Time-Domain Factorized Wave Model and Iterative Beamforming for Localizing Multiple Leaks in Water Pipes

Time-domain full-waveform inversion is a robust method for localizing leaks in urban water distribution pipes. However, its built-in classical wave model suffers from coupled and interdependent leak parameters; thus, the localization of multiple leaks becomes a (Formula presented.) -parameter optimization problem ((Formula presented.) is the number of leaks), which is high-dimensional, non-convex, and riddled with local optima. To address this problem, we analytically derive a time-domain factorized wave model with decoupled leak parameters via the Born approximation. Based on this model, we propose an iterative beamforming algorithm that decomposes the complex (Formula presented.) -dimensional optimization problem into (Formula presented.) sequential one-dimensional sub-problems. This approach largely reduces complexity of both forward modeling and inverse estimation, enabling real-time leak localization. Numerical experiments show that the proposed approach is accurate, efficient, super-resolved, and robust in localizing multiple leaks. Moreover, it can estimate the unknown number of leaks without any prior information. Finally, the proposed approach is verified by recent laboratory experiments conducted in a viscoelastic pipe system, where unknown leaks are successfully localized.