Inverse transient analysis in pipe networks for leakage detection, quantification and roughness calibration


Project Outcomes
EPSRC Report
Water Systems

Project Outcomes

The research work carried out at Exeter University has resulted in the development of new or improved calibration and sampling design methodologies. All methodologies presented here were coded for testing purposes. Coding was done in the C++ programming language. A brief summary of the new or improved methodologies is given below;


Transient simulation model

Initially a transient simulation model for any pipe network configuration was developed. Its main characteristics are as follows:

Based on the method of characteristics numerical scheme.

Support for two unsteady friction models (Trikha, 1975; Vitkovsky et al., 1999)

Use of the time marching technique to determine steady-state heads/flows, where head/flow oscillations are damped using either: (a) unsteady friction coefficients (not been done before) or (b) inertial multipliers (Wylie, 2000).

Object-oriented approach, which has several advantages over the traditional procedural approach, including easier code maintenance.


Software for the calculation of the Jacobian matrix (i.e. partial derivatives of model predictions with respect to analysed calibration parameters)

This was developed for transient, steady-state and EPS model cases. It was necessary to develop such software for:

(a) application of gradient type optimisation methods, e.g. the Levenberg-Marquardt method;

(b) use of post-calibration statistical analysis and

(c) solving the optimal sampling design problem.

For steady-state and extended period simulation (EPS) hydraulic models two methods were developed and coded: the sensitivity equation method and the adjoint method. For the transient WDS model, a novel method based on a variation of the existing sensitivity equation method (Nash et al., 1999) was developed to support any pipe network configuration.


Improved approach for the calibration of WDS hydraulic models

Its main characteristics are as follows:

Approach can be applied for the calibration of all major WDS hydraulic models:
(a) steady-state flow model,
(b) EPS model and
(c) transient model.

The calibration problem is formulated as a constrained optimisation problem with prior information on parameters incorporated in the objective of weighted least square type.

Two existing (genetic algorithm (GA) and Levenberg-Marquardt (LM)) and two novel, hybrid optimisation methods were developed to solve the analysed calibration problem. The hybrid methods were named GALM and HGA.

The use of diagnostic statistics and analysis to identify ill-posed calibration problems and to provide partial insight into the calibration process.

Use of various statistics to thoroughly evaluate calibration process results in terms of:
(a) model fit,
(b) uncertainties (i.e. errors) associated with estimated calibration parameters,
(c) uncertainties (i.e. errors) associated with calibrated model predictions.


Novel sampling design approach for calibration of WDS hydraulic models was developed.

Its main characteristics are as follows:

The sampling design problem is formulated as a multi-objective optimisation problem. The two main objectives are:
(a) maximise calibration accuracy by minimising calibrated model uncertainty and (b) minimise total sampling design costs.

Three calibration accuracy objectives were analysed:

(1) D-optimality,
(2) A-optimality and
(3) V-optimality. Therefore, both model parameter and prediction uncertainties were analysed.

A new single-objective GA (SOGA) optimal sampling design model was developed. The sampling design problem was formulated as a single-objective problem and solved using a standard GA optimisation method. Two objectives are recombined into a weighted single one after normalisation.

A new multi-objective GA (MOGA) optimal sampling design model was developed based on Pareto domination,. The aim was to treat and solve the sampling design problem as a true multi-objective optimisation problem. The MOGA methodology is based on Pareto domination rules, restricted mating and niching. The new MOGA approach was compared to several well-known SD methods from the literature.

All developed calibration and sampling design approaches were tested and verified on multiple case studies involving both relatively simple, small artificial WDS networks and relatively large, complex real-life WDS networks.

Back Next

Copyright 2003.
or problems or questions regarding this web contact [].
Last updated: February 24, 2003.