## 4 Simulations
### Verification of Add-On Model Construction  
In this section, we explore the efficacy of the add-on model. Note that when a factory builds and uses an add-on model, it is possible to (1) use the method proposed in this paper to build a basic model and (2) directly use the company's existing method as a basic model. Thus, we conduct two rounds of experimental simulation. First, we use the proposed method to build a basic model as well as the add-on model. The accuracy of the basic models are 94.4% and 93.8% for the two experiments, respectively. Figures 13 and 14 present the importance rankings of the 21 features found by the RBF-DNN for the add-on model. Specifically, Figure 13 shows the results of identifying products that are too short as well as good products and products that are too long, while Figure 14 displays the results of identifying products that are too long as well as good products and products that are too short. A darker gradient indicates a higher ranking. First, the figures show that for all experiments, energy and root mean square improve significantly compared with the basic model (i.e., Figures 10 and 11). Since the primary learning goal of the add-on model is identifying the difference between the new category of product errors and the old category, the ranking of the place where the difference between the two is the largest will naturally increase. For the machine in this experiment, the length of the spring is related to the amount of time in which the machine outputs the wire and the time in which the machine allows the wire to form a ring. In addition, the length of the wire output time is related to the energy and root mean square of the Z axis. The amount of time the machine allows the wire to form a ring is related to the energy and root mean square of the Y axis, so the rankings of these four features will naturally increase. Second, the importance ranking of most features on the X axis shows a downward trend compared with the ranking of the basic model. This is because the proposed add-on model can take into account less knowledge than the basic model. Therefore, if the basic model learns the features on the X axis (as shown in Figures 10 and 11), then the importance ranking of these repeated features will naturally reduce. Third, the Z-axis features, other than energy and root mean square, are ranked very low in the add-on and basic models. Whether the RBF-DNN is used for the basic or add-on model, it will not select features that are not helpful for modeling. As shown in Figures 10, 11, 13 and 14, Z-axis features other than energy and root mean square are irrelevant to the spring manufacturing process, so they are always ranked low. \begin{table}
\begin{tabular}{c c} \hline \hline
**Inputs of the Basic Model** & **Accuracy** \\ \hline All 21 features & 100\% \\
1 st to 7 th most important features identified using the random forest & 90.2\% \\
8 th to 14 th most important features identified using the random forest & 85.3\% \\
15 th to 21 st most important features identified using the random forest & 83.7\% \\
1 st to 7 th most important features identified using RBF-DNN & 94.4\% \\
8 th to 14 th most important features identified using RBF-DNN & 84.1\% \\
15 th to 21 st most important features identified using RBF-DNN & 81.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of constructing basic model for products that are good and too long.