Rotor wing type pneumatic design method based on forward and reverse hybrid design algorithm

Abstract

The invention provides a rotor wing type design method based on a forward and reverse hybrid design algorithm. The method comprises the following steps: determining a reference wing type; determining a design variable and a design space of a rotor wing design airfoil needing to be designed; determining a forward design target and a reverse design target of a rotor wing design airfoil, and giving a target function expression of forward and reverse hybrid design; randomly sampling in a given design space by adopting a test design method to generate initial sample points, and forming a sample data set; and establishing an agent model according to the sample data set, obtaining newly added sample points through a combined parallel point adding criterion and a sub-optimization method, calculating response values of the newly added sample points for updating the agent model, and repeating the process until convergence. According to the rotor type designed through the method, the aerodynamic characteristics of the airfoil under the forward design target and the reverse design target can be considered at the same time, the comprehensive performance of the airfoil is effectively improved, and the efficiency and practicability of rotor type design are improved.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft design, and in particular to a rotor airfoil aerodynamic design method based on a forward and reverse hybrid design algorithm. Background Art

[0002] As the basic element of the rotor, the airfoil is the key factor affecting the performance of the rotor. The performance of the rotor airfoil has a significant impact on the main performance of the helicopter, such as hovering, forward flight, maneuvering, load, ceiling, range / flight time, maneuverability, noise and vibration level.

[0003] The design of rotor airfoils needs to comprehensively consider flight conditions such as forward flight, hovering, and maneuvering, and has multi-condition, nonlinear, and strongly constrained characteristics. The design requirements under different working conditions are mutually constrained and contradictory, making it difficult for traditional "trial and error" and inverse design methods to achieve the best compromise under these stringent requirements, and facing great difficulties and challenges. In response to this problem, numerical optimization design methods can automatically find the optimal solution that meets complex design requirements based on high-confidence numerical simulation analysis, significantly reducing dependence on designer experience, and gradually becoming the rotor airfoil design technology with the most application potential. Therefore, the research and development of a new generation of high-performance rotor airfoils urgently needs to develop advanced numerical optimization design technologies.

[0004] However, when applied to rotor airfoil design, existing numerical optimization design methods often have certain limitations in that the mathematical optimal solution deviates from the optimal design that conforms to the physical principles of airfoil design. Summary of the invention

[0005] In view of the defects of the prior art, the present invention provides a rotor airfoil aerodynamic design method based on a forward and reverse hybrid design algorithm, which can effectively solve the above problems.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The present invention provides a rotor airfoil design method based on a forward and reverse hybrid design algorithm, comprising the following steps:

[0008] Step 1: determine the reference airfoil of the rotor airfoil to be designed; use the CST airfoil parameterization method to parameterize the reference airfoil to obtain the CST parameters [A1, A2, …, A n ]; where A1, A2, …, A n is n CST parameters; for CST parameters [A1, A2, …, A n ] Make a certain disturbance δ to determine the design space of the design variables Among them, A i represents A1, A2, …, A nThe i-th CST parameter in ; i = 1, 2, ..., n;

[0009] Step 2, determining the design state and design requirements of the rotor design airfoil under different flight conditions;

[0010] Step 3, determining the forward and reverse hybrid design objectives, including the forward design objectives and the reverse design objectives; the forward design objectives are direct design indicators including the aerodynamic force of the airfoil, and the reverse design objectives are flow characteristic design indicators of the airfoil flow including the local pressure distribution of the airfoil; combining the forward design objectives and the reverse design objectives, determining the objective function expression of the forward and reverse hybrid design; determining the constraint function expression according to the design requirements determined in step 2, thereby constructing an optimization mathematical model;

[0011] Step 4: Use the experimental design method to calculate the design space determined in step 1. Extracting initial sample points, obtaining the response value of each initial sample point according to the objective function expression and constraint function expression of the forward and reverse hybrid design, and forming a sample data set; wherein the response value includes the objective function response value and the constraint function response value;

[0012] Step 5: construct a Kriging proxy model based on the sample data set;

[0013] Step 6: Based on the Kriging proxy model, the combined parallel point addition criterion is used to determine the sub-optimization problem; the hybrid sub-optimization method is used to solve the determined sub-optimization problem, and multiple new sample points are obtained in one round of optimization;

[0014] Step 7, evaluating the newly added sample points obtained in step 6, adding the newly added sample points and their response values ​​to the sample data set in step 5, updating the sample data set, and thus updating the Kriging proxy model;

[0015] Step 8, make a convergence judgment. If the optimization has reached the convergence condition, terminate the optimization design, compare the response values ​​of each sample point in the final sample data set, and obtain the sample point with the best response value. This sample point is fitted as the rotor airfoil obtained by the final optimization; otherwise, repeat steps 5 to 8.

[0016] Preferably, the forward design target is the drag coefficient of the rotor design airfoil in the design state when hovering, and the reverse design target is the local pressure distribution characteristics of the rotor design airfoil in the design state when flying forward. The objective function obj of the forward and reverse hybrid design combining the two is:

[0017]

[0018] in:

[0019] w1 and w2 are the weight coefficients of the forward design objective and the reverse design objective respectively;

[0020] obj direct Indicates the forward design goal; obj inverse Indicates the reverse design goal;

[0021] C d It represents the drag coefficient of the rotor design airfoil;

[0022] C d,baseline represents the drag coefficient of the reference airfoil;

[0023] Mach number Ma=0.6、design lift coefficient C l =0.6 and Reynolds number Re = 4.06 × 10 6 , representing the design state when hovering;

[0024] represents the pressure coefficient of the jth airfoil surface data point of the rotor design airfoil obtained in the current iteration calculation; wherein j=1,2,...,k, k represents the total number of airfoil surface data points of the rotor design airfoil;

[0025] represents the target pressure coefficient of the jth airfoil surface data point of the rotor design airfoil;

[0026] represents the pressure coefficient of the jth airfoil surface data point of the reference airfoil;

[0027] Mach number Ma=0.80~0.85, design lift coefficient C l =0.0, Reynolds number Re = Ma × 6.766 × 10 6 , representing the design status during forward flight.

[0028] Preferably, step 5 is as follows:

[0029] Step 5.1, the sample data set is represented as (S, y S ), where S represents the sample point set, S = [x (1) ,x (2) ,...,x (N) ] T , represents a total of N sample points, respectively: x (1) ,x (2) ,...,x (N) ; For sample point x (u) , u=1,2,...,N, is the value of the n-dimensional design variable; y S Represents the response value set, y S =[y (1) ,y(2) ,...,y (N) ] T ; Among them, for the response value y (u) , is the sample point x (u) Response value; Response value in, Represents the sample point x (u) The objective function response value of Represents the sample point x (u) The response value of the lth constraint function; where l = 1, 2, ..., N g , N g Indicates the number of constraint functions;

[0030] Step 5.2, construct the Kriging proxy model of the objective function and each constraint function respectively, the expression is as follows:

[0031]

[0032] Where: x is the design space The unknown sample points in

[0033] Represents the predicted response value of the surrogate model s(x) is the standard deviation of the predicted response value of the surrogate model; when the constructed surrogate model is the Kriging surrogate model of the objective function, and obj (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the objective function; when the constructed surrogate model is the Kriging surrogate model of the lth constraint function, and g,l (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the lth constraint function;

[0034] Represents the mean square error estimate of the predicted response value of the surrogate model; F = [1,…,1] T is a unit column vector;

[0035] and σ 2 are the global trend model and variance respectively; R and r are the correlation matrix and correlation vector respectively, and the expressions are as follows:

[0036]

[0037] R:=[R(x (u) ,x (v) )] uv

[0038] r:=[R(x (u) ,x)] u

[0039] Where: R() represents the correlation function; [R(x (u) ,x (v) )] uv The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) and sample point x (v) , the values ​​of their correlation functions are calculated; where v = 1, 2, ..., N; after the traversal is completed, the values ​​of all correlation functions form a correlation matrix R;

[0040] [R(x (u) ,x)] u The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) , and the values ​​of the correlation functions with the unknown sample point x are obtained; after the traversal is completed, the values ​​of all correlation functions form a correlation vector r.

[0041] Preferably, step 6 is as follows:

[0042] Step 6.1, based on the Kriging surrogate model, determine the sub-optimization problems of the first point-adding criterion, the second point-adding criterion, the third point-adding criterion and the fourth point-adding criterion, thereby obtaining four sub-optimization problems;

[0043] Step 6.2, using the hybrid sub-optimization method, the four sub-optimization problems are solved in parallel to obtain new sample points for each sub-optimization problem. Therefore, four new sample points are obtained, which are expressed as:

[0044] Preferably, the sub-optimization problem determined by the first point adding criterion, the second point adding criterion, the third point adding criterion and the fourth point adding criterion is:

[0045] (1) The sub-optimization problem determined by the first point addition criterion is:

[0046]

[0047] Where: I(x) is the improvement of the objective function; E[I(x)] is the expected value of I(x), expressed as follows:

[0048]

[0049] Where: y min is the current sample data set (S,y S ) in the optimal objective function response value; and obj (x) are the predicted response values ​​and their standard deviations of the proxy models of the objective function; Φ and φ are the standard normal cumulative distribution function and the standard normal distribution probability density function, respectively;

[0050] P g,l represents the probability of satisfying the lth constraint function, N g represents the number of constraint functions, P g,l The expression is as follows:

[0051]

[0052] in: and g,l (x) represents the predicted response value and its standard deviation of the proxy model of the lth constraint function;

[0053] (2) The sub-optimization problem determined by the second point addition criterion is:

[0054]

[0055] (3) The sub-optimization problem determined by the third point addition criterion is:

[0056]

[0057] Where: A is a custom constant, take A = 1;

[0058] (4) The sub-optimization problem determined by the fourth point addition criterion is:

[0059]

[0060] Where: P[I(x)] is the probability of the objective function improvement I(x), expressed as follows:

[0061]

[0062] Thus, each sub-optimization problem is obtained.

[0063] The present invention provides a rotor airfoil aerodynamic design method based on a forward and reverse hybrid design algorithm, which has the following advantages:

[0064] Through the present invention, in the process of forward optimization design of rotor airfoils with aerodynamic force as the target, flow characteristics such as local pressure distribution characteristics can be effectively integrated, providing guidance on airfoil flow characteristics for the automatic optimization process, improving the problem that the mathematical optimal solution may deviate from the optimal design problem that conforms to the physical principles of airfoil design, and significantly improving the engineering applicability of the design optimization solution. The 9% thick rotor airfoil designed by this method effectively improves the drag divergence characteristics in the forward flight state while reducing the aerodynamic drag in the hovering state. The comprehensive aerodynamic characteristics of the optimized airfoil are better than those of the reference airfoil. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A schematic flow chart of a rotor airfoil design method based on a forward and reverse hybrid design algorithm provided by the present invention;

[0066] Figure 2 is a schematic diagram of the geometric shape of the reference airfoil and the design space determined by it;

[0067] Figure 3 This is the pressure distribution characteristic diagram of the “double shock wave” target;

[0068] Figure 4 The schematic diagram of the optimized airfoil geometry using the rotor airfoil design method based on the forward and reverse hybrid design algorithm;

[0069] Figure 5 The pressure distribution diagram of the optimized airfoil in the hovering state using the rotor airfoil design method based on the forward and reverse hybrid design algorithm;

[0070] Figure 6 This is the pressure distribution diagram of the optimized airfoil in high-speed forward flight using the rotor airfoil design method based on the forward-reverse hybrid design algorithm;

[0071] Figure 7 The lift coefficient curve of the optimized airfoil in the low-speed maneuvering state using the rotor airfoil design method based on the forward and reverse hybrid design algorithm;

[0072] Figure 8 The drag coefficient curve of the optimized airfoil in the low-speed maneuvering state using the rotor airfoil design method based on the forward and reverse hybrid design algorithm;

[0073] Fig. 9 It is the moment curve diagram of the optimized airfoil in the low-speed maneuvering state using the rotor airfoil design method based on the forward and reverse hybrid design algorithm;

[0074] Fig.10 This is the lift-drag extreme curve of the optimized airfoil under low-speed maneuvering state using the rotor airfoil design method based on the forward and reverse hybrid design algorithm. DETAILED DESCRIPTION

[0075] The following describes in more detail exemplary embodiments of the present disclosure in conjunction with the accompanying drawings. In order to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art, exemplary embodiments of the present disclosure are shown in the accompanying drawings. It should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments described herein. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0076] For the aerodynamic design of rotor airfoils, the present invention provides a rotor airfoil optimization design method based on a forward and reverse hybrid design algorithm, which can effectively integrate the airfoil flow characteristics into the numerical optimization design, provide guidance for the automatic optimization process, enhance the engineering applicability of the optimization solution, and improve the comprehensive aerodynamic characteristics of the rotor airfoil.

[0077] See also Figure 1 The present invention provides a rotor airfoil design method based on a forward and reverse hybrid design algorithm, comprising the following steps:

[0078] Step 1: determine the reference airfoil of the rotor airfoil to be designed; use the CST airfoil parameterization method to parameterize the reference airfoil to obtain the CST parameters [A1, A2, …, A n ]; where A1, A2, …, A n is n CST parameters; for CST parameters [A1, A2, …, A n ] Make a certain disturbance δ to determine the design space of the design variables Among them, A i represents A1, A2, …, A n The i-th CST parameter in ; i = 1, 2, ..., n;

[0079] Step 2, determining the design state and design requirements of the rotor design airfoil under different flight conditions;

[0080] Step 3, determining the forward and reverse hybrid design objectives, including the forward design objectives and the reverse design objectives; the forward design objectives are direct design indicators including the aerodynamic force of the airfoil, and the reverse design objectives are flow characteristic design indicators of the airfoil flow including the local pressure distribution of the airfoil; combining the forward design objectives and the reverse design objectives, determining the objective function expression of the forward and reverse hybrid design; determining the constraint function expression according to the design requirements determined in step 2, thereby constructing an optimization mathematical model;

[0081] As an implementation mode, the forward design target is the drag coefficient of the rotor design airfoil in the design state when hovering, and the reverse design target is the local pressure distribution characteristics of the rotor design airfoil in the design state when flying forward. The objective function obj of the forward and reverse hybrid design combining the two is:

[0082]

[0083] in:

[0084] w1 and w2 are the weight coefficients of the forward design objective and the reverse design objective respectively;

[0085] obj direct Indicates the forward design goal; obj inverse Indicates the reverse design goal;

[0086] C d It represents the drag coefficient of the rotor design airfoil;

[0087] C d,baseline represents the drag coefficient of the reference airfoil;

[0088] Mach number Ma=0.6、design lift coefficient C l =0.6 and Reynolds number Re = 4.06 × 10 6 , representing the design state when hovering;

[0089] represents the pressure coefficient of the jth airfoil surface data point of the rotor design airfoil obtained in the current iteration calculation; wherein j=1,2,...,k, k represents the total number of airfoil surface data points of the rotor design airfoil;

[0090] represents the target pressure coefficient of the jth airfoil surface data point of the rotor design airfoil;

[0091] represents the pressure coefficient of the jth airfoil surface data point of the reference airfoil;

[0092] Mach number Ma=0.80~0.85, design lift coefficient C l =0.0, Reynolds number Re = Ma × 6.766 × 10 6 , representing the design status during forward flight.

[0093] Step 4: Use the experimental design method to calculate the design space determined in step 1. Extracting initial sample points, obtaining the response value of each initial sample point according to the objective function expression and constraint function expression of the forward and reverse hybrid design, and forming a sample data set; wherein the response value includes the objective function response value and the constraint function response value;

[0094] Step 5: construct a Kriging proxy model based on the sample data set;

[0095] Step 5 is as follows:

[0096] Step 5.1, the sample data set is represented as (S, y S ), where S represents the sample point set, S = [x (1) ,x (2) ,...,x (N) ] T , represents a total of N sample points, respectively: x (1) ,x (2) ,...,x (N) ; For sample point x (u) , u=1,2,...,N, is the value of the n-dimensional design variable; y S Represents the response value set, y S =[y (1) ,y (2) ,...,y (N) ] T ; Among them, for the response value y (u) , is the sample point x (u) Response value; Response value in, Represents the sample point x (u) The objective function response value of Represents the sample point x (u) The response value of the lth constraint function; where l = 1, 2, ..., N g , N g Indicates the number of constraint functions;

[0097] Step 5.2, construct the Kriging proxy model of the objective function and each constraint function respectively, the expression is as follows:

[0098]

[0099] Where: x is the design space The unknown sample points in

[0100] Represents the predicted response value of the surrogate model s(x) is the standard deviation of the predicted response value of the surrogate model; when the constructed surrogate model is the Kriging surrogate model of the objective function, and obj(x), respectively represent the predicted response value and its standard deviation of the surrogate model of the objective function; when the constructed surrogate model is the Kriging surrogate model of the lth constraint function, and g,l (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the lth constraint function;

[0101] Represents the mean square error estimate of the predicted response value of the surrogate model; F = [1,…,1] T is a unit column vector;

[0102] and σ 2 are the global trend model and variance respectively; R and r are the correlation matrix and correlation vector respectively, and the expressions are as follows:

[0103]

[0104] R:=[R(x (u) ,x (v) )] uv

[0105] r:=[R(x (u) ,x)] u

[0106] Where: R() represents the correlation function; [R(x (u) ,x (v) )] uv The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) and sample point x (v) , the values ​​of their correlation functions are calculated; where v = 1, 2, ..., N; after the traversal is completed, the values ​​of all correlation functions form a correlation matrix R;

[0107] [R(x (u) ,x)] u The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) , and the values ​​of the correlation functions with the unknown sample point x are obtained; after the traversal is completed, the values ​​of all correlation functions form a correlation vector r.

[0108] Step 6: Based on the Kriging proxy model, the combined parallel point addition criterion is used to determine the sub-optimization problem; the hybrid sub-optimization method is used to solve the determined sub-optimization problem, and multiple new sample points are obtained in one round of optimization;

[0109] Step 6 is as follows:

[0110] Step 6.1, based on the Kriging surrogate model, determine the sub-optimization problems of the first point-adding criterion, the second point-adding criterion, the third point-adding criterion and the fourth point-adding criterion, thereby obtaining four sub-optimization problems;

[0111] The sub-optimization problems determined by the first, second, third and fourth point-adding criteria are:

[0112] (1) The sub-optimization problem determined by the first point addition criterion is:

[0113]

[0114] Where: I(x) is the improvement of the objective function; E[I(x)] is the expected value of I(x), expressed as follows:

[0115]

[0116] Where: y min is the current sample data set (S,y S ) in the optimal objective function response value; and obj (x) are the predicted response values ​​and their standard deviations of the proxy models of the objective function; Φ and φ are the standard normal cumulative distribution function and the standard normal distribution probability density function, respectively;

[0117] P g,l represents the probability of satisfying the lth constraint function, N g represents the number of constraint functions, P g,l The expression is as follows:

[0118]

[0119] in: and g,l (x) represents the predicted response value and its standard deviation of the proxy model of the lth constraint function;

[0120] (2) The sub-optimization problem determined by the second point addition criterion is:

[0121]

[0122] (3) The sub-optimization problem determined by the third point addition criterion is:

[0123]

[0124] Where: A is a custom constant, take A = 1;

[0125] (4) The sub-optimization problem determined by the fourth point addition criterion is:

[0126]

[0127] Where: P[I(x)] is the probability of the objective function improvement I(x), expressed as follows:

[0128]

[0129] Thus, each sub-optimization problem is obtained.

[0130] Step 6.2, using the hybrid sub-optimization method, the four sub-optimization problems are solved in parallel to obtain new sample points for each sub-optimization problem. Therefore, four new sample points are obtained, which are expressed as:

[0131] Step 7, evaluating the newly added sample points obtained in step 6, adding the newly added sample points and their response values ​​to the sample data set in step 5, updating the sample data set, and thus updating the Kriging proxy model;

[0132] Step 8, make a convergence judgment. If the optimization has reached the convergence condition, terminate the optimization design, compare the response values ​​of each sample point in the final sample data set, and obtain the sample point with the best response value. This sample point is fitted as the rotor airfoil obtained by the final optimization; otherwise, repeat steps 5 to 8.

[0133] The following describes the method in conjunction with a specific implementation method:

[0134] Step 1: Determine a 9% thickness rotor airfoil as a reference airfoil; use the 8th order CST airfoil parameterization method to parameterize the reference airfoil to obtain the CST parameters [A1, A2, …, A 18 ], for CST parameters [A1,A2,…,A 18 ] Perturb up and down by 50% to determine the design space i=1,2,...,18; design space The design variables in are expressed as Design space Unknown sample point x in ;

[0135] Step 2, determine the design status and design requirements of the rotor design airfoil under different flight conditions; according to the design requirements of 9% rotor design airfoils in hovering, forward flight, and maneuvering states, the design status and design requirements under different flight conditions are determined as follows:

[0136]

[0137]

[0138] Where: M dd represents the drag divergence Mach number; α represents the airfoil angle of attack; C m Represents the pitching moment coefficient of the airfoil; C l represents the lift coefficient of the airfoil;

[0139] Step 3, determine the forward and reverse hybrid design objectives, the forward design objectives are direct design indicators such as airfoil aerodynamics, and the reverse design objectives are flow characteristics of the airfoil such as local pressure distribution of the airfoil;

[0140] In this case, the forward design target is the drag coefficient of the rotor design airfoil in the hovering state, and the reverse design target is the "double shock wave" local pressure distribution characteristics of the rotor design airfoil in the forward flight state. The objective function obj combining the two is:

[0141]

[0142] in:

[0143] w1 and w2 are the weight coefficients of the forward design objective and the reverse design objective respectively;

[0144] obj direct Indicates the forward design goal; obj inverse Indicates the reverse design goal;

[0145] C d It represents the drag coefficient of the rotor design airfoil;

[0146] C d,baseline represents the drag coefficient of the reference airfoil;

[0147] Mach number Ma=0.6、design lift coefficient C l =0.6 and Reynolds number Re = 4.06 × 10 6 , representing the design state when hovering;

[0148] represents the pressure coefficient of the jth airfoil surface data point of the rotor design airfoil obtained in the current iteration calculation; wherein j=1,2,...,k, k represents the total number of airfoil surface data points of the rotor design airfoil;

[0149] represents the target pressure coefficient of the jth airfoil surface data point of the rotor design airfoil;

[0150] represents the pressure coefficient of the jth airfoil surface data point of the reference airfoil;

[0151] Mach number Ma=0.80~0.85, design lift coefficient C l =0.0, Reynolds number Re = Ma × 6.766 × 10 6 , representing the design status during forward flight.

[0152] Combining the forward and reverse design goals, the objective function obj expression is given. According to the design requirements determined in step 2, the constraint function expression is given, and the corresponding optimization mathematical model is constructed as follows:

[0153]

[0154] Where: t represents the maximum relative thickness of the airfoil geometry; the subscript baseline represents the aerodynamic coefficient of the baseline airfoil, otherwise it is the aerodynamic coefficient of the rotor design airfoil.

[0155] Step 4: Use Latin hypercube sampling to select the design space determined in step 1. Extract initial sample points from the dataset, and evaluate the response value of each initial sample point, including the objective function response value and the constraint function response value, to form an initial sample data set;

[0156] Step 5: Based on the sample data set, construct the Kriging proxy model of the objective function and each constraint function. The expression is as follows:

[0157]

[0158] Where: x is the design space The unknown sample points in

[0159] Represents the predicted response value of the surrogate model s(x) is the standard deviation of the predicted response value of the surrogate model; when the constructed surrogate model is the Kriging surrogate model of the objective function, and obj (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the objective function; when the constructed surrogate model is the Kriging surrogate model of the lth constraint function, and g,l (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the lth constraint function;

[0160] Represents the mean square error estimate of the predicted response value of the surrogate model; F = [1,…,1] T is a unit column vector;

[0161] and σ 2 are the global trend model and variance respectively; R and r are the correlation matrix and correlation vector respectively, and the expressions are as follows:

[0162]

[0163] R:=[R(x (i) ,x (j) )] ij

[0164] r:=[R(x (i) ,x)] i

[0165] Wherein: R() represents the correlation function, and in this embodiment, a cubic spline function is selected; [R(x (u) ,x (v) )] uv The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) and sample point x (v) , the values ​​of their correlation functions are calculated; where v = 1, 2, ..., N; after the traversal is completed, the values ​​of all correlation functions form a correlation matrix R;

[0166] [R(x (u) ,x)] u The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) , and the values ​​of the correlation functions with the unknown sample point x are obtained; after the traversal is completed, the values ​​of all correlation functions form a correlation vector r.

[0167] Step 6: Based on the Kriging proxy model, the combined parallel adding point criterion is adopted to determine the sub-optimization problem; a hybrid sub-optimization method is adopted, and the Hooke-Jeeves pattern search, SQP gradient algorithm and genetic algorithm (GA) are used to solve the determined sub-optimization problem in parallel, and multiple new sample points are obtained in one round of optimization;

[0168] Step 7, evaluating the newly added sample points obtained in step 6, adding the newly added sample points and their response values ​​to the sample data set in step 5, updating the sample data set, and thus updating the Kriging proxy model;

[0169] Step 8, make a convergence judgment. If the optimization has reached the convergence condition, terminate the optimization design, compare the response values ​​of each sample point in the final sample data set, and obtain the sample point with the best response value. This sample point is fitted as the rotor airfoil obtained by the final optimization; otherwise, repeat steps 5 to 8.

[0170] Through the above steps, an optimal rotor airfoil is obtained by optimization design. The rotor airfoil satisfies all constraints and is stable in the hovering state (Ma = 0.6, C l =0.6,Re=4.06×10 6 ) is lowered, and the drag coefficient is reduced by 1.85% compared with the reference airfoil, and the forward design target is improved. l =0.0,Re=Ma×6.766×10 6 ), the pressure distribution on the lower surface of the rotor airfoil shows two shock waves, achieving the reverse design goal of the "double shock wave" pressure distribution characteristics, thereby reducing the drag coefficient of the rotor airfoil in this state by 6.62%. The optimized airfoil not only meets the requirement of maintaining lift characteristics in low-speed maneuvering state, but also takes into account the aerodynamic characteristics of the airfoil in hovering and forward flight states, and the comprehensive aerodynamic characteristics are improved.

[0171] Through the present invention, in the process of forward optimization design of rotor airfoils with aerodynamic force as the target, flow characteristics such as local pressure distribution characteristics can be effectively integrated, providing guidance on airfoil flow characteristics for the automatic optimization process, improving the problem that the mathematical optimal solution may deviate from the optimal design problem that conforms to the physical principles of airfoil design, and significantly improving the engineering applicability of the design optimization solution. The 9% thick rotor airfoil designed by this method effectively improves the drag divergence characteristics in the forward flight state while reducing the aerodynamic drag in the hovering state. The comprehensive aerodynamic characteristics of the optimized airfoil are better than those of the reference airfoil.

[0172] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be considered as the scope of protection of the present invention.

Claims

1. A rotor airfoil design method based on a forward and reverse hybrid design algorithm, characterized in that: The following steps are involved: Step 1, determining a reference airfoil of a rotor airfoil to be designed; The reference airfoil is parameterized using the CST airfoil parameterization method to obtain the CST parameters [A1, A2, …, A n ]; where A1, A2, …, A n is n CST parameters; for CST parameters [A1, A2, …, A n ] Make a certain disturbance δ to determine the design space of the design variables Among them, A i represents A1, A2, …, A n The i-th CST parameter in ; i = 1, 2, ..., n; Step 2, determining the design state and design requirements of the rotor design airfoil under different flight conditions; Step 3, determining the forward and reverse hybrid design objectives, including forward design objectives and reverse design objectives; the forward design objectives are direct design indicators including airfoil aerodynamics, and the reverse design objectives are flow characteristic design indicators of airfoil flow including local pressure distribution of airfoil; combining the forward design objectives and the reverse design objectives, determining the objective function expression of the forward and reverse hybrid design; determining the constraint function expression according to the design requirements determined in step 2, thereby constructing an optimization mathematical model; Step 4: Use the experimental design method to calculate the design space determined in step 1. Extracting initial sample points, obtaining the response value of each initial sample point according to the objective function expression and constraint function expression of the forward and reverse hybrid design, and forming a sample data set; wherein the response value includes the objective function response value and the constraint function response value; Step 5: construct a Kriging proxy model based on the sample data set; Step 6: Based on the Kriging proxy model, the combined parallel point addition criterion is used to determine the sub-optimization problem; the hybrid sub-optimization method is used to solve the determined sub-optimization problem, and multiple new sample points are obtained in one round of optimization; Step 7, evaluating the newly added sample points obtained in step 6, adding the newly added sample points and their response values ​​to the sample data set in step 5, updating the sample data set, and thus updating the Kriging proxy model; Step 8, make a convergence judgment. If the optimization has reached the convergence condition, terminate the optimization design, compare the response values ​​of each sample point in the final sample data set, and obtain the sample point with the best response value. This sample point is fitted as the rotor airfoil obtained by the final optimization; otherwise, repeat steps 5 to 8.

2. The rotor airfoil design method based on the forward and reverse hybrid design algorithm according to claim 1, characterized in that: The forward design target is the drag coefficient of the rotor design airfoil in the design state when hovering, and the reverse design target is the local pressure distribution characteristics of the rotor design airfoil in the design state when flying forward. The objective function obj of the forward and reverse hybrid design combining the two is: in: w1 and w2 are the weight coefficients of the forward design objective and the reverse design objective respectively; obj direct Indicates the forward design goal; obj inverse Indicates the reverse design goal; C d It represents the drag coefficient of the rotor design airfoil; C d,baseline represents the drag coefficient of the reference airfoil; Mach number Ma=0.6、design lift coefficient C l =0.6 and Reynolds number Re = 4.06 × 10 6 , representing the design state when hovering; represents the pressure coefficient of the jth airfoil surface data point of the rotor design airfoil obtained in the current iteration calculation; wherein j=1,2,...,k, k represents the total number of airfoil surface data points of the rotor design airfoil; represents the target pressure coefficient of the jth airfoil surface data point of the rotor design airfoil; represents the pressure coefficient of the jth airfoil surface data point of the reference airfoil; Mach number Ma=0.80~0.85, design lift coefficient C l = 0.0, Reynolds number Re = Ma × 6.766 × 10 6 , representing the design status during forward flight.

3. The rotor airfoil design method based on the forward and reverse hybrid design algorithm according to claim 1, characterized in that: Step 5 is as follows: Step 5.1, the sample data set is represented as (S, y S ), where S represents the sample point set, S = [x (1) ,x (2) ,...,x (N) ] T , represents a total of N sample points, respectively: x (1) ,x (2) ,...,x (N) ; For sample point x (u) , u=1,2,...,N, is the value of the n-dimensional design variable; y S Represents the response value set, y S =[y (1) ,y (2) ,...,y (N) ] T ; Among them, for the response value y (u) , is the sample point x (u) Response value; Response value in, Represents the sample point x (u) The objective function response value of Represents the sample point x (u) The response value of the lth constraint function; where l = 1, 2, ..., N g , N g Indicates the number of constraint functions; Step 5.2, construct the Kriging proxy model of the objective function and each constraint function respectively, the expression is as follows: Where: x is the design space The unknown sample points in Represents the predicted response value of the surrogate model s(x) is the standard deviation of the predicted response value of the surrogate model; when the constructed surrogate model is the Kriging surrogate model of the objective function, and obj (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the objective function; when the constructed surrogate model is the Kriging surrogate model of the lth constraint function, and g,l (x), respectively represent the predicted response value and its standard deviation of the surrogate model of the lth constraint function; Represents the mean square error estimate of the predicted response value of the surrogate model; F = [1,…,1] T is a unit column vector; and σ 2 are the global trend model and variance respectively; R and r are the correlation matrix and correlation vector respectively, and the expressions are as follows: R:=[R(x (u) ,x (v) )] uv r:=[R(x (u) ,x)] u Where: R() represents the correlation function; [R(x (u) ,x (v) )] uv The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) and sample point x (v) , the values ​​of their correlation functions are calculated; where v = 1, 2, ..., N; after the traversal is completed, the values ​​of all correlation functions form a correlation matrix R; [R(x (u) ,x)] u The meaning is: for the sample point set S = [x (1) ,x (2) ,...,x (N) ] T Traverse the sample points in, and for the traversed sample point x (u) , and the values ​​of the correlation functions with the unknown sample point x are obtained; after the traversal is completed, the values ​​of all correlation functions form a correlation vector r.

4. The rotor airfoil design method based on the forward and reverse hybrid design algorithm according to claim 3 is characterized in that: Step 6 is as follows: Step 6.1, based on the Kriging surrogate model, determine the sub-optimization problems of the first point-adding criterion, the second point-adding criterion, the third point-adding criterion and the fourth point-adding criterion, thereby obtaining four sub-optimization problems; Step 6.2, using the hybrid sub-optimization method, the four sub-optimization problems are solved in parallel to obtain new sample points for each sub-optimization problem. Therefore, four new sample points are obtained, which are expressed as:

5. The rotor airfoil design method based on the forward and reverse hybrid design algorithm according to claim 4, characterized in that: The sub-optimization problems determined by the first, second, third and fourth point-adding criteria are: (1) The sub-optimization problem determined by the first point addition criterion is: Where: I(x) is the improvement of the objective function; E[I(x)] is the expected value of I(x), expressed as follows: Where: y min is the current sample data set (S,y S ) in the optimal objective function response value; and obj (x) are the predicted response values ​​and their standard deviations of the proxy models of the objective function; Φ and φ are the standard normal cumulative distribution function and the standard normal distribution probability density function, respectively; P g,l represents the probability of satisfying the lth constraint function, N g represents the number of constraint functions, P g,l The expression is as follows: in: and g,l (x) represents the predicted response value and its standard deviation of the proxy model of the lth constraint function; (2) The sub-optimization problem determined by the second point addition criterion is: (3) The sub-optimization problem determined by the third point addition criterion is: Where: A is a custom constant, take A = 1; (4) The sub-optimization problem determined by the fourth point addition criterion is: Where: P[I(x)] is the probability of the objective function improvement I(x), expressed as follows: Thus, each sub-optimization problem is obtained.

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