A method for correcting aeroelastic models based on frequency domain response data

Abstract

This invention discloses an aeroelastic model correction method based on frequency domain response data, belonging to the field of aircraft aeroelastic design. The method involves constructing an aeroelastic model of the aircraft under study. First, a ground-based flight control structure coupling test is conducted. Using the frequency response data from the ground test, correction coefficients for the generalized mass, generalized damping, generalized stiffness matrix, and control surface coupled inertial mass matrix are calculated using optimization methods. Then, a flight aerodynamic servo stability test is performed. Based on the corrected structural parameters, correction coefficients for the unsteady aerodynamic coefficient matrix of the body mode and the unsteady aerodynamic coefficient matrix of the control surface deflection mode are calculated, ultimately achieving the correction of the aeroelastic model. This invention overcomes the time-consuming and labor-intensive nature of traditional manual correction, can consider multiple test responses while performing multi-variable corrections, and solves the problem of difficult aerodynamic correction in traditional methods. It corrects the aircraft structure while simultaneously considering aerodynamics, resulting in an accurate aeroelastic model.

Description

Technical Field

[0001] This invention belongs to the field of aeroelastic design of aircraft and relates to a method for correcting aeroelastic models based on experimental frequency domain response data. Background Technology

[0002] In recent years, with the trend towards lighter aircraft design, the aeroelastic effects of aircraft have become more pronounced, bringing a series of design challenges. Among these, flutter and servo stability issues related to aeroelastic dynamic stability, and gust response issues related to aeroelastic dynamic response are particularly prominent. To analyze the impact of aeroelasticity on flight, during the engineering design phase, an aeroelastic model is typically constructed based on the aircraft's structural finite element model and unsteady aerodynamic model for simulation analysis. However, due to certain deviations between the theoretical structure and aerodynamic model and reality, further corrections to the aeroelastic model based on experimental results are necessary during the engineering testing phase.

[0003] Traditional correction methods primarily rely on ground measurements and ground vibration test (GVT) data to manually adjust the structural mass and stiffness of the aircraft's aeroelastic model, ensuring a match between the theoretical model and experimentally measured structural characteristics. This approach is largely experience-based, cumbersome, and does not address aerodynamic model correction. To overcome this issue, methods for identifying aeroelastic models based on experimental response data have been developed. These methods do not depend on the aircraft's structure or aerodynamic model, determining the aeroelastic model solely through experiments. However, the physical meaning of the identified model is unclear and heavily influenced by experimental results. Therefore, in aircraft aeroelastic design, there is an urgent need for a highly efficient, effective, and physically meaningful aeroelastic model correction method. Summary of the Invention

[0004] To address the need for aeroelastic model correction in engineering design and to solve the problems of tedious, time-consuming, and difficult traditional manual correction, this invention proposes an aeroelastic model correction method based on frequency domain response data. The method utilizes optimization to solve for correction coefficients, and corrects the structural stiffness, mass, damping, and control surface coupled inertial mass of the aircraft using frequency response data from ground-based flight control structure coupling tests. Furthermore, it employs frequency response data from flight aerodynamic servo stability tests to correct the unsteady aerodynamic forces of the aircraft, ensuring consistency between theoretical analysis and experimental aeroelastic frequency response characteristics.

[0005] The present invention proposes a method for correcting an aeroelastic model based on frequency domain response data, comprising the following steps:

[0006] Step 1: Construct the aeroelastic model of the aircraft based on the finite element model and unsteady aerodynamic model of the aircraft structure; where the generalized mass M constituting the aeroelastic model is...ξ Generalized damping C ξ Generalized stiffness matrix K ξ , Control surface coupled inertial mass matrix M ξδ The unsteady aerodynamic coefficient matrix A of the body modes ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ There are deviations from the actual aircraft, which need to be corrected. The correction factor will be calculated through the following steps.

[0007] Step 2: Conduct ground-based flight control structure coupling tests, and use the frequency response data from the ground tests to correct the structural parameters of the aeroelastic model, i.e., the generalized mass M. ξ Generalized damping C ξ Generalized stiffness matrix K ξ Coupled with the rudder surface inertial mass matrix M ξδ The optimization method is used to solve for the structural correction coefficients, including: designing the optimization objective function J. g To account for the deviation between the theoretical and experimental frequency domain responses of the aircraft, the correction coefficients of the structural parameter matrix are used to form the optimization variable μ. This optimization variable is then reduced based on the structural terms corresponding to the key modes of the aircraft of interest. Finally, an optimization method is used to solve for the optimal set of optimization variables μ. * Make the objective function J g Minimum. Multiply the corresponding structural parameters by the correction coefficient to obtain the corrected structural parameters.

[0008] Step 3: Aeroelastic model correction based on flight aerodynamic servo stability test. Building upon structural corrections, the aerodynamic component of the model is corrected using frequency response data from the flight test, specifically the unsteady aerodynamic coefficient matrix A of the airframe modes. ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ The aerodynamic correction coefficients are solved using optimization methods, including: designing the objective function J for optimizing the aerodynamic correction coefficients. a The deviation between the theoretical and experimental frequency domain responses of the aircraft is used as the sum of the correction coefficients of the aforementioned aerodynamic parameter matrix to form the optimization variable μ. A The optimization variables are reduced based on the aerodynamic terms corresponding to the key modes of the aircraft of interest, and then the optimal set of optimization variables is solved using optimization methods. Make the objective function J a Minimum. Multiply the corresponding aerodynamic parameters by the correction factor to obtain the corrected aerodynamic parameters.

[0009] Step 4: Update the aeroelastic model of the aircraft using the corrected structural and aerodynamic parameters.

[0010] Step 2 uses an optimization method to solve for the structural correction coefficients, and includes the following steps:

[0011] Step 2-1: Select ground test data and design the objective function for optimizing the correction coefficients as follows:

[0012]

[0013] Where, ω i For the i-th frequency point, i = 1, ..., n, ω1 and ω n These represent the start and end frequencies of the rudder surface sweep signal, respectively. H represents the frequency domain response (frequency response function or power spectral density) obtained from the j-th ground test. j The frequency response result is obtained by simulation using the input signal of the j-th ground test, where l is the number of experiments; λ ij Let be the weight vector, representing the response weight value at the i-th frequency point in the j-th ground test. ||·||2 represents the 2-norm.

[0014] Step 2-2: Select structural correction coefficients to form optimization variables. The correction coefficients include the generalized mass M of the aircraft. ξ Generalized stiffness K ξ Generalized damping C ξ and the coupled inertial mass M of the control surface ξδ Correction factor μ Mξ μ K μ C and μ Mδ Structural parameters in the corrected aeroelastic model and for:

[0015]

[0016] In the formula, diag{·} represents the diagonal matrix transformation of the vector, and ⊙ represents the matrix dot product. Combining the correction coefficients yields the total optimized variable μ=[μ Mξ ,μ K ,μ C ,vec(μ Mδ ) T ], where vec(·) combines the matrix into a column vector; when focusing on the structural terms corresponding to certain key modes of the aircraft, the optimization variables can be reduced, where the optimization variable corresponding to the i-th mode is: μ=[μ Mξ (i),μ K (i),μ C (i),vec(μ Mδ (i,:)) T ].

[0017] Step 2-3: The goal of optimizing the structural correction coefficients is to find the optimal set of optimization variables μ. * Make the objective function Jg Minimum, given the constrained range μ of the optimization variables min ~μ max The constrained optimization problem can be described in the following mathematical form:

[0018]

[0019] An optimization algorithm is used to solve this optimization problem.

[0020] Step 3 employs an optimization method to solve for the aerodynamic correction coefficients. Based on the structural corrections, the aerodynamic correction coefficients are optimized and solved, meaning the coefficients corrected in step 2 are obtained through this optimization. and Replace M in the aeroelastic model ξ K ξ C ξ and M ξδ Then, the aerodynamic coefficient is corrected, including the following steps:

[0021] Step 3-1: Select flight test data and design the objective function for optimizing the correction coefficients as follows:

[0022]

[0023] Where, ω i For the i-th frequency point; G represents the frequency domain response obtained from the j-th flight test. j The frequency response result is obtained by simulating the input signal of the j-th flight test; α ij is a weight vector, representing the response weight value at the i-th frequency point in the j-th flight test.

[0024] Step 3-2: Select aerodynamic correction coefficients to form optimization variables. The correction coefficients include the unsteady aerodynamic coefficient matrix A of the body modes. ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ Correction factor μ Aξ and μ Aδ Aerodynamic parameters in the corrected aeroelastic model and for:

[0025]

[0026] By combining the correction coefficients, the total optimization variable μ is obtained. A =[μ Aξ ,vec(μ Aδ ) T ];

[0027] When focusing on the aerodynamic terms corresponding to certain key modes of an aircraft, the optimization variables can be reduced, where the optimization variable μ corresponding to the i-th mode is... A =[μ Aξ (i),vec(μ Aδ (i,:)) T ].

[0028] Step 3-3: Find the optimal set of optimization variables μ. A * Make the objective function J a Minimum. Given the constrained range μ of the optimization variables. min ~μ max The constrained optimization problem can be described in mathematical form as follows: The optimization problem is solved using an optimization algorithm to obtain μ. A * .

[0029] Compared with existing technologies, the advantages of the aeroelastic model correction method based on frequency domain response data in this invention are:

[0030] (1) The method of the present invention uses frequency response data from ground flight control structure coupling test, and combines optimization method to correct the structural stiffness, mass, damping and control surface coupled inertial mass in the aeroelastic model of the aircraft. It gets rid of the time-consuming and labor-intensive traditional manual correction, and the correction can take into account the response of multiple tests and make corrections of multiple variables at the same time.

[0031] (2) Based on structural correction, the method of the present invention uses frequency response data from flight aerodynamic servo stability test to correct unsteady aerodynamic forces in the aeroelastic model of the aircraft, which solves the problem that aerodynamic correction is difficult in traditional correction. The final correction result is the correction coefficient of structure and aerodynamics, which makes the correction physically meaningful and interpretable.

[0032] (3) Compared with the traditional manual adjustment of correction coefficients, the method of the present invention can adjust multiple correction coefficients at the same time and take into account the deviation between multiple responses, correcting the aircraft structure while taking into account aerodynamics, and obtaining an accurate aeroelastic model. Attached Figure Description

[0033] Figure 1 This is a flowchart of the aeroelastic model correction process based on frequency response data for this invention.

[0034] Figure 2 A comparison of the frequency response functions of pitch angular velocity in experiments and simulations of an aircraft before correction of its aeroelastic model;

[0035] Figure 3 A comparison of the experimental and simulation vertical overload frequency response functions of a certain aircraft before the aeroelastic model was corrected;

[0036] Figure 4 A comparison of the frequency response functions of pitch angular velocity in experiments and simulations after the aeroelastic model of a certain aircraft has been corrected;

[0037] Figure 5 The graph shows a comparison of the experimental and simulated vertical overload frequency response functions of a certain aircraft after the aeroelastic model has been corrected. Detailed Implementation

[0038] The technical solution of the present invention will be described below with reference to the accompanying drawings and embodiments.

[0039] This invention provides an aeroelastic model correction method based on frequency domain response data. It uses frequency response data from ground-based flight control structure coupling tests to correct the structural stiffness, mass, damping, and control surface coupled inertial mass of the aircraft. Furthermore, it utilizes frequency response data from flight aerodynamic servo stability tests to correct the unsteady aerodynamic forces of the aircraft. The implementation process of this invention is as follows: Figure 1 As shown, the aeroelastic model of a certain aircraft can be modified using the method of the present invention in the following four steps.

[0040] Step 1) Construct the aeroelastic model of the aircraft. For the specific aircraft under study, construct the aeroelastic model of the aircraft in modal generalized coordinates based on the finite element model of the aircraft structure and the unsteady aerodynamic model.

[0041] This invention embodiment selects two rigid body modes: longitudinal heave and pitch, the first eight elastic modes of the structure, one control mode: symmetrical deflection of the elevator, two output variables: the pitch angular velocity and vertical acceleration of the aircraft, and two aerodynamic hysteresis roots. The specific model is as follows:

[0042]

[0043] Where: state variables ξ=[η T e T ] T Let N be the modal generalized coordinate vector of the aircraft body, and η be the rigid body motion modal coordinate of the aircraft. η This is a 2×1 dimensional rigid body modal vector, where e is the elastic motion modal coordinate of the aircraft, and N is the 2×1 dimensional rigid body modal vector. e x is a 1×1 dimensional vector, here it is an 8×1 dimensional elastic modal vector. a The hysteresis root of the unsteady aerodynamic forces is N. a A 1×1 dimensional vector, here it is a 2×1 dimensional vector. The superscript T indicates transpose. Output variable y = [y d T y v T y a T ]T y d y v and y a These are the displacement, velocity, and acceleration responses of the aircraft, respectively, M. d ×1、M v ×1 and M a ×1-dimensional vector. The output variable y = [y...] in this embodiment of the invention. v T y a T ] T y v and y a These are the pitch angular velocity and vertical acceleration responses, respectively. Control variables. δ、 and Let A, B, C, and D be the generalized coordinates and their first and second derivatives of the symmetric deflection mode of the aircraft elevator, respectively, both being L×1 dimensional vectors. The state space matrices A, B, C, and D are respectively (2N... η +2N e +N a )×(2N η +2N e +N a ) dimension, (2N η +2N e +N a )×3L dimension, (M d +M v +M a )×(2N η +2N e +N a Peacekeeping (M) d +M v +M a The state space matrices A, B, C, and D in this embodiment of the invention are 22×22, 22×3, 2×22, and 2×3 matrices, respectively. The specific expression for the state space matrix is ​​as follows:

[0044]

[0045] The output of this embodiment of the invention consists of two variables, specifically the state space matrices C and D:

[0046]

[0047] In the matrix, ρ represents atmospheric density, V represents flight velocity, and b represents the spacecraft's reference half-chord length; all are scalars. 0 represents the zero matrix, and I represents the identity matrix. (Intermediate matrix) M ξ C ξ and K ξThe generalized mass, generalized damping, and generalized stiffness matrices, respectively, are obtained from the finite element model of the aircraft structure, and are all (N... η +N e )×(N η +N e M is a 10×10 dimensional matrix. ξδ The coupled inertial mass matrix of the control surfaces, calculated from the finite element model of the aircraft structure, is (N η +N e A 10×1 dimensional vector is used here, which is an L-dimensional matrix. φ represents the mode shape of the aircraft. This corresponds to the pitch angular velocity. and vertical acceleration This represents the mode shape of the rigid body motion of the floating and sinking mechanism; here it is a 1×10 dimensional vector. A ξ0 、A ξ1 、A ξ2 、A δ0 、A δ1 、A δ2 D a R, E ξ and E δ The unsteady aerodynamic force fitting coefficient matrix is ​​mainly calculated in the frequency domain form of the unsteady aerodynamic force coefficient matrix A for the body modes using the rational function method and the dipole lattice method. ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ The result is as follows:

[0048]

[0049]

[0050] In the formula, s is the Laplace variable, and A ξ0 、A ξ1 、A ξ2 The coefficient matrix for fitting unsteady aerodynamic forces of the body modes is denoted as A, and all are 10×10 dimensional matrices. δ0 、A δ1 、A δ2 The coefficient matrix for fitting the unsteady aerodynamic forces of the control surface deflection mode is denoted as D, and each coefficient is a 10×1 dimensional vector. a R and R are the fitting coefficient matrices of the hysteresis roots, which are 10×2 and 2×2 matrices, respectively. E ξ E δ The coefficient matrix for fitting unsteady aerodynamic forces of the body mode and the control surface deflection mode is a 2×10 matrix and a 2×1 vector.

[0051] The aeroelastic model, combined with the actual servo model and flight control system, can be used to simulate the response obtained from flight tests. In addition, when ρ = 0, a model can be obtained to simulate the response of ground tests.

[0052] Due to errors in actual finite element modeling and unsteady aerodynamic force calculations, the generalized mass M constituting the aeroelastic model is affected. ξ Generalized damping C ξ Generalized stiffness matrix K ξ , Control surface coupled inertial mass matrix M ξδ The unsteady aerodynamic coefficient matrix A of the body modes ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ There are certain deviations from the actual aircraft, which require correction. The essence of the correction method in this invention is to multiply these matrices by correction coefficients, and the correction coefficients are obtained using an optimization algorithm.

[0053] Step 2) Aeroelastic model correction based on ground flight control structure coupling test.

[0054] The basic principle of flight control structure coupling tests is to excite the aircraft to generate a response by sweeping the control surfaces on the ground, thereby verifying the stability of the airframe structure and control coupling. The test input is typically a control surface sweep signal, such as a linear sweep signal, a stepped sine wave signal, or a random signal, which is the theoretical input. The test output is the aircraft's time-domain response, such as angle, angular velocity, and acceleration response, which is the measured output. The time-domain response is then transformed into a frequency-domain form, such as power spectral density or frequency response function, and this is used as a basis for model correction, specifically correcting the structural components, i.e., the generalized mass M. ξ Generalized damping C ξ Generalized stiffness matrix K ξ Coupled with the rudder surface inertial mass matrix M ξδ .

[0055] Taking a ground flight control structure coupling test of an aircraft as an example, the test involved linear frequency sweep excitation of the elevator, with a sweep amplitude of 1 degree, a frequency range of 1–30 Hz, and a duration of 30 seconds. The pitch angular velocity and vertical overload response were measured. The correction method of this invention is employed, specifically by solving for the structural correction coefficients using an optimization method, comprising the following steps:

[0056] Step 2-1) Design the objective function for optimizing the structural correction coefficients. Select the response variables from the ground-based experimental data that need to be compared with theoretical calculations, and design the objective function for optimizing the correction coefficients. Specifically, this is expressed as the deviation between the theoretical and experimental frequency domain responses and J. g :

[0057]

[0058] in:

[0059] ω i For the i-th frequency point, i = 1, ..., n, ω1 and ω n These represent the start and end frequencies for comparing the experimental and theoretical responses, respectively. They are chosen as the start and end frequencies of the experimental input signal. For example, if a linear sweep frequency signal is used in the experiment, with a frequency range of 1–30 Hz, then ω1 and ω... n Use 1Hz and 30Hz respectively.

[0060] H represents the frequency domain response (frequency response function or power spectral density) obtained from the j-th ground test. j The frequency response result is obtained by simulating the input signal of the j-th ground test, where j = 1,...,l, and l is the number of the experiment. and H j Including multiple response outputs, key response quantities can be selected based on the validity and importance of the experimental data. In the longitudinal channel elevator frequency sweep test of the aircraft, this embodiment of the invention mainly focuses on the pitch angular velocity h1 and vertical overload h2 response outputs. Therefore, the number of selected responses is 2. Both are 2×1 dimensional function vectors. h1 and h2 are the pitch angular velocity and vertical overload obtained from ground tests. To simulate and obtain pitch angular velocity and vertical overload.

[0061] λ ij is a weight vector, representing the response weight value at the i-th frequency point in the j-th ground experiment. Since the selected response number is 2, it is a 1×2 dimensional real number vector. The larger the weight in the vector, the more important the response variable is in the optimization process, and the closer the correction result is to the experimental value. The default value is 1, which means that the weights of each variable are consistent.

[0062] ||·||2 represents the 2-norm, which can convert the complex difference of the frequency domain response into a real number.

[0063] The objective function design considers multiple sets of experiments and multiple responses. It can select the responses to be compared and the frequency range of interest according to the needs, ensuring the accuracy of the aeroelastic model at certain key modal frequencies. Furthermore, it can set weights between different response quantities, making the optimization closer to the ideal result.

[0064] Step 2-2) Select structural correction coefficients to form optimization variables.

[0065] The correction factor includes the generalized mass M of the aircraft. ξ Generalized stiffness K ξ Generalized damping C ξ and the coupled inertial mass M of the control surface ξδ Correction factor μ Mξμ K μ C and μ Mδ The structural parameters in the corrected aeroelastic model are:

[0066]

[0067] In the formula, diag{·} represents the diagonal matrix transformation of a vector, and ⊙ represents the matrix dot product. μ Mξ μ K μ C 1×(N) η +N e A 3D vector, when the experimental excitation is a multi-channel excitation (n channels), μ Mδ For (N) η +N e A matrix of dimensions N×n, when excited by a single channel, is (N×n) η +N e A 1×1 dimensional vector. An embodiment of the invention, μ. Mξ μ K μ C The vector is 1×10 dimensional. This experiment uses a single-channel excitation, μ Mδ This is a 10×1 dimensional vector. Combining the correction coefficients yields the total optimization variables:

[0068] μ = [μ Mξ ,μ K ,μ C ,vec(μ Mδ ) T ];

[0069] The vec(·) function is a matrix straightening operation that combines the matrix into a column vector.

[0070] The optimization variable μ in this embodiment of the invention is [μ Mξ ,μ K ,μ C ,μ Mδ T ].

[0071] When focusing on the structural terms corresponding to certain key modes of an aircraft, the optimization variables can be reduced, where the optimization variables corresponding to the i-th mode are:

[0072] μ = [μ Mξ (i),μ K (i),μ C (i),vec(μ Mδ (i,:)) T ];

[0073] This invention focuses on the structural terms corresponding to the 3rd and 4th order key modes of the aircraft. The structural correction coefficient vectors for the remaining orders are all set to 1, ensuring that the correction matrix terms for these orders remain consistent with the original. The optimization variables are then reduced to:

[0074] μ = [μ Mξ (3),μ Mξ (4),μ K (3),μ K (4),μ C (3),μ C (4),μ Mδ (3),μ Mδ (4).

[0075] Reducing the number of optimization variables by focusing on key modes can effectively improve optimization efficiency, while also ensuring the corrected physical meaning is clear. The selection of optimization variables above involves multiple variables, which significantly improves efficiency compared to manually correcting a single variable each time.

[0076] Steps 2-3) Optimization of structural correction coefficients.

[0077] Based on the design of the objective function and the selection of optimization variables, the structural correction coefficients are optimized to find the optimal set of optimization variables μ. * Make the objective function J g Minimum, given the constrained range of the optimization variables, is μ. min The maximum value is μ max In this embodiment of the invention, the correction coefficient is set to a value range of 0.5 to 1.5, then μ min A vector consisting of 0.5, μ max The vector consists of 1.5. This constrained optimization problem can be described mathematically as follows:

[0078]

[0079] To solve this optimization problem, optimization algorithms such as genetic algorithms, simulated annealing, and interior-point methods can be used. The general process involves selecting an optimization algorithm, specifying the initial variable μ0 (which can have all vector values ​​of 1) for the algorithm, and defining the range μ of the variable. min ~μ max The algorithm's total number of iterations and convergence conditions are set, and optimization is performed. This embodiment of the invention obtains the optimal correction variable μ for the algorithm. * :

[0080] μ * = [1.11, 1.21, 0.95, 0.96, 1.12, 1.31, 1.25, 1.10];

[0081] Where 1.11 is μ Mξ(3), used for correction The generalized mass term M corresponding to the third-order mode is about to be determined. ξ (3,3) multiplied by the correction factor μ Mξ (3) Make corrections.

[0082] Step 3) Aeroelastic Model Correction Based on Flight Aerodynamic Servo Stability Test. The basic principle of the flight aerodynamic servo stability test is to use the aircraft's control surfaces to sweep frequencies during flight to excite the aircraft and generate a response, thereby verifying the stability of the coupling between the airframe structure, aerodynamics, and control. The input to the test is usually a linear frequency sweep signal from the control surfaces. The output of the test is the aircraft's time-domain response, such as angle, angular velocity, and acceleration response. The time-domain response is transformed into a frequency-domain form, and based on this, combined with the structural correction results, the model aerodynamic correction is performed, i.e., the airframe modal unsteady aerodynamic coefficient matrix A. ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ .

[0083] Taking an aerodynamic servo stability test of an aircraft as an example, the test involved linear frequency sweep excitation of the elevator, with a sweep amplitude of 1 degree, a frequency range of 1–30 Hz, and a duration of 30 seconds. The pitch angular velocity and vertical overload response were measured. The correction method of this invention follows a similar process to step 2, and is divided into the following steps:

[0084] Step 3-1) Design the objective function for optimizing the aerodynamic correction coefficients. The corrected function from Step 2... and Replace M in the aeroelastic model (1) ξ K ξ C ξ and M ξδ Then, flight test data was selected and an objective function J for correction coefficient optimization was designed. a Specifically, this can be expressed as the sum of the deviations between the theoretical and experimental frequency domain responses:

[0085]

[0086] Where ω1 and ω n The frequencies are set to 1Hz and 30Hz. G represents the frequency domain response obtained from the j-th flight test. j The frequency response results are obtained by simulating the input signal of the j-th flight test, specifically the measured pitch angular velocity and vertical overload response. and G j Both are 2×1 dimensional function vectors. α ij Let be a weight vector, representing the response weight value at the i-th frequency point in the j-th flight test, which is a 1×2 dimensional real vector.

[0087] Step 3-2) Select aerodynamic correction coefficients to form optimization variables.

[0088] The correction factors include the unsteady aerodynamic coefficient matrix A of the body modes. ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ Correction factor μ Aξ μ Aδ The aerodynamic parameters in the corrected aeroelastic model are:

[0089]

[0090] Where, μ Aξ 1×(N) η +N e A dimensional vector, when the experimental excitation is multi-channel, such as n channels, μ Aδ For (N) η +N e A matrix of dimensions N×n, when excited by a single channel, is (N×n) η +N e A 1×1 dimensional vector. An embodiment of the invention, μ. Aξ The vector is 1×10 dimensional. This experiment uses a single-channel excitation, μ Aδ This is a 10×1 dimensional vector. Combining the correction coefficients yields the total optimization variables:

[0091] μ A =[μ Aξ ,vec(μ Aδ ) T ];

[0092] The optimization variable μ in this embodiment of the invention A =[μ Aξ ,μ Aδ T ].

[0093] When focusing on the aerodynamic terms corresponding to certain key modes of an aircraft, the optimization variables can be reduced, where the optimization variables corresponding to the i-th mode are:

[0094] μ A =[μ Aξ (i),vec(μ Aδ (i,:)) T ];

[0095] This invention focuses on the aerodynamic terms corresponding to the 3rd and 4th order key modes of the aircraft. The aerodynamic correction coefficient vectors for the remaining orders are all set to 1, ensuring that the corresponding correction matrix terms remain consistent with the original. The optimization variables are then reduced to:

[0096] μ A =[μ Aξ (3),μAξ (4),μ Aδ (3),μ Aδ (4).

[0097] Step 3-3) Optimization solution of aerodynamic correction coefficients.

[0098] Based on structural modifications, the aerodynamic correction coefficients are optimized, i.e., the optimal set of optimization variables is found. Make the objective function J a At the minimum, in this embodiment of the invention, the range of the given optimization variable is limited to 0.5 to 1.5, with a minimum of μ. min A vector consisting of 0.5 has a maximum value of μ. max A vector consisting of 1.5. The constrained optimization problem can be described mathematically as follows:

[0099]

[0100] Optimization algorithms that can be used to solve this problem include genetic algorithms, simulated annealing, and interior-point methods. Given the initial value variable μ0 and the range μ of the variable... min ~μ max The algorithm's total number of iterations and convergence conditions are set, and optimization is performed. This embodiment of the invention obtains the optimal correction variable. for:

[0101]

[0102] Where 0.81 is μ Aξ (3) represents the unsteady aerodynamic coefficient A of the body mode corresponding to the third mode. ξ The correction factor to be multiplied is...

[0103] Step 4) Verify the corrected results. Verify the optimal corrected variable μ. * and Substituting into formulas (5) and (8) yields the corrected result. and Substituting these values ​​into formula (1) yields the final corrected model. Based on this, the elevator deflection excitation signal used in a flight test of a certain aircraft is input for simulation to obtain the pitch angular velocity and vertical overload response.

[0104] Comparison of experimental and simulated frequency response functions of the aeroelastic model before correction in this embodiment of the invention, for example Figures 2-3 As shown in the Bode plot, the peak frequency error of the key mode is greater than 10%, and the amplitude error is greater than 20%. The corrected experimental and simulated frequency response functions are compared to, for example... Figures 4-5As shown, the results indicate that, compared with the experimental data, the frequency response characteristics of the corrected model have a main modal frequency error of less than 5% and an amplitude error of less than 10%, indicating good correction accuracy.

[0105] Except for the technical features described in the specification, all other technologies are known to those skilled in the art. Descriptions of well-known components and technologies are omitted in this invention to avoid redundancy and unnecessary limitation. The embodiments described above do not represent all embodiments consistent with this application. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this invention are still within the protection scope of this invention.

Claims

1. A method for correcting an aeroelastic model based on frequency domain response data, characterized in that, Includes the following steps: Step 1: Construct the aeroelastic model of the aircraft. The generalized mass M in the aeroelastic model... ξ Generalized damping C ξ Generalized stiffness matrix K ξ , Control surface coupled inertial mass matrix M ξδ The unsteady aerodynamic coefficient matrix A of the body modes ξ The unsteady aerodynamic coefficient matrix A of the control surface deflection mode δ There are deviations from the actual aircraft, which need to be corrected; Step 2: Conduct ground-based flight control structure coupling tests, and correct the structural parameters M of the aeroelastic model based on the frequency response data from the ground tests. ξ C ξ K ξ and M ξδ ; The structural correction coefficients are solved using optimization methods, including: designing the optimization objective function J. g The deviation between the theoretical and experimental frequency domain responses of the aircraft is used to form the optimization variable μ by the correction coefficients of the structural parameter matrix. The optimization variable is then reduced based on the structural terms corresponding to the key modes of the aircraft of interest. Finally, an optimization method is used to solve for the optimal set of optimization variables μ. * Make the objective function J g Minimize; multiply the corresponding structural parameters by the correction coefficient to obtain the corrected structural parameters; Step 3: Conduct flight aerodynamic servo stability tests. Based on the corrected structural parameters, use the frequency response data from the flight tests to correct the aerodynamic parameters A of the aeroelastic model. ξ and A δ ; The aerodynamic correction coefficients are solved using optimization methods, including: designing the objective function J for optimizing the aerodynamic correction coefficients. a The deviation between the theoretical and experimental frequency domain responses of the aircraft is used to form the optimization variable μ, which consists of the correction coefficients of the aforementioned aerodynamic parameter matrix. A The optimization variables are reduced based on the aerodynamic terms corresponding to the key modes of the aircraft of interest, and then the optimal set of optimization variables is solved using optimization methods. Make the objective function J a Minimum; Multiply the corresponding aerodynamic parameters by the correction factor to obtain the corrected aerodynamic parameters; Step 4: Substitute the corrected structural and aerodynamic parameters into the aeroelastic model of the aircraft.

2. The method according to claim 1, characterized in that, In step 2, the structural correction coefficients are solved using an optimization method, including: Step 2-1: Select ground test data and design the objective function J for structural correction coefficient optimization. g as follows: Where, ω i For the i-th frequency point, i = 1, ..., n, ω1 and ω n These represent the start and end frequencies of the rudder surface sweep signal, respectively. H represents the frequency domain response obtained from the j-th ground test. j The frequency response result is obtained by simulation using the input signal of the j-th ground test, where l is the number of experiments; λ ij Let be the weight vector, representing the response weight value at the i-th frequency point in the j-th ground test; ||·||2 represents the 2-norm; Step 2-2: Select structural correction coefficients to form optimization variables; the structural correction coefficients include the generalized mass M of the aircraft. ξ Generalized stiffness K ξ Generalized damping C ξ and the coupled inertial mass M of the control surface ξδ Correction factor μ Mξ μ K μ C and μ Mδ The structural parameters in the corresponding modified aeroelastic model are: and as follows: Where diag{·} represents the diagonal matrix transformation of a vector, and ⊙ represents the dot product of matrices; Optimization variable μ = [μ Mξ ,μ K ,μ C ,vec(μ Mδ ) T ], where vec(·) is a matrix straightening operation, combining the matrix column by column into a column vector; based on the structural terms corresponding to the key modes of the aircraft of interest, the optimization variables are reduced, where the optimization variable μ corresponding to the i-th mode is μ=[μ Mξ (i),μ K (i),μ C (i),vec(μ Mδ (i,:)) T The superscript T indicates transpose. Steps 2-3: Based on the given constraints on the optimization variables, use an optimization algorithm to find the optimal set of optimization variables μ. * Make the objective function J g The smallest, as follows: Where, μ min ~μ max To optimize the range of variables.

3. The method according to claim 1, characterized in that, In step 3, the aerodynamic correction coefficients are solved using an optimization method, including: Step 3-1: Update the aeroelastic model using the corrected structural parameters, select flight test data, and design the objective function J for optimizing the aerodynamic correction coefficients. a as follows: Where, ω i For the i-th frequency point, i = 1, ..., n, ω1 and ω n These represent the start and end frequencies of the rudder surface sweep signal, respectively. G represents the frequency domain response obtained from the j-th flight test. j The frequency response result is obtained by simulating the input signal of the j-th flight test; l is the number of experiments; α ij Let be the weight vector, representing the response weight value at the i-th frequency point in the j-th flight test; Step 3-2: Select aerodynamic correction coefficients to form optimization variables; the aerodynamic correction coefficients include A ξ and A δ Correction factor μ Aξ and μ Aδ The corresponding aerodynamic parameters in the modified aeroelastic model and as follows: Combinatorial optimization variable μ A =[μ Aξ ,vec(μ Aδ ) T Based on the aerodynamic terms corresponding to the key modes of the aircraft of interest, the optimization variables are reduced, where the optimization variable μ corresponding to the i-th mode is... A =[μ Aξ (i),vec(μ Aδ (i,:)) T ]; Step 3-3: Based on the given constraints on the optimization variables, use an optimization algorithm to find the optimal set of optimization variables. Make the objective function J a The smallest, as follows: Given optimization variable μ A The initial value and range of values ​​of μ min ~μ max Set the total number of optimization iterations and convergence conditions, and then perform optimization to solve the problem.

4. The method according to claim 1 or 2, characterized in that, In step 2, except for the structural terms corresponding to the key modes of the aircraft of interest, the correction coefficient vectors of the structural terms corresponding to the other key modes are all set to 1 to reduce the optimization variables.

5. The method according to claim 1 or 3, characterized in that, In step 3, except for the aerodynamic terms corresponding to the key aircraft modes of interest, the correction coefficient vectors of the aerodynamic terms corresponding to the other key modes are all set to 1 to reduce the optimization variables.

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