A DMA cell leakage evaluation method based on k-means clustering

Abstract

The invention discloses a DMA cell leakage evaluation method based on k-means mean clustering, and the steps include: counting the minimum nighttime flow of all DMA cells in a certain period; selecting the DMA cells whose leakage situation needs to be evaluated; selecting clustering variables: 7-day average nighttime minimum flow, 7-day average nighttime minimum flow / daily average flow, and unit pipe length nighttime minimum flow; data standardization; determining a reasonable clustering number k according to the leakage evaluation level; using the K-means mean clustering algorithm to perform clustering analysis; evaluating the leakage situations of different DMA cells according to the clustering results and determining the priority of handling the leakage.

Description

Technical Field

[0001] The invention relates to the technical field of DMA partition management, in particular to a DMA cell leakage evaluation method based on k-means mean clustering. Background Art

[0002] At present, the national requirements for the leakage rate of public pipe networks are constantly increasing. In the existing technology, DMA zoning management is a commonly used method. DMA is an independent area separated by a cut in the water supply and distribution system. Usually, valves are closed or flow meters are installed to form a virtual or actual independent area [Zhang Zhiming. Water supply network leakage control zoning metering technology and application [D]. Shanghai: Tongji University, 2006]. Therefore, water companies in various places have established DMA zones at all levels, and installed flow meters and remote transmission devices at the entrance of DMA for real-time monitoring. The leakview leakage management platform established in this way has been adopted by many water companies [Wang Ruibin, Chen Feng, Zhang Rui, etc. Application of DMA management in water supply leakage control in Jinan City [J]. Water Purification Technology, 2019, 38(2): 1-6.; Zhou Chen. Practice and application of LeakView platform in Xuzhou's first pipe network leakage control. Urban Water Supply, 2017, 37(03): 33-39], and many DMA communities have been created. A city often has hundreds of DMA communities, which generate a large amount of data of various types every day. Therefore, how to deeply mine these data, how to use these data to evaluate the leakage situation of so many communities, and how to cluster and grade the leakage communities is a problem worth exploring.

[0003] The MNF method, or the minimum night flow method, is a commonly used analysis and evaluation method. However, using only this indicator to evaluate the leakage of DMA cells is rather one-sided, because MNF is also related to the water consumption and pipeline length of the DMA cell. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a DMA cell leakage evaluation method based on k-means mean clustering, which adopts three variable indicators, namely MNF (minimum flow at night), minimum flow at night / average flow at day, and flow at night per unit pipe length, and uses K-means mean clustering method to perform clustering and graded evaluation on DMA cell leakage.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] A DMA cell leakage evaluation method based on k-means mean clustering, comprising the following steps:

[0007] 1) Count the minimum nighttime traffic of all DMA cells during a certain period;

[0008] 2) Select the DMA cells whose leakage needs to be evaluated;

[0009] 3) Select clustering variables: 7-day average nighttime minimum flow, 7-day average nighttime minimum flow / average daily flow, and nighttime minimum flow per unit pipe length;

[0010] 4) Data standardization;

[0011] 5) Determine the reasonable number of clusters k according to the leakage assessment level;

[0012] 6) Use K-means clustering algorithm for cluster analysis;

[0013] 7) Evaluate the leakage of different DMA cells based on the clustering results and determine the priority for handling the leakage.

[0014] Step 3) is as follows: suppose there are n DMA cells: D1, D2...Dn, count the 7-day average MNF nighttime minimum flow rate, 7-day average nighttime minimum flow rate / daily average flow rate, and unit pipe length nighttime minimum flow rate of n DMA cells, which are recorded as Ave7_MNF, Ave7_RMNF, and UNPI_MNF respectively. In n DMA cells, let ap1 = Ave7_MNF, ap2 =

[0015] Ave7_RMNF,ap3=UNPI_MNF. p=1…n, then the n DMA cell data sets can be expressed as:

[0016] D1(a11, a12, a13),

[0017] D2(a21, a22, a23),

[0018] ………

[0019] Dn(an1, an2, an3).

[0020] Step 4) The Z-score method was used to standardize the data.

[0021] Step 6) Apply k-means algorithm for cluster analysis:

[0022] a) Specify the number of clusters k;

[0023] b) Determine the initial center points of k clusters;

[0024] c) Classification based on the principle of closest distance: calculate the squared Euclidean distance from each data point to the center point of k categories in turn,

[0025] The squared Euclidean distance is defined as follows: The squared Euclidean distance between two individuals (x, y) is the sum of the squares of the differences in the p variable values ​​of the two individuals. The mathematical definition is as follows:

[0026]

[0027] Where: SED(x,y) is the squared Euclidean distance between two volumes (x,y)

[0028] xi is the value of the i-th variable in individual x, i = 1…p

[0029] yi is the value of the i-th variable in individual y, i = 1…p

[0030] Calculate the squared Euclidean distance of each data point to the k class center points in turn, and assign all data points to k classes according to the principle of the shortest distance to the k class center points;

[0031] d) Re-determine the k cluster center points:

[0032] The principle of re-determining the center points of k classes is: calculate the mean of each variable in each class in turn, and use the mean point as the new center point of each class to complete an iteration;

[0033] e) Determine whether the conditions for clustering termination are met:

[0034] It is judged by the degree of deviation of the cluster center point. When the distance between the newly determined cluster center point and the cluster center point of the previous iteration is less than 0.02, clustering is terminated. Otherwise, it returns to step c).

[0035] Step 7) Divide the n DMA cells into k categories, and finally obtain the k-category center points, compare the values ​​of the variables at the k-category center points, and the category with the largest variable value among the k-category center points is the category with the highest leakage degree, followed by the category with the second highest leakage degree, and so on. The leakage processing priority is also in this order.

[0036] Compared with the prior art, the advantages of the present invention are: the present invention utilizes three variable indicators, namely MNF (minimum flow at night), minimum flow at night / average daily flow, and flow at night per unit pipe length, and adopts the k-means mean clustering method to perform cluster leakage analysis and evaluation on DMA cells, and determine the priority of DMA cell leakage processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0038] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0039] like Figure 1 As shown, a DMA cell leakage evaluation method based on k-means mean clustering includes the following steps:

[0040] 1) Count the minimum nighttime traffic of all DMA cells during a certain period;

[0041] 2) Select the DMA cells whose leakage needs to be evaluated;

[0042] 3) Select clustering variables: 7-day average nighttime minimum flow, 7-day average nighttime minimum flow / average daily flow, and nighttime minimum flow per unit pipe length;

[0043] 4) Data standardization;

[0044] 5) Determine the reasonable number of clusters k according to the leakage assessment level;

[0045] 6) Use K-means clustering algorithm for cluster analysis;

[0046] 7) Evaluate the leakage of different DMA cells based on the clustering results and determine the priority for handling the leakage.

[0047] Step 3) is as follows: suppose there are n DMA cells: D1, D2...Dn, count the 7-day average MNF nighttime minimum flow rate, 7-day average nighttime minimum flow rate / daily average flow rate, and unit pipe length nighttime minimum flow rate of n DMA cells, and record them as Ave7_MNF, Ave7_RMNF, Unpi_MNF respectively. In n DMA cells, let ap1 = Ave7_MNF, ap2 =

[0048] Ave7_RMNF,ap3=Unpi_MNF. p=1…n, then the n DMA cell data sets can be expressed as:

[0049] D1(a11, a12, a13),

[0050] D2(a21, a22, a23),

[0051] …….

[0052] Dn(an1, an2, an3).

[0053] At present, our company manages a total of 321 DMA communities. According to the data of the leakview leakage management system on September 1, 2022, most of the MNF is lower than 5 (m3·h-1). According to our experience, the possibility of leakage in these communities is not very high, so 13 communities with a leakage rate of more than 5 (m3·h-1) are selected (see Table 1). The K-means cluster analysis method is used to analyze and evaluate the leakage of these 13 communities as research objects, and the priority of leakage treatment is established based on the clustering results. The selection of clustering variables is very important. The selected variables must be able to have an effect on the target analysis. The goal of our analysis is mainly to analyze and evaluate the leakage of DMA communities. Therefore, three variable indicators are selected: MNF (minimum flow at night), minimum flow at night / average flow at day, and flow at night per unit length. These three are commonly used indicators for leakage evaluation. In order to avoid the interference of outliers, the 7-day average MNF (minimum flow at night), the 7-day average (minimum flow at night / average flow at day), and the minimum flow at night per unit length (MNF / total length of community pipeline) are taken. They are denoted as Ave7_MNF, Ave7_RMNF, and Unpi_MNF as shown in Table 1.

[0054] Table 1 Variable index table of 13 communities

[0055]

[0056] The above three variables have dimensional differences and need to be standardized before cluster analysis. The Z-score method (standard deviation method) is used here, which is a method of standardizing data based on the mean and standard deviation of the original data. After the conversion, the mean of the data is 0 and the standard deviation is 1, as shown in Table 2.

[0057] Table 2 Standardized table of variables for 13 communities

[0058]

[0059] The number of clusters k is a relatively important issue. Considering the purpose of clustering and the small number of selected individuals, the number of clusters k = 3. The leakage is defined as severe, medium, and general respectively.

[0060] SPSS software was used for K-means clustering, the number of clusters k = 3, and the initial cluster center was determined by the software system. The results are shown in Table 3, and then descriptive statistics of each type of data were performed based on the classification results, as shown in Table 4.

[0061] Table 3 Clustering results

[0062]

[0063] Table 4 Mathematical statistics of each category

[0064]

[0065] From the above clustering results, we can see that the first category has 3 communities, which is the least in the three groups, but the mean values ​​of the three variable indicators are very high, the highest in the three categories, which shows that these three communities have serious leakage and should be treated as a priority. Among them, Binjiang Mingzhu Chengdong District and Yikang Garden have very high three variable indicators, but Zhongyi Baodi has a lower Ave7_MNF and a higher Unpi_MNF than other communities in this category, which shows that the minimum flow rate per unit pipe length in this community is high at night, and the leakage is serious. At the same time, since the pipe length is the lowest among the 13 communities (see Table 1), it shows that it is easy to find leakage points in this community.

[0066] The second category has 6 communities, the largest number of communities among the three groups. Among the three variable indicators, the average values ​​of Ave7_MNF and Unpi_MNF are at a medium level among the three categories, while the average value of Ave7_RMNF is 0.29, which is relatively high, slightly lower than the highest average value of 0.3 of the first category. This shows that the ratio of the minimum flow rate at night to the average daily water consumption in this category is high, and the possibility of leakage is relatively high. In general, the leakage of this type of community is moderate, and the priority of treatment should be the second.

[0067] The third category has 4 cells, and the mean values ​​of the three variable indicators are not high, and are the lowest among the three categories. Among the three variable indicators, the mean value of Ave7_MNF is not much different from that of other categories, especially close to that of the second category, but the other two variables Ave7_RMNF and Unpi_MNF are much different from the other two categories. This shows that there is a high possibility that this type of cell has a reasonable minimum nighttime flow. Therefore, the leakage degree of this type of cell is average, and the priority of processing should be the last.

[0068] In summary, the leakage evaluation of the above three types of DMA cells is as follows: first type > second type > third type, and the priority of processing is in this order. From the above analysis, it can be seen that the leakage evaluation of DMA cells should be comprehensively considered by the three variables Ave7_MNF, Ave7_RMNF, and Unpi_MNF, rather than a single evaluation based on the minimum flow at night, because the minimum flow at night, water use scale, and pipeline length of each DMA cell are different. The minimum flow at night is related to the average daily water consumption. The higher the average daily water consumption, the larger the number of users in the cell, and the corresponding increase in the minimum flow at night. The minimum flow at night is also related to the length of the pipeline. The longer the pipeline length, the more users are connected, and the minimum flow at night will also increase accordingly.

[0069] The present invention uses K-means mean clustering method to cluster analysis of 13 DMA communities in Changzhou City, evaluates the leakage degree of DMA communities according to the clustering results, and determines the priority level of leakage treatment of DMA communities. The results show that the k-means mean clustering method is applicable to the leakage analysis and evaluation of DMA communities, and the 13 DMA communities can be divided into 3 categories according to similarity; according to the clustering result analysis, the leakage of the 13 DMA communities is evaluated, the first category> the second category> the third category, and the priority level of leakage treatment is also in this order.

Claims

1. A DMA cell leakage evaluation method based on k-means clustering, characterized by the following steps: include: 1) Count the minimum nighttime traffic of all DMA cells during a certain period; 2) Select the DMA cells whose leakage needs to be evaluated; 3) Select clustering variables: 7-day average nighttime minimum flow, 7-day average nighttime minimum flow / average daily flow, and nighttime minimum flow per unit pipe length; 4) Data standardization; 5) Determine the reasonable number of clusters k according to the leakage assessment level; 6) Use K-means clustering algorithm for cluster analysis; 7) Evaluate the leakage of different DMA cells based on the clustering results and determine the priority of handling the leakage; Step 3) is specifically as follows: suppose there are n DMA cells: D1, D2...Dn, and the 7-day average MNF nighttime minimum flow, 7-day average nighttime minimum flow / daily average flow, and unit pipe length nighttime minimum flow of n DMA cells are counted, which are recorded as Ave7_MNF, Ave7_RMNF, and Unpi_MNF respectively. In the n DMA cells, let ap1 = Ave7_MNF, ap2 = Ave7_RMNF, ap3 = Unpi_MNF, p = 1...n, then the n DMA cell data set can be expressed as: D1(a11, a12, a13), D2(a21, a22, a23), ………. Dn(an1, an2, an3); Step 6) Use SPSS software to perform K-means clustering and apply k-means algorithm for cluster analysis: a) Specify the number of clusters K; b) Determine the initial center points of k clusters; c) Classification based on the principle of closest distance: calculate the squared Euclidean distance from each data point to the center point of k categories in turn, The squared Euclidean distance is defined as follows: The squared Euclidean distance between two individuals (x, y) is the sum of the squares of the differences in the p variable values ​​of the two individuals. The mathematical definition is as follows: Where: SED(x,y) is the squared Euclidean distance between two volumes (x,y) xi is the value of the i-th variable in individual x, i = 1…p yi is the value of the i-th variable in individual y, i = 1…p Calculate the squared Euclidean distance of each data point to the k class center points in turn, and assign all data points to k classes according to the principle of the shortest distance to the k class center points; d) Re-determine the k cluster center points: The principle of re-determining the center points of k classes is: calculate the mean of each variable in each class in turn, and use the mean point as the new center point of each class to complete an iteration; e) Determine whether the conditions for clustering termination are met: It is judged by the degree of deviation of the cluster center point. When the distance between the newly determined cluster center point and the cluster center point of the last iteration is less than 0.02, clustering is terminated. Otherwise, it returns to step c). Step 4) Standardize the data using the Z-score method; Step 7) Divide the n DMA cells into k categories, and obtain the final k-category center points. Compare the values ​​of the variables at the k-category center points. The category with the largest variable values ​​among the k-category center points is the category with the highest leakage degree, followed by the category with the second highest leakage degree, and so on. The leakage processing priority is also in this order.

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