# Blast Loading Prediction of Complex Structures Based on Bayesian Deep Active Learning
## 5 Conclusions  
Using the open-source software blastFoam, numerical simulations were conducted to investigate the interaction between shockwaves and complex structures under various initiation positions, initiation speeds, and detonation source equivalencies. A Bayesian approach was then employed to develop a deep learning model, selecting high-quality samples based on an uncertain selection strategy to iteratively train Bayesian deep neural networks through active learning. This process resulted in a blast loading prediction model that performs similarly to conventional passive deep learning models, despite requiring fewer training data. The experimental results indicate that the BDAL model can predict the blast loading of a single test sample in approximately 20 ms, demonstrating a speed advantage over numerical simulation methods. Using a training set of 324 \(\times\) 200 samples and a test set of 36 \(\times\) 200 samples, the BDAL model achieved MAPE values of 4.3% and 6.1% for peak overpressure predictions, respectively. This model not only provides more accurate predictions but also quantifies the uncertainty of the results. Importantly, the BDAL model requires only 60% of the training data to achieve the same prediction accuracy as the passive learning model, highlighting the effectiveness of the active learning approach based on the uncertain selection strategy in reducing the data needed for training deep learning models.  
From a broader perspective, predicting blast loading is essential for risk mitigation in real-world applications. Compared with existing deep-learning-based methods for blast loading prediction, the BDAL model presented in this study not only enables rapid predictions but also provides confidence levels for these predictions. This information aids researchers in assessing the reliability of the results, which is crucial for emergency response and damage assessment after disasters. Furthermore, the active learning technique based on uncertainty selection significantly reduces the construction costs of deep learning models for blast loading prediction, enhancing the practical value of the proposed approach in real scenarios.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**100\% Training Data**} & \multicolumn{2}{c}{**60\% Training Data**} \\ \cline{2-5}  & **MAPE** & **R2** & **MAPE** & **R2** \\ \hline BDAL & 0.061 & 0.974 & 0.061 & 0.974 \\ FCNN & 0.213 & 0.738 & 0.234 & 0.758 \\ Decision Tree & 0.135 & 0.831 & 0.138 & 0.828 \\ Random Forest & 0.117 & 0.899 & 0.121 & 0.879 \\ XGB & 0.099 & 0.920 & 0.101 & 0.909 \\ DENN & 0.173 & 0.771 & 0.175 & 0.730 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Prediction results of peak overpressure by different methods.  
**Author Contributions:** Conceptualization, W.P. and W.Z.; Methodology, W.P.; Software, M.P. and C.L.; Validation, C.L. and J.Q.; Formal analysis, J.Q. and W.Z.; Investigation, W.P.; Writing--original draft, M.P.; Writing--review & editing, M.P.; Visualization, C.L.; Supervision, W.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Data Availability Statement:** The datasets presented in this article are not readily available because the data are part of an ongoing study. Requests to access the datasets should be directed to [EMAIL_ADDRESS].  
**Conflicts of Interest:** The authors declare no conflict of interest.