## 4 Simulations
### Verification of Basic Model  
In this section, we verify the efficacy of RBF-DNN for the identification of key features for basic model construction. First, Figures 10 and 11 show the importance ranking of the 21 features found by RBF-DNN for the basic model. Specifically, Figure 10 shows the results of constructing the basic model for products that are good and too long, and Figure 11 presents the results of constructing the basic model for products that are good and too short. Higher rankings are indicated by a darker gradient. It can be seen that the importance ranking is generally consistent with better features on the X axis than those on the Y axis, which are better than those on the Z axis. This is not surprising because the machine used in this experiment mainly moves in the direction of the x axis, and then in the direction of the y axis. Thus, the features identified by the RBF-DNN are ranked accordingly. The z axis is only related to the output movement of the wire, and the signal on the accelerometer remains almost unchanged, so the data represented on this axis are unrelated to product damage. Figure 11: Importance ranking of 21 features found by RBF-DNN for basic model (good and too short), where darker gradients indicate higher rankings. Figure 10: Importance ranking of 21 features found by RBF-DNN for basic model (good and too long), where darker gradients indicate higher rankings. Figure 12 shows the results of experiments on selecting the number of key features. The x axis of these two figures represents the use of the first few features to build the basic model, and the y axis represents the accuracy of the established basic model. This figure shows that x = 7 is the watershed for accuracy changes. Before 7, the accuracy slowly increases, but after 7, it remains stable. Therefore, we select seven modeling features for each of the two sets of experiments. Tables 2 and 3 compare the efficacy of the proposed approach (i.e., using the top seven features identified using the RBF-DNN) with other methods for basic model construction. The latter included using all 21 features, with the 8 th to 14 th most important features (seven in total) identified using the RBF-DNN, the 15 th to 21 st most important features identified using the RBF-DNN, the 1 st to 7 th most important features (seven in total) identified using the random forest, the 8 th to 14 th most important features (seven in total) identified using the random forest, and the 15 th to 21 st most important features identified using the random forest for basic model construction. Note that this paper uses random forests as the comparison method because they are the most commonly applied for feature extraction in machine learning. The important feature values are set in units of 7 to allow RBF-DNNs to be compared fairly with random forests. Table 2 shows the results of constructing the basic model for products that are good and too long, and Table 3 presents the results of constructing the basic model for products that are good and too short. It is clear from the two tables that, in most cases, the results of using the features ranked as more important by the RBF-DNN were better than those of using less important features. The accuracy of the model constructed using the last seven features was the poorest. These results demonstrate the effectiveness of the proposed RBF-DNN. Next, using all 21 features to construct the basic model produces better results than using only the top seven features identified using the RBF-DNN. However, the computational costs of using all 21 features for modeling are more than three times as high as those of the proposed approach. As both models offer high accuracy, the additional computational costs of the comparative model seem unnecessary. Finally, comparing the RBF-DNN method with a random forest, we can see that the RBF-DNN method can improve modeling accuracy under only seven features. This further confirms the rationality of using the RBF-DNN in the proposed method.