Real-Time Inversion and Response Planning in Large-Scale Networks

Abstract In this paper we present a mixed-integer linear programming formulation for performing source inversion in drinking water systems using discrete (yes/no) measurements available from manual grab samples. Given the large size of a typical water distribution system, standard water quality models are inappropriate for use in the mixed-integer framework. In this research, we demonstrate the use of an origin-tracking approach to develop the water quality model, and show how this model can be efficiently and exactly reduced prior to the formulation of the MILP, giving rise to a much smaller MILP. Furthermore, we demonstrate that this formulation can be efficiently solved in a real-time setting on large networks with over 10,000 nodes while considering over 100 time discretizations.

[1]  Carl D. Laird,et al.  Nonlinear Programming Strategies for Source Detection of Municipal Water Networks , 2003 .

[2]  Marios M. Polycarpou,et al.  Particle Backtracking Algorithm for Water Distribution System Analysis , 2002 .

[3]  Cynthia A. Phillips,et al.  Sensor Placement in Municipal Water Networks , 2003 .

[4]  Lorenz T. Biegler,et al.  Mixed-Integer Approach for Obtaining Unique Solutions in Source Inversion of Water Networks , 2006 .

[5]  Avi Ostfeld,et al.  Contamination Source Identification in Water Systems: A Hybrid Model Trees–Linear Programming Scheme , 2006 .

[6]  Marios M. Polycarpou,et al.  Development and autocalibration of an input-output model of chlorine transport in drinking water distribution systems , 1998, IEEE Trans. Control. Syst. Technol..

[7]  Avi Ostfeld,et al.  The Battle of the Water Sensor Networks (BWSN): A Design Challenge for Engineers and Algorithms , 2008 .

[8]  Paul F. Boulos,et al.  Numerical Methods for Modeling Water Quality in Distribution Systems: A Comparison , 1996 .

[9]  Mustafa M. Aral,et al.  Identification of Contaminant Sources in Water Distribution Systems Using Simulation-Optimization Method: Case Study , 2006 .

[10]  James G. Uber,et al.  Real-Time Identification of Possible Contamination Sources Using Network Backtracking Methods , 2010 .

[11]  Avi Ostfeld,et al.  Optimal Layout of Early Warning Detection Stations for Water Distribution Systems Security , 2004 .

[12]  Lorenz T. Biegler,et al.  Contamination Source Determination for Water Networks , 2005 .

[13]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[14]  L. Biegler,et al.  Real-time, large scale optimization of water network systems using a subdomain approach. , 2005 .