Distributed observer-based leak detection in pipe flow with nonlinear friction

TL;DR

This work addresses leak detection in pipelines with nonlinear friction by adapting a distributed adaptive observer, originally developed for linear pipe-flow models, to a semilinear, one-dimensional flow description. By transforming the system to Riemann coordinates and linearising about operating points, the authors design an adaptive observer that estimates pressure, flow, leak size $\chi$, and leak location $\delta$, with convergence guarantees in the linear regime. Simulation results at two mean inlet flows demonstrate accurate leak sizing and localization, with faster localization as mean flow increases, indicating applicability to turbulent regimes in water distribution. The approach broadens the practical scope of observer-based leak detection beyond laminar conditions and suggests directions for time-varying gains and rigorous stability analysis.

Abstract

The problem of leak detection in a pipeline with nonlinear friction is considered. A distributed observer-based method is proposed which applies a linearised, distributed adaptive observer design to the nonlinear model. The methodology is tested in simulations for two different operating points.

Figures (2)

• Figure 1: Inlet signal $q_0$ for two cases considered.
• Figure 2: Leak detection results.

Theorems & Definitions (1)

• Lemma 2.1