Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Math detects contamination in water distribution networks

29.11.2012
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.”

Source Article:
Contamination Source Determination in Water Distribution Networks
Martin Gugat, SIAM Journal on Applied Mathematics, 72(6), 1772–1791 (Online publish date: 5 November 2012)
The source article is available for free access at the link above until February 28, 2013.

About the Author:
Martin Gugat is a researcher at the University of Erlangen-Nuremberg, Lehrstuhl f¨ur angewandte Mathematik 2, in Erlangen, Germany. This work was supported by DFG research cluster 1253: Optimization with Partial Differential Equations, grant GU 376/7-1.

About SIAM
The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of over 14,000 individual members, including applied and computational mathematicians and computer scientists, as well as other scientists and engineers. Members from 85 countries are researchers, educators, students, and practitioners in industry, government, laboratories, and academia. The Society, which also includes nearly 500 academic and corporate institutional members, serves and advances the disciplines of applied mathematics and computational science by publishing a variety of books and prestigious peer-reviewed research journals, by conducting conferences, and by hosting activity groups in various areas of mathematics. SIAM provides many opportunities for students including regional sections and student chapters. Further information is available at www.siam.org.

Karthika Muthukumaraswamy | EurekAlert!
Further information:
http://www.siam.org

More articles from Ecology, The Environment and Conservation:

nachricht Coorong Fish Hedge Their Bets for Survival
27.03.2015 | University of Adelaide

nachricht Greener Industry If Environmental Authorities Change Strategy
27.03.2015 | University of Gothenburg

All articles from Ecology, The Environment and Conservation >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Experiment Provides the Best Look Yet at 'Warm Dense Matter' at Cores of Giant Planets

In an experiment at the Department of Energy's SLAC National Accelerator Laboratory, scientists precisely measured the temperature and structure of aluminum as...

Im Focus: Energy-autonomous and wireless monitoring protects marine gearboxes

The IPH presents a solution at HANNOVER MESSE 2015 to make ship traffic more reliable while decreasing the maintenance costs at the same time. In cooperation with project partners, the research institute from Hannover, Germany, has developed a sensor system which continuously monitors the condition of the marine gearbox, thus preventing breakdowns. Special feature: the monitoring system works wirelessly and energy-autonomously. The required electrical power is generated where it is needed – directly at the sensor.

As well as cars need to be certified regularly (in Germany by the TÜV – Technical Inspection Association), ships need to be inspected – if the powertrain stops...

Im Focus: 3-D satellite, GPS earthquake maps isolate impacts in real time

Method produced by UI researcher could improve reaction time to deadly, expensive quakes

When an earthquake hits, the faster first responders can get to an impacted area, the more likely infrastructure--and lives--can be saved.

Im Focus: Atlantic Ocean overturning found to slow down already today

The Atlantic overturning is one of Earth’s most important heat transport systems, pumping warm water northwards and cold water southwards. Also known as the Gulf Stream system, it is responsible for the mild climate in northwestern Europe. 

Scientists now found evidence for a slowdown of the overturning – multiple lines of observation suggest that in recent decades, the current system has been...

Im Focus: Robot inspects concrete garage floors and bridge roadways for damage

Because they are regularly subjected to heavy vehicle traffic, emissions, moisture and salt, above- and underground parking garages, as well as bridges, frequently experience large areas of corrosion. Most inspection systems to date have only been capable of inspecting smaller surface areas.

From April 13 to April 17 at the Hannover Messe (hall 2, exhibit booth C16), engineers from the Fraunhofer Institute for Nondestructive Testing IZFP will be...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

World Conference On Regenerative Medicine 2015: Registration And Abstract Submission Now Open

25.03.2015 | Event News

University presidents from all over the world meet in Hamburg

19.03.2015 | Event News

10. CeBiTec Symposium zum Big Data-Problem

17.03.2015 | Event News

 
Latest News

BLS Cargo orders 15 multisystem locomotives

30.03.2015 | Press release

Shark Tagged by NSU’s Guy Harvey Research Institute Is Apparently Enjoying Time in Warm, Tropical Waters

30.03.2015 | Life Sciences

Antarctic Ice Shelves Rapidly Thinning

30.03.2015 | Earth Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>