# Machine Learning Approaches for Ship Speed Prediction towards Energy Efficient Shipping
## 2 Material and Methodology
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Features** & **Mean** & **Std.** & **Min** & **25\%** & **50\%** & **75\%** & **Max** \\ \hline COG & 172.652 & 98.804 & 0.0000 & 85.100 & 162.800 & 263.100 & 360.000 \\ Total wave height & 2.088 & 0.970 & 0.0002 & 1.421 & 1.964 & 2.573 & 6.759 \\ Total wave direction & 175.432 & 76.611 & 0.2243 & 122.246 & 181.793 & 224.441 & 359.720 \\ Total wave period & 8.371 & 2.293 & 0.8933 & 7.051 & 8.455 & 9.907 & 17.384 \\ Pressure MSL & 1016.53 & 7.08 & 980.06 & 1011.61 & 1016.41 & 1021.10 & 1044.42 \\ Ambient temp & 21.146 & 5.794 & \(-\)8.0820 & 17.855 & 21.718 & 25.695 & 36.110 \\ Sea surface salinity & 35.034 & 1.148 & 28.7284 & 34.573 & 35.362 & 35.605 & 41.126 \\ Wind speed & 6.914 & 3.088 & 0.0874 & 4.693 & 6.747 & 8.820 & 22.836 \\ Wind direction & 157.916 & 93.067 & 0.3399 & 90.167 & 134.010 & 230.064 & 359.863 \\ Current speed & 0.318 & 0.225 & 0.0020 & 0.166 & 0.257 & 0.399 & 1.515 \\ Current direction & 160.511 & 89.145 & 0.8856 & 85.932 & 146.343 & 232.631 & 360.000 \\ Maximum draught & 12.747 & 5.278 & 0.0000 & 8.900 & 12.200 & 15.300 & 23.200 \\ Gross tonnage & 93137 & 67667 & 8231 & 38400 & 79560 & 199959 & 200679 \\ SOC & 12.107 & 1.882 & 5.000 & 11.000 & 12.100 & 13.200 & 22.200 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics of dataset after pre-processing. \begin{table}
\begin{tabular}{c c} \hline \hline Ambient temperature & 0.218750 \\ COG & 0.206953 \\ Gross tonnage & 0.192829 \\ Total wave height & 0.161433 \\ Maximum draught & 0.161050 \\ Total wave direction & 0.124137 \\ Wind speed & 0.104488 \\ Sea surface salinity & 0.07264 \\ Wind direction & 0.062621 \\ Total wave period & 0.059107 \\ Pressure MSL & 0.042215 \\ Current direction & 0.039811 \\ Current speed & 0.002221 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Correlation between input features and SOG. the lower and upper quartile, respectively. Consequently, data points beyond the whiskers are shown individually as a hollow circle. Figure 5 shows that most of the machine learning models, except GBR, delivered a good result, with a mean/median \(R^{2}\) of over 97%. The reason for the low accuracy of GBR is that it is very sensitive to noise and hyperparameters compared to other methods, which results in its failure to generate a generalized model for the test dataset by overfitting the actual training data with high nonlinearity. ETR gave the most accurate result, closely followed by RFR. Table 7 shows the descriptive statistics of the models with total computational time. From the four models, DTR had the least computational time, showing that DTR-based ensemble models improve the accuracy of the single model. Relatively, GBR, LR, and polynomial regression models had lower accuracies than other models. As for the ensemble techniques, bagging provided a better result than boosting, but a single regressor (DTR) still provided a better mean \(R^{2}\) with a slight increase in the variance. The DTR has an acceptable accuracy with a low computational time, but it has larger variability in the performance of the estimated model