Addressing Non-uniqueness in Source Characterization for Multiple Contaminant Source Scenarios in Water Distribution Systems Jitendra Kumar 1, Emily M. Zechman 1, E. Downey Brill 1, Jr., G. Mahinthakumar 1, S. Ranjithan 1, James Uber 2 1 North Carolina State University, Raleigh, NC 2 University of Cincinnati, Cincinnati, OH

Outline Introduction Objectives Methodology Results Observations Ongoing/future work

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

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

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

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

Simulation-optimization approach Mathematical formulation Find –Source location [L(x,y)] –Contaminant loading profile [M t, T s ]

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 8 th Water Dist. Sys. Ana. Symposium, Cincinnati, OH, Aug. 2006

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

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

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

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

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

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

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

Fit obtained at Sensor 2 Fit obtained at Sensor 3

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

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

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

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

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

Scenario 3 : 2 true source, using 6 sensors

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

Scenario 4 : 2 true sources, using 3 sensors

Identified source at single location

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

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

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

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

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

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

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

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

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

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

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