Large-thrust annular propeller blade shape design method

Abstract

The invention provides a large-thrust annular propeller blade shape design method which specifically comprises the following steps: selecting the thickness of an annular propeller, the pitch angle of the propeller and the semi-short axial length of an elliptical blade as design variables, and constructing a target function and constraint conditions; establishing a response surface model of the thickness of the annular propeller, the pitch angle of the propeller, the semi-short axial length of an elliptical blade, the thrust of the annular propeller and the volume of the annular propeller; thrust maximization and volume minimization of the annular propeller are taken as optimization targets, the thrust maximization of the annular propeller ensures excellent hydrodynamic performance of the annular propeller, the volume minimization of the annular propeller aims at achieving the purpose of light weight, and the endurance time can be prolonged and the oil consumption performance can be improved through light weight. And carrying out optimization solution on the output response surface model by adopting a multi-objective genetic algorithm to obtain a Pareto frontier optimal solution. According to the technical scheme, the problems that in the prior art, an annular propeller is low in propelling efficiency and large in energy loss are solved.

Description

Technical Field

[0001] The invention relates to the field of propeller blade design, and in particular to a method for designing the shape of a large-thrust annular propeller blade. Background Art

[0002] In the design and application of propellers, how to maximize thrust under given conditions is the key focus of current underwater vehicle research. In the selection of long-term underwater vehicle propulsion, although the propulsion efficiency of traditional propellers is large enough, the energy loss is also large. Compared with traditional propellers, annular propellers have less energy loss and less noise, but lower propulsion efficiency, so the optimization goal of maximizing thrust is proposed.

[0003] Due to the high efficiency of annular propellers, their application in underwater vehicles has attracted much attention. However, the existing annular propeller models are not mature yet and cannot present an annular propeller structure with maximum thrust.

[0004] Therefore, a method for designing the shape of a high-thrust annular propeller blade with greater propulsion efficiency and less energy loss is now needed. Summary of the invention

[0005] The main purpose of the present invention is to provide a method for designing the blade shape of a large-thrust annular propeller, so as to solve the problems of low propulsion efficiency and large energy loss of annular propellers in the prior art.

[0006] To achieve the above object, the present invention provides a method for designing the shape of a high-thrust annular propeller blade, which specifically comprises the following steps:

[0007] S1, select the annular propeller thickness, propeller pitch angle and the semi-minor axis length b of the elliptical blade as design variables, and construct the objective function and constraint conditions.

[0008] S2, performing multivariate linear fitting on the design variables of step S1, and establishing a response surface model of annular propeller thickness, propeller pitch angle, semi-minor axis length b of the elliptical blade, annular propeller thrust, and annular propeller volume.

[0009] S3, with the annular propeller thrust maximization and volume minimization as the optimization objectives, the multi-objective genetic algorithm NSGA-II is used to optimize and solve the output response surface model to obtain the Pareto front optimal solution.

[0010] Furthermore, the design variables, objective function and constraints in step S1 are:

[0011]

[0012] Among them, x irepresents the design variables, where x1 represents the thickness of the annular propeller in mm, x2 represents the pitch angle of the annular propeller in degrees, and x3 represents the semi-minor axis length b of the elliptical blade in mm; F(x) represents the objective function of the maximum thrust of the annular propeller, and G1(x) represents the thrust function of the annular propeller; V(x) represents the objective function of the minimum volume of the annular propeller, and V1(x) represents the volume function of the annular propeller; g(x) represents the constraint condition; G2(x) represents the vorticity function of the traditional propeller, Max represents the maximum value, and Min represents the minimum value.

[0013] Furthermore, step S2 specifically includes the following steps:

[0014] S2.1, select the second-order model as the response surface model:

[0015]

[0016] Among them, y is the response variable, including: annular propeller thrust and annular propeller volume, x i and x j is the design variable, β0 is a constant term, β i is the coefficient, β ii is the second-order coefficient, β ij is the interaction term coefficient, ∈ is the error term, and k is the number of design variables.

[0017] S2.2, import the library into Python to fit the response surface model.

[0018] S2.3. Save the data set to a NumPy array or a Pandas data frame, and use PolynomialFeatures and LinearRegression to build and fit a response surface model. The data set includes: annular propeller thickness, propeller pitch angle, semi-minor axis length b of the elliptical blade, annular propeller thrust, and annular propeller volume.

[0019] S2.4, make predictions on the original data and calculate the error. First, use the response surface model to predict the predicted value of the original data, then use CFD to output the actual value, and then calculate the mean square error MSE through mean_squared_error():

[0020]

[0021] Among them, Y i is the actual value, Y pred,i is the predicted value, and n is the number of samples.

[0022] Furthermore, step S3 specifically includes the following steps:

[0023] S3.1, determine the objective function and constraints of the multi-objective genetic algorithm NSGA-II. The objective function is the response surface model successfully fitted in step S2, without constraints.

[0024] S3.2, set the upper and lower limits of each influencing factor, the influencing factor is the design variable.

[0025] S3.3, perform non-dominated sorting on the population and divide it into multiple levels.

[0026] S3.4, select parents using a binary tournament selection strategy;

[0027] S3.5, using the SBC genetic operator to perform evolutionary operations on the selected parent generation to generate new offspring;

[0028] S3.6, merge the parent generation and the offspring to form a population of twice the size, and then perform a new non-dominated sort, giving priority to the levels until the population size reaches the preset value; repeat the evaluation, sorting, selection and generation of new offspring until the maximum number of generations or other termination conditions are reached. Finally, the solution set obtained is the Pareto optimal solution set.

[0029] Furthermore, step S3.3 specifically includes the following steps:

[0030] S3.3.1, for each individual p in the population, there are parameters n(p) and S(p), n(p) is the number of solution individuals that dominate individual p in the population, initialized to 0, S(p) is the set of solution individuals dominated by individual p, initialized to an empty set.

[0031] S3.3.2, for each q in the population, check the dominance relationship with p: if p dominates q, add q to S(p); if q dominates p, increase n(p) by 1.

[0032] S3.3.3, put all liberations with n(p)=0 into the first-level frontier, and for each p in the first-level frontier, reduce n(q) by 1 for each q in S(p).

[0033] S3.3.4, if n(q) of a certain q decreases to 0, then q is placed in the frontier of the next layer, and this process is repeated until all individuals are assigned to a certain level.

[0034] Furthermore, step S3.4 specifically includes the following steps:

[0035] S3.4.1, randomly select two candidate individuals A and B. If the levels of A and B are different, select the individual with the lower level. If the levels of A and B are the same, proceed to step S3.4.2 to compare the crowding distances.

[0036] S3.4.2, if the crowding distances of A and B are different, select the individual with the larger crowding distance; if the crowding distances are the same, select an individual at random; crowding distance The formula is as follows:

[0037]

[0038] Among them, f i (k+1) and f i (k-1) are the ranked individual k in target f i The target values ​​of the previous and next individuals on , and is the target i The maximum and minimum values ​​of .

[0039] Furthermore, the crossover formula of the SBX genetic operator in step S3.5 is:

[0040]

[0041] Among them, x (1) and x (2) For two parents, and For the offspring generated by two parents, β is the distribution index η c The random factor of the control is calculated by the following formula:

[0042]

[0043] Where r is a uniform random number in the interval [0, 1], η c is the cross distribution index.

[0044] The mutation formula of the SBX genetic operator in step S3.5 is:

[0045] x i,new =x i +δ×(x max -x min ) (7);

[0046] Among them, x max and x min is the variable x i The upper and lower limits, x i,new is the variable after mutation, δ is the random mutation amplitude, and δ is determined by the following formula:

[0047]

[0048] Among them, r is a random number in the interval [0, 1], η m is the distribution index of variation.

[0049] Furthermore, in step S3.2, the thickness range of the annular propeller is set to be 3.75%D to 7.5%D, the propeller pitch angle range is set to be 10° to 40°, the ratio of the semi-major axis length a to the semi-minor axis length b of the elliptical blade ranges from 3 to 15, and D is the diameter of the annular propeller.

[0050] The present invention has the following beneficial effects:

[0051] 1. Clarify the relationship between the annular propeller thrust and propeller design variables (propeller thickness, propeller pitch angle, and semi-minor axis length of elliptical blades). Based on the response surface methodology and NSGA-II, the implicit functions between the thrust and torque of the annular propeller and the design variables are explicitly fitted.

[0052] 2. The present invention can quickly fit the surface under the action of multi-parameter coupling, has a fast solution speed, and can be used to solve the problem of explicitization of implicit functions under multi-parameters.

[0053] 3. The present invention can achieve multi-objective optimization. The design of annular propellers often involves multiple performance indicators, such as thrust, propulsion efficiency, cavitation performance, noise, etc. There are complex nonlinear relationships between these performances, and they may conflict with each other. This method can effectively solve this problem.

[0054] 4. The present invention makes the design of the annular propeller more targeted, thereby being able to more effectively improve the overall performance of the annular propeller.

[0055] 5. The present invention can improve the robustness and stability of the annular propeller design by considering the design under different working conditions.

[0056] 6. Combining computational fluid dynamics (CFD) with explicit fitting enables multi-disciplinary cross-application.

[0057] 7. The present invention provides designers with a variety of design solutions and flexible choices. They can choose the optimal solution that best suits the application scenario according to different design requirements, and the operability is strong. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the specific implementation or the prior art description. Obviously, the drawings described below are some implementations of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0059] Figure 1 A schematic diagram of the annular propeller blade model is shown.

[0060] Figure 2 A schematic diagram of the finite element model of an annular propeller is shown.

[0061] Figure 3 A flow chart of step S3 is shown. DETAILED DESCRIPTION

[0062] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] A method for designing the blade shape of a large-thrust annular propeller, such as Figure 1 The annular propeller blade shown specifically comprises the following steps:

[0064] S1, select the annular propeller thickness, propeller pitch angle and the semi-minor axis length b of the elliptical blade as design variables, and construct the objective function and constraint conditions.

[0065] Three different sets of data were selected for the design variables to form multiple sets of sampling data. Three values ​​were selected for the thickness of the annular propeller, namely 3.75%D, 5%D, and 7.5%D, where D represents the diameter of the annular propeller in mm. The propeller pitch angle takes three values, namely 10°, 22°, and 40°. The blade shape of the annular propeller takes three different ellipses, which are specifically manifested in the different ratios of the semi-major axis length a to the semi-minor axis length b. a remains unchanged at 50mm, and b takes three different values, namely 8mm, 10mm, and 15mm. 27 annular propeller models were constructed using Solidworks, and the volume of each annular propeller was obtained through the software. The 27 annular propeller models were placed in the flow field, the rotation speed of the annular propeller model and the fluid flow rate in the flow field were set, and the rotation domain and fluid calculation domain of the annular propeller model were determined.

[0066] The rotation domain and flow field calculation domain of the annular propeller are both set according to the diameter D of the annular propeller, where D is kept at 200 mm.

[0067] The flow field calculation domain of the annular propeller model is Figure 2As shown, it is composed of a hemisphere and a cylinder. The axis of the flow field calculation domain is collinear with the hub axis of the annular propeller model. The length of the flow field calculation domain is set to 9D. The diameters of the cylinder and the sphere are 6D. The fluid inlet boundary and the fluid outlet boundary of the fluid calculation domain correspond to the two faces of the body. The fluid inlet boundary is the velocity inlet VI of the fluid calculation domain, and the fluid outlet boundary is the pressure outlet PO of the fluid calculation domain. Among them, the distance between the fluid inlet boundary and the center of the annular propeller is 3D, and the distance between the fluid outlet boundary and the center of the annular propeller model is 6D.

[0068] Figure 2 The rotating domain R of the annular propeller model is located in the flow field calculation domain. It is formed by the rotation of the annular propeller model and is cylindrical. The axis of the rotating domain is collinear with the hub axis in the annular propeller model. The length of the rotating domain is set to 0.6D and the diameter is 1.1D.

[0069] S2, performing multivariate linear fitting on the design variables of step S1, and establishing a response surface model of annular propeller thickness, propeller pitch angle, semi-minor axis length b of the elliptical blade, annular propeller thrust, and annular propeller volume. A quadratic polynomial regression model is used as the response surface model to include interaction terms and square terms between variables.

[0070] S3, with the optimization objectives of maximizing the thrust and minimizing the volume of the annular propeller, uses the multi-objective genetic algorithm NSGA-II to optimize and solve the output response surface model, and obtains the Pareto frontier optimal solution. Maximizing the thrust of the annular propeller ensures the superior hydrodynamic performance of the annular propeller, and minimizing the volume of the annular propeller is to achieve the purpose of lightweighting, which can extend the endurance and improve fuel consumption performance.

[0071] The NSGA-II algorithm was selected because it can handle multiple conflicting objective functions at the same time. Through the mechanism of non-dominated sorting, it can help decision makers choose the best trade-off between different objectives. In addition, as a genetic algorithm, NSGA-II randomly searches in the design space and is not easy to fall into the local optimal solution. Therefore, it has a strong global search capability, especially when dealing with nonlinear and high-dimensional complex problems, which is very important for fitting models that may have multiple local extreme values. In addition, NSGA-II can handle non-convex, discontinuous or highly nonlinear objective functions and constraints. Many fitting models, especially second-order response surface models, may have complex design spaces and boundary conditions. NSGA-II adapts to these complex situations and provides reliable solutions. NSGA-II also adopts an elite strategy, that is, the elite individuals of the previous generation are retained to the next generation to ensure that the quality of the solution will not degenerate. This mechanism plays a significant role in maintaining the stability of the algorithm and accelerating the convergence speed. For the optimization of response surface fitting models, the elite strategy helps to find higher quality solutions. Compared with earlier genetic algorithms, NSGA-II has made improvements in sorting and selection operations, and can converge to the Pareto frontier faster. For complex fitting models, especially in engineering applications, fast convergence capability can reduce calculation time and improve optimization efficiency.

[0072] Specifically, based on STAR-CCM+ fluid analysis software and finite element analysis software, simulations were performed on the finite element models of each annular propeller, and the incoming flow velocity in the flow field was set to 1m / s, and the propeller speed was set to 10m / s, and the thrust of each annular propeller under this working condition was obtained. For each annular propeller finite element model, according to the thrust and volume results of each annular propeller, a parameter data set of the relationship between the annular propeller parameters (propeller thickness, propeller pitch angle, and semi-minor axis length b of the elliptical blade) and the objective function was further sorted out.

[0073] The design variables, objective function and constraints in step S1 are:

[0074]

[0075] Among them, x i represents the design variables, x1 represents the thickness of the annular propeller, the unit is mm, x2 represents the pitch angle of the annular propeller, the unit is degree °, x3 represents the semi-minor axis length b of the elliptical blade, the unit is mm; F(x) represents the objective function of the maximum thrust of the annular propeller, G1(x) represents the function of the thrust of the annular propeller; V(x) represents the objective function of the minimum volume of the annular propeller, V1(x) represents the volume function of the annular propeller; g(x) represents the constraint condition; G2(x) represents the vorticity function of the traditional propeller, Max represents the maximum value, and Min represents the minimum value.

[0076] Specifically, step S2 includes the following steps:

[0077] S2.1, since the first-order response surface model can only describe the linear relationship between the design variables and the response, and in actual engineering, the response functions of many systems show nonlinear characteristics, the second-order model can better approximate the nonlinear relationship by adding quadratic terms and interaction terms, thereby improving the model progress. In addition, the second-order model has relatively low complexity while maintaining high expressive power. Compared with the high-order model, it can more accurately fit the response of the complex system without significantly increasing the computational burden, that is, the second-order model takes into account both computational efficiency and accuracy. Therefore, the second-order model is selected as the response surface model:

[0078]

[0079] Among them, y is the response variable, including: annular propeller thrust and annular propeller volume, x i and x j is the design variable, β0 is a constant term, β i is the coefficient, β ii is the second-order term coefficient, which indicates the quadratic effect of the response variable corresponding to the i-th independent variable, that is, the nonlinear effect, β ij is the interaction term coefficient, which represents the effect of the interaction between the ith and jth independent variables on the response variable, ∈ is the error term, and k is the number of design variables.

[0080] S2.2, import libraries into Python for response surface model fitting. The libraries include NumPy, Pandas, LinearRegression and PolynomialFeatures of scikit-learn, pyplot of Matplotlib, and Axes3D of mpl_toolkits.mplot3d. Among them, NumPy is the basic library for scientific computing, especially in numerical calculation and array processing. In response surface analysis, it is mainly used to generate numerical data and process grid data. Pandas is the core library for data analysis, which is used for loading, processing and organizing data. In the process of response surface fitting, data is usually read from experimental data or files and organized in the form of DataFrame for further processing and analysis. LinearRegression is a linear regression module in scikit-learn, which is used to fit polynomial regression models. PolynomialFeatures is used to generate polynomial features and expand the input independent variables into high-order features such as quadratic and cubic features. In this way, more complex regression models can be established to meet the requirements of quadratic models of response surface. By combining PolynomialFeatures and LinearRegression, we can fit a quadratic regression model (i.e., a common response surface model). Matplotlib is Python's basic drawing library for visualizing data. In response surface analysis, pyplot is used to draw three-dimensional surface plots and contour plots to help intuitively understand the response of the model under different combinations of independent variables. Axes3D is a tool in Matplotlib for creating three-dimensional graphics. It allows the drawing of three-dimensional response surface plots (surface plots), which can intuitively display the relationship between independent variables and dependent variables in three-dimensional space.

[0081] It is known that there are three design variables (propeller thickness, propeller pitch angle, and semi-minor axis length b of the elliptical blade), defined as x1, x2, and x3, and have corresponding response values ​​y1 and y2, which are the annular propeller thrust and annular propeller volume. Save multiple sets of sampled data in a NumPy array or a Pandas data frame. Assume that X is a 27×3 design variable matrix, and y1 and y2 are 27×1 response variable matrices. Construct quadratic polynomial models and fit the data respectively, that is, construct response surface models for annular propeller thrust and annular propeller volume. PolynomialFeatures and LinearRegression are used to construct and fit a quadratic response surface model. The degree of the polynomial is specified to be 2, which means that a quadratic polynomial model will be constructed, including linear terms, cross terms, and square terms. Then create a pipeline to construct a quadratic polynomial regression model. Use PolynomialFeatures to expand the input design variables into a polynomial feature matrix, including all quadratic terms. Use LinearRegression to fit the response variables on the expanded polynomial features. To further confirm the model fitting results, you can view the coefficients and intercept of the model. As well as the predicted values ​​on some new data, this can help verify the accuracy of the model and understand the effect of the polynomial regression model. Among them, the specific steps to check the model fitting include: outputting the intercept and coefficients after the model is successfully fitted; predicting on the original data and calculating the error, first using the model to predict the response value of the original data, then outputting the actual value and the predicted value, and then calculating the mean square error (MSE) through mean_squared_error(). In order to test the generalization ability of the model, enter some new data points for prediction.

[0082] S2.3. Save the data set to a NumPy array or a Pandas data frame, and use PolynomialFeatures and LinearRegression to build and fit a response surface model. The data set includes: annular propeller thickness, propeller pitch angle, semi-minor axis length b of the elliptical blade, annular propeller thrust, and annular propeller volume.

[0083] S2.4, make predictions on the original data and calculate the error. First, use the response surface model to predict the response value of the original data, then use CFD to output the actual value, and then calculate the mean square error MSE through mean_squared_error():

[0084]

[0085] Among them, Y i Let the actual response value, Y pred,i is the predicted response value, and n is the number of samples.

[0086] A certain number of annular propellers are randomly set, and their performance is calculated using the response surface model and finite element software respectively. The difference between the two is compared to test the accuracy of the prediction model. The response value of each new sample point is compared with the value calculated by the finite element software to determine whether it converges. The convergence condition is that the relative error between the response value and the value calculated by the finite element software does not exceed 0.2%.

[0087] like Figure 3 As shown, first initialize the population, that is, set the objective function and the upper and lower limits of each influencing factor; perform non-dominated sorting, use the SBC genetic operator to perform selection, crossover, and mutation to generate a new generation of sub-populations; execute evolutionary generation gen+1; continue to perform selection, crossover, and mutation; merge the parent and child generations; perform fast non-dominated sorting and crowding calculation; select suitable individuals to form a new parent generation; determine whether the evolutionary generation is less than the maximum generation max gen, if so, continue to execute the evolutionary generation gen+1 until it is equal to the maximum generation, and output the optimal solution, which is the optimal solution for the trade-off between maximizing the thrust and minimizing the volume of the annular propeller.

[0088] Specifically, step S3 includes the following steps:

[0089] S3.1, determine the objective function and constraints of the multi-objective optimization of the multi-objective genetic algorithm NSGA-II. The objective function is the response surface model successfully fitted in step S2, without constraints.

[0090] S3.2, set the upper and lower limits of each influencing factor, the influencing factor is the design variable.

[0091] Specifically, in step S3.2, the thickness range of the annular propeller is set to 3.75%D to 7.5%D. If the thickness is less than 3.75%D, the annular propeller does not meet the strength requirements. If the thickness is greater than 7.5%D, the excessive thickness affects the performance of the annular propeller, such as noise and energy consumption. Therefore, this value range is selected, and the thrust maximization and volume minimization of the annular propeller are solved within this value range. The propeller pitch angle range is 10° to 40°, and the ratio of the semi-major axis length a to the semi-minor axis length b of the elliptical blade ranges from 3 to 15.

[0092] Initialize the population number and generation number within the range of the above-mentioned influencing factors. In this embodiment, the population number is set to 200 and the generation number is set to 50.

[0093] S3.3, perform non-dominated sorting on the population and divide it into multiple levels.

[0094] S3.4, select the parent generation using the binary tournament selection strategy.

[0095] S3.5, use the SBC genetic operator to perform evolution operations on the selected parent generation to generate new offspring.

[0096] S3.6, merge the parent generation and the offspring to form a population of twice the size, and then perform a new non-dominated sort, with priority selection by level, until the population size reaches the preset value; repeat the evaluation, sorting, selection and generation of new offspring until the maximum number of generations or other termination conditions are reached, and finally, the solution set obtained is the Pareto optimal solution set. The Pareto optimal solution set constitutes the trade-off solution of the objective function, that is, the trade-off optimal solution of maximizing the thrust and minimizing the volume of the annular propeller.

[0097] Specifically, step S3.3 includes the following steps:

[0098] S3.3.1, for each individual p in the population, there are parameters n(p) and S(p), n(p) is the number of solution individuals that dominate individual p in the population, initialized to 0, S(p) is the set of solution individuals dominated by individual p, initialized to an empty set.

[0099] S3.3.2, for each q in the population, check the dominance relationship with p: if p dominates q, add q to S(p); if q dominates p, increase n(p) by 1.

[0100] S3.3.3, release all n(p)=0 into the first-layer frontier. For each p in the first-layer frontier, reduce n(q) of each q in S(p) by 1 (indicating that p has been eliminated at the current level, reducing the dominance over q).

[0101] S3.3.4, if n(q) of a certain q is reduced to 0, then q is placed in the frontier of the next layer, and the process is repeated until all individuals are assigned to a certain level. The final result is that the solutions in each non-dominated level are mutually non-dominated and arranged in order of superiority.

[0102] Specifically, a binary tournament selection strategy is selected, which is a strategy for selecting parents that combines the non-dominated sorting level and crowding distance to give priority to individuals with higher quality and uniform distribution. In the binary tournament selection, the non-dominated sorting level is given priority, and the crowding distance is given second priority, that is, if two individuals belong to different levels, the individual with the lower level is given priority (the lower the level, the better); if two individuals belong to the same level, the individual with a larger crowding distance is selected (the solution in the area where the individual with a large crowding distance is located is sparser, maintaining population diversity).

[0103] Step S3.4 specifically includes the following steps:

[0104] S3.4.1, randomly select two candidate individuals A and B. If the levels of A and B are different, select the individual with the lower level. If the levels of A and B are the same, proceed to step S3.4.2 to compare the crowding distances.

[0105] S3.4.2, if the crowding distances of A and B are different, select the individual with the larger crowding distance; if the crowding distances are the same, select an individual at random; crowding distance The formula is as follows:

[0106]

[0107] Among them, f i (k+1) and f i (k-1) are the ranked individual k in target f i The target values ​​of the previous and next individuals on , and is the target i The maximum and minimum values ​​of .

[0108] Specifically, the crossover formula of the SBX genetic operator in step S3.5 is:

[0109]

[0110] Among them, x (1) and x (2) For two parents, and For the offspring generated by two parents, β is the distribution index η c The random factor controlled by SBX simulates the exponential distribution effect and is used to adjust the generation range of offspring. It is calculated by the following formula:

[0111]

[0112] Where r is a uniform random number in the interval [0, 1], η c is the cross-distribution index, usually set to 2 or greater.

[0113] The mutation formula of the SBX genetic operator in step S3.5 is:

[0114] x i,new =x i +δ×(x max -x min ) (7);

[0115] Among them, x max and x min is the variable x i The upper and lower limits, x i,new is the variable after mutation, δ is the random mutation amplitude, and δ is determined by the following formula:

[0116]

[0117] Among them, r is a random number in the interval [0, 1], η m is the variation distribution index, usually set to 20 or greater to control the strength of variation.

[0118] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for designing the shape of a high-thrust annular propeller blade, characterized in that: The specific steps include: S1, select the thickness of the annular propeller, the propeller pitch angle and the semi-minor axis length b of the elliptical blade as design variables, and construct the objective function and constraint conditions; S2, performing multivariate linear fitting on the design variables of step S1, and establishing a response surface model of annular propeller thickness, propeller pitch angle, semi-minor axis length b of the elliptical blade, annular propeller thrust, and annular propeller volume; S3, with the annular propeller thrust maximization and volume minimization as the optimization objectives, the multi-objective genetic algorithm NSGA-II is used to optimize and solve the output response surface model to obtain the Pareto front optimal solution.

2. A method for designing the shape of a high-thrust annular propeller blade according to claim 1, characterized in that: The design variables, objective function and constraints in step S1 are: Among them, x i represents the design variables, where x1 represents the thickness of the annular propeller in mm, x2 represents the pitch angle of the annular propeller in degrees, and x3 represents the semi-minor axis length b of the elliptical blade in mm; F(x) represents the objective function of the maximum thrust of the annular propeller, and G1(x) represents the thrust function of the annular propeller; V(x) represents the objective function of the minimum volume of the annular propeller, and V1(x) represents the volume function of the annular propeller; g(x) represents the constraint condition; G2(x) represents the vorticity function of the traditional propeller, Max represents the maximum value, and Min represents the minimum value.

3. A method for designing the shape of a high-thrust annular propeller blade according to claim 1, characterized in that: Step S2 specifically includes the following steps: S2.1, select the second-order model as the response surface model: Among them, y is the response variable, including: annular propeller thrust and annular propeller volume, x i and x j is the design variable, β0 is a constant term, β i is the coefficient, β ii is the second-order coefficient, β ij is the interaction term coefficient, ∈ is the error term, and k is the number of design variables; S2.2, import the library into Python to fit the response surface model; S2.3, save the data set to a NumPy array or a Pandas data frame, and use PolynomialFeatures and LinearRegression to build and fit a response surface model. The data set includes: annular propeller thickness, propeller pitch angle, semi-minor axis length b of the elliptical blade, annular propeller thrust, and annular propeller volume; S2.4, make predictions on the original data and calculate the error. First, use the response surface model to predict the predicted value of the original data, then use CFD to output the actual value, and then calculate the mean square error MSE through mean_squared_error(): Among them, Y i is the actual value, Y pred，i is the predicted value, and n is the number of samples.

4. A method for designing the shape of a high-thrust annular propeller blade according to claim 1, characterized in that: Step S3 specifically includes the following steps: S3.1, determine the objective function and constraints of the multi-objective genetic algorithm NSGA-II, the objective functions are F(x) and V(x), and there are no constraints; S3.2, set the upper and lower limits of each influencing factor, the influencing factor is the design variable; S3.3, perform non-dominated sorting on the population and divide the population into multiple levels; S3.4, select parents using a binary tournament selection strategy; S3.5, using the SBC genetic operator to perform evolutionary operations on the selected parent generation to generate new offspring; S3.6, merge the parent generation and the offspring to form a population of twice the size, and then perform a new non-dominated sort, giving priority to the levels until the population size reaches the preset value; repeat the evaluation, sorting, selection and generation of new offspring until the maximum number of generations or other termination conditions are reached. Finally, the solution set obtained is the Pareto optimal solution set.

5. A method for designing the shape of a high-thrust annular propeller blade according to claim 4, characterized in that: Step S3.3 specifically includes the following steps: S3.3.1, for each individual p in the population, there are parameters n(p) and S(p), n(p) is the number of solution individuals that dominate individual p in the population, initialized to 0, S(p) is the set of solution individuals dominated by individual p, initialized to an empty set; S3.3.2, for each q in the population, check the dominance relationship with p: if p dominates q, add q to S(p); if q dominates p, increase n(p) by 1; S3.3.3, put all liberations with n(p) = 0 into the first level frontier, and for each p in the first level frontier, reduce n(q) by 1 for each q in S(p); S3.3.4, if n(q) of a certain q decreases to 0, then q is placed in the frontier of the next layer, and this process is repeated until all individuals are assigned to a certain level.

6. A method for designing the shape of a high-thrust annular propeller blade according to claim 4, characterized in that: Step S3.4 specifically includes the following steps: S3.4.1, randomly select two candidate individuals A and B. If the levels of A and B are different, select the individual with the lower level. If the levels of A and B are the same, proceed to step S3.4.2 to compare the crowding distances. S3.4.2, if the crowding distances of A and B are different, select the individual with the larger crowding distance; if the crowding distances are the same, select an individual at random; crowding distance The formula is as follows: Among them, f i (k+1) and f i (k-1) are the ranked individual k in target f i The target value of the previous and next individual on i max and f i min is the target i The maximum and minimum values ​​of .

7. A method for designing the shape of a high-thrust annular propeller blade according to claim 4, characterized in that: The crossover formula of the SBX genetic operator in step S3.5 is: Among them, x (1) and x (2) For two parents, and For the offspring generated by two parents, β is the distribution index η c The random factor of the control is calculated by the following formula: Where r is a uniform random number in the interval [0, 1], η c is the cross-distribution index; The mutation formula of the SBX genetic operator in step S3.5 is: x i，new =x i +δ×(x max -x min ) (7); Among them, x max and x min is the variable x i The upper and lower limits, x i,new is the variable after mutation, δ is the random mutation amplitude, and δ is determined by the following formula: Among them, r is a random number in the interval [0, 1], η m is the distribution index of variation.

8. A method for designing the shape of a high-thrust annular propeller blade according to claim 4, characterized in that: In step S3.2, the thickness range of the annular propeller is set to 3.75%D to 7.5%D, the propeller pitch angle range is set to 10° to 40°, the ratio of the semi-major axis length a to the semi-minor axis length b of the elliptical blade ranges from 3 to 15, and D is the diameter of the annular propeller.

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