Aerodynamic design method of rotor airfoil based on forward-inverse hybrid design algorithm

Abstract

The present invention provides a rotor airfoil design method based on a forward-inverse hybrid design algorithm, the method comprising: determining a reference airfoil; determining the design variables and design space of the rotor design airfoil to be designed; determining the forward design target and the inverse design target of the rotor design airfoil, and providing an objective function expression of the forward-inverse hybrid design; using an experimental design method to randomly sample initial sample points within a given design space to form a sample data set; establishing a proxy model based on the sample data set, obtaining new sample points by combining a parallel point addition criterion and a sub-optimization method, calculating their response values ​​for updating the proxy model, and repeating the above process until convergence. The rotor airfoil designed by the present invention can simultaneously take into account the aerodynamic characteristics of the airfoil under both the forward design target and the inverse design target, effectively improving the comprehensive performance of the airfoil, and improving the efficiency and practicality of the rotor airfoil design.

Description

Technical Field

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

[0002] As a fundamental element of the rotor, the airfoil is a key factor affecting rotor performance. Rotor airfoil performance significantly impacts key helicopter performance, including hovering, forward flight, maneuvering, payload, flight ceiling, range / time, maneuverability, and noise and vibration levels.

[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 operating 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 in the present invention is as follows:

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

[0008] Step 1: Determine the reference airfoil of the rotor airfoil to be designed; parameterize the reference airfoil 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 nThe i-th CST parameter in ; i = 1, 2, ..., n;

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

[0010] Step 3: Determine the forward-inverse hybrid design objectives, including forward design objectives and inverse design objectives; the forward design objectives are direct design indicators including the aerodynamic force of the airfoil, and the inverse design objectives are flow characteristic design indicators of the airfoil flow including the local pressure distribution of the airfoil; determine the objective function expression of the forward-inverse hybrid design by combining the forward design objectives and the inverse design objectives; determine the constraint function expression based on the design requirements determined in step 2, and thereby construct an optimization mathematical model;

[0011] Step 4: Use the experimental design method to determine the design space in step 1. Extracting initial sample points, and obtaining the response value of each initial sample point according to the objective function expression and constraint function expression of the forward and inverse hybrid design to form 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 surrogate model, a combined parallel addition criterion is used to determine the sub-optimization problem; a 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: Evaluate the newly added sample points obtained in step 6, add the newly added sample points and their response values ​​to the sample data set in step 5, update the sample data set, and thus update the Kriging proxy model;

[0015] Step 8: Perform convergence judgment. If the optimization has reached the convergence condition, the optimization design is terminated, and the response values ​​of each sample point in the final sample data set are compared to 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 objective is the drag coefficient of the rotor airfoil in the design state when hovering, and the inverse design objective is the local pressure distribution characteristics of the rotor airfoil in the design state when flying forward. The objective function obj of the forward and inverse hybrid design combining the two is:

[0017]

[0018] in:

[0019] w1 and w2 are the weight coefficients of the forward design goal and the reverse design goal 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; where j = 1, 2, ..., k, and 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 the sample point x (u) , u=1,2,...,N, is the value of 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] In step 5.2, construct the Kriging surrogate model of the objective function and each constraint function respectively. The expressions are 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 s obj (x), respectively represent the predicted response value and 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, the and s 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 points 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 the 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 points 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, second, third, and fourth addition criteria, thereby obtaining four sub-optimization problems;

[0043] In step 6.2, the hybrid sub-optimization method is used to solve the four sub-optimization problems 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, second, third and fourth addition criteria 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), which is 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 s 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 s g,l (x) represents the predicted response value and its standard deviation of the surrogate 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), which is expressed as follows:

[0061]

[0062] This leads to the sub-optimization problems.

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

[0064] This invention effectively incorporates flow characteristics, such as local pressure distribution, into the aerodynamically targeted forward optimization of rotor airfoils. This provides guidance for the airfoil flow characteristics during the automated optimization process, mitigates the potential deviation of the mathematically optimal solution from the optimal design that adheres to the physical principles of airfoil design, and significantly enhances the engineering applicability of the optimized design solution. A 9% thick rotor airfoil designed using this method reduces aerodynamic drag in hovering while effectively improving drag divergence in forward flight. The optimized airfoil exhibits superior overall aerodynamic characteristics to the baseline airfoil. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0066] Figure 2 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 Schematic diagram of the optimized airfoil geometry using the rotor airfoil design method based on the forward-inverse hybrid design algorithm;

[0069] Figure 5 This is 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-inverse hybrid design algorithm;

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

[0072] Figure 8 This is a graph showing the drag coefficient of the optimized airfoil in low-speed maneuvering state using the rotor airfoil design method based on the forward-inverse hybrid design algorithm;

[0073] Figure 9 This is a torque curve diagram of the optimized airfoil in low-speed maneuvering state using the rotor airfoil design method based on the forward-inverse hybrid design algorithm;

[0074] Figure 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 exemplary embodiments of the present disclosure in more detail with reference to 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 disclosure and the features in the embodiments can be combined with each other unless there is a conflict.

[0076] For the aerodynamic design of rotor airfoils, the present invention provides a rotor airfoil optimization design method based on a forward-inverse 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 Figure 1 The present invention provides a rotor airfoil design method based on a forward-inverse hybrid design algorithm, comprising the following steps:

[0078] Step 1: Determine the reference airfoil of the rotor airfoil to be designed; parameterize the reference airfoil 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;

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

[0080] Step 3: Determine the forward-inverse hybrid design objectives, including forward design objectives and inverse design objectives; the forward design objectives are direct design indicators including the aerodynamic force of the airfoil, and the inverse design objectives are flow characteristic design indicators of the airfoil flow including the local pressure distribution of the airfoil; determine the objective function expression of the forward-inverse hybrid design by combining the forward design objectives and the inverse design objectives; determine the constraint function expression based on the design requirements determined in step 2, and thereby construct an optimization mathematical model;

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

[0082]

[0083] in:

[0084] w1 and w2 are the weight coefficients of the forward design goal and the reverse design goal 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; where j = 1, 2, ..., k, and 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 determine the design space in step 1. Extracting initial sample points, and obtaining the response value of each initial sample point according to the objective function expression and constraint function expression of the forward and inverse hybrid design to form 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 the sample point x (u) , u=1,2,...,N, is the value of 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] In step 5.2, construct the Kriging surrogate model of the objective function and each constraint function respectively. The expressions are 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 s obj(x), respectively represent the predicted response value and 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, the and s 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 points 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 the 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 points 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 surrogate model, a combined parallel addition criterion is used to determine the sub-optimization problem; a 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, second, third, and fourth addition criteria, thereby obtaining four sub-optimization problems;

[0111] The sub-optimization problems determined by the first, second, third and fourth addition 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), which is 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 s 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 s g,l (x) represents the predicted response value and its standard deviation of the surrogate 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), which is expressed as follows:

[0128]

[0129] This leads to the sub-optimization problems.

[0130] In step 6.2, the hybrid sub-optimization method is used to solve the four sub-optimization problems 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: Evaluate the newly added sample points obtained in step 6, add the newly added sample points and their response values ​​to the sample data set in step 5, update the sample data set, and thus update the Kriging proxy model;

[0132] Step 8: Perform convergence judgment. If the optimization has reached the convergence condition, the optimization design is terminated, and the response values ​​of each sample point in the final sample data set are compared to 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 the 9% thickness rotor airfoil as the reference airfoil; parameterize the reference airfoil using the 8th order CST airfoil parameterization method 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 airfoil under different flight conditions. Based on the design requirements of the 9% rotor airfoil under hovering, forward flight, and maneuvering conditions, 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 Indicates 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 objective is the direct design index such as the airfoil aerodynamic force, and the reverse design objective is the flow characteristics of the airfoil such as the local pressure distribution of the airfoil.

[0140] In this case, the forward design objective is the drag coefficient of the designed rotor airfoil in the hovering state, and the inverse design objective is the "double shock wave" local pressure distribution characteristics of the designed rotor 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 goal and the reverse design goal 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; where j = 1, 2, ..., k, and 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 s obj (x), respectively represent the predicted response value and 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, the and s 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, the 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 points 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 the 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 points 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 surrogate model, a combined parallel addition criterion is used to determine the sub-optimization problem. A hybrid sub-optimization method is used, which simultaneously employs the Hooke-Jeeves pattern search, the SQP gradient algorithm, and the genetic algorithm (GA) to solve the determined sub-optimization problem in parallel, obtaining multiple new sample points in one round of optimization.

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

[0169] Step 8: Perform convergence judgment. If the optimization has reached the convergence condition, the optimization design is terminated, and the response values ​​of each sample point in the final sample data set are compared to 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 reduced, and the drag coefficient is reduced by 1.85% compared with the baseline airfoil, and the forward design target is improved. In the forward flight state (Ma=0.835, C l =0.0,Re=Ma×6.766×10 6 ), the rotor airfoil's lower surface pressure distribution exhibits two shock waves, achieving the reverse design goal of the "double shock wave" pressure distribution characteristic, thereby reducing the rotor airfoil's drag coefficient by 6.62% in this state. The optimized airfoil maintains lift characteristics during low-speed maneuvers while also taking into account the aerodynamic characteristics of the airfoil in hover and forward flight, resulting in improved overall aerodynamic characteristics.

[0171] This invention effectively incorporates flow characteristics, such as local pressure distribution, into the aerodynamically targeted forward optimization of rotor airfoils. This provides guidance for the airfoil flow characteristics during the automated optimization process, mitigates the potential deviation of the mathematically optimal solution from the optimal design that adheres to the physical principles of airfoil design, and significantly enhances the engineering applicability of the optimized design solution. A 9% thick rotor airfoil designed using this method reduces aerodynamic drag in hovering while effectively improving drag divergence in forward flight. The optimized airfoil exhibits superior overall aerodynamic characteristics to the baseline 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 principles of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A rotor airfoil design method based on a forward-inverse 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 CST airfoil parameterization method is used to parameterize the reference airfoil, and 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 airfoil under different flight conditions; Step 3: Determine the forward-inverse hybrid design objectives, including forward design objectives and inverse design objectives; the forward design objectives are direct design indicators including the aerodynamic force of the airfoil, and the inverse design objectives are flow characteristic design indicators of the airfoil flow including the local pressure distribution of the airfoil; determine the objective function expression of the forward-inverse hybrid design by combining the forward design objectives and the inverse design objectives; determine the constraint function expression based on the design requirements determined in step 2, and thereby construct an optimization mathematical model; Step 4: Use the experimental design method to determine the design space in step 1. Extracting initial sample points, and obtaining the response value of each initial sample point according to the objective function expression and constraint function expression of the forward and inverse hybrid design to form 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 surrogate model, a combined parallel addition criterion is used to determine the sub-optimization problem; a 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: Evaluate the newly added sample points obtained in step 6, add the newly added sample points and their response values ​​to the sample data set in step 5, update the sample data set, and thus update the Kriging proxy model; Step 8: Perform convergence judgment. If the optimization has reached the convergence condition, the optimization design is terminated, and the response values ​​of each sample point in the final sample data set are compared to 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-inverse hybrid design algorithm according to claim 1, characterized in that: The forward design objective is the drag coefficient of the rotor airfoil in the design state when hovering, and the reverse design objective is the local pressure distribution characteristics of the rotor 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 goal and the reverse design goal 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; where j = 1, 2, ..., k, and 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-inverse 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 the sample point x (u) , u=1,2,...,N, is the value of 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; In step 5.2, construct the Kriging surrogate model of the objective function and each constraint function respectively. The expressions are 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 s obj (x), respectively represent the predicted response value and 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, the and s 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 points 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 the 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 points 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-inverse hybrid design algorithm according to claim 3, 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, second, third, and fourth addition criteria, thereby obtaining four sub-optimization problems; In step 6.2, the hybrid sub-optimization method is used to solve the four sub-optimization problems 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-inverse hybrid design algorithm according to claim 4, characterized in that: The sub-optimization problems determined by the first, second, third and fourth addition 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), which is expressed as follows: Where: y min is the current sample data set (S,y S ) in the optimal objective function response value; and s 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 s g,l (x) represents the predicted response value and its standard deviation of the surrogate 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), which is expressed as follows: This leads to the sub-optimization problems.

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