# Application of Classified Elastic Waves for AE Source Localization Based on Self-Organizing Map
## 2 AE Source Localization
### Classification of the Waves  
The map defined as the output layer can be used in the classification because the class of \(M_{c}\) implies the class of the data if \(M_{c}\) in the map is chosen by the data. Therefore, if the SOM forms a high S/N class, wherein neurons are updated by high S/N signals, it is supposed that the computed class choses the waves used in AE source localizations.  
The number of vector components implies the characteristics of the measured data. Moreover, since a large number of the characteristics increase the number of classes, the classes are possibly scattered in the map. Furthermore, scattered classes are expected to have identical data classified in different classes. Therefore, the input vector components should be decreased. In order to reduce the input vector components used in this classification, the components are defined as the root-mean-square voltage computed in the equally divided waveform. To illustrate the computation of the components, the divided waveform is shown in Figure 4, and the root-mean-square voltage \(V_{i}\) is obtained as  
\[V_{i}=\sqrt{\frac{1}{T_{i}}\int_{0}^{T_{i}}y^{2}(t)dt}, \tag{8}\]  
where \(T_{i}\) is the duration time in the \(i\)th divided waveform, \(y(t)\) is the divided waveform, and \(t\) is the time. In Figure 4, the waveform is divided into three parts, and it implies that the number of components is three in this SOM analysis. It is supposed that three components are enough for the formation of the class since the SOM has been conducted with RGB values, which are defined as three-dimensional vectors [27].  
Figure 4: Example of the waveform divided for computation of the input vector components.  
Figure 3: The conceptual diagram of SOM.  
To define borders of the classes, the computation of similarity in the weight vectors, for instance, by the K-means algorithm, was applied [28]. In this study, three types of classes, namely, the high S/N, low S/N, and noise classes, are assumed in the measured waves, and the three representative weight vectors in each class are selected to define the border as the minimum Euclidean distance from the neurons to the representative weight vectors. If the representative weight vectors are used for the criterions, the computation of the similarity does not require the same iteration as the K-means algorithm. In the heterogeneous models, the diffraction and refraction waves are generated, and these amplitudes are lower in comparison with the straight waves because of the diffraction and refraction attenuations. Hence, it is expected that the straight waves are the high S/N class, and the diffraction and refraction waves are the low S/N class. Moreover, the noises are assumed to be lower amplitudes than the measured signals, and the noise classes contributed to the classification of noises in the previous study [22]. In Figure 4, a ration of \(V_{3}\) to \(V_{1}\) implies levels of S/N in the measured waveforms because 0 \(\upmu\)s is start of the measurement, and high S/N signals generally start from 0 \(\upmu\)s. Furthermore, the level of S/N \(L_{V}\) is obtained as  
\[L_{V}=20\text{log}\frac{V_{3}}{V_{1}}. \tag{9}\]  
Hence, in the obtained map, it is supposed that the neuron that has the highest \(L_{V}\) belongs to the high S/N class, and the noise class includes the neuron that has the lowest \(L_{V}\). Therefore, the representative weight vectors allocated in the neurons wherein the highest and the lowest \(L_{V}\) are computed are expected to be used for the criterions defining the high S/N class and the noise class. Furthermore, the criterion of the low S/N class is the average vectors computed by other criterions since the amplitudes of the low S/N are assumed to be larger than the amplitudes of noises.