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Non-uniqueness in Source Characterization for Multiple Contaminant Source Scenarios in Water Distribution Systems

This study addresses the problem of non-uniqueness in source characterization for multiple contaminant source scenarios in water distribution systems. The objective is to identify and quantify the non-uniqueness under different scenarios using a simulation-optimization approach. The results show that the number of possible non-unique solutions increases with the availability of sensors in the network. This research provides valuable insights for decision makers in managing contamination events in water distribution systems.

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Non-uniqueness in Source Characterization for Multiple Contaminant Source Scenarios in Water Distribution Systems

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  1. Addressing Non-uniqueness in Source Characterization for Multiple Contaminant Source Scenarios in Water Distribution Systems Jitendra Kumar1, Emily M. Zechman1, E. Downey Brill1, Jr., G. Mahinthakumar1, S. Ranjithan1, James Uber2 1North Carolina State University, Raleigh, NC2University of Cincinnati , Cincinnati, OH

  2. Outline • Introduction • Objectives • Methodology • Results • Observations • Ongoing/future work

  3. Introduction • Contamination threat problem in a water distribution system • Cause short term chaos and long term issues • Diversionary action to cause service outage • Reduction in fire fighting capacity • Distract public & system managers • Non-uniqueness in source characterization problem

  4. contd… • Under a contamination event, multiple contaminant sources may be placed in the network • The number of sources will remain unknown to a decision maker • Non-uniqueness present in a multiple-source identification scenario is expected to increase due to an increased number of possible solutions

  5. Resolving non-uniqueness • Underlying premise • In addition to the “optimal” solution, identify other “good” solutions that fit the observations • Are there different solutions with similar performance in objective space? • Search for alternative solutions

  6. Objectives • Identify possible multiple sources in during a contamination event • Investigate and quantify non-uniqueness under different scenarios

  7. Simulation-optimization approach Mathematical formulation • Find • Source location [L(x,y)] • Contaminant loading profile [Mt, Ts]

  8. Optimization Model • Population based evolutionary algorithm • Niched co-evolution strategy • Alternative solutions • maximally different set of possible sources • maximally distant sources in a solution set Zechman, E.M., Brill, E.D., Mahinthakumar, G., Ranjithan, S., Uber, J., (2006), “Addressing non-uniqueness in a water distribution contamination source identification problem”, Proceedings of 8th Water Dist. Sys. Ana. Symposium, Cincinnati, OH, Aug. 2006

  9. Case Study • 97 nodes • 117 pipes • Hydraulic simulations at 1 hour • Quality simulations at 5 minutes • Network simulated for 24 hours Example network included in EPANET distribution

  10. Scenarios studied • Single source location in true source • Multiple source locations in true source • Under different scenarios of available sensors

  11. Scenario 1: single true source, using 3 sensors • Identified correct source

  12. Observed/Predicted concentrations at Sensor 2 Observed/Predicted concentrations at Sensor 3

  13. Scenario 1: single true source, using 3 sensors …. • Non-unique solution

  14. Observed/Predicted concentrations at Sensor 2 Observed/Predicted concentrations at Sensor 3

  15. Scenario 1: single true source, using 3 sensors …. • Another non-unique solution

  16. Fit obtained at Sensor 2 Fit obtained at Sensor 3

  17. Scenario 2: single true source, using 6 sensors • Identified true source • 1 non-unique solution identified at location close to true location

  18. Observed/Predicted concentrations at Sensor 3 Observed/Predicted concentrations at Sensor 4 Observed/Predicted concentrations at Sensor 6

  19. Scenario 2: single true source, using 6 sensors ……

  20. Observed/Predicted concentrations at Sensor 3 Observed/Predicted concentrations at Sensor 4 Observed/Predicted concentrations at Sensor 6

  21. Observations • Higher non-uniqueness in source characterization when the number of sources are not known • Different sets of sources can match the sensor observations • More number of sensors helps reduce the non-uniqueness

  22. Scenario 3 :2 true source, using 6 sensors

  23. Observed/Predicted concentrations at Sensor 3 Observed/Predicted concentrations at Sensor 4 Observed/Predicted concentrations at Sensor 6

  24. Scenario 4 : 2 true sources, using 3 sensors

  25. Identified source at single location

  26. Observed/Predicted concentrations at Sensor 2 Observed/Predicted concentrations at Sensor 3

  27. Another solution at same location .. Observed/Predicted concentrations at Sensor 2 Observed/Predicted concentrations at Sensor 3

  28. Scenario 4 : 2 true sources, using 3 sensors …..

  29. Observed/Predicted concentrations at Sensor 2 Observed/Predicted concentrations at Sensor 3

  30. Scenario 4 : 2 true sources, using 3 sensors …..

  31. Observed/Predicted concentrations at Sensor 2 Observed/Predicted concentrations at Sensor 3

  32. Observations • Identified sets of multiple sources to explain the observation data • Source acting at a single location might match the sensor observations • Number of possible non-unique solutions increases if less sensors are available

  33. Final Remarks • When the number of source locations are unknown, the uncertainty in the source predictions increases • Different sets of contaminant sources can match the observation data • Available number of sensors in the network has effect on the uniqueness in source identification problem • The method was able to handle the multiple source identification problem

  34. Ongoing/future work • Achieve better convergence in source identification problem • Test the method for searching “n” number of sources in the problem and evaluate the non-uniqueness

  35. Acknowledgement • This work is supported by National Science Foundation (NSF) under Grant No. CMS-0540316 under the DDDAS program.

  36. Thanks & Questions ??

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