Multi-objective optimization method for hydraulic model of high-pressure pump for wide-range and high-efficiency seawater desalination

Abstract

This invention relates to the field of fluid machinery technology, specifically a multi-objective optimization method for a hydraulic model of a high-pressure pump for wide-area high-efficiency seawater desalination. By constructing a parameterized three-dimensional hydraulic model, it integrates a dual-objective optimization framework of design flow point efficiency and wide-area efficiency uniformity. It calculates the impeller head using empirical formulas incorporating hydraulic losses, generates a Pareto optimal solution set by combining the NSGA-II algorithm and a simulated binary crossover strategy, and selects the optimal solution based on entropy weight-TOPSIS decision-making. Closed-loop optimization is achieved through CFD simulation verification and dynamic correction using a Gaussian process model. The invention introduces a necessary cavitation margin constraint mechanism and a dynamic model predictive controller to effectively suppress cavitation risk and improve adaptability under wide-area operating conditions. This invention improves design point efficiency by 8%-12%, expands the high-efficiency flow range to 60%-120% of the design value, and increases optimization efficiency by more than 30%, providing key technical support for the efficient and stable operation of seawater desalination equipment under complex operating conditions.

Description

Technical Field

[0001] This invention relates to the field of fluid machinery technology, specifically to a multi-objective optimization method for a hydraulic model of a high-pressure pump for wide-area, high-efficiency seawater desalination. Background Technology

[0002] With the global water shortage becoming increasingly severe, seawater desalination, as an important freshwater replenishment technology, relies heavily on high-pressure pumps, the core equipment of which directly impacts system energy consumption and operational stability. Traditional seawater desalination high-pressure pumps are typically designed with the highest efficiency at a single design flow point as the optimization objective. However, in actual operation, due to fluctuations in operating conditions (such as ±20% changes in influent flow rate) and environmental factors such as seawater salinity and temperature, the pump needs to maintain efficient and stable operation over a wide flow range. This wide-range operating condition places higher demands on the pump's hydraulic design, but existing technologies have the following significant shortcomings: 1. Single-objective optimization leads to performance imbalance across a wide area. Existing designs often focus on maximizing efficiency at the design point, neglecting efficiency uniformity over a wide flow range. Studies show that traditional centrifugal pumps experience an efficiency drop of 15%-20% when deviating from their design point, particularly under low-load conditions, which can easily lead to cavitation, vibration, and other problems, severely impacting system reliability. For example, a certain type of commercial high-pressure pump exhibited a 22% efficiency reduction compared to its design point at 80% flow rate, and its required net positive suction head (NPSHr) exceeded the allowable value by 18%, resulting in frequent start-ups and shutdowns and increased maintenance costs.

[0003] 2. Accumulation of simplified errors in hydraulic models Traditional hydraulic models often employ simplified Bernoulli equations or neglect the dynamic characteristics of hydraulic losses, leading to significant discrepancies between simulation results and measured values. Although loss coefficient corrections are introduced, the fixed-loss model fails to characterize the impact of changes in the blade inlet angle of attack on flow separation, resulting in a head prediction error exceeding 8%. This error is further amplified under wide operating conditions, causing distortion of the optimization results.

[0004] 3. Multi-objective optimization is inefficient. Existing multi-objective algorithms, when dealing with conflicting objectives such as efficiency and wide-area uniformity, require manually setting weight coefficients, resulting in strong subjectivity and insufficient solution space coverage. In a case study of seawater desalination pump optimization reported in the literature, the Pareto front generation method took as long as 72 hours, and the resulting non-dominated solution set was discretely distributed, indicating poor engineering applicability.

[0005] 4. Inadequate cavitation suppression mechanism Existing technologies mostly estimate NPSHr using empirical formulas, lacking dynamic simulation of cavitation flow. When pumps operate under varying conditions, the expansion rate of the cavitation region at the blade tip can reach 0.3 m / s. Traditional static constraints cannot effectively predict the migration pattern of the cavitation initiation point, leading to frequent cavitation damage in actual operation. Statistical data shows that the annual failure rate of unoptimized pump sets due to cavitation problems is as high as 12%, far exceeding the industry average.

[0006] 5. The optimization process lacks closed-loop feedback. Existing optimization processes typically stop at the numerical simulation stage, without establishing a dynamic calibration mechanism between simulation results and physical experiments. Tests conducted by a well-known international pump manufacturer show that optimization models without CFD-experimental iterative correction generally have efficiency prediction deviations exceeding 10%, severely hindering the practical implementation of optimization solutions. Summary of the Invention

[0007] The purpose of this invention is to provide a multi-objective optimization method for the hydraulic model of a high-pressure pump for wide-area high-efficiency seawater desalination, in order to solve the problems of wide-area operating efficiency imbalance, simplified model error accumulation, and insufficient cavitation suppression caused by the existing single-objective optimization proposed in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A multi-objective optimization method for a hydraulic model of a high-pressure pump in wide-area, high-efficiency seawater desalination, specifically including the following steps: S1. Construction of Parametric Hydraulic Model: Based on the geometric parameters of the high-pressure pump impeller and guide vanes, a parametric three-dimensional hydraulic model is established. The geometric parameters include at least the blade inlet angle β1, blade outlet angle β2, blade wrap angle φ, number of blades Z, impeller outlet diameter D2, and impeller outlet width b2. The hydraulic model is used to calculate the impeller head H under different operating conditions. S2. Definition of Multi-Objective Optimization Function: Establish a function based on the efficiency of the designed flow point. The multi-objective optimization function, with the uniformity of wide-area operating efficiency U as the optimization objective and the required net positive suction head (NPSHr) as the constraint, has the following mathematical expression: ; ; ; in, To optimize the variable vector, it consists of the key geometric parameters from step S1; The design point efficiency is calculated using a hydraulic model. The efficiency uniformity index over a wide region is defined as the negative standard deviation of efficiency within the high-efficiency region. ; The allowable net positive suction head (NPSH) threshold is defined as the high-efficiency zone, which is the flow range where the efficiency is not lower than 97% of the design point efficiency. S3. Optimization solution based on NSGA-II algorithm: The multi-objective optimization function defined in step S2 is solved by using a non-dominated sorting genetic algorithm with an elitist strategy. The Pareto optimal solution set is iteratively searched through population initialization, selection, crossover, mutation and non-dominated sorting. S4. Optimal Solution Selection and Model Validation: Based on the entropy weight-TOPSIS decision method, the comprehensive optimal solution is selected from the Pareto optimal solution set, its three-dimensional hydraulic model is reconstructed, and computational fluid dynamics simulation is performed for verification.

[0009] Preferably, in step S1, the impeller head H of the parameterized hydraulic model is calculated using the following empirical formula that includes hydraulic losses: ; in, ; The impeller outlet circumferential velocity, The impeller outlet axial velocity, It is the acceleration due to gravity. For traffic, For design traffic, and These are the friction loss coefficient and impact loss coefficient obtained through the loss model calibration.

[0010] Preferably, in step S2, the design flow point efficiency... The calculation formula is: ; Where ρ is the density of seawater. The shaft power at the design flow rate was calculated using a hydraulic model. The power loss due to friction of the disk is calculated using an empirical formula: ; K3 is the friction coefficient of the disk, and ω is the angular velocity of the impeller.

[0011] Preferably, in step S3, the crossover operation of the NSGA-II algorithm uses simulated binary crossover, and its offspring individuals... From the parent individual , Generate using the following formula: ; in, According to the distribution index The resulting diffusion factor.

[0012] Preferably, in step S3, after population initialization, each individual X is... i The corresponding hydraulic model is used for rapid single-channel flow field calculation to predict whether it satisfies the NPSHr constraint. A penalty function is applied to individuals that do not meet the constraint. The penalty function is as follows: ; The penalty value is added to the objective function value to guide the search toward the feasible region.

[0013] Preferably, in step S4, the entropy weight-TOPSIS decision method includes: S4.1 Construct a decision matrix consisting of the objective function values ​​corresponding to all solutions in the Pareto solution set; S4.2 Calculate flow point efficiency using the entropy weight method The objective weight w of the wide-area operating efficiency uniformity U j ; S4.3 Calculate the positive ideal solution for each solution. and negative ideal solution The Euclidean distance; S4.4 Calculate the relative closeness of each solution to the ideal solution: ; Select The solution with the largest value is taken as the final optimal solution.

[0014] Preferably, in the optimized variable vector X, the optimization ranges of the blade inlet angle β1 and the blade outlet angle β2 are [18°, 35°] and [20°, 40°], respectively, and the optimization range of the blade wrap angle φ is [85°, 130°].

[0015] Preferably, the high-efficiency flow range of the wide-area efficiency uniformity index U(X) is determined by changing the flow rate Q and calculating the corresponding efficiency η(Q). The calculation also adopts the head formula including hydraulic losses as described in claim 2.

[0016] Preferably, when performing fluid dynamics simulation verification in step S4, if the deviation between the verification result and the prediction result of the optimization model exceeds 5%, the CFD verification data is used as a new sample point, the original parameterized hydraulic model is corrected using a Gaussian stochastic process model, and the process returns to step S3 for a new round of optimization calculation.

[0017] Preferably, in the optimization process of step S3, a dynamic model predictive controller is used to predict the evolutionary direction of the next generation population. The output state of this controller is described by the following formula: ; in, In terms of evolutionary generations The recommended adjustment amount of the optimization variable for the time controller. This indicates the overall performance status of the current generation population. This indicates that the controller retains its state from the previous generation.

[0018] Compared with the prior art, the beneficial effects of the present invention are: 1. Multi-objective collaborative optimization Balancing design point efficiency and wide-area operating conditions: By simultaneously optimizing the efficiency η of the design flow point. d The wide-area efficiency uniformity index U solves the problem of wide-area performance imbalance caused by traditional single-objective optimization. Experimental data shows that while improving the efficiency at the design flow point by 8%-12%, the flow range in the high-efficiency zone expands from the traditional 70%-110% to 60%-120%, significantly broadening the pump's adaptability to different operating conditions.

[0019] Accurate characterization of dynamic loss: The head is calculated using an empirical formula that includes the friction loss coefficient K1 and the impact loss coefficient K2. Combined with dynamic calibration technology, the deviation between the simulation results and the measured values ​​is controlled within 5%. Compared with the traditional simplified Bernoulli equation model, the prediction accuracy is improved by more than 3 times.

[0020] 2. High-precision modeling and loss quantization The head is calculated using an empirical formula that includes hydraulic losses, which accurately reflects the energy loss in actual operation. Combined with the dynamic calibration of friction loss coefficient and impact loss coefficient, the consistency between simulation results and real operating conditions is significantly improved.

[0021] 3. High-efficiency intelligent optimization algorithm The NSGA-II algorithm has been optimized and upgraded by introducing a simulated binary crossover strategy and an elite retention mechanism, combined with a dynamic model prediction controller. This improves the convergence speed of the Pareto front by 40%, the uniformity of the distribution of non-dominated solution sets by 25%, and the optimization efficiency by more than 30% compared with the traditional genetic algorithm.

[0022] 4. Anti-cavitation reinforcement design By using the required net positive suction head (NPSHr) as a hard constraint and employing real-time flow field prediction and penalty function mechanisms, the risk of cavitation can be effectively suppressed, thus extending the service life of the equipment.

[0023] 5. Scientific decision-making and dynamic correction The entropy weight-TOPSIS method is used to objectively integrate efficiency and uniformity indices, avoiding the influence of human preferences. If the deviation between simulation and prediction exceeds 5%, CFD verification and Gaussian process model correction are automatically triggered to form a closed-loop iterative optimization system.

[0024] 6. Enhanced wide-area adaptability By defining the high-efficiency flow range and combining it with a wide-range parameter adjustment strategy for blade geometry, the pump can maintain high-efficiency and stable output even when the flow fluctuates, thus adapting to the complex operating conditions required for seawater desalination.

[0025] 7. Robustness and scalability The optimized variable settings are set within a reasonable range, taking into account both structural feasibility and performance potential; the dynamic controller adaptively adjusts the evolution direction through state memory, making it suitable for parameter tuning needs in multiple scenarios. Attached Figure Description

[0026] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are explained in detail together with the embodiments of the invention, but do not constitute a limitation thereof.

[0027] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a bar chart comparing the optimization effects of the small-scale island seawater desalination system in Embodiment 1 of the present invention. Figure 3 This is a bar chart comparing the optimization effects of a seawater desalination system in a medium-sized industrial park according to Embodiment 2 of the present invention. Figure 4 This is a bar chart comparing the optimization effects of a large-scale coastal city seawater desalination system in Embodiment 3 of the present invention. Detailed Implementation

[0028] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0029] Example 1: Small-scale island seawater desalination system (daily processing capacity 1200 m³) 1. Application Scenarios and Design Fundamentals For an independent water supply scenario on an island, the design flow rate is Qd = 50 m³ / h, the target head is Hd = 120 m, and the allowable net positive suction head (NPSHr0) is 3.5 m. Key parameters: impeller speed n = 5000 r / min, seawater density ρ = 1025 kg / m³, gravitational acceleration g = 9.81 m / s², and disk friction coefficient K3 = 2.5 × 10⁻⁶. -6 The hydraulic loss coefficients are K1=0.002 and K2=0.005.

[0030] 2. Optimization process details Step S1: Construction of Parametric Hydraulic Model The optimization variable vector X=[β1,β2,φ,Z,D2,b2] is strictly defined, with initial values ​​and optimization range adhering to reasonable engineering parameters. Blade inlet placement angle β1: Initially 22°, range [18°, 35°] Blade exit angle β2: Initially 28°, range [20°, 40°] Blade wrap angle φ: Initially 100°, range [85°, 130°] Number of blades Z: Initially 7, range [6,10] Impeller outlet diameter D2: Initially 380mm, ranging from [350mm, 420mm] Impeller outlet width b2: Initially 18mm, range [15mm, 22mm] The hydraulic head is calculated using the formula: H = u²V m2 cotβ2 / g-Hloss, where the impeller outlet circumferential velocity u2≈99.48m / s, and the axial velocity V m2 ≈0.15m / s.

[0031] Step S2: Define the multi-objective optimization function Optimization objective: Maximize F(X) = [ηd(X), U(X)] Design point efficiency ηd(X): Calculated according to the formula in claim 3, the initial value of shaft power Pshaft is ≈18.5kW, the disk friction loss Pdisk is ≈2.1kW, and the initial ηd is ≈78.2%.

[0032] Wide-range efficiency uniformity U(X): The high-efficiency zone is η(Q)≥97%ηd (i.e. ≥75.8%), corresponding to a flow range of 32~68m³ / h; initial value of U = -3.2 (negative standard deviation, the smaller the absolute value, the better the uniformity).

[0033] Constraints: NPSHr(X)≤3.5m, initial NPSHr≈3.8m (requires optimization).

[0034] Step S3: NSGA-II optimization solution Algorithm parameters: population size 50, number of iterations 30, crossover operation uses simulated binary crossover (distribution index ηc=20, diffusion factor β=0.8), mutation probability 0.05.

[0035] Constraint handling: Apply a penalty function to individuals with NPSHr > 3.5m, such as initial individual Penalty = (3.8 - 3.5). 2 =0.09, add objective function to guide the search.

[0036] Dynamic control: A model predictive controller is adopted. Based on the current generation average ηd (78.2%) and the previous generation state, it is recommended that the β1 / β2 adjustment step size be ≤2° to accelerate convergence.

[0037] Step S4: Optimal Solution Selection and CFD Verification Entropy weight-TOPSIS optimization: The decision matrix contains 50 Pareto solutions. The entropy weight is calculated to be ηd weight 0.58 and U weight 0.42. The solution with the largest relative proximity Ci (0.82) is selected as the optimal solution.

[0038] CFD verification: ANSYS Fluent, k-ε turbulence model, inlet flow rate 50 m³ / h, outlet pressure 1.2 MPa; the verification results deviate from the optimized prediction by ≤4.2% (<5%), no correction is required.

[0039] Example 1 Data Table:

[0040] Example 2: Seawater desalination system for a medium-sized industrial park (daily processing capacity 3600 m³) 1. Application Scenarios and Design Fundamentals For industrial park production water, the design flow rate Qd = 150 m³ / h, target head Hd = 150 m, and allowable net positive suction head (NPSHr0) = 3.0 m. Key parameters: impeller speed n = 4500 r / min, ρ = 1025 kg / m³, g = 9.81 m / s², K³ = 2.2 × 10⁻⁶. -6 K1=0.0018, K2=0.0045.

[0041] 2. Optimization process details Step S1: Construction of Parametric Hydraulic Model Optimize the initial values ​​and range of variables: β1: 25° ([18°, 35°]), β2: 32° ([20°, 40°]), φ: 110° ([85°, 130°]) Z: 8 ([7,11]), D2: 450mm ([420mm, 480mm]), b2: 22mm ([20mm, 25mm]) Head calculation: u2≈105.98m / s, V m2 ≈0.21m / s, initial H≈142m (needs to be optimized to 150m).

[0042] Step S2: Define the multi-objective optimization function Initial ηd: Calculated according to claim 3, Pshaft≈58.3kW, Pdisk≈3.5kW, ηd≈80.5%; High efficiency zone: η(Q)≥97%×80.5%≈78.1%, corresponding to a flow rate of 110~190m³ / h, and an initial value of U=-2.8; Constraints: Initial NPSHr≈3.4m (if it exceeds 3.0m, optimization is required).

[0043] Step S3: NSGA-II optimization solution Algorithm parameters: population size 80, number of iterations 40, crossover ηc=25 (β=0.75), mutation probability 0.04; Penalty function: Initial individual Penalty = (3.4 - 3.0) 2 =0.16; Dynamic control: It is recommended that the D2 adjustment step size be ≤15mm and the β2 adjustment step size be ≤1.5°.

[0044] Step S4: Optimal Solution Selection and CFD Verification Entropy-weighted TOPSIS: The optimal solution is ηd weight 0.61, U weight 0.39, and Ci maximum value 0.85. CFD verification: Deviation ≤3.8% (<5%), verification passed.

[0045] The data is shown in the table below:

[0046] Example 3: Large-scale seawater desalination system for coastal cities (daily processing capacity 7200 m³) 1. Application Scenarios and Design Fundamentals For urban municipal water supply, the design flow rate Qd = 300 m³ / h, target head Hd = 180 m, and allowable net positive suction head (NPSHr0) = 2.8 m. Key parameters: impeller speed n = 4200 r / min, ρ = 1025 kg / m³, g = 9.81 m / s², K³ = 2.0 × 10⁻⁶. -6 K1=0.0015, K2=0.004.

[0047] 2. Optimization process details Step S1: Construction of Parametric Hydraulic Model Optimize the initial values ​​and range of variables: β1: 28° ([18°, 35°]), β2: 35° ([20°, 40°]), φ: 120° ([85°, 130°]) Z: 9 ([8,12]), D2: 600mm ([580mm, 630mm]), b2: 25mm ([23mm, 28mm]) Head calculation: u2≈131.95m / s, V m2≈0.28m / s, initial H≈172m (needs to be optimized to 180m).

[0048] Step S2: Define the multi-objective optimization function Initial ηd: Pshaft≈135.6kW, Pdisk≈5.2kW, ηd≈82.3%; High efficiency zone: η(Q)≥97%×82.3%≈79.8%, corresponding to a flow rate of 230~370m³ / h, and an initial value of U=-2.5; Constraints: Initial NPSHr≈3.2m (exceeds 2.8m, requires optimization).

[0049] Step S3: NSGA-II optimization solution Algorithm parameters: population size 100, number of iterations 50, crossover ηc=30 (β=0.7), mutation probability 0.03; Penalty function: Initial individual Penalty = (3.2 - 2.8)² = 0.16; Dynamic control: It is recommended to adjust the φ step size to ≤5° and the Z adjustment to ±1 to improve wide-area uniformity.

[0050] Step S4: Optimal Solution Selection and CFD Verification Entropy-weighted TOPSIS: The optimal solution is ηd weight 0.63, U weight 0.37, and Ci maximum value 0.88. CFD validation: The initial validation bias was 6.1% (>5%). The CFD data was used as new sample points, and the original model was corrected using a Gaussian stochastic process model. After returning to S3 for 10 iterations, the bias was reduced to 3.8% (<5%).

[0051] The data is shown in the table below:

[0052] The multi-objective optimization method for the hydraulic model of a high-pressure pump for wide-area, high-efficiency seawater desalination proposed in this invention has the following advantages: 1. Multi-objective collaborative optimization Balancing design point efficiency and wide-area operating conditions: By simultaneously optimizing the efficiency η of the design flow point. d The wide-area efficiency uniformity index U solves the problem of wide-area performance imbalance caused by traditional single-objective optimization. Experimental data shows that while improving the efficiency at the design flow point by 8%-12%, the flow range in the high-efficiency zone expands from the traditional 70%-110% to 60%-120%, significantly broadening the pump's adaptability to different operating conditions.

[0053] Accurate characterization of dynamic loss: The head is calculated using an empirical formula that includes the friction loss coefficient K1 and the impact loss coefficient K2. Combined with dynamic calibration technology, the deviation between the simulation results and the measured values ​​is controlled within 5%. Compared with the traditional simplified Bernoulli equation model, the prediction accuracy is improved by more than 3 times.

[0054] 2. High-precision modeling and loss quantization The head is calculated using an empirical formula that includes hydraulic losses, which accurately reflects the energy loss in actual operation. Combined with the dynamic calibration of friction loss coefficient and impact loss coefficient, the consistency between simulation results and real operating conditions is significantly improved.

[0055] 3. High-efficiency intelligent optimization algorithm The NSGA-II algorithm has been optimized and upgraded by introducing a simulated binary crossover strategy (β-distribution exponential control of diffusion factor) and an elite retention mechanism, combined with a dynamic model prediction controller (state memory function F(t)). This improves the Pareto front convergence speed by 40%, the uniformity of the non-dominated solution set distribution by 25%, and the optimization efficiency by more than 30% compared with the traditional genetic algorithm.

[0056] 4. Anti-cavitation reinforcement design By using the required net positive suction head (NPSHr) as a hard constraint and employing real-time flow field prediction and penalty function mechanisms, the risk of cavitation can be effectively suppressed, thus extending the service life of the equipment.

[0057] 5. Scientific decision-making and dynamic correction The entropy weight-TOPSIS method is used to objectively integrate efficiency and uniformity indices, avoiding the influence of human preferences. If the deviation between simulation and prediction exceeds 5%, CFD verification and Gaussian process model correction are automatically triggered to form a closed-loop iterative optimization system.

[0058] 6. Enhanced wide-area adaptability By defining the high-efficiency flow range (≥97% of the design point efficiency) and combining it with a wide-range parameter adjustment strategy for blade geometry, the pump can maintain high-efficiency and stable output even when the flow fluctuates, thus adapting to the complex operating conditions of seawater desalination.

[0059] 7. Robustness and scalability Optimize variable settings within a reasonable range (e.g., blade angle 18°-40°) to balance structural feasibility and performance potential; the dynamic controller adaptively adjusts the evolution direction through state memory, making it suitable for parameter tuning needs in multiple scenarios.

[0060] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-objective optimization method for the hydraulic model of a high-pressure pump in wide-area, high-efficiency seawater desalination, specifically including the following steps: S1. Construction of Parametric Hydraulic Model: Based on the geometric parameters of the high-pressure pump impeller and guide vanes, a parametric three-dimensional hydraulic model is established. The geometric parameters include at least the blade inlet angle β1, blade outlet angle β2, blade wrap angle φ, number of blades Z, impeller outlet diameter D2, and impeller outlet width b2. The hydraulic model is used to calculate the impeller head H under different operating conditions. S2. Definition of Multi-Objective Optimization Function: Establish a function based on the efficiency of the designed flow point. The multi-objective optimization function, with the uniformity of wide-area operating efficiency U as the optimization objective and the required net positive suction head (NPSHr) as the constraint, has the following mathematical expression: ； ； ； wherein is the vector of optimization variables, consisting of the key geometric parameters in step S1 ; is the design point efficiency calculated by the hydraulic model; is the wide-range efficiency uniformity index, defined as the negative value of the standard deviation of the efficiencies in the high-efficiency region, i.e. ； The high efficiency region is a flow rate range in which the efficiency is not less than 97% of the design point efficiency for the allowable net positive suction head threshold value. S3. Optimization solution based on NSGA-II algorithm: The multi-objective optimization function defined in step S2 is solved by using a non-dominated sorting genetic algorithm with an elitist strategy. The Pareto optimal solution set is iteratively searched through population initialization, selection, crossover, mutation and non-dominated sorting. S4. Optimal Solution Selection and Model Validation: Based on the entropy weight-TOPSIS decision method, the comprehensive optimal solution is selected from the Pareto optimal solution set, its three-dimensional hydraulic model is reconstructed, and computational fluid dynamics simulation is performed for verification.

2. The wide-range high-efficiency seawater desalination high-pressure pump hydraulic model multi-objective optimization method according to claim 1, characterized in that, In step S1, the impeller head H of the parameterized hydraulic model is calculated using the following empirical formula that includes hydraulic losses: ； in, ； The impeller outlet circumferential velocity, The impeller outlet axial velocity, It is the acceleration due to gravity. For traffic, For design traffic, and These are the friction loss coefficient and impact loss coefficient obtained through the loss model calibration.

3. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 2, characterized in that, In step S2, the design flow point efficiency The calculation formula is: ； in, The density of seawater, The shaft power at the design flow rate was calculated using a hydraulic model. The power loss due to friction of the disk is calculated using an empirical formula: ； K3 is the friction coefficient of the disk, and ω is the angular velocity of the impeller.

4. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 1, characterized in that, In step S3, the crossover operation of the NSGA-II algorithm adopts simulated binary crossover, and the offspring individuals are generated from the parent individuals , according to the following formula: ； wherein is the distribution index the diffusion factor generated.

5. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 1, characterized in that, In step S3, after population initialization, for each individual X... i The corresponding hydraulic model is used for rapid single-channel flow field calculation to predict whether it satisfies the NPSHr constraint. A penalty function is applied to individuals that do not meet the constraint. The penalty function is as follows: ； The penalty value is added to the objective function value to guide the search toward the feasible region.

6. The wide-range high-efficiency seawater desalination high-pressure pump hydraulic model multi-objective optimization method according to claim 1, characterized in that, In step S4, the entropy weight-TOPSIS decision method includes: S4.1 Construct a decision matrix consisting of the objective function values ​​corresponding to all solutions in the Pareto solution set; S4.2, calculate the flow point efficiency by entropy weight method and the objective weight w of wide-range operation efficiency uniformity U j ; S4.3, compute the Euclidean distance of each solution to the positive ideal solution and the negative ideal solution ; S4.4, compute the relative closeness of each solution to the ideal solution: ; selecting the solution with the largest value as the final optimal solution.

7. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 1, characterized in that, In the optimization variable vector X, the optimization ranges of the blade inlet angle β1 and the blade outlet angle β2 are [18°, 35°] and [20°, 40°], respectively, and the optimization range of the blade wrap angle φ is [85°, 130°].

8. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 1, characterized in that, The high-efficiency flow range of the wide-area efficiency uniformity index U(X) is determined by changing the flow rate Q and calculating the corresponding efficiency η(Q). The calculation also adopts the head formula including hydraulic losses as described in claim 2.

9. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 1, characterized in that, If the deviation between the verification result and the prediction result of the optimization model exceeds 5% during the fluid dynamics simulation verification in step S4, the CFD verification data will be used as new sample points, and the original parameterized hydraulic model will be corrected using a Gaussian stochastic process model. Then, the process will return to step S3 for a new round of optimization calculation.

10. The multi-objective optimization method for the hydraulic model of a wide-area high-efficiency seawater desalination high-pressure pump according to claim 1, characterized in that, In the optimization process of step S3, a dynamic model predictive controller is used to predict the evolutionary direction of the next generation of the population. The output state of this controller is described by the following formula: ； in, In terms of evolutionary generations The recommended adjustment amount of the optimization variable for the time controller. This indicates the overall performance status of the current generation population. This indicates that the controller retains its state from the previous generation.

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