## 3 Results
### Optimization of ANN Hyperparameters Using Genetic Algorithm
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hyperparameter** & **Polished Surface** & **Glazed Surface** & **Ground Surface** \\ \hline Number of hidden neurons & 17 & 21 & 20 \\ Transfer function for hidden layer & Softmax Transfer & Softmax Transfer & Logarithmic Sigmoid \\ Transfer function for & Function & Function & Transfer Function \\ Transfer function for & Elliott Sigmoid Transfer & Elliott Sigmoid Transfer & Elliott Sigmoid Transfer \\ output layer & Function & Function & Function \\ Training validation test & 0.97428/ & 0.96174/ & 0.95128/ \\ ratio & 0.012859 & 0.019132 & 0.024359 \\ Number of epochs & 1000 & 1000 & 1000 \\ Training function & Levenberg–Marquardt & Levenberg–Marquardt & Levenberg–Marquardt \\  & Backpropagation & Backpropagation & Backpropagation \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of ANN best models hyperparameters. Figure 7: MSE through optimization processes for different surface types: (**a**) polished surface; (**b**) glazed surface; (**c**) ground surface. neurons, indicates a simpler architecture, suggesting that the patterns in the data for this surface are relatively less complex. Conversely, the glazed surface model employs 21 hidden neurons, implying a more intricate structure to accommodate the potentially higher variability or complexity in its data. The ground surface model, with 20 hidden neurons, represents an intermediate level of complexity, tailored to balance simplicity and effectiveness for this surface type. Regarding the transfer function for the hidden layer, the polished and glazed surface models utilize the Softmax Transfer Function. This choice is often associated with tasks involving multi-class classification or when the network outputs probabilistic distributions. In contrast, the ground surface model adopts the Logarithmic Sigmoid Transfer Function, which is well suited for regression tasks and ensures smoother activations with outputs constrained within a specific range (0 to 1). These distinctions indicate that the activation function was selected to match the expected characteristics of the output data for each surface type. All three models share a common transfer function for the output layer, the Elliott Sigmoid Transfer Function. This function is particularly effective in regression problems, enabling predictions to be scaled within a bounded range, which aligns with tasks requiring precise numerical outputs, such as the minimization of the MSE. The training validation test ratios exhibit slight variations among the surfaces. The polished surface model dedicates 97.428% of the data to training, with only 1.2859% allocated to both validation and testing, emphasizing a focus on model accuracy through extensive training data. The glazed surface model uses a slightly lower training proportion (96.174%) while retaining a comparable split for validation and testing. The ground surface model allocates 95.128% to training, with a relatively larger share (2.4359%) devoted to validation and testing. This increased allocation to validation and testing suggests a greater emphasis on model generalization for the more complex ground surface data. Each model was trained for 1000 epochs, ensuring sufficient iterations for optimizing the network's weights and achieving convergence. This uniform choice across all surface types reflects a consistent training strategy designed to fully leverage the available data. Finally, the models employed the Levenberg-Marquardt backpropagation algorithm for training. This algorithm is renowned for its efficiency and stability, especially with small- to medium-sized datasets, as it combines the advantages of the Gauss-Newton method and gradient descent. Its application underscores a deliberate choice to accelerate convergence while maintaining a robust performance across all models. In summary, the ANN models for the polished, glazed, and ground surfaces demonstrate a thoughtful design and tuning of hyperparameters tailored to the specific data characteristics of each surface type.