Hydraulic transition process optimization method based on tracking population dominant two-stage two-population

Abstract

The application discloses a hydraulic transient process optimization method based on a tracking population dominant two-stage double population, comprising the following steps: S1, constructing a hydraulic transient process calculation model and connecting the double population optimization algorithm; S2, initializing DPTPEA parameters and randomly generating a development population and a tracking population; S3, first-stage double population differentiation screening and stability checking; S4, in the second stage, through dynamic cooperation strategy, boundary point direction sampling strategy and dynamic environment selection cooperation, the double population is cyclically updated; and S5, generating an optimization scheme of the hydraulic transient process. Through the introduction of the dynamic cooperation strategy, the boundary point direction sampling and the dynamic environment selection mechanism, the application fuses the infeasible solution information, enhances the population diversity and adaptively adjusts the search intensity, improves the multi-objective constraint optimization efficiency, avoids the local optimum and the waste of computing resources, and clearly shows the optimized valve pump operation parameters and the system scheme; the synergistic efficient scheme has high feasibility, effectively avoids the safety risk, reduces the energy consumption and the operation and maintenance cost.

Description

Technical Field

[0001] This invention relates to the field of hydraulic transition process technology, and in particular to an optimization method for a two-stage hydraulic transition process based on a tracking population-dominated dual-population population. Background Technology

[0002] Water hammer can cause a sharp increase or decrease in pressure in a pipeline system, leading to pipe rupture, equipment damage, or even system failure. Therefore, optimizing water hammer protection parameters to effectively control and mitigate the water hammer effect is of great significance for ensuring the safe operation of water conservancy systems and extending their service life.

[0003] Currently, the optimization of water hammer protection parameters is mainly based on multi-objective optimization algorithms, such as NSGA-II, MOEA / D, SPEA2, NSGA-III, and MOEA / DD. Compared with traditional single-objective optimization methods, these algorithms significantly improve the adaptability and solution set diversity of high-dimensional objective spaces through improvements such as non-dominated sorting, decomposition strategies, intensity value evaluation, reference point optimization, and hybrid dominance mechanisms. However, existing multi-objective optimization methods still have some limitations when dealing with complex hydraulic transition processes. On the one hand, these methods often struggle to simultaneously consider global search capability and local search accuracy, easily getting trapped in local optima, resulting in less than ideal optimization results. On the other hand, for optimization problems under multiple constraints, existing methods lack effective strategies for handling infeasible solutions, easily leading to a waste of computational resources. Furthermore, existing technologies also have shortcomings in dynamically adjusting optimization strategies to adapt to the optimization needs of different stages. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides an optimization method for a two-stage hydraulic transition process based on a tracking population-dominated dual-population system. This method constructs a hydraulic model using the method of characteristics and couples it with the DPTPEA algorithm. The dual-population system collaboratively explores the global and local environments, selects feasible non-dominated solutions, and outputs optimization results such as valve and pump parameters, as well as system design optimization parameters.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] An optimization method for a two-stage hydraulic transition process based on a tracking population-dominant dual-population population includes the following steps:

[0007] S1. Model building and algorithm coupling:

[0008] Collect basic data, construct a calculation model of the hydraulic transition process, and integrate it into the dual-population two-stage optimization algorithm (DPTPEA);

[0009] S2. Initialize algorithm parameters and generate population:

[0010] Initialize the DPTPEA parameters and randomly generate the development population (expPop) and the tracking population (tracPop).

[0011] S3, Phase 1 - Two-population differential screening and stability verification;

[0012] The dual-population approach expands the range of available solutions through targeted fusion, and combined with differentiated screening, it enhances the local optimization capabilities of the development population and the global exploration capabilities of the tracking population. Through iterative control and state evaluation, it outputs a stable dual-population with excellent optimization capabilities.

[0013] S4, Phase 2 - Dual-population multi-strategy collaborative cyclical update;

[0014] The two populations are updated cyclically through the combined effects of dynamic cooperation strategy, boundary point direction sampling strategy and dynamic environment selection.

[0015] S5. Optimization scheme for generating the hydraulic transition process:

[0016] The final updated expPop and tracPop are merged, and a feasible and non-dominated scheme is selected as the optimal scheme for the hydraulic transition process.

[0017] Furthermore, in step 1, the water hammer control equation of the pipeline system is established by the method of characteristics, and a hydraulic transient process calculation model is constructed by combining the pump and valve boundary conditions as an external program; the two models are coupled by calling the external program through the dual population two-stage optimization algorithm (DPTPEA) main program.

[0018] Furthermore, the combined pump and valve boundary conditions are jointly constituted by the valve boundary calculation model, the pump boundary calculation model, the constant water level boundary calculation model, and the pipeline connection mathematical model.

[0019] Furthermore, step S2 includes the following steps:

[0020] S21. Initialize DPTPEA parameters, including: population size N, number of iterations. Maximum number of iterations Algebraic interval number Switching threshold Tracking the rate of change in the population ;

[0021] S22. Randomly generate an expPop and a tracPop, both with a population size of N.

[0022] The objective function is set, and the calculation formula is as follows:

[0023] (2-1)

[0024] Constraints:

[0025] The decision variable constraints are calculated using the following formula:

[0026] (2-2)

[0027] The target value constraint is calculated using the following formula:

[0028] (2-3)

[0029] In the formula, For decision-making space; It is the objective function, where To minimize the maximum pressure value of the system To minimize the negative pressure value of the system For the pump station unit to have the lowest relative reverse speed, To minimize the overall valve closing time; for One of the solutions, For the quick-closing time of the valve after the pump, For the quick-closing angle of the valve after the pump, This refers to the total closing time of the valves after the pump. This is the shortest possible time for the downstream valve to be controllable. The longest time that the downstream valve can be controlled; This refers to the rated outlet pressure of the water pump unit. This refers to the rated speed of the water pump unit;

[0030] S23. Initialize the population's solutions to ensure that the solutions are within or close to the feasible region.

[0031] Furthermore, in step S3, the differential screening method includes the following steps:

[0032] S31, from expPop g Selecting mating generates N solutions, called offspring 1; from tracPop g Selecting a mating pair generates N solutions, which are called offspring 2;

[0033] S32, merge expPop g Child 1 and Child 2 form Pop1; merge tracPop. g Pop2 is composed of offspring 1 and offspring 2.

[0034] S33. Sort Pop1 according to CDPε=0, select the N better solutions (those with higher non-dominated layers), and generate the next generation development population expPop. g+1 , where ε is the maximum total constraint violation in the current population;

[0035] S34. Sort Pop2 according to CDPε=∞, select the N better solutions (those with higher non-dominated layers), and generate the next generation tracking population tracPop. g+1 ;

[0036] S35. Determine if the following condition is met: number of iterations. If the condition is met, proceed to the next step; otherwise, the iteration count is [number missing]. Add 1, then proceed to step S31.

[0037] Furthermore, in step S3, the stability verification method includes the following steps:

[0038] S36, Calculate the ( ) - ) to the The rate of change of the ideal point, minimum point, and average point of a time is given by the following formula:

[0039] (3-1)

[0040] (3-2)

[0041] (3-3)

[0042] in, These are the tracPop numbers. The ideal point, the lowest point, and the average point of a generation; It is the algebraic interval number; It is a sufficiently small value to ensure that the denominator of the formula is not zero;

[0043] choose , and The maximum value in the value is taken as the rate of change of tracPop, that is:

[0044] (3-4)

[0045] S37. Determine if the following conditions are met: If the condition is met, the state of tracPop is considered stable and close to the unconstrained Pareto front (UPF). Equal to the maximum total constraint violation of the current population Output expPop g+1 and tracPop g+1 Proceed to step S4; otherwise, repeat the iteration. Add 1, then proceed to step S31;

[0046] (3-5)

[0047] in, To constrain the quantity; For the first The degree of violation of a constraint.

[0048] Furthermore, step S4 includes the following steps:

[0049] S41. Calculate the feasibility rate rf of expPop. exp The feasibility rate (rf) of tracPop trac and ε(g);

[0050] S42, according to rf trac The value is used to generate offspring 1 and offspring 2 through a dynamic co-evolutionary strategy (DCS, supported by a dynamic cooperation strategy). If rf exp =0, then offspring 3 is generated according to the dual-population diversity selection (BPDS, implemented by the boundary point direction sampling strategy);

[0051] S43, merge expPop g Child 1, Child 2, and Child 3 form Pop1; merge tracPop. g Pop2 is composed of offspring 1, offspring 2, and offspring 3.

[0052] S44. Sort Pop1 according to CDPε=0, and select the N better solutions (those with higher non-dominated layers) as the next generation development population expPop. g+1 ;

[0053] S45. Select N solutions from Pop2 using the Dynamic Integration Strategy (DES, implemented by the Dynamic Environment Selection Strategy) to form the next-generation tracking population tracPop. g+1 .

[0054] Furthermore, step S42 includes the following steps:

[0055] S421, from expPop g Select A solution is generated by selecting mating pairs. Each descendant solution generates a descendant 1. The calculation formula is as follows:

[0056] (4-1)

[0057] in, It is the feasibility rate of tracPop;

[0058] S422, Merge tracPop g and expPopg The remaining A solution is obtained, forming a mating pool, and a neighborhood pairing strategy is used to generate [the desired mating pool]. Each child solution is generated, i.e., child 2 is generated;

[0059] S423, when rf exp When =0, then in tracPop g Random selection Each reference solution forms a reference solution set repPop;

[0060] S424. Calculate the Euclidean distance between each reference solution and two boundary points in the decision space, using the following formula:

[0061] (4-2)

[0062] (4-3)

[0063] in, For the first A selected reference solution; and Let these represent the lower and upper boundary points in the decision space, respectively.

[0064] S425, according to and and Given the Euclidean distance between them, the number of new solutions generated along these two directions is calculated using the following formula:

[0065] (4-4)

[0066] (4-5)

[0067] along and The new solution generated by the direction can be represented as follows:

[0068] (4-6)

[0069] (4-7)

[0070] in, The number of new solutions generated for each reference solution;

[0071] S426, Merging and , and generate 3 offspring.

[0072] Furthermore, step S45 includes the following steps:

[0073] S451, Calculate tracPop g Feasibility and the ε value of the current generation ;

[0074] S452, when ,and At that time, Pop2 uses the weight vector Assigned to The nth sub-region is defined as follows:

[0075] (4-8)

[0076] in, This is the threshold for feasibility assessment (default is 10). -7 ); ; for and The angle between them;

[0077] S453, Pop2 n Initialize to the target value in Pop2 The solution in;

[0078] S454. Adjust the number of solutions in each sub-region to 1. That is, if the number of solutions in the k-th sub-region is zero, then randomly select a solution from Pop2 and add it to Pop2. n In the middle; if Pop2 n The number of solutions is greater than 1, so CDPε is used for Pop2. n Sort the solutions in the POP2 array and select the highest-ranking |Pop2 n -1 solution from Pop2 n Remove from;

[0079] S455. Merge the solutions in all sub-regions to obtain the next generation of tracking population. ;

[0080] S456, when or At that time, Pop2 is sorted according to CDPε, and N solutions are selected from the better Pop2 (those in the front of the non-dominated layer) to form the next generation tracking population tracPop. g+1 .

[0081] Furthermore, in step S5, the optimization scheme for generating the hydraulic transition process first determines the number of iterations. If the conditions are met, then merge the final updated expPop. g+1 and tracPop g+1Then, select a set of feasible and non-dominated solutions as the optimization scheme for the hydraulic transition process; if the solution is not satisfied, continue execution according to the preset iteration mechanism.

[0082] The beneficial effects of this invention are as follows: This invention provides a two-stage hydraulic transition process optimization method based on a tracking population-dominated dual-population approach, achieving multi-dimensional optimization improvements. It employs a dual-population architecture of a development population and a tracking population to achieve collaborative global and local searches. The development population focuses on in-depth mining of local high-quality solution domains, ensuring optimization accuracy; the tracking population expands the global solution space, effectively avoiding local optimum traps. Combining two-stage iteration with multi-strategy assistance, it balances solution coverage and positioning accuracy. It exhibits outstanding multi-constraint adaptability, ensuring the initial feasible solution ratio during the initialization phase. During iteration, it constructs an identification-guidance-correction closed loop through population information interaction, transforming infeasible solutions into search-guiding information, significantly reducing ineffective iterations and resource consumption. A dynamic cooperation mechanism enhances optimization efficiency: it dynamically adjusts the population cooperation intensity based on the tracking population's feasibility rate, introduces a boundary point direction sampling strategy to improve population diversity, and employs a dynamic environment selection mechanism to prevent the tracking population from over-exploring infeasible domains in the later stages.

[0083] In terms of practicality, the DPTPEA algorithm is deeply coupled with the hydraulic model of the method of characteristics, accurately outputting key parameters such as the maximum / minimum pressure of the pipeline and the maximum reverse speed of the pumping station unit, clarifying the optimized valve and pump operating parameters and system design scheme; the overall coordination is efficient and the scheme is highly feasible, which can effectively avoid operational safety risks, reduce energy consumption and operation and maintenance costs, and ensure the stable operation of the water conveyance system.

[0084] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0085] Figure 1 This is a flowchart of the steps in the hydraulic transition process calculation and optimization method of the present invention;

[0086] Figure 2 This is a flowchart illustrating the calculation and optimization method for the hydraulic transition process of the present invention.

[0087] Figure 3 This is a flowchart of the first stage strategy in step 3 of an embodiment of the present invention;

[0088] Figure 4 This is a flowchart of the second stage strategy in step 4 of an embodiment of the present invention;

[0089] Figure 5 This is a flowchart of the dynamic cooperation strategy in step 4 of an embodiment of the present invention;

[0090] Figure 6 This is a flowchart of the boundary point direction sampling strategy in step 4 of an embodiment of the present invention;

[0091] Figure 7 This is a flowchart of the dynamic environment selection method in step 4 of an embodiment of the present invention. Detailed Implementation

[0092] This embodiment presents an optimization method for a two-stage hydraulic transition process based on a tracking population-dominant dual-population population, such as... Figure 1 , Figure 2 As shown, it includes the following steps:

[0093] S1, Model building and algorithm coupling:

[0094] 1. Data Collection:

[0095] This includes drawings of the water transmission pipeline system, the internal structure of the hydraulic facilities, the structure of the pumping station and the pipeline layout in the plant area, as well as parameters such as the characteristic curves of the pumping station units, pipeline wave velocity, flow rate, design operating pressure, pipe material, wall thickness, roughness, friction coefficient, and local head loss coefficient.

[0096] The parameters to be evaluated in the DPTPEA main program include the valve opening and closing time and angle in the piping system, and the pump start and stop times.

[0097] 2. Model Building:

[0098] The water hammer control equations of the pipeline system are established by using the method of characteristics. Combined with boundary conditions such as pumps and valves, a hydraulic transient process calculation model is constructed as an external program.

[0099] The method of characteristics is a method that transforms partial differential equations into ordinary differential equations, and then further discretizes them into algebraic equations. The main components of constructing a computational model for the hydraulic transient process include: water hammer control equations, valve boundary calculation models, pump boundary calculation models, constant water level boundary calculation models, and pipeline connection mathematical models.

[0100] 1) Water hammer governing equations:

[0101] According to Newton's second law, the equation of motion for a infinitesimal fluid element can be derived, and the calculation formula is as follows:

[0102] (1-1)

[0103] According to the law of conservation of mass, the continuity equation for water hammer calculation can be obtained, and the calculation formula is as follows:

[0104] (1-2)

[0105] Where H represents the water head at a point in the pipe, in meters (m); V represents the water velocity in the pipe, in meters per second (m / s); and g represents the acceleration due to gravity, in meters per second (m / s²). 2f represents the Darcy-Wiesbach friction coefficient; α represents the angle between the horizontal line and the center line of the pipe (°); a represents the water hammer wave propagation speed (m / s); D represents the pipe diameter (m); x represents the position coordinate along the pipe axis (m); t represents time (s).

[0106] The above equation is transformed using the method of characteristics to obtain the equation of characteristics, and the calculation formula is as follows:

[0107] (1-3)

[0108] (1-4)

[0109] 2) Valve boundary calculation model:

[0110] During transient processes, the valve orifice equation under steady-state conditions can be used, and the calculation formula is as follows:

[0111] (1-5)

[0112] The boundary conditions for valve opening and closing are as follows: .

[0113] For valves in pipelines, the calculation formula is as follows:

[0114] (1-6)

[0115] In the formula: .

[0116] When negative flow occurs, the calculation formula is as follows:

[0117] (1-7)

[0118] In the above formula: It is the flow rate through the valve. It is the flow rate when the valve is fully open. This refers to the head difference between the two ends of the valve under actual operating conditions. It is the head difference between the two sides when the valve is fully open. It is the flow coefficient corresponding to the valve opening degree. This refers to the area of ​​the valve opening at the calculated moment. The upstream and downstream pipeline parameters of the valve are indicated by subscripts 1 and 2.

[0119] 3) Pump boundary calculation model:

[0120] The boundary mathematical model of the water pump includes the flow function WH(X) and the torque function WB(X), and the calculation formulas are as follows:

[0121] (1-8)

[0122] (1-9)

[0123] in,

[0124] (1-10)

[0125] In the above formula, N and N r These are the pump speed and the pump rated speed, respectively, in r / min; Q and Q r These are the pump flow rate and the pump rated flow rate, respectively, in m³ / s; H and H r These are the pump head and the rated pump head, respectively, in meters (m); M and M r These are the pump torque and the pump rated torque, respectively, in N·M.

[0126] 4) Calculation model for fixed water level boundary:

[0127] The upstream boundary condition is that the reservoir and the closed pipeline are connected, and the boundary equations are:

[0128] (1-11)

[0129] In the formula, The upstream water level, The first and second nodes of the inlet pipeline are represented by subscripts 1 and 2, and the subscript p represents the end value of the time period.

[0130] The downstream boundary condition is that the regulating tank and the closed pipeline are connected, and its boundary equation is:

[0131] (1-12)

[0132] In the formula, The water level in the downstream regulating reservoir, The subscripts NS and NS-1 represent the last node and the second-to-last node of the pipeline, respectively, and the subscript p represents the value at the end of the current time period.

[0133] 5) Mathematical model for pipe connections:

[0134] The boundary conditions for series, parallel, merging, and branching connections of pipelines need to satisfy the continuity equation and the energy equation.

[0135] Flow continuity equation:

[0136] (1-13)

[0137] Energy equation:

[0138] (1-14)

[0139] in, This indicates the piezometric head and velocity head at the corresponding cross-section. This represents the head loss in the pipeline, and K represents the local loss coefficient. Adding the absolute value ensures that the condition holds true even when the flow is reversed. The two terms on the right side... This indicates the piezometric head and velocity head at the corresponding cross-section.

[0140] 3. Algorithm coupling:

[0141] The coupling of the two models is achieved by calling this external program through the main program of the Dual Population Two-Stage Optimization Algorithm (DPTPEA). Specifically, during DPTPEA's operation, it calls the external hydraulic model program via instructions, simultaneously inputting the parameters to be evaluated into the hydraulic model. Once the hydraulic model program completes its calculations, it returns the calculated results of the pipeline system's maximum and minimum pressure values, the pump station unit's maximum reverse rotation speed, as well as valve opening and closing times and angles, and pump start and stop times, in a predetermined format to the DPTPEA main program, thus enabling coordinated operation between the two.

[0142] In the initial phase of collaborative operation, the DPTPEA main program initializes the population parameters and generates initial parameter combinations based on the characteristics and requirements of the problem. These parameter combinations represent different pipeline system design and operation schemes. The main program then sequentially passes these parameter combinations to the hydraulic modeling program according to a predetermined scheduling strategy.

[0143] After receiving the parameters, the hydraulic model program initiates the calculation process. Based on the water hammer control equations established using the method of characteristics and boundary conditions such as pumps and valves, it simulates the hydraulic transient process of the pipeline system corresponding to each parameter combination. During the simulation, it calculates the pressure distribution, flow rate changes, pump unit speed, and water hammer wave propagation within the pipeline at different times. After the calculation is completed, it returns the key hydraulic parameter results—maximum pressure, minimum pressure, and maximum reverse speed of the pump unit—to the DPTPEA main program.

[0144] S2, Initialize algorithm parameters and generate population:

[0145] The Dual Population Two-Stage Optimization Algorithm (DPTPEA) maintains two sets of data simultaneously (development population and tracking population). The algorithm optimizes the two sets of data step by step to find the optimal solution.

[0146] Initialize DPTPEA parameters; randomly generate the development population (expPop) and the tracking population (tracPop);

[0147] S21, Initialize DPTPEA parameters:

[0148] Population size 100, initial iteration count 1. Maximum number of iterations 200, algebraic interval number 20, switching threshold 0.001, tracking population change rate Initially 1;

[0149] S22, randomly generate the development population (expPop) and the tracking population (tracPop).

[0150] The objective function is set, and the calculation formula is as follows:

[0151] (2-1)

[0152] Constraints:

[0153] The decision variable constraints are calculated using the following formula:

[0154] (2-2)

[0155] The target value constraint is calculated using the following formula:

[0156] (2-3)

[0157] In the formula, For decision-making space; It is the objective function, where To minimize the maximum pressure value of the system To minimize the negative pressure value of the system For the pump station unit to have the lowest relative reverse speed, To minimize the overall valve closing time; for One of the solutions, For the quick-closing time of the valve after the pump, For the quick-closing angle of the valve after the pump, This refers to the total closing time of the valves after the pump. This is the shortest possible time for the downstream valve to be controllable. The longest time that the downstream valve can be controlled; This refers to the rated outlet pressure of the water pump unit. This is the rated speed of the water pump unit.

[0158] S23. Initialize the solution of the population to ensure that the solution is within or close to the feasible region, that is, ensure that the maximum pressure value, minimum pressure value and relative reverse speed of the pump station unit in the hydraulic transition process of the pipeline system meet or are close to the target value constraints.

[0159] S3, Phase 1 - Two-Population Differential Screening and Stability Verification:

[0160] like Figure 3 As shown, the dual population expands the range of possible solutions through targeted fusion, and combined with differentiated screening, it enhances the local optimization capability of the development population and the global exploration capability of the tracking population. Through iterative control and state evaluation, it outputs a stable dual population with excellent optimization capabilities, providing a basis for screening optimization schemes for hydraulic transition processes.

[0161] S31, from expPop g Selecting mating generates N solutions, called offspring 1; from tracPop g Choose from mating to generate N solutions, called offspring 2, N=100;

[0162] S32, merge expPop g Child 1 and Child 2 form Pop1; merge tracPop. g Pop2 is composed of offspring 1 and offspring 2.

[0163] S33. Calculate the constraint violation degree for each solution. Based on the constraint dominance principle (CDPε=0) when ε=0, Pop1 is sorted, and the N best solutions (N=100) are selected (those at the front of the non-dominated layer) to generate the next generation development population expPop. g+1 Where ε is the maximum overall constraint violation in the current population, ε=0 means no relaxation of the constraint violation, and the feasibility is strictly judged: when the overall constraint violation... When the value is 0, the solution is considered feasible.

[0164] Specifically, for any two solutions X1 and X2, solution X1 governs solution X2 if and only if any one of the following conditions is satisfied:

[0165] 1) Solving X1 is feasible ( =0) and solution X2 is not feasible ( >0);

[0166] 2) Both solutions X1 and X2 are feasible, and X1 dominates X2 in the target space Pareto.

[0167] 3) Both solutions X1 and X2 are infeasible, and < .

[0168] Based on the constraint dominance principle of CDPε=0, a standard non-dominated sort is performed on Pop1, resulting in several non-dominated layers from front to back. Individuals are then selected sequentially according to the layer order until N solutions are selected, forming the next generation of the exploration population expPop. g+1This process ensures that feasible solutions are always retained over infeasible solutions, while maintaining Pareto dominance among feasible solutions and prioritizing the retention of individuals with lower constraint violations among infeasible solutions, thus effectively balancing convergence, diversity, and feasibility.

[0169] S34. Sort Pop2 according to CDPε=∞, select the N best solutions (N=100) (with the non-dominated layers at the top), and generate the next generation tracking population tracPop. g+1 Where ε=∞ represents ignoring constraints, that is, regardless of the degree of constraint violation in the solution. The size is such that all solutions are considered feasible.

[0170] S35. Determine if the following condition is met: number of iterations. If the condition is met, proceed to step S36; otherwise, the iteration count is [number missing]. Add 1, then proceed to step S31.

[0171] S36, Calculate the ( ) - ) to the The rate of change of the ideal point, minimum point, and average point of a time is given by the following formula:

[0172] (3-1)

[0173] (3-2)

[0174] (3-3)

[0175] in, These are the tracPop numbers. The ideal point, the lowest point, and the average point of a generation; It is a sufficiently small value to ensure that the denominator of the formula is not zero.

[0176] choose , and The maximum value in the value is taken as the rate of change of tracPop, and the expression is as follows:

[0177] (3-4)

[0178] S37. Determine if the following conditions are met: If the condition is met, the state of tracPop is considered stable and close to the unconstrained Pareto front (UPF). Equal to the maximum total constraint violation of the current population Output expPop g+1 and tracPop g+1Proceed to step S4; otherwise, repeat the iteration. Add 1, then proceed to step S31.

[0179] (3-5)

[0180] in, To constrain the quantity; For the first The degree of violation of a constraint.

[0181] S4, Phase 2 - Dual-population multi-strategy collaborative cyclical update;

[0182] like Figure 4 , Figure 5 , Figure 6 and Figure 7 As shown, the two populations are updated cyclically through the synergistic effect of dynamic cooperation strategy, boundary point direction sampling strategy and dynamic environment selection; this improves the cooperation efficiency in the population update process, avoids the population from getting trapped in local optima, and avoids the tracking population from over-exploring infeasible areas in the later stages of the update, thus avoiding cost waste.

[0183] S41. Calculate the feasibility rate rf of expPop. exp The feasibility rate (rf) of tracPop trac And ε(g), where the feasibility rate is the overall constraint violation rate in the population. The proportion of individuals with a value of 0;

[0184] S42, according to rf trac The value is used to generate offspring 1 and offspring 2 through a dynamic co-evolutionary strategy (DCS, supported by a dynamic cooperation strategy). If rfexp=0, offspring 3 is generated according to dual-population diversity selection (BPDS, implemented by a boundary point direction sampling strategy). The specific steps are as follows:

[0185] S421, from expPop g Select A solution is generated by selecting mating pairs. Each descendant solution generates a descendant 1. The calculation formula is as follows:

[0186] (4-1)

[0187] in, It is the feasibility rate of tracPop.

[0188] S422, Merge tracPop g and expPop g The remaining A solution is obtained, forming a mating pool, and a neighborhood pairing strategy is used to generate [the desired mating pool]. Each child solution is generated, i.e., child 2 is generated;

[0189] S423, when rf exp When =0, then in tracPop g Random selection Each reference solution forms a reference solution set repPop;

[0190] S424. Calculate the Euclidean distance between each reference solution and two boundary points in the decision space, using the following formula:

[0191] (4-2)

[0192] (4-3)

[0193] in, For the first A selected reference solution; and Let represent the lower boundary point and the upper boundary point in the decision space, respectively.

[0194] S425, according to and and Given the Euclidean distance between them, the number of new solutions generated along these two directions is calculated using the following formula:

[0195] (4-4)

[0196] (4-5)

[0197] along and The new solution generated by the direction is expressed by the following formula:

[0198] (4-6)

[0199] (4-7)

[0200] in, The number of new solutions generated for each reference solution;

[0201] S426, Merging and Generate 3 offspring;

[0202] In the Dynamic Co-evolution Strategy (DCS), two populations interact dynamically. expPop provides diversity information, while tracPop focuses on optimizing feasible solutions. By dynamically adjusting the offspring generation strategy, offspring 1 strengthens its advantages, offspring 2 makes up for its shortcomings, and the real-time state of tracPop is precisely matched to achieve co-evolution of the two populations.

[0203] Two-Population Diversity Selection (BPDS) employs a strategy of selecting individuals, prioritizing the retention of solutions with high diversity to enhance population diversity, prevent the population from getting trapped in local optima, avoid algorithm convergence due to the complete infeasibility of exploring the population, and generate new offspring 3 to maintain optimization vitality.

[0204] S43, merge expPop g Child 1, Child 2, and Child 3 form Pop1; merge tracPop. g Pop2 is composed of offspring 1, offspring 2, and offspring 3.

[0205] S44. Sort Pop1 according to CDPε=0, and select the N best solutions (N=100) (with the non-dominated layers at the top) as the next generation development population expPop. g+1 ;

[0206] S45. Select N solutions (N=100) from Pop2 using the Dynamic Integration Strategy (DES, implemented by the Dynamic Environment Selection Strategy) to form the next-generation tracking population tracPop. g+1 ;

[0207] Dynamic ensemble strategy (DES) dynamically adjusts the selection criteria for solutions in the tracking population (tracPop). g+1 During the update process, the overexploration of infeasible regions is accurately identified and avoided. By prioritizing solutions within or closer to the feasible region, resource investment in ineffective regions is reduced, and cost waste caused by meaningless exploration is avoided. This ensures that population updates focus on valuable search spaces. The specific steps are as follows:

[0208] S451, Calculate tracPop g Feasibility and the ε value of the current generation ;

[0209] S452, when ,and At that time, Pop2 uses the weight vector They are assigned to 100 sub-regions, and the nth sub-region is defined as follows:

[0210] (4-8)

[0211] in, This is the threshold for feasibility assessment (default is 10). -7 ); ; for and The angle between them This indicates that for each i in the set {1,2,⋯,100}, the following condition... Both must be established.

[0212] S453, Pop2 n Initialize to the target value in Pop2 The solution in;

[0213] S454. Adjust the number of solutions in each sub-region to 1. That is, if the number of solutions in the k-th sub-region is zero, then randomly select a solution from Pop2 and add it to Pop2. n In the middle; if Pop2 n The number of solutions is greater than 1, so CDPε is used for Pop2. n Sort the solutions in the POP2 array and select the highest-ranking |Pop2 n -1 solution from Pop2 n Remove from;

[0214] S455. Merge the solutions in all sub-regions to obtain the next generation of tracking population. ;

[0215] S456, when or At that time, Pop2 is sorted according to CDPε, and N solutions (N=100) are selected from the better Pop2 (those in the front of the non-dominated layer) to form the next generation tracking population tracPop. g+1 .

[0216] S5. Optimization scheme for generating the hydraulic transition process:

[0217] Merge the final updated expPop and tracPop, and select a feasible and non-dominated solution from them as the optimization scheme for the hydraulic transition process.

[0218] Determine if the following condition is met: number of iterations If the conditions are met, then merge the final updated expPop. g+1 and tracPop g+1 Then, select a feasible and non-dominated solution from these solutions as the optimal solution for the hydraulic transient process; otherwise, the number of iterations... Add 1, then return to step S35.

[0219] By deeply coupling the DPTPEA algorithm with the characteristic line method hydraulic model, an optimized hydraulic transient process scheme is obtained. This scheme accurately outputs key hydraulic parameters such as the maximum and minimum pressure values ​​of the pipeline system and the maximum reverse rotation speed of the pumping station units. It also clarifies optimized valve opening and closing times and angles, pump start and stop times, and other operating parameters and pipeline system design schemes. The overall approach is highly efficient and feasible, effectively mitigating safety risks, reducing energy consumption and maintenance costs, and ensuring the stable operation of the water conveyance system.

[0220] (1) This invention constructs an optimization method for a two-stage hydraulic transition process based on a dominant tracking population. Compared with other methods, this method makes full use of infeasible solution information and improves the algorithm's ability to solve constrained multi-objective optimization problems.

[0221] (2) In the second stage, the present invention proposes a dynamic cooperation strategy, which dynamically adjusts the cooperation intensity between the two populations according to the feasibility of the tracking population, thereby improving the cooperation efficiency in the population renewal process.

[0222] (3) In the second stage, the present invention introduces a boundary point direction sampling strategy to enhance population diversity and avoid the population from easily getting trapped in local optima;

[0223] (4) In the second stage, the present invention adopts a dynamic environment selection method to avoid the tracking population from over-exploring infeasible areas in the later stage of the update, which would result in cost waste.

[0224] Finally, it should be noted that the above is only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. An optimization method for a two-stage hydraulic transition process based on a dominant dual-population population, characterized in that, Includes the following steps: S1. Model building and algorithm coupling: Collect basic data, construct a calculation model of the hydraulic transition process, and integrate it into the dual-population two-stage optimization algorithm (DPTPEA); S2. Initialize algorithm parameters and generate population: Initialize the DPTPEA parameters and randomly generate the development population (expPop) and the tracking population (tracPop). S3, Phase 1 - Two-population differential screening and stability verification; The dual-population approach expands the range of available solutions through targeted fusion, and combined with differentiated screening, it enhances the local optimization capabilities of the development population and the global exploration capabilities of the tracking population. Through iterative control and state evaluation, it outputs a stable dual-population with excellent optimization capabilities. S4, Phase 2 - Dual-population multi-strategy collaborative cyclical update; The two populations are updated cyclically through the combined effects of dynamic cooperation strategy, boundary point direction sampling strategy and dynamic environment selection. S5. Optimization scheme for generating the hydraulic transition process: The final updated expPop and tracPop are merged, and a feasible and non-dominated scheme is selected as the optimal scheme for the hydraulic transition process.

2. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 1, characterized in that, In step 1, the water hammer control equation of the pipeline system is established by the method of characteristics. Combined with the pump and valve boundary conditions, the hydraulic transient process calculation model is constructed as an external program. The external program is called by the main program of the dual population two-stage optimization algorithm (DPTPEA) to realize the coupling of the two models.

3. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 2, characterized in that, The combined pump and valve boundary conditions consist of a valve boundary calculation model, a water pump boundary calculation model, a constant water level boundary calculation model, and a pipeline connection mathematical model.

4. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 1, characterized in that, Step S2 includes the following steps: S21. Initialize DPTPEA parameters, including: population size N, number of iterations. Maximum number of iterations Algebraic interval number Switching threshold Tracking the rate of change in the population ; S22. Randomly generate an expPop and a tracPop, both with a population size of N. The objective function is set, and the calculation formula is as follows: （2-1） Constraints: The decision variable constraints are calculated using the following formula: （2-2） The target value constraint is calculated using the following formula: （2-3） In the formula, For decision-making space; It is the objective function, where To minimize the maximum pressure value of the system To minimize the negative pressure value of the system For the pump station unit to have the lowest relative reverse speed, To minimize the overall valve closing time; for One of the solutions, For the quick-closing time of the valve after the pump, For the quick-closing angle of the valve after the pump, This refers to the total closing time of the valves after the pump. This is the shortest possible time for the downstream valve to be controllable. The longest time that the downstream valve can be controlled; This refers to the rated outlet pressure of the water pump unit. This refers to the rated speed of the water pump unit; S23. Initialize the population's solutions to ensure that the solutions are within or close to the feasible region.

5. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 1, characterized in that, In step S3, the differential screening method includes the following steps: S31, from expPop g Selecting mating generates N solutions, called offspring 1; from tracPop g Selecting a mating pair generates N solutions, which are called offspring 2; S32, merge expPop g Child 1 and Child 2 form Pop1; merge tracPop. g Pop2 is composed of offspring 1 and offspring 2. S33. Sort Pop1 according to CDPε=0, select the N better solutions (those with higher non-dominated layers), and generate the next generation development population expPop. g+1 , where ε is the maximum total constraint violation in the current population; S34. Sort Pop2 according to CDPε=∞, select the N better solutions (those with higher non-dominated layers), and generate the next generation tracking population tracPop. g+1 ; S35. Determine if the following condition is met: number of iterations. If the condition is met, proceed to the next step; otherwise, the iteration count is [number missing]. Add 1, then proceed to step S31.

6. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 1, characterized in that, In step S3, the stability verification method includes the following steps: S36, Calculate the ( ) - ) to the The rate of change of the ideal point, minimum point, and average point of a time is given by the following formula: （3-1） （3-2） （3-3） in, These are the tracPop numbers. The ideal point, the lowest point, and the average point of a generation; It is the algebraic interval number; It is a sufficiently small value to ensure that the denominator of the formula is not zero; choose , and The maximum value in the value is taken as the rate of change of tracPop, that is: （3-4） S37. Determine if the following conditions are met: If the condition is met, the state of tracPop is considered stable and close to the unconstrained Pareto front (UPF). Equal to the maximum total constraint violation of the current population Output expPop g+1 and tracPop g+1 Proceed to step S4; otherwise, repeat the iteration. Add 1, then proceed to step S31; （3-5） in, To constrain the quantity; For the first The degree of violation of a constraint.

7. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 1, characterized in that, Step S4 includes the following steps: S41. Calculate the feasibility rate rf of expPop. exp The feasibility rate (rf) of tracPop trac and ε(g); S42, according to rf trac The value is used to generate offspring 1 and offspring 2 through a dynamic co-evolutionary strategy (DCS, supported by a dynamic cooperation strategy). If rf exp =0, then offspring 3 is generated according to the dual-population diversity selection (BPDS, implemented by the boundary point direction sampling strategy); S43, merge expPop g Child 1, Child 2, and Child 3 form Pop1; merge tracPop. g Pop2 is composed of offspring 1, offspring 2, and offspring 3. S44. Sort Pop1 according to CDPε=0, and select the N better solutions (those with higher non-dominated layers) as the next generation development population expPop. g+1 ; S45. Select N solutions from Pop2 using the Dynamic Integration Strategy (DES, implemented by the Dynamic Environment Selection Strategy) to form the next-generation tracking population tracPop. g+1 .

8. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 7, characterized in that, Step S42 includes the following steps: S421, from expPop g Select A solution is generated by selecting mating pairs. Each descendant solution generates a descendant 1. The calculation formula is as follows: （4-1） in, It is the feasibility rate of tracPop; S422, Merge tracPop g and expPop g The remaining A solution is obtained, forming a mating pool, and a neighborhood pairing strategy is used to generate [the desired mating pool]. Each child solution is generated, i.e., child 2 is generated; S423, when rf exp When =0, then in tracPop g Random selection Each reference solution forms a reference solution set repPop; S424. Calculate the Euclidean distance between each reference solution and two boundary points in the decision space, using the following formula: （4-2） （4-3） in, For the first A selected reference solution; and Let these represent the lower and upper boundary points in the decision space, respectively. S425, according to and and Given the Euclidean distance between them, the number of new solutions generated along these two directions is calculated using the following formula: （4-4） （4-5） along and The new solution generated by the direction can be represented as follows: （4-6） （4-7） in, The number of new solutions generated for each reference solution; S426, Merging and , and generate 3 offspring.

9. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 7, characterized in that, Step S45 includes the following steps: S451, Calculate tracPop g Feasibility and the ε value of the current generation ; S452, when ,and At that time, Pop2 uses the weight vector Assigned to The nth sub-region is defined as follows: （4-8） in, This is the threshold for feasibility assessment (default is 10). -7 ); ; for and The angle between them; S453, Pop2 n Initialize to the target value in Pop2 The solution in; S454. Adjust the number of solutions in each sub-region to 1. That is, if the number of solutions in the k-th sub-region is zero, then randomly select a solution from Pop2 and add it to Pop2. n In the middle; if Pop2 n The number of solutions is greater than 1, so CDPε is used for Pop2. n Sort the solutions in the POP2 array and select the highest-ranking |Pop2 n -1 solution from Pop2 n Remove from; S455. Merge the solutions in all sub-regions to obtain the next generation of tracking population. ; S456, when or At that time, Pop2 is sorted according to CDPε, and N solutions are selected from the better Pop2 (those in the front of the non-dominated layer) to form the next generation tracking population tracPop. g+1 .

10. The optimization method for a two-stage hydraulic transition process based on a dominant dual-population population according to claim 1, characterized in that, In step S5, the optimization scheme for generating the hydraulic transition process first determines the number of iterations. If the conditions are met, then merge the final updated expPop. g+1 and tracPop g+1 Then, select a set of feasible and non-dominated solutions as the optimization scheme for the hydraulic transition process; if the solution is not satisfied, continue execution according to the preset iteration mechanism.

Images