Assessing the quality of the time delay estimate in acoustic leak localisation

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The problem considered in this paper is assessing the quality of the time delay estimate between leak signals measured on water pipes. This is practically important, as a quantitative assessment of the accuracy of time delay estimation (TDE) results makes it possible to infer the reliability of acoustic leak localisation results in a given situation. Three quality assessment approaches are developed by considering the statistical properties of the cross-correlation function (CCF): information-criterion, processing gain, and statistical approaches. In the information-criterion approach, the Bayes factor (BF) is employed to decide the most likely probability distribution of observed CCF peak values. The processing gain approach determines the quality of the time delay estimate using indices that indicate detectability of the CCF peak, namely, the peak-to-side lobe ratio (PSR) and the peak-to-mean ratio (PMR). In the statistical approach, an index termed inconsistency score (ICS) is used to describe the quality of TDE results based on root-mean square of deviations of time delay estimates from their statistical mode. Experimental results show that the proposed approaches provide effective means of assessing the accuracy of the time delay estimate in acoustic leak detection applications. Also, the proposed indices can be employed as figures of merit for selecting best parameters for TDE, for example, filter cut-off frequencies.