# Blast Loading Prediction of Complex Structures Based on Bayesian Deep Active Learning
## 2 Data Generation
### Mesh Refinement  
The numerical simulation software blastFoam uses the blockMesh tool to create a uniform background mesh across the entire computation domain. A denser background grid increases the precision of numerical simulations but also extends the calculation time. Based on the background mesh, local mesh refinement and dynamic mesh refinement can be applied using the snappyHexMesh and dynamicMesh tools, respectively, allowing for higher accuracy while maintaining acceptable computational costs. Local mesh refinement involves further refining the mesh around the structure. At refinement level 0, the mesh near the structure matches the size of the background mesh; at level 1, it doubles in density; and at level 2, it quadruples. This pattern continues with increasing refinement levels. Dynamic mesh refinement, on the other hand, focuses solely on the region through which the shockwave propagates. The relationship between the refinement level and the number of refined grid cells is consistent with that described for local refinement.  
In the numerical simulation experiment conducted with blastFoam, a balance between the calculation time and accuracy was achieved using local and dynamic mesh refinement, as illustrated in Figure 2. Figure 2a shows the pressure cloud image during shockwave propagation (simulation time is 0.15 s), and the spherical surface represents an equivalent surface with a pressure of 110 kpa. Figure 2b shows the grid division in the process of the numerical calculation. The setting of local mesh refinement makes the number of grid cells near the structure significantly larger than that in the free field region without the structure. In the experiment, by comparing the calculation accuracy and calculation time under different grid settings, the grid settings that take into account the calculation speed and calculation accuracy are obtained as follows: the background mesh size is 7.5 m, the local mesh refinement level is 5, and the dynamic mesh refinement level is 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Empirical Constant** & \(A/\)**kPa** & \(B/\)**kPa** & \(R_{1}\) & \(R_{2}\) & \(\lambda\) & \(e/\)**(k\(\cdot\)m\({}^{-3}\))** & \(\rho_{0}/\)**(kg\(\cdot\)m\({}^{-3}\))** \\ \hline Value & 3.737 \(\times\) 10\({}^{8}\) & 3.747 \(\times\) 10\({}^{6}\) & 4.15 & 0.9 & 0.35 & 6.0 \(\times\) 10\({}^{6}\) & 1630 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Values of empirical constants.  
Based on the above settings, the blastFoam solver was used to calculate the propagation process of the shockwave, and the peak overpressure at 200 key positions was taken as the specific quantitative index of the blast loading of the target structure. A total of 360 \(\times\) 200 groups of sample data were obtained after the numerical simulation experiment. The final complete explosion dataset consisted of 72,000 samples, each containing associated scene parameters and peak overpressure labels, which were used for training and testing of the deep learning model.  
Figure 2: Computational grid settings. (**a**) Pressure cloud image; (**b**) grid division during numerical calculation.