## 2 Material and Method
### Modeling of Electricity Pole  
The numerical model of the reinforced concrete electric pole was developed using the ANSYS Workbench platform. In the model, the concrete material was defined with a modulus of elasticity of 35 GPa and a density of 2400 kg/m\({}^{3}\), while the reinforcement steel was assigned a modulus of elasticity of 200 GPa and a density of 7850 kg/m\({}^{3}\). The FE representation of the pole, including the reinforcement detailing and overall geometry, is illustrated in Figure 5. The FE model was constructed using 2880-3802 elements and 20,280-28,392 nodes. In this study, various parameters, including elasticity values, heights, and both lower and upper outer and inner diameters of the electric pole, were identified as significant variables. Figure 6 illustrates the flow chart developed for the purposes of this research. The elasticity values were established at 30, 32, 33, 34, 36, and 37 GPa. The height measurements were defined as 9.3, 10.1, 10.92, 11.73, and 12.54 m, reflecting the heights commonly utilized within the industry. The Lower Inner Diameter (Bid) was designated at 0.125, 0.25, 0.75, and 1 m, which are particularly favored in the sector. To ensure a consistent gradient \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mode No.**} & **Experimental** & **FE Mode** & **Frequency** \\  & **Frequency (Hz)** & **Frequency (Hz)** & **Difference (\%)** \\ \hline
1 & 20.48 & 20.79 & 1.52 \\ \hline
2 & 57.07 & 56.51 & \(-\)0.98 \\ \hline
3 & 112.10 & 113.17 & 0.95 \\ \hline
4 & 169.2 & 174.70 & 3.25 \\ \hline
5 & 183.8 & 192.58 & 4.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental and FE model frequencies of the validated beam and frequency differences. Figure 4: The first five natural frequencies obtained from the FE model of the validated beam. between the top and bottom of the electric pole, the Lower Outer Diameter (Bod), Upper Inner Diameter (Tid), and Upper Outer Diameter (Tod) were calculated in relation to the Bid values. This paper presents a workflow, as illustrated in the accompanying figure, designed to estimate model frequencies for electric poles without the need for detailed analysis. To this end, a sensitivity analysis was conducted utilizing the identified variables relevant to the electric pole, resulting in the acquisition of model frequencies. Subsequently, the data obtained from this analysis underwent a pre-processing stage to prepare it for the regression model. In the dataset analysis, all numerical data underwent standardization. This process resulted in normalized data with a mean of 0 and standard deviation of 1, thereby achieving an approximately normal distribution. This standardization process was crucial for optimizing model performance and ensuring consistent scaling across all variables. The dataset was then divided into training and testing subsets, following a 30-70% split, and estimation analyses were carried out. The estimations derived from the training dataset were rigorously compared with the testing dataset, yielding estimation accuracies for each frequency analyzed. All parameters in the study consisted of continuous numerical values representing the physical properties and dimensions of the electric poles. The standardization process was applied to both input features and target variables, ensuring consistent scaling throughout the dataset. This preprocessing step was fundamental for the performance of the ridge regression model and the reliability of the results. Ten-fold cross-validation is a resampling method employed to reduce bias in the training data and to determine if the model's performance is attributable to randomness. The training data is divided into 10 segments, known as folds. In each iteration, one fold is designated as the validation set, while the other nine folds are utilized for training. After completing this process for all ten folds, the resulting model performances are assessed and averaged to confirm the model's validity. Figure 5: Finite element model of electric pole.