Inverse transient analysis in pipe networks for leakage detection, quantification and roughness calibration (1999-2002)

Funding body: Engineering and Physical Sciences Research Council (EPSRC)

The joint project between the Exeter University's Centre for Water Systems and Imperial College is aimed at developing an integrated, inverse-transient approach to leakage detection and model calibration.

Collaborators: Imperial College (Academic), Yorkshire Water, Bristol Water, Thames Water, Anglian Water, Ewan Optimal Solutions and UKWIR (Industrial)

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In more detail, the initial objectives were as follows:

  1. Development of a new numerical modelling approach by combining the inverse transient analysis (IC), steady-state and transient network analyses and genetic algorithms optimisation (EU) to enable optimal selection of pressure measurement sites for leakage detection and pipe roughness calibration
  2. An experimental programme under strictly controlled laboratory conditions and simulated leaks in pipelines (IC and Thames Water) aimed at acquiring reliable sets of both steady state and transient flow data for testing of the methodology, calibration and verification of the programs
  3. Development of a data mining or some other procedure for establishing rules on how to select pressure measurement sites in new networks (EU)
  4. Field tests (full scale water supply system of Anglian Water) for obtaining reliable sets of transient flow data and their application in the inverse transient method for leak detection and calibration (IC&EU)
  5. Analysis of the methodology on the basis of uncertainty reduction and data reliability improvement (IC&EU), for possible application in the UK Water Industry
  6. Analysis of trends and future research needs.

The research work carried out 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 here below.

Initially, a transient simulation model (i.e. software) for any pipe network configuration was developed. Software for the calculation of the Jacobian matrix (i.e. partial derivatives of model predictions with respect to analysed calibration parameters) was developed for transient, steady-state and extended-period simulation 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. An improved approach for the calibration of WDS hydraulic models was developed. 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 (Kapelan et al., 2001c; Kapelan et al., 2001e).
  • 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 (Kapelan et al., 2000) and HGA (Kapelan et al., 2001a; Kapelan et al., 2001b; Kapelan et al., 2002b; Kapelan et al., 2002a).
  • 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.

A 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 (Kapelan et al., 2001d), (2) A-optimality (Kapelan, 2002) and (3) V-optimality (Kapelan et al., 2002e; Kapelan et al., 2002c). Therefore, both model parameter and prediction uncertainties were analysed.
  • A new single-objective GA (SOGA) optimal sampling design model (Kapelan et al., 2002f; Kapelan et al., 2002g) 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 (Kapelan et al., 2002d) 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 (Ferreri et al., 1994; Bush et al., 1998; De Schaetzen et al., 2000).

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 (Kapelan, 2002).

Since the first results of the research work were published, UK water companies have shown substantial interest in the developed technology. As a result, the EPSRC has recently approved for the research assistant (Dr Kapelan) to be seconded to Ewan Optimal Solutions Ltd, a company collaborating on the original project, on a Research Assistant Industrial Secondment (RAIS) scheme.

References

  • Kapelan, Z.S. (2002), "Calibration of WDS Hydraulic Models", PhD Thesis, Department of Engineering, University of Exeter, 334pp.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2000), "Inverse Transient Analysis in Pipe Networks for Leakage Detection and Roughness Calibration", Proc. Water Network Modelling for Optimal Design and Management, Exeter, UK, D. A. Savic and G. A. Walters, eds., vol. 1, 143-159.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2001a), ?A Hybrid Inverse Transient Model for Leakage Detection and Roughness Calibration in Pipe Networks (1): Theoretical Development?, Journal of Hydraulic Research (IAHR), (accepted for publication).
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2001b), ?A Hybrid Inverse Transient Model for Leakage Detection and Roughness Calibration in Pipe Networks (2): Applications?, Journal of Hydraulic Research (IAHR), (accepted for publication).
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2001c), ?Incorporation of Prior Information on Parameters in Inverse Transient Analysis for Leak Detection and Roughness Calibration?, Urban Water, (accepted for publication).
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2001d), "Optimal Sampling Design Methods for Calibration of Water Supply Network Models", Proc. International Conference on Computing and Control for the Water Industry CCWI 2001, De Montfort University, Leicester, UK, D. Ulanicki, B. Coulbeck and J. P. Rance, eds., vol. 1, 99-109.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2001e), "Use of Prior Information on Parameters in Inverse Transient Analysis for Leak Detection and Roughness Calibration", Proc. World Water & Environmental Resources Congress, Orlando, USA, CD-ROM edition.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002a), "Hybrid GA for Calibration of Water Distribution System Hydraulic Models", Proc. 1st Annual Environmental & Water Resources Systems Analysis (EWRSA) Symposium, Roanoke, Virginia, USA, CD-ROM edition.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002b), "A Hybrid Search Technique for Inverse Transient Analysis in Water Distribution Systems", Proc. 5th International Conference on Adaptive Computing in Design and Manufacture, Exeter, UK, I. C. Parmee, ed., vol. 1, 75-86.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002c), "Multi-objective GA Solution to Problem of Optimal Sampling Design for WDS Hydraulic Model Calibration", Proc. 5th International Conference on Hydroinformatics, Cardiff, UK, vol. 2, 1435-1440.
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002e), "Multi-objective Sampling Design for Water Distribution Model Calibration", Proc. 3rd International Conference on Environmental Management, Johannesburg (RSA).
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002d), ?Multi-objective Sampling Design for Water Distribution Model Calibration?, Journal of Water Resources Planning and Management, ASCE, (submitted for publication).
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002f), ?Optimal Sampling Design Methodologies for Water Distribution Model Calibration: 1. Theory?, Water Resources Research, (submitted for publication).
  • Kapelan, Z.S., Savic, D.A., and Walters, G.A. (2002g), ?Optimal Sampling Design Methodologies for Water Distribution Model Calibration: 2. Applications?, Water Resources Research, (submitted for publication).

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