Centrifugal pump cavitation performance optimization method and system based on feature selection

Abstract

The invention relates to a centrifugal pump cavitation performance optimization method and system based on feature selection, and the method comprises the steps: taking the cavitation entropy production and lift of a centrifugal pump as optimization targets, taking the efficiency as a constraint condition, carrying out the modeling simulation of the centrifugal pump, and determining an initial optimization variable and an optimization space range; extracting a plurality of groups of uniformly distributed variable combination schemes by adopting a test design method based on the optimized space range; carrying out modeling simulation on the variable combination scheme to obtain cavitation entropy production and a lift value, and constructing an initial sample library; training the first approximation model by utilizing the initial sample library, screening out a final optimization variable which has obvious influence on the optimization target, and obtaining a final sample library; and training the second approximation model by utilizing the final sample library, optimizing and verifying by utilizing an optimization algorithm, and outputting an optimal parameter combination. According to the method, parameters which have obvious influence on the optimization target can be better selected as optimization variables, and meanwhile, the cavitation entropy production of the optimization target is introduced, so that the comprehensive optimization effect of cavitation and lift is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of centrifugal pump impeller optimization, and particularly to a method and system for optimizing the cavitation performance of a centrifugal pump based on feature selection. Background Art

[0002] Pumps are one of the most typical and widely used hydraulic machines. As a major category of pump products, centrifugal pumps are widely used in industrial production, residential life and other fields. Cavitation is a core issue of general concern in the field of hydraulic machinery. The occurrence of cavitation will not only cause consequences such as a decline in hydraulic performance and excessive vibration and noise, but also trigger cavitation damage to the flow-through components. In order to enable the centrifugal pump to operate stably, it is necessary to have good cavitation performance. For the above reasons, developing a method for optimizing the cavitation performance of centrifugal pumps and improving the cavitation performance of centrifugal pumps is of great engineering practical significance. Traditional cavitation performance optimization uses the critical cavitation margin or the cavitation volume fraction as the optimization goal, but the above goals have the disadvantages of too high calculation cost or inability to truly reflect the losses caused by cavitation in the pump, and a goal that can more accurately reflect the energy loss caused by cavitation in the pump while having a lower calculation cost is needed.

[0003] In addition, there may be some variables in the initially determined optimization variables that have a relatively insignificant influence relationship with the optimization goal. The existence of these variables will, on the one hand, increase the dimension of the optimization space, and on the other hand, the existence of too many irrelevant variables will also reduce the prediction accuracy of the approximation model. In order to screen out the variables that are more sensitive to the optimization goal from numerous design variables as optimization variables, the Pearson coefficient is usually used as a standard, and the filtering method is used to screen out the variables with a greater correlation with the optimization goal. However, the Pearson coefficient mainly focuses on the linear relationship between variables and the goal, ignores the non-linear relationship, and cannot accurately identify the parameters that have a more significant influence on the optimization goal for optimization.

[0004] In summary, in order to further improve the method for optimizing the cavitation performance of centrifugal pump impellers and enhance the optimization effect of cavitation performance, it is necessary to develop a comprehensive optimization method for cavitation and head of centrifugal pumps based on feature selection. Summary of the Invention

[0005] The object of the present invention is to propose a method for optimizing the cavitation performance of a centrifugal pump based on feature selection, aiming to better select the parameters that have a more significant influence on the optimization goal as optimization variables when comprehensively optimizing the cavitation performance and head of the centrifugal pump impeller, and at the same time introduce an optimization goal with a lower calculation cost and capable of more accurately reflecting the energy loss caused by cavitation in the pump - cavitation entropy production, so as to improve the comprehensive optimization effect of cavitation and head.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A cavitation performance optimization method for centrifugal pumps based on feature selection, comprising:

[0008] Taking the cavitation entropy generation and head of the centrifugal pump as the optimization objectives, and the efficiency as the constraint condition, modeling and simulating the centrifugal pump to determine the initial optimization variables and the optimization space range;

[0009] Based on the optimization space range, using the experimental design method to extract multiple groups of uniformly distributed variable combination schemes;

[0010] Modeling and simulating the variable combination schemes, obtaining the cavitation entropy generation and head values, and constructing an initial sample library;

[0011] Using the initial sample library to train the first approximation model, screening out the final optimization variables that have a significant impact on the optimization objectives, and obtaining the final sample library;

[0012] Using the final sample library to train the second approximation model, using the optimization algorithm to find the optimal solution and verify it, and outputting the optimal parameter combination.

[0013] Optionally, the calculation methods of cavitation entropy generation, head, and efficiency are as follows:

[0014]

[0015] Wherein, is the cavitation entropy generation rate in the pump, is the mass transfer rate in the gas-liquid two-phase phase change process, μ is the dynamic viscosity of the liquid, ρ v is the gas density, EPC is the cavitation entropy generation in the pump, T is the Kelvin temperature, H is the head, P in 、P out are the total pressures at the inlet and outlet of the centrifugal pump respectively, g is the acceleration due to gravity, η is the efficiency, ρ l is the liquid density, Q v is the liquid volume flow rate, T is the impeller torque, and ω is the rotational angular velocity of the centrifugal pump impeller.

[0016] Optionally, the initial optimization variables include:

[0017] The outlet width of the impeller, the blade inlet setting angle, the blade outlet setting angle, the control point coordinates of the blade thickness distribution curve, the control point coordinates of the impeller front shroud shape in the impeller axial projection diagram, and the control point coordinates of the blade inlet edge in the impeller axial projection diagram.

[0018] Optionally, modeling and simulating the variable combination schemes, obtaining the cavitation entropy generation and head values, and constructing an initial sample library includes:

[0019] For each variable combination scheme in the variable combination scheme, perform three-dimensional modeling of the computational domain, mesh generation, and cavitation numerical simulation; among them, the computational domain is the water body area where the three-dimensional model of the impeller is located as the computational domain of the impeller.

[0020] Obtain the cavitation entropy production and head values of different schemes from the results obtained by cavitation numerical simulation through CFD-Post, and construct an initial sample library.

[0021] Optionally, train a first approximation model using the initial sample library, screen out the final optimization variables that have a significant impact on the optimization objectives, and obtain the final sample library including:

[0022] Train a first approximation model using the initial sample library, and use the feature selection method to screen out the features that have a more significant impact on the two optimization objectives respectively. Combine the variables that have the most significant impact on the head and cavitation entropy production to obtain the final optimization variables, and obtain the final sample library after removing the design variables with insignificant effects.

[0023] Optionally, the features that are screened out to have a more significant impact on the two optimization objectives respectively by the feature selection method include:

[0024] Select XGBoost as the first approximation model, and use the wrapper method in the feature selection method to couple XGBoost with the NSGA-II algorithm. After NSGA-II selects a feature subset from the entire feature set each time, use the XGBoost model to evaluate this subset, and use the fitting accuracy of the model as the evaluation criterion. The algorithm iterates continuously until the fitting accuracy of the model reaches the preset degree or the preset number of iterations, and outputs the finally obtained feature subset as the final optimization variables.

[0025] Optionally, training the second approximation model using the final sample library includes:

[0026] Train the second approximation model using the final sample library. If the coefficient of determination of the trained model is greater than the preset value, use the trained model. If it is less than the preset value, perform feature selection again, and then perform model training again until the coefficient of determination of the model is greater than the preset value.

[0027] Optionally, using the optimization algorithm for optimization and verification includes:

[0028] Use the optimization algorithm to find the optimal parameters and verify them using the numerical simulation method. If the error between the numerical simulation result and the optimization result is less than the preset threshold, use the optimization result. If it is greater than the preset threshold, train the second approximation model again and perform optimization until the error is less than the preset threshold, and output the optimal parameters; among them, efficiency is used as a constraint when using the optimization algorithm for optimization; the second approximation model uses the TabPFN model.

[0029] A centrifugal pump cavitation performance optimization system based on feature selection, the system comprising: a three-dimensional simulation module, a sampling module, a sample library construction module, a screening module, and an optimal parameter output module;

[0030] The three-dimensional simulation module is used to model and simulate the centrifugal pump with the cavitation entropy production and head of the centrifugal pump as the optimization objectives and the efficiency as the constraint condition, and determine the initial optimization variables and the optimization space range;

[0031] The sampling module is used to extract multiple groups of uniformly distributed variable combination schemes based on the optimization space range by using the experimental design method;

[0032] The sample library construction module is used to model and simulate the variable combination scheme, obtain the cavitation entropy production and head values, and construct an initial sample library;

[0033] The screening module is used to train a first approximation model using the initial sample library, screen out the final optimization variables that have a significant impact on the optimization objectives, and obtain a final sample library;

[0034] The optimal parameter output module is used to train a second approximation model using the final sample library, optimize and verify using an optimization algorithm, and output an optimal parameter combination.

[0035] Optionally, the initial optimization variables include:

[0036] The impeller outlet width, the blade inlet setting angle, the blade outlet setting angle, the control point coordinates of the blade thickness distribution curve, the control point coordinates of the impeller front shroud shape in the impeller axial projection diagram, and the control point coordinates of the blade inlet edge in the impeller axial projection diagram.

[0037] The beneficial effects of the present invention are:

[0038] The present invention uses the cavitation entropy production in the centrifugal pump to characterize the energy loss caused by cavitation in the pump and reflect the cavitation state in the pump. At the same time, it can be obtained only through one cavitation numerical simulation, while the calculation of NPSHr requires continuous numerical simulations of reducing the inlet pressure of the centrifugal pump, and the calculation time is relatively long. By introducing the cavitation entropy production, the problems that the cavitation volume fraction cannot characterize the energy loss caused by cavitation in the pump and the calculation cost of NPSHr is relatively large are avoided.

[0039] The present invention uses a feature selection method including an encapsulated method and an embedded method to screen out the variables that have the most significant impact on the cavitation entropy production and head from the initial optimization variables as the final optimization variables. By screening and optimizing variables in this way, the problem of insufficient consideration of non-linear relationships when screening optimization variables based on the Pearson coefficient is avoided, and the optimization space is better reduced in dimension. Description of the Drawings

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0041] Figure 1 Schematic diagram of the optimization method for the cavitation performance of a centrifugal pump based on feature selection according to an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of the 10% cavitation distribution isosurface of the original scheme according to an embodiment of the present invention;

[0043] Figure 3 Schematic diagram of the 10% cavitation distribution isosurface of the optimized scheme according to an embodiment of the present invention;

[0044] Figure 4 Comparison diagram of the cavitation characteristics curves before and after optimization according to an embodiment of the present invention. Specific implementation manners

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0046] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the drawings and specific implementation manners.

[0047] As Figure 1 shown, this embodiment proposes an optimization method for the cavitation performance of a centrifugal pump based on feature selection. This embodiment is mainly applied after the preliminary completion of the hydraulic model design of the centrifugal pump to further improve the cavitation performance and head of the centrifugal pump. The steps include:

[0048] S1. Taking the cavitation entropy production and head of the centrifugal pump as the optimization objectives and the efficiency as the constraint condition, the centrifugal pump is modeled and simulated to determine the initial optimization variables and the optimization space range;

[0049] S2. Based on the optimization space range, the experimental design method is used to extract multiple groups of uniformly distributed variable combination schemes;

[0050] S3. The variable combination schemes are modeled and simulated to obtain the cavitation entropy production and head values, and an initial sample library is constructed;

[0051] S4. Train the first approximation model using the initial sample library, screen out the final optimization variables that have a significant impact on the optimization objective, and obtain the final sample library;

[0052] S5. Train the second approximation model using the final sample library, optimize and verify using the optimization algorithm, and output the optimal parameter combination.

[0053] Specifically, in this embodiment, S1. Taking the cavitation entropy generation and head of the centrifugal pump as the optimization objectives and the efficiency as the constraint condition, conduct modeling and simulation on the centrifugal pump to determine the initial optimization variables and the optimization space range, including:

[0054] Determine the cavitation entropy generation and head as the optimization objectives, select the optimization working conditions, and use BladeGen, ICEM CFD, TurboGrid, and CFX in Ansys Workbench to perform three-dimensional modeling of the computational domain, mesh generation, and cavitation numerical simulation on the impeller, volute, and inlet pipe in the original scheme. Calculate and determine the initial values of the optimization objectives according to the following formula, determine the initial design variables according to design experience, and clarify the upper and lower boundaries of the design variables. In this example, the selected optimization working conditions are Q v = 1.0Q vd , P in = 55 kPa (P in is the inlet pressure of the centrifugal pump), perform three-dimensional modeling of the computational domain, mesh generation, and cavitation numerical simulation on the impeller, volute, and inlet pipe in the original scheme. Calculate the cavitation entropy generation (EPC), head (H), and efficiency (η) of the original scheme according to the following formula. At the same time, obtain the critical cavitation margin (NPSH r ) through multiple numerical simulations. The above values are shown in Table 2 below. Select the impeller outlet width x0, blade inlet setting angle x1, blade outlet setting angle x2, control point coordinates x3, x4 of the blade thickness distribution curve, control point coordinates x5 of the impeller front shroud shape in the impeller axial projection diagram, and control point coordinates x6, x7, x8, x9 of the blade inlet edge in the impeller axial projection diagram as the initial optimization variables, and at the same time clarify the upper and lower limits of the optimization variables. Their initial values and upper and lower limits are shown in Table 1 below:

[0055]

[0056]

[0057] Among them, is the cavitation entropy generation rate in the pump, is the mass transfer rate in the gas-liquid two-phase phase change process, μ is the liquid dynamic viscosity, ρ v is the gas density, EPC is the cavitation entropy generation in the pump, T is the Kelvin temperature, take T = 298.1 K; H is the head, P in , P outThey are the total pressures at the inlet and outlet of the centrifugal pump respectively, g is the acceleration due to gravity, and g = 9.8 m 2 / s; η is the efficiency, ρ l is the liquid density, Q v is the liquid volume flow rate, T is the impeller torque, and ω is the rotational angular velocity of the centrifugal pump impeller.

[0058] Table 1 Initial Optimization Variable Table

[0059] Initial optimization variable Value Upper limit Lower limit Unit x0 0.031 0.034 0.030 m x1 39.1 -60.8 -40.8 ° x2 27.2 -62.8 -52.8 ° x3 0.0096 0.011 0.008 - x4 0.005 0.007 0.004 - x5 0.008 0.015 0.005 - x6 0.0079 0.01 0 - x7 0.0621 0.062 0.052 - x8 0.0322 0.041 0.031 - x9 0.0709 0.075 0.065 -

[0060] Table 2 Initial Values of Each Parameter

[0061] Performance parameter EPC (W / K) H (m) η (%) <![CDATA[NPSH r (m)]]> Value 0.105 32.23 82.9 3.54

[0062] Specifically, in this embodiment, S2. Based on the optimization space range, using the experimental design method to extract multiple groups of uniformly distributed variable combination schemes, including:

[0063] With the help of the experimental design method, according to the determined optimization space range, and in accordance with the principle of uniform distribution, perform the extraction operation of the combination scheme for each variable to ensure that the extracted variable combination scheme can comprehensively and effectively cover the design space. In this example, the Latin hypercube sampling method is adopted to uniformly generate 120 groups of variable combination schemes in the design space.

[0064] Specifically, in this embodiment, S3. Model and simulate the variable combination scheme to obtain the cavitation entropy production and head values, and construct the initial sample library, including:

[0065] In Ansys Workbench, use BladeGen, TurboGrid, and CFX to complete the three-dimensional modeling of the computational domain, mesh generation, and cavitation numerical simulation for each variable combination scheme respectively, and obtain the cavitation entropy production and head values of different schemes from the results of the cavitation numerical simulation through CFD-Post to construct the initial sample library. The computational domain is the water body area where the three-dimensional model of the impeller is located as the computational domain of the impeller. Since this method does not involve the geometric parameter optimization of the volute and inlet pipe, the computational domain and mesh of the volute and inlet pipe models are the same as those in the first step.

[0066] Specifically, in this embodiment, S4. Use the initial sample library to train the first approximation model, screen out the final optimization variables that have a significant impact on the optimization objective, and obtain the final sample library, including:

[0067] Train the approximate model Ⅰ using the initial sample library. Adopt the feature selection method to separately screen out the features that have a more significant impact on the two optimization objectives. Combine the variables that have the most significant impact on head and cavitation entropy generation as the final optimization variables, and obtain the sample library after removing the design variables with insignificant influence. In this example, XGBoost is selected as the approximate model Ⅰ, and the wrapper method in the feature selection method is adopted. Couple XGBoost with the NSGA-II algorithm. After NSGA-II selects a feature subset from the full set of features each time, use the XGBoost model to evaluate this subset, and use the fitting accuracy of the model as the evaluation criterion. The algorithm iterates continuously until the model fitting accuracy reaches a certain level or a certain number of iterations, and outputs the finally obtained feature subset as the final optimization variable. Through this method, the variables that have the most significant impact on cavitation entropy generation and head obtained in this example are [x0, x1, x6, x7, x8] and [x0, x1, x2, x7, x9] respectively. Combine the variables that have the most significant impact on head and cavitation entropy generation. The final optimization variables obtained are shown in Table 3 below. Remove the variables with weak influence in the sample library to obtain the final sample library;

[0068] Table 3 Final Optimization Variable Table

[0069] Final optimization variable Value Upper limit Lower limit Unit x0 0.031 0.034 0.030 m x1 39.1 -60.8 -40.8 ° x2 27.2 -62.8 -52.8 ° x6 0.0079 0.01 0 - x7 0.0621 0.062 0.052 - x8 0.0322 0.041 0.031 - x9 0.0709 0.075 0.065 -

[0070] Specifically, in this embodiment, S5. Train the second approximate model using the final sample library, optimize and verify using the optimization algorithm, and the output optimal parameter combination includes:

[0071] Train the approximate model Ⅱ using the finally obtained sample library. If the r 2 coefficient of the trained model is greater than 0.9, it can be adopted. If it is less than 0.9, perform feature selection again, and then train again until the r 2 coefficient is greater than 0.9. After obtaining the approximate model Ⅱ that meets the requirements, use the optimization algorithm to find the optimal parameters, and use the numerical simulation method to verify. If the error between the numerical simulation result and the optimization result is less than 5%, it is considered reasonable, and the optimization result this time can be adopted. If it is greater than 5%, then train and optimize the approximate model Ⅱ again until the error is less than 5%, and output the optimal parameters. In order not to make the efficiency of the optimal solution lower than the original solution, the efficiency is used as a constraint when using the optimization algorithm to optimize. In this step of this example, the TabPFN model is selected as the approximate model Ⅱ, and the cavitation entropy generation prediction model and the head prediction model are respectively trained using the finally obtained sample library. The r 2The coefficients are 0.91 and 0.97 respectively. The NSGA-II optimization algorithm is used for optimization to obtain the optimal parameter combination, and the numerical simulation method is used for verification. The deviation between the simulation results and the optimization results is less than 5%, so it can be adopted. The obtained optimal parameters are related to cavitation entropy production, head, efficiency, and NPSH r The values are shown in the following table. By comparison, it is found that through optimization, the cavitation entropy production in the pump is reduced by 9.9%, the head is increased by 10.46%, the efficiency is increased by 1.1%, and the NPSH r is reduced by about 27.40%.

[0072] Table 4 Comparison table of variables and parameter values before and after optimization

[0073]

[0074] The 10% cavitation distribution isosurfaces in the impeller before and after optimization are as Figure 2 、 Figure 3 shown. It can be found that the cavitation distribution area is reduced to a certain extent, which verifies the optimization effect from the side.

[0075] The cavitation characteristic curves of the centrifugal pump before and after optimization are as Figure 4 shown. It can be found that, on the one hand, the NPSH r decreases to a certain extent, and the cavitation performance of the pump is improved. On the other hand, the head increases, and the work capacity of the pump is enhanced. Figure 4 The red marked points in it indicate that the head drop value here reaches 3%H 1atm , where H 1atm is the head value when the inlet pressure of the centrifugal pump is 1 atmospheric pressure.

[0076] This embodiment introduces cavitation entropy generation, which reduces the computational cost in the cavitation optimization process of centrifugal pumps on the one hand, and more accurately describes the cavitation state inside the pump on the other hand. Taking cavitation entropy generation and head as the optimization objectives, multiple design variables of the centrifugal pump impeller are selected as the initial optimization variables. The experimental design method is used to uniformly extract design schemes in the optimization space, and cavitation numerical simulation is carried out for each scheme to obtain the initial sample library. The feature selection method is adopted to screen out the variables that have a significant impact on the optimization objectives as the optimization variables, avoiding the problem of insufficient consideration of the non-linear relationship between the optimization variables and the optimization objectives when screening the optimization variables based on the Pearson coefficient, and better realizing dimensionality reduction of the optimization space. Subsequently, the sample library after removing the optimization variables with weak influence is obtained, the approximate model is trained, the optimization algorithm is selected for optimization to obtain the optimal result, and the numerical simulation method is used for verification. If the error between the numerical simulation result and the optimization result is less than 5%, it is considered reasonable, and the optimization result can be adopted. If it is greater than 5%, the approximate model II is trained and optimized again until the error is less than 5%, and the optimal parameters are output. Through optimization, compared with the original scheme, the cavitation entropy generation in the pump of the optimal scheme is reduced by 9.9%, the head is increased by 10.46%, the efficiency is increased by 1.1%, and the NPSH r is reduced by about 27.40%.

[0077] This embodiment also proposes a centrifugal pump cavitation performance optimization system based on feature selection. The system includes: a three-dimensional simulation module, a sampling module, a sample library construction module, a screening module, and an optimal parameter output module;

[0078] The three-dimensional simulation module is used to model and simulate the centrifugal pump with the cavitation entropy generation and head of the centrifugal pump as the optimization objectives and the efficiency as the constraint condition, and determine the initial optimization variables and the optimization space range;

[0079] The sampling module is used to extract multiple groups of uniformly distributed variable combination schemes based on the optimization space range by using the experimental design method;

[0080] The sample library construction module is used to model and simulate the variable combination schemes, obtain the cavitation entropy generation and head values, and construct the initial sample library;

[0081] The screening module is used to train the first approximate model with the initial sample library, screen out the final optimization variables that have a significant impact on the optimization objectives, and obtain the final sample library;

[0082] The optimal parameter output module is used to train the second approximate model with the final sample library, optimize and verify by using the optimization algorithm, and output the optimal parameter combination.

[0083] Furthermore, the initial optimization variables include:

[0084] Impeller outlet width, blade inlet setting angle, blade outlet setting angle, coordinates of control points of blade thickness distribution curve, coordinates of control points of the shape of the front shroud of the impeller in the meridional projection of the impeller, coordinates of control points of the inlet edge of the blade in the meridional projection of the impeller.

[0085] The embodiments described above are only descriptions of the preferred embodiments of the present invention and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A cavitation performance optimization method for centrifugal pumps based on feature selection, characterized in that Including: Taking the cavitation entropy production and head of the centrifugal pump as the optimization objectives and the efficiency as the constraint condition, a model simulation of the centrifugal pump is carried out to determine the initial optimization variables and the optimization space range. Based on the optimization space range, the experimental design method is adopted to extract multiple groups of uniformly distributed variable combination schemes. The variable combination schemes are modeled and simulated to obtain the cavitation entropy production and head values, and an initial sample library is constructed. The initial sample library is used to train the first approximation model, the final optimization variables that have a significant impact on the optimization objectives are screened out, and the final sample library is obtained. The final sample library is used to train the second approximation model, and the optimization algorithm is used for optimization and verification to output the optimal parameter combination.

2. The method for optimizing the cavitation performance of a centrifugal pump based on feature selection according to claim 1, characterized in that, The calculation methods of cavitation entropy production, head, and efficiency are as follows: Among them, is the cavitation entropy production rate in the pump, is the mass transfer rate during the gas-liquid two-phase phase change process, μ is the dynamic viscosity of the liquid, ρ v is the gas density, EPC is the cavitation entropy production in the pump, T is the Kelvin temperature, H is the head, P in 、P out are the total pressures at the inlet and outlet of the centrifugal pump respectively, g is the acceleration due to gravity, η is the efficiency, ρ l is the liquid density, Q v is the liquid volume flow rate, T is the impeller torque, and ω is the rotational angular velocity of the centrifugal pump impeller.

3. The cavitation performance optimization method of a centrifugal pump based on feature selection according to claim 1, characterized in that The initial optimization variables include: The impeller outlet width, the blade inlet setting angle, the blade outlet setting angle, the control point coordinates of the blade thickness distribution curve, the control point coordinates of the impeller front shroud shape in the impeller axial projection diagram, and the control point coordinates of the blade inlet edge in the impeller axial projection diagram.

4. The method for optimizing the cavitation performance of a centrifugal pump based on feature selection according to claim 1, wherein The variable combination schemes are modeled and simulated to obtain the cavitation entropy production and head values, and constructing the initial sample library includes: Three-dimensional modeling of the computational domain, mesh generation, and cavitation numerical simulation are carried out for each variable combination scheme in the variable combination scheme; among them, the computational domain is the water body area where the three-dimensional model of the impeller is located as the computational domain of the impeller. The cavitation entropy production and head values of different schemes are obtained from the results of the cavitation numerical simulation through CFD-Post, and an initial sample library is constructed.

5. The cavitation performance optimization method of a centrifugal pump based on feature selection according to claim 1, wherein Using the initial sample library to train the first approximation model and screening out the final optimization variables that have a significant impact on the optimization objectives, obtaining the final sample library includes: Using the initial sample library to train the first approximation model, the feature selection method is used to screen out the features that have a more significant impact on the two optimization objectives respectively, and the variables that have the most significant impact on the head and cavitation entropy production are combined as the final optimization variables to obtain the final sample library after removing the design variables with insignificant effects.

6. The method for optimizing the cavitation performance of a centrifugal pump based on feature selection according to claim 5, characterized in that, The feature selection method is used to screen out the features that have a more significant impact on the two optimization objectives respectively, including: Select XGBoost as the first approximation model, adopt the wrapper method in the feature selection method, couple XGBoost with the NSGA-II algorithm, and after NSGA-II selects a feature subset from the full feature set each time, use the XGBoost model to evaluate the subset, taking the fitting accuracy of the model as the evaluation criterion. The algorithm iterates continuously until the fitting accuracy of the model reaches the preset degree or the preset number of iterations, and the finally obtained feature subset is output as the final optimization variable.

7. The cavitation performance optimization method of a centrifugal pump based on feature selection according to claim 1, characterized in that Using the final sample library to train the second approximation model includes: Using the final sample library to train the second approximation model. If the coefficient of determination of the trained model is greater than the preset value, the trained model is adopted; if it is less than the preset value, feature selection is carried out again, and then model training is carried out again until the coefficient of determination of the model is greater than the preset value.

8. The method for optimizing the cavitation performance of a centrifugal pump based on feature selection according to claim 1, characterized in that Using the optimization algorithm for optimization and verification includes: Optimize using an optimization algorithm to find the optimal parameters, and verify using numerical simulation methods. If the error between the numerical simulation results and the optimization results is less than a preset threshold, then adopt the optimization results. If it is greater than the preset threshold, then train and optimize the second approximation model again until the error is less than the preset threshold, and output the optimal parameters. Among them, efficiency is used as a constraint when optimizing using the optimization algorithm. The second approximation model uses the TabPFN model.

9. A centrifugal pump cavitation performance optimization system based on feature selection, characterized in that, For implementing the method according to any one of claims 1-8, the system includes: a three-dimensional simulation module, a sampling module, a sample library construction module, a screening module, and an optimal parameter output module. The three-dimensional simulation module takes the cavitation entropy production and head of the centrifugal pump as the optimization objectives, and efficiency as the constraint condition, models and simulates the centrifugal pump to determine the initial optimization variables and the optimization space range. The sampling module is used to extract multiple groups of uniformly distributed variable combination schemes based on the optimization space range by using the experimental design method. The sample library construction module is used to model and simulate the variable combination schemes, obtain the cavitation entropy production and head values, and construct an initial sample library. The screening module is used to train the first approximation model using the initial sample library, screen out the final optimization variables that have a significant impact on the optimization objectives, and obtain the final sample library. The optimal parameter output module is used to train the second approximation model using the final sample library, optimize and verify using the optimization algorithm, and output the optimal parameter combination.

10. The centrifugal pump cavitation performance optimization system based on feature selection according to claim 9, characterized in that, The initial optimization variables include: The impeller outlet width, the blade inlet setting angle, the blade outlet setting angle, the control point coordinates of the blade thickness distribution curve, the control point coordinates of the front shroud shape of the impeller in the axial projection of the impeller, and the control point coordinates of the blade inlet edge in the axial projection of the impeller.

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