# A Hybrid Neural Network Model for Predicting Bottomhole Pressure in Managed Pressure Drilling
## 4 Results and Discussion  
In this section, we compare and analyze the performance of the single bottomhole pressure intelligent prediction model and hybrid parallel intelligent prediction model on the test set, find the advantages of different models to capture features, and finally select and evaluate the best intelligent prediction model. Observing the prediction results as shown in Table 5 reveals that the single intelligent models all exhibit similar volatility during the phase when the managed pressure drilling is maintained constant. The best relative performance is the LSTM model with a relative average error of 0.148%, while the relative average errors of BP and 1 DCNN are 0.156% and 0.270%, respectively, and the stability of the models performs poorly. Specifically, the BP model captures the features of the time-series data more evenly and is good at dealing with the point-to-point mapping relationship without considering the contextual information of the time-series data. 1 DCNN shows strong response fluctuations in the abrupt change phase of pressure-controlled drilling, and the model generates a larger feature map because of the relatively small number of channels, which leads to a large computation of the convolution process, so it takes up more memory and takes longer to run. Further analysis shows that the prediction accuracy and stability of the two-hybrid parallel networks have significantly improved when compared with the single network. From Figure 9d,e, the excellent performance of the hybrid model in trend response and wave response is apparent. The CNN-LSTM parallel model has the best performance with an MAPE of 0.031% and the BP-LSTM has an MAPE of 0.040%, which are 78% and 72% lower than the optimal single intelligent model LSTM, respectively. In the CNN-LSTM parallel model, the feature parameters with weak temporal information are input into the CNN branch network and the feature parameters with strong temporal information are input into the LSTM branch network, which makes up for the shortcoming of the 1 DCNN model with abnormal fluctuations at the pressure inflection point, making the prediction result more stable. In the BP-LSTM parallel model, the feature parameters with weak temporal information are input into the BP branch network and the feature parameters with strong temporal information are input into the LSTM branch network, which makes  
Figure 8: CNN-LSTM parallel network internal detailed structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Evaluation** & **BP** & **LSTM** & **1 DCNN** & **BP-LSTM** & **CNN-LSTM** \\
**Indicator** & & & & & \\ \hline Run time (s) & 30.042 & 39.034 & 160.711 & 45.089 & 200.640 \\ MAPE (\%) & 0.156 & 0.148 & 0.270 & 0.040 & 0.031 \\ MAE & 0.092 & 0.087 & 0.158 & 0.023 & 0.018 \\ RMSE & 0.117 & 0.106 & 0.255 & 0.049 & 0.047 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental evaluation results. up for the volatile shortcomings of the single intelligent models of BP and LSTM in the pressure stabilization stage. On the other hand, compared with the CNN-LSTM model, the BP-LSTM model still has local outliers at the pressure changes, and the fluctuation is more intense at the sudden change. Similar to 1 DCNN, the CNN-LSTM parallel model has the longest running time, which is close to four to five times the running time of other models, which has also become one of the important factors to be considered in field practical applications. Overall, these results indicate that the advantages of effectively fusing the extracted features of the model can further improve the accuracy and stability of the prediction model. The BP network extracts the feature information of the data with uniformity and is good at  
Figure 9: Comparison and evaluation results of real and predicted BHP.