# Data Driven Leakage Detection and Classification of a Boiler Tube
## 4 Performance Evaluation and Results  
Acoustic emission signals recoded from the boiler tube under two different conditions (normal, leak) were used to evaluate the leakage identification model developed. The dataset consists of AE signals that were recorded under 0.6 mm, 1 mm, and 2 mm pinholes on the boiler tube. This study has two main parts: (1) wavelet packet decomposition of the AE signals to explore the salient information; and (2) deep neural network adoption for the classification of input data and to identify the samples belonging to the leakage. In Figure 8, AE signals associated with the two different conditions of the boiler tube are given. It can be observed that there are no visible differences between the signals belonging to the two different conditions. Signals under both conditions possess the same pattern of variation with respect to time. Thus, it is hard to identify the signals associated with the leak state of the boiler just by monitoring them. Therefore, in this work, 4-level wavelet packet decomposition was applied to the AE signals associated with both conditions. The 4-level wavelet decomposition resulted in 16 nodes in the last layer of the wavelet tree. The wavelet packet decomposes the signal into a sub-band that provides detailed information, both in the time and frequency domains. After the decomposition, the relative energy and entropy of each subband from the last level of the wavelet tree were computed. Each feature vector for a given sample is 14 points long. The distribution of the two wavelet features is presented in Figure 9. It is evident from the figure that both of the features form a fine cluster with no overlap among the features from different classes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of** & **Pinhole Size** & **Training** & **Validation** & **Test Samples** & **Number of Channels** \\ \hline Normal & 0 & 900 & 300 & 500 & 4 \\ \hline Leak & 0.6, 1, 2 & 900 & 300 & 500 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset description. Figure 8: (**a**) Normal condition signal; (**b**) signal from the leak state of the boiler tube. To classify the data, a deep neural network was used in the current study. The deep architecture of the DNN and the adaptation of the nonlinear activation function make the DNN very effective in learning salient information from the input data. The design parameters of the adopted DNN are given in Table 2. The design parameters were selected based on the cost function of the DNN. The parameters given in Table 2 yielded optimal values for the cost function. The results presented in this paper are according to this architecture. The performance of the leakage classification and identification model developed was evaluated using the k-fold cross validation technique and is given in Figure 10. The dataset obtained was split among training, validation, and test datasets, with approximately 50, 20, and 30 percent of the data, respectively. In the figure, a confusion matrix and the class-wise accuracies of the proposed model are given. It can be observed that the average accuracy of the developed model is 99.2%. This means the proposed model could accurately classify most of the instances present in the test set. Specifically, the proposed model could correctly classify 99% of the samples in the normal class, whereas 99.4% of the samples associated with the leak state of the boiler tube were correctly classified. The model developed could yield enhanced classification performance because it was initially trained well on the wavelet features. Due to the deep architecture, the DNN could easily extract salient information from the distinct wavelet features. The features were already well clustered and had a non-overlapping distribution pattern that made the information extraction and classification task easy for the DNN. \begin{table}
\begin{tabular}{c c c} \hline
**Length of Each Input** & **Total Number of Layers** & **Number of Nodes in Each Layer** \\ \hline
32 & 3 & 15, 10, 5 \\ \hline \end{tabular}
\end{table}