Document Type : Article

**Authors**

^{1}
- 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

^{2}
- School of Science, Southwest University of Science and Technology, 621010, Mianyang, China - V.C. & V.R. Key Lab of Sichuan Province, Sichuan Normal University, 610068, Chengdu, China

^{3}
School of Science, Southwest University of Science and Technology, 621010, Mianyang, China

**Abstract**

The discrete grey modelling technique is a novel methodology of grey prediction

models, which is effective to improve the effectiveness and applicability of grey

models. In order to build a more general and effective univariate grey prediction

model, the discrete grey modelling technique is utilised in this paper to build

a quadratic polynomial discrete grey model, abbreviated as the QPDGM. The

properties of the QPDGM model have been discussed, which indicate that the

new model can be regarded as an extension of the conventional discrete grey

model and nonhomogeneous grey model, and it is also coincidence with three

classes of exponential sequences. The QPDGM model is finally applied to predict

the energy consumption of China, including the electric power, crude oil and

natural gas consumptions. The results have been compared to some commonly

used univariate grey prediction models, which indicates the QPDGM model is

generally more accurate than other models.

models, which is effective to improve the effectiveness and applicability of grey

models. In order to build a more general and effective univariate grey prediction

model, the discrete grey modelling technique is utilised in this paper to build

a quadratic polynomial discrete grey model, abbreviated as the QPDGM. The

properties of the QPDGM model have been discussed, which indicate that the

new model can be regarded as an extension of the conventional discrete grey

model and nonhomogeneous grey model, and it is also coincidence with three

classes of exponential sequences. The QPDGM model is finally applied to predict

the energy consumption of China, including the electric power, crude oil and

natural gas consumptions. The results have been compared to some commonly

used univariate grey prediction models, which indicates the QPDGM model is

generally more accurate than other models.

**Keywords**

**Main Subjects**

References:

1. Johannesen, N., Kolhe, M., and Goodwin, M. "Relative evaluation of regression tools for urban area electrical energy demand forecasting", Journal of Cleaner Production, 218, pp. 555-564 (2019). DOI: 10.1016/j.jclepro.2019.01.108.

2. Nguyen, K. and Kakinaka, M. "Renewable energy consumption, carbon emissions, and development stages: some evidence from panel cointegration analysis", Renewable Energy, 132, pp. 1049-1057 (2019). DOI: 10.1016/j.renene.2018.08.069.

3. Amasyali, K. and Ei-Gohary, N. "A review of datadriven building energy consumption prediction studies", Renewable and Sustainable Energy Reviews, 81, pp. 1192-1205 (2018). DOI: 10.1016/j.rser.2017.04.095.

4. Lu, H., Cheng F., Ma, X., et al. "Short-term prediction of building energy consumption employing an improved extreme gradient boosting model: A case study of an intake tower", Energy, 203, 117756 (2020). DOI: 10.1016/j.energy.2020.117756.

5. Ma, M. and Cai, W. "Do commercial building sectorderived carbon emissions decouple from the economic growth in Tertiary industry? A case study of four municipalities in China", Science of the Total Environment, 650, pp. 822-834 (2019). DOI: 10.1016/j.scitotenv.2018.08.078.

6. Ma, X. "A brief introduction to the grey machine learning", Journal of Grey System, 31(1), pp. 1-12 (2019). DOI: 10.48550/arXiv.1805.01745.

7. Cui, J., Liu, S., Zeng, B., et al. "A novel grey forecasting model and its optimization", Applied Mathematical Modelling, 37(6), pp. 4399-4406 (2013). DOI: 10.1016/j.apm.2012.09.052.

8. Xiang, X., Ma, X., Ma, M., et al. "Research and application of novel euler polynomial-driven grey model for short-term PM10 forecasting", Grey Systems: Theory and Application, 11(3), pp. 498-517 (2021). DOI:10.1108/GS-02-2020-0023.

9. Hu, Y., Ma, X., Li, W., et al. "Forecasting manufacturing industrial natural gas consumption of china using a novel time-delayed fractional grey model with multiple fractional order", Computational and Applied Mathematics, 39(4), pp. 1-30 (2020). DOI: 10.1007/s40314- 020-01315-3.

10. Wei, B., Xie, N., and Hu, A. "Optimal solution for novel grey polynomial prediction model", Applied Mathematical Modelling, 62(10), pp. 717-727 (2018). DOI: 10.1016/j.apm.2018.06.035.

11. Xiong, P., Yin, Y., Shi, J., et al. "Nonlinear multivariate GM(1,N) model based on interval gray number sequence", Journal of Grey System, 30(3), pp. 33-47 (2018).

12. Xiang, X., Ma, X., Fang, Y., et al. "A novel hyperbolic time-delayed grey model with grasshopper optimization algorithm and its applications", Ain Shams Engineering Journal, 12(1), pp. 865-874 (2021). DOI: 10.1016/j.asej.2020.07.019.

13. Zeng, B., Ma, X., and Zhou, M. "A new-structure grey verhulst model for china tight gas production forecasting", Applied Soft Computing, 96, 106600 (2020). DOI: 10.1016/j.asoc.2020.106600.

14. Chen, C.-I., Chen, H., and Chen, S. "Forecasting of foreign exchange rates of Taiwan's major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1)", Communications in Nonlinear Science and Numerical Simulation, 13(6), pp. 1194-1204, (2008). DOI:10.1016/j.cnsns.2006.08.008.

15. Tan, G. "The structure method and application of background value in grey system GM(1,1) model I", Systems Engineering-Theory & Practice, 4, pp. 98-103 (2000). DOI: 10.12011/1000-6788(2000)4-98.

16. Wang, Z., Dang, Y., and Liu, S. "An optimal GM(1,1) based on the discrete function with exponential law", Systems Engineering-Theory & Practice, 2, pp. 61-67 (2008). DOI: 10.1016/S1874-8651(09)60011-9.

17. Xie, N. and Liu, S. "Discrete grey forecasting model and its optimization", Applied Mathematical Modelling, 33(2), pp. 1173-1186 (2009). DOI: 10.1016/j.apm.2008.01.011.

18. Ding, S., Dang, Y., Xu, N., et al. "The optimization of grey Verhulst model and its application", Journal of Grey System, 27(3), pp. 1-12 (2015).

19. Kong, X. and Wei, Y. "Optimization of DGM(2,1)", Journal of Grey System, 12(1), pp. 9-13 (2009). DOI: 10.30016/JGS.200903.0002.

20. Chen, P., Yu, H., and Xie, K. "GM(1,1) model based on optimum parameters of whitenization differential equation and its application on displacement forecasting of foundation pits", The Journal of Grey System, 25(1), pp. 54-62 (2013).

21. Chen, P. and Yu, H. "Foundation settlement prediction based on a novel NGM model", Mathematical Problems in Engineering, 2014(1), pp. 1-8 (2014). DOI:10.1155/2014/242809.

22. Wu, W., Ma, X., Zeng, B., et al. "Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption", Energy, 165, pp. 223-234 (2018). DOI: 10.1016/j.energy.2018.09.155.

23. Ma, X. and Liu, Z. "The GMC(1,n) model with optimized parameters and its applications", Journal of Grey System, 29(4), pp. 121-137 (2017).

24. Cui, L., Liu, S., and Li, Z. "Grey discrete Verhulst model", Systems Engineering and Electronics, 33(3), pp. 590-593 (2011). DOI: 10.3969/j.issn.1001- 506X.2011.03.24.

25. Wu, L., Liu, S., and Zhang, N. "Using a novel grey system model to forecast natural gas consumption in china", Mathematical Problems in Engineering, 2015, pp. 1-7 (2015). DOI: 10.1155/2015/686501.

26. Ma, X., Xie, M., Wu, W., et al. "The novel fractional discrete multivariate grey system model and its applications", Applied Mathematical Modelling, 70, pp. 402-424 (2019). DOI: 10.1016/j.apm.2019.01.039.

27. Ma, X. and Liu, Z. "The kernel-based nonlinear multivariate grey model", Applied Mathematical Modelling, 56(4), pp. 217-238 (2018). DOI:10.1016/j.apm.2017.12.010.

28. Liu, S. and Lin, Y., Grey Systems: Theory and Applications, Springer-Verlag, Berlin Heidelberg (2011).

29. Xie, N., Liu, S., Yang, Y., et al. "On novel grey forecasting model based on non-homogeneous index sequence", Applied Mathematical Modelling, 37(7), pp. 5059-5068 (2013). DOI: 10.1016/j.apm.2012.10.037.

2. Nguyen, K. and Kakinaka, M. "Renewable energy consumption, carbon emissions, and development stages: some evidence from panel cointegration analysis", Renewable Energy, 132, pp. 1049-1057 (2019). DOI: 10.1016/j.renene.2018.08.069.

3. Amasyali, K. and Ei-Gohary, N. "A review of datadriven building energy consumption prediction studies", Renewable and Sustainable Energy Reviews, 81, pp. 1192-1205 (2018). DOI: 10.1016/j.rser.2017.04.095.

4. Lu, H., Cheng F., Ma, X., et al. "Short-term prediction of building energy consumption employing an improved extreme gradient boosting model: A case study of an intake tower", Energy, 203, 117756 (2020). DOI: 10.1016/j.energy.2020.117756.

5. Ma, M. and Cai, W. "Do commercial building sectorderived carbon emissions decouple from the economic growth in Tertiary industry? A case study of four municipalities in China", Science of the Total Environment, 650, pp. 822-834 (2019). DOI: 10.1016/j.scitotenv.2018.08.078.

6. Ma, X. "A brief introduction to the grey machine learning", Journal of Grey System, 31(1), pp. 1-12 (2019). DOI: 10.48550/arXiv.1805.01745.

7. Cui, J., Liu, S., Zeng, B., et al. "A novel grey forecasting model and its optimization", Applied Mathematical Modelling, 37(6), pp. 4399-4406 (2013). DOI: 10.1016/j.apm.2012.09.052.

8. Xiang, X., Ma, X., Ma, M., et al. "Research and application of novel euler polynomial-driven grey model for short-term PM10 forecasting", Grey Systems: Theory and Application, 11(3), pp. 498-517 (2021). DOI:10.1108/GS-02-2020-0023.

9. Hu, Y., Ma, X., Li, W., et al. "Forecasting manufacturing industrial natural gas consumption of china using a novel time-delayed fractional grey model with multiple fractional order", Computational and Applied Mathematics, 39(4), pp. 1-30 (2020). DOI: 10.1007/s40314- 020-01315-3.

10. Wei, B., Xie, N., and Hu, A. "Optimal solution for novel grey polynomial prediction model", Applied Mathematical Modelling, 62(10), pp. 717-727 (2018). DOI: 10.1016/j.apm.2018.06.035.

11. Xiong, P., Yin, Y., Shi, J., et al. "Nonlinear multivariate GM(1,N) model based on interval gray number sequence", Journal of Grey System, 30(3), pp. 33-47 (2018).

12. Xiang, X., Ma, X., Fang, Y., et al. "A novel hyperbolic time-delayed grey model with grasshopper optimization algorithm and its applications", Ain Shams Engineering Journal, 12(1), pp. 865-874 (2021). DOI: 10.1016/j.asej.2020.07.019.

13. Zeng, B., Ma, X., and Zhou, M. "A new-structure grey verhulst model for china tight gas production forecasting", Applied Soft Computing, 96, 106600 (2020). DOI: 10.1016/j.asoc.2020.106600.

14. Chen, C.-I., Chen, H., and Chen, S. "Forecasting of foreign exchange rates of Taiwan's major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1)", Communications in Nonlinear Science and Numerical Simulation, 13(6), pp. 1194-1204, (2008). DOI:10.1016/j.cnsns.2006.08.008.

15. Tan, G. "The structure method and application of background value in grey system GM(1,1) model I", Systems Engineering-Theory & Practice, 4, pp. 98-103 (2000). DOI: 10.12011/1000-6788(2000)4-98.

16. Wang, Z., Dang, Y., and Liu, S. "An optimal GM(1,1) based on the discrete function with exponential law", Systems Engineering-Theory & Practice, 2, pp. 61-67 (2008). DOI: 10.1016/S1874-8651(09)60011-9.

17. Xie, N. and Liu, S. "Discrete grey forecasting model and its optimization", Applied Mathematical Modelling, 33(2), pp. 1173-1186 (2009). DOI: 10.1016/j.apm.2008.01.011.

18. Ding, S., Dang, Y., Xu, N., et al. "The optimization of grey Verhulst model and its application", Journal of Grey System, 27(3), pp. 1-12 (2015).

19. Kong, X. and Wei, Y. "Optimization of DGM(2,1)", Journal of Grey System, 12(1), pp. 9-13 (2009). DOI: 10.30016/JGS.200903.0002.

20. Chen, P., Yu, H., and Xie, K. "GM(1,1) model based on optimum parameters of whitenization differential equation and its application on displacement forecasting of foundation pits", The Journal of Grey System, 25(1), pp. 54-62 (2013).

21. Chen, P. and Yu, H. "Foundation settlement prediction based on a novel NGM model", Mathematical Problems in Engineering, 2014(1), pp. 1-8 (2014). DOI:10.1155/2014/242809.

22. Wu, W., Ma, X., Zeng, B., et al. "Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption", Energy, 165, pp. 223-234 (2018). DOI: 10.1016/j.energy.2018.09.155.

23. Ma, X. and Liu, Z. "The GMC(1,n) model with optimized parameters and its applications", Journal of Grey System, 29(4), pp. 121-137 (2017).

24. Cui, L., Liu, S., and Li, Z. "Grey discrete Verhulst model", Systems Engineering and Electronics, 33(3), pp. 590-593 (2011). DOI: 10.3969/j.issn.1001- 506X.2011.03.24.

25. Wu, L., Liu, S., and Zhang, N. "Using a novel grey system model to forecast natural gas consumption in china", Mathematical Problems in Engineering, 2015, pp. 1-7 (2015). DOI: 10.1155/2015/686501.

26. Ma, X., Xie, M., Wu, W., et al. "The novel fractional discrete multivariate grey system model and its applications", Applied Mathematical Modelling, 70, pp. 402-424 (2019). DOI: 10.1016/j.apm.2019.01.039.

27. Ma, X. and Liu, Z. "The kernel-based nonlinear multivariate grey model", Applied Mathematical Modelling, 56(4), pp. 217-238 (2018). DOI:10.1016/j.apm.2017.12.010.

28. Liu, S. and Lin, Y., Grey Systems: Theory and Applications, Springer-Verlag, Berlin Heidelberg (2011).

29. Xie, N., Liu, S., Yang, Y., et al. "On novel grey forecasting model based on non-homogeneous index sequence", Applied Mathematical Modelling, 37(7), pp. 5059-5068 (2013). DOI: 10.1016/j.apm.2012.10.037.

Transactions on Industrial Engineering (E)

March and April 2024Pages 469-480