## 2 Background Study on Pipeline Leak Detection Methods
### Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)
In general, the optimal kernel size is 3 \(\times\) 3 and the kernel size is 1 \(\times\) 1, which are applied for dimensionality reduction. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sl No** & **Class** & **Average Energy (mV2)** \\ \hline
1 & No leak & 328.16 \\
2 & Leak at a 1 m distance & 2554.71 \\
3 & Leak at a 2 m distance & 13,137.34 \\
4 & Leak at a 3 m distance & 24,754.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The average energy of desired IMFs. When the kernel size is greater than \(5\times 5\), it leads to a longer training time. Meanwhile, the even kernel sizes of \(2\times 2\) and \(4\times 4\) do not have the same capacity as odd-size filters to divide the pixels in the previous layer more symmetrically. The filter size should grow gradually to learn the features appropriately. Figure 8 shows the architectural diagram of a 2 DCNN with its dimensions after considering the above criteria. The input layer dimension is 150 \(\times\) 150 \(\times\) 3. All the convolutional layer's kernel sizes are 3 \(\times\) 3. The convolutional layer's filter sizes are as follows: (1) first convolutional layer--8, (2) second convolutional layer--16, (3) third convolutional layer--32, (4) fourth convolutional layer--64, and (5) fifth convolutional layer--128. The pool size of all max pool layers is 2 \(\times\) 2. The first and second dense layers' neuron sizes are 256 and 128, respectively. The output layer's activation function is softmax, and the number of neurons is kept at four to match the categories the model is supposed to detect and localize the leak with. The optimizer used in this paper for this architecture is Adam, which is used to optimize the hyperparameters. The number of convolutional layers is kept at five because after five layers, the model overfits, and the model does not classify as accurate as with fewer layers. The flatten layer helps to convert the two-dimensional feature size of the convolutional layer to one dimension to make it suitable for the dense layers. The two dense layers help to reduce the dimension of the flatten layer gradually to keep the input to the output layer simpler. ## 5 Results and Discussion

This paper implements (1) MFCC-2 DCNN [10], (2) MFCC with a proposed 2 DCNN architecture, (3) EMD-MFCC with a proposed 2 DCNN architecture, (4) EEMD-MFCC with a proposed 2 DCNN architecture, and (5) CEEMDAN-MFCC with a proposed 2 DCNN architecture to compare the performance of the proposed novel EMD with an optimal mode selector, an MFCC, and a 2 DCNN. As the existing 2 DCNN models are implemented only for leak detection, the proposed 2 DCNN is also modified and implemented for detecting the leak only by keeping the number of neurons in the output layer as two. Similarly, the existing 2 DCNN model's output layer is modified to have four neurons in the output layer for leak detection and localization. Therefore, this paper implements six leak detection and localization models for 2-bar and 3-bar pressure sets. All the model's epochs and batch sizes are set to 50 and 20, respectively. The train, test, and predict ratios, containing 4800 samples in each pressure dataset, are 80%, 16%, and 4%, respectively. Implementing all the methods takes two steps: (1) data preparation, and (2) leak detection and localization. The times taken to process the MFCC, EMD-MFCC, EEMDAN-MFCC, and the novel EMD with an optimal mode selector and MFCC are 819.26, 3748.15, 189,667.23, 395,188.37, and 3988.15 s, respectively. The times taken for the leak detection models 2 DCNN [10] and the proposed 2 DCNN are 504.12 and 356.22 s, respectively. Meanwhile, the time taken for the leak detection and localization models modified from the existing 2 DCNN and the proposed 2 DCNN is 1162.15 and 842.74, respectively. The assessment metrics used to evaluate the models' performance are

Figure 8: Proposed 2 DCNN architecture diagram. prediction accuracy, precision, recall, F-score, and R-square. The observation results are in Tables 2-5.