A Wing Damage Identification Method Based on Structural Mode Shapes

Abstract

The present invention relates to a wing damage identification method based on structural modal vibration shapes, belonging to the technical field of structural health monitoring. The present invention obtains the structural modal vibration shapes of the structure through a parameter identification method based on the displacement response of the structure, and further introduces the curvature modal change rate as an indicator reflecting damage. Whether the structure is damaged can be effectively identified based on single modal vibration shape data alone, without the need for historical vibration shape data. The present invention solves the problem that existing damage detection methods such as non-destructive testing of civil passenger aircraft are time-consuming, labor-intensive and uneconomical, and provides a technical reference for constructing a large aircraft structural health detection system. The method can provide a technical reference for constructing a large aircraft structural health detection system.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and in particular to a wing damage identification method based on structural modal vibration shapes, and in particular to a damage identification method for a high-aspect-ratio aircraft wing based on structural modal vibration shapes. Background Art

[0002] In recent years, large aircraft structural health monitoring has garnered widespread attention in engineering applications. Structural health monitoring makes structural changes a real-time, monitorable process, facilitating decision-making and maintaining structural safety. Monitoring structural health requires effective damage monitoring methods and damage indicators to establish a comprehensive health monitoring system. Existing research has focused on structural modal parameter identification methods and damage indicators, but the transition from structure to modal parameters and then to structural damage identification is insufficient, and research specifically targeting aircraft is also limited.

[0003] Therefore, it is of great significance to build a structural health monitoring system to study the methods of identifying structural modal parameters and effectively reflecting the damage of the structure based on the results of the identification method. Summary of the Invention

[0004] In response to the above issues, the present invention provides a damage detection method based on modal vibration modes. This method obtains the modal vibration modes of the structure through parameter identification based on the displacement response of the structure, and further introduces the modal rate of change of curvature as an indicator of damage. This method can effectively identify structural damage based solely on single modal vibration mode data, without the need for historical vibration mode data. This method addresses the time-consuming, labor-intensive, and uneconomical nature of existing damage detection methods such as non-destructive testing (NDT) on civil airliners, and provides a technical reference for the construction of large aircraft structural health monitoring systems. This method can provide a technical reference for the construction of large aircraft structural health monitoring systems.

[0005] The present invention provides a wing damage identification method based on structural modal vibration shapes, which is particularly suitable for damage identification of large aspect ratio aircraft wings, comprising:

[0006] S1. Obtain multiple nodes of the wing structure based on the wing finite element model;

[0007] Obtaining the displacement of each wing structure node; obtaining a correlation function of the wing structure node displacement response based on the displacement of each wing structure node;

[0008] Preferably, the related function expression of the wing structure node displacement response is:

[0009] R ij，k (τ)=E(x i，k (t+τ)x j，k (t));

[0010] Among them, R ij，k (τ) is the displacement between node i and node j of wing structure k, E(·) is the mathematical expectation of the node displacement of the wing structure, and x i，k represents the displacement of node i of wing structure k; x j，k represents the displacement of node k of the wing structure, t represents the time, t=1, 2, 3...T, T represents the total time, and τ represents the time step.

[0011] S2. Establishing a wing structure impulse response function, replacing the wing structure impulse response function based on the correlation function of the wing structure node displacement response in step S1 to obtain an updated wing structure impulse response function;

[0012] Furthermore, the wing structure impulse response function expression in step S2 is:

[0013]

[0014] Among them, h l , m(a) represents the discrete time a of the output channel when a unit pulse excitation is applied to the input channel m of the wing structure, h(a)=CA a B(a=0,1,2…), m is the number of input channels of the wing structure system; l represents the number of output channels of the wing structure system, a represents discrete time, A represents the wing structure system matrix, A∈R N×N , B represents the wing structure system input matrix, B∈R N×m , C represents the output matrix of the wing structure system, C∈R l×N , N represents the order of the wing structure system.

[0015] S3. Constructing a Hankel matrix of the wing structure, performing singular value decomposition on the Hankel matrix to obtain a system matrix and an output matrix; and obtaining eigenvectors and eigenvalues ​​based on the system matrix;

[0016] Obtaining a wing structure modal vibration shape based on the eigenvectors, eigenvalues ​​and output matrix;

[0017] It can be understood that the system matrix and output matrix are the system matrix and output matrix of the wing structure;

[0018] Furthermore, the matrix expression of the Hankel moment of the wing structure node displacement response function in step S3 is:

[0019]

[0020] Where H(k) is the Hankel matrix of the node displacement response function of the wing structure k, h(·) is the Hankel matrix; b represents the number of row blocks of the observability matrix of the wing structure; and c represents the number of column blocks of the controllability matrix of the wing structure.

[0021] The expression of the system matrix is:

[0022] A=D1 -1f2 P1 T H(1)Q1D1 -1 / 2

[0023] Among them, A is the system matrix, D1 is the singular value matrix, P1 is the left multiplication matrix of the singular value, Q1 T The singular value is multiplied by the matrix on the right, H(1) is the matrix corresponding to k=1 in the Hankel matrix, and T is the transpose.

[0024] Furthermore, the output matrix expression is:

[0025] C=E s T P1D1 1 / 2

[0026] Among them, C is the output matrix, E s T =[I 0], I is the identity matrix, E s T The extended matrix formed by the identity matrix and satisfying the corresponding expression matrix multiplication.

[0027] S4, determining whether the wing structure modal vibration shape conforms to a preset wing structure modal vibration shape; if so, proceeding to step S5; if not, returning to step S1 to modify the wing finite element model according to the wing structure modal vibration shape to obtain an updated wing finite element model;

[0028] S5. Obtaining wing structure nodes based on the wing finite element model or the updated wing finite element model; obtaining a curvature modal change rate image based on the wing structure nodes and the curvature modal change rate; and determining whether the wing structure is damaged based on the curvature modal change rate image.

[0029] Preferably, the specific steps of obtaining the curvature modal change rate image based on the wing structure nodes and the curvature modal change rate in step S5 include:

[0030] The wing structure node is used as the horizontal coordinate and the curvature modal change rate is used as the vertical coordinate to draw a graph to obtain a curvature modal change rate image. Based on the curvature modal change rate image, it is determined whether the wing structure is damaged.

[0031] Furthermore, the expression of the curvature modal change rate in step S5 is:

[0032]

[0033] Among them, q (r，s) represents the curvature modal change rate of the r-order mode at the node s of the wing structure, It represents the curvature modal change rate of the r-order mode at the node s of the wing structure; represents the curvature mode of the r-order mode at the node s+1 of the wing structure; represents the curvature mode of the r-order mode at the node s of the wing structure, and h represents the time it takes for the node s to move to the node node s+1.

[0034] Furthermore, the curvature modal expression of the r-order mode at node i is:

[0035]

[0036] in, represents the curvature mode of the r-order mode at the node s of the wing structure; represents the component of the r-order mode at node s of the wing structure; u represents the node spacing.

[0037] Compared with the prior art, the present invention has at least the following beneficial effects:

[0038] (1) The damage identification method of the present invention is applicable to large aspect ratio aircraft wings. The modal vibration shape of the structure is obtained by algorithm identification based only on the displacement response of the structure through the natural excitation technology characteristics, and the damage status of the wing structure is obtained through the curvature modal change rate image;

[0039] (2) The method of the present invention has a good detection effect on the damage location, and the method only uses the wing displacement data. The theory is concise and clear, and it is easy to apply in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings are only for purposes of illustrating particular embodiments and are not to be considered limiting of the invention.

[0041] Figure 1 is a flow chart of a wing damage identification method based on structural mode shapes in an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of a simplified model parameter diagram of a wing structure in an embodiment of the present invention;

[0043] Figure 3 Schematic diagram of the comparison between the identification result of the first-order modal vibration shape and the theoretical vibration shape in an embodiment of the present invention;

[0044] Figure 4Schematic diagram of the curvature modal change rate identification result when the 20th unit of the structure is damaged in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below.

[0046] A specific embodiment of the present invention, as Figure 1-4 , discloses a wing damage identification method based on structural modal vibration shapes. In order to illustrate the effectiveness of the method proposed by the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment. The specific implementation steps are as follows:

[0047] Example 1

[0048] The present invention provides a wing damage identification method based on structural modal vibration shapes, which is particularly suitable for damage identification of large aspect ratio aircraft wings, comprising:

[0049] S1. Obtain multiple nodes of the wing structure based on the wing finite element model;

[0050] Obtaining the displacement of each wing structure node; obtaining a correlation function of the wing structure node displacement response based on the displacement of each wing structure node;

[0051] Preferably, the related function expression of the wing structure node displacement response is:

[0052] R ij，k (τ)=E(x i，k (t+τ)x j，k (t));

[0053] Among them, R ij，k (τ) is the displacement between node i and node j of wing structure k, E(·) is the mathematical expectation of the node displacement of the wing structure, and x i，k represents the displacement of node i of wing structure k; x j，k represents the displacement of node j of wing structure k, t represents the time, t=1, 2, 3...T, T represents the total time, and τ represents the time step.

[0054] S2. Establishing a wing structure impulse response function, replacing the wing structure impulse response function based on the correlation function of the wing structure node displacement response in step S1 to obtain an updated wing structure impulse response function;

[0055] Furthermore, the wing structure impulse response function expression in step S2 is:

[0056]

[0057] Among them, h l，m (a) represents the discrete time a of the output channel l when a unit pulse excitation is applied to the input channel m of the wing structure, h(a) = CA a B(a=0,1,2…), m is the number of input channels of the wing structure system; l represents the number of output channels of the wing structure system, a represents discrete time, A represents the wing structure system matrix, A∈R N×N , B represents the wing structure system input matrix, B∈R N×m , C represents the output matrix of the wing structure system, C∈R l×N , N represents the order of the wing structure system.

[0058] S3. Constructing a Hankel matrix of the wing structure, performing singular value decomposition on the Hankel matrix to obtain a system matrix and an output matrix; and obtaining eigenvectors and eigenvalues ​​based on the system matrix;

[0059] Obtaining a wing structure modal vibration shape based on the eigenvectors, eigenvalues ​​and output matrix;

[0060] It can be understood that the system matrix and output matrix are the system matrix and output matrix of the wing structure;

[0061] Furthermore, the matrix expression of the Hankel moment of the wing structure node displacement response function in step S3 is:

[0062]

[0063] Where H(k) is the Hankel matrix of the node displacement response function of the wing structure k, h(·) is the Hankel matrix; b represents the number of row blocks of the observability matrix of the wing structure; and c represents the number of column blocks of the controllability matrix of the wing structure.

[0064] The expression of the system matrix is:

[0065] A=D1 -1 / 2 P1 T H(1)Q1D1 -1 / 2

[0066] Among them, A is the system matrix, D1 is the singular value matrix, P1 is the left multiplication matrix of the singular value, Q1 T The singular value is multiplied by the matrix on the right, H(1) is the matrix corresponding to k=1 in the Hankel matrix, and T is the transpose.

[0067] Furthermore, the output matrix expression is:

[0068] C=E s T P1D1 1 / 2

[0069] Among them, C is the output matrix, E s T =[I 0], I is the identity matrix, E s T The extended matrix formed by the identity matrix and satisfying the corresponding expression matrix multiplication.

[0070] S4, determining whether the wing structure modal vibration shape conforms to a preset wing structure modal vibration shape; if so, proceeding to step S5; if not, returning to step S1 to modify the wing finite element model according to the wing structure modal vibration shape to obtain an updated wing finite element model;

[0071] S5. Obtaining wing structure nodes based on the wing finite element model or the updated wing finite element model; obtaining a curvature modal change rate image based on the wing structure nodes and the curvature modal change rate; and determining whether the wing structure is damaged based on the curvature modal change rate image.

[0072] Preferably, the specific steps of obtaining the curvature modal change rate image based on the wing structure nodes and the curvature modal change rate in step S5 include:

[0073] The wing structure node is used as the horizontal coordinate and the curvature modal change rate is used as the vertical coordinate to draw a graph to obtain a curvature modal change rate image. Based on the curvature modal change rate image, it is determined whether the wing structure is damaged.

[0074] Furthermore, the expression of the curvature modal change rate in step S5 is:

[0075]

[0076] Among them, q (r，s) represents the curvature modal change rate of the r-order mode at the node s of the wing structure, It represents the curvature modal change rate of the r-order mode at the node s of the wing structure; represents the curvature mode of the r-order mode at the node s+1 of the wing structure; represents the curvature mode of the r-order mode at the node s of the wing structure, and h represents the time it takes for the node s to move to the node node s+1.

[0077] Furthermore, the curvature modal expression of the r-order mode at node i is:

[0078]

[0079] in, represents the curvature mode of the r-order mode at the node s of the wing structure; represents the component of the r-order mode at node s of the wing structure; u represents the node spacing.

[0080] Example 2

[0081] A uniform cantilever beam wing is selected, and the structural model of the uniform cantilever beam wing is shown in FIG. Figure 2 , length L = 5m, cross-sectional dimensions 0.5*0.5m^2, elastic modulus E = 7E10pa;

[0082] The uniform cantilever beam wing model is divided into equal units along the axial direction (the total number of units in this example is n = 40), and each unit is simplified to two nodes, each of which has one longitudinal degree of freedom and one torsional degree of freedom. Then, the overall mass matrix and stiffness matrix of the uniform cantilever beam wing structure are obtained. The damping adopts the proportional damping model, and a random external load is applied to the 40th node of the structure. The displacement response of the other nodes of the uniform cantilever beam wing structure is obtained by the Newmark-β numerical method and recorded as x 1，40 , x 2，40 Lx 40，40 .

[0083] Step S1, obtain the displacement response (x 1，40 , x 2，40 Lx 40，40 ), and get the correlation function value R between 40 nodes ij，40 (τ);

[0084] Step S2: establishing a wing structure impulse response function, applying single-point loading to the uniform cantilever beam wing structure and obtaining displacement response data of 40 nodes on the uniform cantilever beam wing structure through a numerical method, and modifying the wing structure impulse response function based on the displacement response data to obtain an updated wing structure impulse response function, wherein the number of system input channels m = 1; the number of system output channels l = 40;

[0085] Step S3, constructing the Hankel matrix of the wing structure node displacement response function, assigning k in H(k) to 0 to obtain H(0), and performing singular value decomposition on H(0) (the Hankel matrix corresponding to k=0 in Hankel) to obtain a left multiplication matrix P1, a singular value matrix D1, and a right multiplication matrix Q1; based on the left multiplication matrix P1, the singular value matrix D1, and the right multiplication matrix Q1, obtaining the system matrix A, the input matrix B, and the output matrix C;

[0086] Obtaining the wing structure modal vibration shape based on the system matrix A, input matrix B and output matrix C;

[0087] The observability matrix of the system matrix has a row block number r=15, and the controllability matrix has a column block number s=800;

[0088] Step S4: determining whether the wing structure modal vibration shape conforms to the preset wing structure modal vibration shape; Figure 3 If it meets the requirements, continue to step S5; if it does not meet the requirements, return to step S1 and modify the wing finite element model according to the wing structure modal vibration shape to obtain an updated wing finite element model;

[0089] Step S5: obtaining wing structure nodes based on the finite element model or the updated wing finite element model; obtaining a curvature modal change rate image based on the wing structure nodes and the curvature modal change rate; and determining whether the wing structure is damaged based on the curvature modal change rate image. Figure 4 , u is the node spacing, which is 0.125m in this example. When the 20th node is damaged (the node stiffness decreases by 10%), the damage condition of the wing structure is determined by the curvature modal change rate image.

[0090] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A wing damage identification method based on structural mode shapes, characterized in that: include: S1. Correlation function of wing structure node displacement response obtained based on wing finite element model; S2. Establishing a wing structure impulse response function, and updating the wing structure impulse response function based on the correlation function of the wing structure node displacement response in step S1 to obtain an updated wing structure impulse response function; S3. constructing a Hankel matrix of the wing structure, and decomposing the Hankel matrix to obtain a modal vibration shape of the wing structure; S4, determining whether the wing structure modal vibration shape conforms to a preset wing structure modal vibration shape; Obtain the finite element model of the wing after judgment; S5. Obtaining wing structural nodes based on the finite element model of the wing after the determination; Obtaining a curvature modal change rate image based on the wing structure nodes and the curvature modal change rate; Whether the wing structure is damaged is determined based on the curvature modal rate of change image.

2. The wing damage identification method according to claim 1, characterized in that: The specific steps of obtaining the correlation function of the wing structure node displacement response include: Obtain multiple nodes of the wing structure based on the wing finite element model; The displacement of each wing structure node is obtained; and a correlation function of the wing structure node displacement response is obtained based on the displacement of each wing structure node.

3. The wing damage identification method according to claim 2, characterized in that: The expression of the correlation function of the wing structure node displacement response is: R ij,k (τ)=E(x i,k (t+τ)x j,k (t)); Among them, R ij,k (τ) is the displacement between node i and node j of the wing structure k, E(·) is the mathematical expectation of the displacement of the wing structure node, x i,k represents the displacement of node i of wing structure k; x j,k represents the displacement at node j of wing structure k, t represents the time, t=1,2,3…T, T represents the total time, and τ represents the time step.

4. The wing damage identification method according to claim 3, characterized in that: The expression of the wing structure impulse response function in step S2 is: Among them, h l,m (a) Represents the discrete time a of the output channel l when a unit pulse excitation is applied to the input channel m of the wing structure, where m is the number of input channels of the wing structure; l represents the number of output channels of the wing structure.

5. The wing damage identification method according to claim 4, characterized in that: The specific steps of obtaining the wing structure modal vibration shape in step S3 include: Constructing a Hankel matrix of the wing structure, performing singular value decomposition on the Hankel matrix to obtain a system matrix and an output matrix; obtaining eigenvectors and eigenvalues ​​based on the system matrix; The modal vibration shape of the wing structure is obtained based on the eigenvectors, eigenvalues ​​and output matrix.

6. The wing damage identification method according to claim 5, characterized in that: The expression of the Hankel matrix of the wing structure node displacement response function in step S3 is: Where H(k) is the Hankel matrix of the node displacement response function of the wing structure k, h(·) is the Hankel matrix; b represents the number of row blocks of the observability matrix of the wing structure; and c represents the number of column blocks of the controllability matrix of the wing structure.

7. The wing damage identification method according to claim 6, characterized in that: The specific steps of step S4 of judging whether the wing structure modal vibration shape conforms to the preset wing structure modal vibration shape include: Preset wing structure mode shape; Determine whether the parameters of the wing structure modal vibration shape meet the parameters of the preset wing structure modal vibration shape; if so, continue to step S5; if not, return to step S1, and modify the parameters of the wing finite element model according to the parameters of the wing structure modal vibration shape to obtain an updated wing finite element model.

8. The wing damage identification method according to claim 7, characterized in that: The specific steps of obtaining the curvature modal change rate image based on the wing structure nodes and the curvature modal change rate in step S5 include: The wing structure node is used as the horizontal coordinate and the curvature modal change rate is used as the vertical coordinate to draw a graph to obtain a curvature modal change rate image. Based on the curvature modal change rate image, it is determined whether the wing structure is damaged.

9. The wing damage identification method according to claim 8, characterized in that: The expression of the curvature modal change rate in step S5 is: Among them, q (r,s) represents the curvature modal change rate of the r-order mode at the node s of the wing structure, represents the curvature mode of the r-order mode at the node s+1 of the wing structure; represents the curvature mode of the r-order mode at the node s of the wing structure, and h represents the time it takes for the node s to move to the node s+1.

10. The wing damage identification method according to claim 9, characterized in that: The expression of the curvature mode of the r-order mode at the wing structure node i is: in, represents the component of the r-order mode at node s of the wing structure; u represents the node spacing.

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