## 2 Material and Method
### Model Evaluation Metrics  
In this study, several metrics were employed to assess the models, including Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Correlation Coefficient (R\({}^{2}\)). These metrics have been used to estimate and compare the prediction accuracy and error rates of the models analyzed in the literature ([PERSON] and [PERSON], 2024; [PERSON] et al., 2025; [PERSON] et al., 2025; [PERSON] et al., 2024). MAPE, an evaluation metric, expresses the error rate of the model as a percentageand is calculated as shown in Equation (2). The MAE is determined by taking the absolute value of the difference between each predicted value and the actual value, as illustrated in Equation (3). A lower MAE value, approaching zero, indicates enhanced prediction performance of the model. Another important metric is the RMSE, widely recognized for regression problems, which is computed as outlined in Equation (4). Similarly to the MAE, a lower RMSE signifies more accurate predictions. Since RMSE shares the same units as the dependent variable, it is frequently preferred over Mean Square Error (MSE) and MAE for evaluating the performance of regression models alongside other models. Additionally, the R\({}^{2}\) value, calculated using Equation (5), serves as a regression evaluation criterion that ranges from 0 to 1, with values closer to 1 indicating a superior model fit. The result derived from the R\({}^{2}\) value can also be interpreted as the proportion of variance explained by the model. \[\text{MAPE}=\frac{1}{n}  
Figure 7: _Cont._  
Upon examining the obtained frequencies, it was observed that Frequency (F) 1 and F2 are numerically very close to each other, as are F3 and F4; F5, F6 and F7; F8 and F9; and F10. Consequently, similar numerical frequency values were consolidated as a result of the modal analysis. In this study, F1 and F2 are the mod x and y translations for the first bending mode, F3 and F4 are the mod x and y translations for the second bending mode, F5 is the mod first torsion mode, F6 and F7 are the mod x and y translations for the third bending mode, F8 is the mod x translations for the fourth bending mode, F9 is the mod y translations for the fifth bending mode, and F10 is the mod x translation for the sixth bending mode. Figure 8: _Cont._  
Figure 7: Ten-mode graph for 9.3 m height of electric pole. Additionally, the frequency values obtained from the modal analysis were categorized based on six different variables: Elastic, Height, Bid, Tid, Bod, and Tod. The statistical significance of the model was \(\sigma=0.01\). The results were obtained using the same model as the one in the previous section. Figure 8: Mode shapes of electricity poles with different heights and axis descriptions. properties of these variables corresponding to each frequency value are presented in Table 3. According to the data, the Elastic value ranges from 30 GPa to 37 GPa, while the heights span from 9.3 m to 12.54 m. Furthermore, FE analysis indicated that each successive frequency value exceeds the preceding one when compared across the ten frequency values analyzed. The correlations among the variables Elastic, Height, Bid, Tid, Bod, and Tod--representing distinct frequencies--along with their relationships to frequency values across various modes, are illustrated in Figure 9. Upon examining the high correlation values among these variables, several key observations can be made:  
* A consistent and strong negative correlation exists between the 'height' variable and the '\(\prime\)' variables across all modes. This indicates that as the 'height' increases, the '\(\prime\)' values tend to decrease. Notably, the intensity of this negative correlation generally escalates with higher mode numbers. * A robust positive correlation is observed between the 'bid' and 'tod' variables across all modes (r \(\approx\) 0.85).