Detection of Background Water Leaks Using a High-Resolution Dyadic Transform

This article solves the problem of detecting water leaks with a minimum size of down to 1 mm in diameter. Two new mathematical tools are used to solve this problem: the first one is the T-e cross-spectral density and the second is T-e coherence. These mathematical tools provide the possibility of discriminating spurious frequency components, making use of the property of multi-sensitivity. This advantage makes it possible to maximize the sensitivity of the frequency spectrum. The wavelet function used was Daubechies 45, because it provides an attenuation of 150 dB in the rejection band. The tools were validated with two scenarios. For the first scenario, a synthetic signal was analyzed. In the second scenario, two types of background leakage were analyzed: the first one has a diameter of 1 mm with a signal-to-noise ratio of 2.82 dB and flow rate of 33.7 mL/s, and the second one has a diameter of 4 mm with a signal-to-noise ratio of 9.73 dB with a flow rate of 125.0 mL/s. The results reported in this paper show that both the T-e cross-spectral density and T-e coherence are higher than those reported in scientific literature.