## 3 Numerical Study
### Numerical Study II: Comparison of Responses with Reduced Degrees of Freedom  
The low-fidelity model, which was elaborated and proven to be useful in the numerical Study I, is used here in this study for further parametric studies. A systematic parametric study is carried out in order to evaluate various modeling choices for the low-fidelity model elaborated above. One of the major points looked into was how many DoFs need to be present for the accurate prediction of the structural responses. The number of nodes or elements is systematically reduced in this study. The top-floor displacements, acceleration, and base reactions are the quantities of interest. Sixty elements are considered to comprise the highest resolution model. This resolution was used in the previous study to validate with a high-fidelity model. The major focus of the section is to identify the effect of the number of elements used for FEM modeling and the number of mode shapes considered in modal analysis for a reduction in various quantities of interest. Outline of the Parametric Study  
The parametric study is thought out such that the effect of variations in  
* Load scenario:
* Wind flow angle (\(0^{\circ}\), \(90^{\circ}\))
* Presence of turbulence (smooth exponential inlet profile or with fluctuations in time and space)
* Structural modeling: type of considered models
* Damping characteristics
* Mass and stiffness distribution along the height
* Detailing the level of the model represented by spatial resolution, achieved by \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Mean** & **Std** & **Mean + 3 Std** & **Max** & **99 th Percentile** \\ \hline HFM & \(3.04\times 10^{-2}\) & \(4.01\times 10^{0}\) & \(1.21\times 10^{1}\) & \(1.73\times 10^{1}\) & \(5.04\times 10^{0}\) \\ Fy [MN] & \(-4.66\times 10^{0}\) & \(1.80\times 10^{0}\) & \(7.25\times 10^{-1}\) & \(6.88\times 10^{-1}\) & \(-2.46\times 10^{0}\) \\ Fz [MN] & \(-3.71\times 10^{2}\) & \(4.59\times 10^{1}\) & \(-2.34\times 10^{2}\) & \(-1.73\times 10^{-1}\) & \(-3.78\times 10^{2}\) \\ Mx [MNm] & \(4.70\times 10^{2}\) & \(1.83\times 10^{2}\) & \(1.02\times 10^{3}\) & \(9.73\times 10^{2}\) & \(7.16\times 10^{2}\) \\ My [MNm] & \(1.96\times 10^{0}\) & \(4.22\times 10^{2}\) & \(1.27\times 10^{3}\) & \(1.34\times 10^{3}\) & \(5.52\times 10^{2}\) \\ Mx [MNm] & \(7.72\times 10^{-1}\) & \(2.60\times 10^{1}\) & \(7.88\times 10^{1}\) & \(1.10\times 10^{2}\) & \(3.37\times 10^{1}\) \\ \hline
**LFM** & & & & & \\ Fx [MN] & \(9.17\times 10^{-4}\) & \(3.45\times 10^{0}\) & \(1.03\times 10^{1}\) & \(1.08\times 10^{1}\) & \(4.55\times 10^{0}\) \\ Fy [MN] & \(-4.64\times 10^{0}\) & \(1.63\times 10^{0}\) & \(2.50\times 10^{-1}\) & \(2.95\times 10^{-2}\) & \(-2.64\times 10^{0}\) \\ Fz [MN] & \(-3.67\times 10^{2}\) & \(4.60\times 10^{1}\) & \(-2.29\times 10^{2}\) & \(0.00\times 10^{0}\) & \(-3.76\times 10^{2}\) \\ Mx [MNm] & \(4.58\times 10^{2}\) & \(1.77\times 10^{2}\) & \(9.88\times 10^{2}\) & \(9.59\times 10^{2}\) & \(6.97\times 10^{2}\) \\ My [MNm] & \(1.88\times 10^{0}\) & \(4.16\times 10^{2}\) & \(1.25\times 10^{3}\) & \(1.35\times 10^{3}\) & \(5.44\times 10^{2}\) \\ Mx [MNm] & \(8.72\times 10^{-1}\) & \(2.42\times 10^{1}\) & \(7.36\times 10^{1}\) & \(9.54\times 10^{1}\) & \(3.15\times 10^{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of HFM and LFM—base reaction for for 2.5% damping \(90^{\circ}\) wind. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Case** & **Quantity** & **HFM** & **LFM** & **Difference in \% from HFM** \\ \hline Table 1 & Max \(A_{y}\) [m/s\({}^{2}\)] & 0.373 & 0.365 & 2.14 \\ Table 2 & Max \(A_{x}\) [m/s\({}^{2}\)] & 0.541 & 0.531 & 1.84 \\ Table 3 & Mean \(F_{x}\) [MN] & 8.94 & 8.85 & 1.01 \\ Table 3 & Mean \(M_{y}\) [MNm] & 872 & 853 & 2.18 \\ Table 4 & Mean \(F_{x}\) [MN] & \(-4.66\) & \(-4.64\) & 0.43 \\ Table 2 & Mean \(M_{y}\) [MNm] & 470 & 458 & 2.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the HFM and LFM—summary.