## 5 Result  
To validate our model, we divided the data into training and testing datasets. The data collected during first five months was used to train the model while the remaining two months were used to test the model. To measure the predictive performance of the model, RMSE (residual mean squared error) and R2-score were used. The evaluation result is shown in Table 3. The R2 score is 89.78% which indicates a fairly good performance for the regression.  
In Figure 4, actual propulsion power vs. speed record is compared with the dataset predicted by our SVR model. Each red dot is actual propulsion power in the testing data set given at specific speed of the vessel. As shown in this figure, given the same speed level, the propulsion power shows large deviation. This deviation can be explained by the impact of external factors (wind, wave and tide). The blue dots are the data predicted by the SVR model. As shown in this figure, the SVR model shows almost the same pattern as actual data, which indicates that our SVR is a reliable tool to predict the propulsion power of the vessel.  
Figure 5 shows the relationship between the speed and the propulsion power of the vessel. The green and black lines are estimated speed vs. power curve obtained from ISO15016 method. The green is obtained when the vessel is loaded with the cargo while the black line is obtained when  
Figure 4: Comparison between predicted propulsion power vs. actual data.  
\begin{table}
\begin{tabular}{c l} \hline \hline Training dataset & 2016.01.01 \(\sim\)2016.05.31 \\ Testing dataset & 2016.06.01–2016.07.30 \\ Kernel Function & RBF kernel \\ Hyper parameter & C = 4950, r = 0.6, epsilon = 1.0 \\ R2 score & 89.78\% \\ RMSE & 54 kW \\ Entry 2 & data \\ \hline \hline \end{tabular}
\end{table}
Table 3: Prediction result.  
the vessel is empty. The blue cross dots are speed vs. power relationship predicted by the SVR model while eliminating the impact of external factors. As shown in this figure, the predicted propulsion performance lies between green and black lines, which indicates that SVR model shows generic S/P relationship when it is not affected by the external factors (wind, wave, and tide). The SVR model shows an abnormal pattern when the input is over 18 notes because the data measured with vessel speed being over 18 notes is not available.  
We also have compared the prediction performance of the proposed model with that of an ISO15016 method. In order to do this, we have compared the prediction results of the two methods using the same testing dataset (2016.06.01-2016.08.01). When applying ISO15016 [12], the wind measure is adjusted based on the Fujiwara method (p.41) and the wave feature is adjusted based on the STAWAVE-2 method (p.45). STAWAVE-2 approximates the \(R_{uw}\) in Equation (5) by the following:  
\[\begin{array}{l}R_{wave}\ =\ R_{AWML}+R_{AWRL}\\ R_{AWML}\ =\ 4\rho s\varsigma_{A}^{2}\frac{B^{2}}{L_{pp}}\overline{r_{aw}}( \omega)\\ R_{AWRL}\ =\ \frac{1}{2}\rho s\varsigma_{A}^{2}B\alpha_{1}(\omega)\end{array} \tag{12}\]  
where \(R_{AWML}\) and \(R_{AWRL}\) is mean resistance increase due to wave motion and reflection respectively. \(\overline{r_{aw}}(\omega)\) and \(\alpha_{1}(\omega)\) are functions of circular frequency of regular wave \(\omega\) which are explained in detail in [12]. For a more detailed procedure of STAWAVE-2, the reader is referred to [12].  
The comparison result is shown in Table 4. As shown in the table, the SVR-based model outperforms the ISO15016 in both R2 score and RMSE. The ISO15016 method underperforms the SVR-based model especially when the vessel is in bad weather conditions.  
Figure 5: Predicted propulsion power without external effect.