## 3 Results
### Comparison  
The performance comparison of the three models, support vector machine (SVMs), boosting ensemble decision trees, and long short-term memory (LSTM) neural network, is summarized in Table 5. The comparison focuses on two main aspects: the number of critical errors and the average accuracy achieved by each model. The SVM model outperforms the others with the highest average accuracy of 96.00% and no critical errors. This demonstrates its robustness and reliability for the tool state recognition task in milling processes. This high performance can be attributed to SVM's effectiveness in handling high-dimensional data and its capability of finding the optimal hyperplane that separates the different tool states. The boosting ensemble decision trees, applying a boosting approach with 100 trees, show decent performance with an average accuracy of 89.33%. They encounter only one critical error, indicating reasonable reliability. The ensemble's strength lies in its ability to reduce bias and variance, combining multiple weak learners to improve overall prediction accuracy. In contrast, the LSTM model exhibits a significant drop in performance with the lowest average accuracy of 45.33% and the highest number of critical errors (7). This may be due to the LSTM's sensitivity to parameter settings and the complexity of time-series data in tool state recognition, which poses challenges in capturing temporal dependencies effectively. The comparative analysis of the LSTM, SVM, and boosting ensemble decision trees reveals significant insights into the challenges and advantages of each model in the context of tool state recognition in milling processes. The low effectiveness of the LSTM model is particularly noteworthy, with its challenges attributed to the limited training data, the absence of feature selection for sequential data, and the lack of domain-specific pre-trained models for time series analysis. These factors collectively hinder the LSTM's ability to learn and generalize effectively, leading to its diminished performance compared to SVM and boosting ensemble decision trees. In contrast, the SVM model's superior performance underscores the importance of appropriate feature selection and the advantage of methods well-suited to high-dimensional data. The boosting ensemble decision trees, with their inherent feature selection capabilities and ensemble learning approach, also demonstrate commendable performance, though not matching the SVM's effectiveness. This comparison not only highlights the strengths and weaknesses of each model but also points to broader challenges in applying deep learning models like LSTM to time series data in industrial applications. The absence of pre-trained networks and the critical need for extensive training data and effective feature selection mechanisms are evident challenges that need to be addressed in future research. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Classifier** & **Critical Errors** & **Training Time** & **Prediction Time** & **Accuracy** \\ \hline SVM & 0 & 2 h 34 m 12 s & 0.12 s & 96.00\% \\ Boosting & 1 & 18 m 29 s & 0.05 s & 89.33\% \\ Ensemble DT & 7 & 13 m 17 s & 0.69 s & 45.33 \% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparative analysis of the performance metrics across three different classifiers. Two main parameters are shown: accuracy, which measures the overall amount of correctly classified cases, and the number of critical errors (mistakes between green and red classes) that each classifier performed. Efforts to develop domain-specific pre-trained models for time series data, advanced feature selection techniques, and strategies to augment training data could significantly enhance the applicability and performance of deep learning models in this domain. Such advancements would not only improve model accuracy and reliability but also expand the potential of machine learning in industrial and manufacturing settings, leading to more efficient and automated processes.