Confidence interval localization of pipeline leakage via the bootstrap method

Abstract

Much of the focus of transient-based pipeline leakage detection research has been on deterministic point estimation of leak location. This paper proposes a framework for extending deterministic leakage localization methods so that they can provide decision-makers with not only a point estimation of leak location, but also a confidence interval for the estimation. To address the complex nature of aleatoric uncertainties, a semi-parametric transient model is introduced and the empirical distribution of measurement is built via a limited number of transient tests. The stochastic characteristics of leakage localization are then explored by the bootstrap method. As a result, confidence intervals are constructed to predict the range of leak location. Experimental results demonstrate that the proposed method can localize the actual leak with an accurate coverage probability and satisfactorily match the ground-truth confidence intervals. In the considered scenario, the error of point localization is tolerable with seven transient tests only; with the same amount of data, the proposed bootstrap method provides additional information about the imprecision and uncertainty to the decision-making of pipeline maintenance.