A data-driven airfoil optimization algorithm

Abstract

The application discloses a kind of airfoil optimization algorithm based on data driving, it is related to CFD and artificial intelligence technical field, its target is to improve its aerodynamic characteristics by optimizing airfoil shape.First, airfoil geometry is modeled, and the geometry information is extracted into the information of five dimensions of maximum radian, maximum radian position, maximum thickness, maximum thickness position, leading edge radius index in the format of NACA-4 SERIES-MODIFIED, which will be used as the data characteristics of airfoil geometry.After that, the data characteristic space of airfoil geometry is fully sampled, and the airfoil geometry database to be labeled is obtained.Next, the airfoil data is labeled by CAE software, and the lift coefficient and drag coefficient under different attack angles are calculated.Then, the deep neural network is trained on the labeled database to obtain a differentiable proxy model.Finally, the trained proxy model is used to optimize the shape of the airfoil to be optimized, and the optimization algorithm used is a gradient-based optimization algorithm.The target value and gradient calculation are completed by the proxy model.The application has low calculation cost and higher optimization efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of CFD and artificial intelligence, and particularly to a wing profile optimization algorithm based on data driving. BACKGROUND

[0002] Wing profile optimization is a classic problem in aerodynamic design. The goal is to obtain good aerodynamic performance by optimizing the shape of the wing profile and improve the cruise efficiency.

[0003] The design algorithm disclosed in the prior art is usually gradually fine-tuned by the design experience of engineers or obtained by using the adjoint method. The manual fine-tuning method usually excessively depends on the experience and level of engineers, and has long iteration period and low design efficiency. The adjoint method is to obtain the related gradient by solving the adjoint equation of the corresponding PDE (partial differential equation), and then perform iteration by using the gradient-based optimization, but this method has large calculation amount and is not universal. SUMMARY

[0004] In order to overcome the defects in the prior art, the present application provides a wing profile optimization algorithm based on data driving, which has low calculation cost and higher optimization efficiency.

[0005] To achieve the above object, the present application adopts the following technical scheme, comprising:

[0006] A wing profile optimization algorithm based on data driving comprises the following steps:

[0007] S1, modeling the wing profile, and sampling in the geometric feature space to obtain a wing profile database to be labeled;

[0008] S2, solving the aerodynamic characteristics of the wing profile data to be labeled at different attack angles by using a CAE software, obtaining the lift coefficient and the drag coefficient, and thus obtaining a labeled wing profile database;

[0009] S3, training a deep neural network on the labeled wing profile database, the input being the geometric features of the wing profile and the attack angle, and the output being the lift coefficient and the drag coefficient, and finally obtaining a proxy model;

[0010] S4, sampling a gradient-based algorithm, calculating the corresponding aerodynamic indexes and the gradient of the wing profile to be optimized by using the proxy model, and finally obtaining an optimized wing profile.

[0011] Preferably, in step S1, the wing profile is modeled according to the format of NACA-4 SERIES-MODIFIED, and the geometric features of the wing profile are extracted in five dimensions, including the maximum camber, the maximum camber position, the maximum thickness, the maximum thickness position, and the leading edge radius exponent.

[0012] Preferably, the specific mode of step S1 is:

[0013] S11, through the maximum thickness t max Maximum thickness location u max Calculate the thickness curve using the leading edge radius exponent I:

[0014] First, solve two systems of linear equations:

[0015]

[0016]

[0017] Where k(·) is a B-spline function, obtained by interpolating the data {(0.20,1.00),(0.30,1.17),(0.40,1.575),(0.500,2.325),(0.6,3.500)};

[0018] As an intermediate variable;

[0019]

[0020]

[0021] Where, r LE is the radius of curvature of the leading edge; a0 is the coefficient of the first half of the thickness curve;

[0022] The formula for calculating the thickness curve t(u) is as follows:

[0023]

[0024] Where u represents the horizontal coordinate value; t(u) represents the thickness at the current position;

[0025] S12, using the maximum radian M and the position of the maximum radian P, calculate the radian curve c(u). The formula for calculating the radian curve c(u) is as follows:

[0026]

[0027] Where c(u) represents the middle position of the current position;

[0028] S13, the airfoil profile is obtained by calculating the thickness curve and radii curve, and the airfoil parameters and airfoil profile data are retained;

[0029] The scatter plot data of the airfoil profile was obtained using the following method:

[0030]

[0031] Among them, y upper (u) and ylower (u) respectively represent the upper half profile and the lower half profile of the airfoil.

[0032] Preferably, in step S2, the CAE software framework used is XFoil, and the lift coefficient C l and the drag coefficient C d of the airfoil at different angles of attack are calculated.

[0033] Preferably, the Mach number is taken as 0.785, the Reynolds number is taken as 5x10 6 , and the angle of attack ranges from -5° to 10°.

[0034] Preferably, in step S3, the network framework used is a fully connected neural network, and the activation function is ReLU.

[0035] Preferably, in step S4, the lift coefficient constraint is given, and the optimization objective is:

[0036]

[0037] Preferably, in step S4, the gradient-based algorithm used is the PSQP algorithm.

[0038] An electronic device includes a processor, a memory, and a computer program stored on the memory and executable on the processor, and the processor implements the above-mentioned data-driven airfoil optimization algorithm when executing the computer program.

[0039] A computer program product includes computer programs / instructions that implement the above-mentioned data-driven airfoil optimization algorithm when executed by a processor.

[0040] The advantages of the present application are:

[0041] (1) The present application provides a data-driven airfoil optimization algorithm.

[0042] (2) The proxy model of the present application greatly improves the computational efficiency without sacrificing too much accuracy.

[0043] (3) The optimization algorithm of the present application has strong expandability and can be applied to all gradient-based algorithms.

[0044] (4) Since optimization is performed at the level of geometric features, shape abnormality problems can be avoided. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is a flowchart of a data-driven airfoil optimization algorithm of the present application.

[0046] Figure 2A schematic diagram of geometric parameters in the embodiment.

[0047] Figure 3 A schematic diagram of network structure in the embodiment.

[0048] Figure 4 A schematic diagram of optimization comparison results in the embodiment. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0050] Embodiment 1

[0051] As shown in FIG. 1, a data-driven airfoil optimization algorithm specifically includes the following steps: Figure 1

[0052] S1, modeling the airfoil in the format of NACA-4SERIES-MODIFIED and sampling in the geometric feature space to obtain an airfoil database to be labeled.

[0053] S2, solving the aerodynamic characteristics of the airfoil data to be labeled at different attack angles by a CAE software to obtain the lift coefficient and the drag coefficient, thereby obtaining the labeled airfoil database.

[0054] S3, training the labeled airfoil database by a deep neural network, the input being five-dimensional geometric features of the airfoil data and the attack angle, the output being the lift coefficient and the drag coefficient, and finally obtaining a proxy model;

[0055] S4, sampling gradient type algorithm, calculating the corresponding aerodynamic indexes and the gradient of the airfoil to be optimized by the proxy model, and finally obtaining the optimized airfoil.

[0056] In step S1, the airfoil is modeled in the format of NACA-4SERIES-MODIFIED, and the geometric features of the airfoil include five dimensions of maximum camber M, maximum camber position P, maximum thickness t max , maximum thickness position u max , and leading edge radius exponent r LE .The geometric parameters of the airfoil, i.e., the five-dimensional geometric features, are shown in FIG. 2, wherein the middle blue line represents the camber curve c(u). Figure 2

[0057] S11, calculating the maximum thickness t max ​, maximum thickness position u max and leading edge radius exponent I to calculate the thickness curve. First, solve two linear equations:

[0058]

[0059]

[0060] where k(·) is a B-spline function, which is obtained by interpolating the data {(0.20, 1.00), (0.30, 1.17), (0.40, 1.575), (0.500, 2.325), (0.6, 3.500)};

[0061] is an intermediate variable;

[0062]

[0063]

[0064] where r LE is the radius of curvature of the leading edge; a0 is a known coefficient of the first half of the thickness curve, which can be obtained by the leading edge radius exponent I and the maximum thickness conversion t max , and is also used to assist in calculating the values of other undetermined coefficients a1, a2, a3 of the first half of the thickness curve.

[0065] The calculation formula of the thickness curve t(u) is as follows:

[0066]

[0067] where u represents the horizontal coordinate value, and t(u) represents the thickness at the current position;

[0068] S12, calculate the camber curve c(u) by the maximum camber M and the maximum camber position P. The calculation formula of the camber curve c(u) is as follows:

[0069]

[0070] where c(u) represents the intermediate position at the current position, and details are shown in the intermediate blue curve of Figure 2 ;

[0071] S13, obtain the profile of the airfoil curve by the calculated thickness curve and camber curve, and reserve the airfoil parameters and airfoil profile data. The profile scattered point data of the airfoil is obtained by the following method:

[0072]

[0073] where y upper(u) and y lower (u) represents the upper half profile and the lower half profile of the airfoil, respectively.

[0074] The airfoil data to be labeled is recorded as the geometric feature data of the five dimensions described above, and the airfoil profile can be calculated according to the geometric features of the five dimensions.

[0075] In step S2, the CAE software framework used is XFoil, which is an open source software for calculating airfoils. The method is based on the panel method, and the corresponding lift coefficient C l and drag coefficient C d , where the Mach number is 0.785, the Reynolds number is 5x10 6 , and the angle of attack ranges from -5° to 10°. The CAE software calculates the aerodynamic characteristics of the airfoil at different angles of attack according to the airfoil profile data, and obtains the lift coefficient and the drag coefficient.

[0076] As shown in Figure 3 , in step S3, the network framework used is a fully connected neural network, and the activation function is ReLU. The input is the five-dimensional geometric features of the airfoil data and the angle of attack, and the output is the lift coefficient and the drag coefficient, and finally the proxy model is obtained. The network structure is shown in Table 1 as follows:

[0077] Table 1 Structure of deep neural network

[0078] Linear(6, 128) ReLU Linear(128, 128) ReLU Linear(128, 128) ReLU Linear(128, 128) ReLU Linear(128, 2)

[0079] In step S4, the gradient-based algorithm used is the PSQP algorithm (sequential quadratic programming algorithm), and the specific method is as follows:

[0080] S41, the lift coefficient constraint is given to solve the following optimization problem:

[0081]

[0082] S42, for the airfoil to be optimized, the corresponding aerodynamic indicators, i.e. the lift coefficient C l and the drag coefficient C d , are calculated by the proxy model.

[0083] S43, the gradient required by the optimization algorithm is obtained by automatic differentiation of the proxy model. The gradient is used to indicate the optimization direction; the optimization algorithm needs to calculate the optimization direction according to the gradient, and update iteratively according to the optimization direction; the network model of Pytorch has an automatic differentiation mechanism.

[0084] The optimized airfoil is shown in Figure 4 , and Figure 4The middle black curve is the original airfoil, and the purple curve is the airfoil optimized according to the target parameters (angle of attack, Mach number, etc.).

[0085] Embodiment 2

[0086] An electronic device includes a processor, a memory, and a computer program stored on the memory and executable on the processor, and the processor implements the data-driven airfoil optimization algorithm of embodiment 1 above when executing the computer program.

[0087] The electronic device of the embodiments of the present application can be the mobile device itself or a single device independent of the mobile device, which can communicate with the mobile device to receive the collected input signals therefrom and send the selected target decision behavior thereto.

[0088] The electronic device includes one or more processors and a memory. The processor can be a central processing unit (CPU) or other form of processing unit having data processing and / or instruction execution capabilities, and can control other components in the electronic device to perform desired functions. The memory can include one or more computer program products, which can include various forms of computer readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM), cache memory, and / or the like. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, and / or the like. One or more computer program instructions can be stored on the computer readable storage medium, and the processor can execute the program instructions to implement the decision behavior decision method of various embodiments of the present application described above and / or other desired functions.

[0089] The electronic device can further include an input device and an output device.

[0090] Embodiment 3

[0091] In addition to the above method and device, the embodiments of the present application can also be a computer program product including computer program instructions, which, when executed by a processor, cause the processor to perform the steps of the decision behavior decision method according to various embodiments of the present application described in embodiment 1 above.

[0092] The computer program product can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, C++, or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computing device, partly on the user's device, as a stand-alone software package, partly on the user's computing device and partly on a remote computing device or entirely on the remote computing device or server. The embodiments were chosen in order to provide a practical and

[0093] The above merely provides the preferred embodiments of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present application shall fall within the scope of the present application.

Claims

1. A data-driven based airfoil optimization algorithm, characterized in that, The method comprises the following steps: S1, modeling the airfoil and sampling in the geometric feature space to obtain an airfoil database to be labeled; S2, solving the aerodynamic characteristics of the airfoil data to be labeled at different attack angles by a CAE software to obtain lift coefficients and drag coefficients, thereby obtaining a labeled airfoil database; S3, training a deep neural network on the labeled airfoil database, the input being the geometric features of the airfoil and the attack angle, and the output being the lift coefficient and the drag coefficient, and finally obtaining a proxy model; S4, using a gradient-based algorithm to calculate the corresponding aerodynamic indicators and gradients of the airfoil to be optimized through the proxy model, and finally obtaining an optimized airfoil; The specific method of step S1 is as follows: S11, by maximum thickness t max , maximum thickness position u max and leading edge radius exponent I calculate thickness curve: First, two linear equations are solved: Where k(·) is a B-spline function obtained by interpolating the data {(0.20, 1.00), (0.30, 1.17), (0.40, 1.575), (0.500, 2.325), (0.6, 3.500)}; is an intermediate variable; where r LE is the radius of curvature of the leading edge; a0is a coefficient of the first half of the thickness profile; Then the calculation formula of the thickness curve t(u) is as follows: Where u represents the horizontal coordinate value; t(u) represents the thickness at the current position; S12, the camber curve c(u) is calculated through the maximum camber M and the maximum camber position P, and the calculation formula of the camber curve c(u) is as follows: S13, the airfoil profile is obtained through the calculated thickness curve and camber curve, and the airfoil parameters and airfoil profile data are retained; The airfoil profile scatter point data is obtained by the following method: where y upper (u) and y lower (u) represent the upper and lower half profiles of the airfoil, respectively.

2. The data-driven airfoil optimization algorithm of claim 1, wherein, In step S1, the airfoil is modeled according to the format of NACA-4 SERIES-MODIFIED, and the five-dimensional geometric features of the airfoil, including the maximum camber, the maximum camber position, the maximum thickness, the maximum thickness position and the leading edge radius index, are extracted.

3. The data-driven airfoil optimization algorithm of claim 1, wherein, In step S2, the CAE software framework adopted is XFoil, and the lift coefficient C l and the drag coefficient C d of the airfoil at different angles of attack are calculated.

4. The data-driven airfoil optimization algorithm of claim 3, wherein, Mach number is 0.785, Reynolds number is 5×10 6 , and the angle of attack ranges from -5° to 10°.

5. The data-driven airfoil optimization algorithm of claim 1, wherein, In step S3, the network framework used is a fully connected neural network, and the activation function is ReLU.

6. The data-driven airfoil optimization algorithm of claim 3, wherein, In step S4, a lift coefficient constraint is given The optimization objective is:

7. The data-driven airfoil optimization algorithm of claim 1, wherein, In step S4, the gradient-based algorithm used is the sequential quadratic programming algorithm.

8. An electronic device, comprising: It comprises a processor, a memory, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the data-driven airfoil optimization algorithm of any one of claims 1-7.

9. A computer program product, characterised in that, It comprises a computer program / instruction, which is executed by a processor to implement the data-driven airfoil optimization algorithm of any one of claims 1-7.

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