified discharge rate of industrial wastewater in China. Appl Math Model 35(12):5524–5532. https://doi.org/10.1016/j.apm.2011.05.022
Wang X, Wu YJ, Wang RJ, Wei YY, Gui YM (2018) Gray BP neural network based prediction of rice protein interaction network. Clust Comput 22(S2):4165–4171. https://doi.org/10.1007/s10586-017-1663-0
Wang K, Zhuang X, Zhao X, Wu W, Liu B (2020) Roof pressure prediction in coal mine based on grey neural network. IEEE Access 8:117051–117061. https://doi.org/10.1109/access.2020.3001762
Wang Y, Nie R, Chi P, Ma X, Wu W, Guo B, Zhang Y (2022a) A novel fractional structural adaptive grey Chebyshev polynomial Bernoulli model and its application in forecasting renewable energy production of China. Expert Syst Appl 210:118500. https://doi.org/10.1016/j.eswa.2022.118500
Wang Y, Chi P, Nie R, Ma X, Wu W, Guo B (2022b) Self-adaptive discrete grey model based on a novel fractional order reverse accumulation sequence and its application in forecasting clean energy power generation in China. Energy 253:124093. https://doi.org/10.1016/j.energy.2022.124093
Wei B, Xie N, Yang L (2020) Understanding cumulative sum operator in grey prediction model with integral matching. Commun Nonlinear Sci Numer Simul 82:105076. https://doi.org/10.1016/j.cnsns.2019.105076
Wu CY, Jin T (1993) Forecasting methods for industry and business. Comput Ind Eng 25(1–4):73–76. https://doi.org/10.1016/0360-8352(93)90224-L
Wu WZ, Zhang T, Zheng C (2019) A novel optimized nonlinear grey Bernoulli model for forecasting China’s GDP. Complexity 2019:1–10. https://doi.org/10.1155/2019/1731262
Wu W, Ma X, Zeng B, Lv W, Wang Y, Li W (2020) A novel Grey Bernoulli model for short-term natural gas consumption forecasting. Appl Math Model 84:393–404. https://doi.org/10.1016/j.apm.2020.04.006
Xiao Q, Shan M, Gao M, Xiao X, Goh M (2020) Parameter optimization for nonlinear grey Bernoulli model on biomass energy consumption prediction. Appl Soft Comput 95:106538. https://doi.org/10.1016/j.asoc.2020.106538
Yao X, Mao S (2023) Electric supply and demand forecasting using seasonal grey model based on PSO-SVR. Grey Syst: Theory Appl 13(1):141–171. https://doi.org/10.1108/GS-10-2021-0159
Zeng B, Tong M, Ma X (2020) A new-structure grey Verhulst model: development and performance comparison. Appl Math Model 81:522–537. https://doi.org/10.1016/j.apm.2020.01.014
Zhou W, Pei L (2020) The grey generalized Verhulst model and its application for forecasting Chinese pig price index. Soft Comput 24(7):4977–4990. https://doi.org/10.1007/s00500-019-04248-0
Zhou J, Fang R, Li Y, Zhang Y, Peng B (2009) Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Appl Math Comput 207(2):292–299. https://doi.org/10.1016/j.amc.2008.10.045
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 71801060, 72061007, 71801085), Innovation Project of GUET Graduate Education (Grant Nos. 2023YCXS114) and the Innovation and Entrepreneurship Training Program for College Students of Guangxi Zhuang Autonomous Region (Project No. S202210595236). Authors would like to thank referees for their helpful comments.
Funding
National Natural Science Foundation of China, 71801060, Xiangyan Zeng, 72061007, Xiangyan Zeng, 71801085, Xiangyan Zeng, Innovation Project of GUET Graduate Education, 2023YCXS114, Haoze Cang, Innovation and Entrepreneurship Training Program for College Students of Guangxi Zhuang Autonomous Region, S202210595236, Sixuan Wu.
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Wu, S., Zeng, X., Li, C. et al. CO2 emission forecasting based on nonlinear grey Bernoulli and BP neural network combined model. Soft Comput 27, 15509–15521 (2023). https://doi.org/10.1007/s00500-023-09063-2
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DOI: https://doi.org/10.1007/s00500-023-09063-2