# 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 Rigid Lifting Pipe  
According to the static analysis, the maximum effective tension along the length of the rigid lifting pipe is located at the top end of the pipe and reaches a value of 1509.38 kN. During the dynamic simulation process, the maximum effective tension distribution along the length of the rigid lifting pipe remains at the top end. To ensure the operational safety of the deep-sea mining system, it is imperative to monitor the real-time changes in the effective tension at the critical stress points along the length of the pipe. Therefore, this study uses the 32,064 sets of data obtained from 64 groups of simulations designed through orthogonal experiments to train a BP neural network model.  
Based on the BP neural network structure setup, the simulation sensor data, which includes 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 effective tension at the top end of the rigid lifting pipe serves as the output layer. The neural network topology is illustrated in Figure 12.  
In this study, 80% of the data set (i.e., 25,651 data sets) is selected as the training set for the BP neural network, while the remaining 20% (i.e., 6413 data sets) are used as the test set. The training process is executed 1000 times with a learning rate of 0.01, and the training objective is to achieve a minimum error of 0.00001. The digital twin model is constructed by training the neural network using simulation sensor data.  
The performance of the BP neural network model is evaluated using the mean absolute error (MAE), root mean square error (RMSE), and correlation coefficient. The closer the RMSE is to 0, the better the training effect of the model. A correlation coefficient closer to 1 indicates a strong positive linear correlation between the predicted values and the simulation sensor data. The prediction results of the effective tension at the top end of the rigid lifting pipe using the BP neural network model are shown in Figure 13. As can be seen from the figure, the effective tension at the top end of the rigid lifting pipe varies under different sea conditions.  
Figure 12: Topological structure of the BP neural network for pipeline mechanical characteristics.  
Figure 13: Prediction of effective tension at the top end of the mining hard pipe.  
The results in Figure 13 indicate that the neural network model accurately predicts the effective tension at the top end of the rigid pipe. The red predicted curve closely aligns with the blue simulated value curve in most of the data regions. The mean absolute error (MAE) is 0.2968, the root mean square error (RMSE) is 0.8552, and the correlation coefficient is 0.9963. The maximum value of the effective tension at the top end of the rigid lifting pipe is 1689.27 kN, which is less than the maximum allowable tension of 10,000 kN for the rigid lifting pipe. Therefore, in the 64 operational scenarios based on the actual sea conditions, the maximum effective tension experienced by the deep-sea mining rigid lifting pipe is significantly lower than the maximum allowable effective tension for the pipe. This neural network model can accurately predict the effective tension at the top end of the rigid lifting pipe, forming a predictive model for determining the maximum effective tension distribution along the length of the rigid lifting pipe under different operational conditions.