# A New Method for Calculating Prediction Parameters of Surface Deformation in the Mining Area
## 4 Model Verification  
To verify the generalization performance of the M-CM-GA-ELM model, the subsidence coefficient \(q\) was taken as an example for analysis. There were few measured data (nearly 20) collected in the Huainan mining area, so it was difficult to meet the data requirements of  
Figure 8: Calculation process of M-CM-GA-ELM model. the neural network. In this paper, some measured data were collected from Reference [36]. In addition, there are 70 sets of subsidence coefficient values from observation stations in the Huainan mining area. According to the analysis of Section 3.2, the factors affecting the subsidence are mining depth, thickness of bedrock and thickness of unconsolidated layer. Similar to Section 3.2, this paper constructed a multivariate linear fitting model based on 70 sets of data from observation stations. The fitting results are shown in Figure 9.  
In order to establish the fusion model, 70 groups of data were divided into two groups in this paper. Eighty percent of the measured data (56 groups) were used for modeling, and twenty percent of the data (14 groups) were used to verify the prediction performance of the model. Relevant parameters of the M-CM-GA-ELM model were set as follows. The number of input layer neurons was 2 (\(H_{0}\) and \(h_{\text{s}}\)), the number of hidden layers was 12, the number of output layers was 1, and the activation function adopted the sig function. To reduce the running time, the running times were set to 50 in the CM model. To verify the prediction effect of the M-CM-GA-ELM model, the regression formula of the subsidence coefficient \(q\) with \(H_{0}\) and \(h_{\text{s}}\) was \(q=-0.5114(H_{0}-h_{\text{s}})/H_{0}+1.174\), and the CM-GA-ELM model, CM-ELM model, ELM model, and GA-ELM model were applied for comparison. The results are shown in Figure 10.  
In Figure 10, the violin chart is used to compare the accuracy of five prediction models. It is usually used to show the distribution state and probability density of multiple groups of  
Figure 10: Comparison of prediction results. Figure 9: Relationship between subsidence coefficient and mining depth ratio of bedrock. data, mainly to show the distribution shapes of data. The white dot on the chart represents the median, the black bar represents the range of quartiles, the thin black line represents the 95% confidence interval, and the width of the violin represents the value taking probability of the observed value. The violin chart can show the overall distribution of data in addition to the above statistics. Therefore, Figure 10 can explain different prediction accuracy of the five models. The M-CM-GA-ELM model has the smallest black bar and black line, and the center is around 0, indicating that the error range between the predicted value and the actual value is the smallest. On the other hand, the width of the M-CM-GA-ELM model is relatively wide near 0, where most of the errors are distributed. To sum up, the M-CM-GA-ELM combined model has the highest prediction accuracy. In order to quantitatively analyze differences between the prediction performance of the improved ELM neural network prediction model and that of the conventional ELM neural network model, evaluation indexes of the prediction of the ELM prediction model, the CM-ELM prediction model, the GA-ELM prediction model and the CM-GA-ELM prediction model were calculated, respectively. In this paper, the average relative error and the RMSE of the prediction results were taken as evaluation indexes:  
\[\text{MeaRE}=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{x_{i}^{\prime}-x_{i}}{x_{i}} \right|\times 100\% \tag{12}\]  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(x_{i}^{\prime}-x_{i}\right) ^{2}} \tag{13}\]  
where \(x_{i}^{\prime}\) is the \(i\)th predicted value; \(x_{i}\) is the \(i\)th measured value; \(n\) is the number of predicted samples. Among them, MeaRE represents the stability of the prediction results. The smaller the value, the higher the stability of the prediction model.