Machine learning based tiltrotor aerodynamic force coefficient prediction system and method

Abstract

The application relates to the technical field of tilt-rotor simulation, and particularly discloses a tilt-rotor aerodynamic force 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, attack angles and flow field parameters, so as to obtain information joint representation of the airfoil shape parameters, the attack angles and the flow field parameters. Then, a neural network model is introduced to perform deep joint feature extraction on the airfoil shape parameters, the attack angles and the flow field parameters to predict initial lift coefficients, drag coefficients and boundary layer parameters. In combination with a physical model, compressibility correction and symmetry constraint are performed on the initial predicted parameters, so that the initial predicted parameters conform to the aerodynamic law, and finally, aerodynamic force coefficients are calculated based on the corrected aerodynamic force coefficient related parameters. The method can break through the angle-of-attack limitation of the traditional Viterna extrapolation method, realize full-range coverage, significantly improve the aerodynamic force prediction accuracy in the extreme angle-of-attack region, and greatly improve the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tilt-rotor simulation, and more particularly, to a tilt-rotor aerodynamic force coefficient prediction system and method based on machine learning. BACKGROUND

[0002] Tilt-rotor is an important part of low-altitude economy and is widely used in electric vertical take-off and landing (eVTOL) aircraft. In the field of tilt-rotor simulation, the vortex particle method (VPM) is a meshless numerical method that simulates the dynamic evolution of the flow field by Lagrangian discretization of the vorticity field. However, the traditional VPM is prone to numerical divergence due to insufficient mass conservation and angular momentum conservation in long-time simulation, and the handling of aerodynamic force loading on solid boundaries (such as rotor blades) is complex, which limits its practical application.

[0003] To address these issues, the improved vortex particle method (rVPM) enhances the conservation properties (including mass, momentum, and angular momentum conservation) in the particle control equation, thereby improving numerical stability, and better handles solid boundary conditions through the Actuator Line Model (ALM). The newly developed VPM (rVPM) enhances mass conservation and angular momentum conservation by introducing dynamic evolution of particle size, thereby improving numerical stability. Meanwhile, the Actuator Line Model (ALM) is introduced to the rotor meshless solid boundary, and the XFOIL is used to obtain the airfoil aerodynamic performance at -10~20° angle of attack, which can well simulate multiple rotors and rotor-wing.

[0004] However, there are still some deficiencies in tilt-rotor simulation: the introduction of rotor solid boundary through the Actuator Line Model (ALM) makes the accuracy of rotor performance highly dependent on airfoil aerodynamic data. As shown in FIG. 1, the tilt-rotor has a tilt angle of 0~90°, plus the twist angle of the rotor blade itself, so the local angle of attack of the airfoil at different spanwise positions varies greatly, especially in the state of large tilt angle, some spanwise airfoils will have large angle of attack stall, and the flow will be completely separated, so it is necessary to accurately capture the aerodynamic data of flow separation at large angle of attack, and further expect a tilt-rotor aerodynamic force coefficient prediction system and method based on machine learning. Figure 1 SUMMARY

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

[0006] Correspondingly, according to one aspect of the present application, a machine learning-based tilt-rotor aerodynamic force coefficient prediction method is provided, which comprises:

[0007] inputting airfoil shape parameters, attack angles and flow field parameters;

[0008] embedding and encoding the airfoil shape parameters, the attack angles and the flow field parameters to obtain airfoil shape parameter embedding encoding vectors, attack angle embedding encoding vectors and flow field parameter embedding encoding vectors;

[0009] concatenating the airfoil shape parameter embedding encoding vectors, the attack angle embedding encoding vectors and the flow field parameter embedding encoding vectors to obtain airfoil set-condition joint embedding encoding vectors;

[0010] inputting the airfoil set-condition joint embedding encoding vectors into a neural network inference model to obtain initial output parameters;

[0011] based on a physical model, post-processing and correcting the initial output parameters to obtain aerodynamic force coefficient related parameter decoding results, the aerodynamic force coefficient related parameter decoding results including the logarithmic function values of the lift coefficients, the drag coefficients, the moment coefficients and the boundary layer parameters;

[0012] based on the aerodynamic force coefficient related parameter decoding results, calculating the aerodynamic force coefficients.

[0013] In another embodiment, the airfoil shape parameters, the attack angles and the flow field parameters are embedded and encoded to obtain airfoil shape parameter embedding encoding vectors, attack angle embedding encoding vectors and flow field parameter embedding encoding vectors, wherein the generation of the airfoil shape parameter embedding encoding vectors comprises the following steps:

[0014] functionally mapping the upper surface category parameter, the upper surface shape parameter, the lower surface category parameter and the lower surface shape parameter in the airfoil shape parameters based on the category function and the shape function to obtain the shape parameter embedding encoding vector, and a dimension of the shape parameter embedding encoding vector is 18.

[0015] In another embodiment, the airfoil shape parameters, the angle of attack and the flow field parameters are embedding encoded to obtain an airfoil shape parameter embedding encoding vector, an angle of attack embedding encoding vector and a flow field parameter embedding encoding vector, wherein a generation manner of the angle of attack embedding encoding vector comprises the following steps:

[0016] the angle of attack is converted into a combination of , , and to obtain the angle of attack embedding encoding vector.

[0017] In another embodiment, the airfoil shape parameters, the angle of attack and the flow field parameters are embedding encoded to obtain an airfoil shape parameter embedding encoding vector, an angle of attack embedding encoding vector and a flow field parameter embedding encoding vector, wherein a generation manner of the flow field parameter embedding encoding vector comprises the following steps:

[0018] logarithmically transforming the Reynolds number in the flow field parameters to obtain a logarithmic function value of the Reynolds number;

[0019] 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 to obtain the flow field parameter embedding encoding vector.

[0020] In another embodiment, the airfoil set-operation joint embedding encoding vector is input into a neural network inference model to obtain an initial output parameter, comprising:

[0021] using a multi-level perception machine model of the neural network inference model to perform multi-level full connection encoding on the airfoil set-operation joint embedding encoding vector to obtain an airfoil set-operation joint latent space encoding vector;

[0022] passing the airfoil set-operation joint latent space encoding vector through a decoding layer of the neural network inference model to obtain the initial output parameter.

[0023] In another embodiment, the airfoil set-operation joint latent space encoding vector is passed through a decoding layer of the neural network inference model to obtain the initial output parameter, comprising:

[0024] crossing the airfoil set-operation joint latent space encoding vector and the airfoil set-operation joint embedding encoding vector to obtain an airfoil set-operation multi-dimensional joint encoding vector;

[0025] inputting the airfoil set-operation multi-dimensional joint encoding vector into a decoding layer of the neural network inference model to obtain the initial output parameter.

[0026] In another embodiment, crossing the airfoil set-operation joint latent space encoding vector and the airfoil set-operation joint embedding encoding vector to obtain an airfoil set-operation multi-dimensional joint encoding vector comprises:

[0027] performing sequence feature high-dimensional embedding reconstruction based on time-series convolution feature extraction on the airfoil set-operation joint latent space encoding vector and the airfoil set-operation joint embedding encoding vector to obtain a set of airfoil set-operation joint latent space local feature encoding vectors and a set of airfoil set-operation joint embedding local feature encoding vectors;

[0028] calculating a potential association query space cross-domain interaction association matrix between any one group of airfoil set-operation joint latent space local feature encoding vectors and airfoil set-operation joint embedding local feature encoding vectors in the set of airfoil set-operation joint latent space local feature encoding vectors and the set of airfoil set-operation joint embedding local feature encoding vectors to obtain a set of airfoil set-operation multi-dimensional potential association query space cross-domain interaction association matrices;

[0029] performing dynamic weighted fusion based on sparsity regularization on the set of airfoil set-operation multi-dimensional potential association query space cross-domain interaction association matrices to obtain the airfoil set-operation multi-dimensional joint encoding vector.

[0030] In another embodiment, performing dynamic weighted fusion based on sparsity regularization on the set of airfoil set-operation multi-dimensional potential association query space cross-domain interaction association matrices to obtain the airfoil set-operation multi-dimensional joint encoding vector comprises:

[0031] calculating a spatial sparsity regularization factor of each airfoil set-operation multi-dimensional potential association query space cross-domain interaction association matrix in the set of airfoil set-operation multi-dimensional potential association query space cross-domain interaction association matrices to obtain a set of airfoil set-operation multi-dimensional joint interaction spatial sparsity regularization factors;

[0032] Based on the set of airfoil set-operation multi-dimensional joint interaction space sparsity regularization factors, a set of airfoil set-operation multi-dimensional potential correlation query space cross-domain interaction correlation matrices is dynamically weighted and fused to obtain the airfoil set-operation multi-dimensional joint encoding vector.

[0033] In another embodiment, before the airfoil set-operation joint embedding encoding vector is input into a neural network inference model to obtain initial output parameters, the following steps are further included:

[0034] Based on the airfoil set-operation joint embedding encoding vector, mathematical modeling is performed to generate calculation parameters, and a prediction confidence is generated based on the calculation parameters;

[0035] Based on the prediction confidence and a preset comparison value, an update result corresponding to the neural network inference model is generated, and the neural network inference model corresponding to the airfoil set-operation joint embedding encoding vector is updated based on the update result.

[0036] According to another aspect of the present application, a machine learning-based prediction system for the aerodynamic force coefficients of a tilt-rotor is provided, which includes:

[0037] A parameter input module for inputting airfoil shape parameters, attack angles and flow field parameters;

[0038] An embedding coding module for embedding and coding the airfoil shape parameters, the attack angles and the flow field parameters to obtain airfoil shape parameter embedding coding vectors, attack angle embedding coding vectors and flow field parameter embedding coding vectors;

[0039] A cascading module for cascading the airfoil shape parameter embedding coding vectors, the attack angle embedding coding vectors and the flow field parameter embedding coding vectors to obtain an airfoil set-operation joint embedding coding vector;

[0040] An initial parameter inference module for inputting the airfoil set-operation joint embedding coding vector into a neural network inference model to obtain initial output parameters;

[0041] A parameter correction module for post-processing and correcting the initial output parameters based on a physical model to obtain aerodynamic force coefficient related parameter decoding results, the aerodynamic force coefficient related parameter decoding results including lift coefficients, logarithmic function values of drag coefficients, moment coefficients and boundary layer parameters;

[0042] An aerodynamic force coefficient calculation module for calculating aerodynamic force coefficients based on the aerodynamic force coefficient related parameter decoding results.

[0043] Compared with the prior art, the machine learning-based tilt-rotor aerodynamic force coefficient prediction system and method provided by the application uses parameter embedding coding technology to perform physical embedding processing and cascading fusion on airfoil shape parameters, attack angles and flow field parameters, to obtain information joint representation of the airfoil shape parameters, the attack angles and the flow field parameters. Then, a neural network model is further introduced to perform deep joint feature extraction on the airfoil shape parameters, the attack angles and the flow field parameters to predict initial lift coefficients, drag coefficients and boundary layer parameters. In combination with a physical model, the initial predicted parameters are corrected in compressibility and symmetry constraint to ensure that they conform to the aerodynamic law, and finally, the aerodynamic force coefficients are calculated based on the corrected aerodynamic force coefficient related parameters. The method can break through the angle of attack limit of the traditional Viterna extrapolation method, realize full-range coverage of 0°-360°, significantly improve the aerodynamic force prediction accuracy in the extreme angle of attack region, and greatly improve the calculation efficiency and robustness, and is suitable for real-time wing optimization design tasks in complex scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0044] The above and other objects, features and advantages of the present application will become more apparent from the following detailed description of embodiments of the present application, when taken in conjunction with the accompanying drawings. The drawings provided in the specification and the contents of the specification are to provide further understanding of embodiments of the present application, and constitute a part of the specification, and are used to explain the present application together with embodiments of the present application, and do not constitute a limitation of the present application. In the drawings, the same reference numerals generally designate the same components or steps.

[0045] Figure 1 A schematic diagram of the local angle of attack range change of the tilt-rotor discrete airfoil.

[0046] Figure 2 A flowchart of the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to an embodiment of the present application.

[0047] Figure 3 A data flow schematic diagram of the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to an embodiment of the present application.

[0048] Figure 4 A flowchart of step S4 in the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to an embodiment of the present application.

[0049] Figure 5 A flowchart of step S42 in the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to an embodiment of the present application.

[0050] Figure 6 A flowchart of step S421 in the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to an embodiment of the present application.

[0051] Figure 7Flowchart for machine learning based tilt-rotor aerodynamic force coefficient prediction.

[0052] Figure 8 Block diagram for machine learning based tilt-rotor aerodynamic force coefficient prediction system according to embodiments of the present application.

[0053] Figure 9 is the chord length and twist angle distribution of TUD_F29 propeller and its corresponding geometric profile sketch.

[0054] Figure 10 is the comparison sketch of propeller performance at different tilt angles using the original method and the improved method of the present embodiment. DETAILED DESCRIPTION

[0055] Hereinafter, example embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only a part of embodiments of the present application, and are not all embodiments of the present application, and it should be understood that the present application is not limited to the example embodiments described herein.

[0056] For tilt-rotor numerical simulation, it is generally realized based on derivation of vortex intensity evolution equation, N-S equation vortex form, numerical scheme embodiment, and meshless boundary condition, etc. The derivation of vortex intensity evolution equation, N-S equation vortex form, and numerical scheme embodiment are all derived using existing formulas, which will not be described in detail here.

[0057] In rVPM, the rotor blades are modeled by actuator line model (ALM), the blade geometry is discretized into a series of elements, and the airfoil aerodynamic performance at -10~20° angle of attack is obtained by using XFOIL. Compared with the method of using XFOIL to calculate a small range of angles in rVPM and extrapolating to a larger angle by combining Viterna empirical formula, not only the calculation time is greatly reduced, but also higher precision aerodynamic data at 0~360° angle of attack can be effectively obtained. The vorticity of each blade is introduced into the fluid domain by arranging static particles on its surface, and 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 represent the influence of non-stationary load and wake circulation.

[0058] The particle release frequency per revolution determines the initial spacing ∆x (discretization length) between particles, and the spacing together with the core scale σ (particle radius) determines the spatial resolution of the wake. The necessary condition for numerical convergence and stability is the overlap ratio However, when the particles produce Lagrangian distortion, the overlap will be further reduced, so generally λ>2 is needed. However, too large λ will cause excessive smoothing, which will lead to non-physical wake aerodynamic force. After testing, λ=2.125 is more appropriate.

[0059] For the purpose of improving the applicability of rVPM on tiltrotor, a trVPM-LES method is proposed based on rVPM. By discretizing the vorticity form of N-S equation, an unstructured mesh flow field solving framework is constructed. The control parameters of the vortex intensity evolution equation are changed to enhance the numerical stability. At the same time, the actuator model and data-driven method are combined to obtain the airfoil aerodynamic data in the full angle of attack range to accurately process the boundary conditions of tiltrotor, so as to improve the accuracy of tiltrotor in large tilt angle working conditions.

[0060] The hybrid machine learning model based on neural network and Truong analysis can quickly predict the aerodynamic force coefficients of each section of the blade in the full angle of attack range (0~360°). For the region without stall or slight flow separation, XFOIL can provide high-precision subsonic aerodynamic characteristics, so the neural network trained by XFOIL data is used for prediction. For the high angle of attack region with large-scale flow separation, the post-stall model of Truong is used. Truong model is based on the regression analysis of wind tunnel experiment data, and is specially designed to predict the deep stall state at high angle of attack. The machine learning lift surface particle wake unsteady load discrete blade element particle radius discretization length model can automatically select the output type of the model through calculation credibility. When the credibility is high, it depends on the neural network, and when the credibility is low, it depends on the Truong model, and there is a smooth transition between the two. This method ensures the accuracy and continuity of prediction, and adapts to different airfoils and flow conditions.

[0061] The aerodynamic force coefficient calculation process of neural network can be summarized as follows: ① input processing: accept input parameters, and perform geometry and flow characteristic coding; ② hidden space mapping: use deep neural network to predict hidden space output, and combine physical heuristic method to improve generalization ability; ③ output decoding and physical correction: decode the aerodynamic force coefficient from the hidden space output, and correct it through physical consistency to ensure that the calculation result meets the aerodynamic law.

[0062] For specific content, refer to Figure 2 and Figure 3 , wherein, Figure 2 is a flow chart of the machine learning based tiltrotor aerodynamic force coefficient prediction method according to the embodiments of the application. Figure 3 is a data flow diagram of the machine learning based tiltrotor aerodynamic force coefficient prediction method according to the embodiments of the application. As Figure 2 and Figure 3As shown, the method for predicting the aerodynamic force coefficient of a tilt-rotor based on machine learning according to the embodiments of the present application comprises the following steps: S1, inputting airfoil shape parameters, attack angles, and flow field parameters; S2, embedding and coding the airfoil shape parameters, the attack angles, and the flow field parameters to obtain airfoil shape parameter embedding coding vectors, attack angle embedding coding vectors, and flow field parameter embedding coding vectors; S3, concatenating the airfoil shape parameter embedding coding vectors, the attack angle embedding coding vectors, and the flow field parameter embedding coding vectors to obtain airfoil set-case joint embedding coding vectors; S4, inputting the airfoil set-case joint embedding coding vectors into a neural network inference model to obtain initial output parameters; S5, based on a physical model, post-processing and correcting the initial output parameters to obtain aerodynamic force coefficient related parameter decoding results, the aerodynamic force coefficient related parameter decoding results comprising a lift coefficient, a logarithmic function value of a drag coefficient, a moment coefficient, and a boundary layer parameter; and S6, calculating the aerodynamic force coefficient based on the aerodynamic force coefficient related parameter decoding results.

[0063] In the above method for predicting the aerodynamic force coefficient of a tilt-rotor based on machine learning, the step S1, inputting airfoil shape parameters, attack angles, and flow field parameters. It should be understood that the airfoil shape parameters, the attack angles, and the flow field parameters are basic physical quantities describing the working state of the airfoil in the flow field, and are the original data source for calculating the aerodynamic force coefficient. Specifically, the airfoil shape determines the path and pressure distribution of the airflow flowing through the airfoil surface, the attack angle affects the relative angle of the airflow and the airfoil, and the flow field parameters (such as Reynolds number, Mach number, etc.) reflect the characteristics of the flow field. The three factors jointly affect the size and direction of the aerodynamic force. Because different airfoil shapes, attack angles, and flow field states will cause changes in the aerodynamic force, in order to comprehensively understand the aerodynamic characteristics of the tilt-rotor under a specific working condition, the present application obtains comprehensive information of the airfoil shape parameters, the attack angles, and the flow field parameters, thereby providing a complete information basis for subsequent calculation of the aerodynamic force coefficient.

[0064] In specific implementation, the airfoil geometric parameters describe the specific geometric shape of the airfoil, which is usually determined based on design requirements or existing airfoil databases (such as NACA series, supercritical airfoils, etc.). The attack angle and the flow field parameter describe the directional angle of the airfoil relative to the incoming flow and the dynamic characteristics of the flow field parameter flow field, respectively. In fluid mechanics, the attack angle, the flow field parameter, and the vortex particle are closely related through the dynamic evolution of the flow field, and together describe the physical mechanism of the flow. The airfoil surface generates vortex particles according to the slip velocity related to the attack angle, and therefore, the attack angle and the flow field parameter can be extracted by a vortex-velocity-attack angle coupling equation.

[0065] Specifically, the vortex particle method is based on the discretization of the vorticity equation, and each vortex particle represents a local vorticity distribution. The vorticity of the NS equation is expressed as follows:

[0066]

[0067] where, represents the vorticity, represents the velocity field, represents the kinematic viscosity;

[0068] To accurately simulate the dynamic evolution process of the flow field, in the initialization stage, the initial position of the vortex particle, the kernel function Gaussian kernel or other radial basis function, and the filter width of the kernel function need to be defined . Each vortex particle represents a part of the local vorticity distribution, and by reasonably setting its initial state, the initial flow field situation can be effectively described. The position of the vortex particle determines how it is distributed in the flow field, while the selection of the kernel function and the adjustment of the filter width affect the smoothness and resolution of the vorticity field. For example, a smaller filter width can achieve higher resolution in high-vorticity regions, while appropriately increasing the filter width in the far-field region helps to reduce the computational cost without significantly affecting the accuracy of the results.

[0069] 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):

[0070]

[0071] where, 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, the filter width can be dynamically adjusted according to the local vorticity intensity and particle stretching, effectively handling turbulent structures at different scales, resulting in higher resolution in high-vorticity regions and appropriate coarsening in the far-field region.

[0072] Next, the vorticity distribution of the initial flow field is set. Correct vorticity distribution initialization can ensure the physical authenticity of the simulation, making the evolution of vorticity in the subsequent simulation process more close to the actual situation. Specifically, the vorticity field initialization:

[0073]

[0074] where, is the vorticity field; is the vorticity intensity of the particle; is the position of the particle.

[0075] In VPM unsteady simulation, the angle of attack is determined by the angle between the local flow velocity direction of the blade and the geometric centerline of the airfoil, and is dynamically adjusted over time. Flow field parameters such as Reynolds number, Mach number, etc. are obtained through real-time data acquisition in flow field simulation, ensuring the timeliness and accuracy of the parameters.

[0076] In the above-mentioned machine learning-based tilt-rotor aerodynamic force coefficient prediction method, the step S2 is to embed and encode the airfoil shape parameters, the attack angle and the flow field parameters to obtain an airfoil shape parameter embedding and encoding vector, an attack angle embedding and encoding vector and a flow field parameter embedding and encoding vector. It should be understood that, since the original parameter form may not be conducive to the direct processing of the neural network, the present application further processes the embedding and encoding of the airfoil shape parameters, the attack angle and the flow field parameters to map the original parameters to a high-dimensional embedding space, so as to facilitate the neural network to capture the internal correlation and rules between the parameters.

[0077] Specifically, in order to decompose the complex airfoil geometry into a mathematically analyzable parameter vector, thereby efficiently representing the aerodynamic characteristics of the airfoil, in one specific example of the present application, the upper surface class parameters, the upper surface shape parameters, the lower surface class parameters and the lower surface shape parameters in the airfoil shape parameters are functionally mapped based on a class function and a shape function to obtain the shape parameter embedding and encoding vector, and the dimension of the shape parameter embedding and encoding vector is 18. That is, 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 the combination of a class function (Class Function) and a shape function (Shape Function).

[0078] wherein the Class Function defines the basic class of airfoil (symmetric / asymmetric, leading edge shape, etc.), which is usually defined as a combination of power functions; the Shape Function employs Bernstein Polynomials to flexibly adjust the local curvature of airfoil, controlling the detailed shape. For the upper and lower surfaces, their geometric shape parameters can be parameterized and fitted by the product of the Class Function and the Shape Function. Therefore, based on the basic principle of the CST method, the Class Function and the Shape Function are defined to parameterize the airfoil shape, which can effectively extract the class parameters (such as the upper surface class parameters including the leading edge curvature coefficient, etc.) and shape parameters (such as the upper surface shape parameters being the weight coefficients of Bernstein Polynomials) of the upper and lower surfaces, and generate a shape parameter embedding code vector through parameter combination. Wherein, 9 parameters are generated for each surface (for example, 2 class function parameters + 7 shape polynomial coefficients), and a total of 18-dimensional parameter vectors are generated for the upper and lower surfaces, and the dimension difference is eliminated through normalization or standardization processing, and finally an 18-dimensional shape parameter embedding code vector is formed. The shape parameter embedding code vector not only retains the global contour features of the airfoil, but also captures the sensitive changes of local geometric details, thereby providing a high-fidelity and low-dimensional input representation for the subsequent neural network model, ensuring efficient calculation while maintaining accurate modeling capability for complex airfoil shapes.

[0079] Meanwhile, for the embedding code of the attack angle, the attack angle is converted into the combination of , and to obtain the attack angle embedding code vector. Specifically, since the direct input of the original attack angle will cause the numerical discontinuity problem of the periodic boundary (such as 180° and -180° equivalent). Therefore, the attack angle is converted into the combination of , and to embed its periodicity and nonlinearity related to stall, so as to obtain a 3-dimensional attack angle embedding code vector. Wherein, is used to reflect the periodicity of the attack angle (repeating every 180°); is used to enhance the nonlinear response of high angle of attack (close to 90°), is used to supplement the directional information of the attack angle (distinguish positive and negative angle of attack).

[0080] In a specific example of this application, the flow field parameters include the Reynolds number (Re), turbulence intensity parameter, upper boundary layer transition position parameter, and lower boundary layer transition position parameter. For the embedding encoding of the flow field parameters, this application first performs a logarithmic transformation on the Reynolds number to obtain the logarithmic function value of the Reynolds number; then, it combines 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 to obtain the flow field parameter embedding encoding vector. Specifically, the Reynolds number (Re) is a key parameter describing the fluid flow characteristics, reflecting the ratio between the fluid's inertial force and viscous force. Since the influence of the Reynolds number (Re) on aerodynamic forces is logarithmic, a logarithmic transformation is employed. Linearize its effect on aerodynamic coefficients. Turbulence intensity parameters (such as...) This reflects the turbulent characteristics of the flow field, and its magnitude directly affects the fluctuating pressure and drag on the airfoil surface. Upper boundary layer transition position parameters. and lower boundary layer transition location parameters This describes the transition position between laminar and turbulent flow, and changes in this position significantly affect the aerodynamic performance and stability of the airfoil. A 4-dimensional flow field parameter embedding encoding vector is obtained by combining 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.

[0081] In the aforementioned machine learning-based method for predicting tiltrotor aerodynamic coefficients, step S3 involves cascading the airfoil shape parameter embedding encoding vector, the angle of attack embedding encoding vector, and the flow field parameter embedding encoding vector to obtain an airfoil set-operating condition joint embedding encoding vector. It should be understood that aerodynamics is the coupling result of airfoil geometry, angle of attack, and flow field parameters. Therefore, to comprehensively reflect the combined influence of airfoil shape, angle of attack, and flow field parameters on aerodynamic performance, this application integrates the airfoil shape parameter embedding encoding vector, the angle of attack embedding encoding vector, and the flow field parameter embedding encoding vector through cascading fusion to obtain a joint representation of multi-dimensional parameters, forming an airfoil set-operating condition joint embedding encoding vector. For example, the airfoil set-operating condition joint embedding encoding vector is:

[0082]

[0083] This processing provides input with comprehensive information for subsequent neural network models, enabling the neural network to make more accurate aerodynamic coefficient predictions based on the combined effects of airfoil shape, angle of attack, and flow field parameters.

[0084] In the above machine learning-based tilt-rotor aerodynamic force coefficient prediction method, the step S4 inputs the airfoil set-working condition joint embedding code vector into the neural network inference model to obtain the initial output parameter. It should be understood that the neural network has strong nonlinear fitting capability, can effectively capture the nonlinear coupling relationship between the airfoil shape, angle of attack and flow field parameters, and predict the aerodynamic force related coefficient accordingly. In addition, by means of the fast prediction capability of the neural network, the calculation time of the aerodynamic force coefficient can be significantly shortened, which is suitable for the real-time simulation demand of the unsteady flow field of the tilt-rotor.

[0085] Figure 4 The flow chart of step S4 in the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to the embodiment of the present application is shown in FIG. 4. As shown in FIG. 4, the step S4 includes: S41, using the multi-layer perception model of the neural network inference model to perform multi-level full connection coding on the airfoil set-working condition joint embedding code vector to obtain an airfoil set-working condition joint latent space code vector; and S42, inputting the airfoil set-working condition joint latent space code vector into the decoding layer of the neural network inference model to obtain the initial output parameter. Figure 4

[0086] Specifically, the step S41 uses the multi-layer perception model of the neural network inference model to perform multi-level full connection coding on the airfoil set-working condition joint embedding code vector to obtain an airfoil set-working condition joint latent space code vector. It should be understood that the multi-level full connection coding structure of the multi-layer perception (MLP) model enables it to gradually extract and integrate multi-level features in the airfoil set-working condition joint embedding code vector, mine potential relationships between multi-dimensional parameters, and realize mapping from the input space to the intermediate latent space. Specifically, the MLP model abstracts the input features step by step by stacking the dense layer and the nonlinear activation function (such as Swish), learns the local interaction of the airfoil geometry and the angle of attack (such as the influence of the leading edge curvature on the stall angle of attack), captures the global cross-parameter coupling (such as the modulating effect of the Reynolds number on the high angle of attack separation flow), and thus extracts the aerodynamic force generation law implied in the airfoil set-working condition joint embedding code vector, provides a high information density feature representation for the decoding layer, and obtains the airfoil set-working condition joint latent space code vector. In addition, during the model training stage, by increasing the mirror sample in the training data, the “mirror image” of the flipped airfoil and the angle of attack is analyzed, and the network is forced to output a symmetry constraint, that is, for any combination of airfoils and angles of attack, the airfoil and the angle of attack in the opposite direction of the mirror image should produce the same aerodynamic force coefficient, so as to ensure the odd-even symmetry of the lift coefficient and the drag coefficient.

[0087] ​Specifically, in step S42, 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. That is, the decoding layer of the neural network inference model maps the airfoil set-operating condition joint latent space encoding vector from the latent feature space back to the actual physical quantities. By gradually reducing the dimensionality through stacked fully connected layers and combining the nonlinear transformation of the activation function, the aerodynamic coefficients that can be used in engineering are decoded, such as the lift coefficient, the logarithm of the drag coefficient (to improve the fitting accuracy of low Cd values), the moment coefficient, and boundary layer parameters (such as momentum thickness and shape factor).

[0088] In a preferred example of this application, considering that the airfoil set-operation condition joint latent space encoding vector (high-dimensional features obtained through MLP encoding) contains deeply abstract aerodynamic laws (such as stall critical points and separated flow modes), it may lose local details in the original airfoil set-operation condition joint embedding encoding vector (low-dimensional input features) (such as the direct impact of leading edge sharpness on low angle-of-attack aerodynamic forces). 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, this application proposes a feature cross-order interaction mechanism. Before decoding the airfoil set-operation condition joint latent space encoding vector, the original airfoil set-operation condition joint embedding encoding vector is introduced backtrackingly to improve the model's sensitivity and accuracy in predicting aerodynamic coefficients.

[0089] Figure 5 This is a flowchart of step S42 in the machine learning-based tiltrotor aerodynamic coefficient prediction method according to an embodiment of this application. Figure 5 As shown, step S42 includes: S421, performing feature cross-order interaction on the airfoil set-operation condition joint latent space encoding vector and the airfoil set-operation condition joint embedding encoding vector to obtain the airfoil set-operation condition multi-dimensional joint encoding vector; S422, inputting the airfoil set-operation condition multi-dimensional joint encoding vector into the decoding layer of the neural network inference model to obtain the initial output parameters.

[0090] Specifically, in step S421, the airfoil set-operation condition joint latent space encoding vector and the airfoil set-operation condition joint embedding encoding vector undergo cross-order feature interaction to obtain an airfoil set-operation condition multi-dimensional joint encoding vector. Here, by performing cross-order interaction between the airfoil set-operation condition joint latent space encoding vector and the airfoil set-operation condition joint embedding encoding vector, a multi-dimensional joint encoding vector of the airfoil set-operation condition that simultaneously contains global abstract laws and local detailed features can be constructed. This avoids the information decay problem of deep networks and enhances the model's sensitivity to aerodynamic nonlinear changes (such as stall abrupt changes and boundary layer separation) and prediction accuracy.

[0091] Figure 6 This is a flowchart of step S421 in the machine learning-based tiltrotor aerodynamic coefficient prediction method according to an embodiment of this application. Figure 6 As shown, step S421 includes: S4211, performing high-dimensional embedding reconstruction of sequence features based on temporal convolution feature extraction on the airfoil set-operating condition joint latent space encoding vector and the airfoil set-operating condition joint embedding 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 embedding local feature encoding vectors; S4212, calculating the potential association query space interaction association matrix between any set of airfoil set-operating condition joint latent space local feature encoding vectors and airfoil set-operating condition joint embedding local feature encoding vectors in the set of airfoil set-operating condition joint latent space local feature encoding vectors and the set of airfoil set-operating condition joint embedding local feature encoding vectors to obtain a set of airfoil set-operating condition multi-dimensional potential association query space cross-domain interaction association matrices; S4213, performing dynamic weighted fusion based on sparsity regularization on the set of airfoil set-operating condition multi-dimensional potential association query space cross-domain interaction association matrices to obtain the airfoil set-operating condition multi-dimensional joint encoding vector.

[0092] In a specific example of this application, step S4211 can be expressed by the formula:

[0093]

[0094]

[0095] in, This represents the joint latent space encoding vector of the airfoil set and operating conditions. This represents the joint embedding encoding vector of the airfoil set and operating conditions. This is a temporal convolutional feature extraction network. This represents the set of local feature encoding vectors in the joint latent space of the airfoil set and operating conditions. , , and These respectively represent the 1st, 2nd, and 3rd local feature encoding vectors in the set of airfoil set-operating condition joint latent space. The and the first Airfoil set-operating condition joint latent space local feature encoding vector The number of vectors in the set of local feature encoding vectors in the airfoil set-operating condition joint latent space. This represents the set of local feature encoding vectors jointly embedded by the airfoil set and operating conditions. , , and respectively represent the 1st, 2nd, 3rd and 4th airfoil set- working condition joint embedding local feature encoding vectors in the set of airfoil set- working condition joint embedding local feature encoding vectors.

[0096] It can be understood that, considering that directly interacting features of the airfoil set- working condition joint latent space encoding vector and the airfoil set- working condition joint embedding encoding vector is easy to ignore the local dependence between features, resulting in information loss. Therefore, in order to enhance the perception ability of the internal local structure information of the airfoil set- working condition joint latent space encoding vector and the airfoil set- working condition joint embedding encoding vector, the application adopts time sequence convolution feature extraction to respectively perform sequence feature high-dimensional embedding reconstruction on the two, generates multiple local observation segments through one-dimensional convolution sliding window operation (similar to delay embedding), and mines out the internal potential structure information and dimension correlation of the features (such as the correlation between the airfoil leading edge shape and the stall angle of attack), forms multi-scale and multi-level local feature representation, that is, the set of airfoil set- working condition joint latent space local feature encoding vectors and the set of airfoil set- working condition joint embedding local feature encoding vectors, thereby providing a more rich and detailed feature basis for subsequent feature interaction.

[0097] In one specific example of the present application, the step S4212 can be represented by the formula:

[0098]

[0099] wherein, represents the transpose of a matrix, represents matrix multiplication operation, and respectively represent the airfoil set- working condition joint latent space feature weight matrix and the airfoil set- working condition joint embedding feature weight matrix, is a feature scale factor, represents and between the airfoil set- working condition multidimensional potential correlation query space cross-domain interaction correlation matrix.

[0100] ​​Here, in order to capture the pair-wise interaction relationship between the airfoil set-operation joint hidden space local feature encoding vectors and the airfoil set-operation joint embedding local feature encoding vectors, the application maps the set of airfoil set-operation joint hidden space local feature encoding vectors and the set of airfoil set-operation joint embedding local feature encoding vectors to the same feature space, in which the dot product attention weight between the two is calculated to reveal the potential relevance and mutual influence between different local features, mine and integrate complementary information from different feature spaces, i.e. global abstract rules in the hidden space and local detailed features in the embedding space, to obtain a set of airfoil set-operation multi-dimensional potential relevance query space cross-domain interaction association matrices.

[0101] Then, the spatial sparsity regularization factor of each airfoil set-operation multi-dimensional potential relevance query space cross-domain interaction association matrix in the set of airfoil set-operation multi-dimensional potential relevance query space cross-domain interaction association matrices is calculated to obtain a set of airfoil set-operation multi-dimensional joint interaction space sparsity regularization factors, which is represented by the formula:

[0102]

[0103] wherein, is the association feature strength measurement function, represents the square of the Frobenius norm of the calculation matrix, represents the corresponding airfoil set-operation multi-dimensional joint interaction space sparsity regularization factor.

[0104] That is, by calculating the square of the F-norm of the airfoil set-operation multi-dimensional potential relevance query space cross-domain interaction association matrix as the sparsity regularization factor, the information density is evaluated and the feature importance is quantified, so as to dynamically allocate the aggregation weight to guide the subsequent aggregation process, so that the model focuses on the key interaction mode of the airfoil set-operation joint hidden space encoding vector and the airfoil set-operation joint embedding encoding vector when aggregating, and avoids invalid interaction interference.

[0105] Finally, based on the set of airfoil set-operation multi-dimensional joint interaction space sparsity regularization factors, the set of airfoil set-operation multi-dimensional potential relevance query space cross-domain interaction association matrices is dynamically weighted and fused to obtain the airfoil set-operation multi-dimensional joint encoding vector, which is represented by the formula:

[0106]

[0107]

[0108] wherein, denotes a normalized exponential function, denotes denotes a corresponding normalized airfoil set - operating condition multi-dimensional joint interaction space sparsity regularization factor, denotes an airfoil set - operating condition multi-dimensional joint interaction implicit coding feature sparsity fusion matrix, denotes feature shape remodeling, denotes an airfoil set - operating condition multi-dimensional joint coding vector.

[0109] That is, after the airfoil set - operating condition multi-dimensional joint interaction space sparsity regularization factor set is normalized, it is applied to the aggregation process of the airfoil set - operating condition multi-dimensional latent correlation query space cross-domain interaction correlation matrix set, and through weighted average, redundant information is eliminated and complementary information is amplified to realize effective fusion and complementarity of multi-view interaction information, forming a global airfoil set - operating condition multi-dimensional joint coding vector, thereby providing more comprehensive and accurate input features for aerodynamic force prediction.

[0110] Specifically, in step S422, the airfoil set - operating condition multi-dimensional joint coding vector is input into the decoding layer of the neural network inference model to obtain the initial output parameter. Here, through feature cross-order interaction, the airfoil set - operating condition multi-dimensional joint coding vector not only contains global abstract features extracted by the multi-layer perception model, but also fuses local detail information in the original embedded coding vector, which can more comprehensively and accurately reflect the complex influence of airfoil shape, angle of attack and flow field parameters on aerodynamic performance, thereby improving the prediction ability of the decoding layer for aerodynamic coefficient related parameters.

[0111] In the above machine learning-based tilt rotor aerodynamic force coefficient prediction method, in step S5, the initial output parameter is post-processed and corrected based on a physical model to obtain an aerodynamic force coefficient related parameter decoding result, and the aerodynamic force coefficient related parameter decoding result includes a lift coefficient, a logarithmic function value of a drag coefficient, a moment coefficient and a boundary layer parameter. It should be understood that considering that a pure data-driven model (the neural network inference model) is difficult to accurately extrapolate to operating conditions not covered by the training set, which may lead to prediction results that do not completely conform to actual aerodynamics, therefore, the present application adopts a post-processing correction method based on a physical model to further physically correct the initial output parameter.

[0112] 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, improve the prediction accuracy, and make it conform to the aerodynamic law. The Prandtl-Glauert model is based on small perturbation theory and is used to correct the airfoil aerodynamic force in subsonic compressible flow. It is suitable for low Mach number (Ma < 0.7) and no strong shock wave. In subsonic airflow, air compressibility affects the aerodynamic force characteristics. The model assumes that the airfoil has a small disturbance to the airflow, and by introducing a compressibility correction factor, the aerodynamic force coefficient of incompressible flow is converted to that of compressible flow. The correction formula (taking the lift coefficient as an example) is , is the Mach number. That is, by linearizing the potential flow theory to compensate for the change in pressure distribution caused by air compression, the lift coefficient in incompressible flow is scaled by to reflect the effect of density change on lift.

[0113] The Karman-Tsien model improves the Prandtl-Glauert model and more accurately describes the airfoil aerodynamic force in subsonic compressible flow, which is suitable for a higher subsonic range (0.3 < Ma < 0.9). It improves the Prandtl-Glauert formula through a second-order approximation. Specifically, the Karman-Tsien model is also based on small perturbation theory and introduces a correction term based on the Prandtl-Glauert model to consider the high-order effect of Mach number change on the aerodynamic force coefficient. The lift coefficient correction formula is:

[0114]

[0115] Compared with the Prandtl-Glauert model, the Karman-Tsien model extends the correction range to a higher Mach number 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 airfoil aerodynamic force characteristics in subsonic compressible flow while retaining the high-efficiency prediction capability of the neural network, and provide reliable aerodynamic force input for tilt-rotor unsteady simulation.

[0116] In the above-mentioned machine learning-based tilt-rotor aerodynamic force coefficient prediction method, the step S6 of calculating the aerodynamic force coefficient based on the aerodynamic force coefficient related parameter decoding result. That is, based on the corrected lift coefficient and drag coefficient, combined with local flow velocity, chord length and other parameters, 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 and expressed as:

[0117]

[0118] where, is the air density; is the local flow velocity of the blade; is the chord length of the blade.

[0119] Further, according to the calculated lift and drag, the vorticity evolution and iterative correction can be performed by dynamically correlating the aerodynamic force with the flow field, so as to realize high-precision and high-efficiency flow simulation and analyze the dynamic behavior of the airfoil in the flow field, such as flutter, stall and other phenomena.

[0120] First, the aerodynamic force is converted into vorticity intensity and is smoothly loaded into the flow field through the LES filter. Specifically, the lift L is converted into equivalent vorticity intensity :

[0121]

[0122] After the aerodynamic force is converted into vorticity, it is smoothly loaded into the flow field through the LES filter:

[0123]

[0124] This process combines the kernel function of the particle and embodies the filtering effect of LES on small-scale turbulent structures.

[0125] Then, the induced velocity is solved by the Biot-Savart method to simulate the motion and stretching process of the vortex particle, and the diffusion and splitting mechanism is considered to maintain the stability of the solution.

[0126] Specifically, the local flow velocity induced by the vortex particle is solved by the Biot-Savart method:

[0127]

[0128] where: 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.

[0129] The motion of the vortex particle follows the Lagrangian method:

[0130]

[0131] The vorticity intensity changes due to the stretching effect:

[0132]

[0133] This procedure mimics the energy transport from large-scale vorticity to small-scale structures in LES.

[0134] Vortex particle diffusion simulates sub-grid scale dissipation effects:

[0135]

[0136] where is the eddy viscosity.

[0137] Particles are split when their density or intensity exceeds a certain threshold to maintain the stability of the solution.

[0138] Finally, the local angle of attack and aerodynamic force are iteratively updated until convergence, and the results of thrust, moment, power, and wake vortex distribution are output.

[0139] Specifically, according to the induced velocity and the free stream velocity , the local flow velocity and angle of attack are updated:

[0140]

[0141]

[0142] The aerodynamic force is re-predicted by the neural network, the vortex loading is corrected, and the iteration is performed until convergence.

[0143] Thrust and moment are calculated by integrating the aerodynamic force:

[0144]

[0145] The final results, i.e. thrust, moment, power, and wake vortex distribution in the flow field, are output.

[0146] In summary, the machine learning-based tilt-rotor aerodynamic coefficient prediction method according to the embodiments of the present application is illustrated, 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 parameter, and combine the physical model to correct the compressibility and symmetry constraint of the initial prediction parameter, to ensure that it conforms to the aerodynamics law, and finally calculate the aerodynamic coefficient based on the corrected aerodynamic coefficient related parameters. This method can break through the angle of attack limit of traditional Viterna extrapolation method, realize 0°-360° full range coverage, significantly improve the aerodynamic prediction accuracy in extreme angle of attack area, and greatly improve the calculation efficiency and robustness, suitable for real-time wing optimization design tasks in complex scenarios.

[0147] Referring toFigure 7 Specifically, to enhance the reliability of the neural network inference model outside the training data distribution, before inputting the airfoil set-operation condition joint embedding coding vector into the neural network inference model to obtain an initial output parameter, the following steps are further included:

[0148] Based on the airfoil set-operation condition joint embedding coding vector, mathematical modeling is performed to generate a calculation parameter, and a prediction confidence is generated based on the calculation parameter; based on the prediction confidence and a preset comparison value, an update result corresponding to the neural network inference model is generated, and the neural network inference model corresponding to the airfoil set-operation condition joint embedding coding vector is updated based on the update result. Based on the input airfoil set-operation condition joint embedding coding vector, data modeling is performed, a calculation parameter of Mahalanobis distance is calculated, and a confidence score is converted by the calculation parameter, so as to obtain a confidence analysis score corresponding to the neural network inference model, a reliability of the neural network inference model is generated according to the confidence analysis score, and the neural network inference model is updated according to different reliability values.

[0149] In addition, under large separation flow conditions, an analytical model (such as Truong's post-stall regression model) is combined to improve the accuracy and physical consistency of the results. Through a hybrid machine learning model based on neural networks and Truong's analytical model, the aerodynamic force coefficients of each section of the blade can be quickly predicted over a full range of attack angles (0-360°). For regions where there is no stall or slight flow separation, XFOIL can provide high-precision subsonic aerodynamic characteristics, so the neural network trained using XFOIL data is used for prediction. For high-attack-angle regions where large-scale flow separation occurs, Truong's analytical post-stall model is used. Truong's model is based on regression analysis of wind tunnel experimental data and is specifically designed to predict deep stall conditions at high attack angles. This machine learning lift surface particle wake unsteady load discretization blade element particle radius discretization length model can automatically select the output type of the model through calculation of the confidence. When the confidence is high, the neural network is relied on, when the confidence is low, the Truong model is relied on, and a smooth transition is made between the two. This method ensures the accuracy and continuity of the prediction, while adapting to different airfoils and flow conditions.

[0150] Further, the application also provides a machine learning-based tilt-rotor aerodynamic force coefficient prediction system.

[0151] Figure 8 A block diagram of the machine learning-based tilt-rotor aerodynamic force coefficient prediction system according to an embodiment of the application. As Figure 8As shown, the machine learning-based tilt-rotor aerodynamic force coefficient prediction system 100 according to the embodiment of the present application comprises: 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 airfoil shape parameter embedding coding vectors, angle of attack embedding coding vectors and flow field parameter embedding coding vectors; a concatenation module 130 for concatenating the airfoil shape parameter embedding coding vectors, the angle of attack embedding coding vectors and the flow field parameter embedding coding vectors to obtain airfoil set-condition joint embedding coding vectors; an initial parameter inference module 140 for inputting the airfoil set-condition joint embedding coding vectors into a neural network inference model to obtain initial output parameters; a parameter correction module 150 for post-processing correction of the initial output parameters based on a physical model to obtain aerodynamic force coefficient related parameter decoding results, the aerodynamic force coefficient related parameter decoding results including lift coefficient, logarithmic function value of drag coefficient, moment coefficient and boundary layer parameter; an aerodynamic force coefficient calculation module 160 for calculating aerodynamic force coefficients based on the aerodynamic force coefficient related parameter decoding results.

[0152] Here, those skilled in the art can understand that the specific operations of each module in the above machine learning-based tilt-rotor aerodynamic force coefficient prediction system have been described in detail in the above description of the machine learning-based tilt-rotor aerodynamic force coefficient prediction method according to the embodiment of the present application, and therefore, repeated descriptions thereof will be omitted. Figures 1 to 5

[0153] The machine learning-based tilt-rotor aerodynamic force coefficient prediction system performs the method steps of the above machine learning-based tilt-rotor aerodynamic force coefficient prediction method, can realize 0°-360° full range coverage, and significantly improves the aerodynamic force prediction accuracy in the extreme angle of attack region, while greatly improving the calculation efficiency robustness, and is suitable for real-time wing optimization design tasks in complex scenarios.

[0154] Referring to Figure 9 , Figure 9 is the chord length and twist angle distribution of TUD_F29 propeller and its corresponding geometric profile diagram. Specifically, the TUD_F29 propeller model tested by Stokkermans et al. is adopted, the propeller diameter is 0.3048 m, the number of blades is 4, there are 17 airfoils distributed along the span, the test height is 0 m, the incoming flow velocity is 20 m / s, and the advance ratio is 0.69.

[0155] Figure 10 ​is a comparison diagram of propeller performance at different tilt angles using the original method and the improved method of the present embodiment, wherein the original method refers to the improved vortex particle method, i.e., the rVPM method, and the improved method of the present embodiment refers to the vortex particle-large eddy simulation method suitable for tilt rotors, i.e., the trVPM method, based on the rVPM method, Figure 10 The test diagram for the tilt angle of 0-90° is specifically shown in the middle.

[0156] From Figure 10 It can be found that the gap is not obvious at a smaller tilt angle, because the twist angle of the TUD rotor at the 3 / 4 spanwise position is 17.6°, the blade twist angle itself is about 10-40°, and there is a certain installation angle, so even if there is a smaller tilt angle, the airfoil at the key region (such as the 3 / 4 spanwise position) has not undergone large flow separation, and therefore the rVPM has higher accuracy. At a large tilt angle of 60°-90°, the trVPM has obviously higher accuracy than the rVPM, and can reduce the error to within 5%, so the method can break through the angle of attack limit of the traditional Viterna extrapolation method, realize 0°-360° full-range coverage, and significantly improve the aerodynamic force prediction accuracy in the extreme angle of attack region, while greatly improving the calculation efficiency and robustness, and is suitable for real-time wing optimization design tasks in complex scenarios.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit it, although the present application 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 application can be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for predicting the aerodynamic coefficients of a tilt-rotor based on machine learning, characterized by, The method comprises the following steps: input airfoil shape parameters, angle of attack and flow field parameters; The airfoil shape parameter, the angle of attack and the flow field parameter are embedded 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 generation manner of the angle of attack embedded coding vector comprises the following steps: converting the angle of attack into a combination of , , and to obtain the angle of attack embedded coding vector; embed the airfoil shape parameters, the angle of attack and the flow field parameters into embedding vectors to obtain an airfoil set-operation joint embedding vector; input the airfoil set-operation joint embedding vector into a neural network inference model to obtain initial output parameters; based on a physical model, post-process and correct the initial output parameters to obtain aerodynamic coefficient related parameter decoding results, which include lift coefficient, logarithmic function value of drag coefficient, moment coefficient and boundary layer parameters; calculate the aerodynamic coefficients based on the aerodynamic coefficient related parameter decoding results. 2.The method of claim 1, wherein, The airfoil shape parameters, the angle of attack and the flow field parameters are embedded and coded to obtain airfoil shape parameter embedding vectors, angle of attack embedding vectors and flow field parameter embedding vectors, wherein the generation of the airfoil shape parameter embedding vectors comprises the following steps: map 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 based on category functions and shape functions to obtain the shape parameter embedding vectors, and the dimension of the shape parameter embedding vectors is 18. 3.The method of claim 1, wherein, The airfoil shape parameters, the angle of attack and the flow field parameters are embedded and coded to obtain airfoil shape parameter embedding vectors, angle of attack embedding vectors and flow field parameter embedding vectors, wherein the generation of the flow field parameter embedding vectors comprises the following steps: logarithmically transform the Reynolds number in the flow field parameters to obtain the logarithmic function value of the Reynolds number, wherein the flow field parameters include the Reynolds number, the turbulence intensity parameter, the upper boundary layer transition location parameter and the lower boundary layer transition location parameter; combine 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 to obtain the flow field parameter embedding vector. 4.The method of claim 1 or 3, wherein, Input the airfoil set-operation joint embedding vector into a neural network inference model to obtain initial output parameters, comprising: use a multi-layer perceptron model of the neural network inference model to perform multi-level full connection coding on the airfoil set-operation joint embedding vector to obtain an airfoil set-operation joint latent space embedding vector; pass the airfoil set-operation joint latent space embedding vector through a decoding layer of the neural network inference model to obtain the initial output parameters. 5.The method of claim 4, wherein, Pass the airfoil set-operation joint latent space embedding vector through a decoding layer of the neural network inference model to obtain the initial output parameters, comprising: perform feature cross-order interaction on the airfoil set-operation joint latent space embedding vector and the airfoil set-operation joint embedding vector to obtain an airfoil set-operation multi-dimensional joint embedding vector; input the airfoil set-operation multi-dimensional joint embedding vector into the decoding layer of the neural network inference model to obtain the initial output parameters. 6.The method of claim 5, wherein, The wing profile set-operation joint hidden space coding vector and the wing profile set-operation joint embedding coding vector are subjected to feature cross-order interaction to obtain a wing profile set-operation multi-dimensional joint coding vector, including: The wing profile set-operation joint hidden space coding vector and the wing profile set-operation joint embedding coding vector are subjected to sequence feature high-dimensional embedding reconstruction based on time sequence convolution feature extraction to obtain a set of wing profile set-operation joint hidden space local feature coding vectors and a set of wing profile set-operation joint embedding local feature coding vectors; A potential association query space interaction association matrix between any one group of wing profile set-operation joint hidden space local feature coding vectors and wing profile set-operation joint embedding local feature coding vectors in the set of wing profile set-operation joint hidden space local feature coding vectors and the set of wing profile set-operation joint embedding local feature coding vectors is calculated to obtain a set of wing profile set-operation multi-dimensional potential association query space cross-domain interaction association matrices; The set of wing profile set-operation multi-dimensional potential association query space cross-domain interaction association matrices is subjected to dynamic weighted fusion based on sparsity regularization to obtain the wing profile set-operation multi-dimensional joint coding vector.

7. The machine learning based tilt-rotor aerodynamic force coefficient prediction method of claim 6, wherein, The set of wing profile set-operation multi-dimensional potential association query space cross-domain interaction association matrices is subjected to dynamic weighted fusion based on sparsity regularization to obtain the wing profile set-operation multi-dimensional joint coding vector, including: A spatial sparsity regularization factor of each wing profile set-operation multi-dimensional potential association query space cross-domain interaction association matrix in the set of wing profile set-operation multi-dimensional potential association query space cross-domain interaction association matrices is calculated to obtain a set of wing profile set-operation multi-dimensional joint interaction spatial sparsity regularization factors; Based on the set of wing profile set-operation multi-dimensional joint interaction spatial sparsity regularization factors, the set of wing profile set-operation multi-dimensional potential association query space cross-domain interaction association matrices is subjected to dynamic weighted fusion coding to obtain the wing profile set-operation multi-dimensional joint coding vector. 8.The method of claim 1, wherein, Before the wing profile set-operation joint embedding coding vector is input into a neural network inference model to obtain an initial output parameter, the following steps are further included: Based on the wing profile set-operation joint embedding coding vector, mathematical modeling is performed to generate a calculation parameter, and a prediction confidence is generated based on the calculation parameter; Based on the prediction confidence and a preset comparison value, an update result corresponding to the neural network inference model is generated, and the neural network inference model corresponding to the wing profile set-operation joint embedding coding vector is updated based on the update result.

9. A machine learning based tilt-rotor aerodynamic force coefficient prediction system, characterized by, Including: A parameter input module for inputting a wing profile shape parameter, an angle of attack, and a flow field parameter; an embedding coding module, configured to embed code the airfoil shape parameter, the attack angle and the flow field parameter to obtain an airfoil shape parameter embedding code vector, an attack angle embedding code vector and a flow field parameter embedding code vector, wherein the attack angle embedding code vector is generated in a manner comprising: converting , and into a combination to obtain the attack angle embedding code vector; A cascading module for cascading the wing profile shape parameter embedding coding vector, the angle of attack embedding coding vector, and the flow field parameter embedding coding vector to obtain a wing profile set-operation joint embedding coding vector; An initial parameter inference module for inputting the wing profile set-operation joint embedding coding vector into a neural network inference model to obtain an initial output parameter; a parameter correction module, configured to perform post-processing correction on the initial output parameters based on a physical model to obtain aerodynamic coefficient related parameter decoding results, the aerodynamic coefficient related parameter decoding results including a lift coefficient, a logarithmic function value of a drag coefficient, a moment coefficient, and a boundary layer parameter; an aerodynamic coefficient calculation module, configured to calculate aerodynamic coefficients based on the aerodynamic coefficient related parameter decoding results.

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