## 4 Sound Quality Prediction
### Comparison of Prediction Results
By comparing the prediction accuracy of the three models, it can be found that the GRNN model has the best performance, and it not only has high prediction accuracy when the membership value is large, but it also has strong resistance to large data noise when the membership value is small. The values of R\({}^{2}\) range from 0 to 1, the closer the value is to 1, the better the model fits. If the R\({}^{2}\) value is close to 0, it means that the model is not explaining most of the variation in the data. \[R^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{\sum_{i=1}^{n} \left(y_{i}-\overline{y}\right)^{2}} \tag{7}\]  
where \(n\) is the number of samples, \(\hat{y}_{i}\) is the predicted value of the sample, \(y_{i}\) is the true value of the sample, and \(\overline{y}\) is the average of the predicted values. The comparison of R\({}^{2}\) on the three models is shown in Figure 9. Based on Figure 9, we can see that on the new dataset, the fitting degree of both the GRNN model and the SVR model is positively correlated with the membership value, and the GRNN model is better than the SVR model overall. For the RR model, the fitting degree fluctuates up and down as the membership value decreases. This phenomenon of R\({}^{2}\) value fluctuation indicates that with the decrease in membership value, the degree of disturbance gradually increases, and the noise of data also increases. However, the specific form and distribution of the noise may be different every time, and the RR model cannot handle the influence of these noises well, resulting in the fluctuation of the R\({}^{2}\) value. Compared with the membership value of 1, the fitting degrees of both the GRNN model and SVR model are obviously better when the membership value is 0.7 and 0.9. But when the membership value is less than 0.5, the fitting degree is worse. For the RR model, the fitting degree is lower for all membership values, indicating that the data noise introduced by fuzzy generation damages the performance of the model. By comparing the fitting degree of the three models, it can be found that when the membership degree is large, the fitting degree of the GRNN and SVR models is similar  
Figure 8: Comparison of prediction accuracy. and far better than that of the RR model. When the membership value decreases gradually, it can be seen that the GRNN model has the strongest fitting ability. A high RPD value means that the prediction error of the model is relatively small, indicating that the model has good consistency and stability under different datasets or conditions. \[RPD=\frac{\sqrt{\frac{\sum_{i=1}^{n}\left(y_{i}-\overline{y}\right)^{2}}{n-1}}}{ \sqrt{\frac{\sum_{i=1}^{n}\left[\left(y_{i}-\overline{y}\right)-\left(\overline {y}-y_{i}\right)\right]^{2}}{n-1}}} \tag{8}\]  
where \(n\) is the number of samples, \(\overline{y}_{i}\) is the predicted value of the sample, \(y_{i}\) is the true value of the sample, and \(\overline{y}\) is the average of the predicted values. The comparison of RPD on the three models is shown in Figure 10. As can be seen from Figure 10, after the fuzzy generation method is used, the model stability of the GRNN model is the best, the SVR model is second, and the RR model is the worst. With the decrease in membership value, the RPD values of both the GRNN model and the SVR model show a decreasing trend, which indicates that the stability of the model becomes worse. For the RR model, the RPD value is not related to the size of the membership value, and the stability of the model remains basically unchanged at a low level. Compared with the membership value of 1, the stability of both the GRNN model and the SVR model is greatly improved by using the fuzzy generation method. Even when the membership value is at the minimum of 0.1, they still have a good performance. However, for the RR model, the use of the fuzzy generation method slightly reduces the stability of the model.