# A Gas Emission Prediction Model Based on Feature Selection and Improved Machine Learning

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Data Processing for Gas Emission Prediction

#### 2.1. Initial Index System of Gas Emission Prediction

^{3}/t), the gas content of adjacent seam (X2, m

^{3}/t), coal seam thickness (X3, m), coal seam buried depth (X4, m), coal seam dip angle (X5, °), coal seam spacing (X6, m), interlayer lithology (X7, m), floor elevation (X8, m), advance speed (X9, m/d), gas pressure (X10, MPa), gas extraction pure quantity (X11, m

^{3}/min), and roof management mode (X12). Among them, 24 groups were used as training sets, while the last 6 groups were used as test sets. It can be seen from Figure 1 that there is no obvious linear correlation between mine gas emission and influencing factors(Black square is the fitting equation and related parameters, red line is the fitting curve).

#### 2.2. Data Standardization Processing

_{i}is the original sequence, $\overline{x}$ is the average value of the sequence, s is the standard deviation, and h

_{i}represents the new sequence after transformation, i ∈ [1, n].

## 3. Construction of the Mine Gas Emission Prediction Model

#### 3.1. Determination of Characteristic Parameter Sets for Gas Emission Prediction

#### 3.1.1. Total Subset Regression

^{2}was used. R

^{2}is the determination coefficient that reflects the accuracy of model fitting data and ranges from 0 to 1. The closer the value is to 1, the more the variable in the equation explains y and the better the model fits the data. The least square fitting was applied to all variable combinations, and a total of 18 characteristic parameter sets with a sound fitting effect of R

^{2}≥ 0.90 were selected, which are expressed as F-1, …. At the same time, the original set was expressed as F-0, and the selection of each influencing factor in the set is shown in Table 2 with “☆”.

#### 3.1.2. Kernel Principal Component Analysis (KPCA)

_{k}(k = 0, 1, 2, …, 12; there are 12 factors affecting mine gas emission), X

_{k}∈ R. By introducing a nonlinear function Φ(X

_{k}), the data sample might be converted into a high-dimensional space, and the covariance matrix C is as follows:

_{i}is the Lagrange multiplier. After combining Formulas (2) and (3) and adding kernel function K, we can get:

_{n}represents a matrix of x

_{n}and can represent that the elements in the matrix are $\frac{1}{n}$ (n∈R). According to the formula $\sum _{k=1}^{s}{\lambda}_{k}/{\displaystyle \sum _{k=1}^{m}{\lambda}_{k}}$, the contribution rate of each factor affecting the amount of gas emission can be calculated. Influencing factors with a cumulative contribution rate of more than 85% (Table 3) can be added to the index.

#### 3.2. A Selection of Gas Emission Prediction Algorithms

## 4. Optimal Fusion Model Selection

#### 4.1. Determination of the Optimal Parameter Set

_{o}refers to the observed value, Q

_{m}refers to the simulated value, Q

_{t}represents a value at time t, and ${\stackrel{-}{Q}}_{0}$ represents the overall average observed value. The value of E is negative infinity to 1. Additionally, the closer E is to 1, the higher the quality and credibility of the model.

^{2}: Determination coefficient, which reflects the accuracy of the model fitting data and ranges from 0 to 1. The closer the value is to 1, the more the variable in the equation explains y and the better the model fits to the data.

#### 4.2. Determination of the Optimal Improved Machine Learning Algorithm

## 5. Conclusions

^{2}) being 0.99395, the Nash coefficient (NSE) being 0.99241, the mean absolute error (MAPE) being 0.20306, and the mean absolute percentage error (MAPE) being 1.0595%. Results showed that the model proposed by this paper was better than the original index system and the one undergone KPCA dimensionality reduction by a large margin.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Comparison of the optimization results of different parameter sets under different algorithms.

X_{1} | X_{2} | X_{3} | X_{4} | X_{5} | X_{6} | X_{7} | X_{8} | X_{9} | X_{10} | X_{11} | X_{12} | Y | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 4.55 | 3.78 | 9.84 | 550.32 | 4.20 | 15.83 | 3.02 | 913.54 | 7.40 | 0.35 | 4.80 | 1 | 25.73 |

2 | 3.95 | 3.53 | 8.78 | 577.5 | 3.60 | 20.34 | 3.38 | 920.65 | 7.20 | 0.32 | 4.67 | 1 | 23.44 |

3 | 2.85 | 2.2 | 6.13 | 510.58 | 2.40 | 24.37 | 2.91 | 793.20 | 6.70 | 0.25 | 4.50 | 1 | 18.30 |

4 | 3.81 | 2.93 | 8.51 | 639.53 | 3.70 | 25.22 | 3.48 | 854.84 | 7.30 | 0.27 | 3.72 | 1 | 21.07 |

5 | 4.22 | 3.67 | 7.54 | 650.12 | 3.90 | 26.21 | 3.31 | 872.09 | 7.10 | 0.23 | 4.04 | 1 | 23.30 |

6 | 4.13 | 3.59 | 8.69 | 641.82 | 3.20 | 33.28 | 2.43 | 875.15 | 6.50 | 0.33 | 3.35 | 1 | 22.17 |

7 | 4.34 | 3.72 | 8.74 | 664.48 | 3.90 | 22.06 | 2.90 | 865.18 | 7.20 | 0.35 | 3.11 | 1 | 23.63 |

8 | 4.57 | 3.82 | 10.57 | 720.22 | 4.40 | 17.21 | 3.11 | 925.24 | 7.50 | 0.36 | 3.79 | 1 | 26.12 |

9 | 3.81 | 3.58 | 7.38 | 652.35 | 3.30 | 15.73 | 3.69 | 840.59 | 7.30 | 0.28 | 3.22 | 1 | 22.61 |

10 | 2.89 | 2.35 | 5.96 | 491.75 | 2.50 | 26.87 | 3.56 | 812.59 | 7.40 | 0.29 | 3.01 | 1 | 16.63 |

11 | 3.14 | 3.23 | 6.38 | 508.17 | 2.90 | 29.10 | 2.81 | 834.33 | 6.90 | 0.23 | 3.19 | 1 | 18.25 |

12 | 4.57 | 3.74 | 8.85 | 712.25 | 3.90 | 17.56 | 3.40 | 846.53 | 7.40 | 0.33 | 2.49 | 1 | 24.60 |

13 | 3.51 | 2.76 | 7.26 | 531.35 | 3.20 | 27.76 | 2.85 | 867.83 | 6.80 | 0.28 | 2.50 | 1 | 19.00 |

14 | 3.71 | 2.84 | 9.8 | 629.55 | 3.40 | 13.30 | 3.04 | 913.71 | 7.30 | 0.30 | 3.48 | 1 | 22.67 |

15 | 3.76 | 3.37 | 9.37 | 639.67 | 3.50 | 16.58 | 3.05 | 885.61 | 7.20 | 0.26 | 3.17 | 1 | 23.05 |

16 | 3.15 | 2.51 | 6.36 | 514.03 | 2.80 | 18.90 | 2.50 | 859.43 | 6.80 | 0.22 | 2.89 | 1 | 19.34 |

17 | 4.11 | 3.54 | 7.78 | 597.87 | 3.70 | 11.35 | 3.45 | 871.07 | 6.90 | 0.33 | 2.50 | 1 | 20.93 |

18 | 4.18 | 2.75 | 7.08 | 502.45 | 3.60 | 32.53 | 3.57 | 904.41 | 6.90 | 0.18 | 3.00 | 1 | 18.54 |

19 | 2.71 | 2.81 | 6.45 | 488.96 | 2.70 | 26.46 | 3.46 | 847.72 | 6.80 | 0.15 | 3.30 | 1 | 19.65 |

20 | 3.64 | 2.89 | 6.85 | 465.42 | 3.40 | 28.99 | 2.46 | 816.14 | 6.60 | 0.18 | 3.36 | 1 | 16.65 |

21 | 3.66 | 3.40 | 8.35 | 516.57 | 3.40 | 23.72 | 2.75 | 840.67 | 7.40 | 0.17 | 3.70 | 1 | 18.52 |

22 | 4.07 | 3.09 | 5.48 | 572.34 | 2.80 | 26.16 | 3.33 | 874.15 | 7.00 | 0.20 | 3.64 | 1 | 19.73 |

23 | 3.74 | 3.30 | 8.22 | 623.52 | 3.20 | 13.36 | 2.97 | 847.57 | 6.60 | 0.18 | 3.51 | 1 | 20.85 |

24 | 2.73 | 2.57 | 5.86 | 457.53 | 2.50 | 24.69 | 3.10 | 778.53 | 7.30 | 0.21 | 2.98 | 1 | 15.67 |

25 | 3.42 | 2.30 | 6.13 | 493.20 | 2.20 | 28.17 | 2.91 | 785.41 | 6.60 | 0.20 | 3.29 | 1 | 17.24 |

26 | 3.65 | 3.94 | 6.52 | 584.00 | 2.80 | 23.93 | 2.92 | 793.10 | 6.60 | 0.22 | 4.08 | 1 | 19.76 |

27 | 3.15 | 2.96 | 5.26 | 536.24 | 2.90 | 33.45 | 2.66 | 811.35 | 6.50 | 0.18 | 3.27 | 1 | 18.65 |

28 | 4.13 | 3.32 | 7.18 | 648.45 | 3.90 | 24.19 | 3.47 | 894.11 | 7.30 | 0.34 | 4.52 | 1 | 21.83 |

29 | 4.24 | 3.62 | 8.67 | 671.30 | 3.80 | 17.52 | 2.56 | 861.71 | 7.30 | 0.27 | 4.48 | 1 | 22.15 |

30 | 2.46 | 2.82 | 5.83 | 505.57 | 2.40 | 33.57 | 2.79 | 779.70 | 6.30 | 0.14 | 3.73 | 1 | 14.57 |

Influencing Factor | X_{1} | X_{2} | X_{3} | X_{4} | X_{5} | X_{6} | X_{7} | X_{8} | X_{9} | X_{10} | X_{11} | X_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

F-0 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ |

F-1 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-2 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-3 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-4 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-5 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-6 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-7 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-8 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-9 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-10 | ☆ | ☆ | ☆ | ☆ | ☆ | |||||||

F-11 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-12 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-13 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-14 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-15 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ||||||

F-16 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-17 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ | |||||

F-18 | ☆ | ☆ | ☆ | ☆ | ☆ | ☆ |

Kernel Principal Component | F_{1} | F_{2} | F_{3} | F_{4} | F_{5} | F_{6} | F_{7} | F_{8} | F_{9} | F_{10} | F_{11} | F_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

variance contribution rate % | 53.11 | 11.41 | 8.31 | 6.57 | 5.63 | 4.30 | 3.38 | 2.14 | 1.75 | 1.35 | 0.90 | 0.52 |

Parameter Combinations | Improved Algorithm | RMSE | MAE | MAPE | R^{2} | NSE |
---|---|---|---|---|---|---|

F-0 | GA-HKELM | 0.93431 | 0.63198 | 3.8216% | 0.88091 | 0.87333 |

F-K | SSA-HKELM | 1.02890 | 0.71577 | 4.2977% | 0.88348 | 0.84639 |

F-4 | WOA-HKELM | 0.28456 | 0.25234 | 1.3347% | 0.98987 | 0.98825 |

F-5 | SSA-HKELM | 0.37306 | 0.26626 | 1.3719% | 0.99184 | 0.97980 |

F-5 | SMA-HKELM | 0.25932 | 0.23025 | 1.2184% | 0.99194 | 0.99024 |

F-5 | WOA-HKELM | 0.22865 | 0.20306 | 1.0595% | 0.99395 | 0.99241 |

F-11 | SSA-HKELM | 0.37306 | 0.26626 | 1.3719% | 0.99184 | 0.97980 |

F-11 | MFO-HKELM | 0.31620 | 0.24417 | 1.2260% | 0.99592 | 0.98549 |

F-11 | WOA-HKELM | 0.31637 | 0.24134 | 1.2068% | 0.99594 | 0.98548 |

F-17 | MFO-HKELM | 0.31620 | 0.24417 | 1.2260% | 0.99592 | 0.98549 |

F-17 | WOA-HKELM | 0.31637 | 0.24134 | 1.2068% | 0.99594 | 0.98548 |

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**MDPI and ACS Style**

Shao, L.; Zhang, K.
A Gas Emission Prediction Model Based on Feature Selection and Improved Machine Learning. *Processes* **2023**, *11*, 883.
https://doi.org/10.3390/pr11030883

**AMA Style**

Shao L, Zhang K.
A Gas Emission Prediction Model Based on Feature Selection and Improved Machine Learning. *Processes*. 2023; 11(3):883.
https://doi.org/10.3390/pr11030883

**Chicago/Turabian Style**

Shao, Liangshan, and Kun Zhang.
2023. "A Gas Emission Prediction Model Based on Feature Selection and Improved Machine Learning" *Processes* 11, no. 3: 883.
https://doi.org/10.3390/pr11030883