## 4 Experimental Verification
### Experimental Result
#### 4.2.2 Results and Analysis  
In this study, three sets of comparative tests of the models--KANS-ResNet-34, ResNet-34, and ResNet-50--were conducted. The classification ability of the constructed models served as the evaluation criterion for the tool wear state recognition system. To assess the advantages and disadvantages of the new model constructed in this study compared to the two original models, the classification ability was evaluated using the test set from the experiment. The model performance was evaluated using the following five classification metrics: accuracy, sensitivity, specificity, checking accuracy, and \(F1\) score, which are expressed by the following formulas:  
Accuracy:  
\[Acc=\frac{TP+TN}{TP+TN+FP+FN} \tag{5}\]  
Recall Ratio:  
\[\text{Rec}=\frac{TP}{TP+FN} \tag{6}\]  
Specificity:  
\[Spe=\frac{TN}{TN+FP} \tag{7}\]  
Precision:  
\[\text{Pr}=\frac{TP}{TP+FP} \tag{8}\]  
\(F1\) Score:  
\[F1 score=\frac{2\times Pr\times\text{Rec}c}{\text{Pr}+\text{Rec}c} \tag{9}\]  
where true positive (_TP_) is the number of samples in which the actual wear state matches the predicted wear state, false positive (_FP_) is the number of samples in which another wear state is incorrectly predicted as that wear state, true negative (_TN_) is the number of samples in which other wear states are correctly predicted to not belong to that category, and false negative (_FN_) is the number of samples that were actually in that wear state but were predicted incorrectly. In multi-categorization tasks, the concepts of true-positive (_TP_) and true-negative (_TN_) examples are slightly different from those in binary categorization  
Figure 8: Analyzing three wear stages of AE signals. and need to be subdivided for each category. We usually compute these metrics by treating each category as a separate binary classification problem, and the categorization results used in this manuscript are computed for the categorization results in the network output confusion matrix for the macro concept. The KANS-ResNet-34 model is selected, with an epoch set to 100 iterations, and the improved adaptive learning rate algorithm AdamW is chosen. AdamW, an optimization algorithm based on Adam, improves weight decay, making it more effective in handling regularization and better at avoiding overfitting. The resulting accuracy, loss, and learning rate curves are shown in Figure 9.  
Figure 9 shows that when the epoch number of the KANS-ResNet-34 model reaches 30, the accuracy and loss of both the training and validation sets stabilize and reach a high level. This indicates that the model has achieved convergence, and the learning rate gradually stabilizes at this point. To avoid unnecessary iterative operations and the risk of \"pseudo-convergence,\" the early stopping method is used to select the optimal model. At this point, the model's accuracy reaches 99.37%, with the epoch set to 50 for the entire test, making 50 the number of iterations. KANS-ResNet-34, ResNet-34, and ResNet-50 were trained and tested with an epoch of 50. The accuracy and loss of the three models are shown in Figure 10.  
As shown in Figure 10, the accuracy and loss of all three models stabilized with an increase in the number of iterations, with the most variation occurring in the first five iterations. The KANS-ResNet-34 and ResNet-50 models stabilized around 10 iterations,  
Figure 10: Loss and accuracy plots for three models. Figure 9: Accuracy, loss, and learning rate curves for epochs = 100.  
whereas the ResNet-34 model stabilized only around 15 iterations. The KANS-ResNet-34 and ResNet-50 models both exhibited smaller loss fluctuations compared to the ResNet-34 model. The KANS-ResNet-34 model reached a maximum accuracy of 99.28% at 15 iterations, while the ResNet-50 model achieved a maximum accuracy of 99.64% at 20 iterations. The ResNet-34 model, although achieving its highest accuracy at 20 iterations, had a maximum accuracy of 98.21%, which was slightly lower than that of the other models.