Compressive Sensing-Based Multiple-Leak Identification for Smart Water Supply Systems

In this paper, the identification of multiple leaks in pipes based on transient waves is studied, which is, however, quite challenging due to its nonconvex nature with lots of local optima. Existing approaches need the number of leaks and suffer from a huge computational complexity that is increased exponentially with the number of leaks. To provide a scalable solution, we propose a compressive sensing (CS) framework to solve the multileaks identification. We first exploit the sparseness nature of leak locations through spatial sampling. Then, we formulate the multileak identification as a CS problem, where the spatial sample-dependent components form a basis matrix and the leak sizes are viewed as a sparse signal. We establish the convergence of spatial sampling mismatch and the two-restricted isometry property of basis matrix to justify the proposed CS framework. The proposed CS framework renders a superior-performance solution to multileak identification and its computational complexity is linear with the number of leaks, which is a significant technical improvement over existing approaches. In addition, a closed-form Cramer-Rao lower bound (CRLB) on the leak localization errors is derived. A geometric insight of CRLB evolution is presented to give us an intuitive understanding of the contribution of new measurements to leak localization performance.