Centrifugal pump impeller optimization design method based on feature contribution degree and multi-objective decision

Abstract

The invention belongs to the technical field of centrifugal pump design, and discloses a centrifugal pump impeller optimization design method based on characteristic contribution degree and multi-objective decision, which comprises the following steps: S1, obtaining an initial model and parameters of the initial model according to a geometric structure of a centrifugal pump, obtaining lift, efficiency and a minimum efficiency index, and constructing an optimization data set; s2, optimizing the data set, constructing a regression model, and screening core optimization variables; s3, sampling to generate a secondary data set according to the core optimization variable, and simulating to obtain a lift and a minimum efficiency index value; a decomposition-based multi-objective evolutionary algorithm is adopted to carry out multi-objective optimization, and a Pareto leading-edge solution set is generated; and S4, constructing an SHAP-TOPSIS decision method, and screening the Pareto frontier solution set obtained in the step S3 to obtain an optimal parameter combination. According to the method, Bayesian optimization, SHAP analysis and multi-objective decision are fused, efficient energy-saving design of the centrifugal pump is achieved, and a new thought is provided for intelligent optimization of complex fluid machinery.

Description

Technical Field

[0001] The present invention relates to the technical field of centrifugal pump design, and particularly to an optimized design method for a centrifugal pump impeller based on feature contribution degree and multi-objective decision-making. Background Art

[0002] Traditional centrifugal pump impeller design methods rely on empirical formulas and single-objective optimization, and have the following technical defects: they are highly dependent on the experience of designers and it is difficult to quantify the coupling relationship between multiple objectives; random search or grid search is used for hyperparameter tuning, with low computational efficiency and prone to falling into local optima; feature contribution degree analysis is not introduced, resulting in the lack of interpretability in the screening of optimization variables.

[0003] Chinese invention patent: Publication number "CN117807893B", title "Multi-objective optimization design method for high-speed centrifugal pump impeller", discloses a multi-objective optimization design method for high-speed centrifugal pump impellers. Using a reference point-based non-dominated sorting genetic algorithm, with the highest hydraulic efficiency and the smallest cavitation margin of the high-speed centrifugal pump as the optimization objectives, a corresponding optimization objective function is constructed. According to sensitivity analysis, three parameters, namely the impeller inlet diameter, impeller outlet width, and blade outlet angle, are selected. Using these three parameters as reference points and combining with the non-dominated sorting genetic algorithm for multi-objective optimization calculation, the optimal geometric parameter values corresponding to the above three parameters are obtained. Compared with the existing high-speed centrifugal pump optimization design methods, this technical solution can improve the head and pump efficiency of high-speed centrifugal pumps and reduce the cavitation margin of high-speed centrifugal pumps, and the internal flow field of the pump is significantly improved. However, this technical solution does not involve the adjustment of model hyperparameters when constructing the SVM regression prediction model, with low computational efficiency and prone to falling into local optima.

[0004] Chinese Invention Patent: Publication No. "CN112949165A", titled "A Multi-objective Optimization Method for Jet Pumps Based on Neural Network Model and NSGA-II Genetic Algorithm", discloses a multi-objective optimization method for jet pumps based on neural network model and NSGA-II genetic algorithm. The main steps include: determining the design parameters, optimization objectives, and constraint conditions of the jet pump, and obtaining the sample point design parameters based on the sampling method; obtaining the optimization objective values corresponding to the sample point design parameters through CFD software simulation; using the sample point data to construct a neural network model of the jet pump design parameters and optimization objectives, and verifying its prediction accuracy; based on the neural network model, using the NSGA-II genetic algorithm to obtain the final optimization result. This technical solution combines the CFD method with the neural network model and genetic algorithm, which not only solves the problem of difficult complex optimization design brought by multiple parameters and multiple disciplines, reduces the calculation difficulty, and solves the problems of high cost and long time consumption of the previous optimization design methods based on CFD simulation or experiment, but also realizes the multi-objective optimization of jet pumps, meets the special design requirements of head ratio in actual engineering, and effectively improves the hydraulic performance of jet pumps. However, this technical solution does not involve the decision-making of the optimal solution, and the scientificity of the optimal solution is difficult to guarantee.

[0005] Chinese Invention Patent: Announcement No. "CN108710764B", titled "A Multi-objective Optimization Design Method for Double-suction Pumps Based on Hybrid Approximation Model", discloses a multi-objective optimization design method for double-suction pumps based on hybrid approximation model. The main steps are as follows: First, taking the main geometric parameters of the impeller as the input value and the pump efficiency as the target value, establish a data sample; Second, establish an artificial neural network approximation model and use the particle swarm algorithm to solve the model coefficients; Third, establish a second-order response surface approximation model and use the particle swarm algorithm to solve the model coefficients; Fourth, establish a hybrid approximation model by weighted superposition of the artificial neural network model and the second-order response surface model, and use the particle swarm algorithm to solve the weight coefficients; Fifth, use the multi-objective genetic algorithm to optimize the above hybrid approximation model under three working conditions of 0.8Q, 1.0Q, and 1.2Q to find the optimal design point. This technical solution can establish a more accurate hybrid approximation model, meet the design requirements of broadening the high-efficiency area of double-suction pumps, and at the same time can reduce the design cost. However, when selecting parameters in this technical solution, it is based on design experience, the subjectivity of parameter selection is relatively strong, lacking systematicness, and it is impossible to discover the parameters that have an important impact on the model results. Summary of the Invention

[0006] In order to solve the problems in the above-mentioned prior art that do not involve the adjustment of model hyperparameters, have low calculation efficiency and are prone to falling into local optima, do not involve the decision-making of the optimal solution, and when selecting parameters, it is based on design experience, the subjectivity of parameter selection is relatively strong, lacking systematicness, and it is impossible to discover the parameters that have an important impact on the model results.

[0007] The present invention proposes a design method for centrifugal pumps based on feature contribution degree and multi-objective decision-making, which combines a machine learning model and a multi-objective optimization algorithm to improve the MEI value of the pump, increase efficiency, and optimize the design parameters of the pump.

[0008] The present invention is realized through the following technical solutions: including the following steps:

[0009] S1. According to the geometric structure of the centrifugal pump, perform three-dimensional modeling on it to obtain the initial model and the parameters of the initial model; perform CFD simulation on the initial model to obtain the head, efficiency, and minimum efficiency index MEI, and construct an optimization data set;

[0010] S2. According to the optimization data set obtained in step S1, construct an XGBoost-SHAP regression model, and train prediction models with the head and the minimum efficiency index MEI as optimization objectives respectively; dynamically search for the hyperparameter combination of XGBoost based on the Bayesian optimization algorithm; use the SHAP value calculation module to analyze the global and local contribution degrees of each geometric parameter, and screen the top three parameters with the highest total SHAP value and significant interaction effects as the core optimization variables; the calculation formula of the SHAP value is as follows:

[0011]

[0012] In the formula, F is the set of all features, S is the subset without feature i, and v(S) represents the model prediction value when using the features in the S subset;

[0013] S3. According to the core optimization variables obtained in step S2, use the optimal Latin hypercube sampling to generate a secondary data set, and obtain several groups of different combinations of head and MEI values through CFD simulation; based on the XGBoost-SHAP regression model trained in step S2, use the decomposition-based multi-objective evolutionary algorithm MOEA / D for multi-objective optimization to generate a Pareto front solution set;

[0014] S4. Assign parameter weights based on SHAP values in the TOPSIS algorithm, construct a SHAP-TOPSIS decision method, screen the Pareto front solution set obtained in step S3 to obtain the optimal parameter combination, and perform CFD simulation on it and compare it with the initial model. If the result is better than the initial model, end and output the optimal parameter combination; otherwise, execute step S3.

[0015] As a further preference, the specific steps of step S1 are as follows:

[0016] S11. According to the geometric structure of the centrifugal pump, perform three-dimensional modeling on it to obtain the initial model and the parameters of the initial model; and perform CFD simulation on it, compare the simulation results with the existing test data, if the error is less than the threshold, proceed to the next step, otherwise adjust the model parameters and continue with the CFD simulation;

[0017] S12. Determine the optimization parameters and determine the value range of each parameter;

[0018] S13. Randomly generate several groups of parameter combinations and perform three-dimensional modeling on the several groups of parameter combinations;

[0019] S14. Set three flow rates, namely small flow rate, high-efficiency flow rate, and large flow rate, for each group of parameter combinations respectively, and perform CFD simulation respectively to obtain the small flow rate efficiency η PL of each group of parameter combinations, the high-efficiency flow rate efficiency η BEP , the large flow rate efficiency η 0L and the high-efficiency flow rate head H BEP ;

[0020] S15. According to the small flow rate efficiency η PL , the high-efficiency flow rate efficiency η BEP , the large flow rate efficiency η 0L and the high-efficiency flow rate head H BEP obtained in step S14 for each group of parameter combinations, obtain the constant C MEI of each group of parameter combinations. The formula is as follows:

[0021] x = ln(n s )

[0022] y = ln(Q BEP )

[0023]

[0024] F η = -11.48x 2 - 0.85y 2 - 0.38xy + 88.59x + 13.46y

[0025] C BEP = F η - η BEP

[0026]

[0027] C MEI = max(C BEP , C PL , C OL )

[0028] where, n sis the specific speed; n N is the rated speed; i is the number of pump stages; Q BEP represents the high-efficiency flow rate; C BEP is the high-efficiency flow rate constant; C PL is the small-flow rate constant; C OL is the large-flow rate constant; the constant C MEI is C BEP 、C PL 、C OL is the maximum value among C

[0029] S16. For the constant C of each group of parameter combinations obtained according to step S15 MEI , perform interpolation calculation in combination with the following table to obtain the minimum efficiency index MEI of each group of parameter combinations. The formula and interpolation table are as follows:

[0030]

[0031]

[0032] In the formula, C MEI is the constant of each group of parameter combinations; C 左 is C MEI is the value on the left side within the interpolation table interval; C 右 is C MEI is the value on the right side within the interpolation table interval; MEI 左 is C MEI is the MEI value corresponding to the value on the left side within the interpolation table interval;

[0033] S17. Use the several groups of parameter combinations obtained in step S13, the high-efficiency flow head H of each group of parameter combinations obtained in step S14 BEP , the constant C of each group of parameter combinations obtained in step S15 MEI and the minimum efficiency index MEI of each group of parameter combinations obtained in step S16 as elements to construct an optimization data set.

[0034] As a further optimization, the specific steps of step S4 are as follows:

[0035] S41. Obtain the weight vector according to the SHAP value. The formula is as follows:

[0036]

[0037] In the formula, w j is the weight vector; SHAP j is the SHAP value of the jth feature; represents the sum of the SHAP values of all features in step 3;

[0038] S42. Standardize the decision matrix. The formula is as follows:

[0039]

[0040] where r ij is the value of the i-th solution on the j-th feature; f ij represents the original value of the i-th sample on the j-th feature; represents the sum of squares of the j-th feature over all m samples;

[0041] S43. According to the weight vector w j and the value r ij of the i-th solution on the j-th feature, generate the weighted matrix v ij , and the formula is as follows:

[0042] v ij = w j ·r ij ;

[0043] S44. According to the weighted matrix v ij , the ideal solution, and the negative ideal solution, combine the Euclidean distance to obtain the distances and closeness degrees of each group of parameter combinations to the ideal solution and the negative ideal solution. The formula is as follows:

[0044]

[0045] where represents the ideal solution; represents the negative ideal solution; represents the distance from the i-th parameter combination to the ideal solution; represents the distance from the i-th parameter combination to the negative ideal solution; C i represents the closeness degree of the i-th parameter combination;

[0046] S45. Select the parameter combination with the largest closeness degree as the optimal parameter combination, and perform CFD simulation on it. Compare it with the initial model. If the result is better than the initial model, end and output the optimal parameter combination; otherwise, execute step S3.

[0047] As a further optimization, in step S2, the optimized data set obtained in step S1 is divided into a training set and a test set at a ratio of 8:2.

[0048] As a further optimization, the termination condition of step S2 is that the decrease amplitude of the mean square error for 10 consecutive iterations is less than 1% or the total number of iterations reaches 100 times.

[0049] As a further optimization, the method of randomly generating several groups of parameter combinations in step S13 is to use the optimal Latin hypercube sampling method.

[0050] As a further preference, the number of parameter combinations generated in step S13 is 60 groups.

[0051] As a further preference, in step S14, the small flow rate is 75% of the efficient flow rate, and the large flow rate is 110% of the efficient flow rate.

[0052] As a further preference, the error threshold for comparing the simulation results with the existing test data in step S11 is 5%.

[0053] As a further preference, in step S1, CFturbo is used for impeller parametric modeling, ProE is used to construct the volute and the inlet and outlet sections, ANSYS Meshing is used for unstructured mesh division; ANSYS CFX is used for numerical simulation.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] 1. The design method of the present invention is based on the hyperparameter automatic adjustment method of the XGBoost regression model based on Bayesian optimization. This method constructs a Gaussian process surrogate model by defining the search space of hyperparameters, including key parameters such as learning rate, tree depth, subsample ratio, and regularization coefficient. Compared with the traditional grid search and random search methods, Bayesian optimization uses a probability model to guide the search process, with the determination coefficient R 2 of the regression prediction as the objective function, significantly reducing the number of tuning times required for hyperparameter tuning and improving the model training efficiency. In addition, Bayesian optimization can find better hyperparameter combinations within fewer iterations, especially suitable for hyperparameter tuning of models with high computational costs. This method not only improves the efficiency of model training, but also realizes the efficient exploration of the hyperparameter space through the probability model to guide the search process, improves the model training efficiency, and provides a more scientific and accurate parameter selection means for the training of machine learning models.

[0056] 2. The present invention constructs an XGBoost-SHAP model, and explains the prediction results of the XGBoost regression model (Extreme Gradient Boosting, abbreviated as XGBoost regression model) through SHAP analysis (SHapley Additive exPlanations), quantifying the contribution degree of each feature to the model output. By visualizing the feature contribution degree, the design variables that have a significant impact on the head and the minimum efficiency index (MEI) are screened out, thereby reducing the optimization dimension and improving the optimization efficiency. Combining the advantages of the SHAP value and the XGBoost model, the present invention can improve the interpretability of the model and the scientific nature of the optimization process while meeting the high-precision prediction, improve the overall optimization performance and efficiency, and provide more reliable support for engineering design and decision-making.

[0057] 3. The present invention constructs a SHAP-TOPSIS decision-making method. By calculating the SHAP value, the contribution degree of each feature to the model prediction result is calculated, providing the transparency and interpretability of the model, enabling the weights of the features to be dynamically adjusted to reflect the actual importance, thereby avoiding the bias caused by static weights in traditional methods. The TOPSIS decision-making method (Technique for Order Preference by Similarity to Ideal Solution) evaluates the relative closeness by calculating the distances between each solution and the ideal solution and the negative ideal solution, and selects the optimal solution. Compared with traditional decision-making methods, the SHAP-TOPSIS decision-making method has stronger adaptability and accuracy, can handle complex multi-dimensional and multi-objective problems, and improve the optimization efficiency. Through the contribution degree analysis of the SHAP value, the TOPSIS decision-making method can balance between multiple objectives and provide reliable decision support. At the same time, this method has strong generalization ability and visualization characteristics, can clearly display the logic behind the decision, and improve the transparency of the model and the scientificity of the decision.

[0058] 4. The present invention introduces a new index: the Minimum Efficiency Index (MEI). MEI is a parameter that measures the hydraulic efficiency of a water pump at the high-efficiency point, small flow point (partial load, i.e., 75% of the high-efficiency point flow rate), and large flow point (overload, i.e., 110% of the high-efficiency point flow rate). This index is independent of the water pump size, meaning that regardless of the size of the water pump, its efficiency should meet this minimum requirement. Description of the Drawings

[0059] Figure 1 It is the overall flowchart of the design method of the present invention.

[0060] Figure 2 It is the schematic diagram of the fluid domain grid in the design method of the present invention.

[0061] Figure 3a It is the schematic diagram of the head test set accuracy of the XGBoost-SHAP regression prediction model in the design method of the present invention.

[0062] Figure 3b It is the schematic diagram of the MEI value test set accuracy of the XGBoost-SHAP regression prediction model in the design method of the present invention.

[0063] Figure 4 It is the schematic diagram of the SHAP contribution degree of each feature to the head in the design method of the present invention.

[0064] Figure 5 It is the schematic diagram of the SHAP contribution degree of each feature to the MEI value in the design method of the present invention.

[0065] Figure 6a It is the contour map of the turbulent kinetic energy distribution of the cross-section before optimization in the design method of the present invention.

[0066] Figure 6b It is the contour map of the turbulent kinetic energy distribution of the cross-section after optimization in the design method of the present invention.

[0067] Figure 7a It is the contour map of the relative velocity distribution of the cross-section before optimization in the design method of the present invention.

[0068] Figure 7b It is the contour map of the relative velocity distribution of the cross-section after optimization in the design method of the present invention.

[0069] Figure 8a It is the contour map of the pressure distribution of the cross-section before optimization in the design method of the present invention.

[0070] Figure 8b It is the contour map of the pressure distribution of the cross-section after optimization in the design method of the present invention. Detailed implementation manners

[0071] The advantages and features of the present invention will be illustrated and explained by the following non-limiting description of preferred embodiments, which are given only as examples with reference to the accompanying drawings.

[0072] As Figure 1 shown, the present invention provides an optimization design method for a centrifugal pump impeller based on feature contribution degree and multi-objective decision-making, including the following steps:

[0073] Step 1: According to the geometric structure of the centrifugal pump, perform three-dimensional modeling on it to obtain an initial model, and thus obtain the parameters of the initial model, including the number of blades, blade wrap angle, impeller outlet diameter, impeller inlet diameter, blade outlet width, blade outlet angle, blade inlet angle, and specific speed; perform CFD simulation on the initial model to obtain the head H and the best point efficiency, and thus calculate the minimum efficiency index MEI and construct an optimization data set.

[0074] Step 11: According to the geometric structure of the centrifugal pump, perform three-dimensional modeling on it to obtain the initial model and the parameters of the initial model, including the number of blades, blade wrap angle, impeller outlet diameter, impeller inlet diameter, blade outlet width, blade outlet angle, blade inlet angle, and specific speed; and perform CFD simulation on it, compare the simulation results with the existing test data, if the error is less than the threshold, proceed to the next step, otherwise adjust the model parameters and continue the CFD simulation.

[0075] Step 12: Determine the optimization parameters and determine the value range of each parameter;

[0076] This step can select a hydraulic model that has been verified on-site and has good effects, or determine it according to design experience.

[0077] Step 13: Use the optimal Latin hypercube sampling method to generate several groups of parameter combinations that are evenly distributed in the variable space, and perform 3D modeling on the several groups of parameter combinations.

[0078] In this step, several groups of parameter combinations can be obtained by random combination. To ensure that the design variables are evenly distributed in the variable interval, it is preferably to use the optimal Latin hypercube sampling method to generate several groups of parameter combinations, and the number of parameter combinations is preferably 60 groups.

[0079] Step 14: Set three flow rates, namely small flow rate, efficient flow rate, and large flow rate, for each group of parameter combinations, and perform CFD simulations respectively to obtain the small flow rate efficiency η PL 、efficient flow rate efficiency η BEP 、large flow rate efficiency η 0L and the efficient flow rate head H BEP .

[0080] The small flow rate and the large flow rate are respectively a certain proportion less than or greater than the efficient flow rate. Preferably, the small flow rate is 75% of the efficient flow rate, and the large flow rate is 110% of the efficient flow rate.

[0081] Step 15: According to the small flow rate efficiency η PL 、efficient flow rate efficiency η BEP 、large flow rate efficiency η 0L and the efficient flow rate head H BEP obtained in Step 14 for each group of parameter combinations, obtain the constant C MEI for each group of parameter combinations. The formula is as follows:

[0082] x = ln(n s )

[0083] y = ln(Q BEP )

[0084]

[0085] F η = -11.48x 2 - 0.85y 2 - 0.38xy + 88.59x + 13.46y

[0086] C BEP = F η - η BEP

[0087]

[0088] C MEI = max(C BEP , C PL, C OL )

[0089] Wherein, n s is the specific speed; n N is the rated speed; i is the number of pump stages; Q BEP represents the high-efficiency flow rate; C BEP is the high-efficiency flow rate constant; C PL is the low-flow rate constant; C OL is the high-flow rate constant; the constant C MEI is C BEP , C PL , C OL is the maximum value among C

[0090] Step 16. According to the constant C of each group of parameter combinations obtained in Step 15 MEI , combined with the following table for interpolation calculation, obtain the minimum efficiency index MEI of each group of parameter combinations. The formula and the interpolation table are as follows:

[0091]

[0092]

[0093]

[0094] Wherein, C MEI is the constant of each group of parameter combinations, obtained from Step 15; C 左 is the value on the left side of the interpolation table interval where C MEI falls; C 右 is the value on the right side of the interpolation table interval where C MEI falls; MEI 左 is the MEI value corresponding to the value on the left side of the interpolation table interval where C MEI falls.

[0095] Step 17. Using the several groups of parameter combinations obtained in Step 13, the high-efficiency flow rate head H of each group of parameter combinations obtained in Step 14 BEP , the constant C of each group of parameter combinations obtained in Step 15 MEI and the minimum efficiency index MEI of each group of parameter combinations obtained in Step 16 as elements, construct an optimization data set.

[0096] Based on the geometric parameters of the impeller of a certain type of centrifugal pump, the present invention constructs a parametric three-dimensional model and conducts mesh division. Through automated simulation and CFD simulation, a benchmark data set of head and minimum efficiency index MEI is obtained; key geometric parameters that have a greater impact on the hydraulic performance of the pump are selected as design variables, the value ranges of the variables are determined in combination with excellent hydraulic models, an optimal Latin hypercube sampling is used to generate a multi-dimensional design sample space, and an initial data set is formed through parametric simulation.

[0097] In step S1, based on a centrifugal pump, parametric modeling of the impeller, volute, and inlet and outlet sections is carried out using CFturbo; numerical simulation is completed in ANSYS CFX, with the standard that the error between the external characteristic simulation results and the test data is controlled within 5%; the key geometric parameters to be screened include: the blade outlet width b2, the impeller outlet diameter D2, and the blade outlet angle β2, the blade inlet angle β1, the number of blades Z, the blade wrap angle Φ, and the impeller inlet diameter D j ; referring to excellent domestic hydraulic models to determine the parameter value ranges, 60 design points are generated using the optimal Latin hypercube sampling, and a parametric script is integrated through an automated simulation process to achieve batch mapping of design variables and CFD results. Based on the calculation formula of MEI and head, in the CFtubo-Workbench parametric simulation, the above design variables and the flow rate are used as input parameters, and the head and efficiency are set as output parameters, thus carrying out an automated simulation process.

[0098] As Figure 2 shown, it is a schematic diagram of the fluid domain mesh after mesh division.

[0099] Step 2: According to the optimized dataset obtained in step 1, construct an XGBoost-SHAP joint regression model, and train prediction models with the head and the minimum efficiency index MEI as optimization objectives respectively; dynamically search for the hyperparameter combinations of XGBoost based on the Bayesian optimization algorithm, and iteratively evaluate the optimal configuration of the learning rate, tree depth, and regularization coefficient through a Gaussian process surrogate model; use the SHAP value calculation module to analyze the global and local contribution degrees of each geometric parameter, and screen the top three parameters with the largest sum of SHAP values and significant interaction effects as the core optimization variables; the calculation formula of the SHAP value is as follows:

[0100]

[0101] In the formula, F is the set of all features, S is the subset without feature i, and v(S) represents the model prediction value when using the features in the S subset. This formula fairly distributes the contribution of each feature to the model prediction by performing a weighted average of all possible feature combinations.

[0102] The termination condition of step 2 is that the decline amplitude of the mean square error for 10 consecutive iterations is less than 1% or the total number of iterations reaches 100 times. The optimized dataset obtained in step 1 is divided into a training set and a test set in a ratio of 8:2.

[0103] Although the XGBoost regression model (Extreme Gradient Boosting) is a powerful machine learning model, it is usually regarded as a "black box" model. SHAP values provide a method to explain the prediction results of these complex models, making the behavior of the model more transparent. SHAP analysis (SHapley Additive exPlanations) is a machine learning model interpretation framework based on game theory. By calculating the contribution of each feature to the model prediction, it helps to understand the decision-making process of the model. Based on SHAP analysis, the non-linear contribution of each geometric parameter to the target is analyzed, and the core parameters that have a significant impact on the dual objectives are screened; the coefficient of determination R 2 is used to evaluate the accuracy of the regression prediction model; based on SHAP values, the three parameters that contribute the most to the head and MEI are screened to reduce the optimization dimension.

[0104] In the present invention, a model combining XGBoost and SHAP will be adopted. Under the condition that the regression prediction accuracy meets the standard, the contribution of each of the above-mentioned design variables, i.e., features, to the head and MEI values is calculated, so as to screen and reduce the design variables. The optimized data set obtained in step 1 is randomly divided into a training set and a test set according to 8:2.

[0105] As Figure 3a and Figure 3b shown, they are respectively the schematic diagrams of the head and MEI test set accuracies of the XGBoost-SHAP regression prediction model. As Figure 4 and Figure 5 shown, they are respectively the schematic diagrams of the SHAP value contributions of each feature to the head and MEI.

[0106] Step 3: According to the core optimization variables obtained in step 2, the optimal Latin hypercube sampling is used to generate a secondary data set, and several groups of head and MEI values with different combinations are obtained through CFD simulation; based on the XGBoost-SHAP regression model trained in step 2, the multi-objective evolutionary algorithm MOEA / D based on decomposition is used for multi-objective optimization to generate a Pareto front solution set. The Pareto front solution set is the optimal solution set of all the target parameters to be optimized.

[0107] To optimize the head and MEI simultaneously, the present invention adopts the multi-objective evolutionary algorithm based on decomposition (MOEA / D) to obtain the Pareto front of multiple solutions, and these solutions represent the best trade-off between different design schemes.

[0108] The decomposition-based multi-objective evolutionary algorithm MOEA / D transforms the multi-objective optimization problem into multiple single-objective optimization sub-problems for processing. Through decomposition, the objective space of the entire problem is decomposed into multiple smaller sub-problems, and each sub-problem can be optimized by an evolutionary algorithm. In addition, the MOEA / D algorithm particularly emphasizes neighborhood mating, and performs crossover and mutation operations using the solutions within the neighborhood. This approach utilizes the similarity between neighborhoods for optimization, prompting the entire population to cover the entire objective space as much as possible. In this way, MOEA / D can not only optimize multiple objective functions but also find a good compromise solution among different objectives, that is, the Pareto front.

[0109] Step 4: Assign parameter weights based on SHAP values in the TOPSIS algorithm, construct the SHAP-TOPSIS decision method, screen the Pareto front solution set obtained in Step 3 to obtain the optimal parameter combination, and perform CFD simulation on it. Compare with the initial model. If the result is better than the initial model, end and output the optimal parameter combination; otherwise, execute Step 3.

[0110] Step 41: Obtain the weight vector according to SHAP, and the formula is as follows:

[0111]

[0112] where w j is the weight vector; SHAP j is the SHAP value of the j-th feature; represents the sum of the SHAP values of all features in Step 3.

[0113] Step 42: Standardize the decision matrix, and the formula is as follows:

[0114]

[0115] where r ij is the value of the i-th scheme on the j-th feature; f ij represents the original value of the i-th sample on the j-th feature; represents the sum of squares of the j-th feature on all m samples.

[0116] Step 43: Generate the weighted matrix v j based on the weight vector w ij and the value r ij of the i-th scheme on the j-th feature, and the formula is as follows:

[0117] v ij = w j ·r ij

[0118] Step 44: According to the weighted matrix vij , the ideal solution and the negative ideal solution, and combine the Euclidean distance to obtain the distance and closeness of each set of parameter combinations to the ideal solution and the negative ideal solution. The formula is as follows:

[0119]

[0120] In the formula, represents the ideal solution; represents the negative ideal solution; represents the distance from the i-th parameter combination to the ideal solution; represents the distance from the i-th parameter combination to the negative ideal solution; C i represents the closeness of the i-th parameter combination, and the larger its value, the better the parameter combination.

[0121] Step 45: Select the parameter combination with the largest closeness as the optimal parameter combination, conduct a CFD simulation on it, and compare it with the initial model. If the result is better than the initial model, end and output the optimal parameter combination; otherwise, execute step 3.

[0122] Based on the optimal solution, perform three-dimensional modeling, mesh generation, and CFD numerical calculation on it, and compare it with the existing model pump. Compared with the existing centrifugal pump impeller optimization design method, it can improve the head and MEI of the centrifugal pump, significantly improve the internal flow field of the pump, and be more energy-efficient.

[0123] The TOPSIS decision-making method (Technique for Order Preference by Similarity to Ideal Solution, the method of ranking by approaching the ideal solution, abbreviated as the TOPSIS decision-making method) is a multi-criteria decision-making method that calculates the distance of each solution to the ideal solution and the negative ideal solution, and selects the solution that is closest to the ideal solution and farthest from the negative ideal solution:

[0124] TOPSIS first standardizes the decision matrix:

[0125]

[0126] where r ij is the value of the i-th solution on the j-th feature.

[0127] Combined with the weight vector w j , generate the weighted matrix v ij :

[0128] v ij = w j ·r ij

[0129] Determine the ideal solution and the negative ideal solution Calculate the distance and closeness degree between each solution and the ideal solution and the negative ideal solution through the Euclidean distance:

[0130] Euclidean distance to the ideal solution

[0131] Euclidean distance to the negative ideal solution

[0132] Closeness degree The larger its value, the better the solution.

[0133] In this step S4, during the implementation process, based on the results of the regression prediction model, use SHAP to calculate the importance of each feature; use the SHAP value as the weighting factor for the decision-making problem, that is, the SHAP value of the feature can be used as the weight of each objective in TOPSIS. In this way, the contribution size of the feature determines the importance of the feature in the decision-making; when performing TOPSIS processing, standardize all objective functions so that they are in the same scale range, and then weight the standardized values of each objective according to the weights calculated based on the SHAP value. Finally, calculate the distance between each solution and the ideal solution and the negative ideal solution, and select the solution closest to the ideal solution.

[0134] The SHAP-TOPSIS decision-making method aims to evaluate the importance of each feature in the model by using the SHAP value, and make decisions by combining the weighted objective function through the TOPSIS method, which is manifested as calculating the contribution degree of each feature to the objective through the SHAP value and normalizing it into the weight vector w j , w j will affect the weighted matrix v in TOPSIS ij , thus completing the joint decision-making.

[0135]

[0136] The weights provided by the SHAP value are used as the input of the TOPSIS method, which ensures that the contribution of each feature is considered in the multi-objective optimization, makes the decision-making process more reasonable and transparent. The optimal solution screened by this method does not require manual screening, which avoids subjectivity to a certain extent and enhances the scientificity and accuracy of the multi-objective optimization.

[0137] Example 1:

[0138] Taking the hydraulic diagram of the IS-65-50-160-00 type centrifugal pump as an example, further explain the steps of the present invention.

[0139] Step 11: According to the hydraulic diagram of the IS - 65 - 50 - 160 - 00 type centrifugal pump, conduct 3D modeling on it to obtain the initial model, and perform CFD numerical simulation calculations. Compare with the test data, and if the error is less than the set threshold of 5%, proceed to the next step. The relevant parameters of the initial model are shown in Table 1:

[0140] Table 1

[0141]

[0142] Step 12: Select the blade outlet width b2, impeller outlet diameter D2, blade outlet angle β2, blade inlet angle β1, number of blades Z, blade wrap angle Φ, and impeller inlet diameter D j as design variables, and the variable value ranges are shown in Table 2 below:

[0143] Table 2

[0144]

[0145] In the above technical solution, the 3D model of the model pump is divided into 4 computational domains, namely the inlet pipe, impeller, volute, and outlet pipe. To ensure the full development of the fluid at the pump inlet and outlet, the lengths of the inlet and outlet pipes are 5 times the diameters of the inlet and outlet pipe sections respectively.

[0146] In this application, ANSYS Meshing is used to perform unstructured grid division on the fluid domain. During division, the interfaces of the fluid domain, the edges of the front and rear covers, the blades, and the surfaces with large curvatures on the volute are encrypted to ensure grid quality and calculation accuracy. The specific grid division is as Figure 1 shown. ANSYS CFX is used to perform numerical simulation on the centrifugal pump. The turbulence model selects the standard k - ω model, the rotational speed is 2900 r / min, and the boundary conditions are velocity inlet and pressure outlet.

[0147] Step 13: Use the optimal Latin hypercube sampling method to sample the parameters in Table 2, generate 60 groups of parameter combinations evenly distributed in the variable space, and perform 3D modeling on the 60 groups of parameter combinations.

[0148] Step 14: Set three flow rates, namely small flow rate, high - efficiency flow rate, and large flow rate, for each group of parameter combinations respectively, and perform CFD simulations to obtain the small - flow rate efficiency η PL 、high - efficiency flow rate efficiency η BEP 、large - flow rate efficiency η 0L and high - efficiency flow rate head H BEP for each group of parameter combinations.

[0149] Step 15: According to the small - flow rate efficiency η PL 、high - efficiency flow rate efficiency η BEP, large flow rate efficiency η 0L and high-efficiency flow head H BEP , to obtain the constant C for each group of parameter combinations MEI .

[0150] Step 16: According to the constant C of each group of parameter combinations obtained in Step 15 MEI , perform interpolation calculation in combination with the following table to obtain the minimum efficiency index MEI of each group of parameter combinations.

[0151] Step 17: Use the several groups of parameter combinations obtained in Step 13, the high-efficiency flow head H of each group of parameter combinations obtained in Step 14 BEP , the constant C of each group of parameter combinations obtained in Step 15 MEI and the minimum efficiency index MEI of each group of parameter combinations obtained in Step 16 as elements to construct an optimization data set.

[0152] Step 2: According to the optimization data set obtained in Step 1, construct an XGBoost-SHAP joint regression model, and train prediction models with head and minimum efficiency index MEI as optimization objectives respectively; Screen the top three parameters with the highest sum of SHAP values and significant interaction effects as the core optimization variables;

[0153] As Figure 3a and Figure 3b shown, the coefficient of determination R 2 of the model's prediction for the head in the test set is 0.9713, and the coefficient of determination R 2 of the model's prediction for MEI in the test set is 0.97625. The prediction accuracy of the model for these two objectives is high and the fitting effect is good.

[0154] As Figure 4 and Figure 5 shown, the pink dots indicate that the eigenvalue has a positive impact on the model prediction in this observation (increasing the predicted value); Blue dots: indicate that the eigenvalue has a negative impact on the model prediction in this observation (decreasing the predicted value); The horizontal axis (SHAP value) shows the magnitude of the impact. The farther the point is from the center line (zero point), the greater the impact of the feature on the model output; The features arranged vertically in the figure are sorted in descending order of influence from top to bottom. The features above have a greater overall impact on the model output, while the features below have a smaller impact. The ones with the greatest contribution to the head are b2, β1, D j , and the ones with the greatest contribution to MEI are β2, D2, D j . Considering that D2 has a lower contribution degree to the head, b2, β2, D j are selected as the optimization objectives.

[0155] In the above technical solution, the mathematical expression of the multi-objective optimization of the centrifugal pump impeller is as follows:

[0156]

[0157] The optimization objective function includes: the highest head H, the highest minimum efficiency index MEI, and the optimized design variables need to be within the limited range.

[0158] Step 3: According to the core optimization variables obtained in Step 2, use the optimal Latin hypercube sampling to generate a quadratic data set, and obtain several groups of head and MEI values with different combinations through CFD simulation; based on the XGBoost-SHAP regression prediction model trained in Step 2, use the decomposition-based multi-objective evolutionary algorithm MOEA / D for multi-objective optimization, set the population size to 20, the neighborhood size to 20, the maximum number of iterations to 200 generations, and the crossover probability to 0.85 to generate the Pareto front solution set.

[0159] MOEA / D decomposes the multi-objective optimization problem into a set of single-objective problems by weighting, each sub-problem corresponding to the optimization direction of one objective, and finally obtains the Pareto front of the entire optimization problem, that is, the optimal solution set, through the joint solution of these sub-problems.

[0160] Step 4: Assign parameter weights based on SHAP values in the TOPSIS algorithm to construct the SHAP-TOPSIS decision method, screen the Pareto front solution set obtained in Step 3, and obtain the optimal parameter combination as b2 = 14 mm, β 2: = 29.97°, D j: = 72.65 mm. Conduct CFD simulation on it, compare with the initial model to compare the performance of the centrifugal pump before and after optimization. After optimization, the head of the pump rises by 3.6%, and the MEI value rises by 47.1%. The head and MEI before and after optimization are shown in Table 3.

[0161] Table 3

[0162]

[0163]

[0164] As Figure 6a and Figure 6b shown, they are the contour maps of the turbulent kinetic energy distribution of the cross-section before and after optimization respectively. The distribution of turbulent kinetic energy before optimization is uneven, and the turbulent kinetic energy is relatively high near the back of the blade and the volute wall. After optimization, the distribution of turbulent kinetic energy near the impeller outlet and the tongue is more uniform, and the flow stability is improved.

[0165] As Figure 7a and Figure 7b shown, they are the contour maps of the relative velocity distribution of the cross-section before and after optimization respectively. The local flow velocity of the impeller of the optimized pump is more stable, and there are fewer local sudden change velocities, thus improving the efficiency.

[0166] As Figure 8a and Figure 8b shown, they are respectively the pressure distribution nephograms of the cross-sections before and after optimization. In the initial model pump and the optimized pump, low-pressure zones appear at the impeller inlet. The local low-pressure range of the optimized pump impeller is smaller, and the pressure gradient change from the impeller inlet to the outlet is smaller. The pressure gradually diffuses along the flow channel, the energy transfer is more uniform, the internal energy loss of the impeller is reduced, and the efficiency is higher. In this way, the improvement of the model pump performance is achieved.

[0167] In summary, the present application provides a centrifugal pump impeller design method based on feature contribution degree and multi-objective decision-making, which is characterized in that: the global efficient search of the XGBoost model hyperparameters is realized through the Bayesian optimization algorithm, the core design variables (impeller outlet diameter, blade outlet angle and outlet width) are accurately screened by combining the SHAP value contribution degree analysis, and the multi-objective evolutionary algorithm MOEA / D based on decomposition is used for multi-objective optimization to generate the Pareto front solution set of the head and the minimum efficiency index MEI. Finally, the optimal parameter combination is determined by the SHAP-TOPSIS dynamic weighting decision-making method.

[0168] In addition to the above embodiments, the present invention may also have other implementation manners. All technical solutions formed by equivalent replacement or equivalent transformation fall within the protection scope required by the present invention.

Claims

1. A centrifugal pump impeller optimization design method based on feature contribution degree and multi-objective decision-making, characterized in that: It includes the following steps: S1. Based on the geometric structure of the centrifugal pump, conduct 3D modeling on it to obtain the initial model and the parameters of the initial model; conduct CFD simulation on the initial model to obtain the head, efficiency, and the minimum efficiency index MEI, and construct an optimization data set; S2. Based on the optimization data set obtained in step S1, construct an XGBoost-SHAP regression model, and train prediction models with the head and the minimum efficiency index MEI as optimization objectives respectively; dynamically search for the hyperparameter combination of XGBoost based on the Bayesian optimization algorithm; use the SHAP value calculation module to analyze the global and local contribution degrees of each geometric parameter, and screen the top three parameters with the largest sum of SHAP values and significant interaction effects as the core optimization variables; the calculation formula of the SHAP value is as follows: In the formula, F is the set of all features, S is the subset without feature i, and v(S) represents the model prediction value when using the features in subset S; S3. Based on the core optimization variables obtained in step S2, use the optimal Latin hypercube sampling to generate a quadratic data set, and obtain several groups of head and MEI values with different combinations through CFD simulation; based on the XGBoost-SHAP regression model trained in step S2, use the decomposition-based multi-objective evolutionary algorithm MOEA / D for multi-objective optimization to generate a Pareto front solution set; S4. Assign parameter weights based on the SHAP value in the TOPSIS algorithm, construct a SHAP-TOPSIS decision method, screen the Pareto front solution set obtained in step S3 to obtain the optimal parameter combination, and conduct CFD simulation on it and compare it with the initial model. If the result is better than the initial model, end and output the optimal parameter combination; otherwise, execute step S3.

2. The centrifugal pump impeller optimization design method based on feature contribution degree and multi-objective decision-making according to claim 1, wherein: The specific steps of step S1 are as follows: S11. Based on the geometric structure of the centrifugal pump, conduct 3D modeling on it to obtain the initial model and the parameters of the initial model; and conduct CFD simulation on it, compare the simulation result with the existing test data. If the error is less than the threshold, proceed to the next step; otherwise, adjust the model parameters and continue to conduct CFD simulation; S12. Determine the optimization parameters and the value range of each parameter; S13. Randomly generate several groups of parameter combinations and conduct 3D modeling on several groups of parameter combinations; S14. Set three flow rates, namely small flow rate, high-efficiency flow rate, and large flow rate, for each group of parameter combinations respectively, and conduct CFD simulations separately to obtain the small-flow efficiency η PL of each group of parameter combinations, the high-efficiency flow rate efficiency η BEP , the large-flow efficiency η 0L and the high-efficiency flow rate head H BEP ; S1 5. The small flow efficiency η of each group of parameter combinations obtained according to step S14 PL , the high-efficiency flow efficiency η BEP , the large flow efficiency η 0L and the high-efficiency flow head H BEP , to obtain the constant C of each group of parameter combinations MEI , the formula is as follows: x = ln(n s ) y = ln(Q BEP ) F η = -11.48x 2 - 0.85y 2 - 0.38xy + 88.59x + 13.46y C BEP = F η - η BEP C MEI = max(C BEP , C PL , C OL ) where n s is the specific speed; n N is the rated speed; i is the number of pump stages; Q BEP represents the high-efficiency flow rate; C BEP is the high-efficiency flow rate constant; C PL is the low-flow rate constant; C OL is the high-flow rate constant; the constant C MEI is C BEP , C PL , C OL is the maximum value among them; S16. The constant C of each set of parameter combinations obtained according to step S15 MEI , combined with the following table for interpolation calculation, to obtain the minimum efficiency index MEI of each set of parameter combinations. The formula and the interpolation table are as follows: where C MEI is the constant for each set of parameter combinations; C 左 is the value of C MEI falling on the left side within the interpolation table range; C 右 is the value of C MEI falling on the right side within the interpolation table range; MEI 左 is the MEI value corresponding to the value of C MEI falling on the left side within the interpolation table range. S17. Using the several groups of parameter combinations obtained in step S13, the high-efficiency flow head H of each group of parameter combinations obtained in step S14 BEP , the constant C of each group of parameter combinations obtained in step S15 MEI and the minimum efficiency index MEI of each group of parameter combinations obtained in step S16 as elements, construct an optimization data set.

3. The centrifugal pump impeller optimization design method based on feature contribution degree and multi-objective decision-making according to claim 2, wherein: The specific steps of step S4 are as follows: S41. Obtain the weight vector according to the SHAP value, and the formula is as follows: where w j is the weight vector; SHAP j is the SHAP value of the j-th feature; represents the sum of the SHAP values of all features in step 3; S42. Standardize the decision matrix, and the formula is as follows: where r ij is the value of the i-th solution on the j-th feature; f ij represents the original value of the i-th sample on the j-th feature; represents the sum of squares of the j-th feature over all m samples; S43. According to the weight vector w j and the value r of the i-th solution on the j-th feature ij generate a weighted matrix v ij , the formula is as follows: v ij = w j · r ij ; S44. According to the weighted matrix v ij , the ideal solution, and the negative ideal solution, the distances and closeness degrees between each group of parameter combinations and the ideal solution and the negative ideal solution are obtained by combining the Euclidean distance. The formula is as follows: In the formula, represents the ideal solution; represents the negative ideal solution; represents the distance from the i-th parameter combination to the ideal solution; represents the distance from the i-th parameter combination to the negative ideal solution; C i represents the closeness of the i-th parameter combination; S45. Select the parameter combination with the largest closeness as the optimal parameter combination, and conduct CFD simulation on it and compare it with the initial model. If the result is better than the initial model, end and output the optimal parameter combination; otherwise, execute step S3.

4. The centrifugal pump impeller optimization design method based on feature contribution degree and multi-objective decision-making according to claim 3, characterized in that: In step S2, the optimization data set obtained in step S1 is divided into a training set and a test set in a ratio of 8:

2.

5. The optimized design method of the centrifugal pump impeller based on feature contribution degree and multi-objective decision-making according to claim 3, wherein: The termination condition of step S2 is that the decrease amplitude of the mean square error in 10 consecutive iterations is less than 1% or the total number of iterations reaches 100 times.

6. The optimized design method of a centrifugal pump impeller based on feature contribution degree and multi-objective decision-making according to claim 3, wherein: The method of randomly generating several groups of parameter combinations in step S13 is to use the optimal Latin hypercube sampling method.

7. The optimization design method of a centrifugal pump impeller based on feature contribution degree and multi-objective decision-making according to claim 3, characterized in that: The number of parameter combinations generated in step S13 is 60 groups.

8. The optimization design method of the centrifugal pump impeller based on feature contribution degree and multi-objective decision-making according to claim 3, characterized in that: In step S14, the small flow rate is 75% of the efficient flow rate, and the large flow rate is 110% of the efficient flow rate.

9. The optimization design method of a centrifugal pump impeller based on feature contribution degree and multi-objective decision-making according to claim 3, characterized in that: In step S11, the error threshold for comparing the simulation results with the existing test data is 5%.

10. The centrifugal pump impeller optimization design method based on feature contribution degree and multi-objective decision-making according to claim 3, characterized in that: In step S1, CFturbo is used for parametric modeling of the impeller, volute, and inlet and outlet sections, ANSYS Meshing is used for unstructured grid division; ANSYS CFX is used for numerical simulation.

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