Locating leaks in underground water pipes using the complex cepstrum

Abstract

It is possible to detect the presence of leaks in underground water pipes by measuring, at remote locations such as hydrants, the noise or vibration caused by the leak. The time delay of the leak noise reaching the different sensors can be computed using the cross correlation, and with knowledge of the wave-speed in the pipe, the location of the leak may be pinpointed. This paper presents a new technique for leak detection that employs the cepstrum, rather than the cross correlation, for estimation of the delay time. The delay time manifests as a series of peaks in the cepstrum, rather than a single peak in the correlation, allowing a more robust estimate. A number of cepstrum formulations are presented that are derived from correlation estimators, and it is found that the time delay information is actually contained in the phase component of the cross spectrum. Based on this, a phase cepstrum estimator is developed.