# Application of Classified Elastic Waves for AE Source Localization Based on Self-Organizing Map
## 5 Results  
### Results of the Classification  
In the map shown in Figure 9, the cells imply that the neurons and the center of the cell set to three dimensions of the vectors had the components computed by the root-mean-square voltages. The number of input vectors is 214, the same as the number of the waves measured at S1, S4, S9, and S12. Furthermore, the map consists of 64 neurons, and the number of the neurons is obtained by the use of the heuristic equation applied to an application of the SOM [31]. In Figure 9, the neurons visualize three classes formed by the similarities of the vectors detailed in the Section 3.2. The weight vectors have similarities in neighbor neurons, and the neurons that have fewer similarities with the weight vectors are located further away on the map [20]. Thus, the similarity of the classes is visualized by the distance of the position vectors on the map. In the classification of elastic waves, amplitudes of noises are assumed to be lower in comparison with diffraction waves wherein amplitudes are lower than straight propagation waves. Moreover, the used weight vectors are related with the size of the amplitudes because the used weight vectors were computed from the measured waveform. It is supposed that the location of the high S/N class, wherein straight propagations belong, is closer to the location of the low S/N class, wherein diffraction waves belong, in comparison with the location of the noise class. According to Figure 9, it is confirmed that visualized classes are in the expected location.  
\begin{table}
\begin{tabular}{c c c} \hline
**Sensors** & **x (mm)** & **y (mm)** \\ \hline S1 & 0 & 0 \\ S2 & 300 & 0 \\ S3 & 500 & 0 \\ S4 & 800 & 0 \\ S5 & 0 & 300 \\ S6 & 800 & 300 \\ S7 & 0 & 500 \\ S8 & 800 & 500 \\ S9 & 0 & 800 \\ S10 & 300 & 800 \\ S11 & 500 & 800 \\ S12 & 800 & 800 \\ \hline \end{tabular}
\end{table}
Table 1: Locations of installed sensors in the specimen.  
Figure 8: Locations of PLB points and sensors.  
Three-dimensional vectors computed from each measured wave are applied to the map to conduct the classification. It should be noted that the winning neuron is computed by Equation (5) using the measured waveform, and the class of the winning neuron implies the class of the waveform. The results of the classifications for the measured waves at each sensor are shown in Figure 10. According to Figure 10, high S/N signals are measured at each sensor, but particularly few high S/N signals are acquired at S3 and S4. Since the occurrence of a large amount of diffraction around the defects is expected, S3 and S4 have potential for measuring the larger numbers of diffraction waves in comparison with the number of straight propagation waves. Therefore, it is confirmed that the results of the classification approximate the above prediction. Furthermore, it is expected that the map performs the classification of elastic waves the same as the expected performances. In addition, it should be noted that the performance of the map used for classification will be confirmed if artificial AE arrivals are obtained from the waveform belonging to the high S/N class and the detected arrival times contribute to an improvement of the accuracies of the AE source localizations.