## 4 Simulations
### Verification of Add-On Model Construction
\begin{table}
\begin{tabular}{c c} \hline \hline
**Inputs of the Basic Model** & **Accuracy** \\ \hline All 21 features & 98.5\% \\
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 & 87.9\% \\
15 th to 21 st most important features identified using the random forest & 87.7\% \\
1 st to 7 th most important features identified using RBF-DNN & 93.8\% \\
8 th to 14 th most important features identified using RBF-DNN & 88.1\% \\
15 th to 21 st most important features identified using RBF-DNN & 85.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of constructing basic model for products that are good and too short. Figure 15 shows the experimental results of selecting the number of key features, where the \(x\) axis represents the number of the most important features used for add-on model construction and the \(y\) axis indicates the accuracy in the resulting add-on model. It is clear that there are turning points in error at \(x\) = 7. We therefore selected \(x\) = 7 as the number of features for add-on model construction to strike a balance between prediction accuracy and modelling cost. Tables 4 and 5 compare the efficacy of the proposed approach with that of existing methods in add-on model construction. The latter again included 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 identified using the RBF-DNN for model construction, and the three sets of experiments with the random forest. Table 4 shows the results of identifying products that are too short in addition to products that are good and too long. Table 5 displays  
Figure 14: Importance ranking of 21 features found by RBF-DNN for add-on model (good and too short \(\rightarrow\) too long) using proposed method to construct basic model, where darker gradients indicate higher rankings. Figure 15: The results of selecting the number of key features for the add-on model in the first situation. Figure 13: Importance ranking of 21 features found by RBF-DNN for add-on model (good and too long \(\rightarrow\) too short) using proposed method to construct basic model, where darker gradients indicate higher rankings. the results of identifying products that are too long in addition to products that are good and too short. It is clear that the accuracy of the model constructed using the seven most important features ranked by the RBF-DNN was better than that of using less important features. Next, using all 21 features to construct the add-on model produced slightly better results than using the seven most important features ranked by the RBF-DNN. However, this approach increases the construction costs of the add-on model substantially. Finally, the RBF-DNN outperforms the random forest. This again confirms the rationality of using the RBF-DNN to select features for modeling. The second scenario simulated uses an existing basic model and an add-on model constructed using the proposed method. We adopt the most intuitive approach to the basic model and directly input all 21 features into a neural network implemented using the suite provided by Matlab R2022b. That is, in Tables 2 and 3, all 21 dimensions are used as the control group of model inputs. The accuracy of the basic models was 100% and 98.5% for the two experiments, respectively. First, Figures 16 and 17 show the importance rankings of the 21 features found by the RBF-DNN for the add-on model in this situation. Figure 16 shows the results of identifying products that are too short in addition to products that are good and too long. Figure 17 displays the results of identifying products that are too long in addition to products that are good and too short. Darker gradients indicate higher rankings. Comparing these figures with Figures 13 and 14, we see that the results are almost the same.