A method for optimizing the design of multi-circular arc blade profiles

Abstract

This invention discloses a method for optimizing the profile structure of multi-arc blades, comprising: acquiring structural data of the impeller in a centrifugal pump and performance data of different blades under the same operating conditions; designing profile structure parameters of the multi-arc blades based on the structural data; constructing a convolutional neural network model, wherein the input variables and output variables of the convolutional neural network model are the profile structure parameters and the performance data, respectively; training the convolutional neural network model using the profile structure parameters and the performance data; initializing and iteratively optimizing a particle swarm optimization algorithm model using the trained convolutional neural network model to obtain the prediction results of the optimal performance data and its corresponding optimal profile structure parameters.

Description

Technical Field

[0001] This application relates to the field of blade optimization design technology, and in particular to a method for optimizing the design of multi-circular arc blade profile structure. Background Technology

[0002] The optimization of arc-shaped impeller blades stems from the ever-increasing demands on the hydrodynamic performance of pumps. In modern wind power, aerospace, and hydropower, pumps are critical components, and their efficiency and stability are paramount. As a key structure of the pump, blade improvements can significantly enhance pump efficiency and head. Therefore, by employing advanced computational fluid dynamics simulations, machine learning, and optimization design algorithms, the shape and structure of arc-shaped blades can be finely adjusted to achieve efficient centrifugal pump impeller design. Patent CN113361047A discloses a high-dimensional optimization and selection method for impellers with multi-layered sensing structures. This patent involves NSGA-III (Non-Dominated Sorting Genetic Algorithm). Due to the complex steps involved in non-dominated sorting, individual fitness calculation, and population evolution operations, the computational load increases significantly when dealing with large-scale problems or complex objective functions. For example, when the evaluation of the objective function is very time-consuming (such as involving complex physical simulations or large-scale data processing), the algorithm's runtime may become very long, affecting its efficiency in practical applications. Summary of the Invention

[0003] To overcome the shortcomings of the existing technology, this application provides a method for optimizing the design of multi-arc blade profile structure, which optimizes the profile structure of the arc blades of the impeller to improve the pump efficiency and head of the centrifugal pump.

[0004] According to a first aspect of the embodiments of this application, a method for optimizing the design of multi-circular-arc blade profiles is provided, comprising:

[0005] S1: Obtain structural data of the impeller in the centrifugal pump and performance data of the centrifugal pump under the same operating conditions for different blades;

[0006] S2: Based on the structural data, design the profile structural parameters of the multi-arc blade;

[0007] S3: Construct a convolutional neural network model, wherein the input variables and output variables of the convolutional neural network model are the profile structure parameters and performance data, respectively;

[0008] S4: Train the convolutional neural network model using the aforementioned profile structure parameters and performance data;

[0009] S5: Initialize the particle swarm optimization model using the trained convolutional neural network model and iteratively optimize it to obtain the prediction results of the optimal performance data and its corresponding optimal profile structure parameters.

[0010] Optionally, the structural data includes: blade inlet angle, blade outlet angle, impeller inlet diameter, and impeller outlet diameter; the performance data includes: data obtained from experiments, data obtained from simulation calculations, or data obtained from on-site monitoring.

[0011] Optionally, based on the structural data, the profile structural parameters of the multi-arc blade are designed, including:

[0012] S21. Establish a rectangular coordinate system with the impeller inlet surface as the reference plane, set the center of the impeller's planar circle as the origin O of the planar coordinate system, and determine any point n on the side of the impeller's inner diameter circle. S (x) S y S (), determine any point n on the edge of the impeller's outer diameter circle. L (x) L y L );

[0013] S22, Based on the point n S and n L Determine two straight lines L passing through two points respectively. S and L L Their slopes are tan(blade inlet angle + 90°) and tan(blade outlet angle + 90°), respectively.

[0014] S23, based on the point n S and n L Determine the line segment L formed by connecting the two points. n ;

[0015] S24, according to the line segment L n Determine a location located at L n On the same side of the impeller, outside the inner diameter circle and inside the outer diameter circle, control point n1(x1, y1), along n1 to n L The direction determines a control point n2 that satisfies the same conditions, and i control points n are determined sequentially. i Point n S Point n L and all control points n1, n2, ..., n i Composition of control points P i ;

[0016] S25, Based on the control point combination P i Determine a set of n i straight line L i Its slope is k i And the slope k i It must be greater than the slope k of the previous straight line. i-1And less than the slope k of the next straight line i+1 When i=1, point n i-1 That is, n0 is regarded as point n S k0 is equivalent to the slope of line L0 passing through point n0; when i is at its maximum value, point n i+1 Consider point n L k i+1 Equivalent to passing through point n L at line L L The slope;

[0017] S26. Based on the control point combination P i and slope k i A mathematical model is used to determine the shape and position of the i+1 segment of the arc;

[0018] S27. Based on the mathematical model of the shape and position of the i+1 segment of the arc, determine the profile structure parameters of the arc blade.

[0019] Optionally, the mathematical model is expressed as:

[0020] (xa i ) 2 +(yb i ) 2 =r i 2 ;

[0021] In the formula, x∈(x i x i+1 ), y∈(y i y i+1 ), unknown number a i b i and r i , (x i y i (n) is the control point i The coordinates (x) i+1 y i+1 (n) is the control point i+1 The coordinates;

[0022] Each unknown number a i b i and r i The value is obtained by combining the following equations:

[0023] (x i -a i ) 2 +(y i -b i ) 2 =r i 2 ;

[0024] (x i+1 -a i ) 2 +(y i+1 -b i ) 2 =r i 2 ;

[0025] b i =(-C i -A i a i ) / B i ;

[0026] A i =k i+1 (k i 2 +1) 1 / 2 -k i (k i+1 2 +1) 1 / 2 ;

[0027] B i =(k i 2 +1) 1 / 2 -(k i+1 2 +1) 1 / 2 ;

[0028] C i =k i x i (k i+1 2 +1) 1 / 2 -y i (k i+1 2 +1) 1 / 2 -[k i+1 x i+1 (k i 2 +1) 1 / 2 -y i+1 (k i 2 +1) 1 / 2 ];

[0029] In the formula A i B i C i It is an intermediate variable.

[0030] Optionally, it also includes:

[0031] S6: Based on the prediction results of the optimal performance data and its corresponding optimal blade profile parameters, establish a three-dimensional model of the centrifugal pump, perform mesh generation and flow field calculation on the three-dimensional model of the centrifugal pump, and analyze the head and pump efficiency before and after optimization after the calculation. If the optimization requirements are met, it is considered reasonable, and the blade profile parameters currently used are taken as the final optimization result; if the optimization requirements are not met, repeat S4-S5.

[0032] The technical solutions provided by the embodiments of this application may include the following beneficial effects:

[0033] As can be seen from the above embodiments, this application adopts the method of acquiring centrifugal pump impeller structure and multi-condition performance data, designing profile parameters, constructing and training a convolutional neural network model, and then combining iterative optimization with particle swarm optimization algorithm. This overcomes the technical problems of manual design relying on experience, insufficient global optimization ability, and insufficient ability to process performance data of large-scale pumps and optimize blade profiles. In this way, it achieves the technical effect of efficiently mining the correlation between profile parameters and performance, accurately predicting the optimal performance and matching the best profile structure parameters, improving the multi-condition adaptability and overall performance of centrifugal pumps, and making blade profile design more intelligent and more in line with actual operating needs.

[0034] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0035] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0036] Figure 1 This is a flowchart illustrating an optimized design method for a multi-circular-arc blade profile structure according to an exemplary embodiment.

[0037] Figure 2 This is a schematic diagram of a centrifugal pump structure according to an exemplary embodiment.

[0038] Figure 3 This is a front view of an impeller shown according to an exemplary embodiment.

[0039] Figure 4 This is a schematic diagram of a multi-arc blade profile design, taking three arc segments as an example, according to an exemplary embodiment.

[0040] Figure 5 This is a diagram illustrating the iteration results according to an exemplary embodiment.

[0041] Figure 6 This is a performance comparison chart of head and pump efficiency before and after optimization, according to an exemplary embodiment. Detailed Implementation

[0042] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0043] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0044] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0045] Figure 1 This is a flowchart illustrating an optimized design method for multi-circular-arc blade profiles according to an exemplary embodiment, such as... Figure 1 As shown, the method may include the following steps:

[0046] S1: Obtain structural data of the impeller in the centrifugal pump and performance data of the centrifugal pump under the same operating conditions for different blades;

[0047] Specifically, Figure 2 In the given schematic diagram of the centrifugal pump structure, the different numbers represent the following structures: 1-inlet flow channel; 2-inducer wheel; 3-impeller; 4-volute casing; 5-shaft; 6-pump casing. Figure 3 The given is Figure 2 The front view of the impeller 3 of the structure.

[0048] The structural data includes: blade inlet angle, blade outlet angle, impeller inlet diameter, and impeller outlet diameter; the performance data includes: data obtained from experiments, data obtained from simulation calculations, or data obtained from on-site monitoring.

[0049] S2: Based on the structural data, design the profile structural parameters of the multi-arc blade; this step can include the following sub-steps:

[0050] S21. Establish a rectangular coordinate system with the impeller inlet surface as the reference plane, set the center of the impeller's planar circle as the origin O of the planar coordinate system, and determine any point n on the side of the impeller's inner diameter circle. S (x) S y S (), determine any point n on the edge of the impeller's outer diameter circle. L (x) L y L );

[0051] S22, Based on the point n S and n L Determine two straight lines L passing through two points respectively. S and L L Their slopes are tan(blade inlet angle + 90°) and tan(blade outlet angle + 90°), respectively.

[0052] Specifically, when designing the blades, the inlet angle is designed to be β. S The exit angle is designed to be β. L According to the point n S and n L Then, passing through point n S There is a straight line L S :(yy S )=k S (xx S ), and at the same time, passing through point n L There is a straight line L L :(yy L )=k L (xx L ), constant k S and k L The design parameters for the inlet and outlet angles are determined by k. S =tan(blade inlet angle + 90°) and k L =tan(blade exit angle + 90°), which makes the straight line tangent to one side of the arc in the subsequent design at the endpoint.

[0053] S23, based on the point n S and n L Determine the line segment L formed by connecting the two points. n ;

[0054] Specifically, the connection point n S and n L The expression for the line segment L can be obtained from the coordinates of the two points. n :(yyL )=k L (xx L Combined with S24, it can constrain the coordinates of control points and reduce the amount of calculation.

[0055] S24, according to the line segment L n Determine a location located at L n On the same side of the impeller, outside the inner diameter circle and inside the outer diameter circle, control point n1(x1, y1), along n1 to n L The direction determines a control point n2 that satisfies the same conditions, and i control points n are determined sequentially. i Point n S Point n L and all control points n1, n2, ..., n i Composition of control points P i ;

[0056] Specifically, on line L n Set a set of control points n on the same side i (x) i y i ), control points satisfy x i ∈ (x i-1 x i+1 ), y i ∈ (y i-1 y i+1 ), i=1, 2, 3,... ...; point n S Point n L and all control points n1, n2, ..., n i Composition of control points P i Control point P i Constrained in L n On the same side, reduce the amount of calculation.

[0057] S25, Based on the control point combination P i Determine a set of n i straight line L i Its slope is k i And the slope k i It must be greater than the slope k of the previous straight line. i-1 And less than the slope k of the next straight line i+1 When i=1, point n i-1 That is, n0 is regarded as point n S k0 is equivalent to the slope of line L0 passing through point n0; when i is at its maximum value, point n i+1 Consider point n L k i+1 Equivalent to passing through point n L at line L L The slope;

[0058] Specifically, based on the control point combination P i Determine a set of n i straight line L i Its slope is k i And satisfy k i-1 <k i <k i+1 When i=1, point n i-1 That is, n0 is regarded as point n S k0 is equivalent to the slope of line L0 passing through point n0; when i is at its maximum value, point n i+1 Consider point n L k i+1 Equivalent to passing through point n L at line L L The slope. By increasing the slope sequentially, the direction of concavity and convexity of each segment of the arc in the subsequent design can be made more consistent.

[0059] S26. Based on the control point combination P i and slope k i A mathematical model is used to determine the shape and position of the i+1 segment of the arc;

[0060] Specifically, based on the control point n i (x) i y i ) and slope k i Control point n i+1 (x) i+1 y i+1 ) and slope k i The mathematical model determines the shape and position of the i-th arc segment, with the i-th arc segment represented by point n. i-1 and n i Using L as the starting and ending points, the necessary constraints are imposed on the mathematical expression of the arc, allowing the arc to align with L. i-1 and L i They are tangent at the same time, thus making the first arc segment and the second arc segment tangent to each other in turn.

[0061] The mathematical model is expressed as follows:

[0062] (xa i ) 2 +(yb i ) 2 =r i 2 ;

[0063] In the formula, x∈(x i x i+1 ), y∈(y i y i+1 ), unknown number ai b i and r i , (x i y i (n) is the control point i The coordinates (x) i+1 y i+1 (n) is the control point i+1 The coordinates;

[0064] Each unknown number a i b i and r i The value is obtained by combining the following equations:

[0065] (x i -a i ) 2 +(y i -b i ) 2 =r i 2 ;

[0066] (x i+1 -a i ) 2 +(y i+1 -b i ) 2 =r i 2 ;

[0067] b i =(-C i -A i a i ) / B i ;

[0068] A i =k i+1 (k i 2 +1) 1 / 2 -k i (k i+1 2 +1) 1 / 2 ;

[0069] B i =(k i 2 +1) 1 / 2 -(k i+1 2 +1) 1 / 2 ;

[0070] C i =k i x i (k i+12 +1) 1 / 2 -y i (k i+1 2 +1) 1 / 2 -[k i+1 x i+1 (k i 2 +1) 1 / 2 -y i+1 (k i 2 +1) 1 / 2 ];

[0071] In the formula A i B i C i It is an intermediate variable.

[0072] S27. Based on the mathematical model of the shape and position of the i+1 segment of the arc, determine the profile structure parameters of the arc blade on one side.

[0073] Specifically, Figure 4 The given diagram illustrates a multi-arc blade profile with i=2, meaning a blade with three arc segments. When the target blade is a three-arc blade, the profile structure parameters include: x S x1, x2, x L y S y1, y2, y L k S k1, k2, k L These 12 known parameters will be used as input variables for subsequent machine learning models.

[0074] S3: Construct a convolutional neural network model, wherein the input variables and output variables of the convolutional neural network model are the profile structure parameters and performance data, respectively;

[0075] Specifically, using the prepared sample data, assuming a total of 1000 sets of data were collected, each of these 1000 blade profile samples has 12 blade profile structural parameters and 2 performance indicators. These 12 parameters and 2 performance indicators should be the actual blade profile parameters (the number of 12 parameters described here is the number of parameters used in the example; the actual number of parameters should depend on the actual control points n). i (Number of items).

[0076] These parameters and performance are normalized, and the data is scaled to the range [0,1].

[0077] Then, a function is used to generate a random array of shape (1000, 12) to represent the parameters corresponding to each blade profile sample;

[0078] At the same time, a random array of shape (1000, 2) is generated to represent the performance index corresponding to each blade profile sample;

[0079] Of these 1,000 sample data, 80% was divided into a training set to train the machine model, and 20% was divided into a test set to test the learning results of the machine model.

[0080] Build a neural convolutional network model. Construct a simple neural network using the Sequential model. This model is a linearly stacked model, allowing fully connected layers to be added sequentially (other models such as functional APIs or subclassed models can also be used as needed).

[0081] Using an activation function (such as the ReLU function), the input data has a shape of 12, meaning each sample has 12 parameters;

[0082] Then an output layer with two neurons is added to output the prediction performance metrics.

[0083] S4: Train the convolutional neural network model using the aforementioned profile structure parameters and performance data;

[0084] Specifically, the model is trained using the training set for 10 epochs (i.e., 10 iterations on the entire training set). After each epoch, the model is evaluated using the test set.

[0085] S5: Initialize the particle swarm optimization model using the trained convolutional neural network model and iteratively optimize it to obtain the prediction results of the optimal performance data and its corresponding optimal profile structure parameters.

[0086] Specifically, the particle swarm is initialized. The number of particles and the maximum number of iterations are set, and the dimension of each particle is set; here, the dimension should be 12, consistent with the number of blade profile structural parameters.

[0087] The dimensions (dimension 12) and velocities of the particles are randomly initialized, and the initial position of each particle is taken as its optimal position.

[0088] The trained CNN model is used to predict the fitness value of each particle, and the results are flattened into a one-dimensional array.

[0089] Find the particle with the highest fitness value and set its position as the global optimal position.

[0090] The particle swarm optimization algorithm is iteratively optimized. In each iteration, the velocity and position of each particle are updated according to the velocity and position update formula of PSO.

[0091] Start the iteration and set the number of iterations; set a learning factor and inertia weight for each particle, and update the particle velocity according to the PSO velocity update formula;

[0092] Update the particle's position using the updated particle velocity, and predict the particle's fitness value using the trained CNN model.

[0093] If the current fitness value is greater than the individual's best fitness value, then update the individual's best position and fitness value; if the current fitness value is greater than the global best fitness value, then update the global best position and index.

[0094] Set termination conditions for the particle swarm optimization algorithm (such as reaching the maximum number of iterations or the fitness value converging and stabilizing). When these conditions are met, stop the iteration. At this point, the particle parameters corresponding to the globally optimal position are the optimal profile structure parameters after co-optimization by the convolutional neural network and the particle swarm optimization algorithm; the iteration results are as follows. Figure 5 As shown, where e i This represents the error of the i-th iteration.

[0095] The profile structure parameters at the globally optimal position are input into the trained convolutional neural network model. The performance index output by the model is the best performance index for matching the optimal profile under the current design system.

[0096] To ensure that the blade profile structure truly improves the actual performance of the centrifugal pump, the optimal performance prediction results and corresponding profile parameters obtained from the algorithm are validated in a fluid dynamics scenario that is closer to actual engineering practice. This also includes:

[0097] S6: Based on the prediction results of the optimal performance data and its corresponding optimal blade profile parameters, establish a three-dimensional model of the centrifugal pump, perform mesh generation and flow field calculation on the three-dimensional model of the centrifugal pump, and analyze the head and pump efficiency before and after optimization after the calculation. If the optimization requirements are met, it is considered reasonable, and the blade profile parameters currently used are taken as the final optimization result; if the optimization requirements are not met, repeat S4-S5.

[0098] As can be seen from the above embodiments, this application overcomes the technical problems of manual design relying on experience, insufficient global optimization ability, and insufficient ability to process large-scale pump performance data and optimize blade profiles by acquiring centrifugal pump impeller structure and multi-condition performance data, designing profile parameters, constructing and training a convolutional neural network model, and then combining iterative optimization with particle swarm optimization algorithm. This achieves the technical effect of efficiently mining the correlation between profile parameters and performance, accurately predicting optimal performance and matching the best profile structure parameters, improving the multi-condition adaptability and overall performance of centrifugal pumps, and making blade profile design more intelligent and more in line with actual operating needs.

[0099] Specifically, it utilizes the optimal profile structure parameter x i y i k i The combination of these can yield several specific points n. i and passing through point n i straight line L i Drawing software can be used to draw a series of tangentially connected multi-circular arc segments, which is the optimization design goal of this patent—multi-circular arc blade profile.

[0100] In addition, a corresponding blade model is designed using the multi-circular arc blade profile through modeling software to replace the original blade model. Fluid dynamics calculations are then performed on the entire centrifugal pump to obtain optimized performance data such as head and pump efficiency. By comparing the performance before and after optimization, it is determined whether the optimized design meets the requirements. If it does, the profile structural parameters used in this calculation are taken as the final optimization result; if it does not meet the requirements, the optimization is repeated. The performance comparison results before and after optimization in this example are attached. Figure 6 As shown, the efficiency improvement under rated operating conditions is higher than expected by 5%.

[0101] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0102] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for optimizing the design of multi-circular arc blade profiles, characterized in that, include: S1: Obtain structural data of the impeller in the centrifugal pump and performance data of the centrifugal pump under the same operating conditions for different blades; S2: Based on the structural data, design the profile structural parameters of the multi-arc blade; S3: Construct a convolutional neural network model, wherein the input variables and output variables of the convolutional neural network model are the profile structure parameters and performance data, respectively; S4: Train the convolutional neural network model using the aforementioned profile structure parameters and performance data; S5: Initialize the particle swarm optimization model using the trained convolutional neural network model and iteratively optimize it to obtain the prediction results of the optimal performance data and its corresponding optimal profile structure parameters. The design parameters for the profile structure of multi-arc blades include: S21. Establish a rectangular coordinate system with the impeller inlet surface as the reference plane, set the center of the impeller's planar circle as the origin O of the planar coordinate system, and determine any point n on the side of the impeller's inner diameter circle. S (x) S y S (), determine any point n on the edge of the impeller's outer diameter circle. L (x) L y L ); S22, Based on the point n S and n L Determine two straight lines L passing through two points respectively. S and L L Their slopes are tan(blade inlet angle + 90°) and tan(blade outlet angle + 90°), respectively. S23, Based on the point n S and n L Determine the line segment L formed by connecting the two points. n ; S24, according to the line segment L n Determine a location located at L n On the same side of the impeller, outside the inner diameter circle and inside the outer diameter circle, control point n1(x1, y1), along n1 to n L The direction determines a control point n2 that satisfies the same conditions, and i control points n are determined sequentially. i Point n S Point n L and all control points n1, n2, ..., n i Composition of control point combination P i ; S25, Based on the control point combination P i Determine a set of n i straight line L i Its slope is k i And the slope k i It must be greater than the slope k of the previous straight line. i-1 And less than the slope k of the next straight line i+1 When i=1, point n i-1 That is, n0 is regarded as point n S k0 is equivalent to the slope of line L0 passing through point n0; when i is at its maximum value, point n i+1 Consider point n L k i+1 Equivalent to passing through point n L at line L L The slope; S26. Based on the control point combination P i and slope k i A mathematical model is used to determine the shape and position of the i+1 segment of the arc; S27. Based on the mathematical model of the shape and position of the i+1 segment of the circular arc, determine the profile structure parameters of the circular arc blade.

2. The method according to claim 1, characterized in that, The structural data includes: blade inlet angle, blade outlet angle, impeller inlet diameter, and impeller outlet diameter; the performance data includes: data obtained from experiments, data obtained from simulation calculations, or data obtained from on-site monitoring.

3. The method according to claim 1, characterized in that, The mathematical model is expressed as follows: (x-a i ) 2 +(y-b i ) 2 =r i 2 ; In the formula, x∈(x i x i+1 ), y∈(y i y i+1 ), unknown number a i b i and r i , (x i y i (n) is the control point i The coordinates (x) i+1 y i+1 (n) is the control point i+1 The coordinates; Each unknown number a i b i and r i The value is obtained by combining the following equations: (x i -a i ) 2 +(y i -b i ) 2 =r i 2 ; (x i+1 -a i ) 2 +(y i+1 -b i ) 2 =r i 2 ; b i =(-C i -A i a i ) / B i ; A i =k i+1 (k i 2 +1) 1 / 2 -k i (k i+1 2 +1) 1 / 2 ; B i =(k i 2 +1) 1 / 2 -(k i+1 2 +1) 1 / 2 ; C i =k i x i (k i+1 2 +1) 1 / 2 -y i (k i+1 2 +1) 1 / 2 -[k i+1 x i+1 (k i 2 +1) 1 / 2 -y i+1 (k i 2 +1) 1 / 2 ]; In the formula A i B i C i It is an intermediate variable.

4. The method according to claim 1, characterized in that, Also includes: S6: Based on the prediction results of the optimal performance data and its corresponding optimal blade profile parameters, establish a three-dimensional model of the centrifugal pump, perform mesh generation and flow field calculation on the three-dimensional model of the centrifugal pump, and analyze the head and pump efficiency before and after optimization after the calculation is completed. If the optimization requirements are met, it is considered reasonable, and the blade profile parameters currently used are taken as the final optimization result. If the optimization requirements cannot be met, repeat steps S4-S5.

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