Method for aircraft smart skin damage identification based on complex modal expansion and kalman filtering

Abstract

This invention discloses a method for identifying damage to aircraft smart skin based on complex modal expansion and Kalman filtering. The steps include: acquiring strain values ​​at the location of fiber optic strain sensors; constructing a finite element model of the aircraft smart skin and extracting modal features; constructing a complex modal expansion equation; solving for the full-field strain value of the aircraft smart skin based on the complex modal expansion equation; and obtaining the damage identification result of the aircraft smart skin. This invention uses a finite element model obtained by discretizing a proportional 3D model of the aircraft smart skin to solve for the full-field strain value. It employs a finite fiber optic strain sensor to expand the full-field strain in real time and performs damage identification based on the full-field strain. The finite element model has a simple structure and does not require iterative optimization, effectively improving identification efficiency and robustness while ensuring identification accuracy.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring and relates to an intelligent aircraft skin damage identification method based on complex modal extension and Kalman filtering. Background Technology

[0002] Smart skin for aircraft is a composite structure that integrates sensors, actuators, and smart materials, possessing self-sensing, self-monitoring, and self-regulating functions. During their service life, aircraft are exposed to time-varying environments such as high speed, vibration, and large temperature differences, which can easily lead to damage such as cracks, impact damage, corrosion, and deformation. This can cause a decrease in structural strength during the aircraft's service life, and in severe cases, structural failure or loss of flight control.

[0003] The basic methods for intelligent skin damage identification in aircraft mainly include acoustic emission, ultrasonic guided waves, strain measurement technology, and machine learning. Among these methods, strain measurement-based damage identification detects minute changes or deformations in the structure using strain sensors. When damage occurs, it alters the structural stiffness, thus affecting strain information. This damage identification method is primarily limited by the accuracy of strain information sensing.

[0004] The key and challenge of damage identification methods based on strain measurement lies in acquiring full-field strain sensing information and improving the accuracy of full-field strain sensing. Among these challenges, the amount of full-field strain sensing information is mainly limited by the number of sensors. In order to obtain full-field strain sensing information with higher resolution, a large number of sensors often need to be deployed, which will greatly increase the cost of sensor application. The accuracy of full-field strain sensing is mainly limited by model error and measurement error. To improve model accuracy, for example, patent application CN202311639870.9, entitled "A Method for Identifying Damage Location and Shape of Composite Materials Based on Model Correction," discloses a method for identifying damage to aircraft smart skin. This method includes: step-by-step fiber optic detection of the strain response of a damaged composite material plate under load; parameterized establishment of a random damage finite element model, extracting the strain response of nodes corresponding to the experiment; using the size and location of the damage as correction parameters, with the absolute value of the difference between the actual measured strain and the simulated strain as the objective function; within the constraints of the correction parameters, experimental sampling points are designed to obtain the corresponding objective function, constructing a surrogate model; and a multi-island genetic optimization algorithm is used to find the optimal solution in the surrogate model to determine the size and location of the damage. This invention improves identification accuracy and efficiency, but its drawback lies in the complexity of the constructed random damage finite element model structure and the need for iterative optimization, which affects further improvement in its identification efficiency. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by proposing a method for intelligent aircraft skin damage identification based on complex mode extension and Kalman filtering. This method aims to reduce sensor application costs and improve strain field reconstruction accuracy while ensuring computational efficiency, thereby improving the accuracy of damage identification.

[0006] To achieve the above objectives, the implementation of the present invention includes the following steps:

[0007] (1) Obtain the strain value at the location of the fiber optic strain sensor:

[0008] The position information collected by M fiber Bragg grating strain sensors in the aircraft smart skin at T time points is demodulated to obtain the strain values ​​ε at the positions of the M fiber Bragg grating strain sensors at the T time points. M (T), where M≥5, T≥2s, and the strain value at the position of the m-th fiber optic strain sensor at time t is ε. m (t);

[0009] (2) Construct a finite element model of the aircraft's smart skin and extract modal features:

[0010] The scaled 3D model based on the aircraft's intelligent skin is discretized, and the finite element displacement mode matrix Φ of all nodes in the discretized finite element model is extracted. FE and the finite element strain mode matrix ψ FE ;

[0011] (3) Construct the complex modal extension equations:

[0012] Construct the strain values ​​ε at the M sensor locations at time t+1. M (t+1) is the independent variable, and the displacement mode matrix Φ is used to express the finite element method. FE and the finite element strain mode matrix ψ FE and strain mode matrix Solve for the total strain ε at time t+1. all The complex modal expansion equations for (t+1);

[0013] (4) Solving for the full-field strain values ​​of the aircraft smart skin based on the complex modal expansion equation:

[0014] The strain value ε at the location of M fiber grating strain sensors at each moment is used. M The Kalman filter result of the calculated time mode coefficient q(t) is used to solve the complex mode expansion equation, and the full-field strain value of the aircraft smart skin at time t+1 is obtained.

[0015] (5) Obtain the results of intelligent skin damage identification for aircraft:

[0016] The total strain value at time t+1 After normalization, the strain gradient of each node is calculated based on the normalization result. Then, the presence of damage at each node is determined by the strain gradient and the total normalized strain gradient.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] First, the present invention solves the full-field strain value of the aircraft smart skin by discretizing the proportional three-dimensional model established based on the aircraft smart skin. It uses a finite fiber optic strain sensor to expand the full-field strain in real time and performs damage identification based on the full-field strain. The finite element model has a simple structure and does not require iterative optimization. It effectively improves the identification efficiency and robustness while ensuring the identification accuracy.

[0019] Secondly, this invention reduces measurement errors through Kalman filtering and modeling errors through complex modal expansion, effectively improving the overall strain sensing accuracy. Compared with the traditional modal method, the strain field sensing accuracy is improved by more than 50%, and the improvement in strain field sensing accuracy is even more significant under conditions of large measurement noise and large differences between the finite element method and the actual model. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0021] Figure 2 A strain value diagram at the location of the fiber optic strain sensor for this invention;

[0022] Figure 3 This is a diagram showing the extended effects of the first six strain modes of this invention;

[0023] Figure 4 This is a diagram of strain data after Kalman filtering according to the present invention;

[0024] Figure 5 This is a normalized strain gradient cloud map of the full-field strain values ​​in this invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] Reference Figure 1 The present invention includes the following steps:

[0027] Step 1) Obtain the strain value at the location of the fiber optic strain sensor:

[0028] The position information collected by M fiber Bragg grating strain sensors in the aircraft smart skin at T time points is demodulated to obtain the strain values ​​ε at the positions of the M fiber Bragg grating strain sensors at the T time points. M (T), where M≥5, T≥2s, and the strain value at the position of the m-th fiber optic strain sensor at time t is ε. m (t);

[0029] In this embodiment, the aircraft smart skin is made of composite material, M=20. A carbon fiber composite laminate with embedded fiber optic strain sensors is prepared using a release liner. The cross-section of the composite material is 800×400mm, and the fiber material is stacked in a flat manner, with a total of 100 layers of prepreg and a total thickness of 10mm. When 50 layers are laid, the surface of the composite material is cleaned with alcohol, and 20 fiber optic strain sensors are fixed using AB glue.

[0030] A 1000N linear load was applied to the center of the composite laminate. This load caused deformation of the composite plate, resulting in stretching or compression of the attached fiber Bragg grating (FBG) sensors and a change in their wavelength. The signals collected by the 20 FBG strain sensors in the composite laminate over 3 seconds were demodulated using a FBG demodulator. The strain values ​​at the locations of the 20 FBG strain sensors over those 3 seconds were obtained, and the strain data were plotted as follows: Figure 2 As shown in the figure, the strain values ​​at the locations of the 20 fiber optic strain sensors exhibit noise fluctuations of approximately 3 micro-strain values.

[0031] Step 2) Construct a finite element model of the aircraft's smart skin and extract modal features:

[0032] Using the 3D software UG, a scaled 3D model was created based on the actual aircraft intelligent skin. This model was then imported into Abaqus finite element analysis software for equidistant mesh generation, resulting in a finite element model with 13×5 mesh nodes. Linear perturbation analysis was performed on this finite element model, and the first six displacement mode vectors and strain mode vectors at all mesh nodes were extracted to construct a 65×6 finite element displacement mode matrix Φ. FE Finite element strain mode matrix ψ FE .

[0033] Step 3) Construct the complex modal extension equations:

[0034] (3a) Modal testing was performed on the aircraft's smart skin, and the eigenvectors of the undamped structure obtained from the modal testing were analyzed. Perform singular value decomposition, and then calculate the projection vector p for each modal order based on the transformation matrix T of dimension M×K obtained from the singular value decomposition. k (g):

[0035]

[0036] Where, T∈R M×K R is the set of real numbers, Φ FE,fit Φ is the finite element displacement mode matrix FE The selected fitting set, S(g) is the diagonal selection matrix, and g is the number of modes. For the k-th fitted set real displacement mode, Φ exp The real displacement mode matrix, It is a false rebellion.

[0037] Modal testing was performed on the composite laminate. The testing setup included a test specimen, accelerometers, a force hammer, a dynamic data acquisition system, and modal analysis software. The composite laminate was divided into 65 modal measurement points. Accelerometers were attached to 6 different modal measurement points, and the force hammer was moved to strike the specimens, acquiring the experimental modal frequencies. The sixth-order complex modal frequencies and the eigenvectors under undamped structure were extracted from these frequencies. eigenvectors The conversion to real modes, finite element analysis, and experimental frequency tables are shown in Table 1:

[0038] Table 1 Finite element method and experimental frequency table

[0039]

[0040] (3b) Calculate the confidence level F of the different modes contained in the k-th mode. obs,k (g), and form the optimal projection vector p by taking the optimal number of modes g0 corresponding to the maximum confidence. k (g0), and through p k (g0) and the finite element strain mode matrix ψ FE Calculate the k-th smooth extended strain mode shape The K-order smooth extended strain mode shape forms the strain mode matrix. Where F obs,k (g) and The calculation formulas are as follows:

[0041]

[0042] Where g0 is the optimal number of modes. For the k-th experimental displacement mode shape, The experimental displacement mode shapes are estimated from the obtained observation set.

[0043] The following are the specific steps for smoothly expanding the first-order strain mode matrix:

[0044] Based on the frequencies obtained in Table 1, the distances from each finite element modal frequency to the first experimental modal frequency are constructed, and a modal arrangement order table is constructed from near to far, as shown in Table 2.

[0045] Table 2 Modal arrangement order based on frequency difference

[0046]

[0047] Select the first g-order finite element modal smoothing expansion experimental modes and calculate the modal confidence at the observation points, where g ranges from 1 to 6, resulting in 6 confidence results. Find the mode number g corresponding to the highest confidence level as the optimal mode number g0 to form the optimal projection vector p. k (g0), through calculation, it can be found that when the number of modes is 1, the modal confidence is the highest, that is, the first order of the experimental mode is extended using the previous order of the finite element mode. The optimal number of modes g0 is 1. Through p1(1) and the finite element strain mode matrix ψ FE Calculate the first-order smoothly extended strain mode shape. Similarly, calculate the optimal number of modes g0 for each extended experimental strain mode, obtain the optimal projection vector for each mode, and then calculate the final strain mode matrix containing six modes after smooth extension based on the optimal projection vector. The effect of the first six strain mode extensions is as follows: Figure 3 As shown in the figure, there are certain differences between the finite element mode and the experimental mode. The strain mode at the observation point after expansion is basically consistent with the experimental mode, which verifies that the complex mode expansion method can effectively reduce modeling errors.

[0048] (3c) Construct the strain values ​​ε at the M sensor locations at time t+1. M (t+1) is the independent variable, and the displacement mode matrix Φ is used to express the finite element method. FE and the finite element strain mode matrix ψ FE and strain mode matrix Solve for the total strain ε at time t+1. all The complex modal expansion equations for (t+1) are as follows:

[0049]

[0050] in, ε is the first K order strain mode matrix of all nodes after smooth expansion. M (t+1)∈R M×1 Let M be the strain value at the location of the M sensors at time t+1. The smoothed extended strain mode matrix of the grid nodes at the corresponding locations of M fiber grating strain sensors The false rebellion.

[0051] Based on the strain value ε at the M sensor locations at time t+1 M (t+1) is used to construct the complex modal expansion equation with the independent variable and the strain mode matrix containing the sixth-order mode shape in (3b) through smooth expansion.

[0052] Step 4) Solve for the full-field strain values ​​of the aircraft smart skin based on the complex modal expansion equation:

[0053] The strain value ε at the location of M fiber grating strain sensors at each moment is used. M The Kalman filter result of the calculated time mode coefficient q(t) is used to solve the complex mode expansion equation, and the full-field strain value of the aircraft smart skin at time t+1 is obtained.

[0054] (4a) The strain value ε at the location of the M fiber grating strain sensors at each time step M The time mode coefficients q(t) calculated by (t) are subjected to Kalman filtering to obtain the time mode coefficients at time t+1. Using this time mode coefficient, the measured strain ε of M sensors at time t+1 M Estimate at (t+1):

[0055]

[0056] q(t+1|t)=Aq(t)

[0057] p(t+1|t)=Ap(t)A T +Q

[0058]

[0059] Among them, K t+1 For Kalman gain, Let q(t+1|t) and p(t+1|t) be the optimal estimates of the time mode coefficients and covariance at time t+1, respectively; R is the covariance matrix of the measurement noise; q(t+1|t) and p(t+1|t) are the estimated time mode coefficients and their covariance at time t+1 at time t, respectively; and Q is the covariance matrix of the process noise.

[0060] Kalman filtering is performed on the time mode coefficients calculated from the strain values ​​at the locations of the 20 fiber optic strain sensors obtained in step 1) over 3 seconds to obtain the time mode coefficients at time t+1. Using this time mode coefficient, the measured strain ε of M sensors at time t+1 M (t+1) is estimated to obtain the strain data after Kalman filtering, as follows: Figure 4As shown in the figure, after Kalman filtering, the strain fluctuation is reduced to less than 1 microstrain, thus effectively smoothing the data and reducing measurement error.

[0061] (4b) via ε M The estimated value of (t+1) Calculate the total strain at time t+1

[0062]

[0063] The complex modal expansion equation constructed in step 3) is solved using the filtered strain data to obtain the full-field strain value of the composite material laminate. The reconstruction accuracy of each method is obtained by comparing the root mean square error and maximum error at the observation sensor of the existing method, the traditional modal method, and the unfiltered complex modal expansion method. The results are shown in Table 3.

[0064] Table 3 Comparison of reconstruction accuracy of different reconstruction methods

[0065]

[0066] Step 5) Obtain the aircraft intelligent skin damage recognition results:

[0067] The total strain value at time t+1 After normalization, the strain gradient of each node is calculated based on the normalization result. Then, the presence of damage at each node is determined by the strain gradient and the total normalized strain gradient.

[0068] (5a) Strain values ​​across the entire field Normalization is performed, and the Node in the normalized strain field ρ(t+1) is used as the input. n+1,b Node n-1,b Normalized strain ρ at mesh nodes n+1,b (t+1),ρ n-1,b (t+1) Calculate the grid node Node in the nth row and bth column. n,b strain gradient ξ n,b :

[0069]

[0070] Where, ε max ε min For the whole field of response The maximum and minimum values ​​in x n+1 ,x n-1 These are the grid nodes along the length direction. n+1,b Node n-1,b The coordinates;

[0071] The strain values ​​obtained in step 4) are normalized, and the strain gradient at each grid node is calculated using the normalized strain field.

[0072] (5b) Determine the strain gradient ξ n,b With the normalized strain gradient ξ all Does it satisfy |ξ n,b |>80%ξ all If so, then damage exists at that node; otherwise, no damage exists. The total normalized strain gradient ξ is... all The calculation formula is:

[0073]

[0074] Through (5a) Figure 5 The normalized strain gradient contour plot of the full-field strain values ​​is shown, and it is determined whether the strain gradient at each grid node satisfies |ξ|. n,b |>80%ξ all As can be seen from the figure, |ξ n,b |>80%ξ all The area is concentrated at the two end supports, which indicates that damage has occurred in this area under the current load, thus achieving the purpose of damage identification.

[0075] The scope of this invention is not limited to the examples mentioned above. All equivalent changes and modifications made in accordance with the claims of this invention are within the scope of this invention.

Claims

1. A method for intelligent aircraft skin damage identification based on complex mode extension and Kalman filtering, characterized in that, Includes the following steps: (1) Obtain the strain value at the location of the fiber optic strain sensor: The aircraft smart skin under load Data collected by a fiber optic strain sensor Demodulate the location information at each time point to obtain At that moment Strain values ​​at the locations of fiber optic strain sensors ,in, , , No. At the [time]th moment The strain value at the location of each fiber grating strain sensor is ; (2) Construct a finite element model of the aircraft's intelligent skin and extract modal features: The scaled 3D model based on the aircraft's intelligent skin is discretized, and the finite element displacement mode matrices of all nodes in the discretized finite element model are extracted. and finite element strain mode matrix ; (3) Construct the complex modal extension equations: Constructing the first time Strain values ​​at the locations of fiber optic strain sensors As the independent variable, the displacement mode matrix of the finite element method is used. and finite element strain mode matrix and strain mode matrix Solve the first Full-field strain value at all times The complex modal expansion equations; (4) Solving for the full-field strain values ​​of the aircraft smart skin based on the complex modal expansion equation: Through each moment Strain values ​​at the locations of fiber optic strain sensors Calculated time mode coefficients The Kalman filter results are used to solve the complex mode expansion equations to obtain the first... Full-field strain value of the smart skin of the aircraft ; (5) Obtain the results of intelligent skin damage identification for aircraft: For the Full-field strain value at time 1 After normalization, the strain gradient of each node is calculated based on the normalization result. Then, the presence of damage at each node is determined by the strain gradient and the total normalized strain gradient.

2. The method according to claim 1, characterized in that, The steps for constructing the finite element model of the aircraft's intelligent skin and extracting modal features as described in step (2) are as follows: A scaled 3D model of the aircraft's intelligent skin was created based on the physical model and then divided into equally spaced meshes to obtain the following results: A finite element model of a grid with individual nodes was constructed, and the front data at each grid node was extracted through linear perturbation analysis of the finite element model. The dimensions for constructing the displacement mode vector and strain mode vector are: Finite element displacement mode matrix Finite element strain mode matrix ,in, , These represent the number of grid nodes in the length and width directions, respectively.

3. The method according to claim 2, characterized in that, The proportional 3D model was divided into equally spaced meshes using finite element analysis software.

4. The method according to claim 2, characterized in that, The strain mode matrix mentioned in step (3) The method to obtain it is as follows: (3a) Perform modal testing on the aircraft smart skin, and analyze the eigenvectors of the undamped structure obtained from the modal testing. Perform singular value decomposition, and then the dimension obtained based on the singular value decomposition is... Transformation matrix Calculate the projection vector for each modal order. : ； ； in, , For the set of real numbers, Finite element displacement mode matrix The selected fitting set Choose a matrix for the diagonal. For the number of modes, For the first The first-order fitted set of real displacement modes, The real displacement mode matrix, It is a false rebellion; (3b) Calculate the first Confidence levels of different modes included in the first-order mode And the number of optimal modes corresponding to the maximum confidence level. Forming the optimal projection vector and through With finite element strain mode matrix Calculate the first Smooth extended strain mode shape ,but The strain mode matrix is ​​composed of smooth extended strain mode shapes. ,in and The calculation formulas are as follows: ； ； in, For the optimal number of modes, For the first First-order experimental displacement mode shape, The experimental displacement mode shapes are estimated from the obtained observation set.

5. The method according to claim 4, characterized in that, The solution described in step (3) is as follows Full-field strain value at all times The complex modal expansion equation is expressed as follows: ； ； in, For the first part of all nodes after smooth expansion First strain mode matrix, For the first time Strain values ​​at the locations of fiber optic strain sensors for Smoothly expanded strain mode matrix of grid nodes at the corresponding locations of each fiber optic strain sensor The false rebellion.

6. The method according to claim 5, characterized in that, The steps for solving the full-field strain value of the aircraft smart skin based on the complex modal extension equation in step (4) are as follows: (4a) For each time interval Strain values ​​at the locations of fiber optic strain sensors Calculated time mode coefficients Perform Kalman filtering to obtain Time pattern coefficient : ； ； ； ； ； ； in, For Kalman gain, , The first The optimal estimates of the time pattern coefficients and covariance at time t. To measure the covariance matrix of the noise, and The first Time estimation The time pattern coefficients and their covariance at time t. Let be the covariance matrix of the process noise; (4b) By right time Measured strain of a fiber optic strain sensor Make an estimate, and through The estimated value calculate Response to all situations at any moment : 。 7. The method according to claim 6, characterized in that, The estimated value described in step (4b) The calculation formula is: 。 8. The method according to claim 6, characterized in that, The steps for achieving the aircraft intelligent skin damage identification result described in step (5) are as follows: (5a) Strain values ​​across the entire field Normalization is performed, and the strain field after normalization is used. The Middle , Normalized strain at mesh nodes , Calculate the first Line number List a grid node strain gradient : ； ； in, , For the whole field of response The maximum and minimum values ​​in , These are the grid nodes along the length direction. , The coordinates; (5b) Determine the strain gradient With the normalized strain gradient Does it meet the requirements? If so, then there is damage at that node; otherwise, there is no damage.

9. The method according to claim 8, characterized in that, The total normalized strain gradient described in step (5b) The calculation formula is: 。

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