## 3 Prediction of 3D Ship Airwake Using a BP Neural Network
### BP Neural Network Predictions  
The prediction framework for the high spatiotemporal resolution 3D ship airwake along the glide path is established in this paper; its application mode is shown in Figure 11. A DWL system, deployed on the ship island, performs PPI scanning (with scanning beam number and velocity configured based on the application requirements; for example, the update rate of measurement data is set to 3 Hz) to provide real-time inflow speed and direction values at the bow direction. These measurements are then input into the optimized headwind BP prediction model, crosswind BP prediction model, and vertical wind BP prediction model. The BP neural networks output high spatial resolution (3 m) wind speed values along the glide path, thus enabling accurate prediction of the high spatial and temporal resolution 3D ship airwake along the glide path. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Inflow Speed (m/s)** & **Inflow Angle (\({}^{\circ}\))** & **0** & \(\pm\)**5** & \(\pm\)**9** & \(\pm\)**12** & \(\pm\)**15** & \(\pm\)**30** & \(\pm\)**45** & \(\pm\)**60** \\ \hline
5 & \(\surd\) & \  
To evaluate the performance and generalization ability of the BP prediction models, a testing dataset consisting of 20 samples under different headwind conditions (as summarized in Table 2) was selected. The testing sample data are also derived from the steady RANS computations. The predicted results of the headwind, crosswind, and vertical wind BP models were compared with the testing samples. Figures 12-14 show the prediction results of the BP models along the glide path at various distances behind the stern (0 m, 50 m, 100 m, 150 m, and 200 m). For the headwind BP prediction model, the correlation coefficients between predicted values and sample values at the different distances are 0.9572, 0.9863, 0.9537, 0.9793, and 0.9814, respectively. For the crosswind BP prediction model, the correlation coefficients at the different distances are 0.9131, 0.9701, 0.9348, 0.9872, and 0.9253, respectively. For the vertical wind BP prediction model, the correlation coefficients at the different distances are 0.9114, 0.8650, 0.9245, 0.8163, and 0.9158, respectively. There are often multiple vortices at different positions on the glide path behind the stern of the ship, and the vortex structures and strengths at different distances usually differ under the same inflow condition, potentially leading to inconsistent fluctuations in the vertical wind at different positions on the glide path (considering the non-stationary characteristics of the airflow field around the ship). Therefore, the CFD sample data (the vertical wind at different positions on the glide path (e.g., 0 m, 50 m, 100 m, 150 m, and 200 m) under different inflow conditions) used for vertical wind BP prediction model training may have a greater degree of confusion (e.g., the vertical wind speed corresponding to inflow condition A is easily mistaken as corresponding to another inflow condition B due to the relatively large fluctuations). Moreover, the vertical wind speed is generally much smaller than the headwind or crosswind, so the same numerical fluctuation is relatively larger for the vertical wind, which may be why the correlation between the BP predicted vertical wind and the CFD sample value is poor, while the correlations for other winds (headwind or crosswind) between the BP predicted value and CFD sample value are better. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Inflow Speed (m/s)** & **0** & \(\pm\)**5** & **8** & **12** & **15** & **20** & **60** \\ \hline
8 & \(\surd\) & & \(\surd\) & \(\surd\) & \(\surd\) & & \(\  
Figure 12: Prediction results of the headwind BP model along the glide path at various distances behind the stern (**a**–**e**). Figure 13: Prediction results of the crosswind BP model along the glide path at various distances behind the stern (**a**–**e**).