# Coal and Gas Outburst Risk Prediction and Management Based on WOA-ELM
## 5 Results and Discussion  
### WOA-ELM Model Prediction Analysis  
The prediction results of the WOA-ELM model are compared with those of the ELM, the GA-ELM model, and the Cuckoo Search algorithm optimized ELM (CS-ELM) model. The hidden layer function is a sigmoid function. The number of hidden layer nodes is 10, the population in the GA algorithm is 20, the crossover probability is 0.7, and the mutation probability is 0.1; In the CS algorithm, the population number is 20, and the discovery rate of alien eggs is 0.25. Each algorithm is run 20 times; the results are shown in Figure 5 and Table 9.  
Figure 4(a) compares the prediction results and actual values of the WOA-ELM and the ELM models. It can be seen from the comparison that the prediction results of many samples after ELM model training deviate from the actual values. In contrast, the prediction results of the WOA-ELM model are closer to the actual values [33]. Figure 4(b) compares the predicted results of the ELM model, the GA-ELM model, and the CS-ELM model and the actual values. It can be seen that the distance between the predicted results of the GA-ELM model and the CS-ELM model and the actual values is small, which indicates that the accuracy of the ELM model has been improved after optimization. It can be seen from the comparison between the predicted values of the WOA-ELM, the CS-ELM, and the GA-ELM and the actual values in Figure 4(c),d that the WOA-ELM model is more accurate, and the data in Table 9 can also prove this conclusion. Figure 5: Comparison of predicted values before and after model optimization. The performance of each model can be analyzed through the MAE, SSE, \(R^{2}\), and MRE. Wherein MAE refers to the Mean Absolute Error, the average value of the absolute error, and its expression is shown in Formula (15); SSE refers to the sum of squares of residuals, which is the sum of squares of errors between predicted data and actual data. The closer the SSE is to 0, the better the model fitting is, and the more successful the data prediction is. Its expression is shown in Formula (16); MRE refers to the average relative error, and its expression is shown in Formula (17). \(R^{2}\) measures the correlation between the predicted and actual values, as shown in Formula (18). The closer \(R^{2}\) is to 1, the more accurate the prediction is. \[\text{MAE}=\frac{\sum_{pre=1}^{n}\abs{x_{act}-x_{pre}}}{n} \tag{15}\]  
\[\text{SSE}=\sum_{i=1}^{n}w_{i}\big{(}x_{pre}-x_{act}\big{)}^{2} \tag{16}\]  
\[ \begin{cases}\frac{MRE=\frac{\overline{a}}{\overline{x}}}{\overline{x}=\frac{ \sum_{pre=1}^{n}x_{pre}}{n}}\\ \overline{d}=\frac{\sum_{pre=1}^{n}\abs{x_{pre}-\overline{x}}}{n}\end{cases}  \tag{17}\]  
\[R^{2}=\frac{\sum_{pre=1}^{n}\big{(}x_{pre}-x_{act}\big{)}^{2}}{\sum_{pre=1}^{ n}\big{(}x_{pre}-\overline{x_{pre}}\big{)}^{2}} \tag{18}\]  
where \(x_{pre}\) is the predicted value of each sample; \(x_{act}\) is the actual value; n is the number of samples; \(\overline{x}\) is the average of the predicted values; \(\overline{d}\) is the average error; \(w_{i}\) is the weight, generally \(\frac{1}{n}\);  
Table 10 shows the ELM training set and test set-related statistics before and after optimization, which are determined by correlation analysis. The same data is simulated and predicted by four models: the WOA-ELM, the GA-ELM, the CS-ELM, and the ELM. It can be seen that: (1) although the MAE of the GA-ELM and the CS-ELM is smaller than that of the ELM, the MAE of the WOA-ELM is further reduced on this basis; (2) compared with other models, the SSE of the WOA-ELM model is the closest to 0, and its reasonable degree is better than that of the GA-ELM and the CS-ELM models; and (3) when the WOA-ELM model is used for prediction, the MRE of the training set and test set is the smallest among all models, which is more improved than the GA-ELM and the CS-ELM. Therefore, from this point of view, the WOA-ELM model has higher precision, minor error, and a better fitting degree, which is more advantageous than the GA-ELM and the CS-ELM [39].