Abstract:
A method for the determination of demand zones for use with a water distribution model of a water distribution network, the method comprising the steps of: constructing polygons about clusters of consumption nodes; calculating base load consumption of the nodes within each polygon; assigning a consumption type to each polygon, and; aggregating connected polygons of the same consumption type into demand zones.

Description:
FIELD OF THE INVENTION  
       [0001]    The Invention relates to the modelling of an urban water distribution system. More specifically the invention relates to the initiation and construction of the model prior to the operation of the system. 
       BACKGROUND  
       [0002]    Typical urban water distribution systems have complex topology with numerous branches and loops. This composite structure makes the analysis of the system a very difficult task. Therefore, there is a need simplify the distribution network structure by organizing the water consumers in (virtual) demand zones. 
       SUMMARY OF INVENTION  
       [0003]    In a first aspect the invention provides a method for the determination of demand zones for use with a water distribution model of a water distribution network, the method comprising the steps of: constructing polygons about clusters of consumption nodes; calculating base load consumption of the nodes within each polygon; assigning a consumption type to each polygon, and; aggregating connected polygons of the same consumption type into demand zones 
         [0004]    In one embodiment of the present invention, the consumption nodes are grouped based on a multi-criteria demand zones clustering algorithm at which three criteria were used to identify clusters in the water system such that (1) the within-cluster homogeneity of water consumers&#39; characteristics is maximized; (2) the overall variance between total water consumption of the system&#39;s clusters is minimized; and optionally (3) the number of connecting links between neighboring clusters is minimized. 
         [0005]    Criterion 1 is used to identify areas in the system at which water customers are having similar characteristics (e.g., residential, commercial, or industrial user types) and therefore will not need large adjustments to achieve calibration. To avoid system partition into groups that are too small, comprised of only a few water consumers, a constraint on the lowest total water consumption in each cluster is added. 
         [0006]    Criterion 2 is implemented in parallel to criterion 1 to ensure that the clusters are equal in their total base demand and there are no large variations between demand zones&#39; total consumption that can bias decisions. 
         [0007]    Additionally Criterion 3 may be used to reduce the number of connections between each demand zone to its neighboring zones as it is often noted that node clusters should be thought of as sets of nodes with more and/or better intra-connections than inter-connections. When interested in detecting communities and evaluating their quality, it is preferred to maximize the number of sets that are densely linked inside and sparsely linked to the outside. 
         [0008]    This multi-criteria problem may be solved using graph search algorithms. For instance Breadth-First search and Best First Search and evolutionary optimization approach which partitions the system into homogeneous demand zones (e.g., residential, commercial, industrial) with equal total base demand, and with minimized number of links between them. As often occurs in this type of multi-objective problems, there is no one optimal solution that satisfies all three criteria at the same time and it is anticipated that the three objectives will mutually compete. Therefore, in several cases it will be impossible to find homogeneous demand zones that also comply with the other criteria, and in those cases, the zones will be categorized as mixed clusters (e.g., mixed residential-commercial or mixed commercial-industrial). 
         [0009]    Advantages provided by the invention may include: 
         [0010]    a) Effectiveness in Hydraulic Model Calibration Procedures: 
         [0011]    There are thousands of water consumers with unknown variations in their demand patterns to be estimated in a typical urban water system and only a relatively small number of direct measurements are available. This creates an ill-posed, underdetermined calibration problem which leads to non-unique solutions. This can be overcome by grouping the unknown parameters. Grouping is based on identifying areas of the system at which water customers are having the same characteristics (e.g., residential, commercial, or industrial consumption patterns) and therefore will not need large adjustments to achieve calibration. The main advantage of ‘grouping’ is that the size of the problem is reduced—making it possible to find unique solutions to the optimization problem. 
         [0012]    b) Effectiveness in Leakage Detection and Pressure Management: 
         [0013]    In the UK, district metered areas (DMAs) have been proven to be effective in leakage monitoring and control. The water networks are divided into District Metering Areas (DMAs) which facilitate direct identification and management of water losses and enable flow tracking between different clusters with flow meters at the DMAs boundaries. In addition, pressure management and leakage localization can be implemented by pressure monitoring within the DMAs to achieve improved leakage reduction. 
         [0014]    c) Effectiveness in Improving Water Security: 
         [0015]    Dividing the system into consumption blocks at which all connections between the blocks are known and monitored (e.g., flow rates and water quality parameters) can improve the response to an event of a large scale contamination incident. Combining knowledge about blocks connectivity with the implementation of appropriate operation response (e.g. valves closure and hydrants opening) for isolation and flushing of the contamination from the water network would limit exposure to harmful contaminants and minimize the extent of pipe that would need to be decontaminated. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0016]    It will be convenient to further describe the present invention with respect to the accompanying drawings that illustrate possible arrangements of the invention. Other arrangements of the invention are possible, and consequently the particularity of the accompanying drawings is not to be understood as superseding the generality of the preceding description of the invention. 
           [0017]      FIG. 1  is a plan view of an urban water distribution network; 
           [0018]      FIG. 2  is a plan view of a skeleton of the urban water distribution network of  FIG. 1 ; 
           [0019]      FIG. 3  is a plan view of the urban water distribution network of  FIG. 1  having nodes enmeshed by polygons; 
           [0020]      FIG. 4  is a connectivity graph according to one embodiment of the present invention;  FIG. 5  is a Demand Zone Aggregation according to a further embodiment of the present invention; 
           [0021]      FIG. 6  is a plan view of the urban water distribution network of  FIG. 1  showing the formed demand zones; 
           [0022]      FIGS. 7A to 7C ,  8  and  9  are sequential steps of a connectivity minimization process according to a further embodiment of the present invention; 
           [0023]      FIG. 10  is a plan view of an urban water distribution network following connectivity minimization according to a further embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0024]    The invention provides a method of grouping large numbers of diverse water consumption users to be used in a rational optimization of the water distribution network. Whilst there are a number of procedures for the optimization of such networks dealing with the diversity of users in an urban environment provides a balance between reliable results and managing the needs of said users. 
         [0025]    Accordingly, the present invention provides a process to group said users with the following setting out one such method falling within the scope of the invention. 
         [0026]    Step  1 : Initial Partition Based on the System Main Skeleton 
         [0027]    The main skeleton of the system which is comprised of pipes with diameter ≧12″ (304 mm) is used to construct polygons that bind the system consumption nodes.  FIG. 1  shows the full water network  5  (with the two service reservoirs, 19415 junctions, and 20072 pipes) and  FIG. 2  shows the main skeleton  10  of the system. 
         [0028]      FIG. 3  shows the set of 39 polygons  25  constructed based on the system&#39;s main skeleton  15 . 
         [0029]    All 1717 water consumers  20  (marked in red dotes) in this example network lie inside these polygons  25 : 
         [0030]    GIS tools can be used for the purpose of constructing polygons out of sets of x, y coordinates and for determining if a point lies on the interior of each polygon. Also it is possible to use one of the known algorithms which are available in the literature for this purpose. In this application, the polygons  25  were constructed out of the main skeleton vertices and demand nodes were assigned to polygons by implementing a procedure for determining if a point lies inside a given polygon. 
         [0031]    At the end of this initial step, the total base demand of each polygon is calculated and a consumption type is assigned to each polygon according to the distribution of water consumption  20  within the block (i.e., if more than 60% of the base demand in a block has the same consumption-type then the block is assigned with that consumption type; otherwise the block is assigned with mixed consumption depending on the block components (e.g., mixed residential-commercial, mixed commercial-industrial, and mixed residential-industrial). Table 1 shows these data for the example system: 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                 total Base 
                 Resi- 
                 Com- 
                 Indus- 
                   
               
               
                 Polygon 
                 demand 
                 dential 
                 mercial 
                 trial 
               
               
                 index 
                 (CMH) 
                 use (%) 
                 use (%) 
                 use (%) 
                 User type: 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 26 
                 29.2 
                 70.8 
                 0.0 
                 Commercial 
               
               
                 2 
                 24 
                 0.0 
                 100.0 
                 0.0 
                 Commercial 
               
               
                 3 
                 36 
                 0.0 
                 100.0 
                 0.0 
                 Commercial 
               
               
                 4 
                 124 
                 30.0 
                 67.2 
                 2.8 
                 Commercial 
               
               
                 5 
                 409 
                 1.6 
                 7.1 
                 91.3 
                 Industrial 
               
               
                 6 
                 129 
                 72.2 
                 27.8 
                 0.0 
                 Residential 
               
               
                 7 
                 74 
                 98.0 
                 2.0 
                 0.0 
                 Residential 
               
               
                 8 
                 198 
                 26.8 
                 72.3 
                 0.9 
                 Commercial 
               
               
                 9 
                 246 
                 0.0 
                 0.2 
                 99.8 
                 Industrial 
               
               
                 10 
                 38 
                 7.1 
                 30.1 
                 62.7 
                 Industrial 
               
               
                 11 
                 403 
                 26.9 
                 70.1 
                 2.9 
                 Commercial 
               
               
                 12 
                 74 
                 89.5 
                 10.5 
                 0.0 
                 Residential 
               
               
                 13 
                 126 
                 43.6 
                 53.4 
                 3.0 
                 Mixed commercial- 
               
               
                   
                   
                   
                   
                   
                 residential 
               
               
                 14 
                 354 
                 28.7 
                 66.0 
                 5.3 
                 Commercial 
               
               
                 15 
                 80 
                 0.0 
                 97.9 
                 2.1 
                 Commercial 
               
               
                 16 
                 11 
                 37.9 
                 62.1 
                 0.0 
                 Commercial 
               
               
                 17 
                 63 
                 20.4 
                 79.6 
                 0.0 
                 Commercial 
               
               
                 18 
                 50 
                 0.0 
                 94.4 
                 5.6 
                 Commercial 
               
               
                 19 
                 22 
                 11.2 
                 86.6 
                 2.2 
                 Commercial 
               
               
                 20 
                 1 
                 0.0 
                 100.0 
                 0.0 
                 Commercial 
               
               
                 21 
                 158 
                 0.0 
                 100.0 
                 0.0 
                 Commercial 
               
               
                 22 
                 228 
                 1.3 
                 98.7 
                 0.0 
                 Commercial 
               
               
                 23 
                 273 
                 31.7 
                 68.3 
                 0.0 
                 Commercial 
               
               
                 24 
                 62 
                 26.7 
                 68.0 
                 5.2 
                 Commercial 
               
               
                 25 
                 24 
                 47.3 
                 50.8 
                 1.9 
                 Mixed commercial- 
               
               
                   
                   
                   
                   
                   
                 residential 
               
               
                 26 
                 167 
                 45.4 
                 53.8 
                 0.8 
                 Mixed commercial- 
               
               
                   
                   
                   
                   
                   
                 residential 
               
               
                 27 
                 114 
                 57.9 
                 42.1 
                 0.0 
                 Mixed commercial- 
               
               
                   
                   
                   
                   
                   
                 residential 
               
               
                 28 
                 154 
                 18.6 
                 81.4 
                 0.0 
                 Commercial 
               
               
                 29 
                 117 
                 31.6 
                 66.4 
                 1.9 
                 Commercial 
               
               
                 30 
                 127 
                 69.9 
                 27.2 
                 2.9 
                 Residential 
               
               
                 31 
                 100 
                 61.4 
                 35.8 
                 2.8 
                 Residential 
               
               
                 32 
                 105 
                 43.9 
                 53.9 
                 2.2 
                 Mixed commercial- 
               
               
                   
                   
                   
                   
                   
                 residential 
               
               
                 33 
                 22 
                 98.9 
                 1.1 
                 0.0 
                 Residential 
               
               
                 34 
                 77 
                 86.6 
                 10.3 
                 3.1 
                 Residential 
               
               
                 35 
                 115 
                 88.9 
                 11.1 
                 0.0 
                 Residential 
               
               
                 36 
                 3 
                 0.0 
                 36.4 
                 63.6 
                 Industrial 
               
               
                 37 
                 64 
                 2.4 
                 33.3 
                 64.3 
                 Industrial 
               
               
                 38 
                 210 
                 32.2 
                 6.0 
                 61.8 
                 Industrial 
               
               
                 39 
                 323 
                 90.5 
                 9.1 
                 0.4 
                 Residential 
               
               
                   
               
             
          
         
       
     
         [0032]    Step  2 : Aggregation of the Network&#39;s Nodes Into Demand Zones 
         [0033]    In this step, the aim is to group polygons into demand zones which will have equal (as possible) total base demands and homogeneous (as possible) consumption within each group. It is important to create groups of polygons with roughly the same water consumption since having a very large variance between different clusters might bias the system&#39;s hydraulic model calibration results. 
         [0034]    The process of grouping the basic demand blocks is as follows: 
         [0035]    1. The polygons are sorted according to their connectivity and are organized in a graph  35  ( FIG. 4 ) where the graph vertices are the basic blocks  50  and the edges stand for the connectivity  55  between these blocks: 
         [0036]    2. Best First Search technique which is a type of graph search algorithm is implemented on the graph presented in  FIG. 4  to group the polygons (graph nodes) into equal and homogeneous as possible demand zones: It starts at a root node  45  and exploxes all the nodes which are adjacent to the current node before visiting other nodes. The traversal goes a level at a time  40  and adds a node to a group according to the following preference list sorted from option i which is the best choice to option iii which is the least favorable alternative:
       i. Aggregate adjacent nodes with similar consumption type to a group until the total water consumption reaches the maximum consumption threshold (500 CMH)   ii. If the total consumption is below the minimum consumption threshold (200 CMH) then add nodes with mixed consumption (where at least one of the components of the mixed node is similar to the group&#39;s consumption type). Stop when the total base demand exceeds the minimum boundary   iii. If the total consumption is below the minimum consumption threshold (200 CMH) and there is no better choice, add any adjacent node with any consumption type until the minimum consumption threshold is met   The 200-500 CMH amplitude allows some flexibility in aggregating the nodes into homogeneous as possible groups while keeping the nodes consumption on the same scale.     FIG. 5  demonstrate the results of above procedure on some of the graph nodes:       
 
         [0042]    In this example, polygons  1 ,  2 ,  3  and  4  which have all been designated commercial use are grouped as a first demand zone  60 . Similarly, polygons  6  and  7  which are categorized as residential notes are grouped as a second demand zone  65 . To demonstrate that demand zones may encompass single polygons as demonstrated by the industrial nodes  5  forming a third demand zone  70 , commercial nodes  11  forming a demand zone  75  and resdential nodes  39  forming demand zone  80 . 
         [0043]    At the end of this procedure, the  39  basic blocks were aggregated into 15 demand zones. Table 2 and  FIG. 6  summarize the results of step  2 . Therefore the water network  90  is now divided into various demand zones  95  comprising categorized consumers  100 ,  105  within each demand zone. 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Demand zones details 
               
             
          
           
               
                 Demand 
                 Components 
                 Total base 
                   
               
               
                 zone index 
                 (aggregated polygons) 
                 demand (CMH) 
                 Consumption type 
               
               
                   
               
             
          
           
               
                 1 
                 1, 2, 3, 4 
                 209.7 
                 Commercial 
               
               
                 2 
                 6, 7 
                 202.3 
                 Residential 
               
               
                 3 
                  5 
                 408.7 
                 Industrial 
               
               
                 4 
                 11 
                 402.6 
                 Commercial 
               
               
                 5 
                  9, 10 
                 283.8 
                 Industrial 
               
               
                 6 
                 8, 12, 13, 15, 16 
                 489.4 
                 Mixed commercial- 
               
               
                   
                   
                   
                 residential 
               
               
                 7 
                 14, 17 
                 416.4 
                 Mixed commercial- 
               
               
                   
                   
                   
                 residential 
               
               
                 8 
                 18, 19, 20, 23, 24, 25 
                 431.6 
                 Mixed commercial- 
               
               
                   
                   
                   
                 residential 
               
               
                 9 
                 22, 29 
                 344.8 
                 Commercial 
               
               
                 10 
                 21, 28 
                 311.6 
                 Commercial 
               
               
                 11 
                 30, 31, 35 
                 342.2 
                 Residential 
               
               
                 12 
                 26, 32 
                 271.3 
                 Mixed commercial- 
               
               
                   
                   
                   
                 residential 
               
               
                 13 
                 27, 33, 34 
                 213.5 
                 Residential 
               
               
                 14 
                 36, 37, 38 
                 276.6 
                 Industrial 
               
               
                 15 
                 39 
                 323.0 
                 Residential 
               
               
                   
               
             
          
         
       
     
         [0044]    Step  3 : Minimizing the number of links between neighboring demand zones 
         [0045]    The purpose of this step is to reduce the number of connections between each set and its neighboring sets. This is achieved by solving the following optimization problem for each pair of adjacent demand zones. 
         [0046]    The decision variables of this optimization problem are the water system junctions (with no water consumption) in a range of 500 m 125, 130 from both sides of the border  110  between the two zones  115 ,  120 . All the nodes indexes and the zones that these nodes belong to are written to a matrix.  FIGS. 7A to 7C  describe this procedure: 
         [0047]    The objective function to be minimized with a Genetic Algorithm procedure is the sum of connections between zones i  115  and j  120 . The decision variables values are 0 or 1. If the value equals 1 then the node&#39;s zone index is switched from i to j and vice versa. If the value is zero the node remain in its original demand zone. In the illustrative example given below, each decision variables&#39; string is comprised of 7 random Boolean values for the first GA iteration. At the subsequent iterations (using the GA operators) nodes are shifted from zone to zone until the number of connections between the zones is minimized.  FIGS. 8A and 8B  demonstrate this procedure. 
         [0048]    At the end of the GA procedure nodes were switched (or not switched) from zones i and j and as a result the number of connections between the zones is minimized  150 . See optimal solution for the illustrative example in  FIG. 9 : 
         [0049]    The results of the implementation of the GA procedure on the FCPH network showed that the average optimal number of connections between each set of two neighboring demand zones is 5 (e.g., the number of connecting pipes for zones  1  and  3  is 2; for zones  3  and  4  its 5; for zones  10  and  11  its 1; and for zones  11  and 12 its 10). 
         [0050]      FIG. 10  shows the practical application of the procedure whereby connecting pipes between adjacent zones  2  and  4  are minimized to only 4 pipes. The connection minimization procedure is completed for each of the zonal boundaries throughout the water network.