A method for analyzing the fuzziness of water quality indexes of a water supply network under uncertain conditions

Abstract

This invention provides a fuzzy analysis method for water quality indicators in water supply networks under uncertain conditions. The steps are as follows: Key parameters of the water supply network and its .NET files are collected, including basic network operation data, network attribute data, and actual data. Then, a hydraulic model of the network is established using EPANET software, and its hydraulic simulation function is used to verify the model's effectiveness and accuracy. Uncertain conditions (pipe wall roughness coefficient, chlorine decay coefficient, chlorine wall decay coefficient) are transformed into suitable fuzzy membership functions. Based on the MATLAB environment, a genetic algorithm (GA) is applied at each roughness coefficient α-cut level to obtain the minimum and maximum pipe flow rate and node pressure, using fuzziness measurement (…). FM This invention describes the fuzziness and compares the nodal fuzziness of chlorine concentration with water age. It facilitates the fuzziness analysis of hydraulic simulation results for water supply networks under uncertain pipe roughness coefficients.

Description

Technical Field

[0001] This invention belongs to the field of municipal engineering and relates to a method for analyzing the fuzziness of water quality indicators under uncertain conditions. Background Technology

[0002] Urban water supply networks are complex systems. Public drinking water utilities are responsible for providing safe drinking water to consumers through these systems, which aim to provide high-quality water. In reality, different users have different requirements for water quantity and quality. Water quality simulation is affected by factors such as pipe roughness coefficient, chlorine volume decay coefficient, and chlorine wall decay coefficient. These coefficients are uncertain, making the reactions in the water supply system complex, leading to water quality deterioration and making simulation difficult. Summary of the Invention

[0003] The purpose of this invention is to address the difficulties brought about by uncertainties in water quality analysis of water supply networks. This invention provides an analysis method for the fuzziness of water quality indicators under uncertain conditions, optimizes the uncertainty analysis method and water quality assurance algorithm for water supply networks, and brings practical significance to the research on water quality assurance in water supply networks.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A fuzzy analysis method for water quality indicators in water supply networks under uncertain conditions, the specific steps of which are as follows:

[0006] S1. Collect key parameters of the water supply network and its net files, including basic network operation data, network attribute data, and actual data;

[0007] S2. Establish a hydraulic model of the pipeline network using EPANET software and verify the effectiveness and accuracy of the model using its hydraulic simulation function;

[0008] S3. Transform the uncertain conditions into a suitable fuzzy membership function; where the uncertain conditions include the pipe wall roughness coefficient, the chlorine gas attenuation coefficient, and the chlorine wall attenuation coefficient.

[0009] S4. In a MATLAB-based environment, the Genetic Algorithm (GA) is applied at each α-cut level of the roughness coefficient to obtain the minimum and maximum pipe flow and node pressure. The fuzziness is described by the fuzziness metric FM, and the node fuzziness is compared with that of chlorine concentration and water age.

[0010] Furthermore, in step S1, the basic data for pipeline operation includes node water pressure, water volume, and elevation; the pipeline attribute data includes water pumps, pipes, and water sources; and the actual data includes water volume change curves and pipeline water volume.

[0011] Furthermore, in step S2, the effectiveness and accuracy of the pipeline hydraulic model are determined by its hydraulic reliability. Residual chlorine reliability For verification, please refer to formulas (1) and (2):

[0012]

[0013] in, yes node Reliability of water pressure at all times; Under normal circumstances node The pressure of constant time; yes Minimum acceptable pressure level at the node; yes Node expected pressure level.

[0014]

[0015] in, yes node Reliability of residual chlorine at any given time; Under normal circumstances node The residual chlorine concentration at any given time; It is the lowest acceptable residual chlorine concentration; This is the highest acceptable residual chlorine concentration; This is the expected lower limit of residual chlorine concentration; This is the expected upper limit of residual chlorine concentration.

[0016] Further, in step S3, the fuzzy membership function representing the transformation of the pipe wall roughness coefficient, chlorine gas attenuation coefficient, and chlorine wall attenuation coefficient is expressed as ( , , , ), The subscripts are related to the five α-cuts: 0.2, 0.4, 0.6, 0.8, and 1.0. These variables are normalized according to formula (3):

[0017]

[0018] in, For the normalized value of the variable, For variables The minimum value, For variables The maximum value. After normalization, the variable Defined within the interval [0,1], a normalized trapezoidal membership function is obtained, and the fuzziness of the variable is represented by formula (4):

[0019]

[0020] in, Refers to ambiguity measurement, and Referring to trapezoids and rectangles, the greater the ambiguity, the closer the area of ​​the trapezoid is to that of the rectangle. The ambiguity is highest when the value is 1.0. The ambiguity is minimal when the value is 0.0.

[0021] Furthermore, in step S4, a water quality model is established and analyzed using a genetic algorithm (GA) in the MATLAB environment; the analysis process is as follows:

[0022] (1) Select a water supply network and prepare the input file for the program code by calling the EPANET toolkit;

[0023] (2) Define the upper and lower boundary values ​​of the pipe roughness coefficient, chlorine volume decay coefficient and chlorine wall decay coefficient for each cutting level;

[0024] (3) Run hydraulic and water quality simulations using EPANET and collect simulation results using the EPANET toolkit;

[0025] (4) The extreme values ​​of the output parameters at each cutting level are obtained using a genetic algorithm in the MATLAB environment;

[0026] (5) Plot the distribution function of node chlorine concentration and node water age, use the fuzziness measure FM to describe the fuzziness and compare the node fuzziness of chlorine concentration and water age.

[0027] (6) Obtain the fuzziness results of water quality indicators by analyzing the fuzziness measure FM.

[0028] The beneficial effects of this invention are as follows: Compared to the original triangular fuzzy membership function, the trapezoidal fuzzy membership function results in an output value with a variance closer to the target value and better output stability. Furthermore, the trapezoidal fuzzy model allows for more flexible membership function representations, covering values ​​within a range, while the triangular model can only represent a single peak. The trapezoidal model is more advantageous when representing complex scenarios. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention.

[0030] Figure 2 This is a diagram of the water supply network layout.

[0031] Figure 3 The trapezoidal fuzzy distribution diagram of the input parameters.

[0032] Figure 4 Normalized trapezoidal membership function graph.

[0033] Figure 5 This is a comparison chart of the reliability of water supply networks under three levels of uncertainty.

[0034] Figure 6 Sensitivity analysis diagrams of the effects of independent variables on dependent variables. (a) Sensitivity analysis of reservoir water level on pressure, (b) Sensitivity analysis of node water demand variation coefficient on pressure, (c) Sensitivity analysis of pipeline roughness variation on pressure, (d) Sensitivity analysis of reservoir water level on residual chlorine concentration, (e) Sensitivity analysis of node water demand variation coefficient on residual chlorine concentration, (f) Sensitivity analysis of pipeline roughness variation on residual chlorine concentration, (g) Sensitivity analysis of residual chlorine attenuation coefficient variation on residual chlorine concentration. Detailed Implementation

[0035] The technical solution of the present invention will now be described in full and clearly with reference to the accompanying drawings in the embodiments of the present invention.

[0036] The specific embodiments of this invention patent are as follows:

[0037] like Figure 1 As shown, this invention provides a fuzzy analysis method for water quality indicators in water supply networks under uncertain conditions. The specific steps are as follows:

[0038] 1. Collect key parameters of the water supply network and its .NET files, including basic network operation data (node ​​water pressure, water volume, elevation, etc.), network attribute data (data related to pumps, pipes, water sources, etc.), and actual data (water volume change curves, network water volume).

[0039] 2. Establish a hydraulic model of the pipeline network using EPANET software and verify the effectiveness and accuracy of the model using its hydraulic simulation function.

[0040] 3. Transform the uncertain conditions (pipe wall roughness coefficient, chlorine gas attenuation coefficient, chlorine wall attenuation coefficient) into a suitable trapezoidal membership function.

[0041] 4. Establish a water quality model and analyze it using a genetic algorithm (GA) in the MATLAB environment. The analysis process is as follows:

[0042] (1) Select a water supply network and prepare the input file for the program code by calling the EPANET toolkit;

[0043] (2) Define the upper and lower boundary values ​​of the pipe roughness coefficient, chlorine volume decay coefficient and chlorine wall decay coefficient for each cutting level;

[0044] (3) Run hydraulic and water quality simulations using EPANET and collect simulation results using the EPANET toolkit;

[0045] (4) The extreme values ​​of the output parameters at each cutting level are obtained using a genetic algorithm in the MATLAB environment;

[0046] (5) Plot the distribution function of node chlorine concentration and node water age, use the fuzziness measure FM to describe the fuzziness and compare the node fuzziness of chlorine concentration and water age.

[0047] (6) Obtain the fuzziness results of water quality indicators by analyzing the fuzziness measure FM.

[0048] like Figure 2 As shown, the diagram displays the pipe length (m), pipe diameter (mm), pipe segment number, water demand at each node, and node number for each pipe segment. This pipe network is a single-source network with three loops, 12 pipes, and two pumps.

[0049] like Figure 3 As shown, the three uncertain variables—pipe wall roughness coefficient, chlorine gas attenuation coefficient, and chlorine wall attenuation coefficient—are described as fuzzy parameters with fuzziness, using a trapezoidal membership function.

[0050] like Figure 4 As shown, the ambiguity FM can be obtained from the area of ​​the normalized trapezoidal membership function graph.

[0051] like Figure 5 As shown, the fuzziness of FM is used to describe the existing influencing factors, and three different levels—uncertainty level I, uncertainty level II, and uncertainty level III (uncertainty level from low to high)—are used to measure the uncertainty of the influencing factors. The reliability of the pipeline system is obtained by comprehensively analyzing the reliability of water pressure and residual chlorine at each node after calculating the reliability of water pressure and residual chlorine at each node using formulas (1) and (2). According to the data, the higher the uncertainty level, the lower the reliability of the pipeline system.

[0052] like Figure 6 As shown, taking the output data of the 8th node in the pipeline network system during the 10th time period as an example, the specific effects of the input parameters on the output parameters are as follows: the pressure at the node is positively correlated with the reservoir water level, and negatively correlated with the node water demand and the pipeline roughness coefficient; while the residual chlorine concentration at the node is mainly affected by the pipeline residual chlorine decay coefficient, and its value decreases linearly as the coefficient increases, and there is no obvious correlation with the reservoir water level, the node water demand and the pipeline roughness coefficient.

[0053] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A method for fuzzy analysis of water quality indicators in a water supply network under uncertain conditions, characterized in that, The specific steps are as follows: S1. Collect key parameters of the water supply network and its net files, including basic network operation data, network attribute data, and actual data; S2. Establish a hydraulic model of the pipeline network using EPANET software and verify the effectiveness and accuracy of the model using its hydraulic simulation function; S3. Transform the uncertain conditions into a suitable fuzzy membership function; where the uncertain conditions include the pipe wall roughness coefficient, the chlorine gas attenuation coefficient, and the chlorine wall attenuation coefficient. S4. In a MATLAB-based environment, the Genetic Algorithm (GA) is applied at each α-cut level of the roughness coefficient to obtain the minimum and maximum pipe flow and node pressure. The fuzziness is described by the fuzziness metric FM, and the node fuzziness is compared with that of chlorine concentration and water age.

2. The method for fuzzy analysis of water quality indicators in a water supply network under uncertain conditions according to claim 1, characterized in that: In step S1, the basic data for pipeline operation includes node water pressure, water volume, and elevation; the pipeline attribute data includes water pumps, pipes, and water sources; and the actual data includes water volume change curves and pipeline water volume.

3. The method for fuzzy analysis of water quality indicators in a water supply network under uncertain conditions according to claim 1, characterized in that: In step S2, the validity and accuracy of the pipeline hydraulic model are determined by its hydraulic reliability. Residual chlorine reliability For verification, please refer to formulas (1) and (2): in, yes node Reliability of water pressure at all times; Under normal circumstances node The pressure of constant time; yes Minimum acceptable pressure level at the node; yes Node expected pressure level; in, yes node Reliability of residual chlorine at any given time; Under normal circumstances node The residual chlorine concentration at any given time; It is the lowest acceptable residual chlorine concentration; This is the highest acceptable residual chlorine concentration; This is the expected lower limit of residual chlorine concentration; This is the expected upper limit of residual chlorine concentration.

4. The method for fuzzy analysis of water quality indicators in a water supply network under uncertain conditions according to claim 1, characterized in that: In step S3, the fuzzy membership function representing the transformation of the pipe wall roughness coefficient, chlorine gas attenuation coefficient, and chlorine wall attenuation coefficient is expressed as ( , , , ), The subscripts are related to the five α-cuts: 0.2, 0.4, 0.6, 0.8, and 1.

0. These variables are normalized according to formula (3): in, For the normalized value of the variable, For variables The minimum value, For variables The maximum value; after normalization, the variable Defined within the interval [0,1], a normalized trapezoidal membership function is obtained, and the fuzziness of the variable is represented by formula (4): in, Refers to ambiguity measurement. and Referring to trapezoids and rectangles, the greater the ambiguity, the closer the area of ​​the trapezoid is to that of the rectangle; when... The ambiguity is highest when the value is 1.

0. The ambiguity is minimal when the value is 0.

0.

5. The method for fuzzy analysis of water quality indicators in a water supply network under uncertain conditions according to claim 1, characterized in that: In step S4, a water quality model is established and analyzed using the Genetic Algorithm (GA) in the MATLAB environment; the analysis process is as follows: (1) Select a water supply network and prepare the input file for the program code by calling the EPANET toolkit; (2) Define the upper and lower boundary values ​​of the pipe roughness coefficient, chlorine volume decay coefficient and chlorine wall decay coefficient for each cutting level; (3) Run hydraulic and water quality simulations using EPANET and collect simulation results using the EPANET toolkit; (4) The extreme values ​​of the output parameters at each cutting level are obtained using a genetic algorithm in the MATLAB environment; (5) Plot the distribution function of node chlorine concentration and node water age, use the fuzziness measure FM to describe the fuzziness and compare the node fuzziness of chlorine concentration and water age. (6) Obtain the fuzziness results of water quality indicators by analyzing the fuzziness measure FM.

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