# Forecasting China’s Annual Biofuel Production Using an Improved Grey Model

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## Abstract

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## 1. Introduction

_{2}) producer [8]. With air pollution becoming an increasingly serious issue in China, the use of biofuels, which are essentially novel types of sustainable fuels, has attracted much attention as a way to reduce China’s smog and carbon emissions [5,6,7,8,9]. During the 2014, Asia-Pacific Economic Cooperation (APEC) Meeting in Beijing, Chinese President Xi Jinping and U.S. President Barack Obama jointly issued the China–U.S. Joint Statement on Climate Change. President Obama promised to reduce the U.S.’ carbon emissions by 26% to 28% by 2025 [10]. To achieve this goal, the global demand for biofuels in road transport is expected to rise from 32.4 billion gallons in 2013 to 51.1 billion gallons in 2022, a growth of nearly 60%. The Chinese government has been actively promoting the uptake of biofuels since 2000, recognizing them as a key strategic measure in addressing the challenges of climate change and energy security [11]. In 2010, China’s biofuels industry was listed as one of the national strategic emerging industries. According to the long-term development prospects of renewable energy, by 2020, biofuels could account for 15% of transportation energy consumption, with biofuels substituting 10% of conventional fuels [12]. Keeping these factors in mind and given the rise in China’s overall biofuel production from 2003 to 2012, it is important to devise accurate methods to see whether the production can actually achieve the long-term development of renewable energy.

## 2. Literature Review

#### 2.1. Predicting Biofuel Production

#### 2.2. Problems with Predicting Production

_{2}emissions prediction, coal production [29], and photoelectric output [30], because it requires less data and offers certain advantages, including easy computation and high prediction accuracy. Like other mathematical models, the grey model should be used within its application range to avoid producing large errors. An improved GM (1,1) model, as described below, can not only enhance the accuracy of the prediction model but also increase its application potential.

## 3. Building the Dynamic Grey Fuzzy Markov Prediction Model

#### 3.1. Conventional Grey Model

#### 3.1.1. GM (1,1) Model Building Process

- Accumulated generating operation (AGO)
- Grey modeling
- Inverse accumulated generating operation (IAGO)

#### 3.1.2. Accuracy Considerations

Index | C | P | |
---|---|---|---|

Accuracy grade | Excellent | ≤0.35 | ≥95% |

Well | ≤0.50 | ≥80% | |

Conformity | ≤0.65 | ≥70% | |

Non-conformity | ≥0.80 | ≤60% |

#### 3.2. Dynamic Grey Model

#### 3.3. Dynamic Grey Fuzzy Markov Prediction Model

#### 3.3.1. Fuzzy Classifications

#### 3.3.2. Determination of the State Transition Matrix

_{0}makes ${U}_{{k}_{0}}(x)=\underset{k=1}{\overset{m}{\vee}}\left\{{u}_{{A}_{k}}(x)\right\},1\le {k}_{0}\le m.$ Then, we regard ${A}_{k0}$ as x’s relative membership degree. A

_{1}, A

_{2}, …, A

_{m}are m fuzzy subsets on U. The state transition probability is ${p}_{ij}=\frac{{M}_{ij}}{{M}_{i}},i=1,\mathrm{2...}n$, where ${M}_{ij}$ is the frequency that state ${\mathrm{\Theta}}_{i}$ reaches state ${\mathrm{\Theta}}_{j}$ after the Step 1 transfer, and ${M}_{i}$ is the occurrence frequency of ${\mathrm{\Theta}}_{i}$. $P$ is the transition probability matrix.

#### 3.3.3. Fuzzy Markov Residual Error Correction

## 4. Feasibility Analysis of the Grey Fuzzy Markov Prediction Model

#### 4.1. Data Source

#### 4.2. Results of the GM (1,1) Model

Years | Raw Data | GM (1,1) Data | Residual | Correctly Predicted Percentage |
---|---|---|---|---|

2002 | 148.00 | 148.00 | 0 | 100 |

2003 | 398.00 | 545.29 | 147.29 | 62.9925 |

2004 | 493.00 | 618.65 | 125.65 | 74.5132 |

2005 | 622.00 | 701.88 | 79.88 | 87.1576 |

2006 | 846.00 | 796.31 | –49.69 | 94.1265 |

2007 | 901.00 | 903.44 | 2.44 | 99.7292 |

2008 | 1096.00 | 1025.00 | –71.00 | 93.5219 |

2009 | 1124.00 | 1162.90 | 38.90 | 96.5392 |

2010 | 1441.00 | 1319.30 | –121.70 | 91.5545 |

2011 | 1597.00 | 1496.80 | –100.20 | 93.7257 |

2012 | 1729.00 | 1698.20 | –30.80 | 98.2186 |

2013 | 1680.00 | 1926.70 | 246.7 | 85.3155 |

_{0}= 0.6745 × 110.2 = 74.3299

#### 4.3. Results of the Dynamic Grey Prediction Model

**Table 3.**Dimensions and a posteriori error ratios using the discrete grey forecasting model DGM (1,1).

Dimension | 4 | 5 | 6 | 7 | 8 |

C | 0.2162 | 0.2394 | 0.2193 | 0.2209 | 0.2036 |

Dimension | 9 | 10 | 11 | 12 | - |

C | 0.2245 | 0.2493 | 0.2633 | 0.2079 | - |

Years | Raw Data | DGM (1,1) Data | Residual | Relative Error | Correctly Predicted Percentage |
---|---|---|---|---|---|

2002 | 148.00 | 148.00 | 0 | 0 | 100 |

2003 | 398.00 | 462.58 | −64.58 | −0.1396 | 86.0392 |

2004 | 493.00 | 543.28 | −50.28 | −0.0926 | 90.7451 |

2005 | 622.00 | 638.07 | −16.07 | −0.0252 | 97.4815 |

2006 | 846.00 | 749.39 | 96.61 | 0.1289 | 87.1082 |

2007 | 901.00 | 880.13 | 20.87 | 0.0237 | 97.6288 |

2008 | 1096.00 | 1033.70 | 62.30 | 0.0603 | 93.9731 |

2009 | 1124.00 | 1214.00 | −90.00 | −0.0741 | 92.5865 |

2010 | 1441.00 | 1425.80 | 15.20 | 0.0107 | 98.9339 |

2011 | 1597.00 | 1658.90 | −61.90 | −0.0373 | 96.2686 |

2012 | 1729.00 | 1852.00 | −123.00 | −0.0664 | 93.3585 |

2013 | 1680.00 | 2002.40 | −322.40 | −0.1610 | 83.8993 |

**Figure 4.**Prediction map for biofuel production using the eighth dimension of the discrete grey forecasting model DGM (1,1).

#### 4.4. Results of the Dynamic Grey Fuzzy Markov Prediction Model

**Table 5.**Categorizing China’s yearly biofuel production data into states according to the DGM (1,1) model (2002 to 2009).

Years | Raw Data | DGM (1,1) Data | Residual | Relative Error | State |
---|---|---|---|---|---|

2002 | 148.00 | 148.00 | 0 | 0 | 2 |

2003 | 398.00 | 462.58 | −64.58 | −0.1396 | 1 |

2004 | 493.00 | 543.28 | −50.28 | −0.0926 | 1 |

2005 | 622.00 | 638.07 | −16.07 | −0.0252 | 2 |

2006 | 846.00 | 749.39 | 96.61 | 0.1289 | 3 |

2007 | 901.00 | 880.13 | 20.87 | 0.0237 | 2 |

2008 | 1096.00 | 1033.70 | 62.30 | 0.0603 | 3 |

2009 | 1124.00 | 1214.00 | −90.00 | −0.0741 | 1 |

State | 2010 | 2011 | 2012 | 2013 |
---|---|---|---|---|

1 | 0.4383 | 0.4475 | 0.4429 | 0.4452 |

2 | 0.3150 | 0.3425 | 0.3287 | 0.3356 |

3 | 0.2002 | 0.2100 | 0.2283 | 0.2192 |

Years | DGM (1,1) Data | Improved Result | Upper Limit | Lower Limit | Mid Value | Probability |
---|---|---|---|---|---|---|

2010 | 1425.80 | 1400.13 | 1226.19 | 1368.77 | 1297.48 | 0.44 |

1425.80 | - | 1368.77 | 1482.83 | 1425.80 | 0.32 | |

1425.80 | - | 1482.83 | 1625.41 | 1554.12 | 0.25 | |

2011 | 1658.90 | 1623.44 | 1426.65 | 1592.54 | 1509.60 | 0.45 |

1658.90 | - | 1592.54 | 1725.26 | 1658.90 | 0.34 | |

1658.90 | - | 1725.26 | 1891.15 | 1808.20 | 0.21 | |

2012 | 1852.00 | 1816.05 | 1592.72 | 1777.92 | 1685.32 | 0.44 |

1852.00 | - | 1777.92 | 1926.08 | 1852.00 | 0.33 | |

1852.00 | - | 1926.08 | 2111.28 | 2018.68 | 0.23 | |

2013 | 2002.40 | 1861.67 | 1722.06 | 1922.30 | 1822.18 | 0.45 |

2002.40 | - | 1922.30 | 2082.50 | 2002.40 | 0.34 | |

2002.40 | - | 2082.50 | 2282.74 | 2182.62 | 0.22 |

Years | Raw Data | DGFM (1,1) Data | Residual | Relative Error |
---|---|---|---|---|

2002 | 148.00 | 148 | 0 | 0.0000 |

2003 | 398.00 | 462.58 | −64.58 | −0.1396 |

2004 | 493.00 | 543.28 | −50.28 | −0.0926 |

2005 | 622.00 | 638.07 | −16.07 | −0.0252 |

2006 | 846.00 | 749.39 | 96.61 | 0.1289 |

2007 | 901.00 | 880.13 | 20.87 | 0.0237 |

2008 | 1096.00 | 1033.7 | 62.3 | 0.0603 |

2009 | 1124.00 | 1214 | −90 | −0.0741 |

2010 | 1441.00 | 1400.13 | 40.87 | 0.0292 |

2011 | 1597.00 | 1623.44 | −26.44 | −0.0163 |

2012 | 1729.00 | 1816.05 | −87.05 | −0.0479 |

2013 | 1680.00 | 1861.67 | −181.67 | −0.0976 |

**Figure 5.**Prediction map for biofuel production using the dynamic grey fuzzy Markov DGFM (1,1) prediction model.

## 5. Comparison of the Three Methods

#### 5.1. Comparison in Terms of Prediction Data

Years | Raw Data | GM (1,1) | DGM (1,1) | DGFM (1,1) |
---|---|---|---|---|

2010 | 1441.00 | 1319.30 | 1425.80 | 1400.13 |

2011 | 1597.00 | 1496.80 | 1658.90 | 1623.44 |

2012 | 1729.00 | 1698.20 | 1852.00 | 1816.05 |

2013 | 1680.00 | 1926.70 | 2002.40 | 1861.67 |

#### 5.2. Comparison in Terms of Prediction Accuracy

Prediction Accuracies | GM (1,1) | DGM (1,1) | DGFM (1,1) |
---|---|---|---|

Correctly predicted percentage | 92.20% | 93.11% | 94.91% |

C-value | 0.2079 | 0.2036 | 0.1443 |

p-value | 83.30% | 91.60% | 91.60% |

## 6. Forecasting China’s Biofuel Production from 2015 to 2020 Using the DGFM (1,1) Model

#### 6.1. Forecasting Process

Years | Forcasting Data | Years | Forcasting Data |
---|---|---|---|

2015 | 2203.40 | 2018 | 2835.80 |

2016 | 2413.10 | 2019 | 3115.70 |

2017 | 2595.90 | 2020 | 3436.10 |

Years | Raw Data | DGM Data | Relative Error | State |
---|---|---|---|---|

2002 | 148.00 | 148.00 | 0.0000 | 2 |

2003 | 398.00 | 462.58 | −0.1396 | 1 |

2004 | 493.00 | 543.28 | −0.0926 | 1 |

2005 | 622.00 | 638.07 | −0.0252 | 2 |

2006 | 846.00 | 749.39 | 0.1289 | 3 |

2007 | 901.00 | 880.13 | 0.0237 | 2 |

2008 | 1096.00 | 1033.70 | 0.0603 | 3 |

2009 | 1124.00 | 1214.00 | −0.0741 | 1 |

2010 | 1441.00 | 1425.80 | 0.0107 | 2 |

2011 | 1597.00 | 1658.90 | −0.0373 | 2 |

2012 | 1729.00 | 1852.00 | −0.0664 | 1 |

2013 | 1680.00 | 2002.40 | −0.1610 | 1 |

**Table 13.**Modified forecast of China’s biofuel production for 2015 to 2020 using the DGFM (1,1) model.

Years | Forcasting Data | Years | Forcasting Data |
---|---|---|---|

2015 | 2153.11 | 2018 | 2771.07 |

2016 | 2358.02 | 2019 | 3044.58 |

2017 | 2536.65 | 2020 | 3357.67 |

#### 6.2. Analysis of the Results

## 7. Conclusions

- (1)
- The grey dynamic fuzzy Markov prediction model can blend in new information in a timely and effective manner. Simultaneously, it can discard outdated information, that is, information declines caused by time lapses. Moreover, compared to the conventional model, the results of the grey dynamic fuzzy Markov prediction model closely mirror the actual data.
- (2)
- The grey dynamic fuzzy Markov prediction model is based on the conventional GM (1,1) prediction model. The proposed model is simple and easy to understand. It has strong applicability and shows high precision as a linear prediction model. Thus, it has important practical significance, as shown in this study, for biofuel production prediction.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Geng, N.; Zhang, Y.; Sun, Y.; Jiang, Y.; Chen, D. Forecasting China’s Annual Biofuel Production Using an Improved Grey Model. *Energies* **2015**, *8*, 12080-12099.
https://doi.org/10.3390/en81012080

**AMA Style**

Geng N, Zhang Y, Sun Y, Jiang Y, Chen D. Forecasting China’s Annual Biofuel Production Using an Improved Grey Model. *Energies*. 2015; 8(10):12080-12099.
https://doi.org/10.3390/en81012080

**Chicago/Turabian Style**

Geng, Nana, Yong Zhang, Yixiang Sun, Yunjian Jiang, and Dandan Chen. 2015. "Forecasting China’s Annual Biofuel Production Using an Improved Grey Model" *Energies* 8, no. 10: 12080-12099.
https://doi.org/10.3390/en81012080