Multidisciplinary airfoil inverse design method based on deep neural network

Abstract

The present invention proposes a multidisciplinary airfoil inverse design method based on a deep neural network, comprising the following steps: step 1: selecting an airfoil shape as a design target, and selecting the aerodynamic low detection performance of the airfoil as a design variable; the airfoil shape is the ordinate of the airfoil; determining the aerodynamic and low detection design state; step 2: selecting a set number of airfoils from an existing airfoil library and performing a uniform interpolation process on the abscissas to obtain the ordinate values ​​of the airfoils with uniform abscissas; step 3: for the interpolated airfoils, calculating and obtaining the aerodynamic and low detection performance of the selected airfoils in the design state; step 4: establishing multiple deep neural network proxy models according to the ordinate values ​​of the airfoils obtained in step 2 and the aerodynamic and low detection performance of the airfoils obtained in step 3; step 5: predicting an airfoil with a given aerodynamic and low detection performance according to the deep neural network proxy model obtained in step 4, and obtaining an airfoil shape that meets the aerodynamic and low detection target performance.

Description

Technical Field

[0001] The present invention relates to the field of airfoil design, and specifically to a multidisciplinary airfoil inverse design method based on a deep neural network. Background Art

[0002] In the process of aircraft design, the aerodynamic design methods of airfoils can be divided into two categories. One is the aerodynamic optimization design method formed by combining the solution of aerodynamic direct problems with optimization algorithms, and the other is the inverse design method established by directly solving the aerodynamic inverse problem. Among them, the aerodynamic optimization design method uses the CFD method to determine the relationship between the design variables and the aerodynamic characteristics, and obtains the optimal design solution that meets the design target characteristics through the optimization search method. It can directly provide designers with design results that meet the design goals and constraints. It is widely used in the field of aircraft shape design, but this type of method requires a large amount of CFD calculations, which is time-consuming, and the designed airfoil may not fully meet the aerodynamic performance requirements. It is not targeted, which reduces the efficiency of aircraft design to a certain extent. The inverse design method reverses the airfoil shape based on given performance indicators, such as given lift-to-drag ratio, pressure coefficient curve, etc. This type of method can directly establish the connection between the aerodynamic performance and geometric shape of the airfoil, so it is more direct, faster and more targeted.

[0003] At present, the most commonly used airfoil inverse design method in engineering is the residual correction method, that is, the correction amount of the geometric shape is calculated based on the difference of the initial airfoil target pressure, superimposed on the initial airfoil and iterated repeatedly to obtain the final airfoil. Patent CN104699901A discloses a GappyPOD airfoil inverse design method based on differential sampling solution. This method uses CFD solution in the database sampling and iteration process, and the design process is relatively time-consuming; Patent CN 104834772A discloses an aircraft airfoil / wing inverse design method based on artificial neural network. This method requires parameterization of the pressure distribution curve first. The parameterization method is polynomial fitting, which has a large loss of accuracy, and the neural network is a shallow neural network, which cannot adapt to the complex mapping relationship between aerodynamic parameters and airfoils. At the same time, the above methods are all based on pressure distribution for airfoil inverse design, but in the actual inverse design process, it is very difficult to obtain the pressure distribution curve, which depends largely on the experience of the designer. Patent CN111814246B discloses an airfoil inverse design method based on a generative adversarial network. This method uses a generative adversarial network in deep learning, but only establishes the relationship between aerodynamic parameters and airfoils. It is limited to a single discipline and fails to consider low-detectability parameters. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention proposes a multidisciplinary airfoil inverse design method based on a deep neural network. By establishing a multidisciplinary deep neural network that simultaneously considers aerodynamics and low detection performance for each point ordinate of the airfoil, the airfoil inverse design is realized, and multiple deep neural networks ensure a small loss of accuracy. In addition, the deep neural network of the present invention adopts multiple hidden layers, each layer can extract features at different levels from the data, and the deep neural network applies nonlinear activation functions between the layers, which increases the nonlinear expression ability of the model, enabling it to process more complex data patterns, thereby being able to simultaneously consider aerodynamics and low detectability for multidisciplinary airfoil inverse design.

[0005] The present invention is achieved through the following technical solutions:

[0006] A multidisciplinary airfoil inverse design method based on deep neural network includes the following steps:

[0007] Step 1: Select the airfoil shape as the design target, and select the aerodynamic low detection performance of the airfoil as the design variable; the airfoil shape is the ordinate of the airfoil; the aerodynamic low detection performance includes the lift coefficient, drag coefficient, pitch moment coefficient, and forward radar cross-sectional area of ​​the airfoil; determine the aerodynamic and low detection design states;

[0008] Step 2: Select a set number of airfoils from the existing airfoil library, perform uniform abscissa interpolation processing on the selected airfoil shapes, and obtain the ordinate values ​​of the airfoils with uniform abscissas;

[0009] Step 3: For the airfoil shape obtained by interpolation in step 2, the aerodynamic and low detection performance of the selected airfoil under the design state is obtained by aerodynamic and low detection performance calculation;

[0010] Step 4: Establish multiple deep neural network proxy models according to the airfoil ordinate value obtained in step 2 and the airfoil aerodynamic and low detection performance obtained in step 3; the input of the deep neural network model is the aerodynamic and low detection performance, and the output of the deep neural network model is the airfoil ordinate value;

[0011] Step 5: Predict the airfoil with given aerodynamic and low detection performance according to the deep neural network proxy model obtained in step 4 to obtain an airfoil shape that meets the aerodynamic and low detection target performance.

[0012] Furthermore, the airfoil type selected in step 2 is consistent with the type of the target airfoil.

[0013] Further, the method for performing uniform interpolation processing of the horizontal coordinates of the selected airfoil in step 2 is specifically as follows: using piecewise linear equidistant interpolation to obtain the horizontal coordinates of the original airfoil, setting the horizontal coordinates of the leading edge points of the airfoil to zero, and after performing zero-to-one normalization processing on the chord-wise position of the airfoil, selecting the leading edge points of the airfoil, 100 points on the upper surface of the airfoil, and 100 points on the lower surface of the airfoil, a total of 201 points are selected as control points for controlling the shape of the airfoil, and the vertical coordinate values ​​of the original airfoil at the corresponding horizontal coordinate values ​​are obtained according to the horizontal coordinates of the 201 points. The specific interpolation formula is as follows:

[0014]

[0015] Where (x, y) is the middle point that needs to be interpolated, (x0, y0) and (x1, y1) are the coordinates of two adjacent points on the original airfoil, that is, the coordinates of the two endpoints of the interpolation segment.

[0016] Furthermore, in step 3, the RANS method is used to calculate the aerodynamic performance parameters of the selected airfoil, and the aerodynamic performance parameters include the lift coefficient, drag coefficient and pitch moment coefficient of the airfoil; the moment method is used to calculate the low detection performance parameters of the selected airfoil, and the low detection performance parameters are the forward radar scattering cross-sectional area of ​​the airfoil.

[0017] Furthermore, the number of deep neural networks constructed in step 4 is consistent with the number of airfoil coordinates; the process of establishing multiple deep neural network proxy models is specifically: taking the first ordinate value of all airfoils as the data set of the first deep neural network model, taking the second ordinate value of all airfoils as the data set of the second deep neural network model, and so on until all the ordinate values ​​of all airfoils are taken and the deep neural network model is established.

[0018] Furthermore, the deep neural network model includes an input layer, n hidden layers and an output layer; the hidden layer contains multiple neurons; the data transmission process in the deep neural network is:

[0019] (1) Input layer: The aerodynamic and low-detection parameters of the airfoil are input into the network as input data. These input data contain the correlation information between the geometric characteristics of the airfoil and its aerodynamic low-detection performance;

[0020] (2) First hidden layer: The input data is multiplied by the weight parameters of the first hidden layer and then processed by the neurons in this layer. Each neuron performs a weighted summation on the input data and performs a nonlinear transformation through the ReLU activation function, so that the features of the data are mapped and extracted in a high-dimensional space. The output result is passed to the second hidden layer as input data. At the same time, the gradient of the loss function is calculated through the back-propagation algorithm, and the weight parameters of this layer are updated using the Adam optimizer.

[0021] (3) Second hidden layer: The output data of the first hidden layer is used as input and enters the second hidden layer. It is processed by the neurons in this layer. Each neuron performs a weighted summation on the input data and processes it through the ReLU activation function. The output result is passed to the third hidden layer, and the gradient of the loss function is calculated through the back-propagation algorithm. The weight parameters of this layer are updated using the Adam optimizer.

[0022] (4) The nth hidden layer: The data is passed to the last hidden layer, i.e., the nth hidden layer. In this layer, the data is multiplied by the weight parameter and processed by the ReLU activation function again. The output result is passed to the output layer as input data. At the same time, the gradient of the loss function is calculated through the back-propagation algorithm, and the weight parameters of this layer are updated using the Adam optimizer.

[0023] (5) Output layer: Finally, the output of the nth hidden layer is used as input and enters the output layer; after the data undergoes the final nonlinear transformation and feature extraction in this layer, the shape coordinates of the airfoil are generated.

[0024] Furthermore, each neuron in the deep neural network calculates the weighted sum of the input data. The specific operation process can be expressed as:

[0025]

[0026] Among them, x is the input data of the neuron, and the operator Defined as the inner product, w represents the strength weight coefficient on the neuron, b represents the input offset of the neuron, f represents the activation function, z represents the input parameter of the neuron's activation function, and o represents the output parameter of the neuron's activation function.

[0027] Furthermore, the specific calculation process of the gradient of each hidden layer loss function in the deep neural network can be expressed as follows: Assume a training sample set with a sample size of N, and its input parameter vector set is [x1,...x i ,...x N ], where each input parameter x i is an n-dimensional vector; the corresponding output parameter vector set is [y1,...y i ,...y N ], where each output parameter y i is an m-dimensional vector, then the loss function is:

[0028]

[0029] Where L i Represents the training error of the i-th training sample. To facilitate subsequent calculations, it is defined as half of the square of the Euclidean distance between the sample's output parameter vector and the prediction vector, that is:

[0030]

[0031] Since the gradient is a vector composed of partial derivatives, we have:

[0032]

[0033] For any training sample, the gradient of the loss function is:

[0034]

[0035] Furthermore, in step 5, the aerodynamic low detection performance of the airfoil that the user expects to obtain is input into the trained multiple deep neural network models, each deep neural network will predict a ordinate value of the output airfoil, and these ordinate values ​​are combined with the abscissa value of the airfoil to finally obtain the inversely designed airfoil.

[0036] Beneficial Effects

[0037] The present invention proposes a multidisciplinary airfoil inverse design method based on a deep neural network. By establishing a deep neural network that simultaneously considers aerodynamics and low detection performance for each point ordinate of the airfoil, the airfoil inverse design is realized. Multiple deep neural networks ensure that the accuracy loss is small. At the same time, the present invention only takes a small number of parameters of aerodynamics and low detectability performance as input, and does not require pressure distribution curve data of the airfoil, thereby reducing the dependence on the experience of designers. In addition, the deep neural network of the present invention adopts multiple hidden layers, each layer can extract features of different levels from the data, and the deep neural network applies nonlinear activation functions between layers, which increases the nonlinear expression ability of the model, enabling it to process more complex data patterns, thereby being able to simultaneously consider aerodynamics and low detection for airfoil inverse design. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flowchart of airfoil inverse design based on deep neural network according to an embodiment of the present invention.

[0039] Figure 2 Comparison diagram of the airfoil profile before and after interpolation of the embodiment of the present invention

[0040] Figure 3 A comparison of the rotor airfoil of an embodiment of the present invention before and after the reverse design

[0041] Figure 4 This is an enlarged diagram of the rotor airfoil inverse design error of an embodiment of the present invention

[0042] Figure 5 The pressure cloud diagram of the desired rotor airfoil of the embodiment of the present invention is

[0043] Figure 6The pressure cloud diagram of the rotor airfoil after the reverse design of the embodiment of the present invention

[0044] Figure 7 The forward threat area definition diagram of the airfoil according to the embodiment of the present invention is shown in FIG.

[0045] Figure 8 A comparison of low detection performance before and after the reverse design of the rotor airfoil of an embodiment of the present invention DETAILED DESCRIPTION

[0046] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer and more understandable, and to enable those skilled in the art to better understand the solutions of the present invention, the present invention is further described and fully described in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0047] This embodiment uses a multidisciplinary airfoil inverse design method based on a deep neural network proposed by the present invention to perform inverse design verification on a certain rotor airfoil. Figure 1 As shown, the following steps are included:

[0048] Step 1: Select the airfoil shape as the design target, and select the aerodynamic low detection performance of the airfoil as the design variable; the airfoil shape is the ordinate of the airfoil; the aerodynamic low detection performance includes the lift coefficient, drag coefficient, pitch moment coefficient, and forward radar cross-sectional area of ​​the airfoil; determine the aerodynamic and low detection design states;

[0049] In this embodiment, the pneumatic design state is: Ma = 0.5, Re = 4 × 10 -6 , α=2°; low detection design state: incident wave frequency of 1GHZ;

[0050] Step 2: Select a set number of airfoils from the existing airfoil library, perform uniform abscissa interpolation processing on the selected airfoil shapes, and obtain the ordinate values ​​of the airfoils with uniform abscissas;

[0051] In this embodiment, if Figure 2 As shown in the figure, a rotor airfoil is the target airfoil, and the specific shape is shown in Figure 2The airfoil indicated by origin in the figure; the airfoil type selected from the airfoil library is consistent with the type of the target airfoil, all of which are rotor airfoils. In this embodiment, a total of 21 airfoils are selected; the method for performing unified interpolation processing of the horizontal coordinates on the selected 21 airfoils is specifically: using piecewise linear equidistant interpolation to obtain the horizontal coordinate of the original airfoil, setting the horizontal coordinate of the leading edge point of the airfoil to zero, and after performing zero-to-one normalization processing on the chord-wise position of the airfoil, selecting the leading edge point of the airfoil, 100 points on the upper surface of the airfoil, and 100 points on the lower surface of the airfoil, a total of 201 points are selected as control points for controlling the shape of the airfoil, and the vertical coordinate value of the original airfoil at the corresponding horizontal coordinate value is obtained according to the horizontal coordinate of the 201 points. The specific interpolation formula is as follows:

[0052]

[0053] Where (x, y) is the middle point to be interpolated, (x0, y0) and (x1, y1) are the coordinates of two adjacent points on the original airfoil, i.e., the coordinates of the two end points of the interpolation segment. In order to verify the reliability of the interpolation method of the present invention, the target airfoil is interpolated. Figure 2 A comparison of the target airfoil shape before and after interpolation is given. The circle plus the dotted line represents the position of the airfoil interpolation coordinate point. It can be seen that the airfoil shape after interpolation is consistent with the target airfoil, proving that the interpolation method of the present invention is reliable.

[0054] Step 3: For the airfoil shape obtained by interpolation in step 2, the aerodynamic and low detection performance of the selected airfoil under the design state is obtained by aerodynamic and low detection performance calculation;

[0055] In this embodiment, in step 3, the RANS method is used to calculate the aerodynamic performance parameters of the selected 21 airfoils in the design state, and the aerodynamic performance parameters include the lift coefficient, drag coefficient and pitch moment coefficient of the airfoil; the moment method is used to calculate the low detection performance parameters of the selected 21 airfoils in the design state, and the low detection performance parameters are the forward radar cross-sectional area of ​​the airfoil;

[0056] Step 4: Establish multiple deep neural network proxy models according to the airfoil ordinate value obtained in step 2 and the airfoil aerodynamic low detection performance obtained in step 3; the input of the deep neural network model is the aerodynamic and low detection performance, and the output of the deep neural network model is the airfoil ordinate value;

[0057] In this embodiment, the number of deep neural networks constructed is consistent with the number of airfoil coordinates, which is 201; the process of establishing multiple deep neural network proxy models is specifically as follows: taking the first ordinate value of all airfoils as the data set of the first deep neural network model, taking the second ordinate value of all airfoils as the data set of the second deep neural network model, and so on until all the ordinate values ​​of all 21 airfoils are taken and the deep neural network model is established;

[0058] In this embodiment, the deep neural network model includes an input layer, four hidden layers and an output layer; the hidden layer contains multiple neurons; Table 1 shows the parameter settings of the four hidden layers of the deep neural network used in this embodiment.

[0059] Table 1 Parameter settings of the deep neural network in this embodiment

[0060]

[0061] The data transmission process in the deep neural network is as follows:

[0062] (1) Input layer: The airfoil's aerodynamic low detection parameters are input into the network as input data. These input data contain the correlation information between the airfoil's geometric characteristics and its aerodynamic low detection performance.

[0063] (2) First hidden layer: The input data is multiplied by the weight parameters of the first hidden layer and then processed by the 64 neurons in this layer. Each neuron performs a weighted summation on the input data and performs a nonlinear transformation through the ReLU activation function, so that the features of the data are mapped and extracted in a high-dimensional space. The output result is passed to the second hidden layer as input data. At the same time, the gradient of the loss function is calculated through the back-propagation algorithm, and the weight parameters of this layer are updated using the Adam optimizer.

[0064] (3) Second hidden layer: The output data of the first hidden layer is used as input to the second hidden layer. This layer has 128 neurons. Each neuron performs a weighted summation on the input data and then processes it through the ReLU activation function. The output result is passed to the third hidden layer, and the weight parameters of this layer are updated through back propagation and the Adam optimizer.

[0065] (4) Third hidden layer: The output of the second hidden layer is used as input and enters the third hidden layer, which also contains 128 neurons. In this layer, the data is again multiplied by the weight parameters and processed by the ReLU activation function. The output result is passed to the fourth hidden layer as input data, and the weight parameters of this layer are updated through back propagation and the Adam optimizer.

[0066] (5) Fourth hidden layer: The output data of the third hidden layer is passed to the fourth hidden layer, which contains 64 neurons. In this layer, the data is multiplied by the weight parameters and processed by the ReLU activation function again. The output result is passed to the output layer as input data, and the weight parameters of this layer are updated through back propagation and Adam optimizer.

[0067] (6) Output layer: Finally, the output of the fourth hidden layer is used as input and enters the output layer; after the data undergoes the final nonlinear transformation and feature extraction in this layer, the shape coordinates of the airfoil are generated;

[0068] In this embodiment, each neuron in the deep neural network calculates the weighted sum of the input data. The specific operation process can be expressed as:

[0069]

[0070] Among them, x is the input data of the neuron, and the operator Defined as the inner product, w represents the strength weight coefficient on the neuron, b represents the input offset of the neuron, f represents the activation function, z represents the input parameter of the neuron's activation function, and o represents the output parameter of the neuron's activation function.

[0071] In this embodiment, the specific calculation process of the gradient of each hidden layer loss function in the deep neural network can be expressed as follows: Assume a training sample set with a sample size of N, and its input parameter vector set is [x1,...x i ,...x N ], where each input parameter x i is an n-dimensional vector; the corresponding output parameter vector set is [y1,...y i ,...y N ], where each output parameter y i is an m-dimensional vector, then the loss function is:

[0072]

[0073] Where L i Represents the training error of the i-th training sample. To facilitate subsequent calculations, it is defined as half of the square of the Euclidean distance between the sample's output parameter vector and the prediction vector, that is:

[0074]

[0075] Since the gradient is a vector composed of partial derivatives, we have:

[0076]

[0077] For any training sample, the gradient of the loss function is:

[0078]

[0079] Step 5: Predict the airfoil with a given aerodynamic low detection performance according to the deep neural network proxy model obtained in step 4, and obtain the airfoil shape that meets the aerodynamic low detection target performance; specifically: input the aerodynamic low detection performance of the airfoil that the user expects to obtain into the trained multiple deep neural network models. In this embodiment, the expected airfoil is the selected target airfoil. The aerodynamic low detection parameters of the expected airfoil are shown in Tables 4 and 5, respectively. Each deep neural network will predict a ordinate value of the output airfoil, and combine these ordinate values ​​with the abscissa value of the airfoil to finally obtain the inverse design airfoil.

[0080] Table 2 shows the error distribution of 201 points predicted by the deep neural network used in this embodiment, and Table 3 shows the upper and lower limits of the deep neural network prediction error. According to Tables 2 and 3, the error magnitude is concentrated around 10 -2 Up to 10 -3 mm, the upper limit of error is 1.75x10 -1 mm, the lower limit of error is 2.78x10 -6 mm, indicating that the deep neural network established by the present invention has high prediction accuracy.

[0081] Table 2 Prediction error distribution of the deep neural network in this embodiment

[0082] Error magnitude distribution (mm) quantity <![CDATA[10 -1 ]]> 15 <![CDATA[10 -2 ]]> 136 <![CDATA[10 -3 ]]> 35 <![CDATA[10 -4 ]]> 8 <![CDATA[10 -5 ]]> 4 <![CDATA[10 -6 ]]> 3

[0083] Table 3 Upper and lower limits of prediction error of deep neural network in this embodiment

[0084]

[0085] Figure 3 A comparison of the rotor airfoil before and after the reverse design is given. Figure 4 The enlarged diagram of the inverse design shape error of the rotor airfoil is given. Figure 3 and Figure 4 It can be seen that according to the aerodynamic low detection performance indicators of the expected rotor, the airfoil shape is predicted through the deep neural network, and the obtained airfoil shape is basically consistent with the expected rotor shape.

[0086] Figure 5 Given the pressure contour of the desired rotor airfoil, Figure 6 The pressure cloud diagram of the rotor airfoil after inverse design is given. Table 4 shows the aerodynamic performance comparison of the rotor airfoil before and after inverse design. Figure 5 , Figure 6 As can be seen from Table 4, based on the aerodynamic performance indicators of the expected rotor, the airfoil shape is predicted through a deep neural network, and the obtained airfoil has the same pressure distribution shape as the expected airfoil, and the aerodynamic performance remains consistent.

[0087] Figure 7The definition diagram of the airfoil forward threat area is given. Figure 8 The low detection performance comparison of the rotor airfoil before and after the reverse design is given. Table 5 gives the mean low detection performance of the rotor airfoil before and after the reverse design. Figure 7 , Figure 8 As can be seen from Table 5, according to the expected low detection performance index of the rotor, the low detection performance index of the rotor airfoil predicted by the deep neural network is basically consistent.

[0088] In summary, the airfoil inverse design method based on a deep neural network considering aerodynamic low detection of the present invention has higher design accuracy when performing airfoil inverse design considering both aerodynamics and low detection at the same time.

[0089] Table 4 Comparison of aerodynamic performance of the airfoil before and after the reverse design of the embodiment

[0090]

[0091] Table 5 Comparison of low detection performance before and after the airfoil reverse design of this embodiment

[0092]

[0093] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A multidisciplinary airfoil inverse design method based on deep neural network, characterized by: The steps include: Step 1: Selecting an airfoil shape as a design target and selecting an aerodynamic low detection performance of the airfoil as a design variable; the airfoil shape is the ordinate of the airfoil; The aerodynamic low detection performance includes the lift coefficient, drag coefficient, pitch moment coefficient, and forward radar cross-sectional area of ​​the airfoil; determining the aerodynamic and low detection design state; Step 2: Select a set number of airfoils from the existing airfoil library, perform uniform abscissa interpolation processing on the selected airfoil shapes, and obtain the ordinate values ​​of the airfoils with uniform abscissas; Step 3: For the airfoil shape obtained by interpolation in step 2, the aerodynamic and low detection performance of the selected airfoil under the design state is obtained by aerodynamic and low detection performance calculation; Step 4: Establish multiple deep neural network proxy models according to the airfoil ordinate value obtained in step 2 and the airfoil aerodynamic and low detection performance obtained in step 3; the input of the deep neural network model is the aerodynamic and low detection performance, and the output of the deep neural network model is the airfoil ordinate value; Step 5: Predict the airfoil with given aerodynamic and low detection performance according to the deep neural network proxy model obtained in step 4 to obtain an airfoil shape that meets the aerodynamic and low detection target performance.

2. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 1 is characterized by: The airfoil type selected in step 2 is consistent with the type of the target airfoil.

3. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 2 is characterized by: The method for performing uniform interpolation processing of the horizontal coordinates of the selected airfoil in step 2 is specifically as follows: using piecewise linear equidistant interpolation to obtain the horizontal coordinates of the original airfoil, setting the horizontal coordinates of the leading edge points of the airfoil to zero, and after performing zero-to-one normalization processing on the chord-wise position of the airfoil, selecting the leading edge points of the airfoil, 100 points on the upper surface of the airfoil, and 100 points on the lower surface of the airfoil, a total of 201 points, as control points for controlling the shape of the airfoil, and obtaining the vertical coordinate values ​​of the original airfoil at the corresponding horizontal coordinate values ​​according to the horizontal coordinates of the 201 points. The specific interpolation formula is as follows: Where (x, y) is the middle point that needs to be interpolated, (x0, y0) and (x1, y1) are the coordinates of two adjacent points on the original airfoil, that is, the coordinates of the two endpoints of the interpolation segment.

4. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 1 is characterized by: In the step 3, the aerodynamic performance parameters of the selected airfoil are calculated using the RANS method, and the aerodynamic performance parameters include the lift coefficient, drag coefficient and pitching moment coefficient of the airfoil; The low detection performance parameter of the selected airfoil is calculated by using the moment method, and the low detection performance parameter is the forward radar scattering cross-sectional area of ​​the airfoil.

5. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 1 is characterized by: The number of deep neural networks constructed in step 4 is consistent with the number of airfoil coordinates; the process of establishing multiple deep neural network proxy models is specifically as follows: taking the first ordinate value of all airfoils as the data set of the first deep neural network model, taking the second ordinate value of all airfoils as the data set of the second deep neural network model, and so on until all the ordinate values ​​of all airfoils are taken and the deep neural network model is established.

6. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 5 is characterized by: The deep neural network model includes an input layer, n hidden layers and an output layer; the hidden layer contains multiple neurons; the data transmission process in the deep neural network is: (1) Input layer: The aerodynamic and low-detection parameters of the airfoil are input into the network as input data. These input data contain the correlation information between the geometric characteristics of the airfoil and its aerodynamic low-detection performance; (2) First hidden layer: The input data is multiplied by the weight parameters of the first hidden layer and then processed by the neurons in this layer. Each neuron performs a weighted summation on the input data and performs a nonlinear transformation through the ReLU activation function, so that the features of the data are mapped and extracted in a high-dimensional space. The output result is passed to the second hidden layer as input data. At the same time, the gradient of the loss function is calculated through the back-propagation algorithm, and the weight parameters of this layer are updated using the Adam optimizer. (3) Second hidden layer: The output data of the first hidden layer is used as input and enters the second hidden layer. It is processed by the neurons in this layer. Each neuron performs a weighted summation on the input data and processes it through the ReLU activation function. The output result is passed to the third hidden layer, and the gradient of the loss function is calculated by the back-propagation algorithm, and the weight parameters of this layer are updated using the Adam optimizer; (4) The nth hidden layer: The data is passed to the last hidden layer, i.e. the nth hidden layer. In this layer, the data is again multiplied by the weight parameter and processed by the ReLU activation function. The output result is passed to the output layer as input data. At the same time, the gradient of the loss function is calculated through the back-propagation algorithm, and the weight parameters of this layer are updated using the Adam optimizer. (5) Output layer: Finally, the output of the nth hidden layer is used as input and enters the output layer; after the data undergoes the final nonlinear transformation and feature extraction in this layer, the shape coordinates of the airfoil are generated.

7. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 6 is characterized by: Each neuron in the deep neural network calculates the weighted sum of the input data. The specific operation process can be expressed as: Among them, x is the input data of the neuron, and the operator Defined as the inner product, w represents the strength weight coefficient on the neuron, b represents the input offset of the neuron, f represents the activation function, z represents the input parameter of the neuron's activation function, and o represents the output parameter of the neuron's activation function.

8. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 6 is characterized by: The specific calculation process of the gradient of each hidden layer loss function in the deep neural network can be expressed as follows: Assume a training sample set with a sample size of N, and its input parameter vector set is [x1,...x i ,...x N ], where each input parameter x i is an n-dimensional vector; the corresponding output parameter vector set is [y1,...y i ,...y N ], where each output parameter y i is an m-dimensional vector, then the loss function is: Where L i Represents the training error of the i-th training sample. To facilitate subsequent calculations, it is defined as half of the square of the Euclidean distance between the sample's output parameter vector and the prediction vector, that is: Since the gradient is a vector composed of partial derivatives, we have: For any training sample, the gradient of the loss function is:

9. The multidisciplinary airfoil inverse design method based on deep neural network according to claim 1, characterized in that: In step 5, the aerodynamic low detection performance of the airfoil that the user expects to obtain is input into the trained multiple deep neural network models, each deep neural network will predict a ordinate value of the output airfoil, and these ordinate values ​​are combined with the abscissa value of the airfoil to finally obtain the inversely designed airfoil.

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