Document Type : Article

**Authors**

^{1}
- School of Science, Southwest University of Science and Technology, 621010, Mianyang, China. - V.C. and V.R. Key Lab of Sichuan Province, Sichuan Normal University, 610068, Chengdu, China

^{2}
- School of Science, Southwest University of Science and Technology, 621010, Mianyang, China. - State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, Chengdu, China.

^{3}
- School of Science, Southwest Petroleum University, 610500, Chengdu, China - State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, Chengdu, China

^{4}
College of Engineering and Technology, Southwest University, 400715, Chongqing, China

^{5}
College of Business Planning, Chongqing Technology and Business University, 400067, Chongqing, China

**Abstract**

Energy consumption plays a key role in economics development for all countries. Catching the future trend of energy consumption is very important for the governments and energy companies. In this paper, the primary energy consumption of Saudi Arabia, India, Philippines and Vietnam are systematically studied by various forecasting models. Based on the actual data from 2006 to 2016, a novel grey forecasting model termed NDGM_S (1,1,k,c) is proposed where the Simpson numerical integration formula is applied to construct the background value. The time response function and the restored value of the present model are deduced, and then the unbiased property is proved. As shown in the computational results, the NDGM_S (1,1,k,c) model can achieve better prediction accuracy than other forecasting models, and it is quite suitable for predicting sequence with homogeneous/non-homogeneous exponential law.

**Keywords**

References:

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27. He, G., Wu, W., and Zhang, Y. "Performance analysis of machine repair system with single working vacation", Communications in Statistics-Theory and Methods, 48(22), pp. 5602-5620 (2019).

28. Wang, Y. and Yi, X. "Flow modeling of well test analysis for a multiple fractured horizontal well in triple media carbonate reservoir", International Journal of Nonlinear Sciences and Numerical Simulation, 19(5), pp. 439-457 (2018).

2. Lee, C.C. "Energy consumption and GDP in developing countries: a cointegrated panel analysis", Energy Econ., 27(3), pp. 415-427 (2005).

3. Neto, A.H. and Fiorelli, F.A.S. "Comparison between detailed model simulation and artificial neural network for forecasting building energy consumption", Energy Build., 40(12), pp. 2169-2176 (2008).

4. Ma, M., Cai, W., Cai, W., and Dong, L. "Whether carbon intensity in the commercial building sector decouples from economic development in the service industry? empirical evidence from the top five urban agglomerations in China", J. Cleaner Prod., 222, pp. 193-205 (2019).

5. Ma, M., Ma, X., Cai, W., and Cai, W. "Carbondioxide mitigation in the residential building sector: a household scale-based assessment", Energ. Convers. Manage., https://doi:10.1016/j.enconman.2019.111915 (2019).

6. Wang, Y., Zhang, C., Chen, T., and Ma, X. "Modeling the nonlinear flow for a multiple fractured horizontal well with multiple finite-conductivity fractures in triple media carbonate reservoir", Journal of Porous Media, 21(12), pp. 1283-1305 (2018).

7. Liang, Y., Cai, W., and Ma, M. "Carbon dioxide intensity and income level in the Chinese megacities' residential building sector: decomposition and decoupling analyses", Sci. Toal Environ., 677, pp. 315-327 (2019).

8. Yang, W., Wang, J., Lu, H., Niu, T., and Du, P. "Hybrid wind energy forecasting and analysis system based on divide and conquer scheme: a case study in China", J. Cleaner Prod., 222, pp. 942-959 (2019).

9. Du, P., Wang, J., Yang, W., and Niu, T. "A novel hybrid model for short-term wind power forecasting", Appl. Soft Comput., 80, pp. 93-106 (2019).

10. Wu, L., Liu, S., Yao, L., and Yu, L. "Fractional order grey relational analysis and its application", Scientia Iranica, 22, pp. 1171-1178 (2015).

11. Zeng, B., Duan, H., and Zhou, Y. "A new multivariable grey prediction model with structure compatibility", Appl. Math. Model, 75, pp. 385-397 (2019).

12. Hashem-Nazari, M., Esfahanipour, A., and Ghomi, F.S. "A basic-form focused modeling and a modified parameter estimation technique for grey prediction models", Scientia Iranica, 25, pp. 2867-2880 (2018).

13. Ma, X. "A brief introduction to the grey machine learning", J. Grey System, 31(1), pp. 1-12 (2019).

14. Ma, X., Xie, M., Wu, W., Wu, X., and Zeng, B. "A novel fractional time delayed grey model with grey wolf optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China", Energy, 178, pp. 487-507 (2019.)

15. Deng, J. "Control problems of grey systems", Systems & Control Letters, 1(5), pp. 288-294 (1982).

16. Wu, W., Ma, X., Zeng, B., Wang, Y., and Cai, W. "Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption", Energy, 165, pp. 223-234 (2018).

17. Ma, X., Wu, W., Zeng, B., Wang, Y., and Wu, X. "The conformable fractional grey system model", ISA T., 96, pp. 255-271 https://doi:10.1016/j.isatra.2019.07.009 (2019).

18. Zeng, B. and Chuan, L. "Improved multi-variable grey forecasting model with a dynamic backgroundvalue coefficient and its application", Computers & Industrial Engineering, 118(4), pp. 278-290 (2018).

19. Wang, Z. and Li, Q. "Modelling the nonlinear relationship between CO2 emissions and economic growth using a PSO algorithm-based grey Verhulst model", J. Cleaner Prod., 207, pp. 214-224 (2019).

20. Wu, W., Ma, X., Zeng, B., Wang, Y., and Cai, W. "Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model", Renewable Energy, 140, pp. 70-87 (2019).

21. Ma, X. and Liu, Z. "The GMC(1,n) model with optimized parameters and its application", J. Grey System, 29(4), pp. 122-138 (2017).

22. Mao, S., He, Q., Xiao, X., and Rao, C. "Study of the correlation between oil price and exchange rate under the new state of the economy", Scientia Iranica, 26(4), pp. 2472-2483 (2018). Doi: 1024200/SCI201820448.

23. Ma, X., Xie, M., Wu, W., Zeng, B., Wang, Y., and Wu, X. "The novel fractional discrete multivariate grey system model and its applications", Appl. Math. Modell., 70, pp. 402-424 (2019).

24. Cui, J., Liu, S., Zeng, B., and Xie, N. "A novel grey forecasting model and its optimization", Appl. Math. Modell., 37(6), pp. 4399-4406 (2013).

25. Chen, P. and Yu, H. "Foundation settlement prediction based on a novel NGM model", Mathematical Problems in Engineering, 2014(1), pp. 1-8 (2014).

26. Xie, N., Liu, S., Yang, Y., and Yuan, C. "On novel grey forecasting model based on non-homogeneous index sequence", Appl. Math. Modell., 37(7), pp. 5059-5068 (2013).

27. He, G., Wu, W., and Zhang, Y. "Performance analysis of machine repair system with single working vacation", Communications in Statistics-Theory and Methods, 48(22), pp. 5602-5620 (2019).

28. Wang, Y. and Yi, X. "Flow modeling of well test analysis for a multiple fractured horizontal well in triple media carbonate reservoir", International Journal of Nonlinear Sciences and Numerical Simulation, 19(5), pp. 439-457 (2018).

Transactions on Computer Science & Engineering and Electrical Engineering (D)

November and December 2021Pages 3379-3395