A fixed-wing aircraft element flight aerodynamic modeling method considering wind disturbance

Abstract

The application discloses a kind of fixed-wing aircraft element flight aerodynamic modeling methods considering wind interference, by isolating wind interference influence, using the motion variable of aircraft relative to ground coordinate system is described, based on the theory of Taylor expansion multivariate function decomposition series, construct general fixed-wing aircraft aerodynamic commonality base function analytical model under different wind conditions.Modeling process includes: step 1, obtain the discrete aerodynamic data set under different state conditions, establish the traditional aerodynamic model of fixed-wing aircraft;Step 2, analyze the approximate accuracy of aerodynamic force (moment), determine the Taylor expansion order of each component;Step 3, the commonality base function of fixed-wing aircraft aerodynamic force is calculated to obtain, the commonality base function obtained is used as the basis, the aerodynamic force (moment) of aircraft is approximated, and finally the element flight aerodynamic model is obtained.The application can realize the online prediction of aerodynamic force and aerodynamic moment of fixed-wing aircraft in unknown wind conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aerodynamic modeling of an aircraft, and particularly relates to a fixed-wing aircraft meta-flight aerodynamic modeling method considering wind interference. BACKGROUND

[0002] Wind in the environment seriously affects the flight safety of the aircraft, and the complex aerodynamics of the interaction between the wind and the aircraft can make the aircraft deviate from the route or even lose control. In order to realize accurate control of the aircraft maneuvering flight and improve the safety and reliability of the aircraft flight in the wind environment, it is necessary to accurately predict the aerodynamic force (moment) of the aircraft in the presence of wind interference in real time.

[0003] The traditional fixed-wing aircraft aerodynamic modeling method is aimed at the motion of the aircraft in the airflow coordinate system, and introduces physical variables such as angle of attack and sideslip angle to describe the variation law of the aerodynamic force (moment) of the aircraft. This method has been widely applied, but its online application to predict the aerodynamic force (moment) of the current aircraft requires real-time determination of the angle of attack, sideslip angle and other information. When there is wind interference, the angle of attack and sideslip angle are not easy to measure online, although the wind field motion filtering method and the velocity vector triangle method can be used to determine the wind speed, and then the angle of attack and sideslip angle information can be calculated. However, due to the sensitivity of the traditional aerodynamic model to the angle of attack error, it is difficult to accurately predict the aerodynamic force and moment of the aircraft through the traditional aerodynamic model, and therefore the traditional aerodynamic model is not conducive to the online migration application of the aircraft in flight.

[0004] For online aerodynamic modeling under wind interference, Connell and other scholars based on the meta-learning methodology proposed a "neural-fly" method for rotorcraft, the idea of which is to establish a common aerodynamic force function model for rotorcraft under different wind conditions, so as to realize real-time aerodynamic modeling and migration application under unknown wind conditions. It specifically uses deep meta-learning of the generative adversarial network (GAN) architecture to train the common function neural network model, and realizes accurate prediction of aerodynamic force under strong wind interference. Since the neural-fly aerodynamic model based on the meta-learning methodology has better migration ability, it is conducive to realizing real-time aerodynamic modeling. Compared with rotorcraft, the aerodynamic model of fixed-wing aircraft is more complex, which not only needs to model the aerodynamic force, but also needs to model the aerodynamic moment, and the model input involves more variables such as aircraft angular velocity and rudder deflection angle, which needs to be studied specifically. At the same time, "neural-fly" is a black-box modeling method based on deep neural network, which lacks theoretical explanation and is difficult to analyze theoretically, and cannot answer theoretical questions such as how many common function items can be selected to accurately approximate the original aerodynamic function, which needs a lot of testing and verification, affecting the engineering usability of the method. SUMMARY

[0005] The application provides a fixed-wing aircraft element flight aerodynamic modeling method considering wind disturbance, which is based on Taylor expansion multi-element function decomposition series theory, describes aircraft motion variables relative to a ground coordinate system, constructs a general fixed-wing aircraft aerodynamic common function analytical model under different wind conditions by isolating wind disturbance effects, and realizes online prediction of aerodynamic force and aerodynamic moment of the aircraft under unknown wind conditions.

[0006] To achieve the above object, the application provides the following technical scheme:

[0007] A fixed-wing aircraft element flight aerodynamic modeling method considering wind disturbance comprises the following steps:

[0008] Step 1, acquire discrete aerodynamic data sets under different state conditions, establish a traditional aerodynamic model of the fixed-wing aircraft, and obtain aerodynamic force and aerodynamic moment expressed in the body coordinate system as follows:

[0009]

[0010] In the formula, F x , F y and F z are the axial force, lateral force and normal force of the aircraft respectively; M x , M y and M z are the roll moment, pitch moment and yaw moment of the aircraft respectively; is the dynamic pressure, V is the speed amplitude of the aircraft, and ρ is the air density, which is a function of the height h of the aircraft; S is the reference area of the aircraft, and b and c are the lateral reference length and longitudinal reference length of the aircraft respectively;

[0011] C D , C Y and C L are the drag coefficient, side force coefficient and lift coefficient of the aircraft respectively, and are expressed as:

[0012]

[0013] C l , C m and C n are the roll moment coefficient, pitch moment coefficient and yaw moment coefficient of the aircraft respectively, and are expressed as:

[0014]

[0015] is the direction cosine matrix from the airflow coordinate system to the body coordinate system, and is expressed as:

[0016]

[0017] a is the angle of attack, b is the side slip angle, Ma is the vehicle Mach number, C s l s m s n Cp is the static aerodynamic force moment coefficient, C lp mq np Cp is the static aerodynamic force moment coefficient, C e a r are the elevator, aileron and rudder, respectively, [p q r] T is the angular velocity vector of the aircraft in the body coordinate system, the superscript "T" is the vector transpose symbol; T

[0018] Step 2, based on equation (5), Taylor expansion of the aerodynamic force and aerodynamic moment with respect to the wind velocity vector in the body coordinate system is carried out, the approximation accuracy of the aerodynamic force and aerodynamic moment is investigated, the expansion order of each aerodynamic force and aerodynamic moment component is determined by comparing the approximation accuracy of the original function by the finite order Taylor expansion expressions of different orders, and the total number of terms in each expansion expression is determined;

[0019] Step 3, the commonality basis functions of the air forces of the fixed-wing aircraft are calculated, the aerodynamic force and aerodynamic moment of the aircraft are approximated based on the obtained commonality basis functions, and finally the element flight aerodynamic model is obtained, which is expressed as:

[0020]

[0021] wherein, are the dimensionless aerodynamic force coefficients and aerodynamic moment coefficients; the dynamic pressure matrix Ω = diag([1, 1, 1, b, c, b]); a i , (i = F x , F y , F z , M x , M y , M z ) is a coefficient function only related to the wind speed variable in the ground coordinate system; Ψ is a commonality basis function matrix only related to the aircraft motion variables x, including the height h, the ground speed vector Euler attitude angle Θ = [φ θ ψ] T , angular velocity ω = [p q r] T and rudder deflection angle δ = [δ​​​​​​​a δ e δ r ] T .

[0022] The beneficial effects of the present application are:

[0023] 1) The common air dynamic function built in the meta-flight aerodynamic modeling is described by the motion variables of the aircraft relative to the ground coordinate system. By separating the aircraft motion variables relative to the ground coordinate system from the wind interference variables, the common function independent of the wind condition and the coefficient function independent of the aircraft motion can be obtained, which creates good conditions for accurately identifying the influence of the wind and predicting the aerodynamic force online.

[0024] 2) The meta-flight aerodynamic modeling can effectively isolate the influence of the environmental wind interference variable, and combined with the wind action coefficient function estimated online, the angle of attack and sideslip angle information can be well predicted without the need to obtain the aerodynamic force and moment of the fixed-wing aircraft under unknown wind conditions.

[0025] 3) The present application provides an analytical form of a general air dynamic common function model, which makes the meta-flight aerodynamic model have better migration ability and engineering applicability than the traditional aerodynamic model and the neural meta-flight aerodynamic model based on deep learning. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 A flow chart of a fixed-wing aircraft meta-flight aerodynamic modeling method considering wind interference provided by the embodiment of the present application;

[0027] Figure 2 Taylor expansion approximation results for the axial aerodynamic force coefficient of the aircraft under different wind speeds ;

[0028] Figure 3 Taylor expansion approximation results for the pitch aerodynamic moment coefficient of the aircraft under different wind speeds ;

[0029] Figure 4 A schematic diagram of the prediction results of the meta-flight aerodynamic model in the discrete state case;

[0030] Figure 5 A schematic diagram of the prediction results of the meta-flight aerodynamic model in the continuous state case. DETAILED DESCRIPTION

[0031] The present application will be further described in detail below in combination with the drawings and specific embodiments:

[0032] The coordinate systems related to the meta-flight aerodynamic modeling of the fixed-wing aircraft include the body coordinate system, the airflow coordinate system and the ground coordinate system. The aircraft body coordinate system Sb Fixed to the aircraft, origin at o b Located at the aircraft center of mass, o b x b Axis in the plane of symmetry of the aircraft pointing towards the nose, o b y b Axis normal to the plane of symmetry of the aircraft pointing to the right of the fuselage, o b z b Axis in the plane of symmetry of the aircraft pointing downwards. Airflow coordinate system S a Fixed to the vehicle, origin at o a Located at the vehicle center of mass, o a x a Axis coincident with the airspeed, o a z a Axis in the plane of symmetry of the vehicle pointing downwards, o a x a Axis normal and pointing downwards, o a y a Axis normal to o a x a z a Plane, direction determined by the right-hand rule. Ground coordinate system S g Fixed to the ground, origin at o g Located at some point on the ground, o g x g Axis in the horizontal plane pointing in some determined direction, o g z g Axis normal to the horizontal plane and pointing towards the center of the earth, o g y g Axis determined by the right-hand rule.

[0033] The implementation procedure of the elementary flight aerodynamic modeling for fixed-wing vehicles is shown in Figure 1 , including the following three steps:

[0034] 1) Traditional aerodynamic modeling

[0035] The input of the elementary flight aerodynamic modeling is still the discrete aerodynamic data set obtained by wind tunnel test, CFD numerical calculation and other means under different state conditions. When the discrete data set is modeled traditionally, attention should be paid to the division of the angle of attack and sideslip angle interval, which needs to cover possible wind interference situations. The aerodynamic force and moment model of the fixed-wing vehicle obtained based on the traditional modeling method can be generally expressed as

[0036]

[0037]

[0038] Where D, Y and L are the drag, side force and lift of the vehicle, M x , M yM z are respectively the roll moment, the pitch moment and the yaw moment of the aircraft, C D , C Y are respectively the drag coefficient, the side force coefficient and the lift coefficient of the aircraft, C L , C l , C m , C n are respectively the roll moment coefficient, the pitch moment coefficient and the yaw moment coefficient of the aircraft, is the dynamic pressure, V is the speed amplitude of the aircraft, ρ is the air density which is a function of the height h of the aircraft, S is the reference area, b and c are respectively the lateral reference length and the longitudinal reference length of the aircraft.

[0039] The present application adopts the more common method of modeling aerodynamic force in airflow coordinate system in this step, and in fact, the aerodynamic force can also be modeled in the body coordinate system directly. This processing does not affect the subsequent implementation process of the meta-flight aerodynamic modeling, and the difference is only whether the transformation between the aerodynamic force represented in the airflow coordinate system and the aerodynamic force represented in the body coordinate system is performed. The aerodynamic force coefficient and the aerodynamic moment coefficient of the fixed-wing aircraft are respectively

[0040]

[0041]

[0042] Wherein, α is the angle of attack, β is the sideslip angle, Ma is the Mach number of the aircraft, C s l , C s m , C s n denote the static aerodynamic moment coefficient, C lp , C mq , C np is the dynamic derivative coefficient, δ e , δ a and δ r are respectively the elevator deflection angle, the aileron deflection angle and the rudder deflection angle, [p qr] T is the angular velocity vector of the aircraft represented in the body coordinate, and the superscript “T” is the vector transpose symbol.

[0043] Based on the traditional aerodynamic model given by the above expression, the aerodynamic force and the aerodynamic moment represented in the body coordinate system can be obtained as

[0044]

[0045] Wherein, F x , F y and F z are respectively the axial force, the lateral force and the normal force of the aircraft, The direction cosine matrix of the airflow coordinate system to the body coordinate system is

[0046]

[0047] 2) Unfolding precision analysis

[0048] In traditional aerodynamic modeling, the variables such as velocity amplitude V, angle of attack a, sideslip angle β, and Mach number Ma are all variables describing the motion of the aircraft relative to the airflow coordinate system. In the presence of wind, the representation of the motion speed of the aircraft relative to the ground coordinate system in the body coordinate system is The representation of the wind speed in the body coordinate system of the aircraft is Then the motion speed of the aircraft relative to the atmosphere is

[0049]

[0050] At this time, the velocity amplitude of the aircraft is

[0051]

[0052] The Mach number is

[0053]

[0054] Where c is the local speed of sound, which is a function of the height h of the aircraft. The angle of attack a and the sideslip angle β of the aircraft are

[0055]

[0056]

[0057] In the unfolding precision analysis, the Taylor expansion of equation (5) is performed on the wind speed variable represented in the body coordinate system The approximation precision of the aerodynamic force and the aerodynamic moment is investigated. By comparing the approximation precision of the original function by the finite-order Taylor expansion expressions of different orders, the unfolding order of each aerodynamic force and aerodynamic moment component is determined, and then the total number of terms in the unfolding expression is determined. The total number of terms in the unfolding expression is represented by x , the lateral force F y , the normal force F z , the roll moment M x , the pitch moment M y , and the yaw moment M z

[0058] 3) Determination of common base functions of air forces

[0059] This step calculates the common base functions of air forces of a fixed-wing aircraft. The representation of the wind speed vector in the ground coordinate system is​​ Representation in body coordinate system There is the following relationship:

[0060]

[0061] wherein, is the direction cosine matrix from the ground coordinate system to the body coordinate system, and

[0062]

[0063] In the formula, φ is the roll attitude angle, θ is the pitch attitude angle, and ψ is the yaw attitude angle.

[0064] Using the relationship (12), the wind speed variable in formula (5) is obtained for the ground coordinate system The value of each derivative term is taken by Taylor expansion. In order to reduce the amount of calculation, based on the expansion expression of the aerodynamic force and the aerodynamic moment of the wind speed vector in the body coordinate system, the main and secondary action terms for the approximation of the aerodynamic force and the aerodynamic moment are determined, and the secondary action term can be ignored in the modeling and directly set to zero. The common basis function of each aerodynamic (moment) component is calculated similarly, taking the axial force F x as an example. For the 0-order term, there is

[0065]

[0066] For the 1st-order and kth-order derivative terms, there is

[0067]

[0068] wherein, z i is the i-th component of , P(t1,t2) is the full permutation set of index variables t1,t2, i.e. P(t1,t2)={(t1,t2),(t2,t1)}, P(t1,t2,...,t k ) is the full permutation set of index variables t1,t2,...,t k . An expansion operator is introduced for convenience of expression, which acts on index variables i1,i2,...,i n to generate a vector according to certain rules. In the vector generation, according to the priority of i1,i2,...,i n , assuming that the value range of the index variable is 1 to m, starting from the minimum value i j =1,(j=1,2,...,n), starting from i n , increasing, and the condition i1≤i2≤...≤i n must be met during the increasing process, until the maximum value i j=m, (j = 1, 2, ..., n). If the order of the index variables in parentheses is consistent with the order of the subscripts, the operator is expanded. Subscripts i1i2...i n This can be omitted, i.e., simply denoted as S(·). According to the definition of the extended operator, for index variables i1, i2 ∈ {1, 2, ..., m}, the following partial derivative calculation will generate a dimension of... Vector:

[0069]

[0070] The following variable product will generate a vector:

[0071]

[0072] The following set of indicators will be expanded to:

[0073] S(i1,i2)=[(1,1) (1,2)...(1,m) (2,2)...(2,m)...(m,m)] T

[0074] Furthermore, define the index function Λ(i1,i2,...,i n ), which will have certain index variables i1, i2, ..., i n Value mapping is

[0075]

[0076] In the formula, This represents the number of combinations of choosing l1 elements from n elements, and so on. Represents n-(l1+l2+...+l) k Calculate the number of permutations of 1, l1, l2, ... and ln(l1, l2, ..., ln(l ... k These respectively represent the indicators in the set, namely l1, l2, ... and l k The number of index variables with the same ordinal value and correspondingly different values ​​is n - (l1 + l2 + ... + ln) k Based on the index function Λ(i1,i2,...,i... n According to the definition (18), we have

[0077] Λ(1,2,2)=3

[0078] Λ(1,1,2,2)=6

[0079] The function Λ can be extended to act on the index set vector, whereby it acts on every element of the index set vector, such as...

[0080] Λ([(1,1) (1,2) (1,3)])=[1 2 2]

[0081] Matrix W j The definition of (j = 2, 3, …, k) is

[0082]

[0083] In the formula, (·)! represents the factorial operator.

[0084] In the primary flight aerodynamic modeling, in order to ensure the value of each common base function, the scaling normalization processing can be carried out according to the value magnitude. After determining the common base function, the obtained common base function is directly taken as the base to approximate the aerodynamic force and the aerodynamic moment of the aircraft, and finally the primary flight aerodynamic model is obtained.

[0085]

[0086] In the formula, is the dimensionless aerodynamic force (moment) coefficient, S is the reference area of the aircraft, and it is noted that the dynamic pressure Unlike the dynamic pressure Q in the traditional aerodynamic modeling, the matrix Ω = diag([1, 1, 1, b, c, b]), a i , (i = F x , F y , F z , M x , M y , M z is a coefficient function only related to the wind speed variable related to the aircraft motion variable x, for the fixed-wing aircraft, it is assumed that the state variables of the aircraft affecting the aerodynamic force and the aerodynamic moment relative to the ground coordinate system include the height h, the ground speed vector Euler attitude angle Θ = [φ θ ψ] T and angular velocity ω = [p q r] T , further considering the rudder angle δ = [δ a δ e δ r ] T , then the aircraft motion variable x is The form of the common base function matrix Ψ is

[0087]

[0088] Among them, is the common base function vector, and

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] These represent the dimensions of the different common basis function vectors, and they also specify the coefficient function a. i ,(i=F x ,F y ,F z M x M y M z The dimension of ).

[0096] In the meta-aerodynamic model of flight, due to issues such as function approximation error, quantization errors caused by parameters like density, and linear correlation of basis function values ​​in specific aircraft motions (e.g., steady flight), the actual coefficient function... It does not accurately characterize information related to wind disturbance variables; these need to be determined during application in order to predict aerodynamic forces (moments).

[0097] Example 1

[0098] Meta-aerodynamic modeling of a certain fixed-wing UAV was carried out and verified.

[0099] 1) Meta-flight aerodynamic modeling

[0100] Since traditional aerodynamic modeling is an existing technology, this study directly conducts meta-aerodynamic modeling research based on a publicly available traditional aerodynamic model of a fixed-wing aircraft. The lower the aircraft's ground speed, the greater the wind influence; therefore, the velocity near the left boundary of the flight envelope is selected for analysis. The aircraft's ground speed is randomly generated as follows: wind speed Within the system, from [-10 -10 -10] T The m / s changes linearly to [10 10 10] T m / s. Figure 2 and Figure 3 The axial aerodynamic coefficients of the aircraft at different wind speeds during this process are given respectively. With pitch aerodynamic moment coefficient Taylor expansion approximation results, it can be seen from the figure that the first order approximation exists a large error, the second order approximation can better describe the overall change law of the aerodynamic force coefficient and the aerodynamic moment coefficient, the higher the expansion order, the closer to the true value, the 6 order approximation result is almost completely consistent with the true value. Further develop 1000 times random sampling calculation, the ground speed is set to v f , w f subject to uniform distribution in the interval [-5, 5] m / s, the amplitude of the interference wind speed is The direction is random in the whole three-dimensional space. The average error index E is introduced, defined as

[0101]

[0102] Among them, and respectively represent the true value and the predicted value of the i-th sample, |·| represents the absolute value operator. Taking 1% average error as the standard, it can be seen that for the aerodynamic (moment) coefficient 4 order expansion is needed, 3 order expansion is needed, only 2 order, and 5 order expansion is needed to meet the 1% error requirement.

[0103] The value of the expansion guide function is analyzed, and the mean and mean square deviation are used as two indicators for evaluation. For the axial force coefficient The analysis shows that the term has little effect in the first 4 order expansion; for the normal force coefficient The term has little effect in the first 3 order expansion; for the lateral force coefficient The term has little effect in the first 3 order expansion; for the roll moment coefficient The term has little effect in the first 3 order expansion; for the pitch moment coefficient The term has little effect in the first 2 order expansion; for the yaw moment coefficient The term has little effect in the first 5 order expansion. Take the value of the approximation minor term as zero, calculate the common base function of air resistance, the height h of the aircraft, the ground speed Attitude Θ, angular velocity ω, rudder angle δ are common functions of the input aerodynamic force and moment of the fixed-wing aircraft. For the axial force, the common function has 35 terms; for the normal force, lateral force and roll moment, the common function has 20 terms; for the pitch moment, the common function has 10 terms; for the yaw moment, the common function has 56 terms. In flight, these common functions are used as the basis to construct the fixed-wing aircraft meta-flight aerodynamic model in combination with the wind variable action coefficient determined by the identification method, which can predict the aerodynamic force (moment) received by the fixed-wing aircraft.

[0104] 2) Meta-flight aerodynamic model verification

[0105] The developed meta-flight aerodynamic model is verified, considering two cases.

[0106] a) Discrete state case prediction

[0107] The aerodynamic force and moment prediction of the randomly given aircraft state case is considered. The wind field speed in the environment is set to 20 m / s, and the direction vector in the ground coordinate system is [-1 0 0] T , the aircraft height is h = 900 m, the attitude angle is randomly given, and the representation of the aircraft speed relative to the earth in the body coordinate system is given as u f = 80 m / s, v f , w f comply with the uniform random distribution in the interval [-5, 5] m / s, the representation of the aircraft ground speed in the ground coordinate system is determined by the attitude angle conversion calculation, the angular velocity of the three axes of the aircraft complies with the uniform distribution in the interval [-1, 1] rad / s, the elevator δ e , rudder δ r , aileron δ a comply with the uniform distribution in the interval [-25, 25] deg. Based on the least square method, the aerodynamic force and moment measurement data of the first 500 states are taken as the identification data to determine the wind action coefficient a i , (i = F x , F y , F z , M x , M y , M z , then the aerodynamic force and moment of the last 1500 states are predicted, and there is a 40% level of noise interference in the measurement data. Figure 4 The prediction results of the aircraft aerodynamic force and moment are given, and it can be seen that the prediction value based on the meta-flight aerodynamic model greatly reduces the measurement error, and the result is closer to the true value.

[0108] b) Continuous state case prediction

[0109] The aerodynamic force and moment prediction is considered for the ideal forced pitching motion of the aircraft. The wind velocity in the environment is set to 20 m / s, and the direction is given as [-1 0 0] in the ground coordinate system T , the height of the aircraft is h = 900 m, the pitch attitude angle varies as θ = 10sin(t) + 2 deg, the roll angle and the yaw angle are 0 deg, the corresponding three-axis angular velocity is determined by the attitude angle variation, the flight velocity of the aircraft in the ground coordinate system is given as [3.04 80 -2.09] m / s, the elevator control law is δ e = -10cos(t) deg, the rudder deflection is δ r = 10 deg, the aileron deflection is δ a = 0 deg, and the data sampling time interval is Δt = 0.05 s. Based on the least square method, the wind acting coefficients a i (i = F x , F y , F z , M x , M y , M z ) are determined by taking the aerodynamic force and moment measurement data in the first 10 s as the identification data, and then the aerodynamic force and moment data in the last 40 s are predicted, and there is a 40% level of noise interference in the measurement data. Figure 5 The prediction results of the aerodynamic force and moment are given, and the results show that the predicted values are in good agreement with the true values, which illustrates the effectiveness of the meta-flight aerodynamic model.

[0110] The above only describes the embodiments of the present application, and the specific technical solutions and / or common knowledge of characteristics in the scheme are not described in detail. It should be noted that for those skilled in the art, without departing from the technical solutions of the present application, a number of modifications and improvements can be made, which should also be considered as the protection scope of the present application, and these will not affect the effect and practicality of the present application. The protection scope claimed in the present application should be subject to the content of its claims, and the specific implementation mode and the like in the specification can be used to explain the content of the claims.

Claims

1. A method for modeling the aerodynamics of a fixed-wing aircraft considering wind interference, characterized in that, Includes the following steps: Step 1: Obtain discrete aerodynamic datasets under different conditions, establish a traditional aerodynamic model of the fixed-wing aircraft, and obtain the aerodynamic forces and moments expressed in the body coordinate system. （5）； In the formula, , and These are the axial force, lateral force, and normal force of the aircraft, respectively. , and These are the aircraft's roll moment, pitch moment, and yaw moment, respectively. For dynamic pressure, The velocity amplitude of the aircraft. air density, It is the altitude of the aircraft. The function; For the reference area of ​​the aircraft, , These are the aircraft's lateral reference length and longitudinal reference length, respectively. and These are the drag coefficient, lateral force coefficient, and lift coefficient of the aircraft, respectively, expressed as... （3）； These are the roll moment coefficient, pitch moment coefficient, and yaw moment coefficient of the aircraft, respectively, denoted as... （4）； Let be the direction cosine matrix from the airflow coordinate system to the body coordinate system, denoted as （6）； For the angle of attack, Sideslip angle, For the aircraft's Mach number, Represents the static aerodynamic moment coefficient. , , The coefficient of the moving derivative, , and These are the elevator, ailerons, and rudder; Step 2: Based on equation (5), the aerodynamic forces and aerodynamic moments are expressed relative to the wind speed vector in the body coordinate system. Taylor expansion is performed to examine the approximate accuracy of aerodynamic forces and aerodynamic torques. By comparing the approximation accuracy of the finite-order Taylor expansion expressions for different orders to the original function, the expansion order of each aerodynamic force and aerodynamic torque component is determined, and then the total number of terms in each expansion expression is determined. Step 3: Calculate the common aerodynamic basis functions of the fixed-wing aircraft. Using these common basis functions as a basis, approximate the aerodynamic forces and moments of the aircraft to obtain the meta-aerodynamic model, expressed as follows: （20）； In the formula, , , For dimensionless aerodynamic coefficients and aerodynamic torque coefficients; dynamic pressure ;matrix ; It is only related to the wind speed variable expressed in the ground coordinate system. Related coefficient function, ; It is only related to the aircraft's motion variables Related common basis function matrices, including height Ground velocity vector Euler attitude angle angular velocity and rudder deflection .

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