Adaptive Residual-Based Modulating Function Regressor for Decoupled Estimation of Leak Size and Localization in Uncertain Water Network Systems

Most solutions for detecting, estimating, and localizing leaks in water networks rely on complex banks of Kalman filters (BKFs) or advanced stand-alone Kalman filter (KF) algorithms to account for the network's model uncertainty, requiring extra hardware, extensive calibration, and maintenance. This study proposes a modulating function (MF) regressor based on a lumped model with pressure-flow boundary conditions to detect and localize a single leak in a water network. The uncertainty of the lumped model is reduced by adapting the MF regressor via a Lyapunov-based adaptive law. A real water network system (WNS) test bench was employed to validate the effectiveness of the proposed regressor. Initially, an experimental phase was conducted to identify and analyze the primary sources of uncertainty of the plant models concerning the test setup. Subsequently, the proposed leak detection, estimation, and localization algorithm was tested and compared with the robust adaptive unscented Kalman Filter (RAUKF), showing promising results.