## 5 Results and Discussion
### Optimization Results of Stress Distribution Based on BLSGAOM  
Drawing upon the parameter design presented in Table 2, the contact force dynamics of the gear tooth profile are dissected. This analytical framework then sets the stage for the integration of conformal mapping techniques specific to multi-connected domains. The intricate cycloidal gear tooth profile is seamlessly mapped onto a unit circle through this approach. The magic of this conformal mapping lies in its transformative capability; it simplifies the complex contour of the gear tooth to the elementary geometry of a unit circle. As alluded to in Section 3.3, utilizing the approximate relationships of the scaling factors enables the stress distribution results, which were originally derived from the FEM on the unit circle, to be inversely mapped onto the cycloidal gear tooth profile. This technique substantially curtails the computational overhead that is typically associated with stress distribution calculations, offering both efficiency and precision. For this study, the Least Squares Boosting (LSBoost) method was enlisted to train the machine learning models. This endeavor commenced with the segregation of the dataset; of the 1000 data instances, 80% fueled the training phase, while the remaining 20% were earmarked for testing. Two pivotal hyperparameters--the learning rate and the number of learning epochs--were subjected to rigorous optimization. Specifically, the learning rate oscillated between 0.01 and 0.2, whereas the epochs ranged from 50 to 200. The Bayesian optimization, as depicted in Figure 11, underpinned the hyperparameter tuning phase, selecting the optimum values based on the anticipated improvements. The k-fold cross-validation technique was employed during model training to ensure both a robust assessment of the performance and a bulwark against overfitting. Upon finalizing the hyperparameters, the model was trained using the dataset and subsequently engaged in predictions. To rigorously evaluate the predictive capacity of the model, we employed a comprehensive set of critical performance metrics. The Mean Square Error (MSE), a key indicator of the predictive accuracy, denoted an average squared difference of 9.6527 \(\times\) 10\({}^{-7}\) between the predicted and observed values, highlighting the model's precision. This precision was further reinforced by the Root Mean Square Error (RMSE), valued at 9.8248 \(\times\) 10\({}^{-4}\), and the Mean Absolute Error (MAE), which reflected an average deviation of 2.7699 \(\times\) 10\({}^{-4}\). Additionally, the model's explicative prowess was exemplified by an R-squared value of 0.9998, indicating that it could account for nearly all the variability in the data, as graphically illustrated in Figure 12. In pursuit of sustained research continuity and replicability, the optimally trained model was archived, priming it for prognosticating fresh datasets. This strategic archiving not only ensures seamless future applicability but also fosters the study's replicability in analogous scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline Loading torque, \(T\) (Nm) & 600 & Number of teeth of cycloid gears, \(z_{a}\) & 23 \\ Density, \(\rho\) (Kg/m\({}^{3}\)) & 7830 & Pinion number, \(z_{b}\) & 24 \\ Poisson’s ratio, \(\
u\) & 0.3 & Pitch radius of pin teeth, \(r_{b}\) (mm) & 72 \\ Pin tooth center circle radius, \(R_{b}\) (mm) & 100 & Pitch radius of the cycloid gear, \(r_{a}\) (mm) & 69 \\ Eccentricity, \(e\) (mm) & 3 & Pin tooth radius, \(r_{p}\) (mm) & 10 \\ Elastic modulus, \(E\) (GPa) & 208 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design parameters of the cycloid-pin system for SACGES-CMMD. In the present investigation, the GA was harnessed for model parameter optimization.