# 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  
(1) Study on IP  
(i) Constructing training sample set and test sample sets  
In addressing the IP when the \(\overline{v}\) is 1050 m/s, in order to guarantee the excellent generalization ability of the ANNs, 2000 sample points were generated for the BRVs with the CV of 0.02, and 500 sample points were generated for the BRVs with the CV of 0.005, so as to construct the training sample set with 2500 sample points. Then, a test sample set of 1000 sample points was constructed for the BRVs with each of the CVs of 0.005, 0.01, 0.015, and 0.02. The four test sample sets tested whether the ANNs could accurately calculate the RRs under these randomness conditions. The statistical results of the initiation and non-initiation frequencies of Composition B in these training sample set and test sample sets are shown in Table 4.  
(ii) Determining the structure and important parameters of ANNs  
In this example, according to the numbers of the BRVs and RR in the IP, the neuron numbers of the input layer, first hidden layer, second hidden layer, and output layer of the GABPNN for the IP were, respectively, set as 19, 25, 15, and 1. So, the structure of this GABPNN was \(19\times 25\times 15\times 1\). In addition, the network maximum training time \(T_{\text{max}}\) was set as 20,000, the network training rate \(R_{t}\) was set as 0.05, the network training allowable error \(E_{a}\) was set as 0.001, the population size \(M_{p}\) was set as 20, the maximum generation \(G_{\text{max}}\) was set as 30, the chromosome crossover probability \(P_{c}\) was set as 0.75, the chromosome mutation probability \(P_{m}\) was set as 0.1, and the fitness coefficient \(C\) was set as 20.0. In addition, the structure and corresponding parameters of the BPNN were the same as the corresponding ones of the GABPNN. The neuron numbers of the input layer and output layer of the RBFNN were the same as the corresponding ones of the GABPNN, and the neuron number of the hidden layer of the RBFNN was equal to the sample size \(q\) of the training sample set. (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, with the test results shown in Table 5 and Figure 6. In Table 5, the \(\delta_{T}\) stands for the calculation results of these three ANNs (the actual output results of the \(\delta\)), and the \(\delta_{E}\) the expected output results of the \(\delta\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample Set** & **Sample Size \(q\)** & **Initiation Frequency** & **Non-Initiation Frequency** \\ \hline Training sample set & 2500 & 1554 & 946 \\ CV of BRVs being 0.005 & 1000 & 768 & 232 \\ CV of BRVs being 0.01 & 1000 & 685 & 315 \\ CV of BRVs being 0.015 & 1000 & 612 & 388 \\ CV of BRVs being 0.02 & 1000 & 585 & 415 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: 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 1050 m/s.