# Application of Classified Elastic Waves for AE Source Localization Based on Self-Organizing Map
## 6 Discussion  
In this model test, limited waves measured at the vertexes of the models were applied to the SOM. According to the results of the source localizations, it is confirmed that the obtained map performs classification of the straight propagation waves and improves the AE source localizations in the heterogeneous velocity distributions. Hence, the used measured waves are appropriate for the classification. It is noted that this selection of measured waves assumes that the source localizations are conducted in materials that were locally damaged. If waves are measured at the vertexes of complex structures, measured diffraction waves are increased. According to the SOM algorithm, having a large number of diffraction waves contributes to expanding the size of the low S/N class, and it is expected that classified straight propagations are decreased because of a reduction of the high S/N class. Hence, it implies that localized sources are decreased since few straight propagations are classified. According to the comparison of the source localizations, ray tracing visualizes a larger number of sources than the TDOA method. In this model test, the least squares method is applied to the TDOA method and the location of a source error is iteratively corrected. If detection errors of arrival times are large, a source is firstly localized out of the analytical model. Furthermore, a coefficient matrix used in the least squares method computes the determinant of approximated 0 if a localized source firstly includes a large error. If the determinant is 0, the result of the TDOA method is the divergence. Furthermore, the particular combination of used sensor locations contributes to the computation of the determinant of 0. However, the application of ray tracing is expected to visualize all sources since the computation does not require a coefficient matrix. Therefore, it is noteworthy that the TDOA method has potential to visualize a smaller number of sources in comparison with the number of sources localized by ray tracing if the classified waves \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source Localization** & **Visualized Events** & **Average Errors (mm)** & **Maximum Errors (mm)** & **Computational Time (s)** \\ \hline TDOA & 47 & 15 & 200 & 0.011 \\ Ray tracing & 49 & 15 & 110 & 801 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the source localizations with the classified waves. are applied. Moreover, the maximum localization error generated by the TDOA method is larger than the error of the localization based on the ray tracing. Although the averages of source localization errors are approximated in the two localizations, the number of sources localized by ray tracing includes two of the sources which are not localized by the TDOA method. It should be noted that the arrival-time detection errors generate the determinant of approximated 0 in the coefficient matrix, and this reason is why two of the sources are not localized by the TDOA method. In the localizations based on ray tracing, two of the sources are expected to have larger errors than the average because of the arrival-time detection errors. Therefore, in the application of the classified waves, it is expected that the sources localized by ray tracing are more accurate than the accuracy in the TDOA method. It should be noted that this model of ray tracing set the intervals of the candidates at 20 mm. Moreover, [PERSON] et al. localized sources in which the average error was approximated at half of the interval of the candidates [32]. Owing to the average error of 15 mm in the TDOA method, it is expected that the 20 mm interval of the candidates is sufficient in the localization based on ray tracing using classified waves. Consequently, the localization based on ray tracing is appropriate in the application of classified waves if the interval of 20 mm is used. Although ray tracing more accurately localizes sources than the TDOA method, the computational times of ray tracing are huge.