A method for water supply pipeline optimization reconstruction based on spatial gridding clustering

Abstract

The application discloses a method for water supply pipeline optimization and reconstruction based on spatial gridding clustering, and belongs to the field of urban water supply pipe networks. Spatial autocorrelation analysis is performed on pipeline damage point data, Moran's I is adopted to divide spatial grids with the most obvious clustering characteristics, and pipelines in all the grids are grouped, so as to serve as input data of an optimization model. Failure prediction models with damage number as a dependent variable are established by modeling two kinds of pipe materials respectively with pipe diameter, pipe length and pipe age as influence factors, so as to predict the damage number of each group in the next year, and the fitting degree of the models is judged by adopting R 2 and RMSE. Finally, genetic algorithm is used to optimize the clustered pipelines with the minimum damage number as a target function and the annual fund budget as a constraint condition, so as to determine an optimal annual reconstruction scheme. By considering the spatial factors, the application optimizes the isolated pipeline dispersion problem existing in the attribute clustering reconstruction scheme, and provides a new idea for water supply enterprises to formulate a more cost-effective reconstruction scheme.

Description

Technical Field

[0001] The invention relates to a method for establishing water supply pipeline optimization and transformation based on spatial grid clustering, and belongs to the field of urban water supply pipe networks. Background Art

[0002] As a vital piece of urban infrastructure, water supply networks age over time. These aging pipes often lead to leaks, yellow water, and even bursts, posing serious challenges to their safe management. To reduce leakage and improve service performance, water supply companies must conduct regular, timely, and organized maintenance. Given limited funding, how to manage water supply pipeline renovations has long been a research hotspot in water supply system asset management.

[0003] Currently, one viable approach to effectively developing asset management plans is to establish an optimization model by setting objective functions and constraints. However, as the scale of the water supply network increases, the number of feasible decision variables will increase exponentially, leading to an increase in the complexity and computational complexity of the optimization model. Grouped renovation clusters pipelines with the same physical attributes, such as pipe material, diameter, and age, which simplifies the complexity of the optimization model. However, pipelines clustered by physical attributes are still scattered, with isolated, non-connected sections. Renovating these pipelines will result in frequent service interruptions and higher maintenance resource costs.

[0004] Some research has analyzed the impact of spatial factors on pipeline damage points, expanding on the research on pipeline renovation plans based on attribute clustering. Therefore, to address the issue of dispersed isolated pipe sections, it is necessary to consider establishing a spatially clustered water supply pipeline optimization model to study the impact of spatial factors at damage points on pipeline optimization and renovation. Summary of the Invention

[0005] Given these issues, this method aims to establish an optimization model for water supply pipelines by considering spatial factors. By analyzing the spatial characteristics of pipeline failure points, a cluster grid is created, and the pipelines within the grid are grouped. This cluster grid serves as the input for the optimization model. Next, a failure model is established using GEP to predict the number of failures in each group over the next year. Finally, with minimizing the number of failures as the objective function, an optimization algorithm is used to determine the annual renovation plan, providing a new approach for water supply companies to develop more cost-effective renovation plans.

[0006] The technical solution of this method is as follows:

[0007] A method for optimizing and renovating a water supply pipeline based on spatial grid clustering, the method comprising the following steps:

[0008] Step 1: Preliminary data preparation.

[0009] In the Geographic Information System (GIS) of the urban water supply network, pipeline data, including pipe material, diameter, pipeline burial time, pipeline number, and damage point information, were extracted. The pipeline age was calculated by subtracting the pipeline burial time from the observation time.

[0010] Step 2: Spatial autocorrelation analysis of pipeline damage points.

[0011] (1) Grid division: Use GIS to divide the water supply network into several plane areas, then connect the damage points and pipeline attributes in each area, and calculate the damage density X of the i-th area. i , the expression is as follows:

[0012]

[0013] Where B i sum is the total number of damaged points in the i-th region; S i is the area of ​​the i-th region; L i sum is the total length of pipelines in the i-th area;

[0014] (2) Analysis of the spatial distribution characteristics of damage points: Moran's I index (MI) is used to calculate the degree of aggregation or dispersion of damage points in adjacent spaces. The expression is as follows:

[0015]

[0016] Where N is the number of regions in the water supply network; wij is the spatial weight of the connection between region i and region j; x i 、y j is the damage density corresponding to regions i and j. The calculation of damage density is shown in X i ; is the average damage density of all areas;

[0017] The MI value range is [-1, 1]. When MI>0, it indicates aggregation (positive correlation), indicating that adjacent areas have similar damage densities. The larger the MI value, the stronger the spatial positive correlation. MI<0 indicates dispersion (negative correlation), indicating that adjacent areas have different damage densities.

[0018] (3) Verification of statistical significance: To verify the statistical significance of the calculated MI, it is necessary to combine it with the standardized Z score; the calculation formula is as follows:

[0019]

[0020] Where E[MI] and V[MI] represent the mean and variance of MI, respectively. If the Z score is close to zero, it means that the calculated MI is statistically insignificant, regardless of whether the Z score is positive or negative. If the absolute value of the Z score is very large, the breakpoint event is statistically significant.

[0021] Step 3: Determine the optimal size of the spatial clustering grid.

[0022] Repeat the second step, divide the plane into grid areas of different sizes, and repeatedly calculate the MI and Z scores under different grid sizes, select the optimal value that meets formulas (2) and (3), and finally determine the grid size at the optimal value.

[0023] Step 4: Use GEP to establish a failure prediction model.

[0024] (1) Determine the influencing factors: Based on the complete information of the damaged pipeline, this method selects the pipe length L, pipe age A and pipe diameter D as the influencing factors. The number of damages per year B changes with the influencing factors.

[0025] (2) Data grouping: To obtain statistical significance, pipelines were grouped into homogeneous groups according to pipe diameter and age under the same pipe material conditions, and the total length and number of damaged pipelines in each group were added up respectively;

[0026] (3) GEP parameter setting: Ordinary cast iron pipes and ductile iron pipes were modeled. The independent variables used in the GEP modeling were pipe length L, pipe age A, and pipe diameter D, and the dependent variable was B. The function library was +, -, ×, ÷. Based on the above settings, a pipe network failure prediction model was established.

[0027] (4) Indicators of model fitting accuracy: The fitting accuracy and prediction degree of the failure prediction model are judged according to formulas (4) and (5) respectively;

[0028]

[0029]

[0030] In the formula, y m and Represent the predicted value (model fitting value) and actual predicted value of the mth homogeneous group data, represents the mean of the predicted values ​​(model fitted values), and M represents the total number of homogeneous groups in the failure model;

[0031] Fitting accuracy R 2 , which represents the ratio of the change in the independent variable to the explained response variable in the regression model, R 2 The larger the better. The root mean square error (RMSE) describes the prediction degree of the sample, and the smaller the RMSE, the better.

[0032] Step 5: Use regression analysis to fit the pipeline cost model.

[0033] The direct engineering costs of pipeline reconstruction typically include material costs, labor costs, and machinery costs. Using the Water Supply and Drainage Design Manual as a reference, regression analysis was used to fit a variable cost model per unit length of pipeline reconstruction. The cost depends on the pipe material and diameter, as shown in the following formula:

[0034] C=a+bD α (4)

[0035] Where C is the replacement cost per unit length (yuan / m); D is the pipe diameter; a, b, and α are the fitting coefficients obtained by fitting formula (6) based on the sample data;

[0036] Step 6: Establish optimization model.

[0037] (1) Input optimization data: Based on the optimal grid determined in the third step, and according to the variation pattern of the actual number of damaged pipes in the grid, the pipes in the grid are grouped. Since the divided spatial grid already has the characteristics of aggregation, the pipe diameter is used as the grouping criterion within the spatial grid area (pipes with the same diameter are grouped together).

[0038] (2) Setting the objective function: Structural failure is the main problem of pipeline aging, which usually leads to hydraulic failure and water quality failure. Considering that small-diameter pipelines are more prone to damage, and large-diameter pipelines cause greater damage, the importance weight of the pipe diameter is included to form the objective function (minimizing the number of damages). The specific formula is as follows:

[0039]

[0040] Where w k =D k / D max represents the relative weight of the diameter of the kth group among all the groups in the grid, D k is the diameter of the kth group weighted by the length of the pipe, and Dmax represents the maximum value of the weighted diameter in all grid groups; BR k is the number of broken pipelines in the kth group predicted by the pipeline failure model (calculated by the failure model established in step 4); K is the total number of groups in all grids (see step 6 (1)).

[0041] (3) Setting constraints: The workload of pipeline renovation is subject to the available budget. After determining the annual budget for pipeline renovation, the cost of pipeline renovation is converted into the constraints of the optimization model. The renovation cost is calculated by formula (6):

[0042]

[0043] Where Ck is the renovation cost of the kth group of pipelines; I k Indicates whether the kth group of pipelines has been modified, I k ={0, 1}, 1 means renovation, 0 means no renovation; [C] is the annual budget for the renovation of the entire pipeline network.

[0044] (4) Optimization using genetic algorithm: Using the genetic algorithm tool in Python software, input the optimization data ((1) in the sixth step), the objective function (Formula 7) and the constraint conditions (Formula 8) into the program, and run the program to finally obtain the optimal transformation plan for the pipeline; wherein, the population size of the program is set to 4 to 6 times the number of decision variables; the number of decision variables is the total number of groupings K of all grids; the crossover probability and mutation probability are set to 0.8 and 0.1 respectively; the evolutionary generation is set to 1500 generations.

[0045] Further comparison is made on the number of isolated pipe sections, the number of reduced breakages and the total length of pipelines renovated in the spatially clustered renovation schemes under the same budget constraints.

[0046] The beneficial effects of the present invention are mainly reflected in:

[0047] 1. The pipeline failure prediction model is established using GEP software. This method can quickly fit the model formula, and the formula structure is simple and intuitive, making it easier for water supply companies to understand the relationship between pipeline damage and influencing factors;

[0048] 2. Based on Moran's I spatial autocorrelation analysis, this method can identify the spatial clustering characteristics of damage points and determine hotspots prone to pipeline damage, highlighting key areas for renovation;

[0049] 3. The water supply pipeline renovation optimization model using spatial clustering method helps to reduce the number of isolated pipe sections, form clusters with larger total pipeline length, and reduce the impact of multiple construction sites. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of the present invention's "A method for optimizing and renovating water supply pipelines based on spatial grid clustering";

[0051] Figure 2 The result of spatial analysis of pipeline damage points;

[0052] Figure 3 This is a characteristic diagram of the changes in pipeline damage events, pipe diameter, and pipe age;

[0053] Figure 4 A spatial grid map divided based on the spatial characteristics of the damage point;

[0054] Figure 5The spatial location map of pipeline renovations is a comparison of spatial clustering and attribute clustering and non-clustering sorting. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the examples, but the present invention is not limited to the following examples.

[0056] Example 1

[0057] This example uses the water supply network of a city in northern China. The network is approximately 846 kilometers long and comprises 96,000 pipe sections, with 21.4% of the pipes over 30 years old. The database records physical properties and damage incidents of the pipes from 2009 to 2018, with a total of 1,226 damage points. Over 90% of the pipes in the network are made of conventional cast iron and ductile iron. Because the network has been installing ductile iron pipes on a large scale since 2000, and the total length of conventional cast iron pipes has been decreasing annually, the optimization and renovation targets are limited to conventional cast iron and ductile iron pipes with diameters of DN75 or greater.

[0058] Select the technical solution according to the steps in the invention content. The application results of this example can be seen in the attached Figure 2-5 According to the second step, we can get Figure 2 The results shown, Figure 4 This is the result obtained in the third step. Figure 3 The result obtained in the fourth step is Figure 5 The final result is the result of the plan.

Claims

1. A method for optimizing and renovating water supply pipelines based on spatial grid clustering, characterized in that: The method comprises the following steps: Step 1: Preliminary data preparation; In the urban water supply network's geographic information system (GIS), pipeline data, including pipe material, diameter, pipeline installation time, pipeline number, and damage point information, is extracted. The pipeline age is then calculated by subtracting the pipeline installation time from the observation time. Step 2: Spatial autocorrelation analysis of pipeline damage points; (1) Grid division: Use GIS to divide the water supply network into several plane areas, then connect the damage points and pipeline attributes in each area, and calculate the damage density X of the i-th area. i , the expression is as follows: Where, is the total number of damaged points in the i-th region; S i is the area of ​​the i-th region; is the total length of pipelines in the i-th area; (2) Analysis of the spatial distribution characteristics of damage points: Moran's I index (MI) is used to calculate the degree of aggregation or dispersion of damage points in adjacent spaces. The expression is as follows: Where N is the number of areas in the water supply network; w ij is the spatial weight of the connection between region i and region j; x i 、y j is the damage density corresponding to regions i and j. The calculation of damage density is shown in X i ; is the average damage density of all areas; The MI value range is [-1, 1]. When MI>0, it indicates aggregation, indicating that adjacent areas have similar damage densities. The larger the MI value, the stronger the spatial positive correlation. MI<0 indicates dispersion, indicating that adjacent areas have different damage densities. (3) Verification of statistical significance: To verify the statistical significance of the calculated MI, it is necessary to combine it with the standardized Z score; the calculation formula is as follows: Where E[MI] and V[MI] represent the mean and variance of MI, respectively. If the Z score is close to zero, it means that the calculated MI is statistically insignificant, regardless of whether the Z score is positive or negative. If the absolute value of the Z score is very large, the breakpoint event is statistically significant. Step 3: Determine the optimal size of the spatial clustering grid; Repeat the second step, divide the plane grid area into different sizes, and repeatedly calculate the MI and Z scores under different grid sizes, select the optimal value that meets formulas (2) and (3), and finally determine the grid size at the optimal value; Step 4: Use GEP to establish a failure prediction model; (1) Determine the influencing factors: Based on the complete information of the damaged pipeline, this method selects the pipe length L, pipe age A and pipe diameter D as the influencing factors. The number of damages per year B changes with the influencing factors. (2) Data grouping: To obtain statistical significance, pipelines were grouped into homogeneous groups according to pipe diameter and age under the same pipe material conditions, and the total length and number of damaged pipelines in each group were added up respectively; (3) GEP parameter setting: Ordinary cast iron pipes and ductile iron pipes were modeled. The independent variables used in the GEP modeling were pipe length L, pipe age A, and pipe diameter D, and the dependent variable was B. The function library was +, -, ×, ÷. Based on the above settings, a pipe network failure prediction model was established. (4) Indicators of model fitting accuracy: The fitting accuracy and prediction degree of the failure prediction model are judged according to formulas (4) and (5) respectively; In the formula, y m and Represent the predicted value of the mth homogeneous group data, namely the model fitting value and the actual predicted value, respectively. represents the mean of the predicted values, and M represents the total number of homogeneous groups in the failure model; Fitting accuracy R 2 , which represents the ratio of the change in the independent variable to the explained response variable in the regression model, R 2 The larger the better; the root mean square error RMSE indicates the prediction degree of the sample, the smaller the RMSE, the better; Step 5: Use regression analysis to fit the pipeline cost model; The direct engineering costs of pipeline reconstruction typically include material costs, labor costs, and machinery costs. Using the Water Supply and Drainage Design Manual as a reference, regression analysis was used to fit a variable cost model per unit length of pipeline reconstruction. The cost depends on the pipe material and diameter, as shown in the following formula: C=a+bD α (6) Where C is the replacement cost per unit length, RMB / m; D is the pipe diameter; a, b, and α are the fitting coefficients obtained by fitting formula (6) based on the sample data; Step 6: Establish optimization model; (1) Input optimization data: Based on the optimal grid determined in the third step, and according to the variation pattern of the actual number of damaged pipes in the grid, the pipes in the grid are grouped. Since the divided spatial grid already has the characteristics of aggregation, the diameter is used as the only grouping criterion within the spatial grid area, and pipes with the same diameter are grouped together. (2) Setting the objective function: Structural failure is the main problem of pipeline aging, which usually leads to hydraulic failure and water quality failure. Considering that small-diameter pipelines are more prone to damage, and large-diameter pipelines cause greater damage, the importance weight of the pipe diameter is included to form the objective function, that is, to minimize the number of damages. The specific formula is as follows: Where w k =D k / D max represents the relative weight of the diameter of the kth group among all the groups in the grid, D k is the diameter of the kth group weighted by the length, D max Indicates the maximum value of weighted pipe diameter in all grid groups; BR k is the number of broken pipelines in the kth group predicted by the pipeline failure model; K is the total number of groups in all grids; (3) Setting constraints: The workload of pipeline renovation is subject to the available budget. After determining the annual budget for pipeline renovation, the cost of pipeline renovation is converted into the constraints of the optimization model. The renovation cost is calculated by formula (6): Where C k is the renovation cost of the kth group of pipelines; I k Indicates whether the kth group of pipelines has been modified, I k = {0, 1}, 1 indicates renovation, 0 indicates no renovation; [C] is the annual budget for renovation of the entire pipeline network; (4) Optimization using genetic algorithm: Using the genetic algorithm tool in Python software, input the optimization data, objective function and constraints into the program, and run the program to finally obtain the optimal transformation plan for the pipeline; the population size of the program is set to 4 to 6 times the number of decision variables; the number of decision variables is the total number of groupings K of all grids; the crossover probability and mutation probability are set to 0.8 and 0.1 respectively; the evolutionary generation is set to 1500 generations.

2. The method for optimizing and renovating water supply pipelines based on spatial grid clustering according to claim 1, characterized in that: The number of isolated pipe sections, the number of reduced breakages, and the total length of renovated pipelines in the spatially clustered renovation schemes under the same budget constraints.

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