This is the review of the article " Optimal Locations of Monitoring Stations in Water Distribution System" by Byoung Ho Lee et.al. published in the Journal of Environmental Engineering, ASCE in February 1992.
The Safe water Act requires that water quality in distribution systems is monitored through sampling in various locations that are representative of the system. The authors main objective is to be able to locate optimum number and locations of monitoring stations which will be a representative of the entire system. This is achieved through defining coverage of all the nodes and then trying to find the dependence/influence of neighboring stations/nodes which enhance the coverage. The author also proposes a water fraction W(i,j) which is equal to the ratio of flow from node j to flow coming into node i. The water fractions are calculated for all node contributions and is stored in a water-fraction matrix which can be used to derive other knowledge carrying matrices which may enhance the decision process. A coverage matrix is proposed which shows the coverage of the network obtained by choosing a set of monitoring nodes and some knowledge carrying criteria.
A small network of 7 nodes was proposed as an example. An integer programming optimisation model was formulated for the problem which had 2 sets of variables; xi ( i=1,2,.........,n) denotes if the ith node has a monitoring station and yi (i=1,2,3.....,n) denotes if the demand at node i was met. Both set of variables are 0,1 type variables. It was deduced through careful inspectio that setting monitoring stations at nodes 5,6 can cover all other demands through y3-y7. For larger problems it was proposed to make use of programs like LINDO to solve the integer programming.
Two larger problems were also presented. The first problem was at the city of Flint, Michigan. The distribution system fed on water coming from the Lake Huron consists of a network of 337 pipes and 211 nodes. Before the optimization was applied the set of existing 14 monitoring stations for a maximum daily flow covered about 18.3% of the demand. The formulation had about 211 constraints, 422 variables and 6000 non-zero entries in the table for the 14 stations. Th solution comprised of solving it sequentially on two s/w programs called COVER and COVTOIP resp. The first one generates the coverage matrix whereas the 2nd simply converts the matrix into a standard IP program redable format. The final scenario run had improved the coverage to 54% of the demand which was a significant change over 18.5%. Later the program was run for a single monitoring station on LINDO and was found that a station at node 6 would have covered about 50%.
The 2nd problem was regarding the city of Cheshire, Connecticut. The city gets its supplies from two well fields namely North Well field and South Well field. The demand is abt 2.5 mgd and is equalized using 2 storage tanks of combined capacity of 4.5 mgd. A skeleton water network was designed as the basis for the analysis. To take into account the significant variations in demand and flow over time the analysis was done for 4 different flow and demand patterns called scenarios was carried out. The problem with 245 variables and 197 constraints was solved using the LINDO package. The optimal solutions for varying no. of stations were presented.
In conclusion, the author emphasizes on the importance of such rational mechanisms to come up with the optimum number of monitoring stations. He says the combination of pathway analysis, coverage matrices and IP provides first steps towards a rational algorithm for locating monitoring stations and the results of the two example do show that improvements are possible.
The Safe water Act requires that water quality in distribution systems is monitored through sampling in various locations that are representative of the system. The authors main objective is to be able to locate optimum number and locations of monitoring stations which will be a representative of the entire system. This is achieved through defining coverage of all the nodes and then trying to find the dependence/influence of neighboring stations/nodes which enhance the coverage. The author also proposes a water fraction W(i,j) which is equal to the ratio of flow from node j to flow coming into node i. The water fractions are calculated for all node contributions and is stored in a water-fraction matrix which can be used to derive other knowledge carrying matrices which may enhance the decision process. A coverage matrix is proposed which shows the coverage of the network obtained by choosing a set of monitoring nodes and some knowledge carrying criteria.
A small network of 7 nodes was proposed as an example. An integer programming optimisation model was formulated for the problem which had 2 sets of variables; xi ( i=1,2,.........,n) denotes if the ith node has a monitoring station and yi (i=1,2,3.....,n) denotes if the demand at node i was met. Both set of variables are 0,1 type variables. It was deduced through careful inspectio that setting monitoring stations at nodes 5,6 can cover all other demands through y3-y7. For larger problems it was proposed to make use of programs like LINDO to solve the integer programming.
Two larger problems were also presented. The first problem was at the city of Flint, Michigan. The distribution system fed on water coming from the Lake Huron consists of a network of 337 pipes and 211 nodes. Before the optimization was applied the set of existing 14 monitoring stations for a maximum daily flow covered about 18.3% of the demand. The formulation had about 211 constraints, 422 variables and 6000 non-zero entries in the table for the 14 stations. Th solution comprised of solving it sequentially on two s/w programs called COVER and COVTOIP resp. The first one generates the coverage matrix whereas the 2nd simply converts the matrix into a standard IP program redable format. The final scenario run had improved the coverage to 54% of the demand which was a significant change over 18.5%. Later the program was run for a single monitoring station on LINDO and was found that a station at node 6 would have covered about 50%.
The 2nd problem was regarding the city of Cheshire, Connecticut. The city gets its supplies from two well fields namely North Well field and South Well field. The demand is abt 2.5 mgd and is equalized using 2 storage tanks of combined capacity of 4.5 mgd. A skeleton water network was designed as the basis for the analysis. To take into account the significant variations in demand and flow over time the analysis was done for 4 different flow and demand patterns called scenarios was carried out. The problem with 245 variables and 197 constraints was solved using the LINDO package. The optimal solutions for varying no. of stations were presented.
In conclusion, the author emphasizes on the importance of such rational mechanisms to come up with the optimum number of monitoring stations. He says the combination of pathway analysis, coverage matrices and IP provides first steps towards a rational algorithm for locating monitoring stations and the results of the two example do show that improvements are possible.
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