# Roll Motion Prediction of Unmanned Surface Vehicle Based on Coupled CNN and LSTM
## 4 Experimental Results and Discussion
### Case Study 1: \"JingHai-VI\" USV  
Several time-series data were selected randomly as the training set from the data set of \"JingHai-VI\". These time series data totaled 100,000 time steps. Several representative data were selected as the test sets which were not the part of the training set. These test sets were named \"JingHai-VI\" test set-1, \"JingHai-VI\" test set-2, and \"JingHai-VI\" test set-3, respectively. Test set-1 comprises the data recorded by \"JingHai-VI\" as it moved in a straight line. Test set-2 comprises the data recorded by \"JingHai-VI\" in a circular curve motion. Test set-3 is composed of the data recorded by \"JingHai-VI\" during z-curve movement. There are 2000, 3000, and 5000 time steps in each set, respectively. In Figure 5, panels (a), (b), and (c) are the trajectory history of \"JingHai-VI\" test set-1, \"JingHai-VI\" test set-2, and \"JingHai-VI\" test set-3, respectively. These three trajectories are the most probable for \"JingHai-VI\" to conduct its mission.  
To show the prediction accuracy of the proposed model, the final RMSE and MAE values of each test set are listed in Table 1. Figure 6 shows the part of the final prediction results of our proposed model, where panels (a), (b), and (c) represent the results of \"JingHai-VI\" test set-1, \"JingHai-VI\" test set-2, and \"JingHai-VI\" test set-3, respectively. It can be seen that the predicted values of the proposed model were in good agreement with the actual measured values.  
To reveal the prediction performances of ARIMA, DNN, univariate LSTM, multivariate LSTM, and our proposed model, the results of these three test sets are listed in Tables 2-4, respectively. It can be seen that our proposed model had the best performance among all the above. On the whole, the neural network models outperformed the ARIMA model in proving that the linear method is not precise enough to model the nonlinear USV roll motion. The DNN model and univariate LSTM model performed poorly compared to the multivariate LSTM model and the proposed model. They simply model time-series data without considering additional information. Univariate LSTM performed better than DNN due to its ability to deal with long-term sequence data prediction. Although the multivariate LSTM model considers additional information, it does not effectively extract features of this information. Therefore, it did not perform well compared to the proposed model. The decrease percentages \(M_{2/1}\) in RMSE of the proposed model compared to the other models are shown in Table 5. Compared to the other models, the performance index RMSE of our proposed model was reduced to varying degrees.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Test Set** & **RMSE (*)** & **MAE (*)** \\ \hline “JingHai-VI” test set-1 & 0.14 & 0.11 \\ “JingHai-VI” test set-2 & 0.08 & 0.06 \\ “JingHai-VI” test set-3 & 0.16 & 0.12 \\ \hline \hline \end{tabular}
\end{table}
Table 2: RMSEs and MAEs of each model at “JingHai-VI” test set-1. ARIMA: autoregressive integrated moving average; DNN: deep neural network.  
Figure 5: The trajectory history of “JingHai-VI” test sets: (a) test set-1, (b) test set-2, and (c) test set-3.  
Figure 6: The prediction results of “JingHai-VI” by the proposed model: (a) test set-1; (b) test set-2; and (c) test set-3.