An improved pareto optimization method and system for pipe network hydraulic regulation based on the method of characteristics

Abstract

This invention discloses a method and system for improved Pareto optimization of pipeline hydraulic control based on the method of characteristics, belonging to the field of hydraulic transient calculation technology. The method includes: constructing a one-dimensional characteristic line method numerical simulation model of pipeline transient flow to simulate the transient processes of pressure and flow during pipeline hydraulic control; constructing a multi-objective optimization model and solving it using an intensity Pareto evolution algorithm improved by chaotic mapping to obtain the Pareto optimal solution set; determining the optimal pipeline hydraulic control scheme based on the subjective and objective combination weighting method of entropy weighting and the VIKOR comprehensive evaluation method; substituting the optimal control scheme into the one-dimensional characteristic line method numerical simulation model of pipeline transient flow, comparing it with the initial scheme, and verifying the effectiveness of the optimization algorithm and the control effect. This method can solve the core problems in existing pipeline valve control methods, such as insufficient convergence and solution diversity of multi-objective optimization algorithms, poor suppression of water hammer during valve closure, and insufficient scientific rigor in selecting the optimal scheme.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic transient calculation technology, and specifically relates to an improved Pareto optimization method and system for pipeline hydraulic control based on the method of characteristics. Background Technology

[0002] Pipelines are a crucial component of water supply systems. However, with changing water demand, the investment cost and safe operation of pipelines have become increasingly important. Traditional pipeline design typically relies on designers' experience, using the economic flow velocity method to determine pipe diameter. This method is highly subjective, and the calculated pipe diameter often falls outside the commercially viable range, requiring approximate rounding. This makes it difficult to obtain a globally optimal design, easily leading to problems such as high project investment, high operating energy consumption, and uneven water pressure. Inadequate pipeline engineering can easily cause pipe bursts in areas of excessively high water pressure and unstable water supply in areas of excessively low pressure. Therefore, pipeline engineering planning should consider balancing water pressure within the pipeline system to reduce the probability of accidents and improve the reliability and flow uniformity of the pipeline system.

[0003] In pipeline network operation and management, hydraulic transients (water hammer) caused by valve opening and closing, pump station start-up and shutdown, etc., are one of the main causes of pipeline rupture and equipment damage. The Method of Characteristics (MOC) can handle complex hydraulic systems and boasts high numerical accuracy, simple operation, high feasibility, and strong comprehensive performance. It has become the most commonly used method for numerical calculation of unsteady flow in pipeline hydraulic systems and is widely used for simulation analysis of pipeline transient processes. However, the MOC method itself lacks optimization capabilities. Traditionally, it relies on engineering experience or trial-and-error methods to determine valve operation schemes, making it difficult to achieve optimization of multi-valve joint control in complex pipeline systems.

[0004] In existing technologies, intelligent optimization algorithms such as genetic algorithms and particle swarm optimization have been introduced into valve operation optimization. However, most studies employ single-objective optimization or transform multi-objective problems into single-objective problems, failing to accurately reflect the trade-offs between multiple performance indicators. Pareto genetic algorithms, by introducing Pareto dominance relationships into genetic algorithms, avoid the traditional approach of transforming multi-objective optimization problems into single-objective problems through weight coefficients, thus improving the objectivity of the algorithm's solution. Currently, Pareto genetic algorithms mainly include non-dominated sorting genetic algorithms and intensive Pareto genetic algorithms. The former suffers from high computational complexity when handling high-dimensional multi-objective problems. Strength Pareto Genetic Algorithm (SPEA2) is an optimization algorithm for multi-objective irrigation network optimization problems. SPEA2, also known as the Strength Pareto Evolutionary Algorithm, is a multi-objective evolutionary algorithm that can directly solve for the Pareto optimal solution set, avoiding the subjectivity of weight setting. However, the standard SPEA2 suffers from slow convergence speed, insufficient population diversity, and susceptibility to local optima when dealing with high-dimensional, strongly constrained, and nonlinear transient optimization problems in irrigation networks.

[0005] Therefore, there is an urgent need for an improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics, capable of intelligent optimization and regulation that simultaneously considers pressure safety and irrigation uniformity. This addresses the lack of a systematic approach in existing technologies that deeply couples efficient multi-objective optimization algorithms with high-precision transient flow numerical models, leading to insufficient feasibility and reliability of optimization results in practical engineering, particularly in lightweight pipeline systems such as irrigation networks, where there is a contradiction between water hammer pressure control caused by valve operation and ensuring flow uniformity. Summary of the Invention

[0006] The purpose of this invention is to provide an improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics, comprising the following steps:

[0007] Step S1: Construct a one-dimensional characteristic line method numerical simulation model of transient flow in the pipeline network to simulate the transient process of pressure and flow during hydraulic regulation of the pipeline network.

[0008] Step S2: Construct a multi-objective optimization model, including: constructing the optimization objective and designing constraints;

[0009] Step S3: Solve the multi-objective optimization model using the intensity Pareto evolution algorithm based on chaotic mapping to obtain the Pareto optimal solution set;

[0010] Step S4: Based on the Pareto optimal solution set, the optimal hydraulic control scheme for the pipeline network is determined by combining subjective and objective weighting using the entropy weight method and the VIKOR comprehensive evaluation method.

[0011] Step S5: Input the optimal hydraulic control scheme of the pipeline network into the numerical simulation model of the transient flow of the pipeline network using the one-dimensional characteristic line method, and compare the initial scheme and the optimized scheme to verify the effectiveness and control effect of the optimal hydraulic control scheme of the pipeline network.

[0012] Another objective of this invention is to provide an improved Pareto optimization system for hydraulic regulation of pipe networks based on the method of characteristics, used in accordance with the improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics described in this invention. The improved Pareto optimization system for hydraulic regulation of pipe networks based on the method of characteristics includes: a transient simulation module, an optimization algorithm module, and a scheme decision module.

[0013] The transient simulation module is based on the one-dimensional characteristic line method to realize the numerical simulation of hydraulic transient processes, and is used to simulate the transient processes of pressure and flow in the pipeline during hydraulic regulation of the pipeline network.

[0014] The optimization algorithm module integrates an improved strength Pareto evolutionary algorithm for solving multi-objective optimization problems;

[0015] The scheme decision module uses the VIKOR method to select the optimal control scheme from the Pareto optimal solution set, and obtains the optimal control scheme by comparing and verifying it with the initial scheme.

[0016] The beneficial effects of this invention are as follows:

[0017] This invention discloses an improved Pareto optimization method and system for hydraulic control of pipe networks based on the method of characteristics. This method achieves an improved Pareto (SPEA2) optimization approach for hydraulic control of pipe networks based on the method of characteristics. Through technological innovation and system integration, it realizes high-precision simulation of transient processes in pipe networks and safe and economical synergistic optimization. Practical engineering applications have verified that this method can effectively reduce water hammer risk, improve irrigation uniformity, and optimize operational efficiency, demonstrating good engineering application value and promising prospects for wider application. The implementation of this invention will promote the development of irrigation pipe network systems towards safety, efficiency, and intelligence, providing technical support for the efficient utilization of agricultural water resources and secure food production. With the advancement of smart water conservancy construction, this invention will play an important role in a wider range of fields, specifically including the following beneficial effects:

[0018] A transient flow model of the pipeline network is established by using the one-dimensional method of characteristics, which enables accurate numerical simulation of water hammer wave propagation and flow response, providing high-fidelity objective function values ​​for optimization.

[0019] Constructing a multi-objective optimization model can simultaneously handle multiple conflicting objectives and identify various trade-offs, ensuring the optimization results are feasible in engineering. This forms the basis for an optimization model that accurately reflects the operational contradictions of irrigation network valves and can be effectively solved by subsequent algorithms.

[0020] An improved Intensive Pareto Evolutionary Algorithm based on chaotic mapping is introduced. By leveraging the ergodicity and randomness of chaos, the initial diversity and search escape ability of the population are enhanced. Combined with Pareto non-dominated sorting and external archive maintenance mechanism, the algorithm effectively overcomes the shortcomings of traditional multi-objective algorithms in dealing with high-dimensional, strongly constrained, and nonlinear optimization problems, such as slow convergence speed and easy getting trapped in local optima, and obtains a uniformly distributed Pareto compromise solution set.

[0021] The entropy weight method is used to objectively assign weights to conflicting indicators such as pressure safety and irrigation uniformity, and the VIKOR method is combined to select the optimal solution with the greatest group benefit and the least individual regret from the Pareto frontier.

[0022] The synergistic effect of the above technologies organically unifies physical simulation, intelligent search, and multi-attribute decision-making, providing a systematic quantitative solution path for balancing the typical contradiction between water hammer risk and flow uniformity. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the process of an improved Pareto optimization method for hydraulic control of pipe networks based on the method of characteristics, according to the present invention.

[0024] Figure 2 This is a schematic diagram of the irrigation network layout in an embodiment of the present invention;

[0025] Figure 3 This is a schematic diagram of the pressure fluctuation at the P1 node of the two linear valves in the irrigation group 20 under normal pump operation in this embodiment of the invention.

[0026] Figure 4 This is a schematic diagram of the pressure fluctuation at the P2 node of the two-section linear valve closure in the irrigation group 20 under normal pump operation in this embodiment of the invention.

[0027] Figure 5 This is a schematic diagram of the pressure fluctuation at the P3 node of the two linear valves in the irrigation group 20 under normal pump operation in an embodiment of the present invention.

[0028] Figure 6 This is a schematic diagram of the pressure fluctuation at the P4 node of the two-section linear valve closure in the irrigation group 20 under normal pump operation in this embodiment of the invention.

[0029] Figure 7 This is a schematic diagram of the pressure fluctuation at the P5 node of the two linear valves in the irrigation group 20 under normal pump operation in an embodiment of the present invention.

[0030] Figure 8 This is a schematic diagram of the pressure fluctuation at node P6 of the two-section linear valve closure in the irrigation group 20 under normal pump operation in this embodiment of the invention.

[0031] Figure 9This is a schematic diagram of the pressure fluctuation at the P7 node of the two-section linear valve closure in the irrigation group 20 under normal pump operation in this embodiment of the invention.

[0032] Figure 10 This is a 20 Pareto front diagram of the irrigation group under normal pump operation in an embodiment of the present invention.

[0033] Figure 11 This is a comprehensive evaluation parameter diagram of the 20VIKOR irrigation group under normal pump operation in this embodiment of the invention;

[0034] Figure 12 This is a comparison diagram of the pressure fluctuation at node P1 of the irrigation group 20 under normal pump operation in this embodiment of the invention;

[0035] Figure 13 This is a comparison diagram of the pressure fluctuation at node P2 of the irrigation group 20 under normal pump operation in this embodiment of the invention;

[0036] Figure 14 This is a comparison diagram of the pressure fluctuation at node P3 of the irrigation group 20 under normal pump operation in this embodiment of the invention;

[0037] Figure 15 This is a comparison diagram of the pressure fluctuation at node P4 of the irrigation group 20 under normal pump operation in this embodiment of the invention;

[0038] Figure 16 This is a comparison diagram of the pressure fluctuation at node P5 of the irrigation group 20 under normal pump operation in this embodiment of the invention;

[0039] Figure 17 This is a comparison diagram of the pressure fluctuation at node P6 of the irrigation group 20 under normal pump operation in an embodiment of the present invention.

[0040] Figure 18 This is a comparison diagram of the pressure fluctuation at node P7 of the irrigation group 20 under normal pump operation in this embodiment of the invention;

[0041] Figure 19 This is a schematic diagram of the pressure fluctuation at node P1 of the first type of two-stage linear valve closure in the irrigation group 20 during a power outage and pump stoppage in an embodiment of the present invention.

[0042] Figure 20 This is a schematic diagram of the pressure fluctuation at the first type of two-stage linear valve-closing node P2 of the irrigation group 20 during a power outage and pump stoppage in an embodiment of the present invention.

[0043] Figure 21 This is a schematic diagram of the pressure fluctuation at the P3 node of the first type of two-stage linear valve closure in the pumping unit 20 during a power outage and pump stoppage in an embodiment of the present invention.

[0044] Figure 22 This is a schematic diagram of the outlet flow rate of the first type of pump in the irrigation group 20 during a power outage and pump stoppage in an embodiment of the present invention;

[0045] Figure 23 This is a schematic diagram of the pressure fluctuation at the second type of two-stage linear valve-closing node P1 of the irrigation group 20 during a power outage and pump stoppage in an embodiment of the present invention.

[0046] Figure 24 This is a schematic diagram of the pressure fluctuation at the P2 node of the second type of two-stage linear valve closure in the pumping unit 20 during a power outage and pump stoppage in an embodiment of the present invention.

[0047] Figure 25 This is a schematic diagram of the pressure fluctuation at node P3 of the second type of two-stage linear valve closure in the pumping unit 20 during a power outage and pump stoppage in an embodiment of the present invention.

[0048] Figure 26 This is a schematic diagram of the outlet flow rate of the second type of pump in the irrigation group 20 during a power outage and pump stoppage in an embodiment of the present invention;

[0049] Figure 27 This is a 20 Pareto front diagram of the irrigation group under the power outage and pump stoppage condition in an embodiment of the present invention;

[0050] Figure 28 This is a comprehensive evaluation parameter diagram of the 20VIKOR irrigation group under the power outage and pump stoppage condition in an embodiment of the present invention;

[0051] Figure 29 This is a comparison diagram of the outlet pressure of pump 20 in the irrigation group under the power outage and pump stoppage condition in an embodiment of the present invention;

[0052] Figure 30 This is a comparison chart of the flow rate at the outlet end of pump 20 of the irrigation group under the power outage and pump stoppage condition in an embodiment of the present invention. Detailed Implementation

[0053] This invention provides an improved Pareto optimization method and system for hydraulic control of pipe networks based on the method of characteristics. The invention will be further described in detail below with reference to the accompanying drawings.

[0054] like Figure 1 The embodiments of the present invention provided an improved Pareto (SPEA2) optimization method for hydraulic control of pipe networks based on the method of characteristics. This method aims to address the technical problems of existing pipe network design methods, such as strong subjectivity, inability to consider multiple objective performances, and unscientific valve control rules that easily lead to water hammer accidents. It also addresses the issues of ensuring pressure safety and flow uniformity, achieving multi-objective optimal control of hydraulically transient processes.

[0055] The specific implementation process is as follows:

[0056] This invention provides an improved Pareto (SPEA2) optimization method for hydraulic regulation of pipe networks based on the method of characteristics, the method comprising:

[0057] Step S1: Construct a one-dimensional characteristic line method numerical simulation model of transient flow in the pipeline network to simulate the transient process of pressure and flow during hydraulic regulation of the pipeline network.

[0058] Step S2: Construct a multi-objective optimization model, including: constructing the optimization objective and designing constraints;

[0059] Step S3: Solve the multi-objective optimization model using the intensity Pareto evolution algorithm based on chaotic mapping to obtain the Pareto optimal solution set;

[0060] Step S4: Based on the Pareto optimal solution set, the optimal hydraulic control scheme for the pipeline network is determined by combining subjective and objective weighting using the entropy weight method and the VIKOR comprehensive evaluation method.

[0061] Step S5: Input the optimal hydraulic control scheme of the pipeline network into the numerical simulation model of the transient flow of the pipeline network using the one-dimensional characteristic line method, and compare the initial scheme and the optimized scheme to verify the effectiveness and control effect of the optimal hydraulic control scheme of the pipeline network.

[0062] The following provides a detailed explanation of each step:

[0063] In step S1, a one-dimensional characteristic line method (1D-MOC) numerical simulation model of transient flow in the pipeline is constructed to simulate the transient process of pressure and flow in the pipeline when the valve is controlled according to a specific law;

[0064] The transient processes of pressure and flow during the simulated hydraulic regulation of the pipe network include:

[0065] The valve control law for pressure during the simulated hydraulic regulation of the pipeline network is a two-stage linear closure curve; the transient flow boundary conditions for the transient flow process include: series pipelines, branch pipelines, pipeline end valves, pipeline internal valves, orifice outflow, pumps operating normally in the pipeline, and pumps under emergency shutdown conditions.

[0066] The specific process of constructing the one-dimensional characteristic line method numerical simulation model of pipeline transient flow includes:

[0067] Step S11: Construct the governing equations:

[0068] The transient flow governing equations for the pipeline system are established under the following basic assumptions: the fluid inside the pipe is considered a homogeneous one-dimensional flow; the fluid velocity is assumed to be significantly less than the pressure wave propagation speed; the deformation of the pipe wall and the fluid is assumed to satisfy a linear relationship; and the pipe remains fully filled at all times. These governing equations consist of a momentum equation and a continuity equation, as shown in the formulas below:

[0069]

[0070]

[0071] In the formula, The average flow velocity inside the pipe is given in m / s. The pressure head at the pipe node is in meters (m). Pipe diameter, in meters (m); The water hammer wave velocity is in m / s; This refers to the pipe friction coefficient; Expresses the acceleration due to gravity, m / s² 2 ; Indicates the pipe inclination angle, º.

[0072] The method of characteristics is used to solve the governing equations, transforming the original partial differential form into a total differential form along the direction of the characteristic lines, resulting in two ordinary differential equations. and This is represented as shown in the formula:

[0073]

[0074]

[0075] Integrating the formula along the characteristic line and rewriting it, we get:

[0076]

[0077]

[0078] In the formula:

[0079]

[0080]

[0081]

[0082]

[0083] Step S12: Handling Boundary Conditions: In a pipe network system, solving for transient hydraulic parameters at boundary nodes requires solving the characteristic line equations and the corresponding boundary condition equations simultaneously. For the pipe network, the following boundary conditions are constructed:

[0084] Series pipeline boundary conditions: For a contracting pipe section formed by series connection of pipes of different diameters, the continuity conditions of continuous flow and equal head must be met, that is, the flow rate at the end of the upstream pipe at the series node is equal to the flow rate at the beginning of the downstream pipe, and the head at the end of the upstream pipe is equal to the head at the beginning of the downstream pipe.

[0085] Bifurcation pipeline boundary conditions: For the nodes where bifurcation pipelines intersect, the flow continuity condition must be met, that is, the total flow into the node is equal to the total flow out of the node, and the head of all pipelines at the junction is equal.

[0086] Pipeline end valve boundary conditions: For control valves installed at the end of the pipeline, it is necessary to establish the relationship between valve opening and flow rate, define dimensionless valve opening (1 for fully open and 0 for fully closed), and describe the hydraulic characteristics of the valve under transient conditions through the valve loss coefficient.

[0087] Internal valve boundary conditions in pipelines: For internal valves installed between two pipelines, the flow continuity upstream and downstream of the valve and the head loss relationship must be satisfied simultaneously, and the flow distribution is adjusted by the valve opening.

[0088] Orifice outflow boundary conditions: For cases where the pipeline ends with orifice outflow, it is necessary to establish the correspondence between orifice outflow rate and pressure, and describe the outflow characteristics through the orifice flow coefficient;

[0089] Pump boundary conditions in pipeline: For stable operation of the pump, it is necessary to establish an approximate relationship between pump flow rate and head, determine the constant coefficients through the pump characteristic curve, and solve the pump outlet flow rate and pressure by solving the compatibility equations simultaneously.

[0090] Pump boundary conditions under pump shutdown condition: For pump shutdown accident conditions due to power failure, it is necessary to consider the pump inertial operation process, establish the head balance equation and speed change equation, calculate the transient dynamic head by interpolation through the pump full characteristic curve (Wh and Wb curves), and solve the dimensionless speed and flow parameters simultaneously.

[0091] In step S2, a multi-objective optimization model is constructed, including the construction of optimization objectives and the design of constraints.

[0092] The optimization objectives of hydraulic regulation of the pipeline network under normal pump operation include reliability and efficiency objectives, and the constraints include water pressure constraints, valve opening constraints, and valve closing time constraints. The optimization objectives of hydraulic regulation of the pipeline network under power failure and pump shutdown include reliability and throttling objectives, and the constraints include water pressure constraints, valve opening constraints, outflow time constraints, and valve closing time constraints.

[0093] In step S3, the intensity Pareto evolution algorithm based on chaotic mapping is used to solve the multi-objective optimization model: the initial population and external archive set are generated through Tent chaotic mapping, and the entire process is repeated until the maximum number of iterations is reached. The non-dominated individuals in the external archive set are output to obtain the Pareto optimal solution set.

[0094] In this embodiment, the specific improvement steps of the intensity Pareto evolution algorithm based on chaotic mapping include:

[0095] Tent chaotic mapping is used for population initialization. The ergodicity, randomness and uniform distribution of chaotic sequences are used to generate the initial population, thereby enhancing the diversity of the population and the quality of the initial solution.

[0096] An adaptive crossover and mutation probability mechanism is introduced to dynamically adjust the probabilities of crossover and mutation operations based on the individual's fitness.

[0097] An adaptive penalty function and a distance metric are introduced to modify the objective function, and the individual's objective value and the total number of constraint violations are comprehensively represented.

[0098] A minimum distance truncation method is used as an environmental selection strategy to maintain population diversity during the environmental selection process.

[0099] The Tent chaotic map is a typical one-dimensional piecewise linear chaotic map, and its expression is as follows:

[0100]

[0101] In the formula, Let the value be the value of the kth iteration; select the initial value. By iteratively generating a length of The chaotic sequence is discarded by discarding the first few terms to reduce the impact of initial value sensitivity;

[0102] The chaotic sequence is then mapped to the value range of each decision variable to obtain the initial population individuals:

[0103]

[0104] In the formula, and These are the upper and lower bounds of the j-th decision variable, respectively;

[0105] The decision variable is selected as: the coefficient of valve opening decrease in the first stage. The first turning point Complete shutdown time .

[0106] The expressions for the adaptive crossover probability and mutation probability are:

[0107]

[0108] In the formula, Pc is the adaptive crossover probability. and These represent the maximum and minimum values ​​of the crossover probability, respectively. and These are the average and minimum fitness values ​​of all individuals in the population archive, respectively.

[0109] In step S4, the core principle of the subjective and objective combination weighting based on the entropy weighting method is as follows: when the objective safety weight calculated by the entropy weighting method is lower than the equilibrium threshold, the system identifies a potential risk of redundant safety assessment in the distribution of the solution set information. At this time, subjective experience is activated, and the safety weight is forcibly corrected to the equilibrium range through an adaptive operator to ensure engineering safety. When the objective data has demonstrated sufficient safety, the decision-making system will stop intervening, allowing the weight allocation to evolve freely according to the data distribution characteristics. Its value is shown in the formula:

[0110]

[0111] In the formula, x represents the security weight calculated by the entropy weight method. This mechanism leverages the guiding role of expert experience under extreme biases while preserving the true discriminative power of objective data within the security-sensitive range to the greatest extent possible, enabling the final decision-making results to possess higher scientific reliability and engineering flexibility while ensuring inherent safety.

[0112] The calculation principle and steps of the VIKOR method are as follows:

[0113] Step S41: An initial decision matrix needs to be established. It is assumed that there are m alternative solutions, and each solution corresponds to n optimization objectives.

[0114]

[0115] In the formula, This represents the original observation value of the i-th scheme under the j-th index;

[0116] Step S42: Determine the ideal solution and the negative ideal solution;

[0117] To measure the difference between each Pareto solution and the ideal hydraulic operating state, the ideal solution and negative ideal solution for each evaluation objective are determined. For the j-th objective, its ideal value is defined as the optimal value of the objective in the Pareto solution set, and its negative ideal value is defined as the worst value of the objective.

[0118]

[0119] In the formula: For the ideal solution, It is a negative ideal solution.

[0120] S43, Calculate group utility S i

[0121] Based on the different importance of various hydraulic performance indicators, a target weighting coefficient is introduced. And calculate the group utility index for each option. This index measures the degree to which the overall performance of a valve's opening and closing behavior deviates from the ideal state across all evaluation targets. The smaller the value, the closer the valve's opening and closing behavior is to the ideal hydraulic state in a global sense.

[0122]

[0123] In the formula, The weights for each objective are assigned based on a combination of subjective and objective factors using the entropy weighting method.

[0124] Step S44: Calculate the maximum regret value

[0125] To avoid unacceptable performance degradation in certain hydraulic parameters due to the opening and closing pattern of a particular valve, a maximum regret index is further introduced. This indicator takes the maximum value among the weighted deviations of each evaluation objective and is used to reflect the performance of the scheme under the most unfavorable objective.

[0126]

[0127] Step S45: Calculate the compromise ranking index

[0128] Based on a comprehensive consideration of overall performance and the worst-case scenario performance A compromise ranking index is constructed, which incorporates a trade-off coefficient v to weight and combine a group utility index with a maximum regret index, reflecting the comprehensive ranking result under different decision preferences. When v=0.5, it indicates that a compromise decision is made between the two objectives.

[0129]

[0130] In the formula, v is the decision preference coefficient, which takes a value from 0 to 1.

[0131] Step S46: Sorting and Scheme Determination;

[0132] Based on the compromise ranking index Sort the Pareto solution set in ascending order. The smaller the value, the better the solution. The Pareto optimal solution set is ranked using multiple criteria, and the scheme with the highest approximation is selected as the optimal pipeline hydraulic control scheme.

[0133] In step S5, the optimization scheme is verified by substituting the optimal scheme of hydraulic regulation of the pipeline network into the transient flow calculation model of S1, calculating the transient pressure fluctuation change of the pipeline network and comparing it with the initial scheme to verify the effectiveness of the optimization algorithm and the regulation effect.

[0134] The initial scheme described in this embodiment is the scheme before modification, specifically the initial two-stage linear valve closing scheme set under normal operation and power failure pump shutdown conditions.

[0135] To verify the effectiveness of the improved Pareto optimization method and system for pipeline hydraulic control based on the method of characteristics disclosed in this invention, the specific implementation process is disclosed below for two scenarios: normal pump operation and pump shutdown due to power failure.

[0136] I. Project Overview

[0137] This invention takes a rotating irrigation group 20 in the southern part of a cotton drip irrigation demonstration area as the implementation object. The main economic crop in this irrigation area is cotton, and the irrigation method is drip irrigation. The three-stage pipeline of the irrigation area includes a 200mm diameter main pipe, a 110mm diameter branch pipe, and a 16mm diameter capillary pipe. A KQL150 / 290-22 / 4 vertical single-stage centrifugal pump is selected. Pump outlet node P1, main pipe node P2, branch pipe node P3, and nodes P4 to P7 before and after the valves within the rotating irrigation group 20 are selected as observation nodes for transient processes. The irrigation network layout in this embodiment is as follows: Figure 2 As shown.

[0138] II. Specific Steps

[0139] Specific Implementation Example 1: Optimization of Pipeline Hydraulic Regulation under Normal Operating Conditions

[0140] Step S1: Construct a numerical simulation model of transient flow in the pipeline network using the one-dimensional method of characteristics (1D-MOC) to simulate the transient process of pressure and flow in the pipeline when valves are regulated according to specific rules and when power is cut off and pumps are stopped.

[0141] Discretize the pipe motion equations and continuity equations along the characteristic lines to obtain the characteristic line equations that are easy to solve numerically:

[0142]

[0143]

[0144] Boundary conditions:

[0145] Pipeline end valve boundary conditions: Assuming the slope baseline is set on the valve, the valve satisfies the following formula during the adjustment of its opening:

[0146]

[0147] Pipeline valve boundary conditions: The relationship between the flow rate through the valve and its local head loss during the regulation process is as follows:

[0148]

[0149] Boundary conditions for series piping: The continuity equation between series piping is expressed as:

[0150]

[0151]

[0152] Bifurcation pipeline boundary conditions: The continuity equation for a bifurcation pipeline is expressed as:

[0153]

[0154]

[0155] Orifice outflow boundary conditions: The relationship between flow rate and pressure at the orifice is similar to that of the end valve, and is as follows:

[0156]

[0157] Pump boundary conditions: During the transient process, it is assumed that the head balance equation for the centrifugal pump still applies, the flow rates at the pump inlet and outlet are conserved, and the pressure balance equation is as follows:

[0158]

[0159] During normal operation, the pump inlet and outlet follow the flow balance equation:

[0160]

[0161] During a power outage and pump shutdown, the motor's main torque becomes zero, and the pump impeller begins to decelerate under counter-torque. From theoretical mechanics, we can derive the following formula:

[0162]

[0163] This invention employs a phased valve closure strategy. For the four valves in irrigation group 20, four different valve closure patterns were designed: a total closure time of 120 seconds, with fast closures of 70% and 85% and fast closure durations of 30 and 50 seconds respectively. Hydraulic transient process simulation calculations were performed on the pump-valve-pipeline network. The calculation results are as follows: Figures 3-9The diagram illustrates the pressure fluctuations of the two linear valves P1-P7 in the irrigation group 20 under normal pump operation in this embodiment of the invention. However, the above-mentioned combination of closing parameters for the two stages is only a relatively optimal solution obtained under the current analysis conditions and cannot guarantee that it is the globally optimal solution for all irrigation groups. Due to differences in spatial location, hydraulic boundary conditions, and pipeline characteristics among different irrigation groups, their corresponding optimal valve opening change curves may not be completely consistent. Therefore, it is still necessary to conduct further optimization analysis in a broader parameter space to explore more scientific and efficient valve closing laws, so as to achieve a synergistic improvement in the safety and operational efficiency of the irrigation network system.

[0164] Step S2: Construct a multi-objective optimization model:

[0165] Develop optimization objectives, including:

[0166] ① Reliability Objective: The average extreme water pressure at each node of the pipeline network is used as the reliability evaluation index. The smaller the objective function value, the more stable the pipeline system's operation and the higher its reliability. The objective function expression is:

[0167]

[0168] ② High Efficiency Objective: The total valve control time is used as an evaluation index to measure the operational efficiency of the irrigation network. The smaller the objective function value, the more efficient the valve control process and the higher the system operating efficiency. Its objective function expression is:

[0169]

[0170] In the formula, T1 is the valve action time in the first stage, and T2 is the valve action time in the second stage.

[0171] Design constraints:

[0172] ① Water pressure constraint: During valve closure and control, the instantaneous water pressure at each node in the pipeline network should always be controlled within its allowable operating range, that is, it should not be lower than the minimum allowable water pressure of that node, nor should it exceed its maximum allowable water pressure. As shown in the formula.

[0173]

[0174] In the formula, since the terrain of the irrigation area studied is a plain with gentle slopes, the change in ground elevation is relatively small. Set the value to 0m. Generally, it is taken as 1.5 times the pipeline's design pressure bearing capacity. In agricultural ecological irrigation network systems, considering both pipe material performance and engineering safety requirements, this invention takes... It is 150m.

[0175] ② Valve opening constraint: The valve opening at the previous moment should be greater than the opening at the next moment, and the opening cannot exceed 1. As shown in the formula:

[0176]

[0177] In the formula, and represent and The valve opening at any given time.

[0178] ③ Valve closing time constraint: The time elapsed from the start of valve closing to the complete closure of the valve, as shown in the formula:

[0179]

[0180] In the formula, T is the valve closing time. To allow the maximum valve closing time.

[0181] Step S3: Solve the multi-objective optimization model based on the improved Pareto genetic algorithm.

[0182] For a rotating irrigation group 20, an improved intensity Pareto evolutionary algorithm was used, combined with MATLAB programming language, to optimize the two-stage linear valve closing behavior of the irrigation network valves under normal pump operation conditions. The population size was 20, the maximum and minimum crossover probabilities were set to 0.8 and 0.6 respectively, the maximum and minimum mutation probabilities were set to 0.1 and 0.01 respectively, the maximum number of iterations was set to 300, and the population and external file sizes were both 30.

[0183] After removing non-dominated solutions that violate the constraints and have the same decision variables, a Pareto optimal solution set for irrigation group 20 is finally obtained, with 21 non-dominated individuals in each solution set. The Pareto front plot of irrigation group 20 under normal pump operation in this embodiment of the invention is shown below. Figure 10 The figure shows the distribution of reliability and efficiency objectives in the objective space of the Pareto optimal solution set. The reliability objective value under the optimized scheme ranges from 19.5m to 21.75m, and the efficiency objective value ranges from 60s to 85s. Both are less than the two shortest valve closing times under the constraints. As the efficiency objective value gradually decreases, the reliability objective value gradually increases, indicating a contradiction between these two values. For this multi-objective competitive game dilemma, the key to decision-making lies in finding a balance between optimizing the overall group performance and maximizing the reduction of individual indicator risks (maximum regret value). Therefore, this invention introduces the VIKOR multi-criteria decision model.

[0184] Step S4: Optimal solution selection based on the VIKOR decision method:

[0185] ① Weighting based on a combination of subjective and objective factors using the entropy weighting method;

[0186] This invention introduces the entropy weight method to determine the weights of decision variables. Calculations show that the entropy weight method assigns a weight of 0.37 for safety and 0.63 for efficiency. Due to its high dispersion, the efficiency index is given a higher weight. To balance data and engineering experience, this invention also introduces a strategy of combining subjective and objective weighting. Ultimately, the safety weight for the 20th irrigation group is determined to be 0.559, and the efficiency weight to be 0.441.

[0187] ② Selection of the target solution

[0188] Based on the calculation principle of the VIKOR method, the weight values ​​of the two objectives for the 20th irrigation group are set to safety (0.559) and efficiency (0.441). The final Pareto optimal solution set VIKOR parameters are shown in the figure below for the comprehensive evaluation parameters of the 20th irrigation group under normal pump operation in this embodiment. Figure 11 As shown. The 21 solutions are numbered from smallest to largest based on the efficiency objective value. According to... Figure 11 It can be seen that the scheme with the smallest comprehensive evaluation parameter value is scheme 9, with a corresponding parameter value of 0.01348. In this case, the comprehensive evaluation index Q generated by the VIKOR algorithm exhibits a clear concave function distribution characteristic. As shown in the figure, scheme 9 is identified as the globally optimal solution due to its lowest comprehensive evaluation index Q value (0.0135), namely, the first fast closing time is 20s, the fast closing angle is 89%, and the total valve closing time is 69.98s. This scheme achieves a balance between a pressure difference of 20.64m and a valve closing time of 69.98s. Through slope analysis of the neighborhood of this point, it can be seen that scheme 9 not only meets the threshold for acceptable advantage, but its individual regret value R is also at the lowest level in the entire field. This indicates that while improving the group utility, the scheme effectively avoids the risk of any single indicator deviating too much from the ideal solution.

[0189] Step S5: Verification of the optimization scheme.

[0190] The initial scheme for the 20th irrigation group was a two-stage linear valve closing mechanism. The first stage used a fast closing time of 25.49s and a fast closing angle of 0.606, while the second stage used a slow closing time of 48.64s, for a total duration of 74.13s. The optimized scheme used a first stage fast closing time of 20s and a fast closing angle of 0.89, and a second stage slow closing time of 49.96s, for a total duration of 69.98s. The pressure fluctuations at nodes P1-P7 of the 20th irrigation group under normal pump operation in this embodiment of the invention are compared as follows: Figure 12-18It can be seen that the optimized scheme of the 20th irrigation group exhibited excellent transient suppression performance at all monitoring points. For node P1, the initial scheme induced severe hydraulic fluctuations at the moment of valve closure, with the pressure head rapidly climbing to a peak of 35.5 m, and water hammer was evident. In contrast, the optimized scheme showed a very smooth pressure head evolution process, with almost no pressure fluctuations. The highest pressure was approximately 32.5 m, a decrease of 11.2% compared to the initial scheme, and the maximum pressure difference was 20.65 m. At nodes P2, P3, P4, and P6, the initial scheme generated severe hydraulic fluctuations after valve operation, with the maximum peak occurring at node P3, reaching 68.32 m accompanied by high-frequency oscillations. After optimization, the pressure fluctuation at point P3 decreased to 37.2 m, a 46% reduction in the peak pressure compared to the initial scheme, and quickly entered a state of small-range fluctuations or even no fluctuations after the first wave of hydraulic fluctuations. For nodes P5 and P7 downstream of the valve, the optimized scheme showed a smoother pressure drop trajectory, effectively avoiding the risk of negative pressure cavitation that might be induced by a sudden pressure drop.

[0191] Specific Implementation Example 2: Optimization of hydraulic regulation of pipeline network under power failure and pump stoppage conditions;

[0192] This invention still takes the irrigation group 20 as the research object, simulating the impact of different valve closing rules on the hydraulic transient process of the entire pipeline system when a power outage occurs after the water pump has been running normally for a certain period of time. The characteristics of transient pressure changes are systematically analyzed. Based on this, the calculation results of each operating condition are comprehensively compared to determine a reasonable valve closing rule scheme after the water pump. Step 1 is the same as the step in specific embodiment 1.

[0193] The two-stage linear valve closing pattern falls into two categories: The first category has a total valve closing time of 150 s. In the initial stage, 70% and 85% of the valve opening are rapidly closed in 40 s and 60 s respectively, followed by a slow closure of the remaining 30% and 15% in 110 s and 90 s respectively. The second category has a total valve closing time of 90 s. 70% and 85% of the valve opening are rapidly closed in the first 20 s and 40 s respectively, followed by a slow closure of the remaining 30% and 15% in 70 s and 50 s respectively. Through the transient calculations of valve closing, a systematic analysis of the pressure change process in the pump-valve-pipeline system under pump shutdown conditions is performed, thus providing a basis for determining a reasonable valve closing pattern. The corresponding change patterns are as follows: Figure 19-26 As shown.

[0194] Step S2: Establish a multi-objective optimization model

[0195] Define the optimization goal:

[0196] ① Reliability Target: The mean of the extreme values ​​of the transient pressure at the pump outlet is used as an evaluation index for reliability. The smaller the value of this objective function, the more reliable the target; the larger the value, the greater the hydraulic risk. The expression for the objective function is:

[0197]

[0198] In the formula, and These represent the highest pressure increase and lowest pressure drop at the pump outlet after the valve is fully closed, respectively, in meters (m).

[0199] ② Throttling Target: A throttling target is introduced to determine the effect of valve closing behavior on outflow control. The smaller the objective function value, the more efficient the valve regulation process and the better the water-saving effect. The expression for the objective function is:

[0200]

[0201] In the formula, The time when the valve begins to close. It is the time it takes for the valve to close completely. It is the outlet flow rate at the pump outlet.

[0202] Design constraints:

[0203] ① Water pressure constraint: During valve closure and control, the instantaneous water pressure at each node in the pipeline network should always be controlled within its allowable operating range, that is, it should not be lower than the minimum allowable water pressure of that node, nor should it exceed its maximum allowable water pressure. As shown in the formula.

[0204]

[0205] In the formula, This indicates the minimum allowable pressure, taken as -1m. This indicates the maximum allowable pressure, taken as 5m.

[0206] ② Valve opening constraint: The valve opening at the previous moment should be greater than the opening at the next moment, and the opening cannot exceed 1. As shown in the formula:

[0207]

[0208] In the formula, and represent and The valve opening at any given time.

[0209] ③ Valve closing time constraint: The time elapsed from the start of valve closing to the complete closure of the valve, as shown in the formula:

[0210]

[0211] In the formula, T is the valve closing time. To allow the maximum valve closing time.

[0212] ④ Maximum outflow constraint: The outflow rate from the start of valve closure to the final closure of valve must not exceed a given value to prevent excessive outflow from rendering the optimization meaningless, as shown in the formula:

[0213]

[0214] In the formula, Q represents the outflow rate. To allow the maximum outflow rate.

[0215] Step S3: Solve the multi-objective optimization model based on the improved Pareto genetic algorithm.

[0216] For the rotating irrigation group 20, based on the improved intensity Pareto evolutionary algorithm and combined with the MATLAB programming language, the two-stage linear valve closing law of the irrigation network valves under the power outage and pump stoppage condition is optimized. The Pareto optimal solution for the rotating irrigation group 20 under the power outage and pump stoppage condition is obtained. The Pareto front diagram of the rotating irrigation group 20 under the power outage and pump stoppage condition in this embodiment of the invention is shown below. Figure 27 As shown, each Pareto solution group contains 10 individuals. Individuals are numbered according to their water-saving target values, from smallest to largest, with water-saving targets ranging from 0.044 m³ to 0.046 m³ and reliability targets ranging from 1.2 m to 3.0 m. This invention introduces a VIKOR multi-criteria decision-making model. It seeks a balance between optimizing the overall group performance and maximizing the reduction of individual indicator risks (maximum regret value).

[0217] Step S4: Optimal solution selection based on the VIKOR decision method:

[0218] Step S41: Assigning weights based on a combination of subjective and objective factors using the entropy weight method;

[0219] This invention introduces the entropy weight method to determine the weights of decision variables. Furthermore, to balance data and engineering experience, this invention also incorporates a strategy of combining subjective and objective weighting. Ultimately, the safety weight for the 20th irrigation group was determined to be 0.538, and the final flow-saving weight was 0.462.

[0220] Step S42: Selection of the target solution;

[0221] Based on the calculation principle of the VIKOR method, the weight values ​​of both objectives for the 20th irrigation group were set to safety (0.538) and flow-saving efficiency (0.462). The final Pareto optimal solution set VIKOR parameters are as follows: Figure 28As shown in the figure, the schemes with the smallest comprehensive evaluation parameter values ​​for irrigation group 20 are all in the middle position, corresponding to a parameter value of 0.3995. In this case, the comprehensive evaluation index Q generated by the VIKOR algorithm exhibits a clear concave function distribution characteristic. It can be seen that the optimized scheme for irrigation group 20 is: the first fast closing time is 20.021s, the fast closing angle is 0.90, the second slow closing time is 64.179s, and the total duration is 84.2s. Through slope analysis of the neighborhood of this point, it can be seen that this scheme not only meets the threshold for acceptable advantage, but its individual regret value R is also at the lowest level in the entire field. This indicates that while improving the group utility, the scheme effectively avoids the risk of any single indicator deviating too much from the ideal solution.

[0222] Step S5: Verification of the optimization scheme;

[0223] The initial scheme 20-0 for the 20th irrigation group was a two-stage linear valve closing scheme. The first stage used a fast closing time of 27.08s and a fast closing angle of 0.88, and the second stage used a slow closing time of 52.32s, for a total duration of 79.4s. The optimized scheme used a fast closing time of 20.021s and a fast closing angle of 0.90 for the first stage and a slow closing time of 64.179s for the second stage, for a total duration of 84.2s.

[0224] The pressure and flow rate comparison at the outlet of pump 20 of the irrigation group under the power failure and pump stop condition in the embodiments of the present invention is as follows: Figure 29 and Figure 30 As shown, at the pump outlet, after the valve is fully closed, the optimized scheme has a minimum pressure of -1.002m, a maximum pressure of 0.907m, and a maximum pressure difference of 1.909m. The initial scheme has a minimum pressure of -1.62m, a maximum pressure of 1.207m, and a maximum pressure difference of 2.827m. Compared to the initial scheme, the optimized scheme reduces the pressure difference by 32.472%. From the start of valve closure to the end, the initial scheme resulted in a flow loss of 0.045165m³, while the optimized scheme resulted in a flow loss of 0.044961m³, representing 0.166% of the irrigation quota. The figure shows that the period of greatest flow loss occurs in the initial phase before valve closure. The optimized scheme results in less flow loss during the longer valve closure period because the first rapid valve closure phase closes more of the valve opening in a shorter time, thus reducing flow loss. It not only ensures the safety of the pipeline network during the longer valve closure time, but also sacrifices less flow loss. Therefore, the optimization scheme based on the improved strength Pareto evolution algorithm is more superior.

[0225] Another embodiment of the present invention discloses an improved Pareto optimization system for hydraulic regulation of pipe networks based on the method of characteristics, used in accordance with the improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics described in the present invention. The improved Pareto optimization system for hydraulic regulation of pipe networks based on the method of characteristics includes: a transient simulation module, an optimization algorithm module, and a scheme decision module.

[0226] The transient simulation module is based on the one-dimensional characteristic line method to realize the numerical simulation of hydraulic transient processes, and is used to simulate the transient processes of pressure and flow in the pipeline during hydraulic regulation of the pipeline network.

[0227] The optimization algorithm module integrates an improved strength Pareto evolutionary algorithm for solving multi-objective optimization problems;

[0228] The scheme decision module uses the VIKOR method to select the optimal control scheme from the Pareto optimal solution set, and obtains the optimal control scheme by comparing and verifying it with the initial scheme.

[0229] The improved Pareto optimization method and system for hydraulic control of pipe networks based on the method of characteristics disclosed in this invention can achieve the following technical effects: Excellent multi-objective optimization capability: It directly optimizes pressure safety and flow uniformity in a Pareto sense, without the need for manual weight setting, resulting in more objective and comprehensive results; Fast convergence speed and high solution quality: The improved SPEA2 algorithm improves convergence efficiency while maintaining population diversity, making it suitable for high-dimensional, strongly constrained engineering optimization problems; Strong engineering applicability: The optimization results can be directly applied to actual valve operation, significantly reducing water hammer risk and improving system operational safety and irrigation uniformity; Good system compatibility: It can be embedded into existing pipe network monitoring systems to achieve intelligent control and optimized operation.

Claims

1. An improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics, characterized in that, Includes the following steps: Step S1: Construct a one-dimensional characteristic line method numerical simulation model of transient flow in the pipeline network to simulate the transient process of pressure and flow during hydraulic regulation of the pipeline network. Step S2: Construct a multi-objective optimization model, including: constructing the optimization objective and designing constraints; Step S3: Solve the multi-objective optimization model using the intensity Pareto evolution algorithm based on chaotic mapping to obtain the Pareto optimal solution set; Step S4: Based on the Pareto optimal solution set, the optimal hydraulic control scheme for the pipeline network is determined by combining subjective and objective weighting using the entropy weight method and the VIKOR comprehensive evaluation method. Step S5: Input the optimal hydraulic control scheme of the pipeline network into the numerical simulation model of the transient flow of the pipeline network using the one-dimensional characteristic line method, and compare the initial scheme and the optimized scheme to verify the effectiveness and control effect of the optimal hydraulic control scheme of the pipeline network.

2. The improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics according to claim 1, characterized in that, The transient processes of pressure and flow during the simulated hydraulic regulation of the pipe network include: The valve control law for pressure during the simulated hydraulic regulation of the pipeline network is a two-stage linear closure curve; the transient flow boundary conditions for the transient flow process include: series pipelines, branch pipelines, pipeline end valves, pipeline internal valves, orifice outflow, pumps operating normally in the pipeline, and pumps under emergency shutdown conditions.

3. The improved Pareto optimization method for pipe network hydraulic regulation based on the method of characteristics according to claim 1, characterized in that, The optimization objectives include: optimization objectives for hydraulic control of the pipeline network under normal pump operation and optimization objectives for hydraulic control of the pipeline network under power failure and pump shutdown. The optimization objectives for hydraulic regulation of the pipeline network under normal pump operation include: normal reliability objective and high efficiency objective; The normal reliability objective is: the average extreme water pressure at each node of the pipeline network is used as an evaluation index for reliability. The smaller the objective function value, the more stable the pipeline network system is and the higher its reliability. The objective function expression is: ， The efficiency objective is as follows: the total valve control time is used as an evaluation index to measure the operational efficiency of the irrigation network. The smaller the objective function value, the more efficient the valve control process and the higher the system operating efficiency. Its objective function expression is: ， In the formula, T1 is the valve action time in the first stage, and T2 is the valve action time in the second stage. The optimization objectives of the hydraulic control of the pipeline network under power failure and pump stoppage include: power failure reliability objective and flow throttling objective; The power outage reliability target is as follows: the average extreme value of the transient pressure at the pump outlet is used as the reliability evaluation index. The smaller the objective function value, the more reliable the target; the larger the value, the greater the hydraulic risk. The expression for the objective function is: ， wherein and are the maximum pressure rise and the minimum pressure drop at the pump outlet after the valve is fully closed, respectively, m; The throttling objective is introduced to determine the effect of valve closing behavior on outflow control. A smaller objective function value indicates a more efficient valve control process and better water-saving effect. The expression for the objective function is: ， wherein is the time at which the valve starts to close, is the time at which the valve is fully closed, is the outlet flow rate at the outlet end of the pump.

4. The improved Pareto optimization method for hydraulic regulation of pipe networks based on the method of characteristics according to claim 1, characterized in that, The design constraints include: constraints on hydraulic regulation of the pipeline network under normal pump operation and constraints on hydraulic regulation of the pipeline network under power failure and pump shutdown. The constraints for hydraulic regulation of the pipeline network under normal pump operation include: normal water pressure constraint, normal valve opening constraint, and normal valve closing time constraint. The normal water pressure constraint is as follows: During valve closure and control, the instantaneous water pressure at each node in the pipeline network should always be controlled within its allowable operating range, that is, it should not be lower than the minimum allowable water pressure of that node, nor should it exceed its maximum allowable water pressure; the expression for the normal water pressure constraint is: ， In the formula, represents the water pressure value of the i-th node, with the unit of m; represents the minimum water pressure allowed by the i-th node, with the unit of m; the minimum water pressure takes the pipe center line elevation value. represents the maximum water pressure allowed by the i-th node, with the unit of m, and the value is 1.5 times of the design pressure-bearing capacity of the pipe; The normal valve opening constraint is as follows: the valve opening at the previous moment should be greater than the opening at the next moment, and the opening cannot be greater than 1; the expression for the normal valve opening constraint is: ， In the formula, with represent with valve opening at the moment The normal valve closing time constraint is the time elapsed from the start of valve closing to the complete closure of the valve. The expression for the normal valve closing time constraint is: ， where T is the valve closing time, is the maximum valve closing time allowed; The constraints for hydraulic regulation of the pipeline network under power failure and pump shutdown include: power failure water pressure constraint, power failure valve opening constraint, power failure valve closing time constraint, and power failure maximum outflow constraint. The power-off water pressure constraint is as follows: During valve closure and control, the instantaneous water pressure at each node in the pipeline network should always be controlled within its allowable operating range, that is, it should not be lower than the minimum allowable water pressure of that node, nor should it exceed its maximum allowable water pressure; the expression for the power-off water pressure constraint is: ， wherein represents the minimum pressure allowed, taken as -1 m, represents the maximum pressure allowed, taken as 5 m; The opening constraint of the power-off valve is as follows: the valve opening at the previous moment should be greater than the opening at the next moment, and the opening cannot be greater than 1; the expression for the opening constraint of the power-off valve is: ， In the formula, and represent and Valve opening at current time; The power-off valve closing time constraint is the time elapsed from the start of valve closure to the complete closure of the valve. The expression for the power-off valve closing time constraint is: ， In the formula, T is the valve closing time. To allow the maximum valve closing time; The maximum outflow constraint during power outage is as follows: the outflow rate from the start of valve closure to the final closure of the valve cannot exceed a given value, to prevent excessive outflow from rendering the optimization meaningless. The expression for the maximum outflow constraint during power outage is: ， In the formula, Q represents the outflow rate. To allow the maximum outflow rate.

5. The improved Pareto optimization method for pipeline hydraulic control based on the method of characteristics as described in claim 1, characterized in that, The specific improvement steps of the intensity Pareto evolution algorithm based on chaotic mapping include: Tent chaotic mapping is used for population initialization. The ergodicity, randomness and uniform distribution of chaotic sequences are used to generate the initial population, thereby enhancing the diversity of the population and the quality of the initial solution. An adaptive crossover and mutation probability mechanism is introduced to dynamically adjust the probabilities of crossover and mutation operations based on the individual's fitness. An adaptive penalty function and a distance metric are introduced to modify the objective function, and the individual's objective value and the total number of constraint violations are comprehensively represented. A minimum distance truncation method is used as an environmental selection strategy to maintain population diversity during the environmental selection process.

6. The improved Pareto optimization method for pipeline hydraulic control based on the method of characteristics as described in claim 5, characterized in that, The Tent chaotic map is a typical one-dimensional piecewise linear chaotic map, and its expression is as follows: ， In the formula, This is the value of the kth iteration; Select initial value By iteratively generating a length of The chaotic sequence is discarded by discarding the first few terms to reduce the impact of initial value sensitivity; The chaotic sequence is then mapped to the value range of each decision variable to obtain the initial population individuals: ， In the formula, and These are the upper and lower bounds of the j-th decision variable, respectively; The decision variable is selected as: the coefficient of valve opening decrease in the first stage. The first turning point Complete shutdown time .

7. The improved Pareto optimization method for pipeline hydraulic control based on the method of characteristics as described in claim 5, characterized in that, The expressions for the adaptive crossover probability and mutation probability are: ， In the formula, Pc is the adaptive crossover probability. and These represent the maximum and minimum values ​​of the crossover probability, respectively. and These are the average and minimum fitness values ​​of all individuals in the population archive, respectively.

8. The improved Pareto optimization method for pipeline hydraulic control based on the method of characteristics as described in claim 1, characterized in that, The specific steps for determining the optimal hydraulic control scheme for the pipeline network using the combination of subjective and objective weighting methods based on the entropy weight method and the VIKOR comprehensive evaluation method include: The subjective-objective combined weighting method based on entropy weighting provides a scientific data foundation for the subsequent VIKOR method to seek the optimal solution. The core principle of this subjective-objective combined weighting is: when the objective safety weight calculated by the entropy weighting method is lower than the equilibrium threshold, the system identifies a potential risk of redundant safety assessment in the distribution of the solution set information. At this point, subjective experience is activated, and an adaptive operator forcibly corrects the safety weight to the equilibrium range to ensure engineering safety. When the objective data has demonstrated sufficient safety, the decision-making system will stop intervening, allowing the weight allocation to evolve freely according to the data distribution characteristics. The formula for determining the value of the subjective-objective combined weighting based on the entropy weighting method is: ， In the formula, x is the security weight calculated by the entropy weight method.

9. An improved Pareto optimization system for pipeline hydraulic control based on the method of characteristics, characterized in that, An improved Pareto optimization method for hydraulic control of pipe networks based on the method of characteristics, as described in any one of claims 1-8, wherein the improved Pareto optimization system for hydraulic control of pipe networks based on the method of characteristics comprises: a transient simulation module, an optimization algorithm module, and a scheme decision module; The transient simulation module is based on the one-dimensional characteristic line method to realize the numerical simulation of hydraulic transient processes, and is used to simulate the transient processes of pressure and flow in the pipeline during hydraulic regulation of the pipeline network. The optimization algorithm module integrates an improved strength Pareto evolutionary algorithm for solving multi-objective optimization problems; The scheme decision module uses the VIKOR method to select the optimal control scheme from the Pareto optimal solution set, and obtains the optimal control scheme by comparing and verifying it with the initial scheme.

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