A model of the correlation function of leak noise in buried plastic pipes

A common technique for locating leaks in buried water distribution pipes is the use of the cross-correlation on two measured acoustic signals, on either side of a leak. This technique can be problematic for locating leaks in plastic pipes as the acoustic signals in these pipes are generally narrow-band and low frequency. The effectiveness of the cross-correlation technique for detecting leaks in plastic pipes has been investigated experimentally in an earlier study. This paper develops an analytical model to predict the cross-correlation function of leak signals in plastic pipes. The model is based on a theoretical formulation of wave propagation in a fluid-filled pipe in vacuo and the assumption that the leak sound, at source, has a flat spectrum over the bandwidth of interest. The analytical model is used to explain some of the features of correlation measurements made in actual water pipes. Leak noise signals are generally passed through a band-pass filter before calculating the cross-correlation function. The model is used to demonstrate the importance of the cut-off frequency of the high-pass filter and the insensitivity of the correlation to the cut-off frequency of the low-pass filter.