# 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  
The model for predicting the mechanical properties of the flexible hose is based on static analysis, where the maximum effective tension experienced by the hose is located at a length of 107.5 m along the hose. The minimum bending radius and maximum bending moment along the length of the hose occur at a length of 132.5 m. During the dynamic simulation process, the maximum effective tension, minimum bending radius, and maximum bending moment along the length of the hose remain consistent, with these critical points identified through static analysis, providing the mechanical parameters for dynamic analysis. This ensures the reliability of studying the hose's behavior under dynamic conditions. Similar to the construction of the tension prediction model for the rigid lifting pipe in Section 4.2, this study utilizes 64 sets of simulations designed through orthogonal experiments, resulting in 32,064 data sets used for training the BP neural network model. The simulation sensor data, including sea wind speed, wave period, significant wave height, ocean current speed, ocean current angle, and pipeline strain, are used as the six input layers of the BP neural network. The maximum effective tension, minimum bending radius, and maximum bending moment experienced by the hose are set as the output layers, with a neural network topology similar to that shown in Figure 13.  
The results of the training of the effective tension prediction model at a length of 107.5 m along the hose are depicted in Figure 14. The predicted effective tension at this point aligns closely with the simulated effective tension values, with an average absolute error (MAE) of 0.17854, a root mean square error (RMSE) of 0.2069, and a correlation coefficient of 0.9872. These metrics demonstrate the model's good reliability in accurately predicting the maximum effective tension of the hose. The maximum effective tension at a length of 107.5 m along the hose is 29.38 kN, which is below the maximum allowable effective tension of 200 kN for the hose. In all 64 operational scenarios, the hose operates within a safe tension range. Figure 14: Prediction of effective tension at flexible hose length of 107.5 m.  
The model for predicting the bending radius at a length of 132.5 m along the hose is shown in Figure 15. The predicted bending radius at this point closely aligns with the simulated bending radius values. The prediction model has an average absolute error (MAE) of 0.1436, a root mean square error (RMSE) of 0.1648, and a correlation coefficient of 0.9695, indicating that the model is reliable and can accurately predict the minimum bending radius of the hose. The minimum value of the bending radius at a length of 132.5 m along the hose is 6.12 m, which is greater than the minimum allowable bending radius of 1 m for the hose. This implies that the hose will not undergo excessive bending deformation during operations in all 64 operational scenarios. The training results of the model for predicting the bending moment at a length of 132.5 m along the hose are illustrated in Figure 16. The predicted bending moment at this point closely aligns with the simulated bending moment values, with an average absolute error (MAE) of 0.0367, a root mean square error (RMSE) of 0.0530, and a correlation coefficient of 0.9725. These metrics indicate that the model is reliable and can accurately predict the maximum bending moment of the hose. The maximum value of the bending moment at a length of 132.5 m along the hose is 3.43 kNm. The aforementioned BP neural network models can accurately predict the mechanical parameters of the hose based on the sensor-detectable ocean environmental parameters and simulation sensor data, thereby establishing a predictive model for the mechanical characteristics of deep-sea mining transportation hoses. The results from the 64 simulations indicate that the stress and bending deformation of the hose vary under different sea conditions.