The effects of resonances on time delay estimation for water leak detection in plastic pipes
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In the use of acoustic correlation methods for water leak detection, sensors are placed at pipe access points either side of a suspected leak, and the peak in the cross-correlation function of the measured signals gives the time difference (delay) between the arrival times of the leak noise at the sensors. Combining this information with the speed at which the leak noise propagates along the pipe, gives an estimate for the location of the leak with respect to one of the measurement positions. It is possible for the structural dynamics of the pipe system to corrupt the time delay estimate, which results in the leak being incorrectly located. In this paper, data from test-rigs in the United Kingdom and Canada are used to demonstrate this phenomenon, and analytical models of resonators are coupled with a pipe model to replicate the experimental results. The model is then used to investigate which of the two commonly used correlation algorithms, the Basic Cross-Correlation (BCC) function or the Phase Transform (PHAT), is more robust to the undesirable structural dynamics of the pipe system. It is found that time delay estimation is highly sensitive to the frequency bandwidth over which the analysis is conducted. Moreover, it is found that the PHAT is particularly sensitive to the presence of resonances and can give an incorrect time delay estimate, whereas the BCC function is found to be much more robust, giving a consistently accurate time delay estimate for a range of dynamic conditions.