## 5 Conclusions  
This study presents a machine-learning-based methodology for feed rate optimization in machining, integrating GA-calibrated cutting force modeling with vibration analysis. By leveraging a theoretical cutting force dataset and employing FFT-based frequency analysis, relatively stable machining conditions are identified, enabling the determination of optimal feed rates. The proposed XGBoost regression model, trained using these optimal feed rates, effectively captures the nonlinear relationships between machining parameters and chatter suppression. Bayesian optimization further enhances model performance by fine-tuning hyperparameters, resulting in an R\({}^{2}\) score of 0.7887. The findings demonstrate that this approach provides a reliable, data-driven solution for feed rate determination, eliminating the need for exhaustive experimental trials. The trained model can provide practical machining parameter recommendations, offering guidance on optimal feed rates to minimize chatter and improve process stability. This methodology was experimentally validated using a UR10e robotic arm setup, where the predicted feed rate achieved the lowest Pt value and exhibited the smoothest surface profile, confirming the model's practical effectiveness. Future research can enhance this framework by incorporating additional  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Feed Rate**} & **Pt (\(\mu\)m)** & **Ra (\(\mu\)m)** \\  & **[95\% CI]** & **[95\% CI]** \\ \hline
162 & 18.26 [11.32–25.20] & 0.832 [0.630–1.034] \\
156 & & \\ (mm/min) & 22.55 [17.43–27.66] & 1.094 [0.615–1.572] \\
180 & 21.27 [15.45–27.09] & 0.938 [0.713–1.162] \\
120 & 23.25 [18.26–28.24] & 1.639 [0.914–2.363] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Pt and Ra values with 95% confidence intervals for each tested feed rate.  
Figure 13: Boxplots of surface roughness metrics Pt and Ra were measured under four different feed rates.  
-machining parameters, real-time sensor data, and adaptive control strategies to improve predictive robustness and generalization capabilities.  
Conceptualization, Y.-P.Y. and H.-H.T.; Data curation, Y.-P.Y.; Formal analysis, Y.-P.Y.; Funding acquisition, J.-Y.C.; Methodology, Y.-P.Y. and H.-H.T.; Software, Y.-P.Y. and H.-H.T.; Supervision, J.-Y.C.; Validation, Y.-P.Y.; Writing--original draft, Y.-P.Y.; Writing--review and editing, J.-Y.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Science and Technology Council of Taiwan, grant number NSTC 113-2218-E-007-025.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} GA & Genetic Algorithm \\ FFT & Fast Fourier Transform \\ XGBoost & eXtreme Gradient Boosting \\ Pt & Peak-to-valley height \\ Ra & Arithmetic Average Roughness \\ R\({}^{2}\) & Coefficient of Determination \\ RMSE & Root Mean Squared Error \\ MAE & Mean Absolute Error \\ GP & Gaussian Process \\ EI & Expected Improvement \\ UCB & Upper Confidence Bound \\ PI & Probability of Improvement \\ SMBO & Sequential Model-Based Optimization \\ SVM & Support Vector Machine \\ \end{tabular}