# Nonlinear Response Prediction of Spar Platform in Deep Water Using an Artificial Neural Network
## 4 Discussion  
The performance of the artificial neural network (ANN) model was evaluated primarily using three parameters: root-mean-square errors (RMSE), the coefficient of correlation (\(R\)), and bias (Table 7). The statistical parameters were analyzed from the network-predicted results and the target for the training data. The ANN results exhibited good performance for predicting the wave height and wave period, as revealed by the high correlation coefficient values of 0.996 and 0.989, respectively. The artificial neural network (ANN) model's predictions were compared to the observed values of wave height and wave period. It was critical to train the network so that the series-parallel configuration errors were relatively tiny for the model to be effective in parallel response (iterated prediction). The greatest prediction error was less than \(\pm 1\) per cent, and this model can estimate wave height and period based on randomly selected wind forces. The relative comparison between the ANN and FEM models' results for surge response error is shown in Figure 14. The ANN model's overall performance was obtained to be reliable for predicting surge responses. \begin{table}
\begin{tabular}{l c c c c c} \hline
**Mooring line Tension (N)** & **Min** & **Max** & **Mean** & **Standard Deviation** \\ \hline Resp-Pred & 11,182,323.9 & 17,085,820.59 & 16,263,011 & 463,165.8 \\ FEM & 11,182,200 & 17,062,834.5 & 16,266,318 & 463,666.5 \\ Difference (\%) & 0.001 & 0.13 & 0.020 & 0.108 \\ \hline \end{tabular}
\end{table} 
Table 6: FEM and ANN results for statistical mooring line top tension response for wave height of 12.65 m and time of 11.39 s.  
Figure 13: Top tension response time history predicted for 14.15 s wave period and 11.30 m wave height. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Parameter** & **Max. Error** & **Min Error** &
\begin{tabular}{c} **Standard** \\ **Deviation Error** \\ \end{tabular} & **RMSE** & **Bias** & **R** \\ \hline Wave Height (m) & 0.3368 & \(-\)0.4832 & 0.0662 & 0.0673 & 0.0123 & 0.996 \\ Wave Period (s) & 0.6969 & \(-\)2.1046 & 0.2078 & 0.2106 & 0.0344 & 0.989 \\ \hline \end{tabular}
\end{table} 
Table 7: The statistics of the ANN models for training results. Figure 15 shows the standard error bar of heave responses between the ANN model and FEM results for the 9.65 m wave height and 9.94 s wavelength. The ANN model's response predictions were very accurate. The pitch response error obtained by the difference of predicted responses by ANN and FEM is depicted in Figure 16. The overall prediction performance of the neural network was decent. Figure 14: Surge response error between ANN and FEM model results for wave height of 12.65 m and wave period of 11.39 s.  
Figure 15: Heave response error between ANN and FEM model results for wave height of 9.65 m and the wave period of 9.94 s.  
The maximum mooring line tension response error was calculated based on the difference between the FEM results and ANN results (Figure 17). The predicted FEM and ANN results were plotted for a wave height of 12.65 m and a wave period of 11.39 s.  
The performance of the ANN model was assessed based on how much the predicted responses differed from the obtained FEM results and generated errors. As shown in Table 8, the correlation coefficient (R) and root-mean-square error (RMSE) reflect the network's error function and prediction abilities, respectively. Figure 16: Pitch response error between ANN and FEM model results for wave height of 9.65 m and wave period of 9.94 s. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Parameter** & **MaxE** & **MinE** & **StdevE** & **Bias** & **RMSE** & **R** \\ \hline Surge response (m) & 2.564 & \(-\)2.749 & 0.75 & 0.1005 & 0.757 & 0.9819 \\ Pitch response (rad) & 0.004 & \(-\)0.003 & 0.001 & 0.0001 & 0.001 & 0.999 \\ Heave response (m) & 0.119 & \(-\)0.128 & 0.041 & \(-\)0.0002 & 0.041 & 0.9919 \\ Top tension (N) & 116230 & \(-\)88155 & 35704 & 3307.5 & 35839 & 0.997 \\ \hline \hline \end{tabular}
\end{table}