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) pg. 237-243.
Summary
This paper was quite similar to the last paper. They used a mixed integer programming to optimize placements of sensors in municipal water systems. The objective function was to minimize the fraction of population exposed to contaminants, in which each node of the model was weighed based on population that will consume the water. Currently, the early warning system (EWS) is used, which identifies the contamination incident while allowing time for response. The EPA used these EWS systems by placing sensors at multiple location in which the coverage of flow in terms of detection of contamination is maximized. The way in which a contamination event was to occur was modeled by a fixed probability distribution.
The assumptions that the authors used was: An attack occurs at one point in the network; The total population is considered exposed without looking at health impacts; Downstream populations are protected by nodes with sensors, meaning that a population is considered exposed if its node is reached by a flow path that doesn’t pass a sensor; Time periods are treated independently. These assumptions allowed the researched to ignore both the temporal effects of the contaminant, along with the concentration effects. The authors said that this enabled them to say that their model can be re-used for situations where large volumes of contaminants flow quickly through a network.
The network was modeled in which the pipes were “edges”, and the nodes were vertices. The authors’ input data was: probability of an attack at each node, population density at each node, the network layout. The constraints also included were flow direction constraints along with maximum number of sensors. The authors tested the model with example data sets using the program EPANet. The results showed that the population at risk from contamination is reduced as the number of sensors utilized is increased. When the authors realized that the results were showing little sensitivity to the objection function, they then discussed areas in which their model can be more generalized for every day use: using a model that incorporates temporal effects, placement of sensors other than nodes, incorporating cost and maintenance cost of sensors, modified objective function to relate to multiple objectives.
Discussion
This paper was significant, because this is still quite a large issue in water resources these days. However, there are some faults in this paper. It seems that the model isn’t taking any consideration of the water demands of each node, just the population. The authors put large constraints on the direction of flow, but the velocity of the flow was not incorporated at all. If I were to expand on the research, I would start with the four future goals of the model that the authors discussed at the end of the paper.
Monday, February 23, 2009
Monday, February 16, 2009
Assignment 4
Lee, B. H. and Deininger, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pg. 4-16.
Summary
The Environmental Protection Agency has had a requirement of monitoring water quality of potential drinking water. The guideline of the sampling frequency is based on the size of population that the distribution system serves. Furthermore, the EPA doesn’t prescribe a certain methodology in which monitoring stations should be chosen. This study by Lee and Deininger propose a integer programming model that introduces a rubric that optimizes locations of monitoring station(s).
First, a test model is introduced to explain in detail how the optimized model works. The model first creates a water fraction matrix in which the amount of water going through a certain node is contributed by a certain percentage from another node. From this matrix, a coverage matrix is created in which all the non-zero values above a certain “coverage criterion” are substituted by a 1. The “coverage criterion” is defined by the minimum percentage of flow contributed from node i to node j to be in order to be assigned a coverage value of 1.
The formulation of the optimization model includes an objective function that minimizes the product of the demand of node i and the binary integer that decides whether or not the sampling station will be location at node i. The constraints include the number of sampling stations wished to be used, along with the demand constraints for the nodes.
In the practical models, the demands of the nodes were the maximum daily flow demands for drinking water for the node. The demand coverage was optimized for a location in Michigan, in which the coverage increased from 18.5% to 54%. Also, this example incorporated multiple demand patterns, in which a two-scenario optimization problem was created. There was also a model created for a location in Connecticut that had incorporated four different flow scenarios that included demand nodes and pumping well fields.
Discussion
The authors argue that the EPA has strict requirements to monitor the quality of drinking water at specific locations in the system, however there is no formal procedures that are to be followed. It was interesting that the authors seemed to be completely uneducated about the previous methodologies of the past practices in this field. Surely they knew a little bit of information of why certain stations were monitored.
The authors introduced an integer programming model that optimized certain monitoring locations based on a “coverage criterion”. The authors believe that this factor is the optimal way to choose these specific locations. However is there a different criterion that other researchers have looked into? Also, it seems like a lot of information about the system is omitted, and nothing was added to the system to compensate. Lastly, I would be interested in the further development of this research, post 1992.
Summary
The Environmental Protection Agency has had a requirement of monitoring water quality of potential drinking water. The guideline of the sampling frequency is based on the size of population that the distribution system serves. Furthermore, the EPA doesn’t prescribe a certain methodology in which monitoring stations should be chosen. This study by Lee and Deininger propose a integer programming model that introduces a rubric that optimizes locations of monitoring station(s).
First, a test model is introduced to explain in detail how the optimized model works. The model first creates a water fraction matrix in which the amount of water going through a certain node is contributed by a certain percentage from another node. From this matrix, a coverage matrix is created in which all the non-zero values above a certain “coverage criterion” are substituted by a 1. The “coverage criterion” is defined by the minimum percentage of flow contributed from node i to node j to be in order to be assigned a coverage value of 1.
The formulation of the optimization model includes an objective function that minimizes the product of the demand of node i and the binary integer that decides whether or not the sampling station will be location at node i. The constraints include the number of sampling stations wished to be used, along with the demand constraints for the nodes.
In the practical models, the demands of the nodes were the maximum daily flow demands for drinking water for the node. The demand coverage was optimized for a location in Michigan, in which the coverage increased from 18.5% to 54%. Also, this example incorporated multiple demand patterns, in which a two-scenario optimization problem was created. There was also a model created for a location in Connecticut that had incorporated four different flow scenarios that included demand nodes and pumping well fields.
Discussion
The authors argue that the EPA has strict requirements to monitor the quality of drinking water at specific locations in the system, however there is no formal procedures that are to be followed. It was interesting that the authors seemed to be completely uneducated about the previous methodologies of the past practices in this field. Surely they knew a little bit of information of why certain stations were monitored.
The authors introduced an integer programming model that optimized certain monitoring locations based on a “coverage criterion”. The authors believe that this factor is the optimal way to choose these specific locations. However is there a different criterion that other researchers have looked into? Also, it seems like a lot of information about the system is omitted, and nothing was added to the system to compensate. Lastly, I would be interested in the further development of this research, post 1992.
Sunday, February 8, 2009
Assignment 3
Garrett Hardin, “The Tragedy of the Commons,” Science, 162 (1968): 1243-1248.
Summary
Garrett Hardin writes this article in an attempt to discuss the population increase-related problems across the world. First, he argues that there is no technical solution, but society should not give up on solving it based on a use of morality. Hardin also discusses the phrase “greater food for the greatest number”, identifying with a utopian philosophy, and claiming that the word “good” is a subjective term. This shows that you cannot compare one good to another.
Adam Smith coined the term “invisible hand”, which is the cause for an individual to make decisions for himself that are supporting the public interest. However, Hardin disagrees with this idea by introducing the tragedy of the commons. This idea is best described by an example: if an individual measures the positive effects versus negative (to a group of people) of an action, then he claims the action just if the positive are greater. However, if everyone were to do the same thing, the action will cause resources to be exhausted. This is the effect of depletion to the commons. Another way a commons can become tragic is by pollution: introducing harmful influences to the commons.
Hardin’s argument to reduce pollution to the commons is to set coercive laws and taxes to make the citizen pay the taxes and making it cheaper for him to treat the pollutants as opposed to disposing them. Furthermore, Hardin argues that in order for these to be in effect, the citizens must have recognition of necessity.
Hardin concluded in this paper that the only way that the commons can work is with low-population densities. He claims that the commons will need be abandoned if the population were to increase. The recognition of necessity claims that citizens must be coerced to do actions that will benefit the whole, but may negatively impact their own interests. Hardin stated that the only way that the commons can be preserved is by “relinquishing the freedom to breed”.
Discussion
This is the type of article that I thought would be interesting to read about in this course in terms of optimizing a solution for a model. How would one even begin to create such a model related to this subject? Even Hardin himself claimed that not even a good can be defined because of different perspectives, therefore making a model with inputs and an objective function impossible.
I agree with Hardin in the sense that many citizens are making decisions based on their own self interest, and not paying attention to the society as a whole. However, I am unsure of how much people may or may not pay attention to taxing and laws. The people that make decisions that are of large consequence to society will still do so with or without taxation. Also, it seems that people from the upper class seem to be the ones that get away with illegal actions, which only makes these types of situations worse.
In America, there is a large problem with people polluting, or buying unreasonably large cars that will place toxic pollutants into the environment. There are people that will do this out of their own self interest, even though pollution is a large problem that the world has been facing. The Golden Rule states that one should make decisions not only in their own interests, but in the interests of others. This rule has dated back from the days of the Old Testament, and obviously there are still many problems with people not following it. If everyone were to follow this rule, then society all over the world would be a utopia. There is no taxing or legislation that can eliminate this problem; it is an adjustment of morality that is necessary.
Summary
Garrett Hardin writes this article in an attempt to discuss the population increase-related problems across the world. First, he argues that there is no technical solution, but society should not give up on solving it based on a use of morality. Hardin also discusses the phrase “greater food for the greatest number”, identifying with a utopian philosophy, and claiming that the word “good” is a subjective term. This shows that you cannot compare one good to another.
Adam Smith coined the term “invisible hand”, which is the cause for an individual to make decisions for himself that are supporting the public interest. However, Hardin disagrees with this idea by introducing the tragedy of the commons. This idea is best described by an example: if an individual measures the positive effects versus negative (to a group of people) of an action, then he claims the action just if the positive are greater. However, if everyone were to do the same thing, the action will cause resources to be exhausted. This is the effect of depletion to the commons. Another way a commons can become tragic is by pollution: introducing harmful influences to the commons.
Hardin’s argument to reduce pollution to the commons is to set coercive laws and taxes to make the citizen pay the taxes and making it cheaper for him to treat the pollutants as opposed to disposing them. Furthermore, Hardin argues that in order for these to be in effect, the citizens must have recognition of necessity.
Hardin concluded in this paper that the only way that the commons can work is with low-population densities. He claims that the commons will need be abandoned if the population were to increase. The recognition of necessity claims that citizens must be coerced to do actions that will benefit the whole, but may negatively impact their own interests. Hardin stated that the only way that the commons can be preserved is by “relinquishing the freedom to breed”.
Discussion
This is the type of article that I thought would be interesting to read about in this course in terms of optimizing a solution for a model. How would one even begin to create such a model related to this subject? Even Hardin himself claimed that not even a good can be defined because of different perspectives, therefore making a model with inputs and an objective function impossible.
I agree with Hardin in the sense that many citizens are making decisions based on their own self interest, and not paying attention to the society as a whole. However, I am unsure of how much people may or may not pay attention to taxing and laws. The people that make decisions that are of large consequence to society will still do so with or without taxation. Also, it seems that people from the upper class seem to be the ones that get away with illegal actions, which only makes these types of situations worse.
In America, there is a large problem with people polluting, or buying unreasonably large cars that will place toxic pollutants into the environment. There are people that will do this out of their own self interest, even though pollution is a large problem that the world has been facing. The Golden Rule states that one should make decisions not only in their own interests, but in the interests of others. This rule has dated back from the days of the Old Testament, and obviously there are still many problems with people not following it. If everyone were to follow this rule, then society all over the world would be a utopia. There is no taxing or legislation that can eliminate this problem; it is an adjustment of morality that is necessary.
Sunday, February 1, 2009
Assignment 2
Atwood, Dorothy Fisher, and Gorelick, Steven M. (1985) “Hydraulic Gradient Control for Groundwater Contaminant Removal,” Journal of Hydrology 76, 85-106.
Summary
This study entails a two-stage planning procedure that optimizes a pumping and recharge schedule for wells that will ultimately remove contaminated water. Stage I included a groundwater flow and solute transport model that simulated contaminant removal, and Stage II was a linear programming model that determined the optimal well selection and their schedules by minimizing total pumping and recharge. The stage II program includes the groundwater flow model from stage I as a constraint.
In stage I, the methodology of the plume containment was to control the hydraulic gradient that was aimed at containing and removing the contaminants. An important technique that they used in the groundwater management modeling was the response matrix, which showed the “influence of pumping or recharge of the wells at the potential well sites upon drawdowns at specified observation locations”.
The model that was developed by the authors was tested in the Rocky Mountain Arsenal in Colorado, which is an area where poor disposal of industrial and military chemicals exist. It was found that the northern boundary of the area had a steeper hydraulic gradient compared to the southern end, and the contaminant was more effectively removed in the southern part. This had a great influence on the well chosen, along with the pumping/recharge schedules.
In stage II, an objective function was formulated to minimize the sum of the pumping and recharge rates. The constraints for the model were non-negativity values for the decision variables, along with the hydraulic gradient constraints for the creation of an inward hydraulic gradient. The cost was not taken into account in the objective function, or even in the optimization model as a whole. The linear programming model was solved using the MINOS optimization package. Two solution strategies were used: global (a single global optimization for all pumping periods) and sequential (used a series of sequential optimizations for each pumping period). The results found were that pumping and recharge rates were similar between the two strategies, but the well selection and pumping schedules were quite different. The global optimization was advantageous because it solved the problem over the entire time span and took all constraints at one time. However there are arguments that the sequential optimization is preferred due to other non-hydraulic related criteria, such as social or economic concerns.
The authors discussed that the limitation of this methodology was that it can only be applied to small steady-state flow problems. Excessive computer storage requirements and numerical difficulties made the method infeasible for field-scale problems.
Discussion
This article created an optimization model used to identify the most advantageous wells, along with pumping and recharge rates. This work credited to hydraulic modeling methodology by linearizing nonlinearities in the system. It was also very beneficial that the authors decided to optimize the solution using two different methodologies: global versus sequential. This is because the readers were allowed to compare the results, along with the advantages and disadvantages of both. This proves that there is no right answer to this problem, and it is just relative to the perspective of the user.
The faults of this work deal with the scale in which the model can be applied. Applications of related subjects pertaining to this model are to be used on a larger scale. Also, the model had used information from other models, in which the work wasn’t autonomous entirely. This can be beneficial in the sense that the model must be relatively valid and accurate if it is being reproduced. However, problems could arise if there are not identical constraints and/or assumptions made in both the borrowed and the new models.
If I were to build on this research, I would look into hydraulic related models similar to this one, and see if they separated the models in their studies in a similar fashion as this one due to non-linearity of variables. I would also look into the numerical difficulties that were encountered in the model development that led the authors to claim that the model can only be used on a small scale. I would also see how I could incorporate cost into the objective function or constraints.
Summary
This study entails a two-stage planning procedure that optimizes a pumping and recharge schedule for wells that will ultimately remove contaminated water. Stage I included a groundwater flow and solute transport model that simulated contaminant removal, and Stage II was a linear programming model that determined the optimal well selection and their schedules by minimizing total pumping and recharge. The stage II program includes the groundwater flow model from stage I as a constraint.
In stage I, the methodology of the plume containment was to control the hydraulic gradient that was aimed at containing and removing the contaminants. An important technique that they used in the groundwater management modeling was the response matrix, which showed the “influence of pumping or recharge of the wells at the potential well sites upon drawdowns at specified observation locations”.
The model that was developed by the authors was tested in the Rocky Mountain Arsenal in Colorado, which is an area where poor disposal of industrial and military chemicals exist. It was found that the northern boundary of the area had a steeper hydraulic gradient compared to the southern end, and the contaminant was more effectively removed in the southern part. This had a great influence on the well chosen, along with the pumping/recharge schedules.
In stage II, an objective function was formulated to minimize the sum of the pumping and recharge rates. The constraints for the model were non-negativity values for the decision variables, along with the hydraulic gradient constraints for the creation of an inward hydraulic gradient. The cost was not taken into account in the objective function, or even in the optimization model as a whole. The linear programming model was solved using the MINOS optimization package. Two solution strategies were used: global (a single global optimization for all pumping periods) and sequential (used a series of sequential optimizations for each pumping period). The results found were that pumping and recharge rates were similar between the two strategies, but the well selection and pumping schedules were quite different. The global optimization was advantageous because it solved the problem over the entire time span and took all constraints at one time. However there are arguments that the sequential optimization is preferred due to other non-hydraulic related criteria, such as social or economic concerns.
The authors discussed that the limitation of this methodology was that it can only be applied to small steady-state flow problems. Excessive computer storage requirements and numerical difficulties made the method infeasible for field-scale problems.
Discussion
This article created an optimization model used to identify the most advantageous wells, along with pumping and recharge rates. This work credited to hydraulic modeling methodology by linearizing nonlinearities in the system. It was also very beneficial that the authors decided to optimize the solution using two different methodologies: global versus sequential. This is because the readers were allowed to compare the results, along with the advantages and disadvantages of both. This proves that there is no right answer to this problem, and it is just relative to the perspective of the user.
The faults of this work deal with the scale in which the model can be applied. Applications of related subjects pertaining to this model are to be used on a larger scale. Also, the model had used information from other models, in which the work wasn’t autonomous entirely. This can be beneficial in the sense that the model must be relatively valid and accurate if it is being reproduced. However, problems could arise if there are not identical constraints and/or assumptions made in both the borrowed and the new models.
If I were to build on this research, I would look into hydraulic related models similar to this one, and see if they separated the models in their studies in a similar fashion as this one due to non-linearity of variables. I would also look into the numerical difficulties that were encountered in the model development that led the authors to claim that the model can only be used on a small scale. I would also see how I could incorporate cost into the objective function or constraints.
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