On the relationship between time and frequency domain methods in time delay estimation for leak detection in water distribution pipes

Estimation of time delay in a vibroacoustic system is a problem that occurs in several engineering fields. This can be determined directly in the time domain or in the frequency domain by examining the phase spectrum of two signals. In this paper, the equivalence of these two methods is discussed with particular reference to the problem of determining the position of a leak in water distribution pipes. Popular methods central to this process are based on cross-correlation, and it has been found that pre-whitening the signals prior to determining the cross-correlation function has certain advantages. A new interpretation of the process of cross-correlation for time delay estimation is presented. To support the theoretical findings, analysis is carried out on test data from a specially constructed leak-detection facility located at a National Research Council site in Canada. Test results show that the time delay estimates and their variances calculated using time and frequency domain methods are almost identical.