Parameter Selection of Generalized Morse Wavelets for Water Leakage Classification

Water leakage detection in water distribution networks is crucial to mitigating water scarcity. Machine learning algorithms have been utilized to generate models that detect water leakages by employing vibration, acoustic, flow, and pressure signals. In this sense, time-frequency methods have been widely employed to extract features or represent the signals for water leakage detection. Nevertheless, the challenge of using time-frequency analysis, such as the wavelet transform, is to select an adequate mother wavelet and its parametrization to represent the time-frequency information of the signal correctly. The selection of a mother wavelet is frequently performed arbitrarily or through trial and error, or the parameterization of the wavelet transform is not reported, hindering the studies' reproducibility. Using acceleration data, this paper proposed using the Heisen-berg area and the Average Reconstruction Mean Squared Error (ARMSE) to select the Generalized Morse Wavelets (GMWs) parameters to perform water leakage classification in looped and branched water networks. The generated scalogram was used to fine-tune the GoogLeNet to classify the water leakages in the two water networks. The results of this study showed that the use of the Heisenberg area and the ARMSE to set the parameters of the GMWs led to select a β = 1.6667 and one voice per octave for the looped water network and β =2 and two voices per octave for the branched water network. Furthermore, fine-tuning the GoogLeNet with the generated scalogram shows a testing accuracy of 78.33% for the looped water network and 76.25% for the branched water network.