Hybrid flapping wing type parameter design method based on network self-differentiation

Abstract

The invention discloses a hybrid flapping wing type parameter design method based on network self-differentiation, and relates to the technical field of design and optimization of bionic flapping wing energy collection devices. Inputting the initial design parameters of the mixed flapping wing type into a generative adversarial network to obtain physical field data corresponding to the initial design parameters of the mixed flapping wing type so as to calculate indexes representing energy harvesting characteristics of the mixed flapping wing type; determining a multi-target optimization value according to the index; calculating a loss function through the multi-objective optimization value, calculating the gradient of the loss function relative to the initial design parameters according to network self-differentiation, and updating the initial design parameters according to the gradient; and taking the updated initial design parameters as new initial design parameters, continuing to calculate 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 mixed flapping wing type. According to the method, the optimal design parameters of the mixed flapping wing type can be accurately and quickly determined.

Description

Technical Field

[0001] The present invention relates to the technical field of design and optimization of a bionic flapping-wing energy harvesting device, and in particular to a parameter design method of a hybrid flapping-wing airfoil based on network self-differentiation. Background Art

[0002] The biomimetic oscillating flapping wing design can harvest flow energy under certain oscillation patterns, converting wind and water kinetic energy into electrical energy, offering a new approach to harnessing fluid kinetic energy. Traditional flapping wing research has primarily focused on standard NACA airfoils, which have been widely used in aerospace and other fields due to their geometric simplicity and extensive research base. However, these designs do not specifically address the specific mechanism of flapping wing energy harvesting, namely the complex coupled motion patterns of heaving and pitching. Many highly efficient propulsive organisms in nature, such as fish and marine mammals, have evolved propulsion mechanisms that are highly optimized to adapt to complex and dynamic flow environments. The profiles of these organisms typically exhibit wider leading edges and narrower trailing edges than standard four-digit NACA airfoils. However, the potential of non-standard NACA airfoils, particularly those that mimic those of highly efficient propulsive organisms in nature, for flapping wing energy harvesting has yet to be fully explored.

[0003] To fully tap the potential of non-standard NACA airfoils, researchers have proposed the concept of a hybrid flapping wing, which combines NACA airfoils with different characteristics to optimize the energy harvesting performance of the flapping wing. Traditional research methods for the fluid dynamics of hybrid flapping wings mainly include numerical simulation and experimental measurement. Numerical simulation methods can provide global information about the flow field, but they consume a lot of computing resources and time; experimental measurement methods can provide local information about the flow field, but they require complex experimental equipment and techniques and are limited by experimental conditions and measurement accuracy. Therefore, neither traditional numerical simulation nor experimental measurement methods can meet the requirements 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 the hybrid flapping wing airfoil. Summary of the Invention

[0004] Based on this, it is necessary to provide a parameter design method for a hybrid flapping airfoil based on network self-differentiation to address the above technical problems.

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

[0006] The present invention provides a parameter design method for a hybrid flapping airfoil based on network self-differentiation, comprising:

[0007] Obtaining initial design parameters of the hybrid flapping airfoil;

[0008] The initial design parameters are input into a pre-built generator of a 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 from a numerical simulation of fluid mechanics of the hybrid flapping wing airfoil as training data;

[0009] Based on the initial design parameters and physical field data, the indicators characterizing the energy harvesting characteristics of the hybrid flapping airfoil are calculated.

[0010] Determine the multi-objective optimization value based on the indicators;

[0011] With the goal of maximizing the multi-objective optimization value, the loss function is calculated through the multi-objective optimization value, the gradient of the loss function relative to the initial design parameters is calculated according to the network self-differentiation, and the initial design parameters are updated according to the gradient;

[0012] The updated initial design parameters are used as new initial design parameters, and the calculation of multi-objective optimization values is continued until the preset termination conditions are met. The initial design parameters that meet the termination conditions 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 indicators include instantaneous power and efficiency; and based on the initial design parameters and the physical field data, the indicators characterizing the energy harvesting characteristics of the hybrid flapping airfoil are calculated, including:

[0014] Determine the airfoil position parameters based on the initial design parameters; the airfoil position parameters include the maximum displacement and the coordinates of each point;

[0015] Determine the tangential vector and normal vector of the airfoil edge according to the coordinates of each point, and determine the force and moment on the hybrid flapping airfoil according to the tangential vector and normal vector, as well as the flow field pressure;

[0016] Determine the instantaneous power and average power based on the forces and moments on the hybrid flapping airfoil, as well as the linear and angular velocities;

[0017] The efficiency of the hybrid flapping airfoil is determined based on the average power, maximum displacement, and free stream speed. Optionally, the multi-objective optimization value is calculated as:

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

[0019] Among them, obj (C) represents the multi-objective optimization value corresponding to the design parameter C, ω represents the proportional factor, Ψ p (C) represents the average power corresponding to the design parameter C, 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 the field reconstruction loss based on the predicted flow field data and the sample flow field data;

[0034] Determine the target prediction loss based on the prediction index and sample index;

[0035] Determine the parameter update gradient of the initial generator based on the field reconstruction loss and the target prediction loss;

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

[0037] Optionally, the parameter update gradient of the initial discriminator is obtained as follows:

[0038] Based on the target prediction loss, the parameter update gradient of the initial discriminator is determined.

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

[0040]

[0041] Among them, ε0 is the initial learning rate, υ1 and υ2 are the attenuation coefficients, and F1 and F2 are the attenuation nodes.

[0042] 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, whose 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 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 invention provides a parameter design device for a hybrid flapping airfoil based on network self-differentiation, comprising:

[0044] An acquisition module, used for acquiring initial design parameters of the hybrid flapping wing airfoil;

[0045] A generation module is used to input the initial design parameters into a pre-built generator of a 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;

[0046] a calculation module for calculating an index characterizing energy harvesting characteristics of a hybrid flapping airfoil based on initial design parameters and physical field data;

[0047] A determination module is used to determine the multi-objective optimization value based on the indicators;

[0048] An update module is used to maximize the multi-objective optimization value, calculate the loss function through the multi-objective optimization value, calculate the gradient of the loss function relative to the initial design parameters based on the network self-differentiation, and update the initial design parameters according to the gradient;

[0049] The iterative module is used to use the updated initial design parameters as new initial design parameters to continue calculating the multi-objective optimization values until the preset termination conditions are met, and the initial design parameters that meet the termination conditions are determined as the parameter design strategy of the hybrid flapping airfoil.

[0050] The present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the parameter design method of the hybrid flapping wing airfoil based on network self-differentiation is realized.

[0051] The present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the parameter design method of the hybrid flapping wing airfoil based on network self-differentiation is implemented.

[0052] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects:

[0053] In the present invention, first, simulation data obtained by numerical simulation of fluid mechanics of a 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 parameters, thereby optimizing the design parameters based on the physical field data, and in the optimization process, the gradient of the loss function relative to the design parameters can be efficiently calculated through network self-differentiation, so that the design parameters can be dynamically adjusted in each iteration, gradually approaching the optimal solution, thereby improving the calculation efficiency and accuracy, thereby ensuring the calculation efficiency and accuracy of the optimal design parameters of the hybrid flapping airfoil. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0055] Figure 1 A schematic flow chart of a parameter design method for a hybrid flapping airfoil based on network self-differentiation provided by the present invention;

[0056] Figure 2 A schematic structural diagram of a hybrid flapping airfoil provided by the present invention;

[0057] Figure 3 A training flow chart of an adversarial neural network provided by the present invention;

[0058] Figure 4 A schematic flow chart of another parameter design method for a hybrid flapping airfoil based on network self-differentiation provided by the present invention;

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

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

[0061] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0062] Deep learning methods, particularly convolutional neural networks and generative adversarial networks, offer new perspectives for the design and optimization of flapping wing systems. Deep learning models can learn complex flow patterns from large amounts of data, predict fluid dynamics, and extract key aerodynamic performance parameters. The adaptive nature of these models and their robust nonlinear processing capabilities make them well-suited for solving complex unsteady flow problems. Network self-differentiation, commonly referred to as automatic differentiation, is a computer science technique used to automatically and efficiently compute the derivatives of functions. Unlike symbolic and numerical differentiation, automatic differentiation decomposes complex functions into a series of simple elementary operations (such as addition, multiplication, and exponentials), then uses the chain rule to calculate the derivatives of these elementary operations to obtain the derivative of the entire composite function. For example, neural network training often employs backpropagation, a specialized automatic differentiation technique. Starting from the last layer, the error signal is propagated backward through the network, and the weights of each layer are updated using the chain rule. This allows for the efficient computation of the gradient of the loss function with respect to all parameters, allowing network parameters to be adjusted during training to minimize the loss function. This means that virtually any computable function can be optimized, opening up vast possibilities for the application of deep learning.

[0063] Based on this, the present invention provides a parameter design method for a hybrid flapping wing airfoil based on network self-differentiation, which can accurately and quickly determine the optimal design parameters of the hybrid flapping wing 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 lIndicates the chord length of the leading edge airfoil starting from the leading edge point of the original airfoil, c t Indicates the chord length of the trailing edge airfoil starting from the trailing edge point of the original airfoil, c c represents the chord length of the connecting section, and c represents the total chord length of the airfoil.

[0072] S102, inputting the initial design parameters into a pre-built generator of a 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, a generative adversarial network (GAN) is constructed, and then the constructed GAN is used to generate physical field data corresponding to the initial design parameters.

[0074] Physics data can include: lift, torque, power, efficiency, etc.

[0075] Optionally, the construction process of the generative adversarial network includes: extracting sample design parameters of the sample hybrid flapping airfoil, and performing numerical simulation of fluid mechanics on the sample hybrid flapping airfoil according to the sample design parameters to obtain simulation data; the simulation data includes sample flow field data and sample indicators; dividing the sample design parameters and the corresponding simulation data into a training set and a validation set; obtaining the initial generator and initial discriminator in the initial generative adversarial network; generating predicted flow field data from the sample design parameters through multi-layer convolution and upsampling in the initial generator, and determining the loss function based on the predicted flow field data, the sample flow field data and the sample indicators, and iteratively updating the parameters of the initial generator based on the loss function; 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; when the updated initial generator and initial discriminator both meet the preset iteration conditions, a generative adversarial network is obtained according to the initial generator and initial discriminator that meet the iteration conditions.

[0076] Optionally, a loss function is determined based on the predicted flow field data, sample flow field data and 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 prediction indicators; determining the field reconstruction loss based on the predicted flow field data and the sample flow field data; determining the target prediction loss based on the prediction indicators and the sample indicators; determining the parameter update gradient of the initial generator based on the field reconstruction loss and the target prediction loss; and iteratively updating the parameters of the initial generator based on the parameter update gradient.

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

[0078] Specifically, simulation data is first acquired and processed. This involves extracting flow field data from numerical simulations and converting it into graph-structured data. A flow analysis model based on profile parameters is then established using computer-aided design (CAD) software, automatically generating high-quality structured or unstructured grids. Numerical simulation software scripts and user-defined functions (UDFs) are then combined to perform parametric numerical simulations of flapping wings, enabling comprehensive automated analysis of flapping wing flow characteristics and energy harvesting performance. After the numerical simulations are complete, flow field data at each instant is extracted, including position information, physical field information, velocity components, and metrics characterizing flapping wing energy harvesting characteristics (such as power and efficiency). Next, the flow field data is converted from the structured O-grid to a rectangular grid format suitable for processing by a convolutional neural network (CNN), resulting in a final three-dimensional physical field tensor. Furthermore, the data is normalized to the range [-1, 1] using a maximum-minimum normalization method to ensure that the magnitudes of the input features are similar, facilitating stable neural network training.

[0079] After determining the value ranges of each design parameter, the Latin hypercube sampling method is used to generate multiple sets of design parameter combinations to ensure that all possible value ranges of each parameter are fully explored; a transient numerical solution is performed on each set of design parameters, and multiple instantaneous moment characteristics of the complete flapping wing motion cycle are extracted, along with the flow field data and energy harvesting performance indicators at each instantaneous moment.

[0080] The data include: a. Design data: D∈R N×d ; b. Field data: F∈R N×m ; c. Target data: T∈R N×p ; d, coordinate data: C∈R N×q Where N is the number of samples; d, m, p, q are the dimensions of design data, field data, target data, and coordinate data.

[0081] Design data refers to design parameters.

[0082] The field data refers to physical field data. A flapping wing flow analysis model based on profile parameters is established using computer-aided design software. Structured or unstructured grids are automatically generated. Numerical simulation software scripts and user-defined functions are then used to perform parametric numerical simulations of flapping wings. The flapping wing flow field simulation data is then converted into graph-structured data.

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

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

[0085] Randomly arrange the data, 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: Among them, μ and σ are the mean and standard deviation of the data respectively, D norm 、F norm and T norm They are the normalized design data, field data, and target data respectively.

[0087] Step 2: Divide the data into a training set and a validation set. The training set is used to learn the model, while the validation set is used to verify the reliability of the model's predictions. The generated multiple sets of design parameter combinations and their corresponding flow field data and performance indicators are randomly divided into training and validation sets according to a certain ratio (e.g., 80% training set, 20% validation set) to ensure uniform data distribution and the generalization ability of model training.

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

[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] in,

[0094] The third step is to define the model:

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

[0096] The main purpose of the discriminator J is to determine 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 is to calculate the key physical quantities in fluid mechanics (such as lift, torque, power, efficiency, etc.) in real time based on the input airfoil motion parameters and flow field data. By simulating the dynamic motion of the airfoil (rotation and translation) and calculating the force using the pressure integration method, it verifies whether the design output by the generator conforms to the laws of aerodynamics.

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

[0099] Use the generator G and 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 Where n z The dimension of the input row vector; (2) the input variable z is mapped to a higher-dimensional space through a fully connected layer: in is the weight matrix, b G ∈R d is the bias vector, is the vector after linear transformation. (3) The vector after linear transformation Reshape into a tensor suitable for convolution operation: Where 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. (7) The feature map after global average pooling Flatten and pass through the fully connected layer to output the discrimination result in It is the operation of flattening the feature map after global average pooling into a one-dimensional vector; W J is the weight matrix used to map input features to the output space; b J is a bias vector used to adjust the output offset. The output type of the fully connected layer depends on the task objective and the selected activation function. For binary classification, the Sigmoid activation function is used to output the true or false probability. For multi-classification, the Softmax activation function is used to output the class probability distribution. For single / multi-physics regression, the predicted physical quantity value is directly output linearly.

[0103] Optionally, the specific steps of the dynamic calculation module are as follows: (1) normalize the control frequency fre to a dimensionless form so that it is consistent with the free flow velocity u inf Associated with the characteristic length c, the angle of attack cit and the phase angle phi are converted into radians for subsequent calculations. (2) Calculate the changes of the current angle of attack alf and the current displacement dis over 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 airfoil position foils through the rotation matrix rotation and the translation center center to provide geometric information for subsequent force and torque calculations. The specific formula is: center = [0 dis], updated airfoil position: foil = foil original rotation+center, where foil original is the original airfoil position. (4) Based on the flow field pressure and airfoil geometry, the normal force, and moment are calculated to describe the force state and rotation effect of the flapping wing. The tangential vector T represents the tangential direction of the airfoil edge and is calculated from the coordinate difference between two adjacent points. The specific formula is: T = foil i+1 -foil i , foil i and foil i+1 Represents the coordinates of the i-th and i+1-th points on the airfoil, and 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 airfoil edge, which is obtained by rotating the tangent vector T by 90°. The specific formula is For each infinitesimal segment on the airfoil, the force per unit length ΔF = pt,i ·N·||T||, where p t,i Represents the flow field pressure at the i-th point; integrate the force per unit length along the edge of the airfoil to obtain the total force n is the number of points on the airfoil; for each infinitesimal segment, the moment ΔM Z =ΔF·(foil mid -center), where foil mid Represents the middle coordinates of two adjacent points; similarly, the moment of the infinitesimal segment is integrated along the edge of the airfoil to obtain the total moment (5) Based on force and torque, calculate power: instantaneous power P time =ν·F y +M Z ω, average power efficiency Wherein, ν is the linear velocity, which indicates the speed of the flapping wing in the y direction; ω is the angular velocity, which indicates the speed of the flapping wing rotating around the center; μ inf is the free stream velocity, Δ max Indicates the maximum displacement of the airfoil in the y direction.

[0104] Among them, the model training logic is a dual-path loss constraint and dynamic optimization strategy, which deeply integrates the physical accuracy requirements of numerical simulation with data-driven feature learning, and ultimately realizes a fast and high-fidelity engineering prediction model. It mainly includes the following steps: (1) Constructing the forward prediction of the 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, controlling the generator from d to f pred The mapping of θ J is the trainable parameter of the discriminator, from the physical field f pred Extract target variable t pred ; (2) Calculate the field reconstruction loss: L field =SmoothL1(f field ,f true ), which forces the prediction field output by the generator to be consistent with the true field at the pixel / grid level; Calculate the target prediction loss: L target =SmoothL1(t field ,t true ), which forces the target variable extracted by the discriminator from the physical field to be consistent with the true value; the total loss L total =L field +κL target, κ is the loss weight, which is used to balance the optimization priority between field reconstruction accuracy and target prediction accuracy; (3) Calculate the generator gradient: Used for backpropagation to guide the generator to optimize both the microscopic accuracy of the physical field and the target adaptability; calculate the discriminator gradient: Used for back propagation to guide the discriminator to optimize the ability to extract target features from the physical field; (4) In order to dynamically evaluate the generalization of the model and prevent overfitting, it is verified once every γ 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 piecewise rule, that is, during the training process of the generative adversarial network, the learning rate is updated in a piecewise decay manner; the update rule of the learning rate η is: Where ε0 is the initial learning rate, υ1 and υ2 are the attenuation coefficients, and F1 and F2 are the attenuation nodes.

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

[0106] like Figure 3 As shown in Figure 2, 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 the design parameters through multi-layer convolution and upsampling. The discriminator distinguishes between real and generated data through convolution and pooling, and initializes the model parameters using the Xavier initialization method. Then, the data is loaded and preprocessed, including design parameters, physical field data, target variables, etc., and converted into PyTorch tensors. After the generator generates physical field data from the design parameters, the field reconstruction loss (comparing the point-by-point difference between the generated data and the real data) and the target prediction loss (comparing the target variables extracted from the generated data with the real values) are calculated. The total loss is optimized through back propagation; 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 back propagation; at the same time, the dynamic calculation module verifies whether the physical field data output by the generator conforms to the physical laws, calculates key physical quantities (such as lift, torque, power, efficiency) and compares them with the true values; every certain number of iterations, the loss of the training set and the validation set is calculated and recorded, the changing trend of the field reconstruction loss and the target prediction loss is monitored, and the learning rate is decayed to 0.1 times the previous one every certain number of epochs to accelerate convergence and avoid overfitting; after sufficient training, the field reconstruction loss is reduced to 10 -6 order of magnitude, the target prediction loss is reduced to 10 -5The model's performance is stable and training is complete. The generator can generate physical field data that conforms to physical laws from the design parameters. The discriminator can effectively distinguish between real and generated data. The dynamic calculation module verifies that the results are highly consistent with the true values. The model has good generalization ability and prediction accuracy, providing a reliable tool for subsequent flapping airfoil design optimization. The target prediction loss is the binary cross entropy loss.

[0107] Step 4: Model evaluation:

[0108] Calculate the evaluation metrics for the validation set:

[0109] R 2 score:

[0110] Mean Squared Error (MSE):

[0111] Mean Absolute Error (MAE):

[0112] Among them, T i is the true value, T i ' is the predicted value, is the mean of the true values.

[0113] The trained model is fully evaluated using the validation set, and the prediction performance of the model is measured using a variety of indicators. 2 The score (coefficient of determination) evaluates the model's goodness of fit for target variables (such as power and efficiency). The closer the score is to 1, the more consistent the model's predicted values are with the true values. Secondly, the mean squared error (MSE) and mean absolute error (MAE) are calculated to evaluate the average deviation and absolute deviation between the predicted values and the true values, respectively. The smaller the MSE and MAE, the higher the model's prediction accuracy. Furthermore, through visual analysis, a scatter plot of the predicted values and the true values is drawn to intuitively display the model's prediction effect and check for 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 physical laws, ensuring the reliability and stability of the model in practical applications.

[0114] It should be noted that before the initial design parameters are input into the generative adversarial network, they are first normalized. After the parameter design strategy is obtained, the corresponding design parameters can be denormalized to obtain the final design parameters.

[0115] S103 , calculating an index characterizing energy harvesting characteristics of the hybrid flapping airfoil based on the initial design parameters and the physical field data.

[0116] Indicators include instantaneous power and efficiency. In energy harvesting systems, power reflects the energy output capability, and efficiency reflects the energy utilization capability. Efficiency and power are usually interrelated, but not always positively correlated. Including power and efficiency as components of the indicators facilitates finding the optimal balance in the design.

[0117] Optionally, the physical field data includes flow field pressure, linear velocity, angular velocity, and free stream speed. 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 the airfoil position parameters according to the initial design parameters; the airfoil position parameters include the maximum displacement and the 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 wing airfoil according to the tangential vector and the normal vector, as well as the flow field pressure; determining the instantaneous power and average power according to the force and torque on the hybrid flapping wing airfoil, as well as the linear velocity and angular velocity; determining the efficiency of the hybrid flapping wing airfoil according to the average power, the maximum displacement and the free stream speed.

[0118] The specific calculation method can be determined according to the above embodiment, and will not be described in detail in this embodiment.

[0119] S104: Determine the multi-objective optimization value based on the indicators.

[0120] Among them, the calculation formula of the multi-objective optimization value is: obj (C) = ω × Ψ p (C)+(1-ω)×Ψ η (C);Ψ obj (C) represents the multi-objective optimization value corresponding to the design parameter C, ω represents the proportional 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, with the goal of maximizing the multi-objective optimization value, calculate the loss function through the multi-objective optimization value, calculate the gradient of the loss function relative to the initial design parameters according to the network self-differentiation, and update the initial design parameters according to the gradient.

[0122] Among them, the process of multi-objective optimization in this embodiment to determine the parameter design strategy of the hybrid flapping airfoil is constructed under the framework of a deep convolutional neural network. The key to the construction is to use the gradient information of the neural network to guide the optimization process.

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

[0124] Establish a loss function: define a loss function L obj (C), 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 gradient expression: calculate the loss function L through automatic differentiation technology obj Gradient relative to the operating parameter C: The optimization process uses a gradient-based optimization algorithm, such as the gradient descent method, to update the operating condition parameter C: Optionally, the update formula of the design parameter is:

[0126]

[0127] 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, which controls the size of the iteration step, K total is the maximum number of iterations.

[0128] S106 , using the updated initial design parameters as new initial design parameters, continuing to calculate the multi-objective optimization value until a preset termination condition is met, and determining the initial design parameters that meet the termination condition as the parameter design strategy for the hybrid flapping airfoil.

[0129] In each iteration, the design parameter C is adjusted according to the gradient , in the opposite direction to reduce the value of the loss function. The use of a variable learning rate can speed up the convergence speed in the early stage of iteration and quickly approach the optimal solution; in the later stage of iteration, a smaller learning rate helps to fine-tune the parameters to avoid oscillation near the optimal solution, thereby improving the accuracy of the optimization results. 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, thereby improving the adaptability and robustness of the algorithm. Finally, the termination conditions are defined, such as reaching a certain number of iterations or the change in gradient is less than a preset threshold. Through the above steps, a multi-objective optimization method based on neural network gradient is constructed. During the optimization process, the target extreme value (maximizing power and efficiency) is usually obtained at the point where the gradient is zero, that is, ▽ CL obj (C) = 0. The advancement of this method lies in its ability to leverage the powerful function fitting and automatic differentiation capabilities of deep learning models to provide an effective solution to complex multi-objective optimization problems.

[0130] The final output connection section chord ratio λ, mixing ratio r, leading edge NACA airfoil thickness t l 、Trail edge NACA airfoil thickness t t The global optimal parameter combination, namely the parameter design strategy, is proposed, and the multi-objective trade-off relationship between power density and energy efficiency is verified through the Pareto front, providing an optimization solution with both physical rationality and engineering feasibility for efficient energy harvesting of bionic flapping wings.

[0131] In one embodiment, during the optimization process, an optimization process diagram, a design parameter comparison diagram, and a Pareto front diagram can be constructed; wherein, (1) the optimization process diagram: plots the change of the objective function with the number of iterations; (2) the design variable comparison diagram: plots the comparison between the optimal design variables and the worst design variables; (3) the Pareto front diagram: plots the Pareto front diagram of the multi-objective optimization problem.

[0132] After the optimization is completed, the optimal design parameters, target values and physical field data are first sorted and analyzed, and the design parameters are converted into actual parameters through denormalization to facilitate practical application. At the same time, visualization tools are used to draw the objective function change curve and physical field distribution diagram (such as power and efficiency) to intuitively display the optimization effect, and compare the design parameters and performance indicators before and after optimization to evaluate the optimization improvement; to further analyze the multi-objective optimization effect, Pareto frontier analysis is performed to show the trade-off relationship between power and efficiency. Each point on the Pareto frontier represents an optimal combination. Designers can choose a suitable solution according to their needs. For example, a higher power solution is selected for a high-power scenario, and a higher efficiency solution is selected for a high-efficiency scenario; finally, a detailed statistical report is generated, including key parameters, optimization results, Pareto frontier analysis and performance improvement quantitative indicators, to provide data support for subsequent design improvements, and the optimization effect is evaluated through Pareto frontier analysis, providing a scientific basis for multi-objective decision-making and improving design flexibility and practicality.

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

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

[0135] (1) The present invention fully utilizes the unique advantages of convolutional neural networks in processing flapping wing flow field data by introducing them. Through local receptive fields and weight sharing mechanisms, CNN can efficiently handle complex unsteady flow problems, significantly reduce computational complexity, and retain key features of flow field data (such as vortex structure, pressure distribution, etc.). Its convolution kernel can accurately extract spatial features in the flow field and capture the complex relationship between flapping wing airfoil design parameters and performance indicators (such as power and efficiency). In addition, CNN has powerful nonlinear fitting capabilities and can learn mapping relationships from high-dimensional data to provide accurate model support for optimization. Its translation invariance enables the model to adapt to a variety of working conditions and design requirements, and its strong generalization ability ensures high-precision predictions in different design scenarios.

[0136] (2) The present invention further improves the intelligence level of flapping wing flow field data generation by introducing a generative adversarial network. GAN can generate high-quality flow field data (such as pressure field, velocity field, etc.) that conforms to physical laws through adversarial training between the generator and the discriminator, filling the missing parts 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 results. GAN can generate diversified flow field data, enhance the generalization ability of the model, and adapt to various working conditions and design requirements. The introduction of GAN makes the optimization process more intelligent. The generator can continuously optimize the flow field data according to the feedback of the discriminator, accelerate the optimization process and improve the quality of the optimization results.

[0137] (3) The present invention combines automatic differentiation technology to achieve rapid and accurate calculation of the gradient of the loss function, significantly improving optimization efficiency. Automatic differentiation technology can dynamically calculate the impact of design parameters on performance indicators, ensuring that the optimization process conforms to the laws of fluid mechanics. At the same time, it avoids the precision loss caused by discretization errors in traditional numerical differentiation methods, providing an efficient and reliable solution to complex multi-objective optimization problems.

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

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

[0140] When applying the parameter design method of the hybrid flapping wing airfoil based on network self-differentiation provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

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

[0142] Figure 5 Schematic diagram of a parameter design device for a hybrid flapping airfoil based on network self-differentiation provided by the present invention, the device 500 includes:

[0143] An acquisition module 501 is used to acquire initial design parameters of a hybrid flapping airfoil;

[0144] A generation module 502 is configured to input the initial design parameters into a pre-built generator of a 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 using simulation data obtained by numerical simulation of fluid mechanics of the hybrid flapping wing airfoil as training data;

[0145] A calculation module 503 is used to calculate an index characterizing the energy harvesting characteristics of the hybrid flapping airfoil based on the initial design parameters and the physical field data;

[0146] Determination module 504, for determining the multi-objective optimization value according to the indicators;

[0147] An updating module 505 is configured to calculate a loss function based on the multi-objective optimization value, with the goal of maximizing the multi-objective optimization value, calculate the gradient of the loss function relative to the initial design parameters based on network self-differentiation, and update the initial design parameters based on the gradient;

[0148] The iteration module 506 is used to use the updated initial design parameters as new initial design parameters to continue calculating the multi-objective optimization value until a preset termination condition is met, and the initial design parameters that meet the termination condition are determined as the parameter design strategy of the hybrid flapping airfoil.

[0149] Regarding the specific definition of the parameter design device of the hybrid flapping wing airfoil based on network self-differentiation, please refer to the definition of the parameter design method of the hybrid flapping wing airfoil based on network self-differentiation above, which will not be repeated here. The various modules in the above-mentioned parameter design device of the hybrid flapping wing airfoil based on network self-differentiation can be implemented in whole or in part by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0150] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 1 A parameter design method for hybrid flapping airfoil based on network self-differentiation is provided.

[0151] The present invention also provides Figure 6 The structural diagram of the computer equipment shown in FIG. Figure 6 As shown in the figure, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 1 A parameter design method for hybrid flapping airfoil based on network self-differentiation is provided.

[0152] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention 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 and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0153] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A parameter design method for a hybrid flapping airfoil based on network self-differentiation, characterized in that: include: Obtaining initial design parameters of the hybrid flapping airfoil; Inputting the initial design parameters into a pre-built generator of a 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 the simulation data obtained by numerical simulation of fluid mechanics of hybrid flapping airfoils; Calculating an index characterizing energy harvesting characteristics of a hybrid flapping airfoil based on the initial design parameters and the physical field data; Determining a multi-objective optimization value based on the indicators; With the goal of maximizing the multi-objective optimization value, the loss function is calculated through the multi-objective optimization value, the gradient of the loss function relative to the initial design parameters is calculated according to the network self-differentiation, and the initial design parameters are updated according to the gradient; The updated initial design parameters are used as new initial design parameters, and the calculation of multi-objective optimization values is continued until the preset termination conditions are met. The initial design parameters that meet the termination conditions are determined as the parameter design strategy of the hybrid flapping airfoil.

2. The method according to claim 1, characterized in that The physical field data includes flow field pressure, linear velocity, angular velocity, and free stream velocity; the indicators include instantaneous power and efficiency; and the indicators characterizing the energy harvesting characteristics of the hybrid flapping airfoil are calculated based on the initial design parameters and the physical field data, including: Determining airfoil position parameters according to the initial design parameters; the airfoil position parameters include maximum displacement and coordinates of each point; Determine the tangential vector and normal vector of the airfoil edge according to the coordinates of each point, and determine the force and moment on the hybrid flapping airfoil according to the tangential vector and normal vector, as well as the flow field pressure; Determine the instantaneous power and average power based on the forces and moments on the hybrid flapping airfoil, as well as the linear and angular velocities; Determine the efficiency of a hybrid flapping airfoil based on average power, maximum displacement, and freestream velocity.

3. The method according to claim 1, characterized in that The calculation formula of the multi-objective optimization value is: P obj (C)=ω×Ψ p (C)+(1-ω)×Ψ η (C); Among them, obj (C) represents the multi-objective optimization value corresponding to the design parameter C, ω represents the proportional 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.

4. The method according to claim 1, wherein The loss function is opposite to the multi-objective optimization value and is a negative number corresponding to the multi-objective optimization value.

5. The method according to claim 1, wherein The updating formula of the design parameters is: C k+1 =C k -ε k ▽ C L obj (C k ); 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, ▽ C L obj (C k ) is the gradient at the kth iteration, ε is the initial learning rate, K total is the maximum number of iterations.

6. The method according to claim 1, characterized in that The construction process of the generative adversarial network includes: 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; Divide the sample design parameters and corresponding simulation data into training set and validation set; Get the initial generator and initial discriminator in the initial generative adversarial network; 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; 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; 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.

7. The method according to claim 1, characterized in that The method of determining a loss function based on the predicted flow field data, the sample flow field data, and the sample index, and iteratively updating the parameters of the initial generator based on the loss function, includes: The predicted flow field data is analyzed through the dynamic calculation module to obtain the prediction index; Determine the field reconstruction loss based on the predicted flow field data and the sample flow field data; Determine the target prediction loss based on the prediction index and sample index; Determine the parameter update gradient of the initial generator based on the field reconstruction loss and the target prediction loss; The parameters of the initial generator are iteratively updated according to the parameter update gradient.

8. The method according to claim 7, characterized in that The parameter update gradient of the initial discriminator is obtained as follows: Based on the target prediction loss, the parameter update gradient of the initial discriminator is determined.

9. The method according to claim 6, characterized in that During the training process of the generative adversarial network, the learning rate is updated in a piecewise decay manner; the update rule of the learning rate η is: Among them, ε0 is the initial learning rate, υ1 and υ2 are the attenuation coefficients, and F1 and F2 are the attenuation nodes.

10. The method according to claim 1, characterized in that 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, the starting point of which is the end point of the leading edge airfoil, the end point 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.

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