# Study on Shock Initiation Randomness of Energetic Materials on a Macroscopic Scale
## 4 Applied Example
### Randomness Study
#### 4.3.1 Shock Load Condition Where \(\overline{v}\) Is 1050 m/s
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Test Sample Set** & & \(\delta_{T}\)**Being the Same as \(\delta_{E}\)** & \(\delta_{T}\)**Being Different from \(\delta_{E}\)** & \\ \hline \multirow{3}{*}{**CV of BRVs**} & \multirow{3}{*}{**Test Number**} & **ANN Being** & **Both \(\delta_{T}\)and** & **Both \(\delta_{T}\)and** & \(\delta_{T}\)**Being 1** & \(\delta_{T}\)**Being 0** & **Accuracy of Testing (\%)** \\  & & **Tested** & \(\delta_{E}\)**Being 1** & \(\delta_{E}\)**Being 0** & **Being 0** & **Being 1** & **Precision (\%)** \\ \hline \multirow{3}{*}{0.005} & \multirow{3}{*}{1000} & GABPNN & 723 & 180 & 52 & 45 & 90.3 \\  & & BPNN & 697 & 145 & 87 & 71 & 84.2 \\  & & RBFNN & 746 & 102 & 130 & 22 & 84.8 \\ \hline \multirow{3}{*}{0.01} & \multirow{3}{*}{1000} & GABPNN & 627 & 275 & 40 & 58 & 90.2 \\  & & BPNN & 611 & 269 & 46 & 74 & 88.0 \\  & & RBFNN & 663 & 238 & 77 & 22 & 90.1 \\ \hline \multirow{3}{*}{0.015} & \multirow{3}{*}{1000} & GABPNN & 564 & 358 & 30 & 48 & 92.2 \\  & & BPNN & 548 & 349 & 39 & 64 & 89.7 \\ \cline{1-1}  & & RBFNN & 589 & 331 & 57 & 23 & 92.0 \\ \hline \multirow{3}{*}{0.02} & \multirow{3}{*}{1000} & GABPNN & 553 & 379 & 36 & 32 & 93.2 \\ \cline{1-1}  & & BPNN & 536 & 375 & 40 & 49 & 91.1 \\ \cline{1-1}  & & RBFNN & 561 & 359 & 56 & 24 & 92.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The comparison of the test results of the ANNs in the IP study under the shock load condition where \(\overline{v}\) is 1050 m/s. According to the test results shown in Table 5 and Figure 6, all the test accuracy results with which the GABPNN calculated the 0-1 recognition results of the \(\delta\) corresponding to these 4 test sample sets were above 90%, and these test results were also better than the test results of BPNN and RBFNN. It is proved that the GABPNN has stronger nonlinear mapping ability than the BPNN and RBFNN, and the GABPNN can accurately calculate the 0-1 recognition results of the \(\delta\) corresponding to the BRV sample points. Therefore, the GABPNN can be used as the surrogate model of the IP, and the GABP-MCS can also be used to estimate the \(R\)'s of Composition B. (iv) Estimation of \(R\) based on GABP-MCS  
A prediction sample set with 100,000 sample points was constructed under each of the above 4 randomness conditions, and the 0-1 recognition results of the \(\delta\) corresponding to these 4 prediction sample sets were obtained by the GABP-MCS, so as to obtain accurate estimates of the actual \(R\)'s of Composition B under these 4 randomness conditions. The results are shown in Table 6 and Figure 7.  
Figure 6: The comparison of the testing accuracy of the ANNs in the IP study under the shock load condition where \(\overline{v}\) is 1050 m/s. Figure 7: The correlation curve between the \(R\) of Composition B and the CV of the BRVs under the shock load condition where \(\overline{v}\) is 1050 m/s. According to the statistical data in Table 6 and the correlation curve in Figure 7, it can be concluded that when the \(\overline{v}\) is 1050 m/s, the \(R\) of Composition B is negatively correlated with the CV of the BRVs; that is, the smaller the CV of the BRVs, the higher the \(R\) of Composition B. This is because the smaller the CV of the BRVs, the more concentrated the distribution of the BRV sample points in the corresponding prediction sample sets, the more BRV sample points there are that can lead Composition B to be initiated, the lower the randomness of the SIREM, and the more likely this SIREM is a deterministic problem; thus, the randomness calculation results of this SIREM will be closer to the deterministic results described in Section 4.1. So, it can be further deduced that, if the CV of the BRVs dropped to 0, this SIREM would become a deterministic problem, so Composition B would definitely be initiated (the \(R\) would increase to 1) under the shock load condition where \(\overline{v}\) was 1050 m/s, which would be exactly the same as the deterministic results presented in Section 4.1.