Technology
Networks
Scientific Communities
 Site Literature
News

# Math Detects Contamination in Water Distribution Networks

Published: Friday, November 30, 2012
Last Updated: Friday, November 30, 2012
The identification of contaminants in a water distribution network in considered as an optimal control problem within a networked system.

None of us want to experience events like the Camelford water pollution incident in Cornwall, England, in the late eighties, or more recently, the Crestwood, Illinois, water contamination episode in 2009 where accidental pollution of drinking water led to heart-wrenching consequences to consumers, including brain damage, high cancer risk, and even death. In the case of such catastrophes, it is important to have a method to identify and curtail contaminations immediately to minimize impact on the public.

A paper published earlier this month in the SIAM Journal on Applied Mathematics considers the identification of contaminants in a water distribution network as an optimal control problem within a networked system.

“Water supply networks are an essential part of our infrastructure. Sometimes the water in such a network can be contaminated, often by human error, causing the use of polluted water for drinking water production. In the case of such a situation, it is important to have a method to identify the location of the pollution source,” says the paper’s author, Martin Gugat, explaining the significance of his work.
The paper considers a water distribution network with a finite number of nodes where contamination can occur in the pipes.

“The contamination spreads dynamically through the network with time. So, in order to model the system, a model of the evolution in time is necessary,” explains Gugat. “In our approach, we use a partial differential equation (PDE) to model how pollution spreads in the network.”

By using a PDE model for transport of contaminants, the problem of identifying the source becomes an optimal control problem. The solution is calculated using equidistant time grids, which allows one to determine the values of contamination at all potential sources on the time grid. Available data on pollution and network flow is incorporated into the model.

Employing certain assumptions for travel times through the pipes, the author uses a least-squares method to solve the problem. The least squares method provides approximate solutions to optimization problems that are relatively eﬃcient to compute using the tools of numerical linear algebra.

This provides a fast method to identify possible contamination sources, explains Gugat. “For a really accurate model, however, a full system of three-dimensional PDEs is necessary. But with three-dimensional PDEs, simulation is only possible for small networks,” he says. “This illustrates that to solve real life problems on real networks, there is a trade-off between the accuracy of the model and its utility.”

While the method is tested numerically in the paper, additional work would involve testing the system with an existing water network to demonstrate its workability in practice.

Another future direction is toward elimination of the contaminant. “The second step after the identification of the contamination source is a strategy to flush the polluted water out of the network as fast as possible with acceptable operational cost. The development of an optimal strategy for such a rehabilitation of the water supply is an interesting question for future research,” says Gugat.

“For a more detailed model of the process, more complex nonlinear PDEs could be used,” he continues. “The cost of the numerical treatment of complex PDEs for large networks is prohibitive. Applied mathematics has to offer models that can be used according to the problem requirements to solve problems with network graphs of a realistic size.”

Big Genetics in BC: The American Society for Human Genetics 2016 Meeting
Themes at this year's meeting ranged from the verification, validation, and sharing of data, to the translation of laboratory findings into actionable clinical results.
Stem Cells in Drug Discovery
Potential Source of Unlimited Human Test Cells, but Roadblocks Remain.
Cancer Genetics: Key to Diagnosis, Therapy
When applied judiciously, cancer genetics directs caregivers to the right drug at the right time, while sparing patients of unnecessary or harmful treatments.
BGI Sequences Gingko Tree, Revealing Large, Highly Repetitive Genome
Researchers at BGI have sequenced the more than 10-gigabase ginkgo genome to find a high number of repetitive sequences as well as a number of gene clusters that appear to be involved in defense mechanisms.
Survey of New York City Soil Uncovers Medicine-Making Microbes
Microbes have long been an invaluable source of new drugs. And to find more, we may have to look no further than the ground beneath our feet.
Accelerating the Detection of Foodborne Bacterial Outbreaks
The speed of diagnosis of foodborne bacterial outbreaks could be improved by a new technique developed by researchers at the Georgia Institute of Technology.
Making Personalized Medicine a Reality
Groundbreaking technique developed at McMaster University is helping to pave the way for advances in personalized medicine.
Scientists Identify Unique Genomic Features in Testicular Cancer
The findings may shed light on factors in other cancers that influence their sensitivity to chemotherapy.
Top 10 Life Science Innovations of 2016
2016 has seen the release of some truly innovative products. To help you digest these developments, The Scientist have listed their top picks for the year.
BioCision Forms MedCision
The new company will focus on technologies for the management and automation of vital clinical processes.

Exclusive articles
Latest presentations and webinars
3,900+ scientific and medical posters
5,300+ scientific videos