Water conservancy project water transfer scheme optimization method based on multi-target particle swarm optimization

Abstract

The invention belongs to the technical field of particle swarm optimization, and particularly relates to a water conservancy project water transfer scheme optimization method based on multi-target particle swarm optimization. The method comprises the following steps of: 1, generating a group of initial water transfer flow sequences for each candidate water transfer scheme in a preset discrete time interval; 2, in order to ensure that the water level of the reservoir is always kept in a safe range and prevent sudden change in the water transfer process, constructing a water level physical constraint according to the simulated water level data; and 3, taking the initial water transfer flow sequence as an initial search space of a particle swarm optimization algorithm, taking the comprehensive evaluation function as a target function of the particle swarm optimization algorithm, and finding an optimal water transfer scheme from the candidate water transfer schemes in an iterative updating mode. According to the method, the optimization precision and the result reliability are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of particle swarm optimization, and in particular relates to a method for optimizing a water diversion scheme for a hydraulic project based on multi-objective particle swarm optimization. Background Art

[0002] As the contradiction between global water supply and demand becomes increasingly serious, water conservancy projects play an important role in the allocation and rational use of water resources. As an important infrastructure for regulating the amount of water upstream and downstream, the scientific scheduling and efficient operation of reservoirs are crucial to water resource management and regional economic development. In practical applications, the water diversion process of water conservancy projects involves the dynamic interaction of multiple complex factors, such as changes in inflow, adjustment of water diversion flow, water level safety management, and energy consumption control. These factors are not only highly nonlinear and time-varying, but also have multiple mutually coupled constraints, which makes the optimization of reservoir scheduling extremely complex. Existing technologies have made certain progress in optimizing water diversion schemes, but still face many problems that need to be solved.

[0003] Among the disclosed technologies, traditional reservoir scheduling mostly adopts methods such as linear programming, dynamic programming or genetic algorithms. These methods usually establish a linear relationship model between the water diversion flow and the reservoir water level or use heuristic algorithms for optimization. However, these traditional methods have obvious shortcomings when dealing with actual complex working conditions. First, due to the simplification of assumptions, the linear programming method cannot accurately describe the nonlinear dynamic characteristics of reservoir water level changes, especially under conditions of high head difference and complex flow changes, which can easily lead to large deviations between the water diversion plan and the actual situation. **Secondly, although the dynamic programming method can solve some nonlinear problems through multi-stage optimization, its computational complexity is high, especially in multi-objective optimization scenarios. With the increase of constraints and optimization targets, the computational cost increases exponentially, which is difficult to adapt to real-time scheduling needs. In addition, although heuristic optimization methods such as genetic algorithms and simulated annealing have certain global search capabilities, they are prone to fall into local optimal solutions under multi-objective constraint environments, and due to the lack of an efficient convergence judgment mechanism, the stability of the optimization results is difficult to guarantee. Summary of the invention

[0004] The main purpose of the present invention is to provide a method for optimizing water diversion schemes for water conservancy projects based on multi-objective particle swarm optimization. By constructing a nonlinear second-order dynamic water level model, an energy consumption economic target model, and a water level physical constraint, combined with dynamic modeling of pump station efficiency and a multi-objective comprehensive evaluation function, the present invention achieves energy consumption minimization, water level safety assurance, and water level change stability control in the process of reservoir water diversion. By introducing an improved particle swarm optimization algorithm and an adaptive convergence judgment mechanism, the optimization process is more intelligent and efficient, and the global optimal solution can be found quickly. Compared with traditional methods, the present invention significantly improves the optimization accuracy and reliability of the results, effectively reduces the energy consumption cost in the water diversion process, ensures the long-term stable operation of the reservoir, and has a high practical application value and promotion prospects.

[0005] In order to solve the above technical problems, the present invention provides

[0006] A water diversion scheme optimization method for a hydraulic project based on multi-objective particle swarm optimization, the method comprising:

[0007] Step 1: Generate a set of initial water diversion flow sequences for each candidate water diversion scheme within a preset discrete time interval; For each candidate water diversion scheme, use a second-order dynamic model including water body inertia, damping effect and nonlinear coupling terms to simulate the reservoir water level in a time-varying manner to obtain simulated water level data;

[0008] Step 2: To ensure that the reservoir water level is always kept within a safe range and to prevent sudden changes in the water transfer process, a water level physical constraint is constructed based on the simulated water level data; an economic target model that reflects the energy consumption of the water transfer process is established; and a comprehensive evaluation function is formed based on nonlinear coupling between the economic target model and the water level physical constraint;

[0009] Step 3: Use the initial water diversion flow sequence as the initial search space of the particle swarm optimization algorithm, use the comprehensive evaluation function as the objective function of the particle swarm optimization algorithm, and find the optimal water diversion scheme from the candidate water diversion schemes through iterative updating.

[0010] Furthermore, in step 1, in a discrete time interval t=1, 2, ..., T, an initial water diversion flow sequence is defined for each candidate scheme i, denoted as: Q (i) = {Q i，t |t=1,...,T};Q i，t represents the water diversion flow rate adopted by candidate scheme i within time t; T is the upper limit of the time interval; the initial water diversion flow rate of each candidate scheme i in each time period t The calculation is done using the following formula:

[0011]

[0012] in, is the minimum water transfer flow; is the maximum water transfer flow; V i，t represents the available water volume of candidate solution i in time period t; μ V，t represents the mean water availability of all candidate solutions in time period t, σ V，t represents the standard deviation of available water for all candidate options in time period t.

[0013] Furthermore, in step 1, for candidate solution i in any period t, the dynamic change of reservoir water level satisfies the following second-order dynamic model:

[0014]

[0015] in, represents the reservoir water level of candidate scheme i in time period t, which is used as the simulated water level data; γ is the damping coefficient, which is the set value; A is the effective water storage area of ​​the reservoir; I t is the amount of water flowing into the reservoir during time period t; is the amount of water lost by the reservoir due to evaporation or leakage during period t:

[0016]

[0017] Among them, H max Indicates the highest water level allowed for safe operation of the reservoir; E t is the evaporation and leakage coefficient, ranging from 0.05 to 0.2; L is the periodic modulation coefficient, ranging from 0.1 to 0.3.

[0018] Furthermore, in step 2, the water level physical constraint is expressed using the following formula:

[0019]

[0020] Among them, H min Indicates the lowest water level allowed for safe operation of the reservoir; is the reservoir water level of candidate solution i in time period t-1; η s is the weight of the smoothness constraint; P (i) is the water level physical constraint of candidate solution i.

[0021] Furthermore, in step 2, an economic target model reflecting the energy consumption of the water transfer process is established through the following formula:

[0022]

[0023] Among them, C (i) is the economic target model value of candidate solution i; ρ is the density of water; g is the acceleration of gravity; is the pumping station efficiency function; is the head difference, defined as:

[0024]

[0025] Among them, H target is the target water level; ζ is the flow change sensitivity coefficient, ranging from 0.05 to 0.2; |·| is the absolute value operator; Δt is the time period length.

[0026] Furthermore, the pumping station efficiency function is calculated using the following formula:

[0027]

[0028] Among them, η 0 is the basic pump station efficiency; ξ is the efficiency adjustment factor; is the maximum water diversion flow allowed in time period t.

[0029] Furthermore, in step 2, the comprehensive objective function of candidate solution i is expressed using the following formula:

[0030]

[0031] Among them, F (i) is the comprehensive objective function value of candidate solution i.

[0032] Furthermore, the particle swarm optimization algorithm in step 3 updates the speed of candidate solution i in time period t in turn for all candidate solutions i=1,...,N in each time period t=1,...,T in each iteration k:

[0033]

[0034] in, represents the speed of candidate solution i at the kth iteration in time period t; represents the speed of candidate solution i at the k+1th iteration in time period t; is the water transfer flow of candidate scheme i at the kth iteration in time period t;

[0035]

[0036]

[0037] in, represents the projection operator; x is the projection operator variable; y is the flow variable; λ Π is the regularization weight, ranging from 0.3 to 0.8.

[0038] Furthermore, the particle swarm optimization algorithm in step 3 calculates the convergence index by the following formula:

[0039]

[0040] in, is the water transfer flow of candidate scheme i at the k-1th iteration in time period t; Δ (k) is the convergence index at the kth iteration; when Δ (k) When it is less than the set iteration threshold, the particle swarm optimization algorithm stops iterating, and the corresponding comprehensive objective function value at each iteration is counted, and the candidate water diversion scheme corresponding to the water diversion flow with the minimum comprehensive objective function value is taken as the optimal water diversion scheme.

[0041] The water diversion scheme optimization method of a hydraulic project based on multi-objective particle swarm optimization of the present invention has the following beneficial effects: the present invention introduces a nonlinear second-order dynamic model in the modeling of the dynamic change of the reservoir water level, which can accurately describe the inertia effect, damping effect and complex nonlinear coupling characteristics of the water body, and fully reflects the real dynamic behavior of the water level change under the influence of various factors such as flow, inflow and water loss. Through this dynamic model, the water level change trend under different water diversion schemes can be accurately predicted to ensure that the reservoir water level is always kept within the safe operating range, and to avoid the engineering risks caused by too high or too low water level. This function is extremely scarce in the prior art, especially under long time spans and complex hydrological conditions, traditional methods are difficult to provide the same high-precision water level prediction capability. The present invention comprehensively considers energy consumption targets and water level safety in the optimization process, and realizes a comprehensive balance of multi-dimensional targets by constructing a multi-objective comprehensive evaluation function. The comprehensive objective function not only includes energy consumption calculation and water level physical constraints, but also introduces a stability index of water level changes, ensuring that the final selected water diversion scheme is both economical and efficient, and has good operating stability. Compared with the single-objective optimization method, the present invention can quickly find the global optimal solution under multi-objective constraints, effectively balance the conflicts between different optimization objectives, and improve the comprehensive performance of the water diversion scheme. Especially in terms of energy consumption optimization, the present invention significantly reduces the energy consumption cost during the operation of the water pump, and has high economic benefits and energy-saving effects. The present invention has made a number of improvements in the optimization algorithm, and through an adaptive convergence judgment mechanism, it realizes efficient control of the optimization process. Traditional optimization algorithms usually use a fixed number of iterations as termination conditions, which easily leads to two extreme situations: one is that the optimization stops too early when the global optimal solution has not been reached, resulting in incomplete optimization results; the other is that it continues to iterate when the convergence has reached the optimal solution, wasting computing resources. However, the present invention calculates the convergence index in real time, dynamically monitors the change range of the candidate scheme in continuous iterations, and can flexibly adjust the number of iterations according to the actual convergence state to ensure that the optimization process stops in time after reaching the optimal solution. This adaptive convergence mechanism greatly improves the efficiency of the algorithm, makes the entire optimization process more intelligent and efficient, and avoids unnecessary computational overhead. The present invention also introduces a regularized projection operator in the flow update process, which further enhances the smoothness of the flow distribution and the feasibility of actual operation. Traditional optimization methods are prone to sudden changes or large jumps when adjusting flow, which makes the water diversion scheme unstable in actual operation and may even cause problems such as hydraulic shock or pump station overload. The present invention uses a regularized projection operator to dynamically constrain the flow, ensuring that the water diversion flow always changes smoothly within a reasonable range, effectively avoiding discontinuous jumps and improving the stability and safety of the water diversion scheme. This design provides an important guarantee for the safe operation of the reservoir, especially in high-frequency water diversion scenarios, which can significantly reduce the risk of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0043] Figure 1 A schematic diagram of a method flow of a method for optimizing a water diversion scheme for a water conservancy project based on multi-objective particle swarm optimization provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The method of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments of the present invention.

[0045] Example 1, reference Figure 1 :A water diversion scheme optimization method for a hydraulic project based on multi-objective particle swarm optimization, the method comprising:

[0046] Step 1: Generate a set of initial water diversion flow sequences for each candidate water diversion scheme within a preset discrete time interval; For each candidate water diversion scheme, use a second-order dynamic model including water body inertia, damping effect and nonlinear coupling terms to simulate the reservoir water level in a time-varying manner to obtain simulated water level data;

[0047] The generation of the initial water diversion flow sequence is carried out within a preset discrete time interval, which is usually set according to the actual operation cycle of the water conservancy project, and can be hours, days or longer time scales. Each candidate water diversion scheme consists of a set of water diversion flow sequences, which represent the instantaneous water diversion flow at each time point. The generation method of the initial flow sequence can be based on random initialization, historical data or empirical rules to ensure that the generated water diversion flow sequence is diverse and reasonable. These initial sequences correspond to different particles in the particle swarm in the particle swarm optimization algorithm, representing the initial distribution in the problem solution space. Generating diverse flow sequences is an important step to improve the global search capability of the algorithm, which can effectively prevent the particle swarm from falling into the local optimal solution. Next, for each candidate water diversion scheme, a second-order dynamic water level model is used to simulate the time-varying change of the reservoir water level. The model comprehensively considers the inertial effect, damping effect and external nonlinear coupling of the water body. These three parts work together to determine the dynamic change process of the reservoir water level over time. Among them, the water body inertia effect reflects the hysteresis of the reservoir water level to the changes in the inflow and water transfer flow, that is, the water level change does not immediately respond to the adjustment of the water transfer flow, but there is a certain hysteresis; the damping effect mainly describes the energy dissipation mechanism inside the reservoir system, which is manifested as the process of water level fluctuation gradually tending to stabilize. This effect is particularly obvious in the long-term water transfer process, which helps to avoid large fluctuations in the water level; the nonlinear coupling term reflects the complex hydraulic phenomena in the water transfer process, including the nonlinear effects caused by the mutual influence and coupling of multiple factors. This nonlinear term is particularly critical because it can simulate complex hydraulic boundary conditions and multiple external disturbance factors, making the simulation results more in line with actual working conditions.

[0048] The role of the second-order dynamic model in water level simulation is not only to predict water level changes at future moments, but more importantly to provide accurate water level simulation data for subsequent optimization steps, thereby establishing reliable water level physical constraints. In practical applications, the model input includes the initial reservoir water level, the water transfer flow sequence within the time interval, and other necessary boundary conditions, and the output is a simulated water level data sequence at discrete time points. The simulated water level data will serve as an important basis for the constraints to ensure that the reservoir water level always fluctuates within a safe range, avoiding the risk of dam breach caused by excessively high water levels or the impact of downstream water supply demand caused by too low water levels. In addition, through the time-varying simulation of the dynamic model, the rationality of each initial water transfer scheme can be intuitively identified, providing prior information for optimization. For example, if a candidate scheme causes the reservoir water level to exceed the safe range at a certain point in time, the scheme can be directly excluded in the initial stage to reduce unnecessary computational overhead. This simulation process lays a foundation for high precision and high reliability for the entire optimization method, and also provides accurate data support for the construction of subsequent comprehensive evaluation functions.

[0049] Step 2: To ensure that the reservoir water level is always kept within a safe range and to prevent sudden changes in the water transfer process, a water level physical constraint is constructed based on the simulated water level data; an economic target model that reflects the energy consumption of the water transfer process is established; and a comprehensive evaluation function is formed based on nonlinear coupling between the economic target model and the water level physical constraint;

[0050] During the water diversion process of water conservancy projects, the water level of the reservoir must always be kept within a safe range. Too high a water level may lead to the risk of dam breach, while too low a water level will affect the downstream water supply demand and even endanger the ecological environment. Therefore, the construction of water level physical constraints is an indispensable part of the optimization model. Water level constraints are usually implemented by setting the maximum and minimum allowable values ​​of the water level, that is, at each discrete time point, the simulated water level data must meet these upper and lower limit conditions. If a water diversion scheme causes the simulated water level to exceed the safe range at any time point, the scheme will be regarded as an infeasible solution and eliminated. This process ensures the controllability of the water diversion scheme in terms of water level safety, making the entire optimization model more realistic. However, relying solely on water level constraints cannot fully meet the optimization needs of water conservancy projects. In addition to ensuring water level safety, the water diversion scheme should also minimize energy consumption during the water diversion process to improve economic benefits. Therefore, in step 2, an economic target model with energy consumption as the core is further established. The model models the energy loss during the water diversion process, calculates the total energy consumption value of each candidate water diversion scheme, and uses it as part of the optimization target. The construction of the energy consumption model is mainly based on parameters such as water diversion flow, pump station head and pipeline resistance, and comprehensively considers various energy loss factors in the water diversion process. Generally, energy consumption is nonlinearly related to water diversion flow, and excessive or insufficient flow will lead to unnecessary energy consumption. Therefore, the energy consumption model can effectively guide the water diversion flow to the optimal range during the optimization process and avoid high energy consumption caused by extreme flow.

[0051] In order to achieve the joint optimization of water level constraints and economic goals, step 2 integrates the two into a comprehensive evaluation function through the nonlinear coupling method. Nonlinear coupling can not only consider the complex interaction of the two goals at the same time, but also allocate weights to water level safety and energy consumption according to actual needs, so that the optimization results can achieve a balance between safety and economy. The comprehensive evaluation function is an important part of the particle swarm optimization algorithm and directly determines the direction of optimization search. Its core idea is to transform the water level physical constraint into a penalty function. If the simulated water level of a candidate scheme exceeds the safety range, the score of the scheme in the comprehensive evaluation function is reduced by introducing a larger penalty value. At the same time, the energy consumption target value participates in the evaluation in the form of a positive indicator, and the lower the energy consumption, the higher the score. Therefore, the comprehensive evaluation function can not only exclude the scheme with water level exceeding the safety range, but also give priority to the scheme with lower energy consumption, thereby achieving the dual goals of water level safety and minimization of energy consumption. In addition, the nonlinear characteristics of the comprehensive evaluation function can better reflect the complexity of the actual water diversion process. In water conservancy projects, the water diversion process involves a variety of nonlinear hydrodynamic phenomena, and a single linear model is often difficult to accurately describe the water level changes and energy consumption characteristics. Through nonlinear coupling, not only can these complex interactions be captured, but the evaluation function can also be closer to the actual working conditions, improving the accuracy of the optimization results and the engineering application value. This method greatly improves the effect of water diversion scheme optimization, avoids the local optimal solution problem that may exist in traditional methods, and ensures that the final water diversion scheme has the lowest energy consumption while meeting water level safety.

[0052] Step 3: Use the initial water diversion flow sequence as the initial search space of the particle swarm optimization algorithm, use the comprehensive evaluation function as the objective function of the particle swarm optimization algorithm, and find the optimal water diversion scheme from the candidate water diversion schemes through iterative updating.

[0053] The particle swarm optimization algorithm is a global optimization algorithm based on swarm intelligence, which is inspired by group behaviors such as bird flocks foraging and fish swarms preying. Each particle represents a candidate solution. In the present invention, the particle is a specific water diversion flow sequence. The entire particle swarm moves continuously in the search space, and searches for the solution that optimizes the objective function value by updating the speed and position of the particles. The particle swarm optimization algorithm has the characteristics of simplicity and efficiency, especially when solving nonlinear, complex constraints and multi-objective optimization problems, it can significantly improve the computational efficiency and optimization accuracy. For the optimization of the water diversion scheme of the water conservancy project in the present invention, the initial search space of the particle swarm is determined by the initial water diversion flow sequence generated in step 1, and the diversity of these initial particles provides a good global search basis for subsequent optimization. The optimized objective function is the comprehensive evaluation function constructed in step 2, which takes into account both the physical constraints of the water level and the energy consumption target in the water diversion process. The particle swarm optimization algorithm minimizes the comprehensive evaluation function by continuously updating the state of the particles, thereby ensuring that the water diversion scheme meets both the water level safety requirements and the minimum energy consumption. In each iteration, each particle updates its position and velocity based on its own historical optimal position and the global optimal position of the entire group. This update mechanism enables particles to achieve a balance between local search and global search, quickly converge to a high-quality solution, and effectively avoid falling into a local optimal solution.

[0054] Specifically, in the iterative process of the particle swarm optimization algorithm, each particle, under the guidance of the comprehensive evaluation function, continuously corrects its water flow sequence to optimize the objective function value. The particle's speed update formula determines its motion trajectory in the search space, and the speed update depends on the particle's current state, its own historical optimal solution, and the group's optimal solution. By introducing inertia weights and acceleration coefficients, particles can dynamically adjust their own exploration and development capabilities, tending to global exploration in the early stages to avoid missing potential excellent solutions, and gradually converge to local areas in the later stages to ensure the refinement of the optimization results. After each iteration, the algorithm evaluates the objective function values ​​of all particles and updates the particle's personal optimal position and global optimal position until the termination condition is met. The termination condition may be reaching a preset maximum number of iterations, the change in the comprehensive evaluation function value is less than a certain threshold, or finding an acceptable solution that meets all constraints. In the scenario of the present invention, the particle state update actually means the continuous optimization of the water flow sequence. The initial water flow sequence may be unreasonable, such as causing the water level to exceed the safety range in certain time periods, or causing excessive energy consumption. Through the iterative update of the particle swarm optimization algorithm, the water diversion flow sequence will gradually tend to be rationalized, the water level physical constraints will always be strictly observed, and the energy consumption will continue to decrease. With the increase of the number of iterations, the solutions in the particle swarm will gradually concentrate near the optimal solution, and finally find an optimal water diversion scheme that can both meet the water level safety and minimize energy consumption. Compared with traditional linear programming or other heuristic optimization methods, the particle swarm optimization algorithm has significant advantages. First, it does not depend on the derivative information of the objective function, and is suitable for nonlinear, non-convex and optimization problems with complex constraints, which is highly consistent with the optimization scenario of the water diversion scheme faced by the present invention. Secondly, the particle swarm optimization algorithm has a strong global search capability and can find a better solution set in multi-objective optimization problems. Especially in the water diversion scheme of water conservancy projects, the nonlinear coupling between water level changes and energy consumption makes the problem extremely complex. Traditional methods often find it difficult to balance accuracy and efficiency, and the particle swarm optimization algorithm can achieve more efficient optimization results through the dynamic collaboration of group intelligence.

[0055] Example 2: In step 1, in a discrete time interval t=1, 2, ..., T, an initial water diversion flow sequence is defined for each candidate solution i, denoted as: Q (i) = {Q i，t |t=1,...,T};Q i，t represents the water diversion flow rate adopted by candidate scheme i within time t; T is the upper limit of the time interval; the initial water diversion flow rate of each candidate scheme i in each time period t The calculation is done using the following formula:

[0056]

[0057] in, is the minimum water transfer flow; is the maximum water transfer flow; V i，t represents the available water volume of candidate solution i in time period t; μ V，t represents the mean water availability of all candidate solutions in time period t, σ V，t represents the standard deviation of available water for all candidate options in time period t.

[0058] Specifically, in this formula, the water flow rate is the available water volume V based on candidate solution i in time period t within a given time interval t=1, 2, ..., T i，t The key parameters in the formula include the minimum water transfer flow rate Maximum water flow The mean value of available water μ V，t and standard deviation σ V，t These parameters jointly determine the way the initial water diversion flow is generated, so that the initial flow of each candidate solution can not only reflect the changes in available water under the current hydrological conditions, but also ensure that it fluctuates within a reasonable range to avoid extreme flow values ​​​​posing a threat to the safe operation of the reservoir water level. The core part of the formula is Its function is to standardize and nonlinearly transform the available water of candidate solutions, with the aim of balancing the differences between candidate solutions and avoiding the distribution of available water being too biased towards one extreme. The input of the inverse tangent function is the standardized difference in available water, that is, the deviation of the available water of the candidate solution from the mean of all candidate solutions. The scale of standardization is determined by the standard deviation σ V，t When the deviation is small, the output of the arctan function is close to a linear change, which means that the available water volume of the candidate solution is close to the average level, and the corresponding water transfer flow rate will also be near the middle value; when the deviation is large, the output of the arctan function gradually tends to be flat, avoiding the generation of excessively high or low flow due to extreme available water volume. This nonlinear transformation is smooth and robust, and can effectively reduce the impact of random fluctuations on the initial flow calculation.

[0059] The scaling and translation operations in the formula are also important parts to ensure that the initial water transfer flow is within a reasonable range. The operation changes the output value of the arctan function from its original range Mapped to the interval [0, 1]. This normalization process allows the nonlinearly converted available water values ​​to be compared and operated on the same scale. Subsequently, this result is mapped to the minimum water transfer flow and maximum water diversion flow The final initial water transfer flow is generated This method ensures that the initial water flow rate in each period fluctuates within a safe and controllable range, effectively avoiding the over-range problem that may occur in traditional linear interpolation methods. In addition, the statistical parameter μ in this formula V，t and σ V，t The overall available water distribution characteristics of all candidate schemes in each time period are fully considered, so that the initial water diversion flow sequence has a high distribution consistency. This standardized processing method based on overall distribution can provide a certain balance for the water diversion scheme in the initial stage, reduce the excessive differences in the initial flow sequence of different candidate schemes, avoid some schemes from being eliminated prematurely by the optimization process, and improve the global search ability and convergence speed of the particle swarm optimization algorithm. Especially in the actual operation of water conservancy projects, hydrological conditions often have large spatiotemporal variability. Through this dynamic standardization method, it can better adapt to the changes in hydrological conditions and enhance the robustness of the algorithm. This initial flow generation method has significant advantages under the multi-objective particle swarm optimization framework of the present invention. First, it can improve the search efficiency of the optimization algorithm and shorten the optimization time through reasonable initial solution generation; secondly, through nonlinear mapping and smoothing processing, it reduces the influence of extreme available water on the initial solution, improves the initial quality of the water diversion scheme, and reduces the risk of reservoir water level fluctuation and energy consumption; finally, this flow calculation method based on statistical characteristics provides a diversified initial solution space for the generation of flow sequences in multi-objective optimization, which significantly improves the possibility of finding the global optimal solution.

[0060] Embodiment 3: In step 1, for candidate solution i in any time period t, the dynamic change of the reservoir water level satisfies the following second-order dynamic model:

[0061]

[0062] in, represents the reservoir water level of candidate scheme i in time period t, which is used as the simulated water level data; γ is the damping coefficient, which is the set value; A is the effective water storage area of ​​the reservoir; I t is the amount of water flowing into the reservoir during time period t; is the amount of water lost by the reservoir due to evaporation or leakage during period t:

[0063]

[0064] Among them, H max Indicates the highest water level allowed for safe operation of the reservoir; E t is the evaporation and leakage coefficient, ranging from 0.05 to 0.2; L is the periodic modulation coefficient, ranging from 0.1 to 0.3.

[0065] Specifically, this dynamic model is presented in the form of a second-order differential equation, where the second-order derivative of the water level is The acceleration representing the change of water level reflects the inertial effect of the water body, that is, the delayed response of the water level to the changes in the inflow and water diversion flow. The introduction of the inertial effect allows the model to simulate the dynamic process of the water level gradually stabilizing after being disturbed by the outside world, rather than reaching a new equilibrium state instantly. In addition, the model also includes the first-order derivative of the water level This term reflects the damping effect of the system and describes the dissipation process of the internal energy of the water body. The damping coefficient γ controls the amplitude and frequency of water level fluctuations. Its function is to suppress excessive fluctuations in the water level, prevent large fluctuations in the reservoir water level, and ensure the stability of the water diversion process. On the right side of the model, the water balance part It is the core of the dynamic equation, which describes the change in the net water volume of the reservoir in each time period. Among them, A is the effective water storage area of ​​the reservoir, which determines the degree of influence of water volume changes on the water level. t is the total amount of water flowing into the reservoir during period t, which is usually determined by upstream rivers and precipitation, while the water transfer flow Q i，t is the decision variable in the candidate solution, representing the amount of water transferred out of the reservoir during this period. The basic idea of ​​water balance is that the inflow minus the water transfer flow and reservoir water loss determines the rising or falling trend of the water level. This dynamic balance process reflects the basic operating law of the reservoir as a water storage system and provides a basis for simulating water level changes.

[0066] Water loss function It describes the water loss due to evaporation and leakage and is an important part of the dynamic model. The water loss changes with the water level and is described in the form of a nonlinear function, that is, This function embodies two key characteristics: first, evaporation and leakage are positively correlated with water level. The higher the water level, the greater the loss. Second, the periodic sinusoidal term simulates the impact of seasonal hydrological changes and reservoir environment, especially when the water level is close to the safety upper limit H. max This periodic feature makes the water level simulation more consistent with the complex phenomena in actual reservoir operation and helps to accurately predict the water level changes under different water diversion schemes. In addition, a nonlinear coupling term is introduced in the dynamic model. This term is used to describe the water level feedback effect under high water level conditions. This nonlinear term has little effect on water level changes when the water level is low, but significantly increases the rate of water level rise when the water level is high, playing a role in risk warning and regulation. By introducing this term, abnormal fluctuations under high water level conditions can be amplified during the simulation process, helping to timely identify and adjust possible water level overlimit risks. This nonlinear coupling mechanism makes the model more sensitive, can predict potential risks earlier, and provides a more accurate basis for water level physical constraints in the multi-objective optimization process. This second-order dynamic model can not only truly reproduce the dynamic change process of reservoir water level, but also provide accurate simulation data for the multi-objective particle swarm optimization algorithm, helping the algorithm to quickly exclude candidate solutions that do not meet water level safety requirements during the optimization process. Through this dynamic model, the water level change process of each candidate solution can be accurately predicted, thereby ensuring that each solution operates within a safe range during the optimization process. At the same time, the water balance and water loss function in the model provide comprehensive reservoir operation information, which provides an important reference for subsequent energy consumption targets and economic benefit optimization.

[0067] Embodiment 4: In step 2, the water level physical constraint is expressed using the following formula:

[0068]

[0069] Among them, H min Indicates the lowest water level allowed for safe operation of the reservoir; is the reservoir water level of candidate solution i in time period t-1; η s is the weight of the smoothness constraint; P (i) is the water level physical constraint of candidate solution i.

[0070] Specifically, formula P (i) The structure of can be divided into three parts, corresponding to the lower limit constraint of the water level, the upper limit constraint of the water level, and the smoothness constraint of the water level change. First, for the lower limit constraint of the water level, the formula It is used to detect whether the water level of the candidate solution in the time period t is lower than the minimum water level H allowed for safe operation of the reservoir. min If the water level Higher than H min , this item takes a value of 0, indicating that the water level meets the safety requirements during this period; but if the water level is lower than H min , then this term is accumulated in the water level physical constraint function in the form of the square of the difference. The square operation amplifies the penalty for exceeding the water level limit, especially when the water level deviation is large, which can significantly increase the penalty value and force the optimization algorithm to give priority to candidate solutions with water levels closer to the safe range. This can effectively avoid the reservoir water level from being too low, prevent the downstream water supply from being insufficient and the water ecosystem from being damaged. Similarly, the water level upper limit constraint is obtained by To detect whether the water level of the candidate solution exceeds the safety upper limit H in time period t max Similar to the lower limit constraint, when the water level Lower than H max When the water level exceeds H max , the square of the difference will be accumulated into the constraint function as a penalty value. This design aims to ensure that the reservoir water level always fluctuates within the allowed range to avoid overflow risks or structural damage caused by excessive water levels. The square amplification form makes the optimization algorithm more inclined to choose those solutions with stable water levels, close to the safety upper limit but not exceeding it, thereby minimizing risks while ensuring the reservoir's water storage capacity.

[0071] However, relying solely on the upper and lower limits of the water level is not enough to ensure the stability of the water diversion plan. In actual water conservancy project scheduling, sudden changes in water levels will have an adverse impact on the reservoir structure, downstream rivers and the ecological environment. Therefore, the water level smooth change constraint term is specially introduced in the formula By accumulating the fourth power of the water level change amplitude in adjacent time periods, the drastic water level fluctuations in the candidate schemes are suppressed. Compared with the square penalty mechanism, the fourth power penalty can detect water level mutations more sensitively, especially when the water level changes greatly, its penalty value will increase rapidly, significantly improving the preference of the optimization process for the smooth change scheme. This smooth change constraint can not only avoid the impact of water level mutations on the safety of reservoir operation, but also reduce the energy consumption caused by frequent water level regulation during water diversion, and improve the overall operation efficiency. Smooth constraint weight η s The choice of is critical, as it determines the balance between stability and flexibility. s It can be adjusted according to the specific reservoir operation characteristics and water transfer targets. The weight can be increased when the safety requirements are high, thereby more strictly limiting water level fluctuations, or the weight can be appropriately reduced when greater flexibility is allowed to enhance the diversity of water transfer schemes. The entire water level physical constraint function accumulates the water level deviation and change amplitude in each time period to generate a comprehensive evaluation index P (i), which is used to measure the performance of candidate solutions in terms of water level safety and change stability. In multi-objective particle swarm optimization, this evaluation index and the energy consumption objective function together constitute the optimization goal, guiding the algorithm to give priority to those solutions that can take into account water level safety and energy consumption economy in the process of searching for the optimal water diversion solution. Compared with the traditional single constraint method, this comprehensive physical constraint not only has higher flexibility, but also can more accurately reflect the complexity of actual reservoir operation, making the optimization results closer to the needs of engineering applications. It is worth mentioning that this physical constraint function also has strong adaptability and scalability. By adjusting the upper and lower limits of the water level and the weight parameters, the constraint function can adapt to the scheduling requirements of reservoirs of different scales and functions. For example, for reservoirs mainly for irrigation, the lower limit constraint can be appropriately relaxed to allow lower water levels to meet irrigation needs; while for reservoirs with outstanding flood control functions, the upper limit constraint weight can be increased to ensure that the water level is always within a safe range. This flexibility greatly enhances the practicality and promotion value of the present invention, enabling it to play a role in different water conservancy project scenarios.

[0072] Example 5: In step 2, an economic target model reflecting the energy consumption of the water transfer process is established by the following formula:

[0073]

[0074] Among them, C (i) is the economic target model value of candidate solution i; ρ is the density of water; g is the acceleration of gravity; is the pumping station efficiency function; is the head difference, defined as:

[0075]

[0076] Among them, H target is the target water level; ζ is the flow change sensitivity coefficient, ranging from 0.05 to 0.2; |·| is the absolute value operator; Δt is the time period length.

[0077] Specifically, the mathematical expression of the energy consumption economic target model reflects the total energy consumption required for water to flow through the pump. The core calculation part is based on Based on , where ρ is the density of water, g is the acceleration due to gravity, is the head difference, defined as This part describes the mechanical energy required and the water flow rate Q when water flows through the pump station. i，t , Head difference And the relationship between the time period length Δt. Head difference It is an important factor in determining the energy consumption of the water pump and represents the water level. Relative to the target water level H targetWhen the head difference is large, the pump needs more energy to lift the water to the target water level, so the energy consumption increases significantly; conversely, when the head difference is small, the energy consumption decreases accordingly. Therefore, the model can dynamically reflect the impact of water level changes on energy consumption, so that the optimization process can more accurately consider the actual operation of the reservoir. The key innovation in the model is the introduction of the pump station efficiency function

[0078] It describes the nonlinear characteristics of pump efficiency as it changes with flow and head difference. The efficiency of a pump station is not constant, but varies with operating conditions. It usually reaches a maximum value within a specific range of flow and head difference, and when it exceeds this range, the efficiency drops significantly. This function plays a vital role in the model, guiding the optimization algorithm to adjust the flow within the efficient operating range and avoid energy waste caused by inefficient operation. In addition, The introduction of makes the energy consumption model closer to the actual working conditions and improves the feasibility and accuracy of the optimization results.

[0079] In order to further optimize the energy consumption cost in the water transfer process, a flow rate penalty term is added to the formula Among them, ζ is the flow change sensitivity coefficient, ranging from 0.05 to 0.2, which represents the degree of penalty for sudden flow changes. This item amplifies the impact of the flow change rate through an exponential function. The main purpose is to prevent drastic flow adjustments in candidate solutions, thereby reducing excessive instantaneous energy consumption caused by frequent adjustments to the operating status of the water pump. In actual water conservancy projects, frequent switching of the operating status of the water pump will significantly increase the energy consumption of the system and may shorten the life of the equipment. By introducing this item, the model is more inclined to select those solutions with stable flow changes during the optimization process to ensure that the water diversion process is more economical and efficient. The physical basis of this model can be understood as the conversion of the mechanical energy required by the water pump to increase the water flow into electrical energy consumption, and the changes in actual electrical energy consumption are reflected through the pump station efficiency function. Specifically, the total energy consumption C of the candidate solution (i) It is the cumulative sum of energy consumption per unit time in all time periods. i，t and head difference As the flow rate increases, the energy consumption per unit time will also increase accordingly. However, by optimizing the water diversion scheme, the flow rate and head difference can be controlled within a better range while meeting the water level safety constraint, thereby significantly reducing energy consumption. In addition, under the action of the exponential function, the flow rate change penalty term makes the model have a higher preference for those schemes with smooth flow changes and low energy consumption, greatly improving the economy of the optimization results. It is worth noting that the economic target model has high flexibility and scalability. By adjusting the parameter ζ and the specific form of the pump station efficiency function, the energy consumption model can be personalized according to the actual operation requirements of different types of water pumps and water conservancy projects. For example, during peak water supply periods, the restrictions on the flow rate change rate can be appropriately relaxed to increase the flexibility of water supply; and under the energy-saving priority operation strategy, the value of ζ can be increased to strictly limit flow changes and minimize energy consumption. In addition, the head difference in the model It can also be dynamically adjusted according to specific target water levels to suit different operational objectives, such as flood control, irrigation or power generation.

[0080] Example 6: The pump station efficiency function is calculated using the following formula:

[0081]

[0082] Among them, η 0 is the basic pump station efficiency; ξ is the efficiency adjustment factor; is the maximum water diversion flow allowed in time period t.

[0083] Specifically, in the operation of the pump station, the efficiency shows a significant nonlinear characteristic with the change of flow rate and head difference. i，t The effect on efficiency can be When the flow rate is small, the function value is close to 0, and the pumping station efficiency remains close to the basic efficiency η 0 However, as the flow rate approaches or exceeds the maximum allowable flow rate, The value of the hyperbolic tangent function tends to 1, resulting in a significant decrease in efficiency. This nonlinear change mechanism simulates the phenomenon that the efficiency of an actual pump station decreases when it is running at a high flow rate. In particular, when the flow rate exceeds the optimal working range of the pump station design, the energy consumption of the pump will increase significantly. Therefore, this function guides the optimization algorithm to be more cautious in the process of flow adjustment, avoids operation at excessively high flow rates, reduces unnecessary energy consumption, and improves overall economic benefits. Head difference It is also an important factor affecting the efficiency of the pumping station, which determines the lifting height that the pump needs to overcome. When the head difference is small, the lifting power required by the pump is small and the efficiency can be maintained at a high level. However, as the head difference increases, the lifting height continues to increase, and the efficiency of the pumping station begins to decrease. This nonlinear change process can be accurately described. When the head difference is close to the target water level, the efficiency changes relatively slowly; when the head difference exceeds a certain range, the efficiency drops rapidly, reflecting the energy consumption characteristics of the pump under high head difference conditions. This nonlinear description greatly improves the authenticity of the pump station efficiency model, enabling the optimization algorithm to better avoid the energy loss caused by high head difference operation.

[0084] More importantly, this efficiency function uses the product of two hyperbolic tangent functions. The sensitivity of efficiency changes is further enhanced. The product form makes the decline of pump station efficiency under the dual unfavorable conditions of flow rate and head difference more significant, which prompts the optimization algorithm to give priority to those candidate solutions that maintain both moderate flow rate and small head difference to minimize energy consumption. This dual restriction mechanism ensures that the pump station always operates in a higher efficiency range, avoids the inefficiency caused by a single factor, and makes the optimization results more robust and reliable. Parameter ξ, as an efficiency adjustment factor, has flexible adjustment capabilities. In different application scenarios, the sensitivity of efficiency to changes in flow rate and head difference can be changed by adjusting the value of ξ. For example, in a water diversion strategy that emphasizes energy saving, the value of ξ can be appropriately increased to more strictly limit high flow rate and high head difference operation to ensure that energy consumption is always at a low level; while in peak water supply or emergency water diversion scenarios, the value of ξ can be reduced to increase the tolerance of flow rate and head difference and increase the flexibility of water diversion schemes. It is this flexibility that makes the pump station efficiency function highly adaptable and scalable in practical applications. From an optimization perspective, this efficiency function provides the multi-objective particle swarm optimization algorithm with the ability to dynamically adjust the energy consumption of the pump station. As the flow rate and head difference change during the optimization process, the efficiency value will be adjusted in real time, directly affecting the energy consumption objective function C (i) The calculation results of the optimization algorithm are used to guide the optimization algorithm to continuously evolve towards a more energy-saving direction. Compared with the traditional linear efficiency model, the nonlinear efficiency function can better capture the complexity of the actual pump station operation, making the optimization process more realistic and ultimately improving the economy and feasibility of the water diversion scheme.

[0085] Example 7: In step 2, the comprehensive objective function of candidate solution i is expressed using the following formula:

[0086]

[0087] Among them, F (i) is the comprehensive objective function value of candidate solution i.

[0088] Specifically, the first part of the comprehensive objective function involves the energy consumption target C (i) and water level physical constraint P (i)The two parts represent the economic cost and water level safety requirements of the water diversion process. (i) It reflects the total energy consumed by the pump station during operation. Its calculation includes key variables such as flow rate, head difference and pump station efficiency, and describes the energy consumption characteristics of different schemes in detail. On the other hand, the water level physical constraint P (i) The penalty mechanism is used to ensure that the water level is always within the safe operating range and to avoid drastic fluctuations in the water level that threaten the system safety. (i) and P (i) By combining a nonlinear power relationship and adjusting the relative importance of the two through a weight parameter ξ, the priority of economy and safety can be flexibly adjusted according to the needs of specific scenarios. This nonlinear design ensures the sensitivity of the optimization process to high energy consumption and severe water level deviation schemes, while giving a certain tolerance to smaller energy consumption and water level deviations, thereby improving the practical applicability of the water diversion scheme. The second part of the comprehensive objective function further improves the model by evaluating the smoothness of water level changes. The second derivative of reservoir water level change It is a key indicator to describe the accelerated change of water level and reflects the dynamic characteristics of water level over time. In order to avoid the engineering risks and water diversion efficiency losses that may be caused by drastic fluctuations in water level, the comprehensive objective function accumulates the square value of the second-order derivative to measure the water level stability during the entire water diversion process. The stability of water level fluctuations is crucial for the safe operation of reservoirs and the optimization of pump station energy consumption. Drastic water level changes will increase the operating pressure of pump stations, leading to a surge in energy consumption and may have adverse effects on reservoir structures and downstream ecosystems. By penalizing the square value of the second-order derivative of the water level, this function can effectively guide the optimization algorithm to give priority to candidate solutions with stable water level changes, ensuring the operational stability of the reservoir during the water diversion process.

[0089] The comprehensive objective function also regulates the overall evaluation through a global nonlinear adjustment parameter ζ. This parameter is applied to the entire objective function in the form of a power, which plays a role of global trade-off. A larger ζ value will make the function more sensitive to solutions with high energy consumption or drastic water level fluctuations, and strengthen the focus on these issues during the optimization process; while a smaller ζ value will weaken this sensitivity and pay more attention to the comprehensive performance of the solution. This design gives the optimization algorithm greater flexibility and adaptability, enabling it to be adjusted according to different engineering needs. For example, in a scenario where economic efficiency is the priority goal, the values ​​of ζ and ξ can be appropriately reduced to reduce the weight of energy consumption and water level stability; while in a scenario where safety is the priority goal, these parameters can be increased to further strictly limit water level deviations and fluctuations. The innovation of this comprehensive objective function is that it integrates multiple key factors for optimizing water diversion schemes into an evaluation index in a unified mathematical framework, which can not only accurately reflect the advantages and disadvantages of each scheme, but also provide a clear search direction and weight basis for the multi-objective particle swarm optimization algorithm. Compared with the traditional single-objective optimization model, the comprehensive objective function of the present invention can simultaneously handle the optimization requirements of the three dimensions of economy, safety and stability, and shows higher scientificity and applicability in multi-objective trade-offs. This design effectively overcomes the limitation of traditional methods that it is difficult to balance multiple conflicting objectives in multi-objective optimization. Through this comprehensive objective function, the optimization algorithm can conduct a comprehensive multi-dimensional evaluation of candidate solutions in each iteration, quickly identify and eliminate high-energy consumption or unsafe solutions, and give priority to those solutions that are both economical and efficient and run smoothly. This function is of great significance for the optimization of water diversion schemes in actual water conservancy projects, especially under complex hydrological conditions, and can significantly improve the reliability of the optimization results and the applicability of the project.

[0090] Embodiment 8: In each iteration k, the particle swarm optimization algorithm in step 3 updates the speed of candidate solution i in time period t for all candidate solutions i=1, ..., N in each time period t=1, ..., T in turn:

[0091]

[0092] in, represents the speed of candidate solution i at the kth iteration in time period t; represents the speed of candidate solution i at the k+1th iteration in time period t; is the water transfer flow of candidate scheme i at the kth iteration in time period t;

[0093]

[0094]

[0095] in, represents the projection operator; x is the projection operator variable; y is the flow variable; λ ∏ is the regularization weight, ranging from 0.3 to 0.8.

[0096] Specifically, in each iteration k, the speed of candidate solution i in time period t is The update formula of adopts a mechanism based on the objective function gradient estimation. In the speed update formula, the first part is the inertia term, which reflects the current movement trend of the particle, that is, how the speed of the previous iteration affects the current iteration. This part ensures the global search ability of the particle swarm by maintaining a certain inertia and avoids falling into the local optimum too early. The second part is to use the comprehensive objective function F (i) The rate of change of the particle is used to guide the particle speed adjustment. Here, the objective function F (i) Combined with energy consumption target C (i) , water level physical constraint P (i) and water level stability index are the core evaluation criteria for multi-objective optimization. By calculating the difference in the objective function when the flow increases and decreases, the algorithm can approximate the gradient of the objective function with respect to the flow. The gradient approximation presented in the form of makes the speed update not only consider the current flow, but also dynamically capture the changing trend of the objective function in the current search space. This gradient-based adjustment strategy gives the algorithm stronger local search capabilities, allowing particles to adjust more accurately along the direction of objective function optimization. In addition to the linear influence of the objective function gradient, the speed update formula also introduces a second-order term to capture the second-order nonlinear relationship of the objective function to flow changes. This part is The form of reflects the curvature information of the objective function, that is, the quadratic effect of flow changes on the comprehensive objective function. This design can make the algorithm more sensitive in complex nonlinear optimization space, and can effectively identify subtle changes in local areas, thus avoiding missing potential high-quality solutions.

[0097] Updated speed It is not used directly as the flow value, but is used in the position update formula. When updating the flow, the algorithm introduces a regularized projection operator The updated flow The projection operator is used to ensure that the flow rate always meets the boundary conditions of actual operation, that is, the flow rate does not exceed the minimum flow rate in time period t. and maximum flow In addition, the projection operator optimizes the choice of flow through a regularization term, which is Its physical significance lies in enhancing the smoothness of flow distribution and avoiding excessive discontinuous jumps in water diversion schemes. By mapping the target flow x to the flow y that satisfies the constraints and considering the influence of regularization, the projection operator enables the optimization algorithm to take into account both the actual operating conditions and the smoothness requirements of the flow in the global search. This constraint mechanism further improves the feasibility and stability of the water diversion scheme. In addition, the regularization weight λ introduced by the projection operator Π It can be adjusted within the range of 0.3 to 0.8, and can be flexibly adjusted according to the needs of different water conservancy projects. If the stability of water flow is given priority, λ can be increased. Π If other goals (such as economy or safety) are given priority, λ can be appropriately reduced. Π , allowing the flow rate to have a larger adjustment range within a certain range. This flexible regularization design gives the algorithm stronger adaptability and can meet the needs of diverse engineering applications. During the entire iteration process, the dynamic update of speed and position continuously guides the candidate solution towards the optimization goal. Initially, the speed of each candidate solution is Initialized to initial flow Through multiple iterations, the particle swarm gradually concentrates in areas with lower objective function values, thereby accelerating the convergence process. The combination of inertia terms, gradient terms and second-order terms enables the algorithm to achieve a good balance between global search and local search, which can not only quickly jump out of the local optimal solution, but also realize the refined exploration of the objective function in a complex optimization space. The advantages of the particle swarm optimization algorithm of the present invention in the optimization of water diversion schemes are not only reflected in the improvement of search efficiency, but also in the algorithm's ability to accurately handle multi-objective constraints. Through the combination of the speed update formula and the projection operator, the algorithm can dynamically adapt to complex hydraulic conditions and optimization target requirements, providing a highly flexible and efficient tool for the optimization of water diversion schemes for water conservancy projects. Compared with traditional optimization methods, the algorithm significantly improves the optimization quality of water diversion schemes, and can quickly find the global optimal solution while meeting the multiple requirements of reservoir water level safety, flow stability and energy economy.

[0098] Example 9: The particle swarm optimization algorithm in step 3 calculates the convergence index by the following formula:

[0099]

[0100] in, is the water transfer flow of candidate scheme i at the k-1th iteration in time period t; Δ (k) is the convergence index at the kth iteration; when Δ (k)When it is less than the set iteration threshold, the particle swarm optimization algorithm stops iterating, and the corresponding comprehensive objective function value at each iteration is counted, and the candidate water diversion scheme corresponding to the water diversion flow with the minimum comprehensive objective function value is taken as the optimal water diversion scheme.

[0101] Specifically, in the iterative process of particle swarm optimization, the water diversion flow of each candidate scheme i in each time period t is In each iteration k, it will be adjusted according to the update formula. In order to determine whether the particle swarm has entered a convergence state, the present invention uses the root mean square error to calculate the convergence index Δ (k) , that is, by measuring the change in the water flow rate between the kth iteration and the k-1th iteration, the overall change trend of the particle swarm is monitored in real time. Specifically, Δ (k) It represents the mean change of water flow rate of all candidate schemes in all time periods. Its physical meaning is to reflect the convergence degree of particle swarm in the entire optimization space. (k) When Δ (k) When it gradually decreases and approaches the set convergence threshold, it means that the change of the particle swarm tends to be stable, and the algorithm can be judged to be close to the optimal solution.

[0102] This convergence index has important practical significance. The optimization of water diversion schemes for water conservancy projects involves complex multi-objective constraints, including energy consumption, water level safety, stability and other dimensions. Traditional optimization methods are difficult to accurately determine whether the global optimal solution has been found in a multi-objective environment. The present invention uses dynamic calculation of Δ (k) , which provides a reliable basis for judging the global convergence of the particle swarm. At the end of each iteration, the algorithm calculates the current convergence index Δ (k) And compare it with the preset threshold. (k) If it is less than the threshold, it means that the changes in the candidate solutions have stabilized, the algorithm is judged to be converged and the iteration is terminated, and the result statistics and solution selection stage is entered. Setting an appropriate convergence threshold has a key impact on the performance of the algorithm. The size of the convergence threshold can be adjusted according to the specific needs of the water conservancy project and the availability of computing resources. In scenarios where high-precision optimization results are pursued, a smaller convergence threshold is usually selected so that the algorithm can search the optimization space more finely and find a better water diversion solution; in scenarios where the computing time is limited or the requirements for the accuracy of the optimization results are relatively low, a larger convergence threshold can be selected to speed up the iteration process and reduce computing costs. This flexible design gives the present invention higher adaptability and can meet the needs of different engineering scenarios. After the algorithm is judged to be converged, the system will calculate the comprehensive objective function value F in each iteration. (i) After statistics are performed, the candidate scheme with the smallest comprehensive objective function value is finally selected as the optimal water diversion scheme.(i) It is the core evaluation index of multi-objective optimization, combined with the energy consumption target C (i) , water level physical constraint P (i) and the stability of water level changes, which can comprehensively measure the overall performance of candidate solutions. By selecting the solution with the smallest comprehensive objective function value, it can ensure that the selected water diversion solution has the best comprehensive performance in multi-objective optimization, which can not only effectively reduce energy consumption in the water diversion process, but also ensure the safety and stability of reservoir water levels. This scheme selection mechanism based on the comprehensive objective function not only improves the reliability of the optimization results, but also effectively avoids the problem of result deviation caused by local optimal solutions. It is worth noting that the convergence index Δ (k) The dynamic calculation of also has a certain regulation and feedback effect. In the early stage of the algorithm, the particle swarm is usually in a global exploration state, the candidate solutions vary greatly, and the convergence index is relatively high. The main task of this stage is to find potential high-quality solutions through a large-scale search, rather than pursuing convergence too early. At this stage, a large Δ (k) The value can help the algorithm maintain sufficient exploration ability and avoid falling into the local optimum. In the middle and late stages of the iteration, as the particle swarm gradually gathers in the area with lower objective function values, the convergence index Δ (k) will gradually decrease, indicating that the particle swarm is converging to the global optimal solution. At this time, a smaller convergence threshold can guide the algorithm to adjust the candidate solutions more finely, thereby finding a more accurate optimal solution.

[0103] Although the specific embodiments of the present invention are described above, it should be understood by those skilled in the art that these specific embodiments are only illustrative, and those skilled in the art may omit, replace, and change the details of the above methods and systems in various ways without departing from the principles and essence of the present invention. For example, merging the above method steps so as to perform substantially the same functions in substantially the same manner to achieve substantially the same results is within the scope of the present invention. Therefore, the scope of the present invention is limited only by the appended claims.

Claims

1. A water diversion scheme optimization method for hydraulic engineering based on multi-objective particle swarm optimization, characterized in that: The method comprises: Step 1: Generate a set of initial water diversion flow sequences for each candidate water diversion scheme within a preset discrete time interval; For each candidate water diversion scheme, use a second-order dynamic model including water body inertia, damping effect and nonlinear coupling terms to simulate the reservoir water level in a time-varying manner to obtain simulated water level data; Step 2: To ensure that the reservoir water level is always kept within a safe range and to prevent sudden changes in the water transfer process, a water level physical constraint is constructed based on the simulated water level data; an economic target model that reflects the energy consumption of the water transfer process is established; and a comprehensive evaluation function is formed based on nonlinear coupling between the economic target model and the water level physical constraint; Step 3: Use the initial water diversion flow sequence as the initial search space of the particle swarm optimization algorithm, use the comprehensive evaluation function as the objective function of the particle swarm optimization algorithm, and find the optimal water diversion scheme from the candidate water diversion schemes through iterative updating.

2. The method for optimizing water diversion scheme of hydraulic engineering based on multi-objective particle swarm optimization according to claim 1, characterized in that: In step 1, in the discrete time interval t = 1, 2, ..., T, an initial water diversion flow sequence is defined for each candidate scheme i, denoted as: Q (i) = {Q i，t |t=1,...,T};Q i，t represents the water diversion flow rate adopted by candidate scheme i within time t; T is the upper limit of the time interval; The initial water transfer flow of each candidate scheme i in each period t The calculation is done using the following formula: in, is the minimum water transfer flow; is the maximum water transfer flow; V i，t represents the available water volume of candidate solution i in time period t; μ V，t represents the mean water availability of all candidate solutions in time period t, σ V，t represents the standard deviation of available water for all candidate options in time period t.

3. The method for optimizing water diversion scheme of hydraulic engineering based on multi-objective particle swarm optimization according to claim 2, characterized in that: In step 1, for candidate solution i in any period t, the dynamic change of reservoir water level satisfies the following second-order dynamic model: in, represents the reservoir water level of candidate scheme i in time period t, which is used as the simulated water level data; γ is the damping coefficient, which is the set value; A is the effective water storage area of ​​the reservoir; I t is the amount of water flowing into the reservoir during time period t; is the amount of water lost by the reservoir due to evaporation or leakage during period t: Among them, H max Indicates the highest water level allowed for safe operation of the reservoir; E t is the evaporation and leakage coefficient, ranging from 0.05 to 0.2; L is the periodic modulation coefficient, ranging from 0.1 to 0.

3.

4. The method for optimizing water diversion scheme of a hydraulic project based on multi-objective particle swarm optimization according to claim 3, characterized in that: In step 2, the water level physical constraint is expressed using the following formula: Among them, H min Indicates the lowest water level allowed for safe operation of the reservoir; is the reservoir water level of candidate solution i in time period t-1; η s is the weight of the smoothness constraint; P (i) is the water level physical constraint of candidate solution i.

5. The method for optimizing water diversion scheme of hydraulic engineering based on multi-objective particle swarm optimization according to claim 4, characterized in that: In step 2, an economic target model reflecting the energy consumption of the water transfer process is established through the following formula: Among them, C (i) is the economic target model value of candidate solution i; ρ is the density of water; g is the acceleration of gravity; is the pumping station efficiency function; is the head difference, defined as: Among them, H target is the target water level; ζ is the flow change sensitivity coefficient, ranging from 0.05 to 0.2; |·| is the absolute value operator; Δt is the time period length.

6. The method for optimizing water diversion scheme of a hydraulic project based on multi-objective particle swarm optimization according to claim 5, characterized in that: The pump station efficiency function is calculated using the following formula: Among them, η0 is the basic pump station efficiency; ξ is the efficiency adjustment factor; is the maximum water diversion flow allowed in time period t.

7. The method for optimizing water diversion scheme of a hydraulic project based on multi-objective particle swarm optimization according to claim 6, characterized in that: In step 2, the comprehensive objective function of candidate solution i is expressed using the following formula: Among them, F (i) is the comprehensive objective function value of candidate solution i.

8. The method for optimizing water diversion scheme of a hydraulic project based on multi-objective particle swarm optimization according to claim 7, characterized in that: The particle swarm optimization algorithm in step 3 updates the speed of candidate solution i in time period t for all candidate solutions i=1,...,N in each time period t=1,...,T in each iteration k: in, represents the speed of candidate solution i at the kth iteration in time period t; represents the speed of candidate solution i at the k+1th iteration in time period t; is the water transfer flow of candidate scheme i at the kth iteration in time period t; in, represents the projection operator; x is the projection operator variable; y is the flow variable; λ Π is the regularization weight, ranging from 0.3 to 0.

8.

9. The method for optimizing water diversion scheme of a hydraulic project based on multi-objective particle swarm optimization according to claim 8, characterized in that: The particle swarm optimization algorithm in step 3 calculates the convergence index by the following formula: in, is the water transfer flow of candidate scheme i at the k-1th iteration in time period t; Δ (k) is the convergence index at the kth iteration; when Δ (k) When it is less than the set iteration threshold, the particle swarm optimization algorithm stops iterating, and the corresponding comprehensive objective function value at each iteration is counted, and the candidate water diversion scheme corresponding to the water diversion flow with the minimum comprehensive objective function value is taken as the optimal water diversion scheme.

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