Assignment #5 - Sensor Placement in Municipal Water Networks

Review Article

1) Article Reference
Berry, J., Fleisher, L, Hart, W. Phillips, C. and Watson, J.-P. (2005) “Sensor Placement in Municipal Water Networks”, Journal of Water Resources Planning and Management, 131(3) pp. 237-243

2) Summary
This paper presents an approach for determining the placement of contaminant sensors within a municipal water network. To increase the protection of water supply systems, the use of real time early warning systems (EWS), have been widely adopted. Usually, utilities wish to place online sensors so deployment cost is minimized and the level protection maximized.

Considering a variety of approaches, the paper assumes that a attack occurs only in a single point; consider the total population exposed; the sensors protect downstream populations; and transitions between time periods are ignored. With this assumptions the authors simplify health impacts, ignore concentration and temporal effects.
The objective of the model was to minimize the expected fraction of the population that is at risk for some attack. The attack is modeled as a release of contaminant at a single point of the network. It is assumed that any point downstream of the attack can be contaminated. The EPANET water network simulator was used to determine water flow in the network. The attack scenarios were defined by a probability distribution over all pairs of population weighted flow and attacks points (from experts and scenario development).
To solve the optimization problem it was used mixed integer programming were the objective was to minimize the expected number of exposed people. The constraint considered that if a node is directly attacked it is directly contaminated. The second relate that a sensor can cover flow in a pipe in both directions. The third propagates the contaminant along the flow. One constraint is used to limit the maximum number of sensors.
To evaluate the model it was used three data sets. Two dataset were develop in EPANET and one is real. As all three dataset have some missing data, synthetic data was used to complete the datasets. The EPANET was used to determine flow patterns during four six-hour period with a 24 hour time period. The dataset 1 was adapted from Example Network provided by EPANET 2.0 with 36 nodes, 40 pipes and 1 pump station. The dataset 2 was adapted from Example Network 3 from EPANET 2.0 with 97 nodes, 117 pipes, two reservoirs and three tanks. The dataset 3 was adapted from a real world data with 470 nodes, 621 pipes, three pumps and four tanks.
The results are presented numerically in three tables. For dataset 1 and 2 the maximum number of sensors was 7 while for dataset 3 the maximum was 300. The authors present a comprehensive discussion about the numerical results and some explanations about the unlikely or unexpected outcomes. The conclusions showed that mixed integer programming can be used effectively to solve large scale sensor placement problems. Some ideas of the model generalization are presented relating the temporal effects, placement locations, sensor costs, and performance objective.

3) Discussion
I found this article useful to better understand optimization problems and it s applications and more specifically the integer programming method. I found it very similar to the previous paper. I couldn’t find any problems with the problem proposed. Further research suggestions would be to apply this methodology to real real life problems.

Assignment #4

1) Article Reference
LEE, B. H. and DEININGER, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pp. 4-16

2) Summary
As a requirement of the Safe Drinking Water Act the water quality in water supply systems has to be monitored. Although the sampling frequency and the water quality parameters are prescribed by law, there are no specifications for representatively sampling within the pipe network. Placing a monitoring point in a demand point represents coverage for that specific demand. However this water might be coming from a series of upstream nodes and going to a series of downstream nodes. The water flow path within the network carries water quality information. The nodes upstream or downstream of a monitored node are likely to be known. The water flow in a pipe network is modeled today with a variety of hydraulic models.
The paper presents a small example to demonstrate its methodology. This network with seven nodes and seven demands is used to illustrate the principles of sampling and coverage nodes. “From this network is derived a matrix called the water fraction matrix. From this matrix several knowledge carrying matrices can be derived based on a decision on which fraction of water is acceptable to call a node covered”. A general form algorithm is presented for generating the coverage matrix. To apply this procedure a demand scenario, the flows and the flow directions for a given water distribution system must be knows. Basically one node is chosen arbitrary and all flows upstream are mapped and if the demand is greater than the threshold value its given value one otherwise zero.
An example of the formulation of an optimization model is provided considering the task of placing two monitoring point in a distribution system. The question is where to places this points to maximize the demand coverage. Two sets of variable are used. They are both 0 and 1 value and one represents the whether there is a sampling station or not and the other represents whether the demand is covered or not. A maximization function and constrains are derived for the simple case example.
A case study is presented at the distribution system for the city of Flint, Michigan. The system had 337 pipes, 211 nodes and 14 monitoring points covering 18% of the demands. An integer programming was formulated with 211 constrains, 422 variables and over 6.000 non zero entries in the tableau. The solution was developed using two different programs, the COVER and the COVTOIP. Respectively they are used to solve the hydraulic flows and determine the coverage matrix. An optimal solution if found with a coverage of 54%, considering only one scenario.
The multiple flow scenarios approach permits the inclusion and consideration of the patterns of variation of the demand, such as daily, monthly or seasonally differences. A general optimization equation is provided and a solution for the small example is also provided using LINDO programming.
A second example is provided, with a case study for the city of Cheshire, Connecticut. To model this system four scenarios were used, where each scenario represents a demand and flow pattern pre established. This problem had 245 variables and 197 constrains and was solved using LINDO integer programming code. There were 4 monitoring stations to be optimally placed. The results showed the best location for the monitoring station according with the number of station to be included.
As a conclusion the author demonstrated the importance of an optimal location of monitoring station within a water distribution system as its location can have a great affect in the coverage of the system.

3) Discussion
I really enjoyed reading this article as it is becoming clearer and easier to read this kind of approach. The authors used simple examples to clarify the methodology and presented two specific case studies to illustrate the point. The optimization functions, constrains and the set up of the matrixes were quite interesting. I think further research in this theme would be to verify different methods of optimization and to also implement water quality decays models between the nodes.

Assignment #3: The Tragedy of the Commons

Review Article

1) Article Reference
HARDIN, G. (1968) “The Tragedy of the Commons” Science, 162, pp. 1243 – 1248.

2) Summary
The tragedy of the commons is a classical paper that presents an important recognition by society that a finite resources world would not be able to supply the demands of an exponential increasing human population. Although it was written 40 years ago, by that time, nature was already charging its price and pollution problems become more and more apparent in highly populated places. This recognition can easily be seen as the author says: “A finite world can only support a finite population; therefore the population growth must eventually be equal to zero”. The author analyses the possibility of trying to maximize population and maximize goods and find this goal impossible, as he concludes: “the optimum population is then, less than the maximum”.
The classical story behind the tragedy of commons is based on the example of the “commons” as the place where all the herdsman of a small society would, in common, raised their herbs. The principle of the commons is that everyone could raise it´s herbs inside the collective space. The point is that any rational individual would soon realized that if he increased his number of animals, he would increase not only increase his profit but also share the costs of the resources needed to develop the animal with all society. When each individual increases his herbs to a point where the total herb demand is greater than the resources that the commons could offer, the system collapsed and nobody could than rise their herbs anymore.
The author than point some specific examples of the tragedy of the commons that were taking place by his time. He mentions the national parks that were been overused and over developed. The oceans, which are treated by the nations as a huge “commons”, where each tried to get as much as possible out of it to guarantee it´s profit. The pollution problem illustrates very well the relation of the commons and its tragedy collapse. Pollution in small scale can easily be treated by nature within the natural cycle. But when it overpasses the limit of auto depuration, pollution very quickly demonstrates all the magnitude of the tragedy of the commons.
The author points out the controversial of the United Nations Universal Declaration of Human Rights that states that every family has the right to choose its size. The author recognizes that is very hard for the individuals to give up a share of the commons, as he says “It is a mistake to think that we can control the breeding of mankind in the long run by an appeal to conscience”.
Several alternatives are pointed by the author considering that “Not prohibition, but carefully biased options are what we offer him”. A very good example that society have learned to avoid the tragedy of the commons are the taxes system. Nobody enjoys taxes, but everyone agree to use a compulsory system knowing that in a voluntary system would favor the conscienceless. The author is very prismatic and urges the necessity to control the human breeding is becoming vital to guarantee other and more precious freedoms.

3) Discussion
This paper was published almost 40 years ago at the end of the sixties in a rather different social context than we face today. By that time cold war was taking place in a nuclear world. In the fastest growing cities it was becoming more evident that society was reaching a point where nature could not adequately supply all that mankind was ready to charge.
I think this paper represents the beginning of the human awareness of the earth limited resources and that the increasing population would soon face shortage of basic resources. After this paper many more recent concepts related to this theme have evolved such as pollution control, the sustainable development and clean energies alternatives. Although today we have evolved in many aspects of trying to increase the availability of resources I feel humanity still believes it is possible to maximize population and resources, although it was wisely recognized by the author decades ago that this is not possible.
I recognize that future research within this theme would be how to apply modern optimization techniques to find limits and the best alternatives to use wisely the resources available to an increasing population.

Assignment #2

Review Article

1) Article Reference
ATWOOD, D., F. and GORELICK, S., M. (1985) “Hydraulic gradient control for groundwater contaminant removal” Journal of Hydrology 76 pp. 85 - 106

2) Summary
This paper presents a methodology for determining an optimal operation schedule for an aquifer restoration plan. The aquifer restoration plan consists of the use of wells for both cleaning up pollutants from the aquifer as well as stopping the flow of the contaminant plume to spread out.
A case study was developed in the Rocky Mountain Arsenal, which is a military facility design to manufacture and process toxic chemicals. This aquifer is located near Denver, Colorado. The study area was chosen due the high quantity of hydrological and geological data available.
The groundwater management plan for pollutant removal basically is consisted of wells for pollutant removal (those wells have to be located inside the pollutant plume) and hydraulic gradient control wells (which have to be located outside the plume area) that are used to control the flow of the groundwater (pumping on high elevations or recharging in low elevations). An optimization model is used to find the best operation plan for this purpose. Note that a pump can be inside the plume at the beginning of the operation, but after some clean up, become outside of the plume and could them be used for hydraulic gradient control.
The equations used to model this process were the finite difference model developed by Trescott et al. (1976) for the ground water movement and the solute transport combined with groundwater flow simulation in the computer code developed by Konikow and Bredehoeft (1978) for pollutant transport. The methodology is dived in two main stages. First the velocity field is assumed based on initial data. Within this stage the plume boundary is estimated. With this information the Contamination distribution is approximated. On Stage 2, the optimization for the best well selection and operation is developed. Based on the known velocity field the solution is checked and some interactive process back in Stage 1 can be developed.
For the optimization model, the objective is to minimize the sum of pumping and recharge rates. One constrain is to guarantee the flow to go inwards in the direction of the center of the plume. For this gradient control constraint detailed information is provided.
The results showed that a best selection of wells and operation schedule could be achieved. The two stage procedure allowed a single global optimization for all 32 pumping periods. A verification of the results is provided by running the model with the chosen conditions.

3) Discussion
I think this paper is very interesting and shows the utility of optimization procedures solving water resources problems. It seems to me that optimizations procedures are intrinsically related to modeling practices in the modern time. The application of models that represent a reality is followed by an optimization procedure that allows the decision makers to choose from a set of alternatives the one that best fits the desiring goals.
Still this paper is a little too advanced for me, as some of the constrains and the matrix operation were not very clear to me. But the good part is I can feel is getting much more easy to understand them and I hoping by the end of the semester we will be pretty close to develop applications such as this one.