# Application of Classified Elastic Waves for AE Source Localization Based on Self-Organizing Map
## 5 Results
### Results of AE Source Localizations  
In order to validate the performance of AE source localizations with the classified waves, arrival times were detected from the classified waves which are expected to propagate as straight lines, and the detected arrival times are applied to the source localizations, which are the TDOA method and ray tracing. Moreover, the performance of the classification of the AE source localizations conducted on heterogeneous velocity distributions is  
Figure 10: Results of the classification in each sensor. Figure 9: Results of SOM using artificial AEs measured at S1, S4, S9, and S12. discussed through comparisons with source localizations using all of the measured waves. It should be noted that these models assume the propagation velocity is 5400 m/s, referring to the results of the source localization conducted on an aluminum plate [22]. The results of the TDOA method are shown in Figure 11. Although the localized sources shown in Figure 11a have low accuracies, the localized sources shown in Figure 11b approximate the locations of PLB points. Figure 11a confirms that the diffraction waves contribute to source-localization errors because the algorithm of the TDOA method assumes ray paths to be straight propagations. Thus, the used waveforms in Figure 11b are possibly propagated as straight, and it is demonstrated that the classification improves the results of the TDOA method in the heterogeneous velocity distributions. Furthermore, the classified waves in the source localization based on ray tracing perform as well as in the TDOA method. The sources localized by ray tracing are shown in Figure 12. It is noted that the source is chosen from candidates set with the interval of 20 mm. In the ray-tracing algorithm, diffraction waves are considered on the basis of approximated heterogeneities by the cells in models. The ray tracing is conducted on the homogenous model and the localization errors are generated in Figure 12a. However, the accuracy of the localized sources is reformed in Figure 12b, and it implies that use of ray tracing for the source does not require the approximation of velocity distributions in the model if the straight propagation waves are classified. Figure 11: Results of TDOM method in the heterogeneous elastic velocity distributions: (**a**) non-classification; (**b**) the application of the classification. Figure 12: Results of the source localization using ray tracing: (**a**) non-classification; (**b**) the application of the classification. The results of the source localizations using the classified waves are listed in Table 2. The visualized events imply the number of sources localized in Figures 11b and 12b. In Table 2, the visualized events of the TDOA method exclude two sources that had huge localization errors due to the divergence of the least squares method. Hence, although the number of the sources localized by ray tracing is the same as the number of PLB tests, the number of the sources localized by the TDOA method is smaller in comparison with the number of PLB tests. Moreover, the errors regard Euclidean distance, which is from a PLB point to a localized source. Furthermore, the average and the maximum of errors are computed on the basis of visualized events. In the visualized events, the average errors of TDOA are the approximated results of ray tracing. However, the TDOA method generates a larger maximum error in comparison with the application of ray tracing. It should be noted that the effect of the arrival-time detection error in source localizations with classified waves is expected to be larger in comparison with the effect of diffractions [22]. Although the localized sources have the potential to be visualized out of the analytical model in the TDOA algorithm if the detection errors of arrival times are large, the sources are localized in the analytical model if the ray tracing is applied to a source localization since localized sources are obtained as candidates.