## 4 Results and Discussion
### Discussion  
From Figure 10b, it can be seen that the predicted results of 18 rockburst cases based on the improved VFS method are basically consistent with the actual rockburst strength grade, except for No. 3, 5, and 9. No. 3, 5, and 9 belong to mixed-grade rockburst, and the actual rockburst grades are III-IV, II-III, and III-IV, respectively.  
The new method improves the traditional VFS method from two aspects: simplifying the RMD calculation process and optimizing the SRMD. Then, what are the advantages of the new method compared with the traditional VFS method after such improvement? The following are discussed in detail:  
1. The improved VFS method has higher computational efficiency: Equation (41) can clearly show that the simplified RMD calculation method can reduce the number of RMD function operations at least two times compared with the traditional RMD calculation method. With the number increase of classifications level, indicators, and samples, this advantage will become more prominent. Since the distribution characteristics of RMD functions at different levels are known in advance (Figures 3c, 4c and 5c), the simplified RMD calculation method is simpler and more direct for RMD calculation, which greatly improves the operation efficiency of the improved VFS method.
2. The improved VFS method can verify the correctness of RMD calculation results at all times: RMD is the core theme of the improved VFS method, which concerns whether the final prediction results are correct or not. Therefore, the effective guarantee of the correctness of RMD calculation results is the premise of obtaining high-precision prediction results. According to RMD relationship characteristic Equations (20), (26), and (28), the range of traditional RMD value \([0,\,1]\) is reduced. For example, the eigenvalue of \(\sigma_{\theta}/\sigma_{c}\) in Tianshengqiao II hydropower station is located in the interval of level II, so \(0.5\leq u_{12}(x)\leq 1\), \(0\leq u_{11}(x)\leq 0.5\), and \(0\leq u_{13}(x)\leq 0.5\). In addition, \(u_{11}(x)+u_{13}(x)=0.5\). These features can be used to verify the correctness of RMD calculation results.
3. The improved VFS method has higher prediction accuracy: From Figure 10a, it can be found that the prediction results based on the traditional VFS method are not ideal regardless of the weight. For example, the predicted results of No. 2, 4, and 11 are totally inconsistent with the actual strength grade. However, the prediction accuracy is significantly improved after the optimization of the initial SRMD using the BP neural network. This phenomenon shows that the combination of BP neural network and the VFS method can improve the classification and prediction ability of the model.
4. The improved VFS method has higher fault tolerance and practicability: From Figure 10a, we can also find that the prediction results of traditional VFS method are easily affected by the weight values and that different weight values may lead to different prediction results, resulting in misjudgment. For example, the prediction results of No. 2-4, 8-12, 14, and 18 rockburst cases span different levels in different weights. However, after the initial SRMDs are optimized by using the fuzzy BP optimization neural network model, the prediction results are basically consistent under different weights, which is within the same strength level, except for No. 3. The above results show that the improved VFS method has higher fault tolerance and anti-jamming ability and that its dependence on weight is low, so it has better practicability.