Aerodynamic force modeling method suitable for wide-speed-range small-maneuvering motion of aircraft

Abstract

The invention provides an aerodynamic modeling method suitable for wide-speed-range small-maneuvering motion of an aircraft, and relates to the technical field of aircraft modeling. The method comprises the following steps: firstly, carrying out finite element modeling on a rigid symmetric aircraft, and generating aircraft speed and acceleration sample data under set time length and time step length through a Latin hypercube sampling LHS method; establishing a conversion matrix for converting the fixed coordinate system into an airframe coordinate system, and obtaining a matrix expression of the speed of the aircraft relative to the fixed coordinate system in the airframe coordinate system; performing flow field simulation on the aircraft, acquiring aerodynamic force and torque data of the aircraft, and establishing an aircraft aerodynamic model; substituting the speed sample data, the acceleration sample data and the six-degree-of-freedom coupling item of the aircraft into the aircraft aerodynamic model to finally obtain six groups of equations; and finally, performing coefficient identification on each group of equations to obtain an aerodynamic model preliminarily containing all parameters, and then performing parameter elimination to obtain an aerodynamic model of aircraft force and torque.

Description

Technical Field

[0001] This invention relates to the field of aerospace engineering technology, and in particular to an aerodynamic modeling method applicable to small maneuvering motions of aircraft over a wide speed range. Background Technology

[0002] The aerodynamic characteristics of an aircraft, especially its performance across different speed ranges, play a crucial role in its flight performance and control stability. Because the aerodynamic response of an aircraft in this speed range differs from both the simplified characteristics of high-speed cruise and the strongly nonlinear features of high-maneuver flight, its dynamic modeling faces unique challenges. Changes in the aircraft's shape lead to significant differences in aerodynamic characteristics. Under various flight conditions, including complex maneuvers, existing aerodynamic modeling methods often lack sufficient flexibility to provide accurate predictions when faced with such shape changes.

[0003] Currently, traditional aerodynamic modeling methods are mainly based on the mechanistic analysis of rigidly symmetric aircraft. These models are constructed by establishing equations of motion and using aerodynamic derivatives as core variables. Although this method is theoretically physically interpretable, its application is severely limited, especially when the aircraft's flight state changes, the model's accuracy is often difficult to guarantee. Traditional models typically only have a certain degree of accuracy under small disturbances in level flight; when the flight state deviates from the small disturbance conditions, the prediction results quickly become invalid. Furthermore, existing modeling methods rely on fixed model structures, and cannot flexibly adapt to the aerodynamic differences caused by changes in aircraft shape, resulting in significantly different application effects of the same model on different aircraft. Especially in certain intervals of the wide velocity range, traditional methods fail to fully consider the coupling effect of velocity changes and attitude changes, resulting in insufficient model universality and reliability.

[0004] With the increasing diversity of aircraft shape designs, existing aerodynamic models cannot effectively reflect the impact of shape differences on aerodynamic characteristics, and traditional modeling methods are clearly insufficient in adaptability and flexibility. This makes it difficult for aerodynamic modeling methods based on classic white box models to meet the modeling needs of modern aircraft under various flight conditions, especially in certain actual flight speed ranges, where the applicability and accuracy of existing models cannot be guaranteed.

[0005] Therefore, a new aerodynamic modeling method is urgently needed to provide accurate aerodynamic predictions across a wide range of flight conditions. This method should not only retain the advantages of white-box models in physical modeling but also possess sufficient flexibility to adapt to variations in aircraft shape and ensure good prediction accuracy across a wide speed range, including critical velocity intervals. Simultaneously, this method should allow for verification of the model's accuracy in actual flight tests and simulations, ensuring its broad applicability across different aircraft and various flight conditions. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide an aerodynamic modeling method suitable for small maneuvering motions of aircraft over a wide speed range, which addresses the shortcomings of the prior art and maintains the effectiveness and robustness of the aircraft aerodynamic model within a preset speed range.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an aerodynamic modeling method applicable to small maneuvering motions over a wide speed range for aircraft, comprising:

[0008] Finite element modeling was performed on a rigidly symmetric aircraft, mesh generation was completed, and mesh independence was verified.

[0009] Define a fixed coordinate system, a body coordinate system, and the aircraft's motion parameters for the aircraft.

[0010] The Latin hypercube sampling (LHS) method is used to generate sample data of the aircraft's velocity and acceleration at a set duration and time step, and the Gaussian filtering method is used to smooth the transition between sample points in the obtained sample data.

[0011] Establish the transformation matrix from the fixed coordinate system to the body coordinate system, and obtain the matrix expression of the aircraft's velocity relative to the fixed coordinate system in the body coordinate system;

[0012] The flow field of the aircraft was simulated using simulation software to obtain aerodynamic and torque data. Based on the motion equations of rigid symmetric aircraft proposed by Bryan, an aerodynamic model of the aircraft was then established.

[0013] The velocity and acceleration sample data generated by the Latin hypercube sampling method, along with the six-degree-of-freedom coupling terms of the aircraft, were substituted into the established aerodynamic model, resulting in six sets of equations.

[0014] The sliding window algorithm combined with ridge regression is used to identify the coefficients of each set of equations to obtain a preliminary aerodynamic model that includes all parameters. Then, Lasso regression is used to remove parameters and eliminate unnecessary parameters to obtain the aerodynamic model of the aircraft's forces and moments.

[0015] Furthermore, the method defines a fixed coordinate system Oxo y o z o Where the origin O is the position of the aircraft's center of mass; x o The axis lies in the horizontal plane, with its positive direction pointing in the direction of the aircraft's flight velocity; z o The axis is perpendicular to x in the aircraft reference plane. o The axis points downwards, y o The axis is perpendicular to x o axis and z o The axis points to the right;

[0016] Define the body coordinate system Oxyz, where the origin is located at the center of mass of the aircraft, and the three coordinate axes are: the x-axis is the longitudinal axis, which is defined as the coordinate axis pointing forward on the aircraft reference plane, and is specified to be parallel to the fuselage axis or wing root chord line; the y-axis is the transverse axis, which is defined as the coordinate axis pointing to the right perpendicular to the aircraft reference plane; and the z-axis is the vertical axis, which is defined as the coordinate axis pointing downward perpendicular to the longitudinal axis in the aircraft reference plane.

[0017] The six degrees of freedom data of the aircraft in a fixed coordinate system include: longitudinal, lateral, and vertical velocities of u. o v o w o During flight, the velocity components decomposed onto the three coordinate axes of the aircraft are u, v, and w, and the angular velocities during flight are p, q, and r, which represent the roll angular velocity around the x-axis, the pitch angular velocity around the y-axis, and the yaw angular velocity around the z-axis, respectively.

[0018] The three attitude angles of the aircraft are: roll angle φ, pitch angle θ, and yaw angle ψ;

[0019] The resultant force acting on the aircraft has three components along the x, y, and z axes: X, Y, and Z.

[0020] The three components of the resultant torque acting on the aircraft along the x, y, and z axes are L, M, and N, which represent the rolling moment about the x-axis, the pitching moment about the y-axis, and the yaw moment about the z-axis, respectively.

[0021] The wing reference area of ​​the aircraft is S, and the mean aerodynamic chord length is c. A With wingspan of b and total mass of m; longitudinal, lateral, and vertical accelerations are respectively... , , The roll, pitch, and yaw accelerations are respectively , , The density of an ideal gas, air, is ρ.

[0022] Furthermore, the transformation matrix for converting the fixed coordinate system to the body coordinate system is established, resulting in the matrix expression of the aircraft's velocity relative to the fixed coordinate system in the body coordinate system, specifically as follows:

[0023] Establish a coordinate transformation matrix to convert the fixed coordinate system to the body coordinate system, and represent the motion parameters of the aircraft and the forces and torques acting on the aircraft in the body coordinate system, as shown in the following formula:

[0024] ;

[0025] Furthermore, the matrix expression for the aircraft's velocity relative to the fixed coordinate system in the body coordinate system is obtained:

[0026] .

[0027] Furthermore, based on the equations of motion of a rigidly symmetric aircraft, without considering specific differences in aircraft type, a sliding window algorithm combined with ridge regression is used to identify the coefficients of each set of equations, obtaining a preliminary aerodynamic model containing all parameters. Then, Lasso regression is used to eliminate unnecessary parameters, establishing an aerodynamic model of the aircraft's forces and moments, as shown in the following formula:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ; Among them, X u X p for u、p The first derivative, X uq X vr X wr X ww X wv X qq Let be the second derivatives of the coupling terms uq, vr, wr, ww, wv, and qq; for q and acceleration term The first derivative of Y vr Y qr Y rp Y vrLet vr, qr, rp, vr be the second derivatives of the coupling terms; for u, v, p, q and acceleration term The first derivative, Z qv Z pq Z wq Z vw Let be the second derivatives of the coupling terms qv, pq, wq, and vw; For acceleration term The first derivative, L qr L vq L qv L up L uq L ur Let be the second derivatives of the coupling terms qr, vq, qv, up, uq, and ur. for The first derivative, M qv M qq M pq Let be the second derivatives of the coupling terms qv, qq, and pq; For acceleration term The first derivative, N ur , N wr , N wq , N qr , N vr , N uv For coupling terms ur, wr, wq, qr, vr, UV The second derivative of .

[0034] Furthermore, the function of the ridge regression as follows:

[0035] ;

[0036] in, This is the actual value. Here are the predicted values ​​from the aerodynamic model, and n is the total number of time steps. Here, is the j-th coefficient of the aerodynamic model, and p is the total number of coefficients in the aerodynamic model. It is the standard sum of squared residuals, which measures the goodness of fit of an aerodynamic model. It is the square of the L2 norm of the coefficient vector. For regularization parameters;

[0037] The objective function of the Lasso regression as follows:

[0038] ;

[0039] in, This is the actual value. These are the model's predicted values. These are the coefficients for each item. This is the regularization parameter.

[0040] Secondly, this application proposes an electronic device, comprising: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to perform the aerodynamic modeling method applicable to the wide speed range small maneuvering motion of an aircraft.

[0041] Thirdly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the aerodynamic modeling method applicable to the wide-speed-range small-maneuver motion of an aircraft.

[0042] Fourthly, this application proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned aerodynamic modeling method applicable to small maneuvers in a wide speed range of aircraft.

[0043] The beneficial effects of adopting the above technical solution are as follows: The aerodynamic modeling method for small maneuvering motion of aircraft with a wide speed range provided by the present invention (1) strong applicability of speed range: by covering the speed range through LHS sampling, the model is ensured to remain effective within the preset speed range, breaking through the defect of existing methods being limited to a single working condition; (2) high modeling efficiency: by uniform sampling of multidimensional parameter space and Taylor series expansion, the number of samples required is reduced and the simulation efficiency is improved; (3) robust coefficient identification: by adopting sliding window and ridge regression methods, the multicollinearity problem is effectively alleviated, overfitting is avoided, and parameter estimation is more stable; (4) outstanding engineering value: it can reduce the number of actual test flights and costs, and provide a reliable tool for the design optimization, performance prediction and control law design of light aircraft. Attached Figure Description

[0044] Figure 1 A flowchart of an aerodynamic modeling method for wide-speed-range small-maneuver motion of an aircraft provided in Embodiment 1 of the present invention;

[0045] Figure 2 This is a schematic diagram of the coordinates and variables of the aircraft provided in Embodiment 1 of the present invention;

[0046] Figure 3 The LHS sampling projection distribution diagram in the parameter space provided in Embodiment 1 of the present invention is shown in the figure, wherein (a) is the projection of parameter uv, (b) is the projection of parameter uw, (c) is the projection of parameter up, (d) is the projection of parameter uq, and (e) is the projection of parameter ur.

[0047] Figure 4 The acceleration and angular acceleration curves generated by LHS sampling provided in Embodiment 1 of the present invention are shown in (a) and (b).

[0048] Figure 5 The force and torque fitting effect diagram provided in Embodiment 1 of the present invention is shown in which (a) is axial force, (b) is lateral force, (c) is vertical force, (d) is rolling torque, (e) is pitching torque, and (f) is yaw torque.

[0049] Figures 6(a)-6(i) are comparison charts of the prediction results and experimental data of the model under various typical flight conditions provided in Embodiment 1 of the present invention. Among them, Figures 6(a), 6(b), and 6(c) are comparison charts of the rolling moment coefficient (CI), yaw moment coefficient (CN), and lateral force coefficient (CY) for pitch angle of 9 degrees and sideslip angle of -12 degrees, respectively; Figures 6(d), 6(e), and 6(f) are comparison charts of the rolling moment coefficient (CI), yaw moment coefficient (CN), and lateral force coefficient (CY) for pitch angle of 12 degrees and sideslip angle of -8 degrees, respectively; Figures 6(g), 6(h), and 6(i) are comparison charts of the rolling moment coefficient (CI), yaw moment coefficient (CN), and lateral force coefficient (CY) for pitch angle of 18 degrees and sideslip angle of 4 degrees, respectively. Detailed Implementation

[0050] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0051] Example 1:

[0052] In this embodiment, an aerodynamic modeling method suitable for small maneuvers over a wide speed range of aircraft is described, such as... Figure 1 As shown, it includes the following steps:

[0053] Step S01: Perform 3D modeling for the rigid symmetric aircraft (refer to the RX1E-A aircraft model), complete mesh generation, and verify mesh independence.

[0054] Step S02: Define a fixed coordinate system, a body coordinate system, and the aircraft's motion parameters, such as... Figure 2As shown, sample data of longitudinal velocity u, lateral velocity v, vertical velocity w, roll angular velocity p, pitch angular velocity q, and yaw angular velocity r with a duration of 200 s and a time step of 0.005 s were generated using Latin hypercube sampling (LHS). The sample data ranges were set as follows: u: 50 m / s-70 m / s, v: ±4 m / s, w: ±3 m / s, p: ±60 deg / s, q: 8 deg / s-20 deg / s, r: ±15 deg / s. Gaussian filtering was used to smooth the transition between sample points to prevent excessive acceleration.

[0055] In this embodiment, the projection distribution of LHS samples in the parameter space and the generated acceleration and angular acceleration are as follows: Figure 3 , 4 As shown;

[0056] In this embodiment, a fixed coordinate system Ox is defined. o y o z o Where the origin O is the position of the aircraft's center of mass; x o The axis lies in the horizontal plane, with its positive direction pointing in the direction of the aircraft's flight velocity; z o The axis is perpendicular to x in the aircraft reference plane. o The axis points downwards, y o The axis is perpendicular to x o axis and z o The axis points to the right;

[0057] Define the aircraft coordinate system Oxyz, where the origin is located at the center of mass of the aircraft. The three coordinate axes are: the x-axis, which is the longitudinal axis, defined as the coordinate axis pointing forward on the aircraft reference plane, and is parallel to the fuselage axis or wing root chord; the y-axis, which is the transverse axis, defined as the coordinate axis pointing to the right perpendicular to the aircraft reference plane; and the z-axis, which is the vertical axis, defined as the coordinate axis pointing downward perpendicular to the longitudinal axis in the aircraft reference plane.

[0058] The six degrees of freedom data of the aircraft in a fixed coordinate system include: longitudinal, lateral, and vertical velocities of u. o v o w o During flight, the velocity components decomposed onto the three coordinate axes of the aircraft are u, v, and w, and the angular velocities during flight are p, q, and r, which represent the roll angular velocity around the x-axis, the pitch angular velocity around the y-axis, and the yaw angular velocity around the z-axis, respectively.

[0059] The three attitude angles of the aircraft are: roll angle φ, pitch angle θ, and yaw angle ψ;

[0060] The resultant force acting on the aircraft has three components along the x, y, and z axes: X, Y, and Z.

[0061] The three components of the resultant torque acting on the aircraft along the x, y, and z axes are L, M, and N, which represent the rolling moment about the x-axis, the pitching moment about the y-axis, and the yaw moment about the z-axis, respectively.

[0062] The wing reference area of ​​the aircraft is S, and the mean aerodynamic chord length is c. A With wingspan of b and total mass of m; longitudinal, lateral, and vertical accelerations are respectively... , , The roll, pitch, and yaw accelerations are respectively , , The density of an ideal gas, air, is ρ.

[0063] Latin hypercube sampling is a method for uniform sampling in high-dimensional spaces. It divides the range of each input parameter into several small intervals and then randomly selects a sample point from each interval to ensure that the sample points in each dimension are uniformly distributed. This method can fully cover the entire parameter space.

[0064] Step S03: Establish the transformation matrix for converting the fixed coordinate system to the body coordinate system;

[0065] Establish a coordinate transformation matrix to convert the fixed coordinate system to the body coordinate system, and represent the motion parameters of the aircraft and the forces and torques acting on the aircraft in the body coordinate system, as shown in the following formula:

[0066] (1);

[0067] Using equation (1), the matrix expression for the velocity of the aircraft relative to the fixed coordinate system in the body coordinate system can be derived:

[0068] ;

[0069] Step S04: Referring to the equations of motion for a rigidly symmetric aircraft proposed by Bryan, the aerodynamic and torque terms depend only on the variables of the perturbation motion and their derivatives. This can be conveniently represented as a function consisting of the sum of many Taylor series, each containing one motion variable or its derivative. Since the motion variables are very small, only the highest second-order expansion in each series of the equations is significant. Therefore, the equations of motion for a rigidly symmetric aircraft are as follows:

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] in, ;

[0077] for and acceleration The first derivative, , , Let be the second derivatives of the coupling terms uu, vv, ww, uv, uw, vw, pp, qq, rr, pq, pr, qr;

[0078] for The first derivative, , , Let be the second derivatives of the coupling terms uu, vv, ww, uv, uw, vw, pp, qq, rr, pq, pr, qr;

[0079] for u, w, q and acceleration The first derivative, , , Let be the second derivatives of the coupling terms uu, vv, ww, uv, uw, vw, pp, qq, rr, pq, pr, qr;

[0080] for v, p, r The first derivative, , , Let be the second derivatives of the coupling terms uu, vv, ww, uv, uw, vw, pp, qq, rr, pq, pr, qr;

[0081] Let u, w, q and acceleration be... The first derivative, , , Let be the second derivatives of the coupling terms uu, vv, ww, uv, uw, vw, pp, qq, rr, pq, pr, qr;

[0082] for v, p, r The first derivative, , , Let be the second derivatives of the coupling terms uu, vv, ww, uv, uw, vw, pp, qq, rr, pq, pr, qr;

[0083] g is the acceleration due to gravity.

[0084] Step S05: Based on the Reynolds-averaged Navier-Stokes (RANS) method—a core approach for handling complex turbulence problems in engineering, which uses time averaging to solve the steady-state solution of the flow field, thereby significantly reducing computational costs while ensuring computational accuracy—the STAR-CCM+ simulation software is used to simulate the flow field of the aircraft, obtain aerodynamic and torque data, and then establish a six-degree-of-freedom aerodynamic model of the aircraft. Subsequently, the velocity and acceleration data generated by the Latin hypercube sampling method, as well as the six-degree-of-freedom coupling terms of the aircraft, are substituted into the aerodynamic model of the aircraft to finally obtain six sets of equations.

[0085] Step S06: Use the sliding window algorithm combined with ridge regression to identify the coefficients of each set of equations to obtain the aerodynamic model of the aircraft's forces and moments. Input the simulated force and moment data into the aerodynamic model of the aircraft, and use the sliding window algorithm combined with ridge regression to identify the coefficients to obtain a preliminary aerodynamic model containing all parameters. Then, use Lasso regression to remove unnecessary parameters. The calculated coefficients are shown in Tables 1 and 2.

[0086] Table 1. Dimensionless coefficient values ​​for each aerodynamic nonlinear term.

[0087]

[0088] Table 2. Dimensionless coefficient values ​​for each aerodynamic moment nonlinear term.

[0089]

[0090] Referring to the equations of motion of the rigidly symmetric aircraft mentioned above, an aerodynamic model of the forces and moments of the aircraft is established:

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] Among them, X u X p for u、p The first derivative, X uq X vr X wr X ww X wv X qq Let be the second derivatives of the coupling terms uq, vr, wr, ww, wv, and qq;

[0098] for q and acceleration term The first derivative of Y vr Y qr Y rp Y vr Let vr, qr, rp, vr be the second derivatives of the coupling terms;

[0099] for u, v, p, q and acceleration term The first derivative, Z qv Z pq Z wq Z vw Let be the second derivatives of the coupling terms qv, pq, wq, and vw;

[0100] For acceleration term The first derivative, L qr L vq L qv L up L uq L ur Let be the second derivatives of the coupling terms qr, vq, qv, up, uq, and ur.

[0101] for The first derivative, M qv M qq M pq Let be the second derivatives of the coupling terms qv, qq, and pq;

[0102] For acceleration term The first derivative, N ur , N wr , N wq , Nqr , N vr , N uv For coupling terms ur, wr, wq, qr, vr, UV The second derivative;

[0103] The final simulation software STAR-CCM+ obtained the aircraft's force and moment data from the flight simulation, and the fitting effect of the force and moment data predicted by the aerodynamic model is as follows: Figure 5 As shown.

[0104] The sliding window algorithm is an efficient approach for handling continuous sub-interval problems. Since velocity parameters are randomly and uniformly generated by the LHS (Least Absolute Shrinkage and Selection Operator), they do not exhibit a fixed pattern, allowing for segmented data analysis. The sliding window operates within a fixed-step "window" across the entire data interval, moving a unit until the entire interval is covered. This yields a set of coefficient identification results. Based on these coefficients, Lasso regression (Least Absolute Shrinkage and Selection Operator) is used to eliminate coefficients with negligible impact on the fit, resulting in the final aerodynamic model. To avoid training-validation leakage, the data used for coefficient identification is independent of the subsequent validation dataset, and the excitation methods differ. During the validation phase, multi-frequency sinusoidal / quasi-random excitations are used with fade-in / fade-out settings to improve frequency domain coverage and suppress boundary effects.

[0105] Ridge regression is an improved version of linear regression, specifically designed to address collinearity. Ordinary least squares linear regression aims to find a set of coefficients (θ) that minimizes the sum of squared residuals. However, when features are highly correlated (i.e., collinear), the coefficients estimated by ordinary least squares become highly sensitive to random errors in the data. This leads to: large model variance and poor stability (small changes in training data can cause drastic changes in coefficients); and coefficient values ​​may become abnormally large or even uninterpretable, resulting in overfitting. Ridge regression adds a penalty term to the objective function of ordinary linear regression. This penalty term is λ times the sum of squared coefficients of the aerodynamic model (the square of the L2 norm). The ridge regression function is as follows:

[0106] ;

[0107] in, This is the actual value. These are values ​​predicted by the aerodynamic model. These are the coefficients for each item. It is the standard sum of squared residuals, which measures the goodness of fit of an aerodynamic model. It is the coefficient vector (excluding the intercept). The square of the L2 norm of ) when When the penalty term is zero, ridge regression is equivalent to standard linear regression; when... At this point, the effect of the penalty term becomes infinitely large, and all coefficients are forced to be compressed close to zero. This leads to an oversimplified model (high bias).

[0108] Lasso regression (Least Absolute Shrinkage and Selection Operator) adds an L1 regularization term (the sum of the absolute values ​​of the coefficients of each model term) to the objective function of ordinary linear regression. This extra term penalizes the aerodynamic model to prevent overfitting and can directly compress the coefficients of some unimportant features to 0, thereby achieving feature selection. The objective function of Lasso regression is as follows:

[0109] ;

[0110] in, This is the actual value. These are the model's predicted values. These are the coefficients for each item. This is a regularization parameter that controls the strength of the penalty term.

[0111] This method removes outliers from the coefficient set obtained by combining the sliding window algorithm with ridge regression, thus obtaining the aerodynamic model of the aircraft's forces and moments.

[0112] Step S07 verifies the effectiveness and robustness of the aerodynamic model of aircraft forces and moments obtained in steps S01-S06 within the preset speed range.

[0113] (a) Calculate the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE) of the aerodynamic model of the forces and moments of the aircraft by comparing it with numerical simulation (CFD) or experimental data.

[0114] Among them, the coefficient of determination: , This is the actual value. These are aerodynamic model predictions for the forces and moments of the aircraft. The average of the actual values; This reflects the goodness of fit of the aerodynamic model to the data regarding the forces and moments of the aircraft; the larger the value, the better the model fit.

[0115] Root mean square error: , This is the actual value. is the aerodynamic model prediction value of the force and moment of the aircraft, where n is the total number of samples; RMSE is the average of the squares of the errors of all data points, and the square root of the result is taken. Its unit is the same as the actual data, and the smaller the value, the smaller the error of the aerodynamic model prediction of the force and moment of the aircraft.

[0116] Squared absolute error: , This is the actual value. The aerodynamic model predicts the forces and moments of the aircraft, where n is the total number of samples. MAE measures the mean absolute difference between the predicted and actual values. Compared to RMSE, MAE is less sensitive to outliers.

[0117] Table 3. R values ​​of each component of force and moment predicted by the aerodynamic model of the aircraft. 2 RMSE and MAE values

[0118]

[0119] (b) Under different flight conditions (including acceleration, deceleration, turning, etc.), use independent validation datasets to perform aerodynamic model prediction of aircraft forces and moments, and evaluate the predictive ability of the model;

[0120] (c) Conduct residual analysis and structural consistency verification to ensure that the aerodynamic model of the force and moment of the aircraft can correctly fit the aerodynamic characteristics of the aircraft;

[0121] (d) Through sensitivity analysis and robustness testing, verify the tolerance of the aerodynamic model of the aircraft's forces and moments to operating condition disturbances and noise, and ensure the reliability of the aerodynamic model in practical applications.

[0122] In this embodiment, the aerodynamic model of the aircraft's forces and moments is verified through the following steps:

[0123] Step 1: Construct a validation dataset independent of the identification data;

[0124] To avoid "training-validation leakage," the validation samples are completely independent of the samples used for coefficient identification in step S06. Using the same variable boundaries as in step S02 (u: 50 m / s–70 m / s; v: ±4 m / s; w: ±3 m / s; p: ±60 deg / s; q: 8 deg / s–20 deg / s; r: ±15 deg / s), LHS (Latin Hypercube Sampling) sampling is performed again to generate a six-DOF velocity and angular velocity sequence with a duration of 200 s and a time step of 0.005 s. To suppress non-physical acceleration spikes, the velocity and angular velocity sequences are Gaussian filtered to achieve a smooth transition between sample points. To improve frequency domain coverage, multi-frequency sinusoidal / quasi-random excitations (1–5 coprime frequencies, amplitude not exceeding 20% ​​of their respective boundaries) are superimposed, and linear in / out segments are set at 0s–5s and 195s–200s to avoid boundary effects.

[0125] Step 2: Numerical simulation or experiment;

[0126] The simulation is performed under the same numerical settings as in step S05 (RANS method, same mesh as in S01, and mesh independence verification has been completed). The six-DOF data of the aircraft generated from the verification dataset is input as the boundary conditions for the body motion, and the six-component aerodynamic force and torque time history X, Y, Z, L, M, N in the body coordinate system are output as the "reference true value" curves.

[0127] Step 3: Aerodynamic model prediction of aircraft forces and moments;

[0128] Using the aerodynamic model of aircraft forces and moments obtained in step S06, and inputting the same six-degree-of-freedom time history as in step 1, the aerodynamic model predictions are calculated. And ensure that the coordinate system and dimensions are consistent with those in step 2. The comparison between the predicted values ​​and the wind tunnel data, i.e. the experimental data, is shown in Figures 6(a)-6(i). In the figures, the red scatter plot represents the experimental data, and the green solid line represents the model's predicted values. It can be seen from the figures that the model has a very good prediction effect.

[0129] Step 4: Quantitative evaluation indicators and qualification criteria;

[0130] In this embodiment, the coefficient of determination R² is used as the main index, supplemented by absolute and relative error measures. The coefficient of determination, root mean square error (RMSE), and mean absolute error (MAE) are calculated for the six components of aerodynamic force and torque, respectively.

[0131] In this embodiment, the coefficient of determination R² for the force component is ≥0.90, and the coefficient of determination R² for the torque component is ≥0.85; the root mean square error (RMSE) of the six components does not exceed 10% of the corresponding range.

[0132] Step 5: Residual and structural consistency check;

[0133] For residuals conduct:

[0134] (1) Zero mean and homoscedasticity test; (2) Autocorrelation test (Durbin–Watson / Ljung–Box), requiring that the autocorrelation of the principal lag is not significant; (3) Frequency domain “white noise” test, ensuring that the principal energy of the error is not concentrated near the excitation frequency to avoid structural omissions. If the test fails, backtrack to step S06 to adjust the regularization strength or restore the interpretable mechanism terms that were removed by Lasso.

[0135] Example 2:

[0136] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the aerodynamic modeling method applicable to the wide speed range small maneuvering motion of aircraft.

[0137] The electronic device can be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the aerodynamic modeling method for small maneuvers of aircraft over a wide speed range, as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0138] The processor is used to execute all or part of the steps in the aerodynamic modeling method for wide-speed-range small maneuvers of aircraft as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in an electronic device, as well as application-related data.

[0139] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the aerodynamic modeling method for wide-speed-range small maneuvering motions of aircraft described in the above embodiments.

[0140] Example 3:

[0141] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0142] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the aerodynamic modeling method for wide-speed-range small maneuvering motions of aircraft described in various embodiments of this application.

[0143] The aforementioned storage media include: flash memory, hard disk, multimedia card, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory, etc.), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disk, optical disk, server, APP (Application) application store, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned aerodynamic modeling method applicable to the wide-speed-range small-maneuver motion of aircraft.

[0144] Example 4:

[0145] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aerodynamic modeling method applicable to small maneuvers in a wide speed range of aircraft.

[0146] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0147] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. An aerodynamic modeling method applicable to small maneuvers over a wide speed range for aircraft, characterized in that, include: Finite element modeling was performed on a rigidly symmetric aircraft, mesh generation was completed, and mesh independence was verified. Define a fixed coordinate system, a body coordinate system, and the aircraft's motion parameters for the aircraft. The Latin hypercube sampling (LHS) method is used to generate sample data of the aircraft's velocity and acceleration at a set duration and time step, and the Gaussian filtering method is used to smooth the transition between sample points in the obtained sample data. Establish the transformation matrix from the fixed coordinate system to the body coordinate system, and obtain the matrix expression of the aircraft's velocity relative to the fixed coordinate system in the body coordinate system; The flow field of the aircraft was simulated using simulation software to obtain aerodynamic and torque data. Based on the motion equations of rigid symmetric aircraft proposed by Bryan, an aerodynamic model of the aircraft was then established. The velocity and acceleration sample data generated by the Latin hypercube sampling method, along with the six-degree-of-freedom coupling terms of the aircraft, were substituted into the established aerodynamic model, resulting in six sets of equations. The sliding window algorithm combined with ridge regression is used to identify the coefficients of each set of equations to obtain a preliminary aerodynamic model that includes all parameters. Then, Lasso regression is used to remove parameters and eliminate unnecessary parameters to obtain the aerodynamic model of the aircraft's forces and moments.

2. The aerodynamic modeling method for small maneuvers over a wide speed range of aircraft according to claim 1, characterized in that, The method defines a fixed coordinate system Ox o y o z o Where the origin O is the position of the aircraft's center of mass; x o The axis lies in the horizontal plane, with its positive direction pointing in the direction of the aircraft's flight velocity; z o The axis is perpendicular to x in the aircraft reference plane. o The axis points downwards, y o The axis is perpendicular to x o axis and z o The axis points to the right; Define the body coordinate system Oxyz, where the origin is located at the center of mass of the aircraft, and the three coordinate axes are as follows: the x-axis is the longitudinal axis, which is defined as the coordinate axis pointing forward in the aircraft reference plane and parallel to the fuselage axis or wing root chord; the y-axis is the transverse axis, which is defined as the coordinate axis pointing to the right perpendicular to the aircraft reference plane; and the z-axis is the vertical axis, which is defined as the coordinate axis pointing downward perpendicular to the longitudinal axis in the aircraft reference plane. The six degrees of freedom data of the aircraft in a fixed coordinate system include: longitudinal, lateral, and vertical velocities of u. o v o w o During flight, the velocity components decomposed onto the three coordinate axes of the aircraft are u, v, and w, and the angular velocity components during flight are p, q, and r, which represent the roll angular velocity around the x-axis, the pitch angular velocity around the y-axis, and the yaw angular velocity around the z-axis, respectively. The three attitude angles of the aircraft are: roll angle φ, pitch angle θ, and yaw angle ψ; The resultant force acting on the aircraft has three components along the x, y, and z axes: X, Y, and Z. The three components of the resultant torque acting on the aircraft along the x, y, and z axes are L, M, and N, which represent the rolling moment about the x-axis, the pitching moment about the y-axis, and the yaw moment about the z-axis, respectively. The wing reference area of ​​the aircraft is S, and the mean aerodynamic chord length is c. A With wingspan of b and total mass of m; longitudinal, lateral, and vertical accelerations are respectively... , , The roll, pitch, and yaw accelerations are respectively , , The density of an ideal gas, air, is ρ.

3. The aerodynamic modeling method for small maneuvers over a wide speed range of aircraft according to claim 2, characterized in that, The transformation matrix for converting the fixed coordinate system to the body coordinate system is established, resulting in the matrix expression of the aircraft's velocity relative to the fixed coordinate system in the body coordinate system. Specifically: Establish a coordinate transformation matrix to convert the fixed coordinate system to the body coordinate system, and represent the motion parameters of the aircraft and the forces and torques acting on the aircraft in the body coordinate system, as shown in the following formula: ； Furthermore, the matrix expression for the aircraft's velocity relative to the fixed coordinate system in the body coordinate system is obtained: 。 4. The aerodynamic modeling method for small maneuvers over a wide speed range of aircraft according to claim 3, characterized in that, Based on the equations of motion of a rigidly symmetric aircraft, without considering specific differences in aircraft type, the sliding window algorithm combined with ridge regression is used to identify the coefficients of each set of equations, obtaining a preliminary aerodynamic model that includes all parameters. Then, Lasso regression is used to eliminate unnecessary parameters, establishing the aerodynamic model of the aircraft's forces and moments, as shown in the following formula: ； ； ； ； ； ； Among them, X u X p for u、p The first derivative, X uq X vr X wr X ww X wv X qq Let be the second derivatives of the coupling terms uq, vr, wr, ww, wv, and qq; for q and acceleration term The first derivative of Y vr Y qr Y rp Y vr Let vr, qr, rp, vr be the second derivatives of the coupling terms; for u, v, p, q and acceleration term The first derivative, Z qv Z pq Z wq Z vw Let be the second derivatives of the coupling terms qv, pq, wq, and vw; For acceleration term The first derivative, L qr L vq L qv L up L uq L ur Let be the second derivatives of the coupling terms qr, vq, qv, up, uq, and ur. for The first derivative, M qv M qq M pq Let be the second derivatives of the coupling terms qv, qq, and pq; For acceleration term The first derivative, N ur , N wr , N wq , N qr , N vr , N uv For coupling terms ur, wr, wq, qr, vr, uv The second derivative of .

5. The aerodynamic modeling method for small maneuvers over a wide speed range of aircraft according to claim 4, characterized in that, The objective function of ridge regression as follows: ； in, This is the actual value. Here are the predicted values ​​from the aerodynamic model, and n is the total number of time steps. Here, is the j-th coefficient of the aerodynamic model, and p is the total number of coefficients in the aerodynamic model. It is the standard sum of squared residuals, which measures the goodness of fit of an aerodynamic model. It is the square of the L2 norm of the coefficient vector. For regularization parameters; The objective function of the Lasso regression as follows: ； in, This is the actual value. These are the model's predicted values. These are the coefficients for each item. This is the regularization parameter.

6. An electronic device for executing the aerodynamic modeling method for wide-speed-range small-maneuver motions of aircraft as described in any one of claims 1-5, characterized in that, include: One or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the aerodynamic modeling method applicable to small maneuvers over a wide speed range of aircraft.

7. A computer-readable storage medium storing executable instructions for performing the aerodynamic modeling method for wide-speed-range small maneuvering motions of aircraft as described in any one of claims 1-5, characterized in that, When the instruction is executed, it causes the processor to perform the aerodynamic modeling method applicable to small maneuvers in a wide speed range of aircraft.

8. A computer program product for executing the aerodynamic modeling method for wide-speed-range small maneuvering motions of aircraft as described in any one of claims 1-5, characterized in that, This includes a computer program or instructions that, when executed by a processor, implement the described aerodynamic modeling method applicable to small maneuvers over a wide speed range for aircraft.

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