Joint Leak Estimation and Predictive Pressure Control in Nonlinear Pipeline Networks

This paper presents a joint leak estimation and control framework for a foundational three-node pipeline network. The leak coefficient kℓ is augmented as an unknown state, so an Extended Kalman Filter (EKF) jointly identifies pressures and leak severity rather than assuming kℓ as known. A local observability analysis (rank and condition number of the linearized observability matrix) supports a sensor-placement recommendation and dual pressure sensing where κ≈3.6, chosen via an explicit cost-constrained optimization over eight configurations. The EKF is benchmarked against a UKF, an Ensemble Kalman Filter (EnKF), and an Adaptive Kernel Kalman Filters (AKKF, three variants) under one consistent state model and Monte Carlo protocol. The EKF and UKF are statistically indistinguishable; the EnKF and pure-kernel AKKF are consistently worse, with the AKKF additionally shown to be sensitive to regularization choices left unspecified in prior comparisons. The same estimator, unmodified, tracks a linearly growing leak, a multi-step severity change, and simultaneous leaks at two independent locations via a four-state model extension. A fully specified receding-horizon model predictive control (MPC) scheme regulates upstream pressure using the EKF’s live estimate. We show analytically that an unconstrained objective degenerates to constraint saturation, and resolve this with a service-pressure constraint, reporting both the resulting (7%) and unconstrained (35%) objective reduction with a precise, reproducible definition of each. Finally, we validate the approach on a public experimental testbed and identify and correct a demand-vs-leak-severity labeling error in its prior use: the corrected EKF-based indicator reliably discriminates leak from no-leak conditions, while severity discrimination specifically is topology-dependent, a genuine and reported limitation of indicator-based, rather than physical-flow, leak-severity estimation.