Water transfer scheme optimization method based on multi-objective particle swarm optimization for water conservancy projects

Abstract

The present application 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-objective particle swarm optimization. The method comprises the following steps: step 1: generating a group of initial water transfer flow sequences for each candidate water transfer scheme in a preset discrete time interval; step 2: in order to ensure that the water level of the reservoir is always kept within a safe range and prevent mutation in the water transfer process, constructing a water level physical constraint according to the simulated water level data; and step 3: taking the initial water transfer flow sequence as the initial search space of the particle swarm optimization algorithm, taking the comprehensive evaluation function as the objective function of the particle swarm optimization algorithm, and finding the optimal water transfer scheme from the candidate water transfer schemes through an iterative updating manner. The present application significantly improves the optimization accuracy and the reliability of the result.

Description

TECHNICAL FIELD

[0001] The application 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-objective particle swarm optimization. BACKGROUND

[0002] With the increasing contradiction between global water supply and demand, water conservancy projects play an important role in water resource allocation and rational utilization. Reservoirs, as important infrastructure for regulating upstream and downstream water, their scientific scheduling and efficient operation are crucial for water resource management and regional economic development. In practical applications, the water transfer process of water conservancy projects involves dynamic interactions of multiple complex factors, such as inflow water quantity changes, water transfer flow adjustments, water level safety management, and energy consumption control. These factors not only have high nonlinearity and time-varying characteristics, but also have multiple coupled constraints, making the optimization of reservoir scheduling extremely complex. Existing technologies have made some progress in water transfer scheme optimization, but still face many problems to be solved.

[0003] In the disclosed technology, traditional reservoir scheduling mostly adopts linear programming, dynamic programming or genetic algorithm methods. These methods usually establish a linear relationship model between water transfer flow and reservoir water level or use heuristic algorithms for optimization. However, these traditional methods have obvious shortcomings in dealing with actual complex working conditions. First, the linear programming method cannot accurately describe the nonlinear dynamic characteristics of reservoir water level changes due to the simplification of the assumption conditions, especially under high water head difference and complex flow change conditions, which can easily lead to large deviations between the water transfer scheme and the actual situation. Second, 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, as the number of constraints and optimization objectives increases, the computational cost grows exponentially, making it difficult to meet real-time scheduling requirements. In addition, although heuristic optimization methods such as genetic algorithm and simulated annealing have certain global search ability, they are prone to local optimal solutions in a multi-objective constraint environment, and due to the lack of an efficient convergence judgment mechanism, the stability of the optimization results is difficult to guarantee. SUMMARY

[0004] The main purpose of the present application is to provide a water conservancy project water transfer scheme optimization method based on multi-objective particle swarm optimization, by constructing a nonlinear second-order dynamic water level model, an energy consumption economic objective model and a water level physical constraint, combining dynamic modeling of pump station efficiency and a multi-objective comprehensive evaluation function, the minimization of energy consumption, water level safety guarantee and water level change stability control in the reservoir water transfer process are realized. By introducing the improved particle swarm optimization algorithm and the self-adaptive convergence judgment mechanism, the optimization process is more intelligent and efficient, and the global optimal solution can be quickly found. Compared with the traditional method, the present application significantly improves the optimization accuracy and the reliability of the results, effectively reduces the energy consumption cost in the water transfer process, guarantees the long-term stable operation of the reservoir, and has high practical application value and popularization prospect.

[0005] To solve the above technical problems, the present application provides

[0006] The water conservancy project water transfer scheme optimization method based on multi-objective particle swarm optimization, the method comprises:

[0007] Step 1: generate a set of initial water transfer flow sequences for each candidate water transfer scheme in a preset discrete time interval; for each candidate water transfer scheme, a second-order dynamic model containing water body inertia, damping effect and nonlinear coupling term is used to simulate the time-varying water level of the reservoir, and the simulated water level data is obtained;

[0008] Step 2: in order to ensure that the water level of the reservoir always remains within the safe range and prevent sudden changes in the water transfer process, according to the simulated water level data, a water level physical constraint is constructed; an economic objective model reflecting the energy consumption of the water transfer process is established; based on the economic objective model and the water level physical constraint, a nonlinear coupling is carried out to form a comprehensive evaluation function;

[0009] Step 3: the initial water transfer flow sequence is taken as the initial search space of the particle swarm optimization algorithm, and the comprehensive evaluation function is taken as the objective function of the particle swarm optimization algorithm, and the optimal water transfer scheme is found from the candidate water transfer schemes by iterative updating.

[0010] Further, in step 1, define the initial water transfer flow sequence for each candidate scheme i in the discrete time interval t=1, 2,..., T, denoted as: Q (i) ={Q i，t |t=1,...,T};Q i，t represents the water transfer flow adopted by the candidate scheme i at time t;T is the upper limit of the time interval;the initial water transfer flow of each candidate scheme i at each time period t is calculated by the following formula:

[0011]

[0012] Wherein, is the minimum water transfer flow. Qmaxis the maximum water transfer flow rate; V i，t μi(t) is the available water volume of candidate scheme i at time period t; μ V，t σ is the average of the available water volume of all candidate schemes at time period t; σ V，t σ is the standard deviation of the available water volume of all candidate schemes at time period t.

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

[0014]

[0015] wherein, Hi(t) is the reservoir water level of candidate scheme i at time period t, as the simulated water level data; γ is the damping coefficient, which is a set value; A is the effective water storage area of the reservoir; I t Qi(t) is the water volume flowing into the reservoir at time period t; Qi(t) is the water volume lost by evaporation or seepage of the reservoir at time period t:

[0016]

[0017] wherein, H max Hmaxis the highest water level allowed for safe operation of the reservoir; E t E is the evaporation and seepage coefficient, with a value range of 0.05 to 0.2; λ L λ is the periodic modulation coefficient, with a value of 0.1 to 0.3.

[0018] Further, in step 2, the water level physical constraint is represented by the following formula:

[0019]

[0020] wherein, H min Hminis the lowest water level allowed for safe operation of the reservoir; Hi-1is the reservoir water level of candidate scheme i at time period t-1; η s η is the smoothing constraint term weight; P (i) Piis the water level physical constraint of candidate scheme i.

[0021] Further, in step 2, the economic objective model reflecting the energy consumption of the water transfer process is established by the following formula:

[0022]

[0023] wherein, C (i) Ciis the economic objective model value of candidate scheme i; ρ is the density of water; g is the acceleration of gravity; Peffis the pump station efficiency function; The water head difference is defined as:

[0024]

[0025] where H target is the target water level; ζ is the flow variation sensitivity coefficient, with a value range of 0.05 to 0.2; |·| is the absolute value operator; and Δt is the time period length.

[0026] Further, the pump station efficiency function is calculated using the following formula:

[0027]

[0028] where η0is the basic pump station efficiency; ξ is the efficiency adjustment factor; is the maximum allowable water transfer flow in the time period t.

[0029] Further, in step 2, the comprehensive objective function of the candidate scheme i is represented using the following formula:

[0030]

[0031] where F (i) is the comprehensive objective function value of the candidate scheme i.

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

[0033]

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

[0035]

[0036]

[0037] where represents the projection operator; x is the projection operator variable; y is the flow variable; λ Π is the regularization weight, with a value range of 0.3 to 0.8.

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

[0039]

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

[0041] The water conservancy project water transfer scheme optimization method based on the multi-objective particle swarm optimization of the application has the following beneficial effects: the application introduces a nonlinear second-order dynamic model in the modeling of reservoir water level dynamic changes, which can accurately describe the inertial effect, damping effect and complex nonlinear coupling characteristics of water, and comprehensively reflect the real dynamic behavior of water level changes under the influence of multiple factors such as flow, inflow and water loss. Through this dynamic model, the water level change trend under different water transfer schemes can be accurately predicted, ensuring that the reservoir water level always remains within the safe operation range and avoiding the engineering risks caused by excessively high or low water levels. This function is extremely rare in the prior art, especially under long-time span and complex hydrological conditions, and traditional methods are difficult to provide the same high-precision water level prediction capability. The application comprehensively considers the energy consumption target and water level safety in the optimization process, and realizes the overall trade-off of multi-dimensional targets by constructing a multi-objective comprehensive evaluation function. The comprehensive target function not only includes energy consumption calculation and water level physical constraints, but also introduces a water level change stability index to ensure that the selected water transfer scheme is not only economical and efficient, but also has good operation stability. Compared with the single-objective optimization method, the application can quickly find the global optimal solution under multi-objective constraint conditions, effectively balance the conflicts between different optimization targets, and improve the comprehensive performance of the water transfer scheme. Especially in terms of energy consumption optimization, the application significantly reduces the energy consumption cost in the operation process of the water pump, and has high economic benefit and energy saving effect. The application makes a number of improvements in the optimization algorithm, realizes efficient control of the optimization process through an adaptive convergence judgment mechanism. Traditional optimization algorithms usually use fixed iteration times as the termination condition, which can easily cause two extreme situations: one is to stop too early when the optimization has not reached the global optimal solution, resulting in incomplete optimization results; the other is to continue iteration when the convergence has reached the optimal solution, wasting computing resources. The application can flexibly adjust the number of iterations according to the actual convergence state by real-time calculation of the convergence index and dynamic monitoring of the change amplitude of the candidate scheme in continuous iteration, so as 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, making the entire optimization process more intelligent and efficient, and avoiding unnecessary computing overhead. The application also introduces a regularization projection operator in the flow updating process, further enhancing the smoothness of the flow distribution and the feasibility of actual operation. Traditional optimization methods are prone to sudden changes or large amplitude jumps when adjusting the flow, resulting in unstable water transfer schemes in actual operation, and even causing problems such as hydraulic impact or pump station overload. The application dynamically constrains the flow through the regularization projection operator to ensure that the water transfer flow changes smoothly within a reasonable range, effectively avoiding discontinuous jumps and improving the stability and safety of the water transfer scheme. This design provides an important guarantee for the safe operation of the reservoir, especially in high-frequency water transfer scenarios, which can significantly reduce the system operation risk. BRIEF DESCRIPTION OF DRAWINGS

[0042] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or the prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only aim at the embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of the provided drawings.

[0043] Figure 1 The method flowchart of the water conservancy project water diversion scheme optimization method based on multi-objective particle swarm optimization provided by the embodiments of the present application is shown. DETAILED DESCRIPTION

[0044] The method of the present application will be further described in detail below in combination with the accompanying drawings and the embodiments of the present application.

[0045] Embodiment 1, reference Figure 1 The water conservancy project water diversion scheme optimization method based on multi-objective particle swarm optimization comprises the following steps:

[0046] Step 1: generating a group of initial water diversion flow sequences for each candidate water diversion scheme in a preset discrete time interval; using a second-order dynamic model containing water body inertia, damping effect and nonlinear coupling term to perform time-varying simulation on the reservoir water level for each candidate water diversion scheme to obtain simulated water level data;

[0047] The generation of initial water release flow sequences is performed within a pre-set discrete time interval, which is usually set according to the actual operation period of the water conservancy project and can be hours, days, or longer time scales. Each candidate water release scheme consists of a set of water release flow sequences, with the flow sequence representing the instantaneous water release flow at each time point. The initial flow sequence generation method can be based on random initialization, historical data, or empirical rules, etc., to ensure that the generated water release flow sequences are diverse and reasonable. These initial sequences correspond to different particles 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 ability of the algorithm, which can effectively avoid the particle swarm from falling into a local optimal solution. Next, for each candidate water release scheme, a second-order dynamic water level model is used to simulate the time-varying changes of the reservoir water level. The model takes into account the inertia effect, damping effect, and external nonlinear coupling of the water body, which together determine the dynamic change of the reservoir water level over time. The inertia effect of the water body reflects the hysteresis phenomenon of the reservoir water level in response to changes in inflow and water release flow, i.e., the water level change does not immediately respond to the adjustment of the water release flow, but there is a certain hysteresis. The damping effect mainly describes the energy dissipation mechanism within the reservoir system, which is characterized by the gradual stabilization of water level fluctuations. This effect is particularly evident in long-term water release processes and helps to avoid large fluctuations in water level. The nonlinear coupling term reflects the complex hydrodynamic phenomena during the water release process, including the nonlinear effects caused by the interaction and coupling of various factors. This nonlinear term is particularly critical as it can simulate complex hydraulic boundary conditions and various external disturbance factors, making the simulation results more consistent with actual working conditions.

[0048] The role of the second-order dynamic model in water level simulation is not only to predict the water level change at future time points, 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 release flow sequence within the time interval, and other necessary boundary conditions, and the output is a sequence of simulated water level data at discrete time points. The simulated water level data will serve as an important basis for constraint conditions to ensure that the reservoir water level fluctuates within a safe range at all times, avoiding the risk of dam collapse due to excessively high water levels or affecting downstream water supply requirements due to excessively low water levels. In addition, through the time-varying simulation of the dynamic model, the rationality of each initial water release scheme can be intuitively identified, providing prior information for optimization. For example, if a candidate scheme causes the reservoir water level to exceed the safety range at a certain time point, it can be excluded directly in the initial stage, reducing unnecessary computational overhead. This simulation process lays a foundation for high precision and reliability for the entire optimization method, and provides accurate data support for the construction of the subsequent comprehensive evaluation function.

[0049] Step 2: To ensure that the water level of the reservoir always remains within a safe range and prevent sudden changes during the water transfer process, a water level physical constraint is constructed based on the simulated water level data. An economic objective model reflecting the energy consumption of the water transfer process is established. Nonlinear coupling is performed based on the economic objective model and the water level physical constraint to form a comprehensive evaluation function.

[0050] During the water transfer process of water conservancy projects, the water level of the reservoir must always remain within a safe range. A water level that is too high may lead to the risk of dam collapse, while a water level that is too low may affect downstream water supply needs 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 achieved by setting the maximum and minimum allowable values of the water level, i.e., at each discrete time point, the simulated water level data must satisfy these upper and lower limit conditions. If a water transfer scheme results in a simulated water level that exceeds the safe range at any time point, the scheme will be considered an infeasible solution and will be rejected. This process ensures the controllability of the water transfer scheme in terms of water level safety, making the entire optimization model more adaptable to reality. However, relying solely on water level constraints cannot fully meet the optimization needs of water conservancy projects. In addition to ensuring water level safety, water transfer schemes should also aim to minimize energy consumption during the water transfer process to improve economic efficiency. Therefore, an economic objective model centered on energy consumption is further established in Step 2. This model calculates the total energy consumption of each candidate water transfer scheme by modeling the energy loss during the water transfer process and considers it as part of the optimization objective. The construction of the energy consumption model is mainly based on parameters such as water transfer flow, pump station lift, and pipe resistance, and considers various energy loss factors during the water transfer process. Generally, energy consumption and water transfer flow have a nonlinear relationship, and excessive or insufficient flow will lead to unnecessary energy consumption. Therefore, the energy consumption model can effectively guide the water transfer flow to the optimal interval during the optimization process, avoiding high energy consumption caused by extreme flow.

[0051] To achieve the joint optimization of water level constraints and economic objectives, step 2 integrates both into a comprehensive evaluation function through nonlinear coupling. Nonlinear coupling not only considers the complex interaction of the two objectives simultaneously, but also allows for weight distribution of water level safety and energy consumption according to actual needs, allowing the optimization results to balance between safety and economy. The comprehensive evaluation function is an important part of the particle swarm optimization algorithm, directly determining the direction of optimization search. The core idea is to convert water level physical constraints into a penalty function, if the simulation water level of a candidate scheme exceeds the safety range, a larger penalty value is introduced to reduce the score of the scheme in the comprehensive evaluation function. At the same time, the energy consumption target value participates in the evaluation in the form of a positive index, the lower the energy consumption, the higher the score of the scheme. Therefore, the comprehensive evaluation function can not only exclude schemes with water levels exceeding the safety range, but also prefer schemes with lower energy consumption, thus achieving the dual objectives of water level safety and minimum energy consumption. In addition, the nonlinear characteristics of the comprehensive evaluation function can better reflect the complexity of the actual water transfer process. In water conservancy engineering, the water transfer process involves a variety of nonlinear hydrodynamic phenomena, and a single linear model often cannot accurately describe the water level change and energy consumption characteristics. Through nonlinear coupling, not only can these complex interactions be captured, but also the evaluation function can be more closely related to the actual working conditions, improving the accuracy of the optimization results and the value of engineering application. This method greatly improves the effectiveness of the water transfer scheme optimization, avoids the possible local optimal solution problem in traditional methods, and ensures that the final water transfer scheme meets the water level safety while having the lowest energy consumption.

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

[0053] Particle swarm optimization (PSO) is a global optimization algorithm based on swarm intelligence, which is inspired by the collective behaviors of bird foraging and fish hunting. Each particle represents a candidate solution, and in this invention, a particle is a specific water diversion flow sequence. The whole swarm moves in the search space, and the position and velocity of each particle are updated to find the optimal solution that minimizes the objective function. PSO is simple and efficient, especially when dealing with nonlinear, complex constrained, and multi-objective optimization problems, it can significantly improve the computational efficiency and optimization accuracy. For the water diversion scheme optimization in this invention, the initial search space of PSO is determined by the initial water diversion flow sequences generated in step 1, and the diversity of these initial particles provides a good global search foundation for subsequent optimization. The objective function of optimization is the comprehensive evaluation function constructed in step 2, which considers both the water level physical constraints and the energy consumption goal during the water diversion process. PSO minimizes the comprehensive evaluation function by constantly updating the state of particles, ensuring that the water diversion scheme meets the water level safety requirements and achieves the minimum energy consumption. In each iteration, each particle updates its position and velocity based on its historical best position and the global best position of the whole swarm. This updating mechanism allows particles to balance between local search and global search, quickly converging to high-quality solutions while effectively avoiding being trapped in local optimal solutions.

[0054] Specifically, during the iteration process of the particle swarm optimization algorithm, each particle continuously modifies its water diversion flow sequence under the guidance of the comprehensive evaluation function to optimize the objective function value. The velocity update formula of the particle determines its motion trajectory in the search space, and the update of the velocity depends on the current state of the particle, its historical optimal solution, and the global optimal solution. By introducing the inertia weight and the acceleration coefficient, the particle can dynamically adjust its exploration and exploitation ability, tending to global exploration in the early stage to avoid missing potential good solutions, and gradually converging to the local area in the later stage to ensure the refinement of the optimization result. After each iteration, the algorithm evaluates the objective function value of all particles and updates the personal optimal position and the global optimal position of the particles until the termination condition is met. The termination condition can be reaching the preset maximum number of iterations, the change amplitude of the comprehensive evaluation function value being less than a certain threshold, or finding an acceptable solution that satisfies all constraint conditions. In the scenario of the present application, the state update of the particle actually means the continuous optimization of the water diversion flow sequence. The initial water diversion flow sequence may have unreasonable places, such as causing the water level to exceed the safety range in some time periods or causing excessively high energy consumption. However, through the iterative update of the particle swarm optimization algorithm, the water diversion flow sequence will gradually become rational, the water level physical constraint will always be strictly followed, and the energy consumption will also be continuously reduced. With the increase of the number of iterations, the solutions in the particle swarm will gradually concentrate around the optimal solution, and finally an optimal water diversion scheme that can satisfy the water level safety and minimize the energy consumption will be found. Compared with traditional linear programming or other heuristic optimization methods, the particle swarm optimization algorithm has significant advantages. First, it does not rely on the derivative information of the objective function, and is suitable for optimization problems with nonlinearity, non-convexity, and complex constraints, which is highly consistent with the water diversion scheme optimization scenario faced by the present application. Second, the particle swarm optimization algorithm has strong global search ability 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 change and energy consumption makes the problem extremely complex, and traditional methods often have difficulty in balancing accuracy and efficiency. However, through the dynamic cooperation of swarm intelligence, the particle swarm optimization algorithm can achieve more efficient optimization results.

[0055] In step 1 of embodiment 2, define the initial water diversion flow sequence for each candidate scheme i in the discrete time interval t = 1, 2,..., T, denoted as: Q (i) = {Q i，t | t = 1,..., T}; Q i，t represents the water diversion flow adopted by candidate scheme i at time t; T is the upper limit of the time interval; the initial water diversion flow of each candidate scheme i in each time period t is The following formula is used to calculate:

[0056]

[0057] where, is the minimum water regulating flow; is the maximum water regulating flow; V i，t is the available water volume of candidate scheme i in time period t; μ V，t is the mean of available water volume of all candidate schemes in time period t; σ V，t is the standard deviation of available water volume of all candidate schemes in time period t.

[0058] Specifically, in this formula, the water regulating flow is calculated based on the available water volume V i，t of candidate scheme i in time period t = 1, 2,..., T. The key parameters in the formula include the minimum water regulating flow the maximum water regulating flow the mean μ V，t of available water volume, and the standard deviation σ V，t . These parameters together determine the way of generating the initial water regulating flow, so that the initial flow of each candidate scheme can not only reflect the change of available water volume under the current hydrological condition, but also ensure that it fluctuates within a reasonable range, avoiding extreme flow values that threaten the safe operation of reservoir water level. The most core part of the formula is which serves to standardize and nonlinearly transform the available water volume of candidate schemes, aiming to balance the differences between candidate schemes and avoid the distribution of available water volume being too biased towards one extreme situation. The input of the arctan function is the standardized deviation of available water volume, i.e., the deviation of the available water volume of candidate schemes from the mean of all candidate schemes, and the scale of standardization is controlled by the standard deviation σ V，t . When the deviation is small, the output of the arctan function approximates to linear change, which means that the available water volume of candidate schemes is close to the average level, and the corresponding water regulating flow will also be located 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 has smoothness and robustness, which can effectively reduce the influence of random fluctuations on the calculation of initial flow.

[0059] The scaling and translation operations in the formula are also important parts to ensure that the initial water regulating flow is within a reasonable range. First, through the operation of , the output value of the arctan function is mapped from its original range to the interval [0, 1]. This standardization process enables the values of available water volume after nonlinear transformation to be compared and operated on the same scale. Subsequently, this result is mapped between the minimum water regulating flow and the maximum water regulating flow to generate the final initial water regulating flow This method ensures that the initial water flow of each period fluctuates within a safe and controllable range, effectively avoiding the out-of-range problems that may occur in traditional linear interpolation methods. In addition, the statistical parameters μ V，t and σ V，t in this formula fully consider the overall available water distribution characteristics of all candidate schemes within each period, making the initial water flow sequence have high distribution consistency. This standardized processing based on overall distribution can provide a certain balance for the water diversion scheme at the initial stage, reduce the excessive difference between different candidate schemes in the initial flow sequence, avoid some schemes being eliminated by the optimization process too early, and improve the global search ability and convergence speed of the particle swarm optimization algorithm. Especially in the actual operation of water conservancy projects, the hydrological conditions often have great spatiotemporal variability. Through this dynamic standardization method, the algorithm's robustness can be better adapted to changes in hydrological conditions. This initial flow generation method has significant advantages in the multi-objective particle swarm optimization framework of the invention. First, it can improve the search efficiency of the optimization algorithm and shorten the optimization time through reasonable initial solution generation. Second, by using nonlinear mapping and smoothing processing, the influence of extreme available water on the initial solution is reduced, the initial quality of the water diversion scheme is improved, and the risk of reservoir water level fluctuation and energy consumption is reduced. Finally, this flow calculation method based on statistical characteristics provides a diversified initial solution space for flow sequence generation in multi-objective optimization, significantly improving the possibility of finding the global optimal solution.

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

[0061]

[0062] wherein, H t represents the water level of candidate scheme i in period t, which is the simulated water level data; γ is the damping coefficient, which is a set value; A is the effective storage area of the reservoir; I is the water inflow into the reservoir in period t;

[0063]

[0064] wherein, H max represents the highest water level allowed for safe operation of the reservoir; E t is the evaporation and leakage coefficient, with a value range of 0.05 to 0.2; λ L is the periodic modulation coefficient, with a value of 0.1 to 0.3.

[0065] Specifically, this dynamic model is presented in the form of a second-order differential equation, and the second derivative of the water level The acceleration of water level change reflects the inertial effect of the water body, i.e., the hysteresis response of water level to the inflow and the change of water transfer flow. The introduction of inertial effect makes the model simulate the dynamic process of water level gradually tending to be stable after being disturbed by external factors, rather than instantaneously reaching a new equilibrium state. In addition, the model also contains the first derivative term of water level This term reflects the damping effect of the system, describing the energy dissipation process within the water body. The damping coefficient γ controls the amplitude and frequency of water level fluctuations, and its role is to suppress excessive fluctuations of water level and prevent large fluctuations of reservoir water level, ensuring the stability of water transfer process. On the right side of the model, the water balance part is the core of the dynamic equation, which describes the net water change of the reservoir in each time period. Among them, A is the effective storage area of the reservoir, which determines the influence of water change on water level. t I is the total water inflow into the reservoir in period t, usually determined by the upstream river and precipitation, while the water transfer flow Q i，t is the decision variable in the candidate scheme, representing the water transferred out of the reservoir in that period. The basic idea of water balance is that the inflow water minus the water transfer flow and water loss of the reservoir determines the rising or falling trend of water level. This dynamic balance process reflects the basic operation law of the reservoir as a water storage system, providing a basis for water level change simulation.

[0066] Water loss function describes the water loss caused by evaporation and seepage, which is an important part of the dynamic model. Water loss changes with water level, and is described by a nonlinear function, i.e., This function embodies two key characteristics: first, the evaporation and seepage are positively correlated with water level, the higher the water level, the greater the loss; second, the periodic sine term simulates seasonal hydrological changes and the influence of reservoir environment, especially when the water level is close to the safety upper limit H max , the water loss increases significantly. This periodic feature makes the water level simulation more consistent with the complex phenomena in actual reservoir operation, helping to accurately predict water level changes under different water transfer schemes. In addition, a nonlinear coupling term This term describes the water level feedback effect under high water level conditions. This nonlinear term has little impact on water level changes at low water levels, but significantly increases the rate of water level rise at high water levels, serving as a risk warning and regulation mechanism. By introducing this term, abnormal fluctuations under high water level conditions can be amplified during simulation, helping to identify and adjust potential risks of exceeding water level limits in a timely manner. This nonlinear coupling mechanism gives the model higher sensitivity, enabling earlier prediction of potential risks and providing a more accurate basis for the physical constraints of water level in multi-objective optimization processes. This second-order dynamic model not only realistically reproduces the dynamic changes in reservoir water levels but also provides accurate simulation data for multi-objective particle swarm optimization algorithms, helping the algorithm quickly eliminate candidate schemes that do not meet water level safety requirements during optimization. Through this dynamic model, the water level change process of each candidate scheme can be accurately predicted, ensuring that each scheme operates within a safe range during optimization. Simultaneously, the water balance and water loss functions in the model provide comprehensive reservoir operation information, offering important references for subsequent energy consumption targets and economic benefit optimization.

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

[0068]

[0069] Among them, H min This indicates the minimum water level that is permissible for the safe operation of the reservoir. Let η be the reservoir water level of candidate scheme i during time period t-1; s To smooth the weights of the constraint terms; P (i) The physical constraints on water level for candidate scheme i.

[0070] Specifically, formula P (i) The structure can be divided into three parts, corresponding to the lower limit constraint, the upper limit constraint, and the smoothness constraint of water level changes. First, regarding the lower limit constraint, the formula... This is used to detect whether the water level of a candidate solution is lower than the minimum water level H allowed for safe operation of the reservoir during time period t. min If the water level Higher than H min A value of 0 for this item indicates that the water level meets safety requirements during this period; however, if the water level is lower than H... min This term is accumulated in the form of the squared difference in the water level physical constraint function. The squaring operation amplifies the penalty for exceeding the water level limit, especially when the water level deviation is large. It significantly increases the penalty value, forcing the optimization algorithm to prioritize candidate solutions with water levels closer to the safe range. This effectively prevents reservoir water levels from becoming too low, preventing insufficient downstream water supply and damage to the aquatic ecosystem. Similarly, the upper limit constraint on water level is... to detect whether the water level of the candidate solution exceeds the upper limit H max during the time period t The value of this term is 0 when the water level is below H max , and the square of the difference will be accumulated into the constraint function as a penalty value once the water level exceeds H max . This design aims to ensure that the water level of the reservoir fluctuates within the allowed range, avoiding the risk of overflow or structural damage due to excessively high water levels. The form of square amplification makes the optimization algorithm more inclined to choose solutions with stable water levels close to the safe upper limit but not exceeding it, thereby maximizing the reservoir's water storage capacity while minimizing risks.

[0071] However, relying solely on the upper and lower limits of the water level is not enough to ensure the smoothness of the water transfer scheme. In actual water conservancy engineering dispatching, water level mutations will have adverse effects on reservoir structures, downstream river channels, and ecological environments. Therefore, the formula specifically introduces a water level smooth change constraint term By accumulating the fourth power of the water level change amplitude between adjacent time periods, it suppresses drastic water level fluctuations in the candidate solution. Compared to the square penalty mechanism, the fourth power penalty can more sensitively detect water level mutations, especially when the water level changes significantly, as the penalty value will rapidly increase, significantly improving the optimization process's preference for smooth change solutions. This smooth change constraint not only avoids the impact of water level mutations on reservoir operation safety but also reduces the energy consumption caused by frequent water level adjustments during water transfer, improving overall operational efficiency. The selection of the smoothness constraint weight η s is crucial as it determines the balance between smoothness and flexibility. Typically, η s can be adjusted according to the specific reservoir operation characteristics and water transfer goals, either increasing the weight to more strictly limit water level fluctuations when safety requirements are high or appropriately reducing the weight to enhance the diversity of water transfer schemes when greater flexibility is allowed. The entire water level physical constraint function generates a comprehensive evaluation index P (i), for measuring the performance of candidate schemes in terms of water level safety and change stability. In multi-objective particle swarm optimization, this evaluation index, together with the energy consumption objective function, constitutes the optimization objective, guiding the algorithm in the process of searching for the optimal water regulation scheme to preferentially select those schemes that can balance water level safety and energy consumption economy. Compared with traditional single constraint methods, this comprehensive physical constraint not only has higher flexibility, but also can more accurately reflect the complexity in actual reservoir operation, making the optimization results more close 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 water level and weight parameters, the constraint function can adapt to the requirements of reservoir scheduling of different scales and functions. For example, for a reservoir mainly for irrigation, the lower limit constraint can be appropriately relaxed to allow lower water levels to meet irrigation needs; while for a reservoir with prominent flood control function, the upper limit constraint weight can be increased to ensure that the water level is always within the safe range. This flexibility greatly enhances the practicality and promotional value of the invention, enabling it to play a role in different water conservancy engineering scenarios.

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

[0073]

[0074] where C (i) is the economic objective model value of candidate scheme i; ρ is the density of water; g is the acceleration of gravity; is the pump station efficiency function; is the head difference, defined as:

[0075]

[0076] where H target is the target water level; ζ is the flow change sensitivity coefficient, with a value range of 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 objective model reflects the total energy consumption required for water flow through the water pump, with the core calculation part based on , where ρ is the density of water, g is the acceleration of gravity, is the head difference, defined as This part describes the relationship between the mechanical energy required for water flow through the pump station and the flow rate Q i，t , the head difference , and the time period length Δt. The head difference is an important factor in determining the energy consumption of the water pump, representing the change in water level relative to the target water level H targetThe water head difference is the difference in water levels between the source and the target. When the water head difference is large, the pump needs more energy to lift the water flow to the target water level, resulting in a significant increase in energy consumption; conversely, when the water head difference is small, the energy consumption will decrease accordingly. Therefore, this model can dynamically reflect the impact of water level changes on energy consumption, enabling the optimization process to more accurately consider the actual situation of reservoir operation. The key innovation in the model is the introduction of the pump station efficiency function

[0078] It depicts the nonlinear characteristics of pump efficiency changes with flow and water head difference. Pump station efficiency is not constant, but changes with operating conditions, usually reaching a maximum within a certain range of flow and water head difference, and significantly decreasing outside this range. This function plays a crucial role in the model, guiding the optimization algorithm to adjust the flow within the efficient operating range, avoiding energy waste caused by inefficient operation. In addition, The introduction of makes the energy consumption model more close to the actual working condition, improves the feasibility and accuracy of the optimization results.

[0079] To further optimize the energy consumption cost in the water transfer process, a flow rate change penalty term is added to the formula Where ζ is the flow change sensitivity coefficient, ranging from 0.05 to 0.2, representing the degree of punishment for flow mutation. This term amplifies the impact of flow rate change through an exponential function, the main purpose is to prevent the candidate scheme from appearing drastic flow adjustment, so as to reduce the high instantaneous energy consumption caused by frequent adjustment of pump operating state. In practical water conservancy engineering, frequent switching of pump operating state will significantly increase system energy consumption and may shorten equipment life. By introducing this term, the model is more inclined to choose those with smooth flow change in the optimization process, ensuring that the water transfer process is more economical and efficient. The physical basis of this model can be understood as the mechanical energy required by the pump to lift the water flow being converted into electrical energy consumption, and the actual electrical energy consumption is reflected through the pump station efficiency function. Specifically, the total energy consumption C (i) of the candidate scheme is the cumulative sum of unit time energy consumption in all time periods, which changes with flow Q i，t and water head difference As the increase of the water level, the energy consumption per unit time will also increase accordingly. However, by optimizing the water transfer scheme, the flow and water head difference can be controlled in an optimal range while meeting the water level safety constraints, thereby significantly reducing energy consumption. In addition, the flow rate change penalty term, under the action of the exponential function, makes the model have a higher preference for those schemes with smooth flow rate changes and lower energy consumption, greatly improving the economy of the optimization results. It is worth noting that this economic objective model has high flexibility and scalability. By adjusting the parameters ζ and the specific form of the pump station efficiency function, the energy consumption model can be personalized according to different types of water pumps and actual operation needs of water conservancy projects. For example, during the peak water supply period, the flow rate change limit can be appropriately relaxed to increase the flexibility of water supply; while in the energy-saving priority operation strategy, the value of ζ can be increased to strictly limit the flow change and minimize energy consumption. In addition, the water head difference in the model can also be dynamically adjusted according to the specific target water level to adapt to different operation goals, such as flood control, irrigation, or power generation, etc.

[0080] Example 6: Pump station efficiency function

[0081]

[0082] where η0 is the basic pump station efficiency; ξ is the efficiency adjustment factor; is the maximum allowable water transfer flow in period t.

[0083] Specifically, in the operation of the pump station, the efficiency changes significantly nonlinearly with the flow and the water head difference. The influence of the flow Q i，t on the efficiency can be described by When the flow is small, the function value is close to 0, and the pump station efficiency remains at a high level close to the basic efficiency η0. However, as the flow gradually approaches or exceeds the maximum allowable flow , the hyperbolic tangent function value tends to 1, resulting in a significant decrease in efficiency. This nonlinear change mechanism simulates the phenomenon of reduced efficiency of actual pump stations when running at high flow, especially when the flow exceeds the optimal working interval of the pump station design, the energy consumption of the water pump will increase significantly. Therefore, this function guides the optimization algorithm to be more cautious in the flow adjustment process, avoids high flow operation, reduces unnecessary energy consumption, and improves overall economic efficiency. The water head difference , which is also an important factor affecting the efficiency of the pump station, determines the lifting height that the water pump needs to overcome. When the water head difference is small, the lifting power required by the water pump is small, and the efficiency can be maintained at a high level. However, as the water head difference increases, the lifting height increases, and the pump station efficiency begins to decrease. By This nonlinear variation process can be accurately described. When the head difference approaches the target water level, the efficiency changes more gently; while the head difference exceeds a certain range, the efficiency decreases 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 consumption loss caused by high head difference operation.

[0084] More importantly, the product form of two hyperbolic tangent functions is adopted in this efficiency function, which further enhances the sensitivity of efficiency changes. The product form makes the pump station efficiency decline more significantly under the double adverse conditions of flow and head difference, thus prompting the optimization algorithm to preferentially select candidate solutions that maintain moderate flow and small head difference, achieving minimum energy consumption. This double restriction mechanism ensures that the pump station always operates in a high-efficiency interval, avoiding the problem of low efficiency caused by a single factor, making the optimization result more stable and reliable. The parameter ξ as an efficiency adjustment factor has flexible adjustment ability. In different application scenarios, the sensitivity of efficiency changes with flow and head difference can be changed by adjusting the value of ξ. For example, in the water diversion strategy emphasizing energy saving, the value of ξ can be appropriately increased to more strictly limit high flow and high head difference operation, ensuring that energy consumption is always at a low level; while in the peak water supply or emergency water diversion scenario, the value of ξ can be reduced to increase the tolerance of flow and head difference, increasing the flexibility of the water diversion scheme. It is this flexibility that makes the pump station efficiency function highly adaptable and scalable in practical applications. From the 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. With the changes in flow and head difference during the optimization process, the efficiency value will be adjusted in real time, directly affecting the calculation results of the energy consumption objective function C (i) , and then guiding the optimization algorithm to continuously evolve towards a more energy-saving direction. Compared with the traditional linear efficiency model, this nonlinear efficiency function can better capture the complexity of actual pump station operation, making the optimization process more realistic and ultimately improving the economic efficiency and feasibility of the water diversion scheme.

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

[0086]

[0087] where 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 objective C (i) and the water level physical constraint P (i)nonlinear superposition of the economic cost and the water level safety requirement in the water transfer process. The energy consumption target C (i) reflects the total energy consumed by the pump station during operation, which includes key variables such as flow rate, head difference, and pump station efficiency, and details the energy consumption characteristics of different schemes. On the other hand, the water level physical constraint P (i) ensures that the water level is always within the safe operating range and avoids the threat of severe water level fluctuations to system safety. The C (i) and P (i) are combined in a nonlinear power relationship, with a weight parameter ξ adjusting the relative importance of the two. The priority of economy and safety can be flexibly adjusted according to specific scene requirements. This nonlinear design ensures sensitivity to high energy consumption and severe water level deviation schemes during the optimization process, while giving a certain tolerance to smaller energy consumption and water level deviation, thereby improving the practical applicability of the water transfer 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 the reservoir water level is a key indicator of accelerated water level changes, reflecting the dynamic characteristics of water level over time. To avoid the engineering risks and efficiency losses that may be caused by severe water level fluctuations, the comprehensive objective function accumulates the square value of the second derivative to measure the water level smoothness during the entire water transfer process. Water level fluctuation smoothness is crucial for the safe operation of the reservoir and the optimization of pump station energy consumption. Severe water level changes increase the operating pressure of the pump station, leading to a surge in energy consumption and potentially causing adverse effects on the reservoir structure and downstream ecosystems. By penalizing the square value of the second derivative of the water level, this function can effectively guide the optimization algorithm to prefer candidate schemes with smooth water level changes, ensuring the stability of the reservoir during the water transfer 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 a power form, playing a role of global trade-off. A larger ζ value will make the function more sensitive to schemes with high energy consumption or large water level fluctuations, strengthening the focus on these issues during optimization; while a smaller ζ value will weaken this sensitivity, focusing more on the overall performance of the scheme. This design gives the optimization algorithm higher flexibility and adaptability, allowing it to be adjusted according to different engineering needs. For example, in scenarios where economy is the priority, the values of ζ and ξ can be appropriately reduced, thereby reducing the weight of energy consumption and water level stability; while in scenarios where safety is the priority, these parameters can be increased to further restrict water level deviation and fluctuations. The innovation of this comprehensive objective function is that it integrates multiple key factors of water transfer scheme optimization into one evaluation index in a unified mathematical framework, not only accurately reflecting the pros and cons of each scheme, but also providing a clear search direction and weight basis for the multi-objective particle swarm optimization algorithm. Compared with traditional single-objective optimization models, the comprehensive objective function of the invention can simultaneously handle optimization requirements in the three dimensions of economy, safety, and stability, showing higher scientificity and applicability in multi-objective trade-offs. This design effectively overcomes the limitations of traditional methods in balancing multiple conflicting objectives in multi-objective optimization. Through this comprehensive objective function, the optimization algorithm can perform a comprehensive multi-dimensional evaluation of candidate schemes in each iteration, quickly identifying and eliminating high-energy or unsafe schemes, while preferentially retaining those that are both economically efficient and stable in operation. This function is of great significance for the optimization of water transfer schemes in actual water conservancy projects, especially under complex hydrological conditions, significantly improving the reliability and engineering applicability of the optimization results.

[0090] In each iteration k, the particle swarm optimization algorithm in step 3 updates the speed of each candidate scheme i = 1,..., N at each time period t = 1,..., T in sequence:

[0091]

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

[0093]

[0094]

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

[0096] Specifically, in each iteration k, the speed of candidate solution i in time period t. The update formula employs a mechanism based on the gradient estimation of the objective function. In the velocity update formula, the first part... This is the inertia term, reflecting the current motion trend of the particles, i.e., how the velocity of the previous iteration affects the current iteration. This part, by maintaining a certain degree of inertia, ensures the global search capability of the particle swarm and avoids prematurely getting trapped in local optima. The second part synthesizes the objective function F... (i) The rate of change of the objective function F guides the adjustment of the particle's velocity. (i) Combined with energy consumption target C (i) Water level physical constraints P (i) The water level stability index is a core evaluation criterion for multi-objective optimization. By calculating the difference in the change of the objective function when the flow rate increases and decreases, the algorithm can approximately estimate the gradient of the objective function with respect to the flow rate. The gradient approximation presented in the form of [formula missing] allows the velocity update to consider not only the current flow rate but also to dynamically capture the changing trend of the objective function within the current search space. This gradient-based adjustment strategy gives the algorithm stronger local search capabilities, enabling particles to adjust more precisely along the direction of objective function optimization. In addition to the linear effect of the objective function gradient, the velocity update formula also introduces a second-order term to capture the second-order nonlinear relationship between the objective function and flow rate changes. This part [details missing]. The form reflects the curvature information of the objective function, that is, the secondary impact of flow rate changes on the comprehensive objective function. This design enables the algorithm to exhibit higher sensitivity in complex nonlinear optimization spaces, effectively identifying subtle changes in local regions and thus avoiding missing potential high-quality solutions.

[0097] Updated speed It is not directly used as a flow value, but rather incorporated into the location update formula. During flow updates, the algorithm introduces a regularized projection operator. Updated traffic The projection is applied to the allowable water diversion flow range. The function of the projection operator is 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 within time period t. and maximum flow Furthermore, the projection operator optimizes the selection of the flow through a regularization term, which is based on... in the form of a projection operator, which physically means to enhance the smoothness of the flow distribution and avoid large discontinuous jumps in the water diversion scheme. By mapping the target flow x to the flow y that satisfies the constraints while considering the influence of regularization, the projection operator enables the optimization algorithm to balance 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 Π can be adjusted in the range of 0.3 to 0.8, allowing flexible adjustment according to different water conservancy engineering needs. If the smoothness of the water diversion flow is prioritized, the value of λ Π can be increased, thereby more strictly limiting the flow jump; if other objectives (such as economy or safety) are prioritized, λ Π can be appropriately reduced, allowing a larger adjustment range for the flow within a certain range. This flexible regularization design gives the algorithm greater adaptability, enabling it to meet diverse engineering application needs. Throughout the iteration process, the dynamic updating of speed and position continuously guides the candidate scheme towards the optimization target. Initially, the speed of each candidate scheme is initialized to the initial flow Through multiple iterations, the particle swarm gradually concentrates in the region with lower objective function values, thereby accelerating the convergence process. The combination of the inertia term, the gradient term, and the second-order term achieves a good balance between global search and local search, enabling the algorithm to quickly escape from local optimal solutions and achieve fine exploration of the objective function in complex optimization spaces. The particle swarm optimization algorithm of the present invention has advantages not only in improving search efficiency but also in precise handling of 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 water diversion scheme optimization. Compared with traditional optimization methods, this algorithm significantly improves the optimization quality of the water diversion scheme, enabling it to quickly find the global optimal solution while meeting the multiple requirements of reservoir water level safety, flow smoothness, and energy economy.

[0098] In step 3, the particle swarm optimization algorithm is calculated by the following formula:

[0099]

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

[0101] Specifically, in the iteration process of particle swarm optimization, the water diversion flow of each candidate scheme i at each time period t is adjusted according to the update formula in each iteration k. In order to determine whether the particle swarm has entered the convergence state, the convergence index Δ (k) is calculated by using the root mean square difference, which measures the change amplitude of the water diversion flow between the kth iteration and the (k-1) th iteration, and monitors the change trend of the particle swarm in real time. Specifically, Δ (k) represents the average change of the water diversion flow of all candidate schemes at all time periods, which reflects the convergence degree of the particle swarm in the entire optimization space. When Δ (k) is large, it means that the change amplitude of the candidate scheme in the continuous two iterations is large, and the particle swarm is still actively exploring the optimization space and has not converged. When Δ (k) 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 determined to be close to the optimal solution.

[0102] This convergence index has important practical significance. The water diversion scheme optimization of water conservancy projects involves complex multi-objective constraints, including energy consumption, water level safety and stability, etc. In the multi-objective environment, the traditional optimization method is difficult to accurately determine whether the global optimal solution has been found, and the present application provides a reliable basis for judging the global convergence of the particle swarm by dynamically calculating Δ (k) . At the end of each iteration, the algorithm calculates the current convergence index Δ (k) and compares it with the preset threshold. If Δ (k) is less than the threshold, it means that the change of the candidate scheme has tended to be stable, the algorithm is determined to be converged and the iteration is terminated, and the result statistics and scheme 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 water conservancy project requirements and the availability of computing resources. In the scene of pursuing high-precision optimization results, a smaller convergence threshold is usually selected, so that the algorithm can search the optimization space more finely and find a better water diversion scheme. In the scene of limited computing time or relatively low requirement for optimization result precision, a larger convergence threshold can be selected to speed up the iteration process and reduce the calculation cost. This flexible design gives the present application higher adaptability, which can meet the needs of different engineering scenes. After the algorithm is determined to be converged, the system will calculate the comprehensive objective function value F (i) at each iteration, and finally select the candidate scheme with the minimum comprehensive objective function value as the optimal water diversion scheme. The comprehensive objective function F(i) is the core evaluation index of multi-objective optimization, which combines the energy consumption target C (i) , the water level physical constraint P (i) and the smoothness of water level change, and can comprehensively measure the overall performance of the candidate scheme. By selecting the scheme with the minimum comprehensive objective function value, it can ensure that the selected water regulation scheme has the optimal comprehensive performance in multi-objective optimization, which can not only effectively reduce the energy consumption in the water regulation process, but also ensure the safety and smoothness of the reservoir water level. This scheme selection mechanism based on the comprehensive objective function not only improves the reliability of the optimization result, but also effectively avoids the problem of result deviation caused by local optimal solution. It is worth noting that the dynamic calculation of the convergence index Δ (k) also has certain adjustment and feedback effects. In the early stage of the algorithm, the particle swarm is usually in a global exploration state, and the variation range of the candidate scheme is large, and the convergence index is also relatively high. The main task of this stage is to find potential high-quality solutions through large-scale search, rather than pursuing convergence too early. In this stage, the larger Δ (k) value can help the algorithm maintain sufficient exploration ability and avoid falling into local optimum. In the middle and later stages of iteration, as the particle swarm gradually gathers in the area with lower objective function value, the convergence index Δ (k) will gradually decrease, indicating that the particle swarm is converging to the global optimal solution. At this time, through the smaller convergence threshold, the algorithm can be guided to adjust the candidate scheme more finely, so as to find a more accurate optimal solution.

[0103] Although the specific embodiments of the present application are described above, those skilled in the art should understand that these specific embodiments are only illustrative, and those skilled in the art can make various omissions, substitutions and changes to the details of the above method and system without departing from the principles and essence of the present application. For example, combining the above method steps, so as to perform substantially the same function to achieve substantially the same result according to the substantially same method, is within the scope of the present application. Therefore, the scope of the present application is only limited by the appended claims.

Claims

1. A method for optimizing water diversion schemes in water conservancy projects based on multi-objective particle swarm optimization, characterized in that, The method includes: Step 1: Generate a set of initial water diversion flow sequences for each candidate water diversion scheme within a preset discrete time interval; use a second-order dynamic model that includes water body inertia, damping effect and nonlinear coupling term to simulate the reservoir water level for each candidate water diversion scheme in a time-varying manner, and obtain simulated water level data. Step 2: To ensure that the reservoir water level remains within a safe range and to prevent sudden changes during the water transfer process, physical constraints on the water level are constructed based on simulated water level data; an economic target model reflecting the energy consumption of the water transfer process is established; and a comprehensive evaluation function is formed by nonlinear coupling of the economic target model and the physical constraints on the water level. Step 3: Using the initial water diversion flow sequence as the initial search space for the particle swarm optimization algorithm, and the comprehensive evaluation function as the objective function of the particle swarm optimization algorithm, the optimal water diversion scheme is found from the candidate water diversion schemes through iterative updates; in Step 1, the discrete time interval is set as... Within, for each candidate solution Define the initial water diversion flow sequence as: ; Indicate candidate solutions In time The water diversion flow rate used internally; The upper limit of the time interval; each candidate solution In each time period Initial water diversion flow rate within The following formula is used for calculation: ； in, Minimum water diversion flow rate; This is the maximum water diversion flow rate; To represent candidate solutions During the period Available water volume within; This indicates that all candidate solutions are in the time period Average available water volume within the area To represent all candidate solutions during the time period Standard deviation of available water volume within; In step 1, for candidate solutions At any time period The dynamic changes in the reservoir water level satisfy the following second-order dynamic model: ； in, Indicate candidate solutions During the period The water level of the reservoir inside is used as simulated water level data; Here, is the damping coefficient, and is the set value; The effective water storage area of ​​the reservoir; For the time period The amount of water flowing into the reservoir; For the reservoir during the period Water loss due to internal evaporation or leakage: ； in, This indicates the highest water level that is permissible for the safe operation of the reservoir. The evaporation and leakage coefficient ranges from 0.05 to 0.

2. The periodic modulation coefficient has a value ranging from 0.1 to 0.

3. In step 2, the physical constraints on water level are expressed using the following formula: ； in, This indicates the minimum water level that is permissible for the safe operation of the reservoir. Candidate solutions During the period The water level of the reservoir inside; To smooth out the weights of the constraint terms; Candidate solutions Water level physical constraints; In step 2, an economic target model reflecting the energy consumption of the water transfer process is established using the following formula: ； in, Candidate solutions The economic target model value; The density of water; It is the acceleration due to gravity; The efficiency function of the pumping station; The head difference is defined as: ； in, The target water level; This is the sensitivity coefficient for flow rate changes, with a value ranging from 0.05 to 0.

2. This is the absolute value operator; This represents the duration of the time period.

2. The method for optimizing water diversion schemes in water conservancy projects based on multi-objective particle swarm optimization as described in claim 1, characterized in that, The pump station efficiency function is calculated using the following formula: ； in, To improve the efficiency of basic pumping stations; As an efficiency adjustment factor; For time period The maximum permissible water diversion flow rate within the facility.

3. The method for optimizing water diversion schemes in water conservancy projects based on multi-objective particle swarm optimization as described in claim 2, characterized in that, In step 2, candidate solutions The comprehensive evaluation function is expressed by the following formula: ； in, Candidate solutions The comprehensive evaluation function value.

4. The method for optimizing water diversion schemes in water conservancy projects based on multi-objective particle swarm optimization as described in claim 3, characterized in that, The particle swarm optimization algorithm in step 3 is used in each iteration. Within, for all candidate solutions In each time period Candidate solutions in turn During the period Update at a rapid pace: ； in, Indicate candidate solutions During the period In the first Speed ​​during the next iteration; ; Indicate candidate solutions During the period In the first Speed ​​during the next iteration; Candidate solutions During the period In the first Water diversion flow rate during the next iteration; ； ； in, Represents the projection operator; For projection operator variables; Flow variables; This is the regularization weight, with a value ranging from 0.3 to 0.

8.

5. The method for optimizing water diversion schemes in water conservancy projects based on multi-objective particle swarm optimization as described in claim 4, characterized in that, The particle swarm optimization algorithm in step 3 calculates the convergence metric using the following formula: ； in, Candidate solutions During the period In the first Water diversion flow rate during the next iteration; For the first The convergence metric at the next iteration; when When the flow rate is less than the set iteration threshold, the particle swarm optimization algorithm stops iterating, and the comprehensive evaluation function value corresponding to each iteration is counted. The candidate water transfer scheme corresponding to the water transfer flow rate with the smallest comprehensive evaluation function value is taken as the optimal water transfer scheme.

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