## 2 Numerical Modelling
### Validation of the Basic Model
In addition, the natural frequency of the tower-bottom fixing is 0.502 Hz. Figure 4: Dimension and nonlinear variation of elastic modulus of numerical model. Figure 3: Schematic diagram of numerical model for monopile supported offshore wind turbine. Another computation was carried out to further verify the effectiveness of the numerical model established above. Using this model, the natural frequencies of offshore wind turbines at the North Hoyle Wind Farm were determined. The parameters of the pile are as follows: The pile diameter is 4 m and the buried depth is 33 m, and the wall thickness is 50 mm. The blades and turbine are modeled as a 100-ton concentrated mass. The tower features a total height of 67 m, with a top diameter of 2.3 m, a bottom diameter of 4 m, and a wall thickness of 35 mm. The transition section has an overall height of 7 m, a diameter of 4 m, and a wall thickness of 50 mm [29]. The elastic modulus and density of the tower, pile, and transition section match those used in the previous calculation. In addition, the soil site condition is also mainly dense sand, so the soil parameters are still referring to Table 1.  
The same method was used to calculate the natural frequency. Displacement loads of 8 cm and 5 cm were imposed at the tower's top, respectively. The loads were then removed, allowing the structure to vibrate freely. A time-history of dynamic response is generated, corresponding to Figure 4(b), while the power spectrum is presented in Figure 4(b). As shown above, the natural frequency is 0.349 Hz, while that linked to tower-top fixing stands at 0.494 Hz. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wind Power** & **Measured** & **Calculated Frequency/Hz** & \multicolumn{2}{c}{**Error**} \\
**Plant Name** & **Frequency/Hz** & **NO-SSI** & **SSI** & **NO-SSI** & **SSI** \\ \hline Belwind & 0.361 & 0.502 & 0.353 & 39\% & 2.2\% \\ North Hoyle & 0.350 & 0.494 & 0.349 & 41\% & 0.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of natural frequency for numerical results and measured data. Figure 5: Time-history curve of lateral response displacement for tower-top. Figure 6: Power spectrum of the tower-top response. The comparison between the numerical results and the measured data from the study by [PERSON] et al. [28] is presented in Table 1. This measurement is conducted at the Belwind wind farm. Ten sensors in total were used to collect measurements at four levels across nine locations. Data acquisition proceeds continuously, with data transmitted to the onshore server every 10 min. The long-term measured results are used to evaluate the results of calculated method. It can be noted from Table 1. When the tower-bottom is fixed, the errors between measured data and calculated results are great. Nevertheless, upon taking soil-pile interaction into account, the discrepancies in both cases are found to be around 2.0%, indicating a notable improvement in accuracy. Research indicates that soil-pile interaction should be taken into account when calculating natural frequencies. At the same time, it is verified that the established numerical model is very effective in this study, so the numerical calculated method is used to obtain the natural frequency in the following study.