Flutter analysis modal tracking method based on modal confidence

Abstract

The invention relates to a flutter analysis modal tracking method based on modal confidence, and belongs to the technical field of aeroelasticity. According to the flutter analysis modal tracking method, modal eigenvalues and right eigenvectors are matched and tracked in combination with the modal confidence and eigenvalue continuity under different airspeeds, and the flutter analysis modal tracking method based on the modal confidence is obtained. Therefore, the correctness and robustness of the corresponding relation between the characteristic values are maintained, the problems of large calculation amount, insufficient precision and failure under specific conditions of a modal tracking method in the prior art are solved, and the precision and reliability of modal tracking are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of aeroelasticity, and particularly to a modal tracking method for flutter analysis based on modal confidence. Background Art

[0002] Flutter refers to a self-excited vibration phenomenon in which, during the flight of an aircraft, when the speed reaches a certain specific critical value, due to the interaction between aerodynamic force, elastic force, and inertial force, the amplitude of vibration does not decay continuously. This kind of vibration is extremely destructive and may cause serious damage to the structure of the aircraft, even leading to catastrophic consequences. In order to avoid this phenomenon, it is necessary to conduct flutter analysis and suppression on the aircraft to ensure that the aircraft can operate safely and stably under various flight conditions.

[0003] When performing flutter analysis, usually, trend graphs of the modal frequencies and damping of the structure varying with airspeed are plotted, namely the airspeed-frequency graph (V-f graph) and the airspeed-damping graph (V-g graph). By observing the modal branches that cross the horizontal axis in the V-g graph, the crossing modes and flutter critical speed can be determined; in the V-f graph, the flutter frequency can be accurately identified based on the crossing modes and flutter critical speed. During this process, the curves of some modes may intersect, namely the so-called "branch jumping" phenomenon. To prevent this phenomenon from interfering with the analysis results, modal tracking is required to ensure the correct front-back correspondence relationship of the modes during the change of airspeed.

[0004] The core of modal tracking lies in matching the eigenvalue at different airspeeds to ensure the correct correspondence relationship of the eigenvalues at different airspeeds before and after. The correct modal correspondence relationship is crucial for identifying flutter modes, evaluating aeroelastic stability, and providing a scientific basis for flutter suppression design. In traditional methods, analysts visually track the frequency and damping values at different flight states, but this method may be difficult when the modal frequencies are dense, and its accuracy is also difficult to guarantee. Summary of the Invention

[0005] In view of the above problems, the present invention provides a modal tracking method for flutter analysis based on modal confidence. The present invention combines modal eigenvalues and right eigenvectors, and combines modal confidence MAC and eigenvalue continuity to match and track the eigenvalues at different airspeeds, so as to maintain the correctness and robustness of the front-back correspondence relationship of the eigenvalues, overcome the problems of large computational amount, insufficient accuracy, and failure in specific cases in the existing modal tracking methods, and improve the accuracy and reliability of modal tracking.

[0006] The present invention provides a modal tracking method for flutter analysis based on modal confidence, which is characterized by including:

[0007] Step S1: Establish a structural finite element model;

[0008] Step S2: Establish an aerodynamic model;

[0009] Step S3: Couple the structural finite element model with the aerodynamic model, establish the flutter motion equation of the linear aeroelastic system, and perform flutter solution to obtain the modal eigenvalues and corresponding right eigenvectors of each order at each airspeed;

[0010] Step S4: Let l = 1. When l = 1, it represents the initial airspeed; let i = 1. When i = 1, it represents the first order mode of the l-th airspeed;

[0011] Step S5: Obtain the i-th order modal eigenvalue and corresponding right eigenvector of the l-th airspeed;

[0012] Step S6: Based on the i-th order modal eigenvalue and corresponding right eigenvector of the l-th airspeed, obtain multiple modal confidence levels of the i-th order modal eigenvalue of the l-th airspeed and the improved Euclidean distances;

[0013] Step S7: Based on the multiple modal confidence levels of the i-th order modal eigenvalue of the l-th airspeed and the improved Euclidean distances, obtain multiple improved modal confidence levels, and establish a corresponding improved modal confidence level data set;

[0014] Step S8: Repeat Steps S5 - S7 to obtain the modal eigenvalues of each order of the l-th airspeed and their corresponding improved modal confidence level data sets;

[0015] Step S9: Sort the modal eigenvalues of each order of the l-th airspeed to obtain the sorted modal eigenvalues of each order of the l-th airspeed;

[0016] Step S10: Determine whether l is greater than or equal to L. L represents the total number of airspeeds. If so, obtain the sorted modal eigenvalues of each order of each airspeed. If not, let l = l + 1 and return to Step S5;

[0017] Based on the sorted modal eigenvalues of each order of each airspeed, complete the modal tracking of each order of all airspeeds. Optionally, the specific steps for obtaining the modal eigenvalues of each order and corresponding right eigenvectors in Step S3 include:

[0018] Perform modal analysis using multi-disciplinary structural finite element analysis software, then apply the aeroelastic module in the flight load and dynamic simulation system to establish an aerodynamic model, couple the structural finite element model with the aerodynamic model, obtain the flutter motion equation of the linear aeroelastic system, and perform flutter solution; obtain the aerodynamic force influence matrix, solve it, and obtain the modal eigenvalues of each order and their right eigenvectors of each airspeed.

[0019] Optionally, the l-th airspeed Vl The expressions for multiple modal confidence levels of the i-th order modal eigenvalue are as follows:

[0020]

[0021] Where MAC ij is the modal confidence level between the i-th order modal eigenvalue of the l-th airspeed V l and the j-th order modal eigenvalue of the (l - 1)-th airspeed V l-1 , Φ i,l represents the right eigenvector of the i-th order modal eigenvalue of the l-th airspeed V l , Φ j,l-1 represents the right eigenvector of the j-th order modal eigenvalue of the (l - 1)-th airspeed V l-1 . The eigenvalue of MAC ranges from 0 to 1, where 1 represents a perfect fit, i = 1, 2, 3...n, j = 1, 2, 3...n, and n represents the total number of modal orders;

[0022] Optionally, the specific steps for obtaining multiple modal confidence levels of the i-th order modal eigenvalue of the l-th airspeed and the improved Euclidean distances in step S6 include:

[0023] Based on the right eigenvector of the i-th order mode of the l-th airspeed and the right eigenvectors of each order of the (l - 1)-th airspeed, obtain multiple modal confidence levels of the i-th order modal eigenvalue of the l-th airspeed;

[0024] Calculate the Euclidean distances between the i-th order modal eigenvalue of the l-th airspeed and the modal eigenvalues of each order of the (l - 1)-th airspeed respectively, and improve them to obtain the improved Euclidean distances.

[0025] Optionally, the specific steps for obtaining the sorted modal eigenvalues of the l-th airspeed in step S9 include:

[0026] Step S91: Let a = 1. When a = 1, it represents the first remaining set D l,a , D l,a = [B i …B I , and the remaining set includes the improved modal confidence level MAC data groups of the modal eigenvalues of each order of the l-th airspeed, that is, it includes multiple improved modal confidence levels;

[0027] Step S92: Obtain the a-th remaining set D a,l of the modal eigenvalues of each order of the l-th airspeed;

[0028] Find the smallest improved modal confidence level B a,l from the a-th remaining set D a,l, obtain the improved modal confidence data group where it is located and its corresponding modal eigenvalue F a,l ;

[0029] Step S93: Obtain the eigenvalue F of the (l - 1)-th airspeed feature a,l-1 of the modal order E a,l-1， Assign it to the modal eigenvalue F a,l of the modal order E a,l ;

[0030] Step S94: Complete the a-th sorting of the modal eigenvalues of each order of the airspeed V l , and proceed to the next step;

[0031] Step S95: Delete the improved modal confidence data group B where the minimum improved modal confidence B a,l is located i , obtain the updated remaining set corresponding to the l-th airspeed as the (a + 1)-th remaining set D l，a+1 , and record it;

[0032] Step S96: Determine whether a is greater than or equal to A, where A represents the total number of remaining sets of the modal eigenvalues of each order of the l-th airspeed. If so, complete the sorting of the modal eigenvalues of each order of the l-th airspeed and proceed to the next step; if not, let a = a + 1 and return to Step S92.

[0033] Optionally, each of the improved Euclidean distances has the following expression:

[0034]

[0035] where is the i-th order modal eigenvalue of the l-th airspeed, is the i-th order modal eigenvalue of the (l - 1)-th airspeed, d′(·) is the Euclidean distance, α is the coefficient for adjusting the real part weight, Re represents the real part of a complex number, and Im represents the imaginary part of a complex number.

[0036] Optionally, the expression for the improved modal confidence of the i-th order modal eigenvalue of the l-th airspeed V l is as follows:

[0037]

[0038] where is the improved modal confidence of the i-th order modal eigenvalue of the l-th airspeed V l , and β is the coefficient for adjusting the modal confidence weight

[0039] Compared with the prior art, the present invention has at least the following beneficial effects:

[0040] (1) The modal tracking method for flutter analysis based on modal confidence in the present invention comprehensively considers factors such as the change in airspeed, the continuity of eigenvalues, the orthogonality of eigenvectors, and the computational complexity.

[0041] (2) The modal tracking method for flutter analysis based on modal confidence in the present invention, during the modal tracking process, through the initial eigenvalue sorting and the improved modal confidence value measurement criterion, can gradually match the modal eigenvalues at different airspeeds until the sorting of all eigenvalues is completed, effectively reducing the modal tracking errors caused by too large a speed step or near the flutter critical point, taking into account both computational accuracy and efficiency, and is applicable to fields such as aerospace for modal tracking.

[0042] (3) The present invention proposes an improved modal confidence MAC value method, which comprehensively considers the continuity of eigenvalues and the orthogonality of eigenvectors, and has a better sorting effect when approaching the flutter speed, effectively improving the accuracy of sorting when the speed step is too large. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings are only for the purpose of showing specific embodiments and are not considered as a limitation to the present invention.

[0044] Figure 1 It is a schematic diagram of the flowchart of modal tracking for flutter analysis based on modal confidence in the embodiment of the present invention;

[0045] Figure 2 It is a schematic diagram of a rectangular flat plate wing in the embodiment of the present invention;

[0046] Figure 3 It is a schematic diagram of a finite element model in the embodiment of the present invention;

[0047] Figure 4 It is a schematic diagram of an airspeed-frequency diagram of the wing without sorting in the embodiment of the present invention;

[0048] Figure 5 It is a schematic diagram of an airspeed-damping diagram of the wing without sorting in the embodiment of the present invention;

[0049] Figure 6 It is a schematic diagram of an airspeed-frequency diagram of the wing with sorting in the embodiment of the present invention;

[0050] Figure 7 It is a schematic diagram of an airspeed-damping diagram of the wing with sorting in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] To more clearly understand the above objects, features and advantages of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. In addition, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0052] A specific embodiment of the present invention, such as Figure 1-7 , discloses a modal tracking method for flutter analysis based on modal confidence, and the specific implementation steps are as follows:

[0053] Step S1, establish a structural finite element model;

[0054] Step S2, establish an aerodynamic model;

[0055] Step S3, couple the structural finite element model with the aerodynamic model, establish the flutter motion equation of the linear aeroelastic system, and perform flutter solution to obtain the aerodynamic influence matrix. Solve the aerodynamic influence matrix to obtain the modal eigenvalues and corresponding right eigenvectors of each order at each airspeed;

[0056] It can be understood that the modal eigenvalues of each order refer to the frequency and damping of each order of the mode;

[0057] Optionally, the specific steps of obtaining the modal eigenvalues and corresponding right eigenvectors of each order at each airspeed in step S3 include:

[0058] Use MSC.Nastran for modal analysis, and then apply the aeroelastic module in the flight load and dynamic simulation system MSC.Flightloads to establish an aerodynamic model, couple the structural finite element model with the aerodynamic model, obtain the flutter motion equation of the linear aeroelastic system, and perform flutter solution; obtain the aerodynamic influence matrix, solve it, and obtain the modal eigenvalues of each order and their right eigenvectors at each airspeed.

[0059] Optionally, the expression of the flutter motion equation of the linear aeroelastic system in step S3 is:

[0060]

[0061] where M is the generalized mass matrix, D is the generalized damping matrix, K is the generalized stiffness matrix; q d is the air dynamic pressure, Q is the generalized unsteady aerodynamic coefficient matrix, which is a continuous function of the airspeed and the system reduced frequency, q is the generalized modal coordinate describing the system motion, is the second derivative of the modal coordinate q, that is, the acceleration, is the first derivative of the modal coordinate q, i.e., the velocity.

[0062] Step S4: Let l = 1. When l = 1, it represents the initial airspeed. Let i = 1. When i = 1, it represents the first-order mode of the l-th airspeed V l ;

[0063] Step S5: Obtain the i-th order modal eigenvalue and the corresponding right eigenvector of the l-th airspeed V l ;

[0064] Step S6: Based on the right eigenvector of the i-th order mode of the l-th airspeed V l and the right eigenvectors of each order mode of the (l - 1)-th airspeed V l-1 , obtain multiple modal confidence degrees of the i-th order modal eigenvalue of the l-th airspeed V l ;

[0065] Optionally, the expression for multiple modal confidence degrees of the i-th order modal eigenvalue of the l-th airspeed V l is:

[0066]

[0067] where MAC ij is the modal confidence degree between the i-th order modal eigenvalue of the l-th airspeed V l and the j-th order modal eigenvalue of the (l - 1)-th airspeed V l-1 , Φ i,l represents the right eigenvector of the i-th order modal eigenvalue of the l-th airspeed V l , Φ j,l-1 represents the right eigenvector of the j-th order modal eigenvalue of the (l - 1)-th airspeed V l-1 . The eigenvalue of MAC ranges between 0 and 1, where 1 represents a perfect fit. i = 1, 2, 3... n, j = 1, 2, 3... n, and n represents the total number of modes;

[0068] Step S7: Calculate the Euclidean distances between the i-th order modal eigenvalue of the l-th airspeed V l and the modal eigenvalues of each order of the (l - 1)-th airspeed V l-1 to obtain multiple Euclidean distances The expression is:

[0069]

[0070] where is the i-th order modal eigenvalue of the l-th airspeed, is the i-th order modal eigenvalue of the (l - 1)-th airspeed, is the j-th order modal eigenvalue of the l-th airspeed V l , and d(·) is the Euclidean distance.

[0071] For each Euclidean distance improve it to obtain the improved Euclidean distances The expression is:

[0072]

[0073] where α is the coefficient for adjusting the real part weight, Re represents the real part of a complex number, and Im represents the imaginary part of a complex number.

[0074] Step S8: Based on the multiple modal confidence degrees of the i-th order modal eigenvalues of the l-th airspeed V l and each of the improved Euclidean distances, obtain multiple improved modal confidence degrees, and establish a corresponding improved modal confidence degree data group;

[0075] Optionally, the expression for the improved modal confidence degree of the i-th order modal eigenvalue of the l-th airspeed V l is:

[0076]

[0077] where is the improved modal confidence degree of the i-th order modal eigenvalue of the l-th airspeed V l , and β is the coefficient for adjusting the modal confidence degree weight.

[0078] Step S9: Traverse the I-th order modal eigenvalues of the l-th airspeed V l , and repeat steps S4 - S8 to obtain the improved modal confidence degree data groups corresponding to each order modal eigenvalues of the l-th airspeed V l ;

[0079] Step S10: Let a = 1. When a = 1, it means the first remaining set D l of each order modal eigenvalues of the l-th airspeed V l,a , D l,a = [B i …B I , and the remaining set includes the improved modal confidence degree MAC data groups of each order modal eigenvalues of the l-th airspeed V l , that is, includes multiple improved modal confidence degrees;

[0080] Step S11: Obtain the a-th remaining set D l of each order modal eigenvalues of the l-th airspeed V a,l ;

[0081] Find the minimum improved modal confidence degree B a,l from the a-th remaining set D a,l , and obtain the improved modal confidence degree data group where it is located and its corresponding modal eigenvalue Fa,l ;

[0082] Step S12: Obtain the modal order E of the eigenvalue F in the (l - 1)-th airspeed a,l-1 and assign it to the modal eigenvalue F a,l-1， of the modal order E a,l ; a,l ;

[0083] Step S13: Complete the a-th sorting of the modal eigenvalues of each order of the airspeed V l and proceed to the next step;

[0084] Step S14: Delete the improvement modal confidence data group B a,l where the minimum improvement modal confidence B is located i,l to obtain the updated remaining set corresponding to the airspeed V l as the (a + 1)-th remaining set D l，a+1 and record it;

[0085] Step S15: Determine whether a is greater than or equal to A, where A represents the total number of remaining sets of the modal eigenvalues of each order of the l-th airspeed V l If so, complete the sorting of the modal eigenvalues of each order of the l-th airspeed V l and proceed to the next step; if not, let a = a + 1 and return to Step S11;

[0086] Step S16: Determine whether l is greater than or equal to L, where L represents the total number of airspeeds. If so, obtain the modal eigenvalues of each order after sorting for each airspeed;

[0087] Based on the modal eigenvalues of each order after sorting for each airspeed, complete the modal tracking of each order for all airspeeds. If not, let l = l + 1 and return to Step S5;

[0088] The present invention further includes: Step S17: Based on the modal eigenvalues of each order after sorting for each airspeed and the modal eigenvalues of each order of each airspeed described in Step S3, obtain the flutter speed and its corresponding flutter frequency.

[0089] In the present invention, the modal tracking method is used to evaluate the consistency between different modal vectors and match the corresponding modes in different analyses. The core principle of this method is based on the orthogonality of modal shapes. By transforming the problem into the modal coordinate system, the eigenvectors exhibit weighted orthogonality and self-orthogonality with respect to the mass and stiffness matrices, making the MAC value method more efficient in practical applications.

[0090] Embodiment 1

[0091] A rectangular flat plate wing with a fixed root is used as the research object. The wing parameters are as follows: chord length 0.3m, span 1.8m, thickness 0.008m, elastic modulus 3GPa, Poisson's ratio 0.3, and material density 380kg / m 3 . The schematic diagram of the rectangular flat plate wing is as shown in Figure 2 ;

[0092] The specific implementation method of the modal tracking method in the present invention includes:

[0093] Step S1: Use the finite element software MSC.Patran to establish a finite element model of the wing. The CQUAD4 element is used to simulate the wing surface, and the root is fixed with six degrees of freedom. The information of the finite element model is shown in Table 1. The finite element model has a total of 287 GRID nodes and 240 CQUAD4 shell elements. The schematic diagram of the finite element model is as shown in Figure 3 ;

[0094] Table 1 Information of the finite element model

[0095] Number of model nodes 287 Number of model shell elements 240

[0096] Step S2: Use MSC.Nastran for modal analysis, then apply the aeroelastic module in MSC.Flightloads to establish an aerodynamic model, couple the structural model and the aerodynamic model, select the p-k method for flutter solution. After the solution is completed, read all the eigenvalues and their right eigenvectors of each airspeed from the f06 file;

[0097] Step S3: Use the improved Modal Assurance Criterion (MAC) value method. According to a certain eigenvalue and its right eigenvector at the current airspeed, calculate the improved MAC values between it and all the eigenvalues and their right eigenvectors at the previous airspeed, and obtain a set of improved MAC values. This calculation process needs to be carried out in a loop until all the eigenvalues and their right eigenvectors at the current airspeed state have completed the corresponding improved MAC value calculation. If the total number of eigenvalues at the current airspeed state is n, then n groups of improved MAC values are calculated, a total of n 2 improved MAC values;

[0098] Step S4: At the initial airspeed state, sort the eigenvalues according to the imaginary part from small to large to determine the eigenvalue order of each mode. For each subsequent airspeed, the present invention adopts a one-by-one processing method to complete the sorting of eigenvalues at different airspeed states in turn until all airspeed states are traversed.

[0099] Specifically, at a certain specific airspeed, the total number of eigenvalues is 5, so there are 5 groups of improved MAC values corresponding to it. The present invention adopts the following steps to determine the corresponding relationship of eigenvalues at this airspeed:

[0100] From the 5 groups (25 in total) of improved MAC values, the smallest improved MAC value is selected to determine the corresponding relationship between a certain eigenvalue at the current airspeed and a certain eigenvalue in the previous airspeed state. After confirming the corresponding relationship, the entire data group where the smallest improved MAC value is located is removed. Subsequently, the above process is repeated to continue searching for the smallest improved MAC value in the remaining data groups to establish a new corresponding relationship between eigenvalues until all eigenvalues at the current airspeed are arranged in order;

[0101] Step S5: Repeat steps S3 - S4 until the modal tracking for all airspeed states is completed;

[0102] Based on the airspeed, frequency, damping, etc. data before and after sorting, use Origin software for data analysis, plot the V - f and V - g graphs before and after sorting, and analyze the flutter speed and flutter frequency.

[0103] In the unsorted V - f graph and V - g graph, as Figure 4 and Figure 5 shown, obvious modal crossing phenomena can be observed, making it difficult to accurately identify the flutter modal branches.

[0104] After sorting, the V - f graph and V - g graph, as Figure 6 and Figure 7 shown, show smoother and more reasonable curves. From them, it can be clearly identified that the fifth - order mode is the crossing mode, and the flutter speed is estimated to be about 50 m / s and the flutter frequency is about 15.5 Hz.

[0105] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A modal tracking method for flutter analysis based on modal confidence, characterized in that, Including: Step S1: Establish a structural finite element model; Step S2: Establish an aerodynamic model; Step S3: Couple the structural finite element model with the aerodynamic model, establish the flutter motion equation of the linear aeroelastic system, and perform flutter solution to obtain the modal eigenvalues and corresponding right eigenvectors of each order at each airspeed; Step S4: Let l = 1. When l = 1, it represents the initial airspeed; let i = 1. When i = 1, it represents the first-order mode of the l-th airspeed; Step S5: Obtain the modal eigenvalue of the i-th order and the corresponding right eigenvector of the l-th airspeed; Step S6: Based on the modal eigenvalue of the i-th order and the corresponding right eigenvector of the l-th airspeed, obtain multiple modal confidence levels of the modal eigenvalue of the i-th order of the l-th airspeed and the improved Euclidean distances; Step S7: Based on multiple modal confidence levels of the modal eigenvalue of the i-th order of the l-th airspeed and the improved Euclidean distances, obtain multiple improved modal confidence levels, and establish a corresponding improved modal confidence level data set; Step S8: Repeat Steps S5 - S7 to obtain the modal eigenvalues of each order of the l-th airspeed and their corresponding improved modal confidence level data sets; Step S9: Sort the modal eigenvalues of each order of the l-th airspeed to obtain the sorted modal eigenvalues of each order of the l-th airspeed; Step S10: Determine whether l is greater than or equal to L, where L represents the total number of airspeeds. If so, obtain the sorted modal eigenvalues of each order of all airspeeds. If not, let l = l + 1, and return to Step S5; Based on the sorted modal eigenvalues of each order of the above-mentioned airspeeds, complete the modal tracking of each order of all airspeeds.

2. The flutter analysis modal tracking method based on modal confidence according to claim 1, characterized in that The specific steps of obtaining the modal eigenvalues of each order and the corresponding right eigenvectors of each airspeed in Step S3 include: Perform modal analysis using multidisciplinary structural finite element analysis software, then apply the aeroelastic module in the flight load and dynamic simulation system to establish an aerodynamic model, couple the structural finite element model with the aerodynamic model to obtain the flutter motion equation of the linear aeroelastic system, and perform flutter solution; obtain the aerodynamic force influence matrix, solve it, and obtain the modal eigenvalues of each order and their right eigenvectors of each airspeed.

3. The flutter analysis modal tracking method based on modal confidence according to claim 1, characterized in that The l-th airspeed V l The expression of multiple modal confidence degrees of the i-th order modal eigenvalue is as follows: Among them, MAC ij is the modal confidence of the i-th order modal eigenvalue of the l-th airspeed V l and the j-th order modal eigenvalue of the (l - 1)-th airspeed V l-1 , Φ i,l represents the right eigenvector of the i-th order modal eigenvalue of the l-th airspeed V l , Φ j,l-1 represents the right eigenvector of the j-th order modal eigenvalue of the (l - 1)-th airspeed V l-1 , i = 1, 2, 3...n, j = 1, 2, 3...n, and n represents the total order of the mode.

4. The flutter analysis modal tracking method based on modal confidence according to claim 1, characterized in that The specific steps of obtaining multiple modal confidence levels of the modal eigenvalue of the i-th order of the l-th airspeed and the improved Euclidean distances in Step S6 include: Based on the right eigenvector of the i-th order of the l-th airspeed and the right eigenvectors of each order of the (l - 1)-th airspeed, obtain multiple modal confidence levels of the modal eigenvalue of the i-th order of the l-th airspeed; Calculate the Euclidean distances between the modal eigenvalue of the i-th order of the l-th airspeed and the modal eigenvalues of each order of the (l - 1)-th airspeed respectively, and improve them to obtain the improved Euclidean distances.

5. The flutter analysis modal tracking method based on modal confidence according to claim 1, characterized in that The specific steps of obtaining the modal eigenvalues of each order after sorting the l-th airspeed described in step S9 include: Step S91: Let a = 1. When a = 1, it represents the first remaining set D of the modal eigenvalue of each order of the l-th airspeed l,a , D l,a = [B i … B I , and the remaining set includes the improved modal confidence MAC data group of the modal eigenvalue of each order of the l-th airspeed; Step S92, obtain the a-th remaining set D of the modal eigenvalues of each order of the l-th airspeed a,l ; Find the minimum improved modal confidence B a,l from the a-th remaining set D a,l , and obtain the improved modal confidence data group where it is located and its corresponding modal eigenvalue F a,l ; Step S93: Obtain the eigenvalue F of the (l - 1)-th airspeed a,l-1 of the modal order E a,l-1， Assign it to the modal eigenvalue F a,l of the modal order E a,l ; Step S94, complete the airspeed V l The a-th sorting of the modal eigenvalues of each order, proceed to the next step; Step S95: Delete the smallest improvement mode confidence level B a,l from the improvement mode confidence level data group B i to obtain the updated remaining set corresponding to the l-th airspeed, which serves as the (a + 1)-th remaining set D l，a+1 , and record it; Step S96: Determine whether a is greater than or equal to A, where A represents the total number of remaining sets of modal eigenvalues of each order of the l-th airspeed. If so, complete the sorting of the modal eigenvalues of each order of the l-th airspeed and proceed to the next step; if not, let a = a + 1 and return to step S92.

6. The flutter analysis modal tracking method based on modal confidence according to claim 1, characterized in that The improved Euclidean distances The expression is: wherein, is the i-th order modal eigenvalue of the l-th airspeed, is the i-th order modal eigenvalue of the (l - 1)-th airspeed, d′(·) is the Euclidean distance, α is the coefficient for adjusting the real part weight, Re represents the real part of a complex number, and Im represents the imaginary part of a complex number.

7. The flutter analysis modal tracking method based on modal confidence according to claim 6, characterized in that The improved modal confidence of the $i$-th order modal eigenvalue of the $l$-th airspeed $V$ l is expressed as follows: Among them, is the improved modal confidence of the i-th order modal eigenvalue of the l-th airspeed V l , and β is the coefficient for adjusting the modal confidence weight.

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