Leak localisation in water distribution networks: Regularisation of an ill-posed inverse problem
File(s)
Author(s)
Blocher, Caroline
Type
Thesis
Abstract
A critical task for water companies is the reduction of water losses to meet regulatory requirements and to reduce costs. Fast and reliable leak localisation techniques are required to identify leakage hotspots in a cost-effective manner. This thesis considers the problem of leak localisation in water distribution networks as an inverse problem, where the unknown leak parameters are estimated from flow and pressure measurements using a hydraulic model of the network. The problem is ill-posed due to a small number of measurement locations in comparison to the number of possible leak locations, as well as due to uncertainty in the hydraulic model. Therefore, it may not have a unique solution that fits the measured data exactly.
The research studies the formulation of the inverse problem as an optimisation problem. As in previous work, the objective is to estimate the leak parameters by minimising the difference between measurements and simulated hydraulic states. The thesis proposes to mitigate the effects of ill-posedness by adding a regularisation term to the objective function. The resulting optimisation problem is non-convex, and non-smooth due to the modelling of the frictional head losses in the constraints. The application of a quadratic approximation to the head loss model enables solving the optimisation problem using smooth optimisation methods.
To investigate the performance of the different leak localisation methods, a metric is proposed to quantify the success of the leak localisation. The metric enables a comparison of different regularisation terms, as well as a comparison of the proposed method with the sensitivity matrix method.
The performance of the leak localisation method is investigated using two numerical case studies considering no uncertainty. A strategy is proposed to select the weight for the regularisation term when large-scale operational networks are considered and the localisation performance in scenarios with multiple leaks is investigated. The performance of the method under uncertainty is investigated using a leak detection and localisation benchmarking data set.
The research studies the formulation of the inverse problem as an optimisation problem. As in previous work, the objective is to estimate the leak parameters by minimising the difference between measurements and simulated hydraulic states. The thesis proposes to mitigate the effects of ill-posedness by adding a regularisation term to the objective function. The resulting optimisation problem is non-convex, and non-smooth due to the modelling of the frictional head losses in the constraints. The application of a quadratic approximation to the head loss model enables solving the optimisation problem using smooth optimisation methods.
To investigate the performance of the different leak localisation methods, a metric is proposed to quantify the success of the leak localisation. The metric enables a comparison of different regularisation terms, as well as a comparison of the proposed method with the sensitivity matrix method.
The performance of the leak localisation method is investigated using two numerical case studies considering no uncertainty. A strategy is proposed to select the weight for the regularisation term when large-scale operational networks are considered and the localisation performance in scenarios with multiple leaks is investigated. The performance of the method under uncertainty is investigated using a leak detection and localisation benchmarking data set.
Version
Open Access
Date Issued
2021-03
Date Awarded
2021-08
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Stoianov, Ivan
Sponsor
Cla-Val UK Ltd
Engineering and Physical Sciences Research Council- Centre for Doctoral Training in Sustainable Civil Engineering
Grant Number
EP/L016826/1
Publisher Department
Civil and Environmental Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)