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

Abstract

This article solves the problem of detecting water leaks with a minimum size of down to (Formula presented.) in diameter. Two new mathematical tools are used to solve this problem: the first one is the (Formula presented.) cross-spectral density and the second is (Formula presented.) 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 (Formula presented.), because it provides an attenuation of (Formula presented.) 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 (Formula presented.) with a signal-to-noise ratio of (Formula presented.) and flow rate of (Formula presented.), and the second one has a diameter of (Formula presented.) with a signal-to-noise ratio of (Formula presented.) with a flow rate of (Formula presented.). The results reported in this paper show that both the (Formula presented.) cross-spectral density and (Formula presented.) coherence are higher than those reported in scientific literature.