## 3 Application and Results
### Convolutional Neural Network Training Set Extension and Update  
From the forward extrapolation results of the test dataset, the probability of each test waveform in the two classification results can be obtained. The expectations of the classification labels for neutron and gamma are calculated separately and the specific calculation method is shown in Equation (11):  
\[E=\frac{\exp(output_{neutron})}{\exp(output_{neutron})+\exp(output_{gamma} )}\times label_{neutron}+\frac{\exp(output_{gamma})}{\exp(output_{neutron})+ \exp(output_{gamma})}\times label_{gamma} \tag{11}\]  
where \(E\) is the expected value of the particle inference result; _labelneutron_ refers to the label for neutron classification by the CNN, which is 0; and _labelgamma_ refers to the label for gamma classification by the CNN, which is 1. The logarithmic calculation part is the SoftMax calculation process for the neutron and gamma classification results, thereby obtaining the classification probabilities for neutron and gamma.  
Table 9 shows the expected distribution of neutron and gamma in the final output of the CNN test dataset.  
Figure 13: Physical diagram of CNN operation platform.  
\begin{table}
\begin{tabular}{c c c} \hline
**Test Data and Floating-Point** & **Test Data and Fixed-Point** & **Floating-Point and** \\
**Result Compliance** & **Compliance** & **Fixed-Point Number** \\ \hline
97.900\% & 97.800\% & 99.900\% \\ \hline \end{tabular}
\end{table}
Table 8: Comparison table of test data and floating-point and fixed-point numbers.  
The distributions of the classification expectations are plotted in Figure 14a,b.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Expected Value** & \
\begin{tabular}{c} **Neutron Distribution** \\ **Frequency** \\ \end{tabular} &
\begin{tabular}{c} **Gamma** \\ **Distribution Frequency** \\ \end{tabular} \\ \hline
0 & 0 & 0 \\  
& 3 & 451 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Expected value and distribution frequency.  
The method for calculating the \(PSD\) parameter using pulse waveform analysis [17] is shown in Equation (12):  
\[PSD=\frac{Q_{t}-Q_{p}}{Q_{t}} \tag{12}\]  
where \(Q_{t}\) is the total window charge integral and \(Q_{p}\) is the prompt window charge integral. The schematic diagram is shown in Figure 15.  
By calculating the PSD parameters for all neutron and gamma test waveforms, a table of PSD parameters and the frequency of each interval can be obtained, as shown in Table 10.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**PSD Value**} & \multicolumn{1}{c}{**Neutron Distribution Frequency**} & \multicolumn{1}{c}{**Gamma**} \\  & & **Distribution Frequency** \\ \hline
0.51 & 0 & 0 \\
0.52 & 1 & 0 \\
0.53 & 4 & 3 \\
0.54 & 24 & 4 \\
0.55 & 233 & 9 \\
0.56 & 194 & 13 \\
0.57 & 41 & 48 \\
0.58 & 3 & 65 \\
0.59 & 0 & 78 \\
0.6 & 0 & 81 \\
0.61 & 0 & 97 \\
0.62 & 0 & 70 \\
0.63 & 0 & 29 \\
0.64 & 0 & 3 \\
0.65 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 10: PSD parameter and distribution frequency.  
Figure 14: (**a**) Distribution of neutron classification expectations. (**b**) Gamma classification expectation distribution.  
Figure 15: The pulse shape and time window of neutron and gamma in CLYC.  
The distribution state diagram is shown in Figure 16.  
From the calculations, it can be observed that the expected FOM value of CNN classification for neutron gamma is 133, while the FOM value of the PSD method is 0.8. In addition, the dataset with neutron expectation values less than 0.05 and gamma expectation values greater than 0.95 is selected as the extended dataset, which has 463 neutrons and 466 gamma rays.