## 4 Results
### Analysis Method and Results  
As an index showing the accuracy of the analysis method, absolute error, which is the difference between the calculated and the pre-set value, was used to plot the frequency count histogram with a cumulative percent series. Additionally, the percent errors of generation time, the coordinate (\(x\), \(y\), and \(z\)), and the distance, \(d\), were used to evaluate the accuracy of the AE source location technique through the following equations,  
\[t\_error=\left|\frac{t-t_{0}}{t_{0}}\right|\times 100\% \tag{5}\]  
\[x\_error=\frac{x-x_{0}}{x_{0}}\times 100\% \tag{6}\]  
\[y\_error=\frac{y-y_{0}}{y_{0}}\times 100\% \tag{7}\]  
\[z\_error=\frac{z-z_{0}}{z_{0}}\times 100\% \tag{8}\]  
\[d=\sqrt{x^{2}+y^{2}+z^{2}} \tag{9}\]  
\[d_{0}=\sqrt{x_{0}^{2}+y_{0}^{2}+z_{0}^{2}} \tag{10}\]  
\[d\_error=\frac{d-d_{0}}{d_{0}}\times 100\% \tag{11}\]  
where \(t_{0}\) and \(t\) are the recorded trigger time and the calculated generation time, respectively; \(x_{0}\), \(y_{0}\), and \(z_{0}\) are the locations of the pre-set PLB sources as, shown in Table 2; \(x\), \(y\), and \(z\) are the locations of the calculated PLB sources; \(d_{0}\) and \(d\) are the pre-set and calculated distance from the coordinate origin, respectively; and \(t\_error\), \(x\_error\), \(y\_error\), \(z\_error\), and \(d\_error\) are the percent errors of generation time, location, and distance, respectively. According to the analysis method, the results are shown in Figure 6a-i. Figure 6a shows the percent error of generation time. It was found that all results of generation time were within an error of 7% and around 95% of them are within an error of 5%, which suggests that the calculated generation time has a good accuracy in this AE source location technique. Figure 6: _Cont._Figure 6: Evaluation of generation time, the coordinate (\(x\), \(y\), and \(z\)), and the distance from the coordinate origin: (**a**) Time percent error; (**b**) Frequency count histogram with a cumulative percent series and (**c**) the percent error along the \(x\) axis; (**d**) Frequency count histogram with a cumulative percent series and (**e**) the percent error along the \(y\) axis; (**f**) Frequency count histogram with a cumulative percent series and (**g**) the percent error along the \(z\) axis; (**h**) Frequency count histogram with a cumulative percent series and (**i**) the percent error, of the \(d\) value. From Figure 6b-i, the absolute error and the percent error of the coordinates (\(x\), \(y\), and \(z\)) and the distance from the origin are presented. For the distance, \(d\), as shown in Figure 6h,i, except for several points with a large error, around 90% of the PLB sources were within an absolute error of \(\pm\) 15 mm and a percent error of \(\pm\)10%. This is in good agreement with the study conducted by [PERSON] et al. [11]. Thus, the existing AE source location technique is believed to be reliable, according to the generation time and the distance. For the specified coordinates along the \(x\), \(y\), and \(z\) axes, more than 90% of the PLB sources along the \(x\) and \(z\) axes were within an absolute error of \(\pm\)15 mm, while along \(y\) axis, around 80% of the sources were within \(\pm\)15 mm. Regarding the percent error, most of them were within \(\pm\)30%. Thus, the existing AE method is proven to have the least error for the distance from the coordinate origin, with some errors along the \(x\), \(y\), and \(z\) axes. This suggests that the existing AE source location technique still needs further improvement. For the z position, as shown in Figure 6f,g, it was found that the results on A point, marked as red columns, were within an error of \(\pm\)10%. Most of them were negative, which means that the calculated result was lower than the pre-set PLB source. The results on B point, marked as black columns, were around the line of 0 percent error, suggesting that there was a higher accuracy around B point, with an error lower than \(\pm\)5%.