Aerofoil profile geometric parameterization method of self-adaptive order, program, equipment and storage medium

Abstract

The invention relates to the technical field of airfoil profile optimization design, and particularly discloses an airfoil profile geometric parameterization method and program with self-adaptive orders, equipment and a storage medium. The method aims to solve the problem that precision and efficiency are difficult to balance due to the fact that the order of a Bernstein polynomial depends on manual presetting in an existing CST parameterization technology. According to the core scheme, the method comprises the steps of obtaining airfoil profile coordinate data and performing normalization processing; determining a class function according to the airfoil profile type; automatically searching and determining the optimal order of the Bernstein polynomial by combining a genetic optimization algorithm and taking the relative change rate of the fitting error as a judgment criterion; and constructing a parameterized model based on the optimal order and outputting geometric parameters. The method has the beneficial effects that the self-adaptive determination of the order is realized, overfitting and calculation redundancy are effectively avoided, the design efficiency is improved while the precision is ensured, and the method has good universality and is suitable for parameterization design of various airfoils.

Description

Technical Field

[0001] This invention relates to the field of airfoil optimization design technology, and in particular to a method, program, device, and storage medium for airfoil geometry parameterization with self-adaptive order. Background Technology

[0002] Airfoil geometry parameterization is a core step in the aerodynamic design process of aerospace vehicles. Its core function is to transform the complex two-dimensional profile curves of the airfoil into design parameters with controllable quantity and clear physical meaning. The accuracy and efficiency of the parameterization results directly determine the reliability and cycle time of subsequent aerodynamic analysis and shape optimization.

[0003] Among numerous parametric methods, the Class-Shape Transformation (CST) method has become one of the mainstream technologies in the field of airfoil design both domestically and internationally due to its significant advantages of fewer parameters, strong profile controllability, and wide adaptability. The CST method constructs an airfoil profile model through the product of a class function and a shape function. The class function defines the basic category characteristics of the airfoil, while the shape function is responsible for depicting the detailed profile of the airfoil. The core building block of the shape function is the Bernstein polynomial, whose characteristics directly affect the modeling capability of the CST method.

[0004] Current CST parametric technology still faces key bottlenecks in engineering applications. The order of the Bernstein polynomial needs to be manually preset and cannot be adaptively adjusted according to the profile complexity of the target airfoil. This deficiency leads to a common dilemma in the actual design process: on the one hand, for symmetrical airfoils with simple profiles, if the preset polynomial order is too high, it will result in redundant parameters of the shape function, which will not only increase the computational load of subsequent aerodynamic optimization but may also introduce overfitting, making the model overly sensitive to local noise of the original airfoil and reducing the stability of the parametric results. On the other hand, for airfoils with complex profiles, if the preset order is too low, the Bernstein polynomial's fitting ability is insufficient, and it cannot accurately reproduce the blunt characteristics of the airfoil's leading edge, the turning structure of the trailing edge flap, or the local bulge morphology of the airfoil surface. This will cause the deviation between the parametric model and the original airfoil to exceed the allowable range in engineering, thus affecting the accuracy of subsequent aerodynamic performance calculations. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned prior art by providing a method, program, device, and storage medium for airfoil geometry parameterization with an adaptive order. This invention automatically determines the optimal order of the Bernstein polynomial through a genetic optimization algorithm, ensuring airfoil fitting accuracy while avoiding overfitting and reducing computational costs, thereby achieving automation and intelligence in airfoil parameterization.

[0006] This invention proposes a method, program, device, and storage medium for airfoil geometry parameterization with self-adaptive order, the core of which includes the following technical solutions:

[0007] A self-adaptive order airfoil geometry parameterization method includes the following steps:

[0008] Step 1: Obtain the actual coordinate dataset of the airfoil, including the upper surface, lower surface, leading edge, and trailing edge, as well as the airfoil type data; set the maximum order and initialize the order.

[0009] Step 2: Using the chord length of the airfoil as a reference, normalize the airfoil profile coordinate dataset to obtain a normalized coordinate vector.

[0010] Step 3: Based on the airfoil type data and normalized coordinates, determine the class function and obtain the class function vector.

[0011] Step 4: Based on the normalized coordinates and combined with the genetic optimization algorithm, optimize the shape function to obtain the optimized shape function.

[0012] Step 5: Calculate the airfoil geometric parameterized ordinate vector based on the class function and the optimized shape function.

[0013] Step 6: Calculate the fitting error for the current order based on the normalized coordinate vector and the airfoil geometric parameterized ordinate vector.

[0014] Step 7: Determine if the current order has reached the maximum order. If so, the process ends, output the current order and airfoil geometric parameters, and complete the geometric parameterization of the airfoil; otherwise, calculate the relative rate of change of the fitting error and proceed to the next step.

[0015] Step 8: Check if the relative rate of change of the fitting error is greater than the threshold. If so, update the order and return to step 4; otherwise, output the current order as the optimal order and output the airfoil geometric parameters at the same time to complete the geometric parameterization of the airfoil.

[0016] Furthermore, the normalized coordinate vector described in step 2 The specific calculation methods include:

[0017] For each actual coordinate point of the airfoil in the actual coordinate dataset, normalization is performed to obtain normalized coordinate points. ;

[0018]

[0019] in, For the first The actual coordinates of each airfoil. The chord length of the airfoil, , This represents the actual number of coordinate points of the airfoil.

[0020] Combine all normalized coordinate points into a vector form to obtain the normalized coordinate vector. ;

[0021]

[0022]

[0023] in, This is for transpose calculation.

[0024] Further, step 3 involves determining the class function to obtain the class function vector. The methods specifically include:

[0025]

[0026] in, and These are all function parameters, and their values ​​are determined based on the airfoil type; This is an element-by-element calculation.

[0027] Furthermore, the shape function described in step 4 includes the Bernstein polynomial basis function matrix. and Bernstein polynomial coefficient vector :

[0028]

[0029]

[0030]

[0031] in, Let be the order of the Bernstein polynomial. The exponent is the polynomial index, and the exponent is the factorial symbol. To design the matrix.

[0032] Furthermore, the airfoil geometric parameterization ordinate vector described in step 5 The specific calculation methods include:

[0033] .

[0034] Furthermore, the fitting error of the current order The specific calculation methods include:

[0035]

[0036] in, For the airfoil geometry parameterized ordinate vector In the middle, the first The ordinate of the geometric parameters of each airfoil.

[0037] Furthermore, the relative rate of change of the fitting error The specific calculation methods include:

[0038]

[0039] in, The order is The fitting error at that time.

[0040] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described above.

[0041] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0042] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the method described above.

[0043] The beneficial effects of this invention are as follows: First, it exhibits strong adaptability, eliminating the need for manually pre-setting the Bernstein polynomial order. Instead, it automatically matches the complexity of the airfoil profile through a genetic algorithm, thus solving the problem of order selection relying on experience, effectively reducing the trial-and-error costs for engineers, and shortening the airfoil design cycle. Second, this method balances accuracy and efficiency, ensuring that the fitting accuracy meets engineering requirements while avoiding overfitting and computational redundancy caused by excessively high orders. This helps reduce the computational load of subsequent aerodynamic optimization and improves overall design efficiency. Finally, this technology has wide applicability, not only suitable for various airfoils such as symmetrical airfoils, asymmetrical airfoils, supercritical airfoils, and high-lift airfoils, but also able to flexibly adapt to airfoil design requirements in different scenarios by adjusting the class function form and fitness weight coefficients. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the process of the present invention.

[0045] Figure 2 This is a comparison diagram of the fitting curve of the SD7032 airfoil by the 8th order CST method in an embodiment of the present invention and the original SD7032 airfoil.

[0046] Figure 3 This is a graph showing the fitting error of the SD7032 airfoil using CST methods of different orders in embodiments of the present invention. Detailed Implementation

[0047] The following is combined Figure 1 , Figure 2 and Figure 3 The present invention will be further described below.

[0048] A self-adaptive order airfoil geometry parameterization method includes the following steps:

[0049] Step 1: Obtain the actual coordinate dataset of the airfoil, including the upper surface, lower surface, leading edge, and trailing edge, as well as the airfoil type data; set the maximum order and initialize the order.

[0050] Step 2: Using the chord length of the airfoil as a reference, normalize the airfoil profile coordinate dataset to obtain a normalized coordinate vector.

[0051] The normalized coordinate vector The specific calculation methods include:

[0052] For each actual coordinate point of the airfoil in the actual coordinate dataset, normalization is performed to obtain normalized coordinate points. ;

[0053]

[0054] in, For the first The actual coordinates of each airfoil. The chord length of the airfoil, , This represents the actual number of coordinate points of the airfoil.

[0055] Combine all normalized coordinate points into a vector form to obtain the normalized coordinate vector. ;

[0056]

[0057]

[0058] in, This is for transpose calculation.

[0059] Step 3: Based on the airfoil type data and normalized coordinates, determine the class function and obtain the class function vector.

[0060] The determined class function is used to obtain the class function vector. The methods specifically include:

[0061]

[0062] in, and These are all function parameters, and their values ​​are determined based on the airfoil type; This is an element-by-element calculation.

[0063] Step 4: Based on the normalized coordinates and combined with the genetic optimization algorithm, optimize the shape function to obtain the optimized shape function.

[0064] The shape functions include Bernstein polynomial basis function matrices. and Bernstein polynomial coefficient vector ;

[0065]

[0066]

[0067]

[0068] in, Let be the order of the Bernstein polynomial. The exponent is the polynomial index, and the exponent is the factorial symbol. To design the matrix.

[0069] Step 5: Calculate the airfoil geometric parameterized ordinate vector based on the class function and the optimized shape function.

[0070] The geometric parameterized ordinate vector of the airfoil The specific calculation methods include:

[0071] .

[0072] Step 6: Calculate the fitting error for the current order based on the normalized coordinate vector and the airfoil geometric parameterized ordinate vector.

[0073] The fitting error of the current order The specific calculation methods include:

[0074]

[0075] in, For the airfoil geometry parameterized ordinate vector In the middle, the first The ordinate of the geometric parameters of each airfoil.

[0076] Step 7: Determine if the current order has reached the maximum order. If so, the process ends, output the current order and airfoil geometric parameters, and complete the geometric parameterization of the airfoil; otherwise, calculate the relative rate of change of the fitting error and proceed to the next step.

[0077] The relative rate of change of the fitting error The specific calculation methods include:

[0078]

[0079] in, The order is The fitting error at that time.

[0080] Step 8: Check if the relative rate of change of the fitting error is greater than the threshold. If so, update the order and return to step 4; otherwise, output the current order as the optimal order and output the airfoil geometric parameters at the same time to complete the geometric parameterization of the airfoil.

[0081] Example

[0082] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0083] This embodiment relates to a self-adaptive order airfoil geometry parameterization method, which mainly focuses on self-adapting the order of the CST equation. Figure 1 The flowchart includes the following:

[0084] Step S1: Select the airfoil that needs to be geometrically parameterized; collect the contour coordinate data of the target airfoil, including the coordinate points of the leading and trailing edges of the upper and lower surfaces, and normalize the coordinates to the 0-1 range based on the airfoil chord length;

[0085] Step S2: Determine appropriate class function coefficients based on the airfoil type to perfectly fit the airfoil;

[0086] Step S3: Optimize the CST parameterization method based on the genetic optimization algorithm. The optimization variable is the order of the CST parameterization method, and the optimization objective is that the relative change rate of the fitting error between the two orders is less than 5%.

[0087] Step S4: Based on the Bernstein polynomial of a determined order, construct the CST parameterized equation and solve the Bernstein polynomial coefficients using the selected airfoil coordinates.

[0088] Step S5: Construct the CST parameterized equation using the Bernstein polynomial coefficients obtained in Step S4, input the x-coordinate of the airfoil, and solve for the y-coordinate of the airfoil.

[0089] Step S6: Calculate the fitting error according to the fitting error calculation formula. If the relative rate of change of the fitting error between the two orders is less than 5%, the optimal solution is obtained. At this time, the order of the Bernstein polynomial minus 1 is the order of the CST method; otherwise, continue to optimize.

[0090] Furthermore, in step S1, the airfoil coordinates need to be normalized based on the chord length, i.e., satisfying the following relationship:

[0091]

[0092] In the formula, These are the normalized coordinates along the chord length of the airfoil. This represents the actual coordinates of the airfoil along the chord length. This represents the actual chord length of the airfoil. Similarly, the airfoil's... The coordinates must also be divided by the chord length accordingly, satisfying the following relationship:

[0093]

[0094] Preferably, the sampling should cover the upper wing surface, lower wing surface, leading edge arc and trailing edge area, with no less than 50 sampling points along the chord direction. The leading edge area requires more frequent sampling due to the sudden change in curvature.

[0095] Furthermore, the CST parameterization method describes the airfoil's geometry through the product of a class function and a shape function, satisfying the following:

[0096]

[0097] In the formula, The function represents airfoil coordinates. The function; The shape function representing the airfoil is the airfoil coordinate system. The function.

[0098] Furthermore, the formula responsible for controlling the specific geometric details of the airfoil is shown below:

[0099]

[0100] In the formula, This represents the Bernstein polynomial weight coefficient matrix. Let represent the Bernstein polynomial basis function matrix.

[0101]

[0102] In the formula, represents the order of the Bernstein polynomial;

[0103] Furthermore, the formula for the class function in step S2 is as follows:

[0104]

[0105] Preferably, airfoils can be classified according to their airfoil shape, and a suitable airfoil shape type can be selected based on the type of airfoil to be fitted. and When the airfoil to be fitted is a round-nosed, pointed-tail-edge airfoil, and Take values ​​of 0.5 and 1 respectively, as in the NACA series airfoils.

[0106] Furthermore, formula (2) can be written in the following form:

[0107]

[0108] Furthermore, the errors in the airfoil coordinates and the airfoil coordinates obtained through CST parameterization are defined as follows:

[0109]

[0110] In the formula, This indicates the airfoil fitting error. Indicates the normalized airfoil coordinate, This represents the airfoil coordinates obtained through the CST parameterization method.

[0111] Furthermore, the relative rate of change of the fitting error is defined as follows:

[0112]

[0113] Furthermore, in the CST parameterization method of step S3, the Bernstein polynomial order of formula (4) is... As an optimization variable, the relative change rate of fitting error in formula (8) is less than 5% is set as the optimization objective.

[0114] Preferably, the order is set to a range of 3 to 12 to avoid insufficient fitting accuracy due to too low an order or parameter redundancy due to too high an order.

[0115] Furthermore, during the optimization process, the least squares method is used to solve for the Bernstein polynomial coefficient matrix of different orders in formula (6). At this point, the CST equations are transformed into a system of linear equations:

[0116]

[0117] Substituting formula (10) into formula (7) yields:

[0118]

[0119] Furthermore, by solving the linear equation system using the least squares method (11), the Bernstein polynomial coefficient matrix is ​​obtained. for:

[0120]

[0121] In the formula, The inverse matrix of the product is ensured to be invertible through singular value decomposition to avoid numerical ill-conditioning.

[0122] Furthermore, such as Figure 2 As shown, the Bernstein polynomial coefficient matrix is ​​obtained using the least squares method. Substituting into formula (6), by inputting the airfoil's... Using coordinates to solve for the corresponding airfoil coordinate.

[0123] Furthermore, such as Figure 3 As shown, the residuals of the airfoil fitting are calculated using formula (7). and The relative rate of change of the fitting residuals between orders is less than 5%. The Bernstein polynomial of order 1 is the optimal order.

[0124] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for parameterizing airfoil geometry with a self-adaptive order, characterized in that, Includes the following steps: Step 1: Obtain the actual coordinate dataset of the airfoil, including the upper surface, lower surface, leading edge, and trailing edge, as well as airfoil type data; Set the maximum order and initialize the order; Step 2: Using the chord length of the airfoil as a reference, normalize the airfoil profile coordinate dataset to obtain a normalized coordinate vector; Step 3: Based on the airfoil type data and normalized coordinates, determine the class function and obtain the class function vector; Step 4: Based on the normalized coordinates and combined with the genetic optimization algorithm, optimize the shape function to obtain the optimized shape function; Step 5: Calculate the airfoil geometric parameterized ordinate vector based on the class function and the optimized shape function; Step 6: Calculate the fitting error for the current order based on the normalized coordinate vector and the airfoil geometric parameterized ordinate vector; Step 7: Determine if the current order has reached the maximum order. If so, the process ends, output the current order and airfoil geometric parameters, and complete the geometric parameterization of the airfoil; otherwise, calculate the relative rate of change of the fitting error and proceed to the next step. Step 8: Check if the relative rate of change of the fitting error is greater than the threshold. If so, update the order and return to step 4; otherwise, output the current order as the optimal order and output the airfoil geometric parameters at the same time to complete the geometric parameterization of the airfoil.

2. The method for self-adaptive order airfoil geometry parameterization according to claim 1, characterized in that, The normalized coordinate vector in step 2 The specific calculation methods include: For each actual coordinate point of the airfoil in the actual coordinate dataset, normalization is performed to obtain normalized coordinate points. ; in, For the first The actual coordinates of each airfoil. The chord length of the airfoil, , This represents the actual number of coordinate points for the airfoil. Combine all normalized coordinate points into a vector form to obtain the normalized coordinate vector. ; in, This is for transpose calculation.

3. The method for self-adaptive order airfoil geometry parameterization according to claim 2, characterized in that, Step 3 involves determining the class function to obtain the class function vector. The methods specifically include: in, and These are all function parameters, and their values ​​are determined based on the airfoil type; This is an element-by-element calculation.

4. The airfoil geometry parameterization method with self-adaptive order according to claim 3, characterized in that, The shape functions mentioned in step 4 include the Bernstein polynomial basis function matrix. and Bernstein polynomial coefficient vector : in, Let be the order of the Bernstein polynomial. The exponent is the polynomial index, and the exponent is the factorial symbol. To design the matrix.

5. The method for self-adaptive order airfoil geometry parameterization according to claim 4, characterized in that, Step 5 describes the airfoil geometric parameterization of the ordinate vector. The specific calculation methods include: 。 6. The method for self-adaptive order airfoil geometry parameterization according to claim 5, characterized in that, The fitting error of the current order The specific calculation methods include: in, For the airfoil geometry parameterized ordinate vector In the middle, the first The ordinate of the geometric parameters of each airfoil.

7. The method for self-adaptive order airfoil geometry parameterization according to claim 6, characterized in that, The relative rate of change of the fitting error The specific calculation methods include: in, The order is The fitting error at that time.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method of claim 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the method of claim 7.

10. A computer program product comprising computer instructions, characterized in that: When the computer instructions are executed by the processor, they implement the steps of the method of claim 7.

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