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Non-uniqueness in Contaminant Source Identification |
The source of contamination in a water distribution system may be
identified through a simulation-optimization approach. The optimization
method searches for the contaminant source characteristics by
iteratively estimating the contaminant plume concentrations until they
match observations at sensors. The amount of information available for
characterizing the source depends on the number and spatial locations of
the sensors, as well as on the temporally varying stream of sensed data.
The accuracy of the source characterization depends on the amount of
observations available. A major factor affecting this accuracy is the
degree of non-uniqueness present in the problem, which may cause
misidentification of the source characteristics. As more sensors are
added to the network, the non-uniqueness may be reduced and a unique
solution may be identified. Thus, a key consideration when solving these
problems is to assess whether the solution identified is unique, and if
not, what other possible solutions are present. A systematic search for
a set of alternatives that are maximally different in solution
characteristics can be used to address and quantify non-uniqueness. For
example, if the most different set of solutions that are identified by a
search procedure are very similar, then that solution will be considered
as the unique solution with a higher degree of certainty.
Alternatively, identification of a set of maximally different solutions
that vary widely in solution characteristics will indicate that
non-uniqueness is present in the problem, and the range of solutions can
be used as a general representation of the amount of non-uniqueness.
This investigation uses an evolutionary algorithm (EA)-based
alternatives generation procedures to quantify and address
non-uniqueness present in a contaminant source identification problem
for a water distribution network. As additional sensors may decrease
the amount of non-uniqueness, different sensor configurations are being
tested to investigate and quantify the improvement in uniqueness as more
information is used in the source characterization.
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