## 4 Results and Analysis
We used sigmoid activation in the BPNN because the sample dataset was nonlinear. The same set of time-domain statistical features were provided to the BPNNs. We repeated the experiment with the BPNN multiple times to obtain stable results. The results of the proposed model are shown in Figure 10. The average classification accuracy of the proposed model for AE signals acquired from a spherical tank under normal and leak conditions was better than 95%. The model was able to accurately classify instances from the pinhole crack condition: This classification accuracy was 100%. However, under normal conditions, a few instances were misclassified because the time-domain statistical features did not provide enough discriminative information to the subsequent classifier. This means that some of the features in this class overlapped the features of the second class, so the SVM misclassified them. The average classification accuracy of the BPNN was 61.63% for the same experimental setup. The normal-condition classification accuracy was 47.60%, and the fault-condition classification accuracy was 75.66%. This shows that the BPNN was unable to properly differentiate some of the instances into the normal and cracked classes, reducing the average classification accuracy. Figure 8: The rise angle produced due the crack development on the spherical tank. Figure 7: (**a**) Normal acoustic emission signals from the spherical tank; (**b**) Acoustic emission signals from the spherical tank with a 3 mm pinhole crack. In addition to the classification results, we estimate the crack location in this study. The location of the crack is estimated based on the source localization technique given in [24]. The source can be localized by geometrical arguments by using the following formula:  
\[D_{i}=\sqrt{\left(x_{i}-x\right)^{2}+\left(y_{i}-y\right)^{2}} \tag{6}\]  
In the above equation, if the position of each sensor \(S_{i}\) is given by \(S_{i}(x_{i},y_{i})\) and the source location is given by \(S_{i}(x,y)\), then the resulting quantity \(D_{i}\) is the desired distance among the source and the sensors. In Figure 11, a planer diagram by using the geometrical relationship of the sensors and the source for our experiment is presented. The red points show the estimated location about the source of origin of the AE signals for the four pencil lead break (PLB) tests. It can be observed that the density  
Figure 10: Classification accuracy comparison of the proposed spherical tank leakage detection model with a back propagation neural network. Figure 9: SVM boundary line identification around the two feature vectors of the two classes. The blue samples belong to the normal condition and the red samples belong to the crack condition. of the estimated points was near to the channel 4, and thus it can be assumed that the location of the signals originating from the crack was near to this channel. The notion about the estimated source location can be consolidated by analyzing the waveforms of the AE signals obtained during the four PLB tests. Theoretically, the location of the crack was near to the sensor which has minimum arrival time of the signals. The arrival time of a signal to a sensor can be obtained from the signal waveform. In this study, four PLB tests were conducted to excite the crack and get the crack signal. The signals obtained during the four PLB tests are given in Figures 12-15. It is evident that in all the four tests, channel 4 first received the signals. We can also observe that channel 2 received the signals a little later as compared to channel 4 and the next one in line was channel 1. In all the tests, channel 3 was the last one to receive the signals, as the time of arrival of the signals was maximum in this case. Another trait worth noticing is that the amplitude of the signals for the channel 4 was grater compared to the signals of the other channels in all the PLB tests.