# Study on Shock Initiation Randomness of Energetic Materials on a Macroscopic Scale
## 4 Applied Example
### Randomness Study
#### 4.3.2 Shock Load Condition Where \(\overline{v}\) Is 1000 m/s  
(1) Study on IP  
(i) Constructing training sample set and test sample sets  
In addressing the IP when the \(\overline{v}\) is 1000 m/s, in order to guarantee the excellent generalization ability of the ANNs and sufficient training sample points for the DPR, 3000 sample points were generated for the BRVs with the CV of 0.02, and 1000 sample points were generated for the BRVs with the CV of 0.005, so as to construct the training sample set with 4000 sample points. Then, a test sample set with 1000 sample points was constructed for the BRVs with each of the CVs of 0.005, 0.01, 0.015, and 0.02. Table 9 shows the statistical results of the initiation and non-initiation frequencies of Composition B in these training sample set and test sample sets. (ii) Determining the structure and important parameters of ANNs  
In this stage, under the shock load condition that the \(\overline{v}\) is 1000 m/s, the setting of the structure and important parameters of the GABPNN, BPNN, and RBFNN is the same as the corresponding operation under the shock load condition where the \(\overline{v}\) is 1050 m/s; see Section 4.3.1. (iii) Performance comparison of ANNs  
Firstly, the GABPNN, BPNN, and RBFNN were trained by the above training sample set. Then, these three trained ANNs were tested by each of the above four test sample sets, and the test results shown in Table 10 and Figure 10 were obtained. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Test Sample Set**} & \multicolumn{3}{c}{\(\delta_{T}\) **Being the Same as \(\delta_{E}\)**} & \multicolumn{3}{c}{\(\delta_{T}\) **Being Different from \(\delta_{E}\)**} & \multirow{2}{*}{**Accuracy of Testing (\%)**} \\ \cline{3-3} \cline{5-6} \multirow{2}{*}{**CV of BRVs**} & \multirow{2}{*}{**Test Number**} & \multirow{2}{*}{**ANN Being**} & \multirow{2}{*}{**Both \(\delta_{T}\) and**} & \multirow{2}{*}{**Both \(\delta_{T}\) and**} & \(\delta_{T}\) **Being 1** & \(\delta_{T}\) **Being 0** \\  & & & \(\delta_{E}\) **Being 1** & \(\delta_{E}\) **Being 0** & **Being 1** \\ \hline \multirow{3}{*}{0.005} & \multirow{3}{*}{1000} & GABPNN & 196 & 684 & 58 & 62 & 88.0 \\  & & BPNN & 198 & 667 & 75 & 60 & 86.5 \\  & & RBFNN & 115 & 688 & 54 & 143 & 80.3 \\ \hline \multirow{3}{*}{0.01} & \multirow{3}{*}{1000} & GABPNN & 311 & 572 & 61 & 56 & 88.3 \\  & & BPNN & 309 & 567 & 66 & 58 & 87.6 \\  & & RBFNN & 275 & 596 & 37 & 92 & 87.1 \\ \hline \multirow{3}{*}{0.015} & \multirow{3}{*}{1000} & GABPNN & 341 & 553 & 49 & 57 & 89.4 \\  & & BPNN & 334 & 542 & 60 & 64 & 87.6 \\ \cline{1-1}  & & RBFNN & 321 & 561 & 41 & 77 & 88.2 \\ \hline \multirow{3}{*}{0.02} & \multirow{3}{*}{1000} & GABPNN & 405 & 504 & 42 & 49 & 90.9 \\ \cline{1-1}  & & BPNN & 390 & 503 & 43 & 64 & 89.3 \\ \cline{1-1}  & & RBFNN & 398 & 520 & 26 & 56 & 91.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The comparison of the test results of the ANNs in the IP study under the shock load condition where \(\overline{v}\) is 1000 m/s. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Sample Set**} & \multicolumn{1}{c}{**Sample Size \(q\)**} & \multicolumn{1}{c}{**Initiation Frequency**} & \multicolumn{1}{c}{**Non-Initiation Frequency**} \\ \hline Training sample set & 4000 & 1580 & 2420 \\ \hline \multirow{3}{*}{Test sample set} & CV of BRVs being 0.005 & 1000 & 258 & 742 \\  & CV of BRVs being 0.01 & 1000 & 367 & 633 \\  & CV of BRVs being 0.015 & 1000 & 398 & 602 \\  & CV of BRVs being 0.02 & 1000 & 454 & 546 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The statistical results of the initiation and non-initiation frequencies of Composition B in the training sample set and test sample sets under the shock load condition where \(\overline{v}\) is 1000 m/s.