Introduction
Category | Author(s) | Model designation | Case |
---|---|---|---|
Statistical models | Azadeh et al. [8] | Fuzzy regression + ANOVA | Oil consumption in Canada, United States, Japan and Australia from 1990 to 2005 |
Dritsaki et al. [6] | ARIMA | Oil consumption in Greece during 1960–2020 | |
Alkhathlan and Javid [9] | Structural time-series technique | Total oil consumption of Saudi Arabia over the period from 1971 to 2013 | |
Machine learning methods | Al-Fattah and Aramco [10] | Artificial intelligence GANNATS model | Crude oil demand for Saudi Arabia and China |
Turanoglu et al. [5] | ANNs | Oil consumption in Turkey from 1965 to 2010 | |
Huang et al. [11] | Four neutral network methods | Oil consumption demand of China | |
Grey forecasting models | Yao and Wang [12] | LSTM network + GM (1,1) | The US West Texas Intermediate (WTI) crude oil price from January 2, 1986, to January 31, 2020 |
Lu and Tsai [13] | EWMA + REGM(1,1) | Annual petroleum demand in Taiwan | |
Yang et al. [14] | GGNN | China's oil consumption | |
Current study | ONGBM(1,1,k,c) | China’s petroleum consumption and terminal consumption from 2001 to 2018 |
Optimized nonlinear grey Bernoulli model
Combined fractional accumulated generation operator
Model establishment
Exact solution to ONGBM(1,1,k,c)
Parameter estimation
Optimization of hyperparameters
Evaluation criterion
Numerical validation
Year | Raw data | GM(1,1) | ONGBM(1,1) | ONGBM(1,1,k,c) | |||
---|---|---|---|---|---|---|---|
Value | APE | Value | APE | Value | APE | ||
Training stage | |||||||
2000 | 21,232.01 | 21,232.01 | 0.00 | 21,232.01 | 0.00 | 21,232.01 | 0.00 |
2001 | 21,342.74 | 23,120.30 | 8.33 | 21,315.46 | 0.13 | 21,194.82 | 0.69 |
2002 | 22,544.05 | 24,606.03 | 9.15 | 23,626.75 | 4.80 | 23,224.32 | 3.02 |
2003 | 24,922.00 | 26,187.24 | 5.08 | 25,732.38 | 3.25 | 25,334.16 | 1.65 |
2004 | 28,749.31 | 27,870.06 | 3.06 | 27,777.16 | 3.38 | 27,508.17 | 4.32 |
2005 | 30,088.94 | 29,661.02 | 1.42 | 29,822.70 | 0.88 | 29,746.24 | 1.14 |
2006 | 32,245.20 | 31,567.07 | 2.10 | 31,902.62 | 1.06 | 31,792.33 | 1.40 |
2007 | 34,031.60 | 33,595.61 | 1.28 | 34,038.54 | 0.02 | 34,286.48 | 0.75 |
2008 | 35,498.24 | 35,754.50 | 0.72 | 36,246.07 | 2.11 | 36,588.54 | 3.07 |
2009 | 38,128.59 | 38,052.12 | 0.20 | 38,537.61 | 1.07 | 39,018.60 | 2.33 |
2010 | 42,874.55 | 40,497.39 | 5.54 | 40,923.73 | 4.55 | 41,448.62 | 3.33 |
2011 | 43,965.84 | 43,099.80 | 1.97 | 43,413.94 | 1.26 | 43,878.60 | 0.20 |
2012 | 46,678.92 | 45,869.44 | 1.73 | 46,017.17 | 1.42 | 46,500.56 | 0.38 |
2013 | 48,652.15 | 48,817.06 | 0.34 | 48,742.03 | 0.18 | 49,122.45 | 0.97 |
2014 | 51,596.95 | 51,954.10 | 0.69 | 51,597.05 | 0.00 | 51,680.28 | 0.16 |
2015 | 54,788.28 | 55,292.73 | 0.92 | 54,590.79 | 0.36 | 54,430.10 | 0.65 |
2016 | 57,125.93 | 58,845.90 | 3.01 | 57,731.93 | 1.06 | 57,179.84 | 0.09 |
MAPE | 2.68 | 1.50 | 1.42 | ||||
NMAPE | 2.31 | 1.37 | 1.29 | ||||
RMSE | 1114.44 | 713.41 | 641.48 | ||||
NRMSE | 0.03 | 0.02 | 0.00 | ||||
Test stage | |||||||
2017 | 59,402.17 | 62,627.40 | 5.43 | 61,029.40 | 2.74 | 59,865.53 | 0.78 |
2018 | 63,004.33 | 66,651.91 | 5.79 | 64,492.38 | 2.36 | 62,743.20 | 0.41 |
2019 | 67,268.27 | 70,935.03 | 5.45 | 68,130.38 | 1.28 | 65,684.80 | 2.35 |
MAPE | 5.56 | 2.13 | 1.18 | ||||
NMAPE | 5.55 | 3.45 | 1.21 | ||||
RMSE | 3519.09 | 2242.26 | 964.41 | ||||
NRMSE | 0.06 | 0.04 | 0.00 |
Application in China’s petroleum consumption
Data collection and experimental design
Year | Petroleum consumption | Terminal consumption |
---|---|---|
2001 | 22,888.40 | 20,407.10 |
2002 | 24,789.20 | 21,992.20 |
2003 | 27,125.80 | 24,062.50 |
2004 | 31,700.50 | 28,062.70 |
2005 | 32,547.00 | 29,495.60 |
2006 | 34,876.20 | 31,614.10 |
2007 | 36,658.70 | 33,857.60 |
2008 | 37,302.90 | 34,702.90 |
2009 | 38,384.50 | 35,689.90 |
2010 | 44,101.00 | 41,243.40 |
2011 | 45,378.50 | 42,727.30 |
2012 | 47,797.30 | 45,080.70 |
2013 | 49,970.60 | 47,458.80 |
2014 | 51,859.40 | 49,309.00 |
2015 | 55,960.20 | 52,945.70 |
2016 | 57,692.90 | 54,387.00 |
2017 | 60,395.90 | 56,880.00 |
2018 | 62,245.10 | 58,623.00 |
Experimental results
Year | Data | GM(1,1) | ONGBM(1,1) | PR | ANN | SVR | ONGBM(1,1,k,c) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | ||
Training stage | |||||||||||||
2001 | 22,888.40 | 22,888.40 | 0.00 | 22,888.40 | 0.00 | 23,248.20 | 1.57 | 22,888.40 | 0.00 | 22,888.40 | 0.00 | 22,888.40 | 0.00 |
2002 | 24,789.20 | 26,735.05 | 7.85 | 24,900.39 | 0.45 | 25,420.52 | 2.55 | 24,789.20 | 0.00 | 24,789.20 | 0.00 | 24,791.69 | 0.01 |
2003 | 27,125.80 | 28,336.73 | 4.46 | 27,900.26 | 2.86 | 27,599.32 | 1.75 | 27,125.80 | 0.00 | 27,125.80 | 0.00 | 28,866.36 | 6.42 |
2004 | 31,700.50 | 30,034.36 | 5.26 | 30,431.76 | 4.00 | 29,784.60 | 6.04 | 31,700.50 | 0.00 | 31,700.50 | 0.00 | 31,344.86 | 1.12 |
2005 | 32,547.00 | 31,833.70 | 2.19 | 32,746.91 | 0.61 | 31,976.36 | 1.75 | 32,547.00 | 0.00 | 32,547.00 | 0.00 | 33,150.25 | 1.85 |
2006 | 34,876.20 | 33,740.84 | 3.26 | 34,950.86 | 0.21 | 34,174.59 | 2.01 | 33,704.23 | 3.36 | 35,051.04 | 0.50 | 34,857.97 | 0.05 |
2007 | 36,658.70 | 35,762.23 | 2.45 | 37,098.66 | 1.20 | 36,379.31 | 0.76 | 36,028.68 | 1.72 | 36,517.36 | 0.39 | 36,637.84 | 0.06 |
2008 | 37,302.90 | 37,904.73 | 1.61 | 39,223.32 | 5.15 | 38,590.50 | 3.45 | 38,608.23 | 3.50 | 37,376.01 | 0.20 | 38,564.13 | 3.38 |
2009 | 38,384.50 | 40,175.57 | 4.67 | 41,346.58 | 7.72 | 40,808.18 | 6.31 | 40,497.16 | 5.50 | 38,053.10 | 0.86 | 40,668.96 | 5.95 |
2010 | 44,101.00 | 42,582.47 | 3.44 | 43,483.85 | 1.40 | 43,032.33 | 2.42 | 41,798.82 | 5.22 | 38,300.44 | 13.15 | 42,962.50 | 2.58 |
2011 | 45,378.50 | 45,133.56 | 0.54 | 45,646.68 | 0.59 | 45,262.96 | 0.25 | 45,151.50 | 0.50 | 46,014.98 | 1.40 | 45,321.46 | 0.13 |
2012 | 47,797.30 | 47,837.48 | 0.08 | 47,844.17 | 0.10 | 47,500.07 | 0.62 | 48,048.54 | 0.53 | 47,981.56 | 0.39 | 47,782.52 | 0.03 |
2013 | 49,970.60 | 50,703.40 | 1.47 | 50,083.80 | 0.23 | 49,743.66 | 0.45 | 50,378.39 | 0.82 | 49,695.47 | 0.55 | 50,277.75 | 0.61 |
Testing stage | |||||||||||||
2014 | 51,859.40 | 53,741.00 | 3.63 | 52,371.93 | 0.99 | 51,993.73 | 0.26 | 53,158.52 | 2.51 | 50,359.65 | 2.89 | 52,835.24 | 1.88 |
2015 | 55,960.20 | 56,960.59 | 1.79 | 54,714.16 | 2.23 | 54,250.27 | 3.06 | 55,903.91 | 0.10 | 52,804.11 | 5.64 | 55,371.19 | 1.05 |
2016 | 57,692.90 | 60,373.07 | 4.65 | 57,115.53 | 1.00 | 56,513.30 | 2.04 | 58,990.34 | 2.25 | 57,433.38 | 0.45 | 57,919.65 | 0.39 |
2017 | 60,395.90 | 63,989.98 | 5.95 | 59,580.69 | 1.35 | 58,782.80 | 2.67 | 61,919.58 | 2.52 | 59,137.13 | 2.08 | 60,444.52 | 0.08 |
2018 | 62,245.10 | 67,823.58 | 8.96 | 62,114.02 | 0.21 | 61,058.79 | 1.91 | 64,660.15 | 3.88 | 61,567.91 | 1.09 | 62,962.36 | 1.15 |
MAPE(%) | NMAPE(%) | RMSE | NRMSE | |
---|---|---|---|---|
Training stage | ||||
GM(1,1) | 2.87 | 2.64 | 3076.17 | 0.03 |
ONGBM(1,1) | 1.89 | 1.86 | 1088.07 | 0.03 |
PR | 2.30 | 2.19 | 1043.16 | 0.03 |
ANN | 1.63 | 1.78 | 1019.75 | 0.03 |
SVM | 1.34 | 1.61 | 1624.97 | 0.04 |
ONGBM(1,1,k,c) | 1.71 | 1.65 | 949.66 | 0.03 |
Testing stage | ||||
GM(1,1) | 4.99 | 5.11 | 3339.50 | 0.06 |
ONGBM(1,1) | 1.16 | 1.14 | 752.38 | 0.01 |
PR | 1.99 | 2.02 | 1291.73 | 0.02 |
ANN | 2.25 | 2.29 | 1518.44 | 0.03 |
SVM | 2.43 | 2.38 | 1692.37 | 0.03 |
ONGBM(1,1,k,c) | 0.91 | 0.89 | 611.14 | 0.01 |
Year | Data | GM(1,1) | ONGBM(1,1) | PR | ANN | SVR | ONGBM(1,1,k,c) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | Forecast value | APE(%) | ||
Training stage | |||||||||||||
2001 | 22,888.40 | 22,888.40 | 0.00 | 22,888.40 | 0.00 | 23,248.20 | 1.57 | 22,888.40 | 0.00 | 22,888.40 | 0.00 | 22,888.40 | 0.00 |
2002 | 24,789.20 | 26,735.05 | 7.85 | 24,900.39 | 0.45 | 25,420.52 | 2.55 | 24,789.20 | 0.00 | 24,789.20 | 0.00 | 24,791.69 | 0.01 |
2003 | 27,125.80 | 28,336.73 | 4.46 | 27,900.26 | 2.86 | 27,599.32 | 1.75 | 27,125.80 | 0.00 | 27,125.80 | 0.00 | 28,866.36 | 6.42 |
2004 | 31,700.50 | 30,034.36 | 5.26 | 30,431.76 | 4.00 | 29,784.60 | 6.04 | 31,700.50 | 0.00 | 31,700.50 | 0.00 | 31,344.86 | 1.12 |
2005 | 32,547.00 | 31,833.70 | 2.19 | 32,746.91 | 0.61 | 31,976.36 | 1.75 | 32,547.00 | 0.00 | 32,547.00 | 0.00 | 33,150.25 | 1.85 |
2006 | 34,876.20 | 33,740.84 | 3.26 | 34,950.86 | 0.21 | 34,174.59 | 2.01 | 33,704.23 | 3.36 | 35,051.04 | 0.50 | 34,857.97 | 0.05 |
2007 | 36,658.70 | 35,762.23 | 2.45 | 37,098.66 | 1.20 | 36,379.31 | 0.76 | 36,028.68 | 1.72 | 36,517.36 | 0.39 | 36,637.84 | 0.06 |
2008 | 37,302.90 | 37,904.73 | 1.61 | 39,223.32 | 5.15 | 38,590.50 | 3.45 | 38,608.23 | 3.50 | 37,376.01 | 0.20 | 38,564.13 | 3.38 |
2009 | 38,384.50 | 40,175.57 | 4.67 | 41,346.58 | 7.72 | 40,808.18 | 6.31 | 40,497.16 | 5.50 | 38,053.10 | 0.86 | 40,668.96 | 5.95 |
2010 | 44,101.00 | 42,582.47 | 3.44 | 43,483.85 | 1.40 | 43,032.33 | 2.42 | 41,798.82 | 5.22 | 38,300.44 | 13.15 | 42,962.50 | 2.58 |
2011 | 45,378.50 | 45,133.56 | 0.54 | 45,646.68 | 0.59 | 45,262.96 | 0.25 | 45,151.50 | 0.50 | 46,014.98 | 1.40 | 45,321.46 | 0.13 |
2012 | 47,797.30 | 47,837.48 | 0.08 | 47,844.17 | 0.10 | 47,500.07 | 0.62 | 48,048.54 | 0.53 | 47,981.56 | 0.39 | 47,782.52 | 0.03 |
2013 | 49,970.60 | 50,703.40 | 1.47 | 50,083.80 | 0.23 | 49,743.66 | 0.45 | 50,378.39 | 0.82 | 49,695.47 | 0.55 | 50,277.75 | 0.61 |
Testing stage | |||||||||||||
2014 | 51,859.40 | 53,741.00 | 3.63 | 52,371.93 | 0.99 | 51,993.73 | 0.26 | 53,158.52 | 2.51 | 50,359.65 | 2.89 | 52,835.24 | 1.88 |
2015 | 55,960.20 | 56,960.59 | 1.79 | 54,714.16 | 2.23 | 54,250.27 | 3.06 | 55,903.91 | 0.10 | 52,804.11 | 5.64 | 55,371.19 | 1.05 |
2016 | 57,692.90 | 60,373.07 | 4.65 | 57,115.53 | 1.00 | 56,513.30 | 2.04 | 58,990.34 | 2.25 | 57,433.38 | 0.45 | 57,919.65 | 0.39 |
2017 | 60,395.90 | 63,989.98 | 5.95 | 59,580.69 | 1.35 | 58,782.80 | 2.67 | 61,919.58 | 2.52 | 59,137.13 | 2.08 | 60,444.52 | 0.08 |
2018 | 62,245.10 | 67,823.58 | 8.96 | 62,114.02 | 0.21 | 61,058.79 | 1.91 | 64,660.15 | 3.88 | 61,567.91 | 1.09 | 62,962.36 | 1.15 |
MAPE(%) | NMAPE(%) | RMSE | NRMSE | |
---|---|---|---|---|
Training stage | ||||
GM(1,1) | 2.84 | 2.10 | 1027.63 | 0.03 |
ONGBM(1,1) | 2.36 | 1.76 | 1127.25 | 0.03 |
PR | 2.12 | 1.58 | 826.00 | 0.02 |
ANN | 2.75 | 2.08 | 1057.03 | 0.03 |
SVR | 5.88 | 4.13 | 2227.24 | 0.06 |
ONGBM(1,1,k,c) | 1.58 | 1.18 | 851.53 | 0.02 |
Testing stage | ||||
GM(1,1) | 7.93 | 7.71 | 4967.93 | 0.09 |
ONGBM(1,1) | 3.01 | 2.91 | 1764.76 | 0.03 |
PR | 7.64 | 7.46 | 5062.82 | 0.09 |
ANN | 4.38 | 4.23 | 2561.14 | 0.05 |
SVR | 2.51 | 2.33 | 2031.48 | 0.04 |
ONGBM(1,1,k,c) | 0.71 | 0.68 | 446.85 | 0.01 |
Out-of-sample predictions and suggestion
Year | Petroleum consumption | Terminal consumption |
---|---|---|
2019 | 64,704.31 | 60,820.74 |
2020 | 66,999.01 | 62,916.77 |
2021 | 69,279.32 | 64,993.39 |
2022 | 71,548.23 | 67,053.98 |
2023 | 73,808.16 | 69,101.31 |