# Prediction of Ship-Unloading Time Using Neural Networks
## 3 Related Methods
### Stochastic Configuration Networks
The results of the tests are assessed using the root mean square error (RMSE) metric. The findings are presented in \[\beta^{*}=\underset{\beta}{\text{argmin}}\|G_{L}\beta-Y\|^{2}=G_{L}^{+}Y, \tag{16}\]1

For the RVFL, the objective of the test is to determine the optimal number of nodes in the hidden layer and the appropriate range of random weights based on the RMSE measure. The results are presented in \[\beta^{*}=\underset{\beta}{\text{argmin}}\|G_{L}\beta-Y\|^{2}=G_{L}^{+}Y, \tag{16}\]2

### Performance

We evaluated the performance of three models in conjunction with two widely recognized algorithms, Support Vector Regression (SVR) and Random Forest (RF), across four datasets. A total of 100 independent trials were conducted for each model and dataset. The evaluation metrics used include Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and \(R^{2}\). The test results are presented in Table 3, while the fitting curves are illustrated in Figures 2-5. Based on the evaluation results, we found that the SCN model outperformed all other models across every dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Number 1** & **Number 2** & **Range** \\ \hline DB1 & 5 & 30 & [0, 50] \\ DB2 & 10 & 40 & [0, 50] \\ DB3 & 50 & 10 & [0, 50] \\ DB4 & 30 & 5 & [0, 50] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: BP network structure on datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Number 1** & **Number 2** & **Range** \\ \hline DB1 & 80 & [\(-\)40, 40] & [\(-\)50, 50] \\ DB2 & 100 & [\(-\)20, 20] & [\(-\)50, 50] \\ DB3 & 100 & [\(-\)5, 5] & [\(-\)50, 50] \\ DB4 & 100 & [\(-\)10, 10] & [\(-\)50, 50] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RVFL network structure on datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Model** & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**MAPE**} & \multirow{2}{*}{\(R^{2}\)} \\ \cline{3-4} \cline{6-6}  & & **Mean \(\pm\) (SD)** & **Best** & **Mean \(\pm\) (SD)** & **Best** \\ \hline \multirow{6}{*}{DB1} & SVR & 0.0703 \(\pm\) 0.0002 & 0.0700 & 30.1491 \(\pm\) 0.9152 & 28.3137 & 0.0045 \\  & RF & 0.0085 \(\pm\) 0.0007 & 0.0076 & 7.7704 \(\pm\) 2.7491 & 3.7731 & 0.9994 \\  & BP & 0.0122 \(\pm\) 0.0123 & 0.0115 & 37.6948 \(\pm\) 23.3176 & 13.7574 & 0.9976 \\  & RVFL & 0.0484 \(\pm\) 0.0006 & 0.0484 & 66.1857 \(\pm\) 14.4562 & 39.9376 & 0.9824 \\  & SCN & 0.0074 \(\pm\) 0.0024 & 0.0024 & 5.6983 \(\pm\) 2.6124 & 0.8440 & 0.9995 \\ \hline \multirow{6}{*}{DB2} & SVR & 0.1996 \(\pm\) 0.0009 & 0.1982 & 21.4102 \(\pm\) 0.1986 & 21.1481 & 0.0594 \\  & RF & 0.0064 \(\pm\) 0.0005 & 0.0056 & 0.4135 \(\pm\) 0.0150 & 0.3944 & 0.9993 \\  & BP & 0.0761 \(\pm\) 0.0100 & 0.0601 & 6.2884 \(\pm\) 1.9444 & 6.4121 & 0.0963 \\  & RVFL & 0.1084 \(\pm\) 0.0005 & 0.1084 & 7.3193 \(\pm\) 0.0225 & 7.3171 & 0.8197 \\  & SCN & 0.0008 \(\pm\) 0.0039 & 0.0008 & 0.0050 \(\pm\) 0.0008 & 0.0038 & 0.9999 \\ \hline \multirow{6}{*}{DB3} & SVR & 0.0536 \(\pm\) 0.0027 & 0.0492 & 2.7469 \(\pm\) 0.1562 & 2.5131 & 0.9460 \\  & RF & 0.03968 \(\pm\) 0.0036 & 0.0333 & 1.9413 \(\pm\) 0.1555 & 1.6562 & 0.9049 \\ \cline{1-1}  & BP & 0.0602 \(\pm\) 0.0155 & 0.0386 & 10.4826 \(\pm\) 1.9601 & 7.5725 & 0.9454 \\ \cline{1-1}  & RVFL & 0.0687 \(\pm\) 0.0001 & 0.0686 & 14.2589 \(\pm\) 0.0001 & 14.2578 & 0.9170 \\ \cline{1-1}  & SCN & 0.0388 \(\pm\) 0.0012 & 0.0357 & 1.8707 \(\pm\) 0.0483 & 1.7650 & 0.9681 \\ \hline \multirow{6}{*}{DB4} & SVR & 0.0885 \(\pm\) 0.0045 & 0.0823 & 20.8771 \(\pm\) 1.0710 & 19.1571 & 0.8147 \\ \cline{1-1}  & RF & 0.0961 \(\pm\) 0.0080 & 0.0785 & 18.3751 \(\pm\) 1.1851 & 16.4298 & 0.7839 \\ \cline{1-1}  & BP & 0.0911 \(\pm\) 0.0087 & 0.0796 & 19.5973 \(\pm\) 1.7310 & 17.1850 & 0.8029 \\ \cline{1-1}  & RVFL & 0.1932 \(\pm\) 0.0001 & 0.1922 & 41.6601 \(\pm\) 2.4803 & 33.1910 & 0.4144 \\ \cline{1-1}  & SCN & 0.0870 \(\pm\) 0.0060 & 0.0767 & 21.8238 \(\pm\) 1.2261 & 19.3793 & 0.8135 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison among different models on four datasets.