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**

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Nonlinear Sciences and Numerical Simulation, 19(5),

pp. 439{457 (2018).

W. Wu et al./Scientia Iranica, Transactions D: Computer Science & ... 28 (2021) 3379{3395 3395

Econ., 27(3), pp. 415{427 (2005).

3. Neto, A.H. and Fiorelli, F.A.S. Comparison between detailed model simulation and arti cial 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 ve 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

ow for a multiple fractured horizontal

well with multiple nite-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 modi ed

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

coecient 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).

W. Wu et al./Scientia Iranica, Transactions D: Computer Science & ... 28 (2021) 3379{3395 3395

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

November and December 2021Pages 3379-3395