## 4 Validation of the Numerical Algorithm for Simulated Bare Riser VIV Response  
In this section, a validation of the proposed algorithm using the VIVANA program is explained. A numerical case study for a bare riser at a flow speed of 1.0 m/s is conducted. The analysis results with default excitation coefficient parameters from VIVANA are compared with the newly generated excitation coefficient parameters until the predicted response frequency, the mode number and the maximum fatigue damage matches with the default test data provided by VIVANA. The obtained excitation coefficients are compared with the default values to examine the validity of the algorithm.  
In this validation study, new sets of excitation coefficient parameters are generated after applying the modification factors. The non-dimensional frequency for this section ranges between 0.130-0.190 with a step of 0.002, whereas the modification factors for \(A/D\) and \(Cc\) ranges between 0.5-1.2 with a step of 0.1, and 0.9-1.6 with a step of 0.05, respectively. Table 2 shows the newly generated data sets with \(\gamma_{A/D}\) ranging from 0.5-1.2 and \(\gamma_{Cc}=0.8\). In the present analysis, the flow of current is perpendicular to the riser model.  
Based on the non-dimensional frequency range and the modification factors, 3720 different sets of excitation parameters are generated. Thus, 3720 simulations with these input parameters are carried out. Examples of new parameter sets are presented in Table 2. The set of parameters which presents good approximation with default parameters is selected based on specified criteria as presented in Table 3.  
The optimal parameter set presented in Table 4. The corresponding fatigue damage comparison is shown in Figure 4. The comparison of the predicted mode number, response frequency is presented in Table 5. The prediction with set no. 2660, the mode number and response frequency are identical to the default test case with 4 and response frequency 2.78 Hz, respectively. The maximum accumulated fatigue damage for set no. 2660 is 6.5% less than the default test case which is acceptable based on the specified criteria as shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Set No.** & \(\overset{\star}{f_{CF}}\) & (_A/D_)\({}_{C_{CF}=0}\) & (_A/D_)\({}_{C_{CF}=max}\) & \(\textit{Ce}_{CF}\)=max_ & \(\textit{Ce}_{CF,A/D}\)=0 & \(\mathcal{Y}_{A/D}\) & \(\mathcal{Y}_{C_{s}}\) \\ \hline
2660 & 0.12 & 0.149 & 0.100 & 0.10 & 0.000 & - & - \\
0.170 & 0.900 & 0.430 & 0.80 & 0.400 & 1.0 & 1.0 \\
0.300 & 0.160 & 0.100 & 0.100 & 0.000 & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Identified optimal parameter set.  
Figure 4: Comparison of the predicted fatigue damage between parameter set no. 2660 and default parameters. The results using the default parameters overlap with the results using parameter set no. 2660.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Specified Criteria** & **Deviation of Predicted Response from Test Case** \\ \hline Mode number & 0 \\ Response Frequency & \(\pm\)10\% \\ Fatigue damage & \(\pm\)10\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Specified criteria for selecting the optimal set of parameters.  
The identified excitation coefficient parameter corresponds to a lower non-dimensional frequency (yellow line in Figure 5b) compared to the default values (middle red line in Figure 5a). The comparison of the identified parameters and the default parameters are presented in Table 6. The comparison shows that this algorithm can identify the simplified excitation coefficient database with good accuracy.