# Research on Predicting the Mechanical Characteristics of Deep-Sea Mining Transportation Pipelines
## 4 Construction of the Predictive Model for Pipeline Mechanical Characteristics
### Model for Predicting the Mechanical Properties of Flexible Hose
Therefore, the accurate monitoring of the mechanical state parameters of the hose through the predictive model is necessary to ensure the operational safety of deep-sea mining systems. Figure 16: Prediction of bending moment at flexible hose length of 132.5 m.  
Figure 15: Prediction of bending radius at flexible hose length of 132.5 m.  
Among the same wind speed and wave parameters, the ocean current speed and ocean current angle have a more significant impact on deep-sea mining pipelines. The variation patterns of the effective tension at a length of 107.5 m along the hose, the minimum bending radius at a length of 132.5 m, and the bending moment are illustrated in Figure 17a, Figure 17b, and Figure 17c, respectively. Due to the changes in the shape of the hose during deep-sea mining operations with variations in operational conditions and sea conditions, the position of the maximum effective tension, maximum bending moment, and minimum bending radius along the length of the hose may vary. Therefore, this study constructs a predictive model for the mechanical parameters of each node of the hose. The simulated model of the hose consists of 102 nodes, and the prediction model for the overall mechanical characteristics of the hose involves predicting the mechanical parameters of each node. The construction method of the predictive model for the overall mechanical characteristics of the hose is similar to the construction of the digital twin model for the critical points mentioned earlier. The BP neural network model's predictive effectiveness for the mechanical parameters of each node of the hose is illustrated in Figure 18.  
Figure 17: Influence of ocean current speed and angle on the mechanical parameters of flexible hose: (**a**) variation in effective tension at flexible hose length of 107.5 m; (**b**) variation in bending radius at flexible hose length of 132.5 m; (**c**) variation in bending moment at flexible hose length of 132.5 m.  
Figure 18: Prediction effectiveness of mechanical parameters for each node on the flexible hose by the BP neural network model: (**a**) MAE value; (**b**) correlation coefficient. The results in Figure 18a indicate that the average absolute error (MAE) values for the effective tension prediction of each node of the hose range between 0.0587 and 0.8328, for the prediction of each node's bending radius, the MAE values range between 0.0576 and 0.6473, and for the prediction of each node's bending moment, the MAE values range from 0.0171 to 0.2305. The root mean square error (RMSE) trends for model training are consistent with the MAE values, with the RMSE values for the effective tension prediction of each node ranging between 0.0816 and 1.0116, for the prediction of each node's bending radius, the RMSE values range between 0.0890 and 0.8330, and for the bending moment prediction of each node, the RMSE values range from 0.0238 to 0.3244. The results from the model training indicate that the BP neural network model performs well in predicting the mechanical parameters of each node of the hose, with the RMSE values close to 0, demonstrating a certain level of reliability in the model's training effect. As shown in Figure 18b, the correlation coefficients for the effective tension prediction of each node range between 0.9772 and 0.9854, for the bending radius prediction of each node, the correlation coefficients range between 0.9656 and 0.9819, and for the bending moment prediction of each node, the correlation coefficients range from 0.9711 to 0.9907. With correlation coefficients close to 1, indicating a linear relationship between predicted and simulated values, the model exhibits good prediction performance.