## 4 Simulations
### Verification of Transfer Learning for the Combination of Basic and Add-On Models  
The experimental results shown in Table 8 confirm the effectiveness of transfer learning in the combination of basic and add-on models to upgrade existing fault detection systems. There are three sets of experiments in total, and the values in each set of experiments in the table are the best results of 30 experiments. The first group uses all 21 features to establish three categories of classification models as the control group. These classification models were implemented using Matlab's NNstart toolbox and the deep neural network kit [56]. The network directly uses the toolbox's default value. Deep neural networks use six hidden layers and one output layer. Each hidden layer uses the tangent sigmoid function as the activation function, and the last layer uses SoftMax. As for other parameters, we use the Adam accelerator for training and early stops to avoid overfitting. This control group represents the case in which a factory does not use the transfer learning concept and directly uses the old categories with a new error category (which is the most common scenario in practice). The second and third groups are the two sets of experiments we conducted in the above two sections. These two sets of experiments can also be regarded as the results of using basic and add-on models to realize the concept of transfer learning. Note that although the basic model considers different types of errors in these two sets of experiments, they still identify the same three categories of errors with the add-on model. We thus compared these with the control group. The results in Table 8 show the superiority of the experimental results of the control group. This is not surprising, because if all categories of data are given to the model at once, the model will be able to fully consider the differences in the three categories of data when learning and thus obtain the highest recognition accuracy. However, we observe the results of these sets of experiments from the perspective of statistical significance, as shown in Figure 19, where the highest, middle, and lowest values of each set represent the mean + standard deviation, mean, and mean\(-\)standard deviation results of 30 experiments. As shown, the numerical ranges between the four groups of experiments overlap, which means that there is no statistically significant difference between them. Therefore, the results of the proposed method are similar to those of the control group, but the proposed model enables factories to upgrade existing models without abandoning the original model or using a low-cost model with fewer features to build an add-on model. This means that the proposed model approach is in line with real-world demands. This conclusion verifies the effectiveness of the transfer learning concept.  
\begin{table}
\begin{tabular}{c c} \hline
**Inputs of Basic Model** & **Accuracy** \\ \hline All 21 features & 94\% \\
1 st to 7 th most important features identified using the random forest & 91.4\% \\
8 th to 14 th most important features identified using the random forest & 89.1\% \\
15 th to 21 st most important features identified using the random forest & 88.1\% \\
1 st to 7 th most important features identified using RBF-DNN & 91.8\% \\
8 th to 14 th most important features identified using RBF-DNN & 90.2\% \\
15 th to 21 st most important features identified using RBF-DNN & 84.6\% \\ \hline \end{tabular}
\end{table}
Table 7: Results of constructing add-on model for existing model for products that are too long.  
\begin{table}
\begin{tabular}{l c} \hline
**Control group: one model (good + too long + too short)** & \\ \hline Method & Accuracy \\ \hline All 21 features + Matlab’s NNstart toolbox & 94.5\% \\ \hline All 21 features + deep neural network kit & 93.6\% \\ \hline \end{tabular}
\end{table}
Table 8: Best results of combining basic and add-on models.