A parameter design method of hybrid flapping airfoil based on network self-differentiation

Abstract

The application discloses a parameter design method of a hybrid flapping airfoil based on network self-differentiation, and relates to the technical field of design and optimization of a bionic flapping energy collection device. Initial design parameters of the hybrid flapping airfoil are input into a generative adversarial network to obtain physical field data corresponding to the initial design parameters of the hybrid flapping airfoil, so as to calculate indexes representing energy collection characteristics of the hybrid flapping airfoil. According to the indexes, multi-objective optimization values are determined. A loss function is calculated through the multi-objective optimization values, a gradient of the loss function with respect to the initial design parameters is calculated according to network self-differentiation, and the initial design parameters are updated according to the gradient. The updated initial design parameters are taken as new initial design parameters, and the calculation of the multi-objective optimization values is continuously performed until a preset termination condition is met. The initial design parameters meeting the termination condition are determined as a parameter design strategy of the hybrid flapping airfoil. The method can accurately and quickly determine optimal design parameters of the hybrid flapping airfoil.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of design and optimization of bionic flapping energy harvesting devices, and particularly relates to a parameter design method of hybrid flapping airfoils based on network self-differentiation. BACKGROUND

[0002] Oscillating flapping wings based on bionics can harvest flow energy under certain oscillation modes, realizing the conversion from wind energy, water kinetic energy to electric energy, and providing a new idea for human beings to utilize fluid kinetic energy. Traditional flapping wing research mainly focuses on standard NACA airfoils, which have been widely used in aerospace and other fields due to their simple geometric structure and extensive research foundation. However, these designs are not specifically designed for the specific mechanism of flapping energy harvesting, i.e., the complex coupling motion mode of heave and pitch. There are many efficient propulsion organisms in nature, such as fish and marine mammals, whose propulsion mechanisms have been highly optimized through long-term evolution to adapt to complex and changeable flow environments. The profiles of these organisms usually exhibit a wider leading edge and a narrower trailing edge than the standard NACA four-digit series airfoils. The potential of non-standard NACA airfoils, especially those mimicking high-efficiency propulsion organisms in nature, in flapping energy harvesting has not been fully tapped.

[0003] In order to fully tap the potential of non-standard NACA airfoils, researchers have proposed the concept of hybrid flapping wings, i.e., combining NACA airfoils with different characteristics to optimize the energy harvesting performance of flapping wings. Traditional methods of studying the fluid dynamics of hybrid flapping wings mainly include numerical simulation and experimental measurement. Numerical simulation methods can provide global information of the flow field, but require a large amount of computational resources and time; experimental measurement methods can provide local information of the flow field, but require complex experimental equipment and techniques, and are limited by experimental conditions and measurement accuracy. Therefore, traditional numerical simulation and experimental measurement methods cannot meet the demand of high-precision and rapid analysis of flapping wing fluid dynamics, resulting in the inability to accurately and quickly determine the optimal design parameters of hybrid flapping wing airfoils. SUMMARY

[0004] Therefore, it is necessary to provide a parameter design method of hybrid flapping wing airfoils based on network self-differentiation to solve the above technical problems.

[0005] The present application adopts the following technical solutions:

[0006] The present application provides a parameter design method of hybrid flapping wing airfoils based on network self-differentiation, comprising:

[0007] obtaining initial design parameters of the hybrid flapping wing airfoils;

[0008] input the initial design parameters into a generator of a pre-constructed generative adversarial network to obtain physical field data corresponding to the initial design parameters of the hybrid flapping airfoil; the generative adversarial network is trained based on simulation data obtained by numerical simulation of fluid mechanics of the hybrid flapping airfoil as training data;

[0009] According to the initial design parameters and the physical field data, an index representing the energy harvesting characteristics of the hybrid flapping airfoil is calculated;

[0010] According to the index, a multi-objective optimization value is determined;

[0011] The multi-objective optimization value is maximized, and a loss function is calculated based on the multi-objective optimization value. The gradient of the loss function with respect to the initial design parameters is calculated based on network self-differentiation, and the initial design parameters are updated based on the gradient;

[0012] The updated initial design parameters are used as new initial design parameters to continue the calculation of the multi-objective optimization value until a preset termination condition is met. The initial design parameters that meet the termination condition are determined as the parameter design strategy of the hybrid flapping airfoil.

[0013] Optionally, the physical field data includes flow field pressure, linear velocity, angular velocity, and free stream velocity; the index includes instantaneous power and efficiency; according to the initial design parameters and the physical field data, the index representing the energy harvesting characteristics of the hybrid flapping airfoil is calculated, including:

[0014] According to the initial design parameters, the airfoil position parameters are determined; the airfoil position parameters include maximum displacement and coordinates of each point;

[0015] The tangential vector and normal vector of the airfoil edge are determined according to the coordinates of each point, and the force and torque on the hybrid flapping airfoil are determined according to the tangential vector and normal vector, and the flow field pressure;

[0016] The instantaneous power and average power are determined according to the force and torque on the hybrid flapping airfoil, as well as the linear velocity and angular velocity;

[0017] The efficiency of the hybrid flapping airfoil is determined according to the average power, maximum displacement and free stream velocity. Optionally, the calculation formula of the multi-objective optimization value is:

[0018] Ψ obj (C)=ω×Ψ p (C)+(1-ω)×Ψ η (C);

[0019] Ψ obj (C) represents the multi-objective optimization value corresponding to the design parameter C, ω represents a proportion factor, and Ψ p (C) represents the average power corresponding to the design parameter C, and Ψη (C) represents the efficiency corresponding to the design parameter C.

[0020] Optionally, the loss function is opposite to the multi-objective optimization value, and is the negative number corresponding to the multi-objective optimization value.

[0021] Optionally, the update formula of the design parameters is:

[0022]

[0023] Among them, C k+1 is the design parameter for the k+1th iteration, C k The design parameter at the kth iteration, ε k is the learning rate at the kth iteration, is the gradient at the kth iteration, ε is the initial learning rate, K total is the maximum number of iterations.

[0024] Optionally, the construction process of the generative adversarial network includes:

[0025] Extracting sample design parameters of the sample hybrid flapping wing airfoil, and performing fluid dynamics numerical simulation on the sample hybrid flapping wing airfoil according to the sample design parameters to obtain simulation data; the simulation data includes sample flow field data and sample indicators;

[0026] Divide the sample design parameters and corresponding simulation data into training set and validation set;

[0027] Get the initial generator and initial discriminator in the initial generative adversarial network;

[0028] Generate predicted flow field data from sample design parameters through multi-layer convolution and upsampling in the initial generator, determine the loss function based on the predicted flow field data, sample flow field data and sample indicators, and iteratively update the parameters of the initial generator based on the loss function;

[0029] Based on the sample flow field data, the predicted flow field data is discriminated by the initial discriminator, the target prediction loss is calculated, and the parameters of the initial discriminator are iteratively updated based on the target prediction loss;

[0030] When the updated initial generator and initial discriminator both meet the preset iteration conditions, a generative adversarial network is obtained based on the initial generator and initial discriminator that meet the iteration conditions.

[0031] Optionally, a loss function is determined based on the predicted flow field data, the sample flow field data, and the sample index, and the parameters of the initial generator are iteratively updated based on the loss function, including:

[0032] The predicted flow field data is analyzed through the dynamic calculation module to obtain the prediction index;

[0033] determine a field reconstruction loss according to the predicted flow field data and the sample flow field data;

[0034] determine a target prediction loss according to the predicted indicator and the sample indicator;

[0035] determine a parameter update gradient of the initial generator according to the field reconstruction loss and the target prediction loss;

[0036] iteratively update the parameters of the initial generator according to the parameter update gradient.

[0037] Optionally, the parameter update gradient of the initial discriminator is obtained in the following manner:

[0038] determine a parameter update gradient of the initial discriminator according to the target prediction loss.

[0039] Optionally, in the process of training the generative adversarial network, the learning rate is updated in a segmented decay manner; the update rule of the learning rate η is:

[0040]

[0041] wherein ε0 is an initial learning rate, υ1 and υ2 are decay coefficients, F1 and F2 are decay nodes.

[0042] Optionally, the hybrid flapping airfoil is formed by combining a front section of a NACA airfoil with a first thickness and a rear section of a NACA airfoil with a second thickness to form a new airfoil composed of a leading edge airfoil, a connecting section and a trailing edge airfoil; the connecting section is constructed using a fourth-order Bezier curve, the starting point of which is the end point of the leading edge airfoil, the terminal point of which is the starting point of the trailing edge airfoil, and the two control points are set as the next node of the original leading edge airfoil and the previous node of the original trailing edge airfoil, respectively; the first thickness is greater than the second thickness.

[0043] The present application provides a parameter design device for a hybrid flapping airfoil based on network self-differentiation, comprising:

[0044] an acquisition module for acquiring initial design parameters of the hybrid flapping airfoil;

[0045] a generation module for inputting the initial design parameters into a generator of a pre-constructed generative adversarial network to obtain physical field data corresponding to the initial design parameters of the hybrid flapping airfoil; the generative adversarial network is trained based on simulation data obtained by numerically simulating the fluid mechanics of the hybrid flapping airfoil as training data;

[0046] a calculation module for calculating an indicator representing the energy harvesting characteristics of the hybrid flapping airfoil according to the initial design parameters and the physical field data;

[0047] A determination module is configured to determine the multi-objective optimization value according to the index;

[0048] An updating module is configured to maximize the multi-objective optimization value, calculate the loss function through the multi-objective optimization value, calculate the gradient of the loss function with respect to the initial design parameter through the network self-differentiation, and update the initial design parameter according to the gradient.

[0049] An iteration module is configured to continue the calculation of the multi-objective optimization value by taking the updated initial design parameter as a new initial design parameter until a preset termination condition is met, and determine the initial design parameter meeting the termination condition as the parameter design strategy of the hybrid flapping airfoil.

[0050] The application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the above-mentioned parameter design method of the hybrid flapping airfoil based on network self-differentiation.

[0051] The application provides a computer device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the above-mentioned parameter design method of the hybrid flapping airfoil based on network self-differentiation when executing the program.

[0052] The above-mentioned at least one technical scheme adopted by the application can achieve the following beneficial effects:

[0053] In the application, simulation data obtained by numerical simulation of fluid mechanics of the hybrid flapping airfoil is used as training data to train a generative adversarial network, so that the generative adversarial network can accurately and quickly determine the physical field data of the design parameter, thereby optimizing the design parameter based on the physical field data, and efficiently calculating the gradient of the loss function with respect to the design parameter through network self-differentiation in the optimization process, so that the design parameter can be dynamically adjusted in each iteration, gradually approaching the optimal solution, improving the calculation efficiency and accuracy, and thereby ensuring the calculation efficiency and accuracy of the optimal design parameter of the hybrid flapping airfoil. BRIEF DESCRIPTION OF DRAWINGS

[0054] The accompanying drawings, which are included to provide a further understanding of the application, constitute a part of this application and illustrate certain illustrative embodiments of the application and its description, and do not constitute an improper limitation of the application. In the drawings:

[0055] Figure 1 A parameter design method of a hybrid flapping airfoil based on network self-differentiation provided by the application is shown in the flowchart;

[0056] Figure 2 A structure of a hybrid flapping airfoil provided by the application is shown in the structural diagram;

[0057] Figure 3 A training flowchart of a neural network is provided for the present application;

[0058] Figure 4 Another parameter design method flowchart of a hybrid flapping airfoil based on network self-differentiation is provided for the present application;

[0059] Figure 5 A parameter design device schematic diagram of a hybrid flapping airfoil based on network self-differentiation is provided for the present application;

[0060] Figure 6 A computer device schematic diagram for implementing a parameter design method of a hybrid flapping airfoil based on network self-differentiation is provided for the present application. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical scheme and advantages of the present application clearer, the technical scheme of the present application will be described clearly and completely below in combination with specific embodiments of the present application and corresponding drawings. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0062] Deep learning methods, especially convolutional neural networks and generative adversarial networks, provide a new perspective for the design and optimization of flapping systems. Deep learning models can learn complex patterns of flow fields from large amounts of data, predict dynamic changes of fluids, and extract key aerodynamic performance parameters. The adaptive ability and powerful nonlinear processing capability of these models make them very suitable for solving complex unsteady flow problems. Network self-differentiation, commonly known as automatic differentiation, is a computer science technology used to automatically and efficiently calculate the derivative of a function. Unlike symbolic differentiation and numerical differentiation, automatic differentiation decomposes complex functions into a series of simple basic operations (such as addition, multiplication, exponentiation, etc.), and then uses the chain rule to calculate the derivative of these basic operations to obtain the derivative of the entire composite function. For example, the training of neural networks often uses backpropagation, a special automatic differentiation technique that starts from the last layer, propagates error signals through the network in reverse, and updates the weights of each layer using the chain rule. It can efficiently calculate the gradient of the loss function with respect to all parameters, and adjust the network parameters during the training process to minimize the loss function. This means that almost any computable function can be optimized, opening up vast possibilities for deep learning applications.

[0063] Based on this, the present application provides a parameter design method of a hybrid flapping airfoil based on network self-differentiation, which can accurately and quickly determine the optimal design parameters of the hybrid flapping airfoil.

[0064] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0065] Figure 1 The figure is a flow chart of a parameter design method for a hybrid flapping airfoil based on network self-differentiation in the present invention, which specifically includes the following steps:

[0066] S101, obtaining initial design parameters of a hybrid flapping airfoil.

[0067] Optionally, the hybrid flapping airfoil is formed by combining a NACA airfoil front section of a first thickness with a NACA airfoil rear section of a second thickness to form a new airfoil consisting of a leading edge airfoil, a connecting section and a trailing edge airfoil; the connecting section is constructed using a fourth-order Bezier curve, and the fourth-order Bezier curve is determined by the positions of four points, namely a starting point, two control points and an end point, wherein the starting point is the end point of the leading edge airfoil, and the end point is the starting point of the trailing edge airfoil, and the two control points are respectively set to the next node of the original leading edge airfoil and the previous node of the original trailing edge airfoil to ensure a smooth transition and consistent characteristics. The two control points selected close to the leading edge and the trailing edge can ensure the smoothness of the transition and avoid introducing a mutation between the leading edge and the trailing edge. At the same time, it also ensures that the transition curve has similar characteristics under different leading edge and trailing edge characteristic differences, thereby not introducing additional influencing factors. The first thickness is greater than the second thickness. The hybrid flapping airfoil adopts a design with a thicker front section and a thinner rear section. The front section enhances structural strength and optimizes airflow guidance, while the rear section reduces drag and mitigates the effects of wake vortices. This mimics the morphological characteristics of efficient propulsion organisms in nature and improves overall aerodynamic performance. The final first and second thicknesses can be determined based on the NACA airfoil model used.

[0068] like Figure 2 As shown, Figure 2 Schematic diagram of the structure of the hybrid flapping airfoil.

[0069] The Latin hypercube sampling method is used to generate initial design parameters, which may include multiple groups of design parameter combinations.

[0070] Among them, a set of design parameters includes the connecting section chord ratio λ, the mixing ratio r, the leading edge NACA airfoil thickness t l and the trailing edge NACA airfoil thickness t t as a key design parameter.

[0071] in, Define the chord length c of the intercepted leading edge airfoil l and the trailing edge airfoil chord length c t The ratio is the mixing ratio r, which represents the relative length of the leading edge feature and the trailing edge feature, and is expressed as follows: Where: c lrepresents a chord-wise length of the leading edge airfoil taken from the original airfoil leading edge point, c t represents a chord-wise length of the trailing edge airfoil taken from the original airfoil trailing edge point, c c represents a chord-wise length of the connecting section, c represents a total chord-wise length of the airfoil.

[0072] S102, input the initial design parameters into the generator of the pre-constructed generative adversarial network to obtain physical field data corresponding to the initial design parameters of the hybrid flapping wing airfoil; the generative adversarial network is trained based on simulation data obtained by numerical simulation of fluid mechanics of the hybrid flapping wing airfoil as training data.

[0073] First, the generative adversarial network (GAN) is constructed, and then the initial design parameters corresponding to the physical field data are generated by the constructed generative adversarial network.

[0074] The physical field data can include: lift, torque, power and efficiency, etc.

[0075] Optionally, the construction process of the generative adversarial network includes: extracting sample design parameters of a sample hybrid flapping wing airfoil, and performing numerical simulation of fluid mechanics on the sample hybrid flapping wing airfoil according to the sample design parameters to obtain simulation data; the simulation data includes sample flow field data and sample indicators; the sample design parameters and the corresponding simulation data are divided into a training set and a validation set; an initial generator and an initial discriminator in an initial generative adversarial network are obtained; the initial generator generates predicted flow field data from the sample design parameters through multi-layer convolution and up-sampling, and determines a loss function based on the predicted flow field data, the sample flow field data and the sample indicators, and iteratively updates the parameters of the initial generator based on the loss function; based on the sample flow field data, the initial discriminator discriminates the predicted flow field data, calculates a target prediction loss, and iteratively updates the parameters of the initial discriminator based on the target prediction loss; in the case that the updated initial generator and the initial discriminator both satisfy a preset iteration condition, the generative adversarial network is obtained according to the initial generator and the initial discriminator that satisfy the iteration condition.

[0076] Optionally, the loss function is determined based on the predicted flow field data, the sample flow field data and the sample indicators, and the parameters of the initial generator are iteratively updated based on the loss function, including: analyzing the predicted flow field data through a dynamic calculation module to obtain predicted indicators; determining a field reconstruction loss according to the predicted flow field data and the sample flow field data; determining a target prediction loss according to the predicted indicators and the sample indicators; determining a parameter update gradient of the initial generator according to the field reconstruction loss and the target prediction loss; and iteratively updating the parameters of the initial generator according to the parameter update gradient.

[0077] The parameter update gradient of the initial discriminator is obtained according to the target prediction loss.

[0078] Specifically, first, the simulation data is obtained and processed, that is, the flow field data extracted in the numerical simulation is converted into graph structure data. A flow analysis model based on the loft parameter is established through the computer-aided design (CAD) software, a high-quality structured or unstructured grid is automatically generated, and the parameterized numerical simulation of the flapping wing is performed in combination with the numerical simulation software script and the user-defined function (UDF), so that the comprehensive and automatic analysis of the flow characteristics and energy harvesting performance of the flapping wing is realized. After the numerical simulation is completed, the flow field data at each instantaneous time is extracted, including the position information, the physical field information and the velocity component, and the indexes (such as the power and the efficiency) representing the energy harvesting characteristics of the flapping wing. Then, the flow field data is converted from the structured O-type grid to the rectangular grid format suitable for the convolutional neural network (CNN) processing, so as to obtain the final three-dimensional physical field tensor. At the same time, the maximum-minimum normalization method is adopted to normalize the data to the range of [-1, 1], so as to ensure that the magnitudes of the various input features are similar, which is conducive to the stable training of the neural network.

[0079] After the value range of each design parameter is determined, the Latin hypercube sampling method is adopted to generate multiple sets of design parameter combinations, so as to ensure that all possible value ranges of each parameter are fully explored. The transient numerical solution is performed on each set of design parameters, the characteristics of the flapping wing at multiple instantaneous times in a complete motion cycle are extracted, and the flow field data and the energy harvesting performance indexes at each instantaneous time are extracted.

[0080] The data includes: a, design data: D e R N×d ; b, field data: F e R N×m ; c, target data: T e R N×p ; d, coordinate data: C e R N×q . Wherein, N is the sample quantity; d, m, p and q are the dimensions of the design data, the field data, the target data and the coordinate data.

[0081] The design data is the design parameter.

[0082] The field data is the physical field data. The flapping wing flow analysis model based on the loft parameter is established through the computer-aided design software, the structured or unstructured grid is automatically generated, and the parameterized numerical simulation of the flapping wing is performed in combination with the numerical simulation software script and the user-defined function, so that the flapping wing flow field simulation data is obtained, and the simulation data is converted into the graph structure data.

[0083] The target data consists of efficiency and power. In an energy harvesting system, power reflects the output capability of energy, and efficiency reflects the utilization capability of energy. Efficiency and power are usually correlated, but not always positively correlated. Taking power and efficiency as components of target data facilitates finding the optimal balance point in the design.

[0084] The coordinate data refers to the spatial coordinate information associated with the design data, field data, and target data. It is mainly used to define the shape and structure of the flapping wing model and to associate physical quantities (such as pressure, temperature, velocity, etc.) with geometric positions, facilitating the generation of new geometric shapes in the optimization process.

[0085] Randomly arrange the data to generate a random index I, and rearrange the data: D, F, T, C = D[I], F[I], T[I], C[I].

[0086] Normalize the design data, field data, and target data: where μ and σ are the mean and standard deviation of the data, respectively, and D norm , F norm , and T norm are the normalized design data, field data, and target data, respectively.

[0087] Step 2: Divide the data into training set and validation set. The training set is used for model learning, and the validation set is used to verify the credibility of the model prediction. The generated multiple sets of design parameters and their corresponding flow field data and performance indicators are randomly divided into training set and validation set according to a certain proportion (such as 80% training set, 20% validation set), ensuring the uniformity of data distribution and the generalization ability of model training.

[0088] Divide the data into training set and validation set:

[0089] D train = D[:N train ], D valid = D[N train :];

[0090] F train = F[:N train ], F valid = F[N train :];

[0091] T train = T[:N train ], D valid = D[N train :];

[0092] C train = C[:N train ], Dvalid = D[N train ];

[0093] wherein,

[0094] Third step, define the model:

[0095] The main purpose of the generator G is to generate physical field data from the design parameters, providing physical field prediction capability for subsequent performance optimization. The input design data D, the output generated field data F', the mapping relationship is F' = G(D).

[0096] The main purpose of the discriminator J is to judge whether the input data is real data or generated data by learning the difference between real physical field data and generated physical field data.

[0097] The dynamic calculation module refers to the real-time calculation of key physical quantities (such as lift, torque, power, efficiency, etc.) in fluid mechanics according to the input airfoil motion parameters and flow field data, and the verification of whether the generator output design conforms to the aerodynamic law by simulating the dynamic motion (rotation and translation) of the airfoil and calculating the force by pressure integration method.

[0098] The logic of the generative adversarial network training is: jointly optimize the generator and the discriminator through supervised learning and adversarial learning.

[0099] Use the generator G and the discriminator J to predict the training set: F' train = G(D train ), T' train = J(D' train ).

[0100] Use the generator G and the discriminator J to predict the validation set: F' valid = G(D valid ), T' valid = J(D' valid ).

[0101] Optionally, the generator structure is as follows: (1) input vector wherein n z is the dimension of the input row vector; (2) map the input variable z to a higher-dimensional space through a fully connected layer: wherein is the weight matrix, b G ∈ R d is the bias vector, is the vector after linear transformation. (3) reshape the vector after linear transformation to a tensor suitable for convolution operation: wherein C is the number of channels, is the initial height, is the initial width. (4) Use the convolution layer to extract features and add residual connections. The mapping relationship is Among them, Conv is the convolution operation, defined as: Among them, Wi ,j is the convolution kernel weight, k is the convolution kernel size, is the feature map after convolution. (5) Use bicubic interpolation to enlarge the feature map, and its mapping relationship is Where I is the interpolation function, defined as: Among them, w i,j (x,y) is the weight function of bicubic interpolation, is the upsampled feature map. (6) The convolution layer is used to generate the final output, and its mapping relationship is in, is the final generator output.

[0102] Optionally, the discriminator has the following structure: (1) Input data Where B is the batch size, C in is the number of channels of input data, H in is the height of the input data, W in is the width of the input data; (2) Use the convolution layer to extract features, and its mapping relationship is is the feature map after convolution, where C1 is the number of output channels, H1 is the height of the feature map after convolution, and W1 is the width of the feature map after convolution; (3) Perform batch normalization and output The mapping relationship is Among them, μ J and σ J2 are the mean and variance of the feature map, γ J and β J is the scaling and offset parameter of the science department, ε J is a small constant used for numerical stability. (4) The feature map after convolution Apply activation function LeakyReLU, output The mapping relationship is in: α is the slope of the negative interval. (5) The feature map after activation Perform the maximum pooling operation and output The mapping relationship is H2 and W2 are the height and width of the feature map after pooling. (6) Perform global average pooling and output The mapping relationship is Global average pooling compresses the feature map of each channel into a single value. Flatten the feature map after global average pooling and output the discrimination result through the fully connected layer Wherein is the operation of flattening the feature map after global average pooling into a one-dimensional vector; W J is a weight matrix used to map input features to an output space; b J is a bias vector used to adjust the offset of the output. The output type of the fully connected layer depends on the task objective and the choice of activation function. For binary classification, the Sigmoid activation function is used to output the true / false probability; for multi-classification, the Softmax activation function is used to output the class probability distribution; for single / multi-physical quantity regression, the physical quantity prediction value is directly linearly outputted.

[0103] Optionally, the specific steps of the dynamic calculation module are as follows: (1) Normalize the control frequency fre to a dimensionless form, which is associated with the free stream velocity u inf and the characteristic length c, and convert the angle of attack cit and the phase angle phi to radians for subsequent calculations. (2) Calculate the change of the current angle of attack alf and the current displacement dis with time t to describe the motion state of the flapping wing. The specific formula is alf = cit·sin(2πt+φ), dis =-amp·c·sin(2πt), where: amp is the displacement amplitude. (3) Update the foil position foils by the rotation matrix rotation and the translation center center, which provides geometric information for subsequent force and moment calculation. The specific formula is: center = [0 dis], the updated foil position: foil = foil original ·rotation+center, where foil original is the original foil position. (4) Based on the flow field pressure and the foil geometry, calculate the normal force and the moment to describe the force state and rotation effect of the flapping wing. The tangent vector T represents the tangent direction of the foil edge, which is calculated by the coordinate difference of the adjacent two points. The specific formula is: T = foil i+1 -foil i , foil i and foil i+1 represent the coordinates of the i-th and i+1-th points on the foil, respectively. The modulus of the tangent vector T x and T y represent the components of the tangent vector T in the x and y directions, respectively; the normal vector N represents the normal direction of the foil edge, which is obtained by rotating the tangent vector T by 90°, and the specific formula is For each infinitesimal segment on the foil, the force per unit length ΔF = pt,i • N || T ||, where p t,i represents the flow field pressure at the i-th point; the total force is obtained by integrating the force per unit length along the airfoil edge n is the number of points on the airfoil; for each micro-element segment, the torque ΔM Z = ΔF • (foil mid -center), where foil mid represents the intermediate coordinates of the adjacent two points; similarly, the total torque is obtained by integrating the torque of the micro-element segment along the airfoil edge (5) Based on the force and torque, the power is calculated: the instantaneous power P time = v • F y + M Z • ω, the average power efficiency where v is the linear velocity, representing the movement speed of the flapping wing in the y direction; ω is the angular velocity, representing the speed of the flapping wing rotating around the center; μ inf is the free stream velocity, and Δ max represents the maximum displacement of the airfoil in the y direction.

[0104] where the model training logic is a two-way loss constraint and a dynamic optimization strategy, which combines the physical precision requirement of numerical simulation and the depth of data-driven feature learning, and finally realizes a fast and high-fidelity engineering prediction model. Mainly includes the following steps: (1) Forward prediction of end-to-end prediction chain: f pred = G(d; θ G ) → t pred = J(f pred ; θ J ), where θ G is the trainable parameter of the generator, which controls the generator mapping from d to f pred ; θ J is the trainable parameter of the discriminator, which extracts the target variable t pred from the physical field f pred ; (2) Calculate the field reconstruction loss: L field = SmoothL1(f field , f true ), which forces the predicted field output by the generator to be consistent with the true field at the point-by-point pixel / grid level; calculate the target prediction loss: L target = SmoothL1(t field , t true ), which forces the target variable extracted from the physical field by the discriminator to be consistent with the true value; the total loss L total = L field + κL target, k is the loss weight, used to balance the optimization priority of field reconstruction accuracy and target prediction accuracy; (3) Calculate the generator gradient: for backpropagation to guide the generator to optimize the microscopic accuracy of the physical field and the adaptability of the target simultaneously; Calculate the discriminator gradient: for backpropagation to guide the discriminator to optimize the ability to extract target features from the physical field; (4) In order to dynamically evaluate the model generalization and prevent overfitting, validate every g training cycles (epochs), and the indicators are: field reconstruction accuracy: MSE(f field ,f true ) and target prediction error MAE(t field ,t true ); (5) In order to balance the training speed and convergence stability, the learning rate is decayed according to the segmented rule, that is, in the process of training the generative adversarial network, the learning rate is updated in a segmented decay manner; The update rule of learning rate η is: where ε0is the initial learning rate, υ1and υ2are the decay coefficients, and F1and F2are the decay nodes.

[0105] It should be noted that the general function formula of SmoothL1() in the field reconstruction loss and the target prediction loss is:

[0106] As shown in Figure 3 , the training process of the generative adversarial model specifically includes: initializing the generator G and the discriminator J, the generator generates physical field data from design parameters through multi-layer convolution and upsampling, the discriminator distinguishes between real and generated data through convolution and pooling, and simultaneously uses the Xavier initialization method to initialize the model parameters; Then, load and preprocess the data, including design parameters, physical field data, target variables, etc., and convert them into PyTorch tensors; After the generator generates physical field data from the design parameters, calculate the field reconstruction loss (compare the point-by-point difference between the generated data and the real data) and the target prediction loss (compare the target variables extracted from the generated data with the real values), and optimize the total loss through backpropagation; The discriminator inputs the real physical field data and the physical field data generated by the generator, calculates the target prediction loss, and optimizes the discriminator parameters through backpropagation; At the same time, the dynamic calculation module verifies whether the physical field data output by the generator conforms to the physical law, calculates the key physical quantities (such as lift, moment, power, efficiency) and compares them with the real values; Calculate and record the loss of the training set and the validation set every certain number of iteration cycles, monitor the change trend of the field reconstruction loss and the target prediction loss, and decay the learning rate to 0.1 times of the previous value every certain number of epochs to speed up convergence and avoid overfitting; After sufficient training, the field reconstruction loss is reduced to 10 -6 orders of magnitude, and the target prediction loss is reduced to 10 -5The model performance is stable, the training is completed, the generator can generate physical field data conforming to physical laws from the design parameters, the discriminator can effectively distinguish between real and generated data, the dynamic calculation module verification result is highly consistent with the true value, the model has good generalization ability and prediction accuracy, and provides a reliable tool for subsequent flapping wing airfoil design optimization. The target prediction loss is a binary classification cross-entropy loss.

[0107] Step 4, model evaluation:

[0108] Calculate the evaluation indicators of the verification set:

[0109] R 2 Score:

[0110] Mean squared error MSE:

[0111] Mean absolute error MAE:

[0112] Where T i is the true value, T i ' is the predicted value, is the mean of the true value.

[0113] The trained model is comprehensively evaluated using the verification set, and multiple indicators are used to measure the prediction performance of the model. First, the R 2 score(determination coefficient) is used to evaluate the fitting degree of the model to the target variable(such as power and efficiency), and the closer the score is to 1, the higher the consistency between the predicted value and the true value of the model; secondly, the mean squared error(MSE) and the mean absolute error(MAE) are calculated, which respectively evaluate the average deviation and absolute deviation between the predicted value and the true value, and the smaller the MSE and MAE, the higher the prediction accuracy of the model. In addition, through visual analysis, scatter plots of predicted values and true values are drawn to visually display the prediction effect of the model, and to check whether there are systematic deviations or outliers. Finally, combined with the verification results of the dynamic calculation module, it is further confirmed whether the physical field data output by the generator conforms to the physical law, to ensure the reliability and stability of the model in practical application.

[0114] It should be noted that before inputting the initial design parameters into the generative adversarial network, the initial design parameters are first normalized, and after obtaining the corresponding design parameter strategy, the design parameters can be denormalized to obtain the final design parameters.

[0115] S103, according to the initial design parameters and the physical field data, calculate the indicators representing the energy harvesting characteristics of the hybrid flapping wing airfoil.

[0116] The indicators include instantaneous power and efficiency; in the energy harvesting system, the power reflects the output capacity of the energy, and the efficiency reflects the utilization capacity of the energy, the efficiency and the power are usually interrelated, but not always positively correlated, and taking the power and the efficiency as the components of the indicators facilitates finding the optimal balance point in the design.

[0117] Optionally, the physical field data include flow field pressure, linear velocity, angular velocity, and velocity of free flow. According to the initial design parameters and the physical field data, the indicators characterizing the energy harvesting characteristics of the hybrid flapping wing airfoil are calculated, including: determining airfoil position parameters according to the initial design parameters; the airfoil position parameters include maximum displacement amount and coordinates of each point; determining tangent vectors and normal vectors of an airfoil edge according to the coordinates of each point, and determining forces and moments on the hybrid flapping wing airfoil according to the tangent vectors and the normal vectors and the flow field pressure; determining instantaneous power and average power according to the forces and the moments on the hybrid flapping wing airfoil and the linear velocity and the angular velocity; and determining efficiency of the hybrid flapping wing airfoil according to the average power, the maximum displacement amount and the velocity of the free flow.

[0118] The specific calculation manner can be determined according to the above-mentioned embodiments, and the embodiments will not be described here.

[0119] S104, determining a multi-objective optimization value according to the indicators.

[0120] The calculation formula of the multi-objective optimization value is: Ψ obj (C) = ω x Ψ p (C) + (1-ω) x Ψ η (C) ; Ψ obj (C) represents the multi-objective optimization value corresponding to the design parameter C, ω represents a proportion factor, Ψ p (C) represents the average power corresponding to the design parameter C, Ψ η (C) represents the efficiency corresponding to the design parameter C.

[0121] S105, taking maximizing the multi-objective optimization value as an objective, calculating a loss function through the multi-objective optimization value, calculating a gradient of the loss function with respect to the initial design parameters according to network self-differentiation, and updating the initial design parameters according to the gradient.

[0122] Wherein, the process of the multi-objective optimization of the embodiments determines the parameter design strategy of the hybrid flapping wing airfoil, which is constructed under the framework of a deep convolutional neural network, and the key of the construction is to use the gradient information of the neural network to guide the optimization process.

[0123] First, the optimization objective is defined, and the optimization objective is to maximize the periodic average indicator Ψ(C), which is a composite function of the working condition parameter C. For the power Ψ p (C) and the efficiency Ψ ηThe implementation method of the multi-objective optimization of (C) can be defined as follows: Ψ obj (C) = ω x Ψ p (C) + (1 - ω) x Ψ η (C), and the optimization objective is defined as Ψ obj (C).

[0124] Establish a loss function: define a loss function L obj (C), and the loss function is opposite to the multi-objective optimization value, which is the negative number corresponding to the multi-objective optimization value, that is, L obj (C) = - Ψ obj (C).

[0125] Establish a gradient expression: calculate the loss function L obj The gradient with respect to the working condition parameter C: The optimization process uses a gradient-based optimization algorithm, such as gradient descent, to update the working condition parameter C: optionally, the update formula of the design parameter is:

[0126]

[0127] Where C k+1 is the design parameter at the k+1 iteration, C k is the design parameter at the k iteration, ε k is the learning rate at the k iteration, is the gradient at the k iteration, ε is the initial learning rate, which controls the size of the iteration step, and K total is the maximum number of iterations.

[0128] S106, the updated initial design parameter is taken as the new initial design parameter, and the calculation of the multi-objective optimization value is continued until the preset termination condition is met, and the initial design parameter that meets the termination condition is determined as the parameter design strategy of the hybrid flapping airfoil.

[0129] In each iteration, the design parameter C is updated in the opposite direction of the gradient to reduce the value of the loss function. Using a variable learning rate can speed up the convergence in the early iterations and quickly approach the optimal solution; in the later iterations, a smaller learning rate helps to fine-tune the parameters and avoid oscillation around the optimal solution, thereby improving the accuracy of the optimization result. This adaptive learning rate adjustment method can dynamically adjust the learning rate according to the complexity of the problem and the actual situation of the optimization process, improving the adaptability and robustness of the algorithm. Finally, define the termination condition, such as reaching a certain number of iterations or the gradient changing less than a preset threshold. Through the above steps, a multi-objective optimization method based on neural network gradient is constructed, and in the optimization process, the target extreme value (maximize power and efficiency) is usually obtained at the point where the gradient is zero, that is, ▽ CL obj (C) = 0. The advantage of this method is that it can utilize the powerful function fitting and automatic differentiation capabilities of deep learning models to provide an effective solution for complex multi-objective optimization problems.

[0130] The final output connects the chordwise ratio lambda, the mixing ratio r, the NACA airfoil thickness t of the leading edge l , the NACA airfoil thickness t of the trailing edge t The global optimal parameter combination, i.e. the parameter design strategy, is obtained, and the multi-objective trade-off relationship between power density and energy efficiency is verified through the Pareto front, providing an optimized solution for efficient energy harvesting of biomimetic flapping wings that is both physically reasonable and engineering feasible.

[0131] In one embodiment, during the optimization process, an optimization process graph, a design parameter comparison graph, and a Pareto front graph can be constructed; wherein (1) the optimization process graph: the target function is plotted against the number of iterations; (2) the design variable comparison graph: the optimal design variable is compared with the worst design variable; (3) the Pareto front graph: the Pareto front graph of the multi-objective optimization problem is plotted.

[0132] After optimization, first, the optimal design parameters, target values, and physical field data are sorted and analyzed, the design parameters are converted to actual parameters through inverse normalization, which is convenient for practical application, and the target function variation curve and physical field distribution graph (such as power and efficiency) are plotted using visualization tools to intuitively display the optimization effect, and the design parameters and performance indicators before and after optimization are compared to evaluate the optimization improvement; for further analysis of the multi-objective optimization effect, Pareto front analysis is performed to show the trade-off relationship between power and efficiency, each point on the Pareto front represents an optimal combination, and the designer can select the appropriate solution according to the requirements, for example, high power scenarios select solutions with higher power, and high efficiency scenarios select solutions with higher efficiency; finally, a detailed statistical report is generated, including key parameters, optimization results, Pareto front analysis, and performance improvement quantitative indicators, which provides data support for subsequent design improvement, and evaluates the optimization effect through Pareto front analysis, provides a scientific basis for multi-objective decision-making, and improves design flexibility and practicality.

[0133] In one embodiment, the present application also provides a parameter design method for hybrid flapping airfoils based on network self-differentiation, as shown in Figure 4As shown, the embodiment includes: (1) data loading and preprocessing: preparing data to ensure that the data is suitable for model training; (2) data division: dividing the training set and the validation set for model training and evaluation; (3) model definition: constructing the generator and discriminator models for generating and evaluating physical field data; (4) optimization process: based on the network self-differentiation optimization method, the airfoil design optimization method is constructed; (5) result statistics and visualization: draw optimization process graph, design variable comparison graph and Pareto.

[0134] The present application has at least the following beneficial technical effects:

[0135] (1) The present application introduces a convolutional neural network, which fully utilizes its unique advantages in processing flapping wing flow field data. CNN can efficiently process complex unsteady flow problems through local receptive field and weight sharing mechanism, significantly reduce the computational complexity, and retain the key features of flow field data (such as vortex structure, pressure distribution, etc.). Its convolution kernel can accurately extract the spatial features in the flow field, capture the complex relationship between flapping wing airfoil design parameters and performance indicators (such as power, efficiency), etc. In addition, CNN has strong nonlinear fitting ability, which can learn the mapping relationship from high-dimensional data and provide accurate model support for optimization. Its translation invariance makes the model adapt to various working conditions and design requirements, with strong generalization ability, ensuring high precision prediction in different design scenarios.

[0136] (2) The present application introduces a generative adversarial network, which further improves the intelligent level of flapping wing flow field data generation. GAN can generate high-quality flow field data (such as pressure field, velocity field, etc.) that meets the physical laws through the adversarial training of generator and discriminator, filling the missing part of experimental or simulation data. The generator is continuously optimized through adversarial training, making the generated flow field data more accurate, thereby improving the accuracy of the optimization result. GAN can generate diverse flow field data, enhancing the generalization ability of the model and adapting to various working conditions and design requirements. The introduction of GAN makes the optimization process more intelligent, and the generator can continuously optimize the flow field data according to the feedback of the discriminator, accelerating the optimization process and improving the quality of the optimization result.

[0137] (3) The present application combines automatic differentiation technology to realize fast and accurate calculation of the gradient of the loss function, significantly improving the optimization efficiency. Automatic differentiation technology can dynamically calculate the influence of design parameters on performance indicators, ensuring that the optimization process conforms to the laws of fluid mechanics, while avoiding the precision loss caused by discretization error in traditional numerical differentiation method, providing an efficient and reliable solution for complex multi-objective optimization problems.

[0138] (4) The application can simultaneously optimize power density and energy efficiency through a multi-objective optimization method, and verify the trade-off relationship between the two through a Pareto frontier analysis, so as to not only output a globally optimal design parameter combination, but also provide multiple feasible optimization solutions for engineering practice to meet the needs of different application scenarios, so that the application has both physical rationality and engineering feasibility in the design of bionic flapping wings, and provides a scientific basis and technical support for efficient energy harvesting.

[0139] The method can efficiently and accurately determine the optimal combination of design parameters such as chordwise ratio λ of the connecting section, mixing ratio r, NACA airfoil thickness t l and trailing edge NACA airfoil thickness t t of the leading edge, so as to improve the power and efficiency of the flapping wing energy harvesting device.

[0140] In the application of the parameter design method of the hybrid flapping wing airfoil based on network self-differentiation provided by the application, each step can be executed according to the order shown in the figure, and the execution order of each step can be determined according to the needs, and the application does not limit this. Figure 1

[0141] The parameter design method of the hybrid flapping wing airfoil based on network self-differentiation provided by one or more embodiments of the application is based on the same idea, and the application also provides a corresponding parameter design device of the hybrid flapping wing airfoil based on network self-differentiation, as shown in the figure. Figure 5

[0142] Figure 5 A parameter design device of a hybrid flapping wing airfoil based on network self-differentiation provided by the application is shown in the figure, and the device 500 comprises:

[0143] The acquisition module 501 is configured to acquire initial design parameters of the hybrid flapping wing airfoil.

[0144] The generation module 502 is configured to input the initial design parameters into a generator of a pre-constructed generative adversarial network to obtain physical field data corresponding to the initial design parameters of the hybrid flapping wing airfoil; the generative adversarial network is trained based on simulation data obtained by numerical simulation of fluid mechanics of the hybrid flapping wing airfoil as training data.

[0145] The calculation module 503 is configured to calculate an index representing energy harvesting characteristics of the hybrid flapping wing airfoil according to the initial design parameters and the physical field data.

[0146] The determination module 504 is configured to determine a multi-objective optimization value according to the index.

[0147] ​​The updating module 505 is configured to maximize the multi-objective optimization value, calculate a loss function through the multi-objective optimization value, calculate a gradient of the loss function with respect to the initial design parameter through network self-differentiation, and update the initial design parameter according to the gradient.

[0148] The iteration module 506 is configured to continue the calculation of the multi-objective optimization value by taking the updated initial design parameter as a new initial design parameter until a preset termination condition is met, and determine the initial design parameter meeting the termination condition as the parameter design strategy of the hybrid flapping airfoil.

[0149] The specific limitations of the hybrid flapping airfoil parameter design device based on network self-differentiation can refer to the limitations of the hybrid flapping airfoil parameter design method based on network self-differentiation, which will not be repeated here. Each module in the hybrid flapping airfoil parameter design device based on network self-differentiation can be realized by software, hardware, and combinations thereof, in whole or in part. The above-mentioned modules can be embedded in or independent of the processor in the computer device in hardware form, or can be stored in the memory in the computer device in software form, so as to be called and executed by the processor to perform the operations corresponding to each module.

[0150] The application further provides a computer readable storage medium, which stores a computer program, and the computer program can be used to execute the above-mentioned Figure 1 The application provides a hybrid flapping airfoil parameter design method based on network self-differentiation.

[0151] The application further provides a computer readable storage medium, which stores a computer program, and the computer program can be used to execute the above-mentioned Figure 6 The structure of the computer device is shown in the structure diagram of the computer device. Figure 6 As shown in the structure diagram of the computer device, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory, and of course can also include other hardware required by the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs to realize the above-mentioned Figure 1 The application provides a hybrid flapping airfoil parameter design method based on network self-differentiation.

[0152] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the above-mentioned embodiments of the methods. In the embodiments of the present application, any reference to memory, storage, database or other medium can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0153] The technical features of the above embodiments can be combined in any way. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, but as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

Claims

1. A parameter design method of hybrid flapping airfoils based on network self-differentiation, characterized in that, The method comprises the following steps: obtaining initial design parameters of a hybrid flapping airfoil; inputting the initial design parameters into a generator of a pre-constructed generative adversarial network to obtain physical field data corresponding to the initial design parameters of the hybrid flapping airfoil; the generative adversarial network is trained based on simulation data obtained by numerical simulation of fluid mechanics of the hybrid flapping airfoil as training data; calculating an index representing energy harvesting characteristics of the hybrid flapping airfoil according to the initial design parameters and the physical field data; determining a multi-objective optimization value according to the index; maximizing the multi-objective optimization value as the target, calculating a loss function through the multi-objective optimization value, calculating the gradient of the loss function with respect to the initial design parameters according to the network self-differentiation, and updating the initial design parameters according to the gradient; taking the updated initial design parameters as new initial design parameters to continue the calculation of the multi-objective optimization value until a preset termination condition is met, and determining the initial design parameters meeting the termination condition as the parameter design strategy of the hybrid flapping airfoil; wherein the physical field data includes flow field pressure, linear velocity, angular velocity, and free stream velocity; the index includes instantaneous power and efficiency; and the calculation of the index representing the energy harvesting characteristics of the hybrid flapping airfoil according to the initial design parameters and the physical field data comprises: determining airfoil position parameters according to the initial design parameters; the airfoil position parameters include maximum displacement and coordinates of each point; determining the tangential vector and normal vector of the airfoil edge according to the coordinates of each point, and determining the force and torque on the hybrid flapping airfoil according to the tangential vector and normal vector and the flow field pressure; determining the instantaneous power and average power according to the force and torque on the hybrid flapping airfoil, the linear velocity, and the angular velocity; determining the efficiency of the hybrid flapping airfoil according to the average power, the maximum displacement, and the free stream velocity.

2. The method of claim 1, wherein, The calculation formula of the multi-objective optimization value is: ； wherein, represents a multi-objective optimization value corresponding to the design parameter C, represents a scaling factor, represents an average power corresponding to the design parameter C, represents an efficiency corresponding to the design parameter C.

3. The method of claim 1, wherein, The loss function is opposite to the multi-objective optimization value, which is the negative number corresponding to the multi-objective optimization value.

4. The method of claim 1, wherein, The update formula of the design parameters is: ； ； in, For the The design parameters at the iteration, No. The design parameters at the iteration, For the The learning rate at the iteration, For the The gradient at iteration , is the initial learning rate, is the maximum number of iterations.

5. The method of claim 1, wherein, The construction process of the generative adversarial network comprises: extracting sample design parameters of sample hybrid flapping airfoils, and performing numerical simulation of fluid mechanics on the sample hybrid flapping airfoils according to the sample design parameters to obtain simulation data; the simulation data includes sample flow field data and sample indexes; dividing the sample design parameters and the corresponding simulation data into a training set and a validation set; obtaining an initial generator and an initial discriminator in an initial generative adversarial network; generating predicted flow field data from the sample design parameters through multi-layer convolution and up-sampling in the initial generator, determining a loss function based on the predicted flow field data, the sample flow field data, and the sample indexes, and iteratively updating the parameters of the initial generator based on the loss function; discriminating the predicted flow field data through the initial discriminator based on the sample flow field data, calculating a target prediction loss, and iteratively updating the parameters of the initial discriminator based on the target prediction loss; under the condition that the updated initial generator and the initial discriminator both meet a preset iteration condition, obtaining the generative adversarial network according to the initial generator and the initial discriminator meeting the iteration condition.

6. The method of claim 5, wherein, The loss function is determined based on the predicted flow field data, the sample flow field data and the sample index, and the parameters of the initial generator are iteratively updated based on the loss function, including: The predicted index is obtained by analyzing the predicted flow field data through the dynamic calculation module; The field reconstruction loss is determined according to the predicted flow field data and the sample flow field data; The target prediction loss is determined according to the predicted index and the sample index; The parameter update gradient of the initial generator is determined according to the field reconstruction loss and the target prediction loss; The parameters of the initial generator are iteratively updated according to the parameter update gradient.

7. The method of claim 6, wherein, The parameter update gradient of the initial discriminator is determined according to the target prediction loss. The mixed flapping airfoil is formed by combining a front section of a NACA airfoil with a first thickness and a rear section of a NACA airfoil with a second thickness to form a new airfoil composed of a leading edge airfoil, a connecting section and a trailing edge airfoil; the connecting section is constructed using a fourth-order Bezier curve, the starting point of which is the end point of the leading edge airfoil, the terminal point of which is the starting point of the trailing edge airfoil, and the two control points are respectively set as the next node of the original leading edge airfoil and the previous node of the original trailing edge airfoil; the first thickness is greater than the second thickness.

8. The method of claim 5, wherein, In the training process of the generative adversarial network, the learning rate is updated in a segmented decay manner; the update rule of the learning rate is as follows: ； wherein, initial learning rate, and are decay coefficients, and are decay nodes.

9. The method of claim 1, wherein, ​

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