## 2 Background Study on Pipeline Leak Detection Methods
### Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)
### Novel EMD with Optimal Mode Selector, MFCC, and 2 DCNN

EMD helps to denoise any non-stationary signal, and the only problem with the EMD is its mode mixing. Contrarily, the EEMD and CEEMDAN aid in mitigating the issue of mode mixing. Although all three methods help to denoise, none gives a rule of thumb by which to select the appropriate IMF. This paper addresses this issue by proposing a novel EMD with an optimal mode selector for noise removal. The novel EMD with an optimal mode selector chooses the IMF automatically based on the energy value of the IMF. Equation (8) gives the formula for calculating the energy of a signal, and Figure 7 gives the flowchart of the novel EMD with an optimal mode selector. The novel EMD with an optimal mode selector algorithm is in Algorithm 4. \[S(t)=\sum_{k=1}^{K}\widetilde{I}_{k}+r_{k} \tag{3}\]4

where \(E\) is the energy calculated and \(I_{n}(t)\) is the IMF. The average energy of the desired IMF (\(I_{d}(t)\)) is in \[S(t)=\sum_{k=1}^{K}\widetilde{I}_{k}+r_{k} \tag{3}\]5 The range of the average energy varies from \(-1000\) mV\({}^{2}\) to \(+1000\) mV\({}^{2}\) for each class. \[S(t)=\sum_{k=1}^{K}\widetilde{I}_{k}+r_{k} \tag{3}\]6 Workflow of proposed leak detection and localization method. \[S(t)=\sum_{k=1}^{K}\widetilde{I}_{k}+r_{k} \tag{3}\]7 Flowchart for novel EMD with optimal mode selector. The EMD and the other EMD variants denoise any signal by identifying the local minima and maxima. The first IMF considers the highest frequency content captured from the signal. The frequency content reduces as the order of the IMFs increases. The desired energy of the frequency component that holds the information about the necessary pipeline leak data is in \[S(t)=\sum_{k=1}^{K}\widetilde{I}_{k}+r_{k} \tag{3}\]8 The proposed novel EMD with an optimal mode selector is designed in such a way that it screens the signal and chooses the appropriate IMF. After selecting the optimal IMF, the one-dimensional data are feature-extracted and converted into two-dimensional data using MFCC. Then, the MFCC with the shape of 13 \(\times\) 40 is converted and saved as a JPEG image with the dimensions of 640 \(\times\) 480 and a resolution of 100 dpi in a folder with the name of the sample's category name. Similarly, 9600 images of the novel EMD with an optimal mode selector and an MFCC are created and stored under their corresponding category names under both pressure sets. ### 2 dcnn

The layers in the proposed 2 DCNN architecture in this study contain one input, five convolutional, four max pools, one flatten, two dense, and one output. A max pool layer follows each convolutional layer. A convolutional layer executes a convolutional operation involving the input to the layer along with its weights and bias, as described by the given Equation (9). \[S(t)=\sum_{k=1}^{K}\widetilde{I}_{k}+r_{k} \tag{3}\]9

where \(Conv_{out}\) is convolutional layer-generated output, \(A_{in}\) is the convolutional layer's input, \(w_{i}\) is the weight variable, and \(\alpha\) is a bias variable. Convolutional layers can employ various activation functions, such as ReLU, sigmoid, tanh, and linear. Due to its ability to mitigate exponential computational growth, practitioners commonly use the ReLU function among these options, as defined in Equation (10). \[D(k)=\sum_{t=0}^{T-1}I_{d}(t)e^{-j2 nk\frac{t}{t}} \tag{4}\]0

Equation (10) defines the ReLU function, which yields an output of either \(max(Conv_{out})\) or 0. Following the convolutional layer, a max pooling layer reduces the number of parameters. \[D(k)=\sum_{t=0}^{T-1}I_{d}(t)e^{-j2 nk\frac{t}{t}} \tag{4}\]1

Equation (11) involves the max pool operation, which selects the maximum value from a set of pool size n. The last layer in a CNN is the classification layer, which categorizes according to the defined classes. The configurations and quantities of the convolutional and max pooling layers differ based on the specific applications.