In this section, the proposed model was employed to predict the attitude motions and states in different databases. Then, the prediction performance of the model will be compared with different methods.
4.1. The Performance of the Model on Different Datasets
The occurrence of surf-riding, wave-blocking, and broaching should be determined by the definition mentioned in
Section 2.2. The specific information on the different navigation conditions is shown in
Table 9 and
Table 10. In the table, O
MS represents the occurrence of a marginal surf-riding event, O
MB represents the occurrence of a marginal broaching event and O
W represents the occurrence of a wave-blocking event.
Figure 10 shows the visualization of the states of the ships in different conditions. Each plot contains the nozzle deflection angle
δ, the heading angle
, the ratio of ship velocity and wave celerity and the trajectory of the ship. The occurrence and duration of surf-riding, wave-blocking and broaching is labeled. These cases cover most conditions and are helpful for the subsequent training of LSTM neural network prediction models.
The motion features and state features are combined as the input features to train the model in this section. The prediction effect of the Bi-LSTM model under different navigation conditions could be observed through full-feature learning.
Figure 11 shows the prediction results in different datasets, and the occurrence of surf-riding, wave blocking and broaching has been marked in the figures based on the state features.
Figure 12 shows the three evaluation metrics of the prediction results. Before the first red dotted line is the data used to train the model, between the two red dotted lines is the input validation data set, and after the second red line is the prediction.
Figure 11 shows that the model achieves good performance under different navigation conditions, with minor deviations between the prediction results and the real data across all conditions. The most apparent deviation occurs in Dataset #4.3. While the performance of Dataset #4.3 is slightly lower compared to Datasets #4.1 and #4.2, it excels in capturing the occurrences and ends of the ship’s states. The variation in predictive performance from Dataset #4.1 to Dataset #4.3 further highlights that as the complexity of the ship’s navigation conditions increases, the model’s predictive accuracy also changes. This highlights the importance of introducing state features, which enable the model to better capture and adapt to these variations in the complexity of the navigation states.
Figure 12 shows the MAE, RMSE, and R
2 values of the prediction under different conditions. It is evident from the figure that Dataset #4.3 exhibits the highest MAE and RMSE values and the lowest R
2 value, indicating the largest deviations between the predicted and actual values. Despite this, Dataset #4.3 still effectively captures critical events like surf-riding, wave blocking and broaching, as previously mentioned. In contrast, Datasets #4.1 and #4.2 display a better overall prediction performance, with lower MAE and RMSE values and higher R
2 values. This suggests that the model performs more accurately under less complex navigation conditions. However, the introduction of state features significantly enhances the proposed model’s ability to adapt to and predict the increased complexity in Dataset #4.3. The observed changes in predictive performance across the datasets underscore the model’s sensitivity to varying navigation conditions. As the complexity of the ship’s navigation state increases from Dataset #4.1 to Dataset #4.3, the prediction accuracy of the model diminishes slightly but remains robust due to the introduction of the state features. The robust performance of the proposed model across different datasets based on the analyses of
Figure 11 and
Figure 12 demonstrates its capability to handle and predict effectively under diverse and challenging maritime conditions.
4.2. The Performance of the Model Compared with Other Methods
In former studies, the prediction of several states’ occurrence has mainly relied on predicting the motions of ships in sailing. Then, assessing whether surf-riding, wave-blocking or broaching events occur based on several motion features (such as
,
, and
/
). In this section, two models are employed: one is the proposed Bi-LSTM model, and the other is the conventional LSTM model. Three prediction strategies based on the two models will be compared, and their specific methods are shown in
Table 11. Both models used Dataset #4.1 to Dataset #4.3 as the training datasets, with the new dataset shown in
Table 12 serving as the validation set. The state-prediction model needs more preprocessing of datasets than the motion-prediction model before producing a prediction.
Figure 13 shows the prediction results of three different methods based on two models. The conventional LSTM model of ship motion predicted the data of ship attitude motions and then identified the state based on the definition. In Method #4.3, the features (
,
, and
/
) were replaced by the state features.
Figure 14 shows the three evaluation metrics of the prediction results.
Figure 13 presents a comparison between the predicted and actual data, demonstrating the effectiveness of the proposed Bi-LSTM model in predicting ship attitude motions. The model, trained on the three datasets described in
Section 4.1, performed well on unseen data, particularly in predicting attitude motions. However, all three models faced challenges in accurately identifying the occurrence of wave blocking.
Among the methods evaluated, Method #4.3 exhibited the best performance in terms of both prediction accuracy and the timing of state occurrences, aligning more closely with the real data than the other models. The bidirectional learning capability of the Bi-LSTM model enables it to better capture temporal changes in the ship’s state, optimizing the model’s predictive abilities. By replacing the original three features with state features that directly determine the ship’s condition, the model is able to output state predictions directly rather than indirectly, leading to an improved accuracy in predicting surf-riding and broaching events.
In contrast, when state features are not included, the performance of both the LSTM and Bi-LSTM models are similar. However, the Bi-LSTM model, due to its bidirectional nature, requires more computational resources and longer training times compared to LSTM models. While LSTM models are computationally simpler, they are prone to challenges such as the difficulty in capturing long-term dependencies and the susceptibility to vanishing gradients. These limitations are more pronounced in complex and dynamic maritime scenarios.
Methods #4.1 and #4.2 show significant deficiencies when compared to Method #4.3 in terms of both prediction accuracy and the timing of state occurrences. These methods fail to capitalize on the enhanced feature set and the bidirectional capabilities of the Bi-LSTM model, resulting in less accurate and reliable predictions.
Figure 14 shows the MAE, RMSE, and R
2 values for each method, clearly illustrating that Method #4.3 consistently outperforms Methods #4.1 and #4.2 across all evaluation metrics. Specifically, Method #4.3 demonstrates the lowest MAE and RMSE values, indicating more precise predictions with smaller errors. Additionally, Method #4.3 achieves the highest R
2 value, reflecting its superior ability to explain the variance in the ship’s attitude motions and states.
The superior performance of Method #4.3 can be attributed to several key factors. First, the Bi-LSTM model’s bidirectional learning capability enables it to capture both past and future states effectively, which is particularly crucial for complex maritime events where significant changes occur before and after these events. The ability to process information in both directions enhances the model’s capacity to predict these changes more accurately than traditional LSTM models. Secondly, by replacing the original features with state features that directly determine the ship’s condition, the model can provide direct predictions with reduced complexity. This direct approach minimizes errors associated with indirect prediction methods, leading to an improved overall performance.
In comparison, Methods #4.1 and #4.2 exhibit considerable shortcomings. These methods, lacking the bidirectional capabilities and the enhanced feature set of Method #4.3, fail to achieve the same level of prediction accuracy. Method #4.1 and Method #4.2 show higher MAE and RMSE values and lower R2 values, indicating less precise predictions and a diminished ability to explain the variance in the data.
Moreover, while the LSTM and Bi-LSTM models perform similarly in the absence of state features, the Bi-LSTM model requires more computational resources and longer training times due to its complexity. The LSTM model, although simpler, faces limitations such as the difficulty in capturing long-term dependencies and the susceptibility to vanishing gradients, which can lead to performance degradation, particularly in highly dynamic maritime scenarios.
In conclusion, the results clearly indicate that Method #4.3, which incorporates the Bi-LSTM architecture and direct state feature outputs, offers superior prediction accuracy, robustness, and overall performance. This method is particularly effective in predicting ship attitude motions and states across a range of conditions, and its incorporation of bidirectional learning and state features makes it a valuable tool in the field of ocean engineering.
