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 Dune ecosystem modelling
23.06.2017 | Albert-Ludwigs-Universität Freiburg im Breisgau

nachricht Understanding animal social networks can aid wildlife conservation
23.06.2017 | Leibniz-Institut für Gewässerökologie und Binnenfischerei (IGB)

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: Can we see monkeys from space? Emerging technologies to map biodiversity

An international team of scientists has proposed a new multi-disciplinary approach in which an array of new technologies will allow us to map biodiversity and the risks that wildlife is facing at the scale of whole landscapes. The findings are published in Nature Ecology and Evolution. This international research is led by the Kunming Institute of Zoology from China, University of East Anglia, University of Leicester and the Leibniz Institute for Zoo and Wildlife Research.

Using a combination of satellite and ground data, the team proposes that it is now possible to map biodiversity with an accuracy that has not been previously...

Im Focus: Climate satellite: Tracking methane with robust laser technology

Heatwaves in the Arctic, longer periods of vegetation in Europe, severe floods in West Africa – starting in 2021, scientists want to explore the emissions of the greenhouse gas methane with the German-French satellite MERLIN. This is made possible by a new robust laser system of the Fraunhofer Institute for Laser Technology ILT in Aachen, which achieves unprecedented measurement accuracy.

Methane is primarily the result of the decomposition of organic matter. The gas has a 25 times greater warming potential than carbon dioxide, but is not as...

Im Focus: How protons move through a fuel cell

Hydrogen is regarded as the energy source of the future: It is produced with solar power and can be used to generate heat and electricity in fuel cells. Empa researchers have now succeeded in decoding the movement of hydrogen ions in crystals – a key step towards more efficient energy conversion in the hydrogen industry of tomorrow.

As charge carriers, electrons and ions play the leading role in electrochemical energy storage devices and converters such as batteries and fuel cells. Proton...

Im Focus: A unique data centre for cosmological simulations

Scientists from the Excellence Cluster Universe at the Ludwig-Maximilians-Universität Munich have establised "Cosmowebportal", a unique data centre for cosmological simulations located at the Leibniz Supercomputing Centre (LRZ) of the Bavarian Academy of Sciences. The complete results of a series of large hydrodynamical cosmological simulations are available, with data volumes typically exceeding several hundred terabytes. Scientists worldwide can interactively explore these complex simulations via a web interface and directly access the results.

With current telescopes, scientists can observe our Universe’s galaxies and galaxy clusters and their distribution along an invisible cosmic web. From the...

Im Focus: Scientists develop molecular thermometer for contactless measurement using infrared light

Temperature measurements possible even on the smallest scale / Molecular ruby for use in material sciences, biology, and medicine

Chemists at Johannes Gutenberg University Mainz (JGU) in cooperation with researchers of the German Federal Institute for Materials Research and Testing (BAM)...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Plants are networkers

19.06.2017 | Event News

Digital Survival Training for Executives

13.06.2017 | Event News

Global Learning Council Summit 2017

13.06.2017 | Event News

 
Latest News

Quantum thermometer or optical refrigerator?

23.06.2017 | Physics and Astronomy

A 100-year-old physics problem has been solved at EPFL

23.06.2017 | Physics and Astronomy

Equipping form with function

23.06.2017 | Information Technology

VideoLinks
B2B-VideoLinks
More VideoLinks >>>