## 5 Experiments and Discussions
### Cutting-Tool Wear Classification  
For the implementation of the HDL algorithm, the hardware used in this paper comprises six Intel Xeon Gold 6142 processors (3.5 GHz, 27.1 GB, Intel Corporation, Santa Clara, CA, USA) and NVIDIA RTX 3080 graphics processors (10.5 GB, NVIDIA Corporation, Santa Clara, CA, USA). The Stochastic Gradient Descent (SGD) optimizer is used to train the HDL model, and the fixed step-size decay (StepLR) learning strategy is used to make the model converge quickly in the later stage. The parameter settings for HDL model training are shown in Table 8.  
Figure 11: Dynamic frequency response diagram of cutting force estimation. Figure 12: Cutting force of sinusoidal morphology estimated by system identification method. The data results obtained through training are shown in Table 9. The classification accuracies of the models trained from the force data collected by the Kistler dynamometer were all higher than the models trained from the estimated force data. The resolution on the cutting force of the dynamometer is better than the HDL-based cutting force estimation model, which may lead to the acquisition of force signals being more accurate than the estimated force signals. At the same time, there are also many noises in the machining signals obtained by the grating ruler and acquisition card. These noises may also have a great influence on the classification results, which results in low classification accuracy. Through the training results, it can be seen that the errors of the trained HDL model on the training set are close to 0, and the classification accuracy on the training set and the test set is higher than 85%. However, the accuracy of the two models on the training set is higher than that on the test set, indicating that the models still have the phenomenon of overfitting, and the generalization ability of the models still needs to be improved. The classification errors mainly appeared in the classification of no wear and slight wear, but the classification errors for severe wear were few. The reason is that the amount of datasets used for training is small. To obtain a model with stronger generalization ability, the datasets need to be further augmented. The HDL proposed in this paper was compared with other neural network models including AlexNet and VGG. The estimated cutting force data were input into these other networks. The classification results of the three networks are shown in Table 10.  
Through the comparison of classification results, it can be seen that the HDL model proposed in this paper has higher accuracy classification results than other network models. AlexNet has fewer network structure parameters (occupying 1.4 GB memory) than the network structure parameters used in this paper (occupying 1.5 GB memory), and its convergence speed in the training process is slower. While the network structure parameters of VGG (occupying 1.6 GB memory) are more complex, the main reason for its low classification accuracy is the phenomenon of overfitting, indicating that the network structure is too complex compared to the amount of training datasets. Therefore, the HDL model proposed in this paper is more consistent with the amount of datasets collected, so the training effect is better. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**HDL**} & \multicolumn{2}{c}{**AlexNet**} & \multicolumn{2}{c}{**VGG**} \\ \hline Cases & Horizontal & Inclined & Horizontal & Inclined & Horizontal & Inclined \\ \hline Accuracy & 89.3\% & 86.6\% & 84.3\% & 79.4\% & 75.7\% & 80.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Classification results of different models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Learning Rate** & **Weight Decay** & **Step Size** & **Epoch Times** & **Batch Size** \\ \hline Value/Type & 0.01 & 0.001 & 10 & 100 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameter settings of HDL.