A ducted propeller multi-objective optimization design method

Abstract

The present application relates to a kind of ducted propeller multi-objective optimization design method, comprising: obtaining a group of chord length parameters of airfoil section at different radius of blade hub to blade tip;Performance parameters of ducted propeller are constructed about objective function;A group of target chord length parameters is generated and as initial sample, obtain the multiple objective function values corresponding to initial sample;Predictive model is obtained, and corresponding proxy model is constructed for each performance parameter;The final population corresponding to each initial population is obtained;The optimal chord length parameter of ducted propeller is obtained.The present application can obtain the optimal chord length parameter under the limited number of simulation calculation based on the comprehensive consideration of each performance index of ducted propeller, and based on the optimal chord length parameter, the ducted propeller with excellent comprehensive performance can be designed, to improve the accuracy of optimization result.

Description

TECHNICAL FIELD

[0001] The present application relates to the underwater vehicle propulsion technical field, and in particular to a ducted propeller multi-objective optimization design method. BACKGROUND

[0002] In the field of ocean engineering, with the development of human resources and the continuous deepening of marine scientific research, the demand for underwater equipment is increasing, including underwater vehicles, underwater robots and other underwater equipment, their functions cover the fields of marine scientific research, marine resource exploration and development, submarine pipeline laying and maintenance, and marine environment monitoring. Among these underwater equipment, the ducted propeller is often used as a propulsion device due to its simple structure, mature manufacturing process and reliable use. Compared with traditional single propeller, the duct structure around the propeller blade not only increases the thrust, reduces the cavitation and reduces the noise, but also protects the propeller blade. The performance of the ducted propeller directly affects the control ability, navigation speed and energy utilization efficiency of the equipment. Therefore, the design of the ducted propeller is of great significance to the ocean equipment.

[0003] Currently, the propeller blade design of the ducted propeller is mostly based on the lift method, which assumes that each airfoil section is two-dimensional, ignoring the three-dimensional effect, and the calculation of induced velocity is based on the simplified vortex theory, which cannot accurately capture the real distribution of induced velocity. Therefore, although the lift method can quickly obtain the preliminary design of the propeller blade, the designed propeller blade is not accurate enough.

[0004] Therefore, it is necessary to provide a ducted propeller multi-objective optimization design method to solve the above problems. SUMMARY

[0005] The present application provides a ducted propeller multi-objective optimization design method to solve the problem that the current propeller blade design of the ducted propeller is mostly based on the lift method, which assumes that each airfoil section is two-dimensional, ignoring the three-dimensional effect, and the calculation of induced velocity is based on the simplified vortex theory, which cannot accurately capture the real distribution of induced velocity. Therefore, although the lift method can quickly obtain the preliminary design of the propeller blade, the designed propeller blade is not accurate enough.

[0006] The ducted propeller multi-objective optimization design method of the present application adopts the following technical scheme, comprising:

[0007] A plurality of groups of variables are preset, and each group of variables is taken as a group of chord length parameters of the airfoil section at different radii from the hub to the blade tip of the propeller blade, and the chord length parameters of the airfoil section at different radii from the hub to the blade tip satisfy the condition of first increasing and then decreasing;

[0008] The performance parameters of the ducted propeller are taken as optimization objectives, and each set of chord length parameters is taken as an independent variable to construct an objective function about the performance parameters of the ducted propeller, wherein the performance parameters include thrust of the ducted propeller, efficiency of the ducted propeller, minimum pressure on the surface of the blade in a three-dimensional flow field, maximum deformation of the blade, and vibration frequency of the blade.

[0009] Optimized Latin hypercube sampling is used to generate a set of target chord length parameters of the ducted propeller, and the set of target chord length parameters is taken as initial samples to input into the objective function to obtain a plurality of objective function values corresponding to the initial samples.

[0010] All the objective function values corresponding to the initial samples are non-dominantly sorted based on the SDR dominance relation to obtain the dominance levels of the sample points, a prediction model from the sample points to the dominance levels is established, and a corresponding surrogate model is constructed for each performance parameter.

[0011] Optimized Latin hypercube sampling algorithm is used to re-generate a plurality of sets of initial chord length parameters, each set of initial chord length parameters is taken as an initial population, and each initial population and the corresponding surrogate model of each performance parameter are used to optimize each performance parameter in a preset chord length distribution range by using three evolutionary algorithms, respectively. After iteration, the corresponding populations generated by each initial population under the three evolutionary algorithms are obtained, and the three populations are combined to obtain a final population corresponding to each initial population.

[0012] The individuals of each final population are non-dominantly sorted according to the dominance relation to obtain a first dominance level sequence, and the second dominance level sequence of each individual of each final population is predicted according to the prediction model. The final samples are obtained according to the first dominance level sequence and the second dominance level sequence corresponding to each final population, and a final sample library is formed.

[0013] According to a preset number threshold of the number of sample points in the final sample library, an optimal sample point satisfying the dominance relation is obtained, and the chord length parameters corresponding to the optimal sample point are taken as the optimal chord length parameters of the ducted propeller.

[0014] Preferably, the step of obtaining the performance parameters is:

[0015] A ducted propeller model and a flow field model are constructed.

[0016] The blade rotation domain and the outer flow domain of the ducted propeller model are meshed.

[0017] The flow field of the blade rotation domain and the outer flow domain is solved by using Fluent to obtain the thrust of the ducted propeller and the efficiency of the ducted propeller.

[0018] The minimum pressure on the surface of the blade in the flow field solving result is extracted.

[0019] The pressure on the surface of the blade in the solution result of the flow field is solved by finite element method to obtain the maximum deformation of the blade;

[0020] The modal analysis is performed on the blade to obtain the first-order modal frequency, the second-order modal frequency and the third-order modal frequency of the blade;

[0021] The vibration frequency of the blade is obtained according to the first-order modal frequency, the second-order modal frequency and the third-order modal frequency of the blade.

[0022] Preferably, the steps of constructing the ducted propeller model and the flow field model are as follows:

[0023] According to the classical axial flow pump circulation curve, the circulation values of the airfoil sections at different radii of the blade are obtained;

[0024] According to the chord length and the circulation value of the airfoil sections at different radii of the blade, and by using the cascade correction formula, the pitch angle of the airfoil sections at different radii is obtained;

[0025] According to the pitch angle and the chord length of the airfoil sections at different radii, and by using the propeller coordinate conversion formula, the value point coordinates of the propeller are obtained;

[0026] The initial points and the end points of all the airfoil sections are connected to generate the leading edge and the trailing edge of the propeller blade, and the value point coordinates are input into a three-dimensional modeling software to complete the modeling of the propeller blade and the duct by lofting and rotating commands to obtain the ducted propeller model;

[0027] The flow field model is generated according to the ducted propeller model.

[0028] Preferably, the expression of the vibration frequency of the blade is:

[0029]

[0030] In the formula, represents the vibration frequency of the blade; represents the first-order modal frequency of the blade; represents the second-order modal frequency of the blade; represents the third-order modal frequency of the blade.

[0031] Preferably, the expression of the target function of the performance parameters of the ducted propeller is:

[0032]

[0033] In the formula, is a preset set of variables; is a preset chord length distribution range; represents the thrust of the propeller; represents the efficiency of the propeller; represents the minimum pressure of the blade surface in the three-dimensional flow field; represents the maximum deformation of the blade, represents the vibration frequency of the blade.

[0034] Preferably, the step of obtaining the final sample according to the first and second dominance rank sequences corresponding to each final population is:

[0035] obtaining the sum value of the dominance ranks and the absolute value of the difference value of the individuals corresponding to the first and second dominance rank sequences;

[0036] obtaining the final dominance rank sequence of the individuals in the final population according to the sum value and the absolute value of the difference value of the dominance ranks corresponding to each individual in the final population, and based on the non-dominant sorting of the Pareto dominance relationship;

[0037] the individual corresponding to the lowest dominance rank value in the final dominance rank sequence is taken as the individual of the final sample.

[0038] Preferably, the step of obtaining the optimal sample point satisfying the dominance relationship according to the number threshold value preset according to the number of sample points in the final sample library is:

[0039] If the number of sample points in the final sample library is equal to the preset number threshold value, the sample points in the final sample library are taken as the optimal sample points satisfying the dominance relationship;

[0040] If the number of sample points in the final sample library is less than the preset number threshold value, the final population is reacquired in turn, and the individual corresponding to the lowest dominance rank value in the final dominance rank sequence corresponding to the final population is added to the final sample library until the number of sample points in the final sample library is equal to the preset number threshold value, and the sample points in the final sample library are taken as the optimal sample points satisfying the dominance relationship.

[0041] Preferably, the step of predicting the second dominance rank sequence of each individual in the final population according to the prediction model is:

[0042] obtaining the maximum dominance rank value in the first dominance rank sequence;

[0043] using the prediction model to predict the dominance rank prediction value of all individuals in each final population;

[0044] taking the maximum dominance rank value as the number of clustering clusters, and clustering the dominance rank prediction value to obtain the prediction dominance rank corresponding to the individual of the final population;

[0045] sorting the prediction dominance rank to obtain the second dominance rank sequence.

[0046] Preferably, the proxy model adopts a Kriging proxy model.

[0047] The beneficial effects of the present application are:

[0048] The present application applies the proxy model assisted multi-objective optimization algorithm in the optimization process of the ducted propeller, not only considers the hydrodynamic performance of the ducted propeller (i.e. the thrust of the propeller and the efficiency), but also considers the cavitation performance of the ducted propeller and the structural strength and vibration performance of the ducted propeller, then, the performance parameters of the ducted propeller are taken as the optimization target, and each group of chord length parameters is taken as the independent variable, the objective function about the performance parameters of the ducted propeller is constructed, the multi-objective optimization algorithm formed based on three evolution algorithms can obtain the optimal chord length parameters under the limited number of simulation calculations on the basis of comprehensively considering the performance indicators of the ducted propeller, and the ducted propeller with excellent comprehensive performance can be designed based on the optimal chord length parameters, that is, the present application approximates the complex model or the actual problem by constructing the proxy model, greatly reduces the calculation cost of the optimization process, solves the high-dimensional and multi-objective complex optimization problem, and thus improves the accuracy of the optimization result.

[0049] Secondly, the computational fluid dynamics (CFD) and the finite element calculation (FEA) are important methods for evaluating the hydrodynamic performance and the structural strength performance of the equipment. With the help of the proxy assisted optimization algorithm and the high precision simulation performance of the CFD / FEA, the multi-performance indicators of the ducted propeller are comprehensively considered on the basis of not significantly increasing the real function evaluation, and it is of great significance for improving the comprehensive performance indicators of the ducted propeller. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0051] Figure 1 The flow chart of the multi-objective optimization design method of the ducted propeller of the present application;

[0052] Figure 2 The flow chart of obtaining performance parameters in the multi-objective optimization design method of the ducted propeller of the present application;

[0053] Figure 3 The flow chart of the proxy model assisted multi-objective optimization algorithm iteration optimization in the multi-objective optimization design method of the ducted propeller of the present application;

[0054] Figure 4 The schematic diagram of the parameterization of the ducted propeller blade in the embodiment of the present application. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0056] An embodiment of a ducted propeller multi-objective optimization design method of the present application, as shown in the figure, comprises: Figure 1

[0057] S1, a set of chord length parameters of airfoil sections at different radii from a hub to a tip of a blade are obtained;

[0058] Specifically, a plurality of groups of variables are preset, and each group of variables is taken as a set of chord length parameters of airfoil sections at different radii from the hub to the tip of the blade, and the chord length parameters of the airfoil sections at the different radii from the hub to the tip satisfy the condition of first increasing and then decreasing.

[0059] In the embodiment, a set of design variables are used to represent the chord length parameters of the airfoil sections at the different radii, and the airfoil sections are sequentially constructed with an interval of 0.1R, and there are 6 airfoil sections.

[0060] S2, a target function about performance parameters of the ducted propeller is constructed;

[0061] Specifically, the performance parameters of the ducted propeller are taken as optimization targets, and each group of chord length parameters is taken as an independent variable, and the target function about the performance parameters of the ducted propeller is constructed, that is, in the working condition of 300 RPM, the performance parameters of the ducted propeller are taken as optimization targets, and a set of chord length parameters of the 6 airfoil sections uniformly distributed from r / R=0.5 to r / R=1 are taken as independent variables, and the target function about the performance parameters of the ducted propeller is constructed, wherein the performance parameters include: the thrust of the ducted propeller and the efficiency of the ducted propeller, the minimum pressure on the surface of the blade in the three-dimensional flow field, the maximum deformation of the blade, and the vibration frequency of the blade.

[0062] Step 21, the expression of the target function about the performance parameters of the ducted propeller is:

[0063]

[0064] In the formula, is a preset set of variables; is a preset chord length distribution range; represents the thrust of the propeller; represents the efficiency of the propeller; represents the minimum pressure on the surface of the blade in the three-dimensional flow field;​ is the maximum deformation of the blade, is the vibration frequency of the blade.

[0065] wherein the step of obtaining the performance parameter is:

[0066] Step 211, constructing a ducted propeller model and a flow field model; specifically, the step of constructing the ducted propeller model and the flow field model is: step 2111, obtaining the circulation value of the airfoil section at different radii of the blade according to the circulation curve of the classic axial flow pump; step 2112, introducing a cascade correction formula to obtain the pitch angle of the airfoil section at different radii according to the chord length and the circulation value of the airfoil section at different radii of the blade, considering the mutual influence between cascades; step 2113, obtaining the coordinate of the profile point of the propeller by using the propeller coordinate conversion formula according to the pitch angle and the chord length of the airfoil section at different radii; step 2114, connecting the initial point and the end point of all airfoil sections to generate the leading edge and the trailing edge of the propeller blade, inputting the coordinate of the profile point into a three-dimensional modeling software to complete the modeling of the propeller blade and the duct by lofting and rotating commands to obtain the ducted propeller model, and generating a flow field model for CFD calculation according to the ducted propeller model; in the present embodiment, the ducted propeller uses a specified duct, and the circulation distribution of the blade uses the circulation distribution curve in the design of the axial flow pump, wherein the result of the parameterization of the blade is as shown in Figure 4 .

[0067] wherein in the present embodiment, the required thrust of the propeller is determined according to the speed, resistance, main body size and design requirements of the underwater equipment, and the required thrust allocated to each blade is determined according to the diameter and the number of blades of the ducted propeller blade; the thrust allocated to each blade is determined according to the required thrust of the blade; the lift coefficient of the airfoil section at different radii is determined by using the classic propeller circulation distribution formula ; in the present embodiment, the medium-sized underwater vehicle MK46 has a speed of 10 kn, the rotating speed of the ducted propeller is 300 RPM, the hub diameter ratio is 0.5, and the number of blades is 9; first, the resistance of the MK46 at a speed of 10 kn is calculated ; the thrust of each blade is calculated according to the resistance ; then, the required lift of the airfoil section at different radii is determined according to the circulation distribution function; considering that the cascade density will affect the performance of the airfoil section, a cascade correction formula is introduced to correct the performance of the airfoil section, that is, the cascade correction formula is:

[0068]

[0069]

[0070] wherein, is the influence coefficient of the cascade on the angle of attack without lift, is the cascade solidity, , At the time of incomplete design, let , use , to obtain the geometric camber of the airfoil, wherein is the camber ratio, is the camber ratio of the modified airfoil. Considering that the airfoil in the embodiment is a symmetric airfoil without camber, the camber correction amount needs to be converted into the angle of attack reduction without lift in the cascade, that is,

[0071] ;

[0072] According to the required of the cross-sectional airfoil and the chord length of the airfoil section at the radius , the airfoil attack angle satisfying the requirements is obtained according to the aerodynamic performance of the airfoil in the airfoil library , and then the modified airfoil attack angle is obtained according to the considered modification mode of the airfoil attack angle , and then the pitch angle can be obtained according to the modified airfoil attack angle ; the airfoil value points of the airfoil on the two-dimensional plane are converted to the coordinates of the airfoil value points of the propeller on the three-dimensional cylindrical coordinate system by using the coordinate conversion equation of the airfoil at different cross sections of the blade in turn.

[0073] Step 212, input the flow field model into the fluent meshing grid division software to divide the grid of the rotating region of the blade of the ducted propeller and the outer flow field to obtain a high-quality CFD calculation network.

[0074] Step 213, import the CFD calculation network into the CFD software, use Fluent to solve the flow field of the rotating region of the blade and the outer flow field, and obtain the thrust of the ducted propeller and the efficiency of the ducted propeller.

[0075] Step 214, extract the minimum pressure on the surface of the blade in the flow field solving result , and evaluate the cavitation performance of the ducted propeller through ; it needs to be explained that the pressure on the surface of the blade and the pressure value of the flow field near the inlet of the ducted propeller ; the pressure reduction coefficient of the blade , the cavitation number , wherein is the density of water, is the inlet velocity, is the critical pressure at which cavitation occurs on the blade surface at the temperature; the cavitation performance of the blade can be determined according to the relative size of the pressure reduction coefficient of the blade surface and the cavitation number , and the pressure reduction coefficient of the blade surface is the smallest at the minimum pressure of the blade surface . Therefore, the cavitation performance of the blade can be determined using .

[0076] Step 215, in the finite element solver (Workbench-Mechanical), define fixed constraints at the blade root, define fluid-structure coupling surfaces on the blade surface, import the pressure distribution of the blade surface obtained from the flow field solution into the finite element solver for finite element calculation, and obtain the maximum deformation of the blade .

[0077] Step 216, modal analysis is performed on the blade to obtain the first-order modal frequency, the second-order modal frequency, and the third-order modal frequency of the blade; the vibration frequency of the blade is obtained according to the first-order modal frequency, the second-order modal frequency, and the third-order modal frequency of the blade, wherein the expression of the vibration frequency of the blade is:

[0078]

[0079] In the formula, represents the vibration frequency of the blade; represents the first-order modal frequency of the blade; represents the second-order modal frequency of the blade; represents the third-order modal frequency of the blade.

[0080] S3, generate a set of target chord length parameters as initial samples, and obtain a plurality of target function values corresponding to the initial samples;

[0081] A set of target chord length parameters of the catheter propeller are generated by using optimized Latin hypercube sampling, and the set of target chord length parameters are input into the target function as initial samples to obtain a plurality of target function values corresponding to the initial samples.

[0082] S4, obtain a prediction model, and construct a corresponding proxy model for each performance parameter;

[0083] All target function values corresponding to the initial samples are non-dominant sorted based on the SDR dominance relationship to obtain the dominance level of each sample point, a prediction model from the sample point to the dominance level is established according to the dominance level of the sample point, and a corresponding proxy model is constructed for each performance parameter.

[0084] S5, obtain a final population corresponding to each initial population;

[0085] The optimization Latin hypercube sampling algorithm is used to regenerate multiple sets of initial chord length parameters, each set of initial chord length parameters is taken as an initial population, and each performance parameter is optimized in a preset chord length distribution range by using three evolutionary algorithms respectively according to each initial population and the corresponding proxy model of each performance parameter, wherein the proxy model acts as a sample fitness evaluation in the algorithm, and after iteration, the corresponding population generated by each initial population under the three evolutionary algorithms is obtained, and the three populations are combined to obtain the final population corresponding to each initial population.

[0086] In this embodiment, the three evolutionary algorithms are NSGA-II, IBEA and RVEA.

[0087] S6, obtaining the optimal chord length parameter of the ducted propeller;

[0088] Specifically, the individuals of each final population are non-dominantly sorted according to the dominance relationship to obtain a first dominance level sequence, and the second dominance level sequence of the individuals of each final population is predicted according to the prediction model; the final samples are obtained according to the first dominance level sequence and the second dominance level sequence corresponding to each final population, and a final sample library is formed; the optimal sample point satisfying the dominance relationship is obtained according to the number threshold value of the sample points in the final sample library, and the chord length parameter corresponding to the optimal sample point is taken as the optimal chord length parameter of the ducted propeller.

[0089] Specifically, as shown in Figure 3 , step 61, the step of non-dominantly sorting the individuals of each final population according to the dominance relationship to obtain a first dominance level sequence is: performing SDR-based non-dominant sorting on the final population , to obtain the dominance level of all individuals in the final population and the maximum dominance level value n, and the first dominance level sequence is obtained by sorting according to the dominance level of all individuals in the final population .

[0090] Step 62, the step of predicting the second dominance level sequence of the individuals of each final population according to the prediction model is: in this embodiment, the prediction model uses the RBF function, which is a continuous function, and the dominance level prediction value of all individuals in each final population is obtained by using the RBF function based on the individuals of the final population, then the maximum dominance level value n in the final population is taken as the number of clustering clusters, and the dominance level prediction value is clustered by k-means to obtain the prediction dominance level corresponding to the individuals of the final population, and the second dominance level sequence is obtained by sorting the prediction dominance level .

[0091] Step 63, the step of obtaining the final sample according to the first dominance level sequence and the second dominance level sequence corresponding to each final population is: obtaining the first dominance level sequence and the second dominance rank sequence the sum of the dominance ranks corresponding to each individual in the final population, and the absolute value of the difference of the dominance ranks; the final dominance rank sequence of the individuals in the final population is obtained according to the sum of the dominance ranks corresponding to each individual in the final population and the absolute value of the difference of the dominance ranks, and based on the non-dominated sorting of the Pareto dominance relationship; and the individual corresponding to the lowest dominance rank value in the final dominance rank sequence is taken as the individual of the final sample. That is, the expression is:

[0092]

[0093]

[0094] wherein, is the i th sample in the first dominance rank sequence; is the i th sample in the second dominance rank sequence; is the sum of the dominance ranks corresponding to the i th sample in the first dominance rank sequence and the i th sample in the second dominance rank sequence, is the absolute value of the difference of the dominance ranks corresponding to the i th sample in the first dominance rank sequence and the i th sample in the second dominance rank sequence; wherein, in the present embodiment, is the quality of the solution corresponding to the individual; and is the uncertainty information of the solution corresponding to the individual, and the final population is based on and the final dominance rank sequence of the individuals in the final population is obtained based on the non-dominated sorting of the Pareto dominance relationship.

[0095] Step 64: the step of obtaining the optimal sample points satisfying the dominance relationship according to the number threshold value of the sample points in the final sample library is: if the number of the sample points in the final sample library is equal to the preset number threshold value, the sample points in the final sample library are taken as the optimal sample points satisfying the dominance relationship; if the number of the sample points in the final sample library is less than the preset number threshold value, the final population is reacquired in turn, and the individual corresponding to the lowest dominance rank value in the final dominance rank sequence corresponding to the final population is added to the final sample library until the number of the sample points in the final sample library is equal to the preset number threshold value, and then the sample points in the final sample library are taken as the optimal sample points satisfying the dominance relationship.

[0096] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for co-objective optimization design of a ducted propeller, characterized in that, include: Multiple sets of variables are preset, and each set of variables is used as a set of chord length parameters of the airfoil section at different radii from the blade hub to the blade tip. The chord length parameters of the airfoil section at different radii from the blade hub to the blade tip satisfy the condition of first increasing and then decreasing. The performance parameters of the ducted propeller are used as optimization objectives, and each set of chord length parameters are used as independent variables to construct an objective function for the performance parameters of the ducted propeller. The performance parameters include: the thrust and efficiency of the ducted propeller, the minimum pressure on the blade surface in the three-dimensional flow field, the maximum deformation of the blade, and the vibration frequency of the blade. A set of target chord length parameters for the duct propeller is generated by using optimized Latin hypercube sampling, and the set of target chord length parameters is used as the initial sample input to the objective function to obtain multiple objective function values ​​corresponding to the initial sample; Based on the SDR dominance relationship, all objective function values ​​corresponding to the initial sample are sorted in non-dominated order to obtain the dominance level of each sample point. A prediction model from the sample point to the dominance level is established based on the dominance level of the sample point, and a corresponding surrogate model is constructed for each performance parameter. Multiple sets of initial chord length parameters are regenerated using the optimized Latin hypercube sampling algorithm. Each set of initial chord length parameters is used as an initial population. Based on each initial population and the surrogate model corresponding to each performance parameter, three evolutionary algorithms are used to optimize each performance parameter within the preset chord length distribution range. After the iteration, the corresponding populations generated by each initial population under the three evolutionary algorithms are obtained, and the three populations are merged to obtain the final population corresponding to each initial population. The individuals in each final population are sorted non-dominated according to the dominance relationship to obtain the first dominance level sequence. The second dominance level sequence of the individuals in each final population is predicted according to the prediction model. The final samples are obtained and the final sample library is formed according to the first dominance level sequence and the second dominance level sequence corresponding to each final population. Based on the preset threshold of the number of sample points in the final sample library, the optimal sample point that satisfies the dominance relationship is obtained, and the chord length parameter corresponding to the optimal sample point is taken as the optimal chord length parameter of the duct propeller.

2. The co-objective optimization design method for a ducted propeller according to claim 1, characterized in that, The steps to obtain performance parameters are as follows: Construct a duct-propeller model and a watershed model; Mesh the blade rotation domain and external flow domain of the ducted propeller model; Fluent was used to solve the flow field in the blade rotation domain and the external flow domain to obtain the thrust and efficiency of the ducted propeller. Extract the minimum pressure on the blade surface from the flow field solution results; The pressure on the blade surface in the flow field solution is obtained by finite element analysis to obtain the maximum deformation of the blade. Modal analysis was performed on the blades to obtain the first-order modal frequencies, second-order modal frequencies, and third-order modal frequencies of the blades. The vibration frequency of the blade is obtained from the first-order, second-order, and third-order modal frequencies of the blade.

3. The co-objective optimization design method for a ducted propeller according to claim 2, characterized in that, The steps for constructing the duct propeller model and the watershed model are as follows: Based on the circulation curve of a classic axial flow pump, the circulation values ​​of the airfoil section at different radii of the blade are obtained; Based on the chord length and circulation of the airfoil section at different radii of the blade, and using the blade cascade correction formula, the pitch angle of the airfoil section at different radii is obtained. Based on the pitch angle and chord length of the airfoil section at different radii, and using the propeller coordinate transformation formula, the coordinates of the propeller's shape value point are obtained; Connect the initial and final points of all airfoil sections to generate the guide edge and trailing edge of the propeller blade. Input the coordinates of the model value points into the 3D modeling software, and complete the modeling of the propeller blade and duct through lofting and rotation commands to obtain the ducted propeller model. A watershed model is generated based on the duct propeller model.

4. The co-objective optimization design method for a ducted propeller according to claim 2, characterized in that, The expression for the vibration frequency of the blade is: In the formula, Indicates the vibration frequency of the blade; This represents the first-order modal frequency of the blade; This represents the second-order modal frequency of the blade; This represents the third-order modal frequency of the blade.

5. The co-objective optimization design method for a ducted propeller according to claim 1, characterized in that, The objective function for the performance parameters of the ducted propeller is expressed as follows: In the formula, A pre-defined set of variables; This is the preset chord length distribution range; Indicates the thrust of the propeller; Indicates the efficiency of the thruster; This represents the minimum pressure on the blade surface in a three-dimensional flow field; This represents the maximum deformation of the blade. denoted as the vibration frequency of the blade.

6. The co-objective optimization design method for a ducted propeller according to claim 1, characterized in that, The steps to obtain the final sample based on the first and second dominance level sequences corresponding to each final population are as follows: Obtain the sum of the dominance levels of the individuals corresponding to the first dominance level sequence and the second dominance level sequence, as well as the absolute value of the difference in dominance levels; The final dominance level sequence of individuals in the final population is obtained by summing the dominance levels of each individual in the final population and the absolute value of the difference, and by non-dominance sorting based on Pareto dominance relations. The individual corresponding to the lowest dominance level value in the final dominance level sequence is taken as the individual in the final sample.

7. The co-objective optimization design method for a ducted propeller according to claim 6, characterized in that, The steps to obtain the optimal sample points that satisfy the dominance relationship, based on a preset threshold for the number of sample points in the final sample library, are as follows: If the number of sample points in the final sample library is equal to the preset number threshold, then the sample points in the final sample library will be used as the optimal sample points that satisfy the dominance relationship. If the number of sample points in the final sample library is less than the preset threshold, the final population is obtained again in sequence, and the individual corresponding to the lowest dominance level value in the final dominance level sequence corresponding to the final population is added to the final sample library until the number of sample points in the final sample library is equal to the preset threshold. Then, the sample points in the final sample library are taken as the optimal sample points that satisfy the dominance relationship.

8. The co-objective optimization design method for a ducted propeller according to claim 1, characterized in that, The steps for predicting the second dominance rank sequence of individuals in each final population based on the prediction model are as follows: Obtain the highest dominance level value in the first dominance level sequence; The dominance level of all individuals in each final population is predicted using a predictive model. Using the maximum dominance level value as the number of clusters, the predicted dominance level values ​​are clustered to obtain the predicted dominance level corresponding to the individual in the final population. The predicted dominance levels are sorted to obtain the second dominance level sequence.

9. The co-objective optimization design method for a ducted propeller according to claim 1, characterized in that, The proxy model adopted is the Kriging proxy model.

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