# Research on a Coal Seam Gas Content Prediction Method Based on an Improved Extreme Learning Machine
## 2 Development of Prediction Models for Coal Seam Gas Content
### Development of a Gas Content Prediction Model Based on the GASA-KELM Algorithm
#### 3.2.2 Primary Controlling Factors of Gas Content Based on Grey Correlation Analysis  
The prediction of gas content is a challenging nonlinear prediction problem that is affected by various factors. Grey system theory is a suitable method for such problems with limited data, and grey correlation analysis can determine the extent to which each reference sequence affects the parent sequence. The quantitative ordering of correlations provides a clear comprehension of the relationship between various influencing factors and helps identify the principal controlling factors of gas content.  
The GRA method is used to screen the main controlling factors for the model's input. The steps of the grey relational calculation are as follows [35]:  
1. Setting reference sequence and comparison sequence: Reference sequence: Gas content (\(X_{0}\)), Comparison sequence: Eight influencing factors of coal seam gas content.
2. Data preprocessing and normalization: According to Formula (8), the data will be normalized. \[x_{l}^{\prime}(h)=\frac{x_{l}(h)-x_{min}}{x_{max}-x_{min}}\] (8) where \(x_{l}(h)\) is the value of the \(l\)-th evaluation index of the sample with the number \(h\); \(h\) represents the sample number, \(h\) = 1, 2,..., \(n\); \(l\) represents the evaluation index, \(l\) = 1, 2,..., \(m\); and \(x_{max}\) and \(x_{min}\) are the maximum and minimum values of the evaluation index, respectively.
3. To calculate the correlation coefficient: The calculation of correlation coefficient is obtained according to Formula (9). \[\xi_{e}(k)=\frac{\underset{e}{min}\underset{k}{min}|x_{0}(k)-x_{e}(k)|+\rho \underset{e}{max}\underset{k}{max}|x_{0}(k)-x_{e}(k)|}{|x_{0}(k)-x_{e}(k)|+\rho \underset{e}{max}\underset{k}{max}|x_{0}(k)-x_{e}(k)|}\] (9)  
The symbol \(\xi_{e}(k)\) denotes the correlation coefficient of the comparison sequence \(x_{e}\) with respect to the reference sequence \(x_{0}\) on index \(k\), where \(k\) ranges from 1 to \(n\). The parameter \(\rho\), which takes a value between 0 and 1, is the resolution coefficient.
4. To compute the correlation degree: Calculate the correlation degree using Formula (10). \[r_{e}=\frac{1}{n}{\sum_{k=1}^{n}w_{k}\xi_{e}(k)}\] (10) where \(n\) is the number of samples, \(r_{e}\) is the correlation degree of the comparison sequence \(x_{e}\) with the reference sequence \(x_{0}\), and \(w_{k}\) is the weight of the indicator.
5. Ranking of correlation and determination of input parameters  
Table 4 presents the results of the correlation analysis, revealing that the correlation coefficients of the influencing factors \(X_{3}\) and \(X_{4}\) fall below 0.5, indicating a low correlation. Consequently, these factors are eliminated. This brings the number of input layer nodes to 6, as the data dimension in Table 3 is reduced from 8 to 6. The six highly correlated gas content influencing factors are the only inputs for the model, whereas the other two factors are no longer involved in the modeling process.