## 6 Supervised and Unsupervised Machine Learning Model
### Unsupervised Machine Learning
#### 6.2.1 Artificial Neural Network Model (Black Box Model)
In some cases, where there is a lack of data collected from the ships and environment due to difficulty in data collection or incomplete dataset, the grey box model (GBM), which is a hybrid of a white-box model (WBM) and BBM, could be utilized in the data prediction. To predict the fuel consumption of a tugboat, for instance, the BBM is trained by using historical operational data to forecast the ship FOC. To improve the accuracy in the data prediction, one of the possibilities is to include the ship resistance as part of the data training. However, as the ship resistance is not easy to obtain (recorded) by sensors, this could be carried out by using a WBM where the ship resistance under various sea \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **MSE** & **Iteration** & **Configuration** & \(R\) **Values** \\ \hline S10 & 0.1963 & 29 & 7-4-3-1 & 0.9118 \\ S11 & 0.1711 & 30 & 7-4-4-1 & 0.9235 \\ S12 & 0.1648 & 33 & 7-4-5-1 & 0.9309 \\ S13 & 0.1799 & 30 & 7-4-6-1 & 0.9227 \\ S14 & 0.1808 & 32 & 7-4-7-1 & 0.9317 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variation in configuration affecting \(R\) values [25]. Figure 20: Clustering of data using GMM [25] 6.2.2. Grey Box Model (Hybrid Black Box–White Box Model). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **Customized Function** & \(R\) **Values** & **Time (s)** \\ \hline \multirow{3}{*}{ANN} & Exponential sigmoid & 0.9636 & 0.5200 \\  & Tangent sigmoid & 0.9383 & 0.4585 \\  & ReLU & 0.8790 & 0.5439 \\ \hline \multirow{3}{*}{Regression Method} & Linear & 0.0449 & 0.1167 \\  & Interaction & 0.2862 & 0.1892 \\ \cline{1-1}  & Pure Quadratic & 0.1526 & 0.1425 \\ \cline{1-1}  & Full Quadratic & 0.3582 & 0.2406 \\ \hline \multirow{3}{*}{Support Vector} & Gaussian RBF & 0.0813 & 0.4109 \\ \cline{1-1}  & Linear & 0.0071 & 6.5650 \\ \cline{1-1}  & Quadratic & 0.4810 & 380.9915 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Models Performance [25]. conditions could be obtained via numerical simulation or experimental test. Thus, the inclusion of operational data and simulated ship resistance used in the ML produce the GBM that may increase the accuracy of the predicted data. [PERSON] et al. [29] conducted a study to examine the capability of the GBM for a Handymax product tanker. The research considered the parametric calculation to forecast ship resistance in calm water for the WBM. Although the calculated outcome is marginally off compared with its counterpart predicted by the computational fluid dynamic (CFD) model, the slightly inaccurate resistance data complement the historical operational data to optimize the model performance to a greater extent. Due to the domain knowledge of the vessel characteristics preserved by the WBM, the GBM can achieve an equally high precision as the BBM in predicting FOC with limited historical operational data available. Figure 21 shows the comparison of the least mean per centage absolute error (MAPE) between the GBM and BBM. It can be seen that the MAPE reduces significantly for the Naive (N)-GBM and Advanced (A)-GBM, thus implying that the WBM helps in increasing the accuracy of the predicted data.