Transient Wave-Based Data Assimilation for Localizing Multiple Leaks in Water Pipe Networks

Abstract

Due to aging without timely renewal, hidden leaks continually occur in urban water distribution systems. Time-domain full-waveform inversion is a robust and flexible method for localizing multiple leaks in water pipe networks. However, as a deterministic estimator, this method assumes precise knowledge of model parameters and only gives a single-point estimate of unknown leak parameters, which is insufficient for decision-making as it fails to quantify the localization confidence and uncertainty. Moreover, the equifinality of underlying physics violates the uniqueness of inverse problem and makes this method a high-dimensional non-convex optimization. To address these problems, this paper proposes a stochastic Bayesian estimator, namely iterative local updating ensemble smoother (ILUES), for localizing multiple leaks in water pipe networks. ILUES explores the possible multi-modal posterior distributions of leak parameters, which not only localize leaks but also quantify localization confidence. Numerical experiments indicate that ILUES maintains robust localization accuracy in environments with significant model parameter uncertainties and strong ambient noise, even at signal-to-noise ratio as low as $-10$ dB. It also gives good estimation of unknown number of leaks. For the challenging equifinality problem, ILUES successfully identifies all potential leak locations in a symmetric pipe network and super-resolves two close leaks separated below half the minimum probing wavelength. Finally, the proposed approach is validated by recent laboratory experiments conducted in a viscoelastic pipe system, where unknown leaks are successfully localized.