## 2 Background Study on Pipeline Leak Detection Methods
### Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)
An additional twelve data samples are taken from the 2-bar set at a 1 m distance, as the cross-correlation needs two sensors for localization. The results of the cross-correlation are in Table 6.

Table 6 lists the cross-correlation results along with the relative error and accuracy. Among the results, the highest observed accuracy is 99.31%, the lowest observed accuracy is 77.92%, and the average accuracy is 89.95%. The average accuracy of the cross-correlation is closer to the localization accuracy of the modified existing MFCC-2 DCNN. The results conclude that the proposed novel EMD with an optimal mode selector, an MFCC, and a 2 DCNN detects and localizes the leak more accurately at the two different pressures than all of the other methods discussed in this paper. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SI No** & **Actual Distance** & **Calculated Distance** & **Relative Error** & **Accuracy \%** \\ \hline
1 & L1 = 1 & L1 = 1.007 & 0.007 & 99.31 \\  & L2 = 1 & L2 = 0.993 & & \\
2 & L1 = 1 & L1 = 1.133 & 0.133 & 86.71 \\  & L2 = 1 & L2 = 0.867 & & \\
3 & L1 = 1 & L1 = 1.108 & 0.108 & 89.21 \\  & L2 = 1 & L2 = 0.892 & & \\
4 & L1 = 1 & L1 = 1.221 & 0.221 & 77.92 \\  & L2 = 1 & L2 = 0.779 & & \\
5 & L1 = 1 & L1 = 0.985 & 0.011 & 98.87 \\  & L2 = 2 & L2 = 2.015 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of cross-correlation at 2-bar pressure. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sl No** & **Models** & **Prediction** &
\begin{tabular}{c} **Precision** \\ **Accuracy** \\ \end{tabular} & **Recall** & **F-Score** & **R2** \\ \hline
1 & Modified MFCC-2 DCNN & 85.42 & 83.56 & 83.99 & 83.77 & 85.72 \\
2 & MFCC-proposed 2 DCNN & 92.63 & 93.86 & 92.63 & 93.24 & 90.88 \\
3 & EMD-MFCC-proposed & 98.79 & 98.67 & 98.69 & 98.68 & 98.01 \\  & 2 DCNN & 98.83 & 98.85 & 98.73 & 98.79 & 98.69 \\
4 & EEMD-MFCC-proposed & 98.83 & 98.85 & 98.83 & 98.85 & 98.77 \\  & 2 DCNN & 99.55 & 98.95 & 98.87 & 98.91 & **99.18** \\
6 & **spector**, **MFCC, and** & & & & & \\
**2 DCNN** & **spector** & **spector** & **spector** & **spector** & **spector** & **spector** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results for leak detection and localization at 3-bar pressure. ## 6 Conclusions

In conclusion, this paper significantly contributes to water pipeline leak detection and localization by introducing a novel and practical approach. This paper's proposed independent pipeline leak detection and localization architecture comprises a novel EMD with an optimal mode selector, an MFCC, and a 2 DCNN with a single acousto-optic sensor. This paper also implemented a modified existing MFCC-2 DCNN, variants of EMD-2 DCNN, and cross-correlation to validate the leak localization credibility of the novel EMD with an optimal mode selector, an MFCC, and a 2 DCNN. The findings demonstrate that the novel EMD with an optimal mode selector, an MFCC, and a 2 DCNN gives higher leak detection and localization accuracy than traditional signal processing and state-of-the-art DL techniques. The EMD variants help to overcome the mode mixing problem in EMD. Even though the EMD variants denoise more accurately, the time taken for the EMD variants to denoise is very high. The proposed novel EMD with optimal mode selector helps to denoise more accurately in less time. Since the novel EMD with an optimal mode selector, an MFCC, and a 2 DCNN detects and localizes the leak at different pressures with similar accuracies, the proposed method is reliable. The proposed method localizes the leak accurately at the new location within the specified range. If the range of the unknown location is exceeded, then it will not localize accurately. This issue can be resolved by introducing more datasets with different locations. Conceptualization, U.R. ; methodology, U.R. ; software, U.R. ; validation, U.R. and M.K. ; formal analysis, U.R. ; investigation, M.K. ; resources, M.K. and C.H.P. ; data curation, U.R. and C.H.P. ; writing--original draft preparation, U.R. ; writing--review and editing, [PERSON] and M.K.