Tilt rotor aerodynamic coefficient prediction system and method based on machine learning

Abstract

The invention relates to the technical field of tilt rotor simulation, and particularly discloses a tilt rotor aerodynamic coefficient prediction system and method based on machine learning, and the method employs a parameter embedding coding technology to carry out physical embedding processing and cascade fusion on airfoil shape parameters, attack angles and flow field parameters. Then, a neural network model is introduced to carry out deep joint feature extraction on the airfoil profile shape parameter, the attack angle and the flow field parameter so as to predict an initial lift coefficient, an initial resistance coefficient and an initial boundary layer parameter; and carrying out compressibility correction and symmetry constraint on the initial prediction parameters in combination with a physical model to ensure that the initial prediction parameters conform to the aerodynamic law, and finally calculating the aerodynamic coefficient based on the corrected related parameters of the aerodynamic coefficient. According to the method, the attack angle limitation of a traditional Viterna extrapolation method can be broken through, full-range coverage is achieved, the aerodynamic force prediction precision of the extreme attack angle area is remarkably improved, and meanwhile the calculation efficiency is greatly improved.

Description

Technical Field

[0001] The present application relates to the field of tiltrotor simulation technology, and more specifically, to a tiltrotor aerodynamic coefficient prediction system and method based on machine learning. Background Art

[0002] Tiltrotors are a crucial component of the low-altitude economy and are widely used in electric vertical take-off and landing (eVTOL) aircraft. In the field of tiltrotor simulation technology, the vortex particle method (VPM), a meshless numerical approach, simulates the dynamic evolution of the flow field by performing Lagrangian discretization of the vorticity field. However, traditional VPM is prone to numerical divergence during long simulations due to insufficient conservation of mass and angular momentum, and the complex handling of aerodynamic loading on solid boundaries (such as rotor blades) limits its practical application.

[0003] To address these issues, the improved vortex particle method (rVPM) enhances numerical stability by strengthening conservation properties in the particle governing equations (including conservation of mass, momentum, and angular momentum). It also better handles solid boundary conditions through the actuator line model (ALM). The reformulated VPM (rVPM) incorporates the dynamic evolution of particle size, strengthening conservation of mass and angular momentum, thereby improving numerical stability. Furthermore, the actuator line model (ALM) incorporates a meshless solid boundary for the rotor, allowing XFOIL to capture the aerodynamic performance of airfoils at angles of attack between -10° and 20°, effectively simulating multi-rotor and rotor-wing applications.

[0004] However, there are still some shortcomings for tiltrotors: the rotor solid boundary is introduced through the actuator line model, and the accuracy of the rotor performance is highly dependent on the aerodynamic data of the airfoil. Figure 1 As shown in the figure, due to the tilt angle of 0~90° and the twist angle of the rotor blade itself, the local angle of attack of the airfoil at different spanwise positions varies greatly. Especially at large tilt angles, some spanwise airfoils will experience high angle of attack stall and complete flow separation. Therefore, it is necessary to accurately capture the aerodynamic data of flow separation at these large angles of attack, and then look forward to a tiltrotor aerodynamic coefficient prediction system and method based on machine learning. Summary of the Invention

[0005] In order to solve the above technical problems, the present application is proposed. The embodiment of the present application provides a tilt-rotor aerodynamic coefficient prediction system and method based on machine learning, which uses parameter embedding coding technology to perform physical embedding processing and cascade fusion on airfoil shape parameters, angle of attack and flow field parameters to obtain information joint representation of airfoil shape parameters, angle of attack and flow field parameters. Then, a neural network model is further introduced to perform deep joint feature extraction on airfoil shape parameters, angle of attack and flow field parameters to predict the initial lift coefficient, drag coefficient and boundary layer parameters, and the initial predicted parameters are corrected for compressibility and symmetry constraints in combination with the physical model to ensure that they comply with aerodynamic laws. Finally, the aerodynamic coefficient is calculated based on the corrected aerodynamic coefficient related parameters. This method can break through the angle of attack limitation of the traditional Viterna extrapolation method, achieve full coverage of 0°-360°, and significantly improve the aerodynamic force prediction accuracy in extreme angle of attack areas, while greatly improving computational efficiency and robustness. It is suitable for real-time wing optimization design tasks in complex scenarios.

[0006] Accordingly, according to one aspect of the present application, a method for predicting aerodynamic coefficients of a tiltrotor based on machine learning is provided, comprising: Input airfoil shape parameters, angle of attack and flow field parameters; Embedding the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector; Cascading the airfoil shape parameter embedding coding vector, the angle of attack embedding coding vector, and the flow field parameter embedding coding vector to obtain an airfoil set-operating condition joint embedding coding vector; Inputting the airfoil set-operating condition joint embedding coding vector into a neural network inference model to obtain initial output parameters; performing post-processing correction on the initial output parameters based on the physical model to obtain decoding results of parameters related to aerodynamic coefficients, wherein the decoding results of parameters related to aerodynamic coefficients include logarithmic function values ​​of lift coefficient and drag coefficient, moment coefficient and boundary layer parameters; The aerodynamic force coefficient is calculated based on the decoding result of the aerodynamic force coefficient related parameters.

[0007] In another embodiment, the airfoil shape parameters, the angle of attack, and the flow field parameters are embedded and encoded to obtain an airfoil shape parameter embedded encoding vector, an angle of attack embedded encoding vector, and a flow field parameter embedded encoding vector, wherein the airfoil shape parameter embedded encoding vector is generated by the following steps: Based on the category function and the shape function, the upper surface category parameters, the upper surface shape parameters, the lower surface category parameters and the lower surface shape parameters in the airfoil shape parameters are functionally mapped to obtain the shape parameter embedded coding vector, and the dimension of the shape parameter embedded coding vector is 18.

[0008] In another embodiment, the airfoil shape parameters, the angle of attack, and the flow field parameters are embedded and coded to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector, wherein the angle of attack embedded coding vector is generated by the following steps: The angle of attack Convert to 、 and to obtain the attack angle embedding coding vector.

[0009] In another embodiment, the airfoil shape parameters, the angle of attack, and the flow field parameters are embedded and encoded to obtain an airfoil shape parameter embedded encoding vector, an angle of attack embedded encoding vector, and a flow field parameter embedded encoding vector, wherein the flow field parameter embedded encoding vector is generated by the following steps: Performing logarithmic transformation on the Reynolds number in the flow field parameters to obtain a logarithmic function value of the Reynolds number; The logarithmic function value of the Reynolds number, the turbulence intensity parameter, the upper boundary layer transition position parameter and the lower boundary layer transition position parameter are combined to obtain the flow field parameter embedding coding vector.

[0010] In another embodiment, the airfoil set-operating condition joint embedding coding vector is input into a neural network inference model to obtain initial output parameters, including: Performing multi-level fully connected encoding on the airfoil set-operating condition joint embedding coding vector using a multi-layer perceptron model of the neural network inference model to obtain an airfoil set-operating condition joint latent space coding vector; The airfoil set-operating condition joint latent space encoding vector is passed through the decoding layer of the neural network inference model to obtain the initial output parameters.

[0011] In another embodiment, passing the airfoil set-operating condition joint latent space encoding vector through a decoding layer of the neural network inference model to obtain the initial output parameters includes: Performing feature cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding encoding vector to obtain an airfoil set-operating condition multi-dimensional joint encoding vector; The airfoil set-operating condition multi-dimensional joint encoding vector is input into the decoding layer of the neural network inference model to obtain the initial output parameters.

[0012] In another embodiment, performing feature cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding encoding vector to obtain the airfoil set-operating condition multi-dimensional joint encoding vector includes: Performing sequence feature high-dimensional embedding reconstruction based on temporal convolution feature extraction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedded encoding vector to obtain a set of airfoil set-operating condition joint latent space local feature encoding vectors and a set of airfoil set-operating condition joint embedded local feature encoding vectors; Calculating a potential correlation query space interaction correlation matrix between any set of airfoil set-condition joint latent space local feature coding vectors and airfoil set-condition joint embedded local feature coding vectors in the set of the airfoil set-condition joint latent space local feature coding vectors and the set of the airfoil set-condition joint embedded local feature coding vectors to obtain a set of airfoil set-condition multi-dimensional potential correlation query space cross-domain interaction correlation matrices; The set of cross-domain interactive correlation matrices of the airfoil set-operating condition multi-dimensional potential correlation query space is dynamically weighted fused based on sparsity regularization to obtain the airfoil set-operating condition multi-dimensional joint encoding vector.

[0013] In another embodiment, a set of cross-domain interaction correlation matrices of the airfoil set-operating condition multi-dimensional potential correlation query space is dynamically weighted fused based on sparsity regularization to obtain the airfoil set-operating condition multi-dimensional joint encoding vector, including: Calculating the spatial sparsity regularization factor of each airfoil set-operating condition multidimensional potential correlation query space cross-domain interaction correlation matrix in the set of airfoil set-operating condition multidimensional potential correlation query space cross-domain interaction correlation matrices to obtain a set of airfoil set-operating condition multidimensional joint interaction space sparsity regularization factors; Based on the set of sparsity regularization factors of the airfoil set-operating condition multidimensional joint interaction space, the set of cross-domain interaction correlation matrices of the airfoil set-operating condition multidimensional potential association query space is dynamically weighted fusion encoded to obtain the airfoil set-operating condition multidimensional joint encoding vector.

[0014] In another embodiment, before inputting the airfoil set-operating condition joint embedding coding vector into a neural network inference model to obtain initial output parameters, the following steps are further included: Performing mathematical modeling based on the airfoil set-operating condition joint embedded coding vector to generate calculation parameters, and generating prediction confidence based on the calculation parameters; An updated result corresponding to the neural network inference model is generated based on the prediction confidence and the preset comparison value, and the neural network inference model corresponding to the airfoil set-working condition joint embedded coding vector is updated based on the updated result.

[0015] According to another aspect of the present application, a tiltrotor aerodynamic coefficient prediction system based on machine learning is provided, comprising: Parameter input module, used to input airfoil shape parameters, angle of attack and flow field parameters; An embedded coding module, configured to perform embedded coding on the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector; a cascade module, configured to cascade the airfoil shape parameter embedded coding vector, the angle of attack embedded coding vector, and the flow field parameter embedded coding vector to obtain an airfoil set-operating condition joint embedded coding vector; an initial parameter inference module, configured to input the airfoil set-operating condition joint embedding coding vector into a neural network inference model to obtain initial output parameters; a parameter correction module, configured to perform post-processing correction on the initial output parameters based on a physical model to obtain decoding results of parameters related to aerodynamic coefficients, wherein the decoding results of parameters related to aerodynamic coefficients include logarithmic function values ​​of lift coefficient and drag coefficient, moment coefficient, and boundary layer parameters; The aerodynamic coefficient calculation module is used to calculate the aerodynamic coefficient based on the decoding result of the aerodynamic coefficient related parameters.

[0016] Compared with the existing technology, the machine learning-based tiltrotor aerodynamic coefficient prediction system and method provided in this application use parameter embedding coding technology to perform physical embedding processing and cascade fusion on airfoil shape parameters, angle of attack, and flow field parameters to obtain a joint representation of information on airfoil shape parameters, angle of attack, and flow field parameters. Then, a neural network model is further introduced to perform deep joint feature extraction on airfoil shape parameters, angle of attack, and flow field parameters to predict the initial lift coefficient, drag coefficient, and boundary layer parameters. The initial predicted parameters are corrected for compressibility and symmetry constraints in combination with the physical model to ensure that they conform to the laws of aerodynamics. Finally, the aerodynamic coefficients are calculated based on the corrected aerodynamic coefficient-related parameters. This method can break through the angle of attack limitation of the traditional Viterna extrapolation method, achieve full coverage of the 0°-360° range, and significantly improve the aerodynamic force prediction accuracy in extreme angle of attack areas. At the same time, it greatly improves computational efficiency and robustness, making it suitable for real-time wing optimization design tasks in complex scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and other purposes, features, and advantages of the present application will become more apparent through a more detailed description of the embodiments of the present application in conjunction with the accompanying drawings. The accompanying drawings are intended to provide a further understanding of the embodiments of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the present application and do not constitute a limitation of the present application. In the drawings, the same reference numerals generally represent the same components or steps.

[0018] Figure 1 Schematic diagram of the change in the local angle of attack range of the tiltrotor discrete airfoil.

[0019] Figure 2 Flowchart of a method for predicting aerodynamic coefficients of a tilt-rotor based on machine learning according to an embodiment of the present application.

[0020] Figure 3 Schematic diagram of data flow of a tilt-rotor aerodynamic coefficient prediction method based on machine learning according to an embodiment of the present application.

[0021] Figure 4 This is a flowchart of step S4 in the tilt-rotor aerodynamic coefficient prediction method based on machine learning according to an embodiment of the present application.

[0022] Figure 5 This is a flowchart of step S42 in the tilt-rotor aerodynamic coefficient prediction method based on machine learning according to an embodiment of the present application.

[0023] Figure 6 This is a flowchart of step S421 in the tilt-rotor aerodynamic coefficient prediction method based on machine learning according to an embodiment of the present application.

[0024] Figure 7 Flowchart for prediction of aerodynamic coefficients of tiltrotors based on machine learning.

[0025] Figure 8 4 is a block diagram of a tilt-rotor aerodynamic coefficient prediction system based on machine learning according to an embodiment of the present application.

[0026] Figure 9 This is a schematic diagram of the chord length and torsion angle distribution of the TUD_F29 propeller and its corresponding geometric shape.

[0027] Figure 10 1 is a schematic diagram comparing the propeller performance at different tilt angles using the original method and the improved method of this embodiment. DETAILED DESCRIPTION

[0028] Below, the exemplary embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application, and it should be understood that the present application is not limited to the exemplary embodiments described herein.

[0029] The numerical simulation of tiltrotors is generally implemented based on the derivation of the vortex intensity evolution equation, the vortex form of the NS equation, the embodiment of the numerical scheme, and the meshless boundary conditions. The derivation of the vortex intensity evolution equation, the vortex form of the NS equation, and the embodiment of the numerical scheme are all derived using existing formulas, so I will not go into details here.

[0030] In rVPM, the rotor blades are modeled using the actuator line model (ALM). By discretizing the blade geometry into a series of units, XFOIL is used to obtain the aerodynamic performance of the airfoil at an angle of attack of -10 to 20 degrees. Compared to the practice of using XFOIL to calculate a small range of angles in rVPM and extrapolating the Viterna empirical formula to larger angles, not only is the calculation time significantly reduced, but higher-precision aerodynamic data for angles of attack of 0 to 360 degrees can also be effectively obtained. The vorticity of each blade is introduced into the fluid domain by placing static particles on its surface. These particles are used to capture the circulation distribution of the blade. At the same time, free particles are released at the trailing edge to characterize the effects of unsteady loads and trailing vortex circulation.

[0031] The frequency of particle release per revolution determines the initial spacing ∆x between particles (discretization length), which together with the core size σ (particle radius) determines the spatial resolution of the wake. A necessary condition for numerical convergence and stability is the degree of overlap. However, when particles produce Lagrangian distortion, the overlap is further reduced, so λ>2 is generally required. However, if λ is too large, excessive smoothing will lead to unphysical wake aerodynamics. Alvarez et al. found that λ of 2.125 is more appropriate.

[0032] To improve the applicability of rVPM for tiltrotors, this application proposes a vortex particle-large eddy simulation (trVPM-LES) method for tiltrotors based on rVPM. By discretizing the vorticity form of the NS equations, a gridless flow field solution framework is constructed. The control parameters of the vortex intensity evolution equation are modified to enhance numerical stability. At the same time, an actuator model and a data-driven approach are combined to obtain airfoil aerodynamic data across the full angle of attack range to accurately process the tiltrotor's boundary conditions, thereby improving the accuracy of the tiltrotor at large tilt angles.

[0033] A hybrid machine learning model based on a neural network and Truong analysis enables rapid prediction of aerodynamic coefficients for each blade section over the full angle of attack range (0-360°). For regions without stall or with minimal flow separation, XFOIL provides highly accurate subsonic aerodynamic characteristics, so predictions are made using a neural network trained on XFOIL data. For high-angle-of-attack regions where large-scale flow separation occurs, Truong's analytical post-stall model is used. Based on regression analysis of wind tunnel data, the Truong model is specifically designed to predict deep stall conditions at high angles of attack. This machine learning model for the unsteady loading of lifting surface particles, trailing blades, and discretized blade element particle radius lengths automatically selects the model output type based on calculated confidence. High confidence levels rely on the neural network, while low confidence levels rely on the Truong model, with a smooth transition between the two. This approach ensures accurate and consistent predictions while adapting to varying airfoil shapes and flow conditions.

[0034] The aerodynamic coefficient calculation process of the neural network can be summarized as follows: ① Input processing: accepting input parameters and encoding geometric and flow characteristics; ② Latent space mapping: using deep neural networks to predict latent space outputs and combining physical inspiration methods to improve generalization capabilities; ③ Output decoding and physical correction: decoding the latent space output to obtain the aerodynamic coefficients, and performing physical consistency correction to ensure that the calculation results conform to the laws of aerodynamics.

[0035] Specific content reference Figure 2 and Figure 3 ,in, Figure 2 Flowchart of a method for predicting aerodynamic coefficients of a tilt-rotor based on machine learning according to an embodiment of the present application. Figure 3 Schematic diagram of data flow of the tiltrotor aerodynamic coefficient prediction method based on machine learning according to an embodiment of the present application. Figure 2 and Figure 3As shown, according to the machine learning-based aerodynamic coefficient prediction method of the tilt-rotor according to the embodiment of the present application, the steps include: S1, inputting airfoil shape parameters, angle of attack and flow field parameters; S2, embedding and encoding the airfoil shape parameters, the angle of attack and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector and a flow field parameter embedded coding vector; S3, cascading the airfoil shape parameter embedded coding vector, the angle of attack embedded coding vector and the flow field parameter embedded coding vector to obtain an airfoil set-working condition joint embedded coding vector; S4, inputting the airfoil set-working condition joint embedded coding vector into a neural network inference model to obtain initial output parameters; S5, post-processing and correcting the initial output parameters based on the physical model to obtain a decoding result of aerodynamic coefficient-related parameters, wherein the decoding result of aerodynamic coefficient-related parameters includes the logarithmic function value of the lift coefficient and the drag coefficient, the moment coefficient and the boundary layer parameter; S6, calculating the aerodynamic coefficient based on the decoding result of the aerodynamic coefficient-related parameters.

[0036] In the aforementioned machine learning-based method for predicting aerodynamic coefficients for a tiltrotor, step S1 inputs airfoil shape parameters, angle of attack, and flow field parameters. It should be understood that these parameters are fundamental physical quantities that describe the airfoil's operating state in a flow field and serve as the primary data source for calculating aerodynamic coefficients. Specifically, the airfoil shape determines the path and pressure distribution of airflow across the airfoil surface; the angle of attack affects the relative angle between the airflow and the airfoil; and flow field parameters (such as the Reynolds number and Mach number) reflect the characteristics of the flow field. These three parameters work together to influence the magnitude and direction of the aerodynamic force. Because different airfoil shapes, angles of attack, and flow field states can lead to variations in aerodynamic forces, this application, in order to fully understand the aerodynamic characteristics of a tiltrotor under specific operating conditions, provides a complete information foundation for subsequent aerodynamic coefficient calculations by acquiring comprehensive information on airfoil shape parameters, angle of attack, and flow field parameters.

[0037] In practice, airfoil geometry describes the specific geometry of the airfoil and is typically determined based on design requirements or existing airfoil databases (e.g., NACA series, supercritical airfoils, etc.). The angle of attack and flow field parameters describe the angle of the airfoil relative to the incoming flow and the dynamic characteristics of the flow field, respectively. In fluid mechanics, the angle of attack, flow field parameters, and vortex particles are closely related through the dynamic evolution of the flow field, jointly describing the physical mechanism of the flow. The airfoil surface generates vortex particles based on the slip velocity associated with the angle of attack. Therefore, the angle of attack and flow field parameters can be characterized using the vorticity-velocity-angle of attack coupling equation.

[0038] Specifically, the vortex particle method is based on the discretization of the vorticity equation. Each vortex particle represents a local vorticity distribution. The vorticity of the NS equation is expressed as follows: in, represents the vorticity, represents the velocity field, represents kinematic viscosity; In order to accurately simulate the dynamic evolution of the flow field, in the initialization stage, it is necessary to define the initial position of the vortex particles, the kernel function (Gaussian kernel or other radial basis function) and the filter width of the kernel function. . Each vortex particle represents a part of the local vorticity distribution. By reasonably setting its initial state, the flow field conditions at the initial moment can be effectively described. The position of the vortex particles determines how they are distributed in the flow field, while the choice of kernel function and the adjustment of the filter width affect the smoothness and resolution of the vorticity field. For example, using a smaller filter width in high vorticity areas can achieve higher resolution, while appropriately increasing the filter width in the far field area can help reduce the computational cost without significantly affecting the accuracy of the results.

[0039] The particle kernel function is not only used to construct a continuous vorticity field, but also serves as a spatial filter for LES (large eddy simulation): in, is the filter width of the kernel function, corresponding to the filter scale in LES; is the distribution of the kernel function in space. In the flow field, it can be dynamically adjusted according to the local vorticity intensity and particle stretching changes. , effectively processing turbulent structures at different scales, resulting in higher resolution in high vorticity regions and appropriate coarsening in far-field regions.

[0040] Next, the vorticity distribution of the initial flow field is set. Correct vorticity distribution initialization can ensure the physical authenticity of the simulation and make the evolution of vorticity in the subsequent simulation process closer to the actual situation. Specifically, the vorticity field is initialized: in, is the vorticity field; is the vorticity intensity of the particle; is the position of the particle.

[0041] In VPM unsteady simulations, the angle of attack is determined by the angle between the local flow velocity on the blade and the geometric centerline of the airfoil, and is dynamically adjusted over time. Flow field parameters, such as the Reynolds number and Mach number, are acquired through real-time data from the flow field simulation, ensuring their timeliness and accuracy.

[0042] In the above-mentioned machine learning-based tiltrotor aerodynamic coefficient prediction method, step S2 embeds and encodes the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedding encoding vector, an angle of attack embedding encoding vector, and a flow field parameter embedding encoding vector. It should be understood that since the original parameter form may not be conducive to direct processing by a neural network, the present application further embeds and encodes the airfoil shape parameters, the angle of attack, and the flow field parameters to map the original parameters into a high-dimensional embedding space, thereby facilitating the neural network to capture the inherent correlations and regularities between the parameters.

[0043] Specifically, to decompose the complex airfoil geometry into a mathematically analyzable parameter vector, thereby efficiently characterizing the airfoil's aerodynamic characteristics, in a specific example of this application, a function mapping is performed on the upper surface class parameters, upper surface shape parameters, lower surface class parameters, and lower surface shape parameters of the airfoil shape parameters based on a class function and a shape function to obtain the shape parameter embedded encoding vector. The dimension of the shape parameter embedded encoding vector is 18. In other words, the airfoil shape is converted into 18-dimensional CST parameters (9 parameters for the upper and lower surfaces respectively) to achieve efficient mathematical representation of any airfoil. Specifically, CST describes the airfoil shape through a combination of a class function and a shape function.

[0044] The class function defines the basic airfoil category (symmetric / asymmetric, leading edge shape, etc.), and its mathematical form is typically defined as a combination of power functions. The shape function uses Bernstein polynomials to flexibly adjust the local curvature of the airfoil and control the detailed shape. For the upper and lower surfaces, their geometric shape parameters can be parameterized by multiplying the class function and the shape function. Therefore, based on the basic principles of the CST method, this application defines a class function and a shape function to parametrically describe the airfoil shape. This effectively extracts the class parameters (e.g., the upper surface class parameters include the leading edge curvature coefficient) and shape parameters (e.g., the upper surface shape parameters are the weight coefficients of the Bernstein polynomials) for the upper and lower surfaces. This parameter combination generates a shape parameter embedding encoding vector. Nine parameters are generated for each surface (e.g., two class function parameters + seven shape polynomial coefficients), totaling an 18-dimensional parameter vector for the upper and lower surfaces. Normalization or standardization eliminates dimensional differences, ultimately forming an 18-dimensional shape parameter embedding encoding vector. The shape parameter embedding encoding vector not only retains the global contour features of the airfoil, but also captures sensitive changes in local geometric details, thereby providing a high-fidelity and low-dimensional input representation for the subsequent neural network model, ensuring efficient calculation while maintaining the ability to accurately model complex airfoil shapes.

[0045] At the same time, for the embedded coding of the attack angle, this application converts the attack angle Convert to 、 and to obtain the attack angle embedding coding vector. Specifically, since the original attack angle Direct input will lead to numerical discontinuity problems at periodic boundaries (such as 180° and -180° are equivalent). Convert to 、 and The combination of , embeds its periodicity and nonlinear characteristics related to stall to obtain a 3D angle of attack embedding encoding vector. Used to reflect the periodicity of the angle of attack (repeated every 180°); Used to enhance the nonlinear response at high angles of attack (near 90°), Used to supplement angle of attack directionality information (distinguishing between positive and negative angles of attack).

[0046] In a specific example of the present application, the flow field parameters include the Reynolds number (Re), the turbulence intensity parameter, the upper boundary layer transition position parameter, and the lower boundary layer transition position parameter. For the embedded coding of the flow field parameters, the present application first performs a logarithmic transformation on the Reynolds number in the flow field parameters to obtain the logarithmic function value of the Reynolds number; then, the logarithmic function value of the Reynolds number, the turbulence intensity parameter, the upper boundary layer transition position parameter, and the lower boundary layer transition position parameter are combined to obtain the embedded coding vector of the flow field parameters. Specifically, the Reynolds number (Re) is a key parameter that describes the flow characteristics of the fluid, and reflects the ratio between the inertial force and the viscous force of the fluid. Since the influence of the Reynolds number (Re) on the aerodynamic force is logarithmic, the logarithmic transformation is adopted. Linearize its effect on the aerodynamic coefficients. Turbulence intensity parameters (such as ) reflects the turbulent characteristics of the flow field, and its size directly affects the pulsating pressure and drag on the airfoil surface. Upper boundary layer transition position parameter and the lower boundary layer transition position parameter This describes the transition location between laminar and turbulent flow, and changes in its location significantly affect the aerodynamic performance and stability of the airfoil. By combining the logarithmic function value of the Reynolds number, the turbulence intensity parameter, the upper boundary layer transition location parameter, and the lower boundary layer transition location parameter, a four-dimensional flow field parameter embedding encoding vector is obtained.

[0047] In the above-mentioned tilt-rotor aerodynamic coefficient prediction method based on machine learning, in step S3, the airfoil shape parameter embedded coding vector, the angle of attack embedded coding vector and the flow field parameter embedded coding vector are cascaded to obtain an airfoil set-working condition joint embedded coding vector. It should be understood that aerodynamic force is the coupling result of airfoil geometry, angle of attack and flow field parameters. Therefore, in order to fully reflect the joint influence of airfoil shape, angle of attack and flow field parameters on aerodynamic performance, the present application integrates information of the airfoil shape parameter embedded coding vector, the angle of attack embedded coding vector and the flow field parameter embedded coding vector through cascade fusion to obtain a joint representation of multi-dimensional parameters and form an airfoil set-working condition joint embedded coding vector. For example, the airfoil set-working condition joint embedded coding vector is: Through this processing, comprehensive information input can be provided to the subsequent neural network model so that the neural network can make more accurate predictions of aerodynamic coefficients based on the combined effects of airfoil shape, angle of attack and flow field parameters.

[0048] In the aforementioned machine learning-based tiltrotor aerodynamic coefficient prediction method, step S4 involves inputting the airfoil set-operating condition joint embedding encoding vector into a neural network inference model to obtain initial output parameters. It should be understood that neural networks possess powerful nonlinear fitting capabilities, effectively capturing the nonlinear coupling relationships between airfoil shape, angle of attack, and flow field parameters, and using this to predict aerodynamic coefficients. Furthermore, leveraging the rapid prediction capabilities of neural networks, the calculation time of aerodynamic coefficients can be significantly shortened, making this method suitable for real-time simulation of unsteady flow fields for tiltrotors.

[0049] Figure 4 FIG4 is a flow chart of step S4 in the method for predicting aerodynamic coefficients of a tilt rotor based on machine learning according to an embodiment of the present application. Figure 4 As shown, the step S4 includes: S41, using the multi-layer perceptron model of the neural network inference model to perform multi-level fully connected encoding on the airfoil set-working condition joint embedded coding vector to obtain the airfoil set-working condition joint latent space coding vector; S42, passing the airfoil set-working condition joint latent space coding vector through the decoding layer of the neural network inference model to obtain the initial output parameters.

[0050] Specifically, step S41 uses a multi-layer perceptron model within the neural network inference model to perform multi-level fully connected encoding on the airfoil set-operating condition joint embedding vector to obtain a joint airfoil set-operating condition latent space encoding vector. It should be understood that the multi-level fully connected encoding structure of the multi-layer perceptron (MLP) model enables it to gradually extract and integrate multi-level features within the joint airfoil set-operating condition embedding vector, exploring potential connections between multidimensional parameters to achieve a mapping from the input space to the intermediate latent space. Specifically, the MLP model, by stacking fully connected layers and nonlinear activation functions (such as Swish), gradually abstracts input features, learns local interactions between airfoil geometry and angle of attack (such as the effect of leading edge curvature on stall angle of attack), and captures global cross-parameter coupling (such as the modulation of Reynolds number on separated flows at high angles of attack). This extracts the aerodynamic force generation patterns implicit in the joint airfoil set-operating condition embedding vector, providing a high-information-density feature representation for the decoding layer, and ultimately obtaining the joint airfoil set-operating condition latent space encoding vector. In addition, during the model training stage, by adding mirror samples to the training data, the "mirror" of the flipped airfoil and angle of attack is analyzed, forcing the network output to meet the symmetry constraints, that is, for any combination of airfoil and angle of attack, its mirror-symmetrical airfoil and angle of attack in the opposite direction should produce the same aerodynamic coefficient, thereby ensuring the odd-even symmetry of the lift coefficient and drag coefficient.

[0051] Specifically, step S42 passes the airfoil set-operating condition joint latent space encoding vector through the decoding layer of the neural network inference model to obtain the initial output parameters. That is, the decoding layer of the neural network inference model is used to map the airfoil set-operating condition joint latent space encoding vector from the latent feature space back to the actual physical quantity. By stacking fully connected layers, the dimensionality is gradually reduced. Combined with the nonlinear transformation of the activation function, the aerodynamic coefficients usable in engineering are decoded, such as the lift coefficient, the logarithm of the drag coefficient (to improve fitting accuracy for low Cd values), the moment coefficient, and boundary layer parameters (such as momentum thickness and shape factor).

[0052] In a preferred example of the present application, considering that the airfoil set-operating condition joint latent space encoding vector (high-dimensional features obtained by MLP encoding) contains deep abstract aerodynamic laws (such as the stall critical point and separated flow pattern), it may lose local detail information in the original airfoil set-operating condition joint embedded encoding vector (low-dimensional input features) (such as the direct impact of leading edge sharpness on low-angle aerodynamic force). Therefore, in order to better integrate the complementary information of high- and low-order features and improve the accuracy and robustness of aerodynamic coefficient prediction, the present application proposes a feature cross-order interaction mechanism. Before decoding the airfoil set-operating condition joint latent space encoding vector, the original airfoil set-operating condition joint embedded encoding vector is introduced by backtracking to improve the model's sensitivity and accuracy in predicting aerodynamic coefficients.

[0053] Figure 5 FIG4 is a flow chart of step S42 in the method for predicting aerodynamic coefficients of a tilt rotor based on machine learning according to an embodiment of the present application. Figure 5 As shown, the step S42 includes: S421, performing feature cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedded encoding vector to obtain the airfoil set-operating condition multi-dimensional joint encoding vector; S422, inputting the airfoil set-operating condition multi-dimensional joint encoding vector into the decoding layer of the neural network inference model to obtain the initial output parameters.

[0054] Specifically, step S421 performs a feature cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding encoding vector to obtain an airfoil set-operating condition multi-dimensional joint encoding vector. Here, by performing a cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding encoding vector to construct an airfoil set-operating condition multi-dimensional joint encoding vector that contains both global abstract laws and local detail features, the information attenuation problem of deep networks can be avoided, and the model's sensitivity to nonlinear changes in aerodynamic forces (such as stall mutations and boundary layer separation) and prediction accuracy can be enhanced.

[0055] Figure 6 FIG4 is a flow chart of step S421 in the method for predicting aerodynamic coefficients of a tilt rotor based on machine learning according to an embodiment of the present application. Figure 6 As shown, the step S421 includes: S4211, performing sequence feature high-dimensional embedding reconstruction based on temporal convolution feature extraction on the airfoil set-working condition joint latent space coding vector and the airfoil set-working condition joint embedded coding vector to obtain a set of airfoil set-working condition joint latent space local feature coding vectors and a set of airfoil set-working condition joint embedded local feature coding vectors; S4212, calculating the potential association query space interaction correlation matrix between any group of airfoil set-working condition joint latent space local feature coding vectors and airfoil set-working condition joint embedded local feature coding vectors in the set of airfoil set-working condition joint latent space local feature coding vectors and the set of airfoil set-working condition joint embedded local feature coding vectors to obtain a set of airfoil set-working condition multi-dimensional potential association query space cross-domain interaction correlation matrices; S4213, performing dynamic weighted fusion based on sparsity regularization on the set of airfoil set-working condition multi-dimensional potential association query space cross-domain interaction correlation matrices to obtain the airfoil set-working condition multi-dimensional joint coding vector.

[0056] In a specific example of the present application, step S4211 can be expressed as follows: in, represents the airfoil set-operating condition joint latent space encoding vector, represents the airfoil set-operating condition joint embedding coding vector, It is a temporal convolutional feature extraction network. represents the set of local feature encoding vectors of the joint latent space of airfoil set and working condition, 、 、 and They represent the first, second, and third vectors in the set of local feature encoding vectors of the airfoil set-operating condition joint latent space. and Airfoil set-operating condition joint latent space local feature encoding vector, is the number of vectors in the set of local feature encoding vectors of the airfoil set-operating condition joint latent space, represents the set of airfoil set-operating condition joint embedded local feature encoding vectors, 、 、 and They represent the first, second, and third in the set of the airfoil set-operating condition joint embedded local feature coding vectors. and The airfoil set-operating condition is jointly embedded into the local feature encoding vector.

[0057] It should be understood that, considering that directly performing feature interaction on the airfoil set-working condition joint latent space encoding vector and the airfoil set-working condition joint embedded encoding vector is prone to ignoring the local dependencies between features, resulting in information loss. Therefore, in order to enhance the perception of the local structural information within the airfoil set-working condition joint latent space encoding vector and the airfoil set-working condition joint embedded encoding vector, the present application adopts temporal convolution feature extraction to perform high-dimensional embedding reconstruction of sequence features on both respectively, generates multiple local observation segments through a one-dimensional convolution sliding window operation (similar to delayed embedding), mines the potential structural information and dimensional correlation within the features (such as the correlation between the airfoil leading edge shape and the stall angle of attack), and forms a multi-scale, multi-level local feature representation, namely, a set of local feature encoding vectors of the airfoil set-working condition joint latent space and a set of local feature encoding vectors of the airfoil set-working condition joint embedded, thereby providing a richer and more detailed feature basis for subsequent feature interaction.

[0058] In a specific example of the present application, step S4212 can be expressed as follows: in, represents the transpose of the matrix, represents the matrix multiplication operation, and They represent the airfoil set-operating condition joint latent space feature weight matrix and the airfoil set-operating condition joint embedding feature weight matrix, is the characteristic scale scaling factor, express and The cross-domain interaction correlation matrix between the airfoil set and the multi-dimensional potential correlation query space of the working condition.

[0059] Here, in order to capture the pairwise interaction relationship between the local feature coding vectors of the joint latent space of the airfoil set and the joint embedded local feature coding vectors of the airfoil set and the working condition, the present application maps the set of the local feature coding vectors of the joint latent space of the airfoil set and the working condition and the set of the local feature coding vectors of the joint embedded local feature coding vectors of the airfoil set and the working condition to the same feature space, and calculates the dot product attention weight between the two in this feature space to reveal the potential correlation and mutual influence between different local features, and mines and integrates the complementary information from different feature spaces, namely the global abstract laws in the latent space and the local detail features in the embedded space, to obtain a set of cross-domain interaction correlation matrices of the multi-dimensional potential correlation query space of the airfoil set and the working condition.

[0060] Next, the spatial sparsity regularization factor of each airfoil set-operating condition multidimensional potential correlation query space cross-domain interaction correlation matrix in the set of airfoil set-operating condition multidimensional potential correlation query space cross-domain interaction correlation matrices is calculated to obtain a set of airfoil set-operating condition multidimensional joint interaction space sparsity regularization factors, which is expressed as follows: in, is the correlation feature strength measurement function, It means to calculate the square of the Frobenius norm of the matrix. express The corresponding airfoil set-operating condition multi-dimensional joint interaction spatial sparsity regularization factor.

[0061] That is, by calculating the square of the F-norm of the cross-domain interaction correlation matrix of the airfoil set-working condition multi-dimensional potential correlation query space as a sparsity regularization factor, its information density is evaluated and its feature importance is quantified, so as to dynamically allocate aggregation weights to guide the subsequent aggregation process, so that the model focuses on the key interaction patterns of the airfoil set-working condition joint latent space encoding vector and the airfoil set-working condition joint embedded encoding vector during aggregation, avoiding invalid interaction interference.

[0062] Finally, based on the set of sparsity regularization factors of the airfoil set-operating condition multi-dimensional joint interaction space, the set of cross-domain interaction correlation matrices of the airfoil set-operating condition multi-dimensional potential association query space is dynamically weighted fused and encoded to obtain the airfoil set-operating condition multi-dimensional joint encoding vector, which is expressed as follows: in, represents the normalized exponential function, express The corresponding normalized airfoil set-operating condition multi-dimensional joint interaction space sparsity regularization factor, Represents the sparsity fusion matrix of the airfoil set-operating condition multi-dimensional joint interaction implicit coding feature, represents the feature shape reshaping, Represents the airfoil set-operating condition multi-dimensional joint encoding vector.

[0063] That is, after the set of sparsity regularization factors of the airfoil set-operating condition multi-dimensional joint interaction space is normalized, it is applied to the aggregation process of the set of cross-domain interaction correlation matrices of the airfoil set-operating condition multi-dimensional potential correlation query space. By weighted averaging, redundant information is eliminated and complementary information is amplified to achieve effective fusion and complementarity of multi-perspective interactive information, forming a global airfoil set-operating condition multi-dimensional joint encoding vector, thereby providing more comprehensive and accurate input features for aerodynamic force prediction.

[0064] Specifically, step S422 involves inputting the airfoil set-operating condition multidimensional joint encoding vector into the decoding layer of the neural network inference model to obtain the initial output parameters. Here, through cross-order feature interaction, the airfoil set-operating condition multidimensional joint encoding vector not only incorporates the global abstract features extracted by the multi-layer perceptron model, but also incorporates the local detail information embedded in the original embedded encoding vector. This allows for a more comprehensive and accurate reflection of the complex effects of airfoil shape, angle of attack, and flow field parameters on aerodynamic performance, thereby enhancing the decoding layer's ability to predict parameters related to aerodynamic coefficients.

[0065] In the aforementioned machine learning-based tiltrotor aerodynamic coefficient prediction method, step S5 involves post-processing and correcting the initial output parameters based on a physical model to obtain decoded aerodynamic coefficient-related parameter results. The decoded aerodynamic coefficient-related parameter results include the logarithmic function values ​​of the lift coefficient and the drag coefficient, the moment coefficient, and the boundary layer parameters. It should be understood that, given the difficulty of accurately extrapolating a purely data-driven model (the neural network inference model) to operating conditions not covered by the training set, this may result in prediction results that do not fully conform to actual aerodynamic laws. Therefore, this application employs a post-processing correction method based on a physical model to further physically correct the initial output parameters.

[0066] In a specific example of the present application, the physical model is the Prandtl-Glauert model or the Karman-Tsien model. Specifically, the Prandtl-Glauert model and the Karman-Tsien model correct the initial output parameters by considering compressibility, improving the prediction accuracy to conform to the aerodynamic laws. The Prandtl-Glauert model is based on the small perturbation theory and is used to correct the aerodynamic forces of airfoils in subsonic compressible flows. It is applicable to cases with low Mach numbers (Ma < 0.7) and no strong shock waves. In subsonic airflows, the compressibility of air affects the aerodynamic characteristics. The model assumes that the airfoil causes a small perturbation to the airflow. By introducing a compressibility correction factor, the aerodynamic force coefficient of incompressible flow is converted into the aerodynamic force coefficient of compressible flow. The correction formula (taking the lift coefficient as an example) is , where Ma is the Mach number. That is, by compensating for the change in pressure distribution caused by air compressibility through linearized potential flow theory, the lift coefficient in incompressible flow is scaled by to reflect the effect of density change on lift.

[0067] The Karman-Tsien model improves the Prandtl-Glauert model and more accurately describes the aerodynamic forces of airfoils in subsonic compressible flows. It is applicable to a higher subsonic range (0.3 < Ma < 0.9) and improves the Prandtl-Glauert formula through second-order approximation. Specifically, the Karman-Tsien model is also based on the small perturbation theory. On the basis of the Prandtl-Glauert model, a correction term is introduced to consider the high-order effect of Mach number change on the aerodynamic force coefficient. The lift coefficient correction formula is: Compared with the Prandtl-Glauert model, the Karman-Tsien model extends the correction range to higher Mach numbers by adding a correction term. By dynamically selecting the Prandtl-Glauert or Karman-Tsien model for post-processing correction, the present application can significantly improve the prediction accuracy of the aerodynamic characteristics of airfoils in subsonic compressible flows while retaining the high-efficiency prediction ability of the neural network, providing reliable aerodynamic inputs for the unsteady simulation of tiltrotors.

[0068] In the above method for predicting the aerodynamic force coefficients of tiltrotors based on machine learning, in step S6, based on the decoding results of the parameters related to the aerodynamic force coefficients, the aerodynamic force coefficients are calculated. That is, based on the corrected lift coefficient and drag coefficient, combined with parameters such as local flow velocity and chord length, the lift (L) and drag (D) of each section of the blade are calculated. Specifically, according to the lift coefficient and drag coefficient, the lift L and drag D of each section of the blade can be calculated as: in, is the air density; is the local velocity of the blade; is the blade chord length.

[0069] Furthermore, based on the calculated lift and drag, the aerodynamic force can be dynamically associated with the flow field to perform vorticity evolution and iterative correction, thereby achieving high-precision and high-efficiency flow simulation and analyzing the dynamic behavior of the airfoil in the flow field, such as flutter, stall and other phenomena.

[0070] First, the aerodynamic force is converted into vorticity intensity and smoothly loaded into the flow field through the LES filter. Specifically, the lift force L is converted into the equivalent vorticity intensity : After the aerodynamic force is converted into vorticity, it is smoothly loaded into the flow field through the LES filter: This process combines the kernel function of the particles and reflects the filtering effect of LES on small-scale turbulent structures.

[0071] Then, the induced velocity is solved by the Biot-Savart method to simulate the motion and stretching process of vortex particles, and the diffusion and splitting mechanisms are considered to maintain the stability of the solution.

[0072] Specifically, the local flow velocity induced by vortex particles is solved by the Biot-Savart method: in: is the induced velocity in the flow field; is the vorticity intensity of the particle; is the position of the particle; is the unit vector in the vertical direction.

[0073] The motion of vortex particles follows the Lagrangian method: The vorticity intensity changes due to the stretching effect: This process simulates the energy transfer from large-scale vorticity to small-scale structures in the LES.

[0074] Vortex particle diffusion simulates subgrid-scale dissipation effects: in is the eddy viscosity coefficient.

[0075] When the particle density or intensity exceeds a certain threshold, the particles are split to maintain the stability of the solution.

[0076] Finally, the local angle of attack and aerodynamic force are iteratively updated until convergence, and the results of thrust, torque, power and wake vortex distribution are output.

[0077] Specifically, according to the induction speed and free flow speed , update the local flow velocity and angle of attack: The aerodynamic forces are re-predicted through the neural network, the vorticity loading is corrected, and the iteration is carried out until convergence.

[0078] The thrust and torque are calculated by aerodynamic integration: The final results are output, namely thrust, torque, power and wake vortex distribution in the flow field.

[0079] In summary, according to the embodiment of the present application, a machine learning-based aerodynamic coefficient prediction method for a tiltrotor is explained. It uses parameter embedding coding technology to perform physical embedding processing and cascade fusion on the airfoil shape parameters, angle of attack, and flow field parameters to obtain a joint representation of the information of the airfoil shape parameters, angle of attack, and flow field parameters. Then, a neural network model is further introduced to perform deep joint feature extraction on the airfoil shape parameters, angle of attack, and flow field parameters to predict the initial lift coefficient, drag coefficient, and boundary layer parameters. The initial predicted parameters are corrected for compressibility and symmetry constraints in combination with the physical model to ensure that they conform to the laws of aerodynamics. Finally, the aerodynamic coefficients are calculated based on the corrected aerodynamic coefficient-related parameters. This method can break through the angle of attack limitation of the traditional Viterna extrapolation method, achieve full coverage of the 0°-360° range, and significantly improve the aerodynamic force prediction accuracy in extreme angle of attack areas. At the same time, it greatly improves the computational efficiency and robustness, making it suitable for real-time wing optimization design tasks in complex scenarios.

[0080] Reference Figure 7 Specifically, in order to enhance the reliability of the neural network inference model outside the training data distribution, before inputting the airfoil set-operating condition joint embedding coding vector into the neural network inference model to obtain the initial output parameters, the following steps are also included: Mathematical modeling is performed based on the airfoil set-operating condition joint embedding coding vector to generate calculation parameters, and prediction confidence is generated based on the calculation parameters; an update result corresponding to the neural network inference model is generated based on the prediction confidence and a preset comparison value, and the neural network inference model corresponding to the airfoil set-operating condition joint embedding coding vector is updated based on the update result. Data modeling is performed based on the input airfoil set-operating condition joint embedding coding vector, calculation parameters of the Mahalanobis distance are calculated, and the calculation parameters are converted into confidence scores to obtain a confidence analysis score corresponding to the neural network inference model; the credibility of the neural network inference model is generated based on the confidence analysis score, and the neural network inference model is updated according to different credibility values.

[0081] Furthermore, in highly separated flow conditions, the combination of analytical models (such as Truong's post-stall regression model) improves the accuracy and physical consistency of the results. A hybrid machine learning model based on a neural network and Truong's analytical approach enables rapid prediction of aerodynamic coefficients for each blade section over the full angle of attack range (0-360°). For regions without stall or with minimal flow separation, XFOIL provides highly accurate subsonic aerodynamic characteristics, so predictions are made using a neural network trained with XFOIL data. For high-angle-of-attack regions where large-scale flow separation occurs, Truong's analytical post-stall model is used. Based on regression analysis of wind tunnel data, the Truong model is specifically designed for predicting deep stall conditions at high angles of attack. This machine learning model for the discretized blade element radius and discretized length of unsteady loads on lifting surface particle wakes automatically selects the model output type based on calculated confidence. High confidence levels rely on the neural network, while low confidence levels rely on the Truong model, with a smooth transition between the two. This approach ensures accurate and consistent predictions while adapting to varying airfoils and flow conditions.

[0082] Furthermore, the present application also provides a tilt-rotor aerodynamic coefficient prediction system based on machine learning.

[0083] Figure 8 FIG. 1 is a block diagram of a tiltrotor aerodynamic coefficient prediction system based on machine learning according to an embodiment of the present application. Figure 8As shown, according to the machine learning-based tiltrotor aerodynamic coefficient prediction system 100 of the embodiment of the present application, it includes: a parameter input module 110, for inputting airfoil shape parameters, angle of attack and flow field parameters; an embedding coding module 120, for embedding coding the airfoil shape parameters, the angle of attack and the flow field parameters to obtain an airfoil shape parameter embedding coding vector, an angle of attack embedding coding vector and a flow field parameter embedding coding vector; a cascade module 130, for cascading the airfoil shape parameter embedding coding vector, the angle of attack embedding coding vector and the flow field parameter embedding coding vector to obtain an airfoil shape parameter embedding coding vector. A set-operating condition joint embedded coding vector; an initial parameter inference module 140, used to input the airfoil set-operating condition joint embedded coding vector into a neural network inference model to obtain initial output parameters; a parameter correction module 150, used to perform post-processing correction on the initial output parameters based on a physical model to obtain a decoding result of aerodynamic coefficient related parameters, wherein the decoding result of aerodynamic coefficient related parameters includes the logarithmic function value of the lift coefficient and the drag coefficient, the moment coefficient and the boundary layer parameter; an aerodynamic coefficient calculation module 160, used to calculate the aerodynamic coefficient based on the decoding result of the aerodynamic coefficient related parameters.

[0084] Here, those skilled in the art will appreciate that the specific operations of each module in the above-mentioned tiltrotor aerodynamic coefficient prediction system based on machine learning have been described in the above-mentioned Figures 1 to 5 The description of the machine learning-based tilt-rotor aerodynamic coefficient prediction method has been introduced in detail, and therefore, its repeated description will be omitted.

[0085] The machine learning-based tiltrotor aerodynamic coefficient prediction system executes the method steps of the above-mentioned machine learning-based tiltrotor aerodynamic coefficient prediction method, which can achieve full range coverage of 0°-360° and significantly improve the aerodynamic force prediction accuracy in extreme angle of attack areas, while greatly improving computational efficiency and robustness, and is suitable for real-time wing optimization design tasks in complex scenarios.

[0086] Reference Figure 9 , Figure 9 The following is a schematic diagram of the chord length and twist angle distribution of the TUD_F29 propeller, along with its corresponding geometric shape. Specifically, the standard TUD_F29 propeller model tested by Stokkermans et al. is used. This propeller has a diameter of 0.3048m, four blades, and 17 airfoils distributed along the span. The test altitude was 0m, the incoming flow velocity was 20m / s, and the advance ratio was 0.69.

[0087] Figure 10: is a schematic diagram comparing the propeller performance at different tilt angles using the original method and the improved method of this embodiment. The original method is based on the improved vortex particle method, i.e., the rVPM method, while the improved method of this embodiment is based on the rVPM, and is a vortex particle-large eddy simulation method suitable for tilt rotors, i.e., the trVPM method. Figure 10 Specifically shown is a schematic diagram of the test for a tilt angle of 0~90°.

[0088] from Figure 10 It can be found that at smaller tilt angles, the difference is not obvious. This is because the twist angle of the TUD rotor at the 3 / 4 span position is 17.6°, and the blade twist angle itself ranges from approximately 10 to 40°. Taking into account the existence of a certain installation angle, even with a smaller tilt angle, the airfoil in key areas (such as the 3 / 4 span position) still does not experience significant flow separation, so rVPM also has higher accuracy. At large tilt angles of 60° to 90°, trVPM has significantly higher accuracy than rVPM, reducing the error to less than 5%. Therefore, this method can break through the angle of attack limitations of the traditional Viterna extrapolation method, achieve full coverage of 0°-360°, and significantly improve the aerodynamic force prediction accuracy in extreme angle of attack areas. At the same time, it greatly improves computational efficiency and robustness, making it suitable for real-time wing optimization design tasks in complex scenarios.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting aerodynamic coefficients of a tiltrotor based on machine learning, characterized in that: The following steps are involved: Input airfoil shape parameters, angle of attack and flow field parameters; Embedding the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector; Cascading the airfoil shape parameter embedding coding vector, the angle of attack embedding coding vector, and the flow field parameter embedding coding vector to obtain an airfoil set-operating condition joint embedding coding vector; Inputting the airfoil set-operating condition joint embedding coding vector into a neural network inference model to obtain initial output parameters; Post-processing and correcting the initial output parameters based on the physical model to obtain decoding results of parameters related to aerodynamic coefficients, wherein the decoding results of parameters related to aerodynamic coefficients include logarithmic function values ​​of lift coefficient and drag coefficient, moment coefficient and boundary layer parameters; The aerodynamic force coefficient is calculated based on the decoding result of the aerodynamic force coefficient related parameters.

2. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 1, characterized in that: Embedding the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector, wherein the airfoil shape parameter embedded coding vector is generated by the following steps: Based on the category function and the shape function, the upper surface category parameters, the upper surface shape parameters, the lower surface category parameters and the lower surface shape parameters in the airfoil shape parameters are functionally mapped to obtain the shape parameter embedded coding vector, and the dimension of the shape parameter embedded coding vector is 18.

3. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 1 or 2, characterized in that: Embedding the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector, wherein the angle of attack embedded coding vector is generated by the following steps: The angle of attack Convert to 、 and to obtain the attack angle embedding coding vector.

4. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 3, characterized in that: The airfoil shape parameters, the angle of attack, and the flow field parameters are embedded and coded to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector, wherein the flow field parameter embedded coding vector is generated by the following steps: Performing logarithmic transformation on the Reynolds number in the flow field parameters to obtain a logarithmic function value of the Reynolds number; The logarithmic function value of the Reynolds number, the turbulence intensity parameter, the upper boundary layer transition position parameter and the lower boundary layer transition position parameter are combined to obtain the flow field parameter embedding coding vector.

5. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 1 or 4, characterized in that: The airfoil set-operating condition joint embedding coding vector is input into a neural network inference model to obtain initial output parameters, including: Performing multi-level fully connected encoding on the airfoil set-operating condition joint embedding coding vector using a multi-layer perceptron model of the neural network inference model to obtain an airfoil set-operating condition joint latent space coding vector; The airfoil set-operating condition joint latent space encoding vector is passed through the decoding layer of the neural network inference model to obtain the initial output parameters.

6. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 5, characterized in that: Passing the airfoil set-operating condition joint latent space encoding vector through a decoding layer of the neural network inference model to obtain the initial output parameters includes: Performing feature cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding encoding vector to obtain an airfoil set-operating condition multi-dimensional joint encoding vector; The airfoil set-operating condition multi-dimensional joint encoding vector is input into the decoding layer of the neural network inference model to obtain the initial output parameters.

7. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 6, characterized in that: Performing feature cross-order interaction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding encoding vector to obtain an airfoil set-operating condition multi-dimensional joint encoding vector, including: Performing sequence feature high-dimensional embedding reconstruction based on temporal convolution feature extraction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedded encoding vector to obtain a set of airfoil set-operating condition joint latent space local feature encoding vectors and a set of airfoil set-operating condition joint embedded local feature encoding vectors; Calculating a potential association query space interaction correlation matrix between any set of airfoil set-operating condition joint latent space local feature coding vectors and airfoil set-operating condition joint embedded local feature coding vectors in the set of the airfoil set-operating condition joint latent space local feature coding vectors and the set of the airfoil set-operating condition joint embedded local feature coding vectors to obtain a set of airfoil set-operating condition multi-dimensional potential association query space cross-domain interaction correlation matrices; The set of cross-domain interactive correlation matrices of the airfoil set-operating condition multi-dimensional potential correlation query space is dynamically weighted fused based on sparsity regularization to obtain the airfoil set-operating condition multi-dimensional joint encoding vector.

8. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 7, characterized in that: The set of cross-domain interactive correlation matrices of the airfoil set-operating condition multi-dimensional potential correlation query space is dynamically weighted fused based on sparsity regularization to obtain the airfoil set-operating condition multi-dimensional joint encoding vector, including: Calculating the spatial sparsity regularization factor of each airfoil set-operating condition multidimensional potential correlation query space cross-domain interaction correlation matrix in the set of airfoil set-operating condition multidimensional potential correlation query space cross-domain interaction correlation matrices to obtain a set of airfoil set-operating condition multidimensional joint interaction space sparsity regularization factors; Based on the set of sparsity regularization factors of the airfoil set-operating condition multidimensional joint interaction space, the set of cross-domain interaction correlation matrices of the airfoil set-operating condition multidimensional potential association query space is dynamically weighted fusion encoded to obtain the airfoil set-operating condition multidimensional joint encoding vector.

9. The method for predicting aerodynamic coefficients of a tiltrotor based on machine learning according to claim 1, characterized in that: Before inputting the airfoil set-operating condition joint embedding coding vector into a neural network inference model to obtain initial output parameters, the following steps are also included: Performing mathematical modeling based on the airfoil set-operating condition joint embedded coding vector to generate calculation parameters, and generating prediction confidence based on the calculation parameters; An updated result corresponding to the neural network inference model is generated based on the prediction confidence and the preset comparison value, and the neural network inference model corresponding to the airfoil set-working condition joint embedded coding vector is updated based on the updated result.

10. A tiltrotor aerodynamic coefficient prediction system based on machine learning, characterized in that: include: Parameter input module, used to input airfoil shape parameters, angle of attack and flow field parameters; An embedded coding module, configured to perform embedded coding on the airfoil shape parameters, the angle of attack, and the flow field parameters to obtain an airfoil shape parameter embedded coding vector, an angle of attack embedded coding vector, and a flow field parameter embedded coding vector; a cascade module, configured to cascade the airfoil shape parameter embedded coding vector, the angle of attack embedded coding vector, and the flow field parameter embedded coding vector to obtain an airfoil set-operating condition joint embedded coding vector; an initial parameter inference module, configured to input the airfoil set-operating condition joint embedding coding vector into a neural network inference model to obtain initial output parameters; a parameter correction module, configured to perform post-processing correction on the initial output parameters based on a physical model to obtain decoding results of parameters related to aerodynamic coefficients, wherein the decoding results of parameters related to aerodynamic coefficients include logarithmic function values ​​of lift coefficient and drag coefficient, moment coefficient, and boundary layer parameters; The aerodynamic coefficient calculation module is used to calculate the aerodynamic coefficient based on the decoding result of the aerodynamic coefficient related parameters.

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