A water supply network optimal chlorination method based on a type-2 fuzzy chance-constrained programming model

Abstract

This invention proposes an optimal chlorination method for water supply networks based on a Type 2 fuzzy chance-constrained programming (T2FCCP) model, and applies it to a case study of a water supply system (WDS) to verify the effectiveness of the hydraulic cost optimization method under uncertainty. After establishing the T2FCCP model, the model is transformed into upper and lower membership function sub-models and solved to obtain the minimum chlorination cost under different confidence levels and manager attitudes. The results show that the minimum minimum upper membership function (UMF), minimum lower membership function (LMF), and compromise cost are only related to α2. U α2 L Furthermore, the λ value, reflecting the manager's optimistic attitude, and the relationship between α and α also affect the minimum hydraulic cost. This invention can effectively handle multiple uncertainties in water quality indicators. Under the premise of ensuring water supply safety, it optimizes chlorination costs by coordinating the manager's risk preferences, providing scientific support for dynamic disinfection decisions in complex environments.

Description

Technical Field

[0001] This invention belongs to the field of municipal engineering and relates to an optimal chlorination method for water supply networks based on a type 2 fuzzy chance-constrained programming model. Background Technology

[0002] Water distribution networks (WDS) provide drinking water and safe drinking water to two-thirds of the world's population, making them a vital infrastructure asset for society. However, this transportation process is not stable, and water quality can degrade through biological and chemical processes with natural organic matter. For example, chlorine can react with microorganisms in bulk water and pipe walls to form carcinogenic disinfection byproducts (DBPs), potentially posing health risks, especially chlorine. A common approach is to begin conventional chlorine-enhanced disinfection at the early stages of WDS deployment. However, this disinfection approach is often complex because the reaction processes in WDS are not fully understood. Furthermore, unknown reaction processes can interact with uncertain parameters (such as node requirements, reaction rates, and cost coefficients), which can affect water supply schemes. Therefore, effective and economical booster schemes are needed to address complex and uncertain problems. This invention uses a type 2 fuzzy chance-constrained model to address chlorination strategies in water transport and attempts to find methods to reduce costs. Summary of the Invention

[0003] The purpose of this invention is to address the difficulty in predicting chlorination strategies under uncertain chlorine concentration conditions. This invention introduces a Type 2 fuzzy chance-constrained programming (T2FCCP) model to find chlorination strategies that reduce hydraulic costs, while considering the uncertainty of chlorine concentration and the manager's optimism to obtain the lowest chlorination cost.

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

[0005] An optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model includes the following steps:

[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 uncertainty conditions in the water supply network into a suitable trapezoidal membership function;

[0009] S4. Using the Type 2 Fuzzy Chance Constraint Programming (T2FCCP) model, we consider the chlorine concentration uncertainty condition and the manager's optimistic attitude.

[0010] S5. Obtain the optimal chlorination amount under different confidence levels and the manager's optimistic attitude.

[0011] 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.

[0012] Furthermore, in step S2, the hydraulic model of the pipe network is as follows:

[0013]

[0014]

[0015] Among them, Q in and Q out Let q represent the flow rates at the inflow and outflow nodes, q be the node demand, and ΔH be the pipe head loss. These flow rate and head constraints are implemented using hydraulic and water quality simulations in EPANET software.

[0016] Further, in step S3, the uncertainty conditions include the pipe wall roughness coefficient, the chlorine bulk attenuation coefficient, and the chlorine pipe wall attenuation coefficient; the corresponding trapezoidal fuzzy membership function is:

[0017]

[0018] in, UMF is the upper membership function. The membership function is the lower membership function (LMF). Let x be the x-coordinate of the trapezoidal vertex in the UMF; Let x be the x-coordinate of the trapezoidal vertex of the LMF; These are the heights of the UMF and LMF, respectively.

[0019] Furthermore, in step S4, the T2FCCP model of type 2 fuzzy chance constraint programming is used to consider the chlorine concentration uncertainty condition and the manager's optimistic attitude; the specific steps are as follows:

[0020] (1) Establish a type 2 fuzzy chance-constrained programming (T2FCCP) model;

[0021] (2) The T2FCCP model is divided into an upper membership function UMF sub-model and a lower membership function LMF sub-model and solved separately to obtain the minimum upper membership function UMF, minimum lower membership function LMF and compromise cost under different pre-confidence levels α and manager optimistic and pessimistic attitude values ​​λ; among them, the UMF and LMF corresponding to the upper and lower limits of chlorine concentration are α1U, α1L, α2U and α2L, respectively;

[0022] (3) The T2FCCP model was applied to a water supply network example for analysis by establishing a pipeline hydraulic model using EPANET software and performing hydraulic simulation.

[0023] (4) Controlling variables, analyzing data, and obtaining the patterns of the influence of credibility level and managerial optimism on it; that is, the minimum UMF, LMF, and compromise cost are only related to α2U and α2L; and reflecting the λ value of managerial optimism and the relationship between α and λw L The relationship also affects the minimum hydraulic cost.

[0024] The Type 2 fuzzy chance-constrained programming (T2FCCP) model is as follows:

[0025]

[0026] in, Let be the chlorination dosage decision vector for each chlorination station; Let A be the total cost function for chlorination; A is the chlorine concentration response coefficient matrix. The interval is a type-II fuzzy set representing the upper limit of chlorine concentration; The interval is a type-II fuzzy set representing the upper limit of chlorine concentration; These represent the pre-confidence levels of the upper and lower bound constraints, respectively. A measure of the credibility of ambiguous events.

[0027] The upper membership function UMF sub-model and the lower membership function LMF sub-model are respectively:

[0028]

[0029]

[0030] in, The minimum chlorination cost is obtained for the UMF sub-model and the LMF sub-model, respectively. To determine the pre-confidence level of the upper and lower limits of chlorine concentration constraints in the UMF sub-model; To determine the pre-confidence level of the upper and lower limits of chlorine concentration constraints in the LMF sub-model;

[0031] The minimum upper membership function (UMF), minimum lower membership function (LMF), and compromise cost under different pre-confidence levels α and the manager's optimistic and pessimistic attitude values ​​λ are as follows: .in, To compromise on chlorination costs, the arithmetic average of UMF and LMF costs was used as a cost reference for the final solution.

[0032] The λ value of the manager's optimistic attitude and α and The relationship affects the minimum hydraulic cost as follows: the minimum chlorination cost obtained under an optimistic attitude (i.e., a higher λ value) is greater than the minimum chlorination cost obtained under a pessimistic attitude (i.e., a lower λ value), and this is true when the confidence level satisfies... The minimum compromise cost of chlorination at that time is much smaller than Cost of time.

[0033] Furthermore, in step S5, the optimal chlorination amount under different confidence levels and the manager's optimistic attitude is: by solving the separated UMF and LMF deterministic sub-models, the chlorination amount decision vector x at each node that minimizes the total hydraulic chlorination cost z under the constraints of the current confidence level α and the manager's attitude parameter λ is output. j The optimal solution.

[0034] The beneficial effects of this invention are: it can effectively handle multiple uncertainties in water quality indicators, and under the premise of ensuring water supply safety, it optimizes chlorination costs by coordinating the risk preferences of managers, thus providing scientific support for dynamic disinfection decisions in complex environments. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention.

[0036] Figure 2 The diagrams show the minimum UMF, LMF, and compromise chlorination cost for different λ values ​​and pre-confidence levels. (a) shows the minimum UMF chlorination cost for different λ values ​​and pre-pre-confidence levels, (b) shows the minimum LMF chlorination cost for different λ values ​​and pre-pre-confidence levels, and (c) shows the minimum compromise chlorination cost for different λ values ​​and pre-pre-confidence levels. Detailed Implementation

[0037] 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.

[0038] The specific embodiments of this invention patent are as follows:

[0039] like Figure 1 As shown, this invention provides an optimal chlorination method for water supply networks based on a type 2 fuzzy chance-constrained programming model, comprising the following steps:

[0040] 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).

[0041] 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.

[0042] 3. Transform the uncertainty conditions (pipe wall roughness coefficient, chlorine gas attenuation coefficient, chlorine wall attenuation coefficient) into a suitable trapezoidal membership function.

[0043] 4. The uncertainty of chlorine concentration and the manager's optimistic attitude are considered using a Type 2 fuzzy chance-constrained programming (T2FCCP) model. The specific steps are as follows:

[0044] (1) Establish a Type 2 fuzzy chance-constrained programming (T2FCCP) model.

[0045] (2) The T2FCCP model is divided into an upper membership function (UMF) sub-model and a lower membership function (LMF) sub-model, which are solved separately to obtain the minimum upper membership function (UMF), minimum lower membership function (LMF), and compromise cost under different pre-confidence levels α and manager's optimistic and pessimistic attitude values ​​λ; among them, the UMF and LMF corresponding to the upper and lower limits of chlorine concentration are respectively α1 U α1 L α2 U α2 L .

[0046] (3) The hydraulic model of the pipeline network was established by EPANET software and the T2FCCP was applied to the water supply network example for analysis.

[0047] (4) Controlling variables and analyzing data, we can obtain the patterns of the influence of credibility level and managerial optimism on it; that is, the minimum UMF, LMF, and compromise cost are only related to α2. U α2 L Related to; and reflecting the λ value and α value of managers' optimistic attitude. The relationship also affects the minimum hydraulic cost.

[0048] 5. Finally, the optimal chlorination amount was obtained under different confidence levels and the manager's optimistic attitude.

[0049] like Figure 2 As shown, the minimum UMF chlorination cost, minimum LMF chlorination cost, and compromise minimum chlorination cost all increase with increasing pre-confidence level. At a given pre-confidence level, UMF, LMF, and compromise minimum chlorination cost all increase with increasing λ value. The results indicate that the minimum chlorination cost planned under an optimistic attitude is higher than that planned under a pessimistic attitude; furthermore, when the pre-confidence level satisfies... At that time, the minimum compromise cost of chlorination obtained was far lower than This provides managers with an intuitive strategic reference for controlling the economic costs of pipeline networks by adjusting risk tolerance.

[0050] 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. An optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model, characterized in that, Includes the following steps: 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 uncertainty conditions in the water supply network into a suitable trapezoidal membership function; S4. Using the Type 2 Fuzzy Chance Constraint Programming (T2FCCP) model, we consider the chlorine concentration uncertainty condition and the manager's optimistic attitude. S5. Obtain the optimal chlorination amount under different confidence levels and the manager's optimistic attitude.

2. The optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model 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 optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model according to claim 1, characterized in that, In step S2, the hydraulic model of the pipeline network is as follows: Among them, Q in and Q out Let q represent the flow rates at the inflow and outflow nodes, q be the node demand, and ΔH be the pipe head loss. These flow rate and head constraints are implemented using hydraulic and water quality simulations in EPANET software.

4. The optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model according to claim 1, characterized in that, In step S3, the uncertainty conditions include the pipe wall roughness coefficient, the chlorine bulk attenuation coefficient, and the chlorine pipe wall attenuation coefficient; the corresponding trapezoidal fuzzy membership function is: in, UMF is the membership function. Let LMF be the membership function. Let x be the x-coordinate of the trapezoidal vertex in the UMF; Let x be the x-coordinate of the trapezoidal vertex of the LMF; These are the heights of the UMF and LMF, respectively.

5. The optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model according to claim 1, characterized in that, In step S4, the T2FCCP model of type 2 fuzzy chance constraint programming is used to consider the chlorine concentration uncertainty condition and the manager's optimistic attitude. The specific steps are as follows: (1) Establish a type 2 fuzzy chance-constrained programming (T2FCCP) model; (2) The T2FCCP model is divided into an upper membership function UMF sub-model and a lower membership function LMF sub-model and solved separately to obtain the minimum upper membership function UMF, minimum lower membership function LMF and compromise cost under different pre-confidence levels α and manager optimistic and pessimistic attitude values ​​λ; among them, the UMF and LMF corresponding to the upper and lower limits of chlorine concentration are α1U, α1L, α2U and α2L, respectively; (3) The T2FCCP model was applied to a water supply network example for analysis by establishing a pipeline hydraulic model using EPANET software and performing hydraulic simulation. (4) Controlling variables, analyzing data, and obtaining the patterns of the influence of credibility level and managerial optimism on it; that is, the minimum UMF, LMF, and compromise cost are only related to α2U and α2L; and reflecting the λ value of managerial optimism and the relationship between α and The relationship also affects the minimum hydraulic cost.

6. The optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model according to claim 5, characterized in that, The Type 2 fuzzy chance-constrained programming (T2FCCP) model is as follows: in, : Decision vector for chlorination dosage at each chlorination station; Let A be the total cost function for chlorination; A is the chlorine concentration response coefficient matrix. The interval is a type-II fuzzy set representing the upper limit of chlorine concentration; The interval is a type-II fuzzy set representing the upper limit of chlorine concentration; These represent the pre-confidence levels of the upper and lower bound constraints, respectively. For measuring the credibility of ambiguous events; The upper membership function UMF sub-model and the lower membership function LMF sub-model are respectively: in, The minimum chlorination cost is obtained for the UMF sub-model and the LMF sub-model, respectively. To determine the pre-confidence level of the upper and lower limits of chlorine concentration constraints in the UMF sub-model; To determine the pre-confidence level of the upper and lower limits of chlorine concentration constraints in the LMF sub-model; The minimum upper membership function (UMF), minimum lower membership function (LMF), and compromise cost under different pre-confidence levels α and the manager's optimistic and pessimistic attitude values ​​λ are as follows: ;in, To compromise on chlorination costs, the arithmetic average of UMF and LMF costs was used as a cost reference for the final solution. The λ value α of the manager's optimistic attitude and its relation to The relationship affects the minimum hydraulic cost as follows: the minimum chlorination cost obtained under an optimistic attitude is greater than the minimum chlorination cost obtained under a pessimistic attitude; and, when the confidence level meets the following conditions... The minimum compromise cost of chlorination at that time is much smaller than Cost of time.

7. The optimal chlorination method for water supply networks based on a type-2 fuzzy chance-constrained programming model according to claim 1, characterized in that, In step S5, the optimal chlorination amount under different confidence levels and the manager's optimistic attitude is: by solving the separated UMF and LMF deterministic sub-models, the chlorination amount decision vector x at each node is output, which minimizes the total hydraulic chlorination cost z under the constraints of the current confidence level α and the manager's attitude parameter λ. j The optimal solution.

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