A method for monitoring elastic modulus of composite materials based on deep learning

Abstract

The present invention discloses a method for monitoring the elastic modulus of composite materials based on deep learning, which is characterized by using a deep neural network to establish a complex relationship between the dispersion curve of guided waves propagating in the composite material and the elastic modulus of the composite material, thereby realizing accurate detection of the elastic constant of the composite material. At the same time, the method proposes to use a semi-analytical finite element method improved by a spectral element method to generate a relevant data set for training the neural network. The method can be applied to industrial facilities, aerospace equipment, etc., to realize rapid ultrasonic non-destructive detection of the elastic properties of composite materials.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering acoustics, and in particular to a method for monitoring the elastic modulus of a composite material based on deep learning. Background Art

[0002] Composite materials are becoming more and more common in engineering and aerospace due to their light weight and excellent structural performance. However, composite materials may be impacted during use, which may lead to a decrease in their mechanical properties. Therefore, non-destructive testing (NDT) and structural health monitoring (SHM) of composite materials have become a widely discussed issue. Most techniques require prior knowledge of the elastic properties of the material. However, due to the anisotropy of the lamination and elastic properties of composite materials, it is always difficult to characterize the elastic properties of composite materials. The complex relationship between the dispersion curve of guided waves propagating in composite materials and the elastic modulus of composite materials is difficult to express with a specific mathematical relationship. In addition, the uncertainty of the composite material manufacturing process, the presence of material impurities, and the degradation of material properties over time during use make it so that composite materials can only be monitored through online non-invasive detection technology of elastic property changes. Therefore, non-invasive non-destructive testing technology for identifying the elastic properties of composite materials is of great significance for quantitatively determining the elastic properties of composite structures. Summary of the invention

[0003] The purpose of the present invention is to provide a method for detecting elastic constants of composite materials based on deep neural networks to address the defects of the prior art. The method can be applied to industrial facilities, aerospace equipment, etc. to achieve rapid ultrasonic nondestructive testing of elastic properties of composite materials.

[0004] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0005] A method for monitoring elastic modulus of composite materials based on deep learning, characterized in that it comprises the following steps:

[0006] Step 10: Based on the elastic properties of the composite material, including density, thickness, orientation of reinforcing fibers, number of stacked layers, and elastic constants, a data set suitable for deep neural network training is constructed using the semi-analytical finite element method;

[0007] Step 20: In the composite material structure to be tested, an actuator and a sensor are arranged to transmit and receive the guided wave signal;

[0008] Step 30: reconstruct the waveguide signals transmitted and received in step 20 by using a two-dimensional Fourier transform (2D-FFT) to obtain a waveguide dispersion curve of the composite material to be tested;

[0009] Step 40: Train a deep neural network using the data set described in step 10;

[0010] Step 50: Input the waveguide dispersion curve reconstructed in step 30 into the deep neural network trained in step 40 to obtain the elastic modulus of the material to be tested.

[0011] Furthermore, the step of constructing a data set suitable for deep neural network training using the semi-analytical finite element method in step 10 is:

[0012] Step 11: Model the composite material to be tested and establish a global Cartesian coordinate system, where the axis x is parallel to the thickness direction and the reinforcing fibers are set at an angle θ relative to the axis z. Assume that the elastic modulus is independent of the frequency variable and viscoelasticity is not considered here. Since the direction of each layer is described as a rotation angle θ relative to the axis z, the elastic modulus is

[0013]

[0014] in

[0015] s=sin(θ), c=cos(θ), C 12 =C 21 , C 13 =C 31 , C 23 =C 32

[0016] Step 12: Introduce the arbitrary propagation angle of the guided wave into the guided wave number vector k,

[0017]

[0018] Where k represents the wave number, β represents the wave propagation angle, and represents the direction unit vector,

[0019] Introducing a one-dimensional spectral element, the displacement u at a point (x, y, z) within the unit is written as:

[0020]

[0021] in is the finite element shape function, d (e) is the nodal displacement, ω is the angular frequency, e is the element label,

[0022] Thus, the strain tensor ε in the unit is obtained,

[0023] ε=[B1-jk y B2-jk z B3]d (e)exp[j(ωt+ksin(β)y-kcos(β)z)]

[0024] Where: B1 = L x N x ,B2=L y N,B3=L z N, N x is the derivative of N in the x direction, k y , k z represents the components of the wave number in the y and z directions, and n is the number of nodes in the unit;

[0025] Step 13: Element elastic modulus matrix and the element mass matrix m e Respectively expressed as:

[0026]

[0027] m e =∫ρN T Nx

[0028] Where ρ represents the material density, the overall governing equation is rewritten in linear form:

[0029] [A-γB]V=0where

[0030]

[0031] V = [d γd] T

[0032] Where γ = jk, s′ = sin(β), c′ = cos(β), K is the cumulative elastic modulus matrix, and M is the cumulative mass matrix;

[0033] Step 14: The overall control equation is used to study the elastic modulus of the composite material through the elastic modulus matrix, and is numerically solved to construct a theoretical phase velocity dispersion curve of the multilayer composite material at each frequency and a data set for deep neural network training.

[0034] Furthermore, the deep neural network includes several convolutional neural layer CNN blocks and a fully connected layer FCN block, the number of CNN blocks depends on the size of the data set, each CNN block contains multiple one-dimensional convolutional neural layers 1D-CNN and a maximum pooling layer, and the FCN block contains multiple FCN layers.

[0035] Furthermore, the process of training the deep neural network in step 40 includes the FCN block identifying all waveguide dispersion curve features extracted by the CNN block after the flattening operation, and outputting the required elastic modulus.

[0036] Furthermore, the deep neural network structure includes three CNN blocks and one FCN block, the CNN block has only one convolutional layer, the CNN block selects three types of convolution kernels with sizes of 3×3, 5×5 and 7×7, the number of filters of the CNN block is set to 16, 32 and 64, and the first layer of the FCN block has 64 kernels.

[0037] Compared with the prior art, the beneficial effects of the present invention are: 1. It has very high accuracy, is extremely convenient to use, has low cost, and is very suitable for industrial applications; 2. The present invention applies deep neural networks to composite material detection, which is an important way to monitor the elastic modulus of composite materials in real time; 3. This method can be applied to industrial facilities, aerospace equipment, etc., for ultrasonic non-destructive evaluation and structural health monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the steps of the present invention;

[0039] Figure 2 This is a structural diagram of the deep neural network of the present invention;

[0040] Figure 3 Figure 1. Modeling diagram of composite materials in semi-analytical finite element method;

[0041] Figure 4 This is a graph of the training results of a deep neural network;

[0042] Figure 5 This is a diagram of the test results of a numerical simulation demonstration using the present invention. DETAILED DESCRIPTION

[0043] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings. The embodiments are only used to explain the present invention and do not constitute a limitation on the protection scope of the present invention.

[0044] like Figure 1 As shown, a specific embodiment of a method for monitoring elastic modulus of a composite material based on deep learning comprises the following steps:

[0045] Step 10: Based on the elastic properties of the composite material, including density, thickness, orientation of reinforcing fibers, number of stacked layers, and elastic constants, a data set suitable for deep neural network training is constructed using the semi-analytical finite element method;

[0046] Step 20: In the composite material structure to be tested, an actuator and a sensor are arranged to transmit and receive the guided wave signal;

[0047] Step 30: reconstruct the waveguide signals transmitted and received in step 20 by using a two-dimensional Fourier transform (2D-FFT) to obtain a waveguide dispersion curve of the composite material to be tested;

[0048] Step 40: Train a deep neural network using the data set in step 10;

[0049] Step 50: Input the waveguide dispersion curve reconstructed in step 30 into the deep neural network trained in step 40 to obtain the elastic modulus of the material to be tested.

[0050] Preferably, the step of constructing a data set suitable for deep neural network training using the semi-analytical finite element method in step 10 is:

[0051] Step 11: Model the composite material to be tested and establish a global Cartesian coordinate system, where the axis x is parallel to the thickness direction and the reinforcing fibers are set at an angle θ relative to the axis z. Assume that the elastic modulus is independent of the frequency variable and viscoelasticity is not considered here. Since the direction of each layer is described as a rotation angle θ relative to the axis z, the elastic modulus is

[0052]

[0053] in

[0054] s=sin(θ), c=cos(θ), C 12 =C 21 , C 13 =C 31 , C 23 =C 32 ,

[0055] therefore, The 9 independent coefficients in can represent the elastic modulus of the orthotropic linear elastic material.

[0056] Step 12: In contrast to isotropic materials, guided wave propagation in anisotropic materials is more complicated because the propagation angle affects the guided wave properties such as directional velocity, wave attenuation, etc. In general, the arbitrary propagation angle of the guided wave is introduced into the guided wave number vector k to obtain,

[0057]

[0058] Where k represents the wave number, β represents the wave propagation angle, and represents the direction unit vector,

[0059] Introducing a one-dimensional spectral element, the displacement u at a point (x, y, z) within the unit is written as:

[0060]

[0061] in is the finite element shape function, d (e) is the nodal displacement, ω is the angular frequency, e is the element label,

[0062] d (e) =[u x，1 ,u y，1 ,u z，1 ...u x,n ,u y，n ,u z，n ] T

[0063] u x，n represents the x-direction displacement component at node n, u y , n represents the y-direction displacement component at node n, u z,n represents the z-direction displacement component at node n, thus obtaining the strain tensor ε in the element,

[0064] ε=[B1-jk y B2-jk z B3]d (e) exp[j(ωt+ksin(β)y-kcos(β)z)]

[0065] Where: B1 = L x N x , B2=L y N,B3=L z N, N x is the derivative of N in the x direction, k y , k z represents the components of the wave number in the y and z directions, and n is the number of nodes in the unit;

[0066] Step 13: Element elastic modulus matrix and the element mass matrix m e Respectively expressed as:

[0067]

[0068] m e =∫ρN T Nx

[0069] Where ρ represents the material density,

[0070] Rewrite the overall governing equation into linear form:

[0071] [A-γB]V=0

[0072] in

[0073]

[0074] V = [d γd] T

[0075] Where γ = jk, s′ = sin(β), c′ = cos(β), K is the cumulative elastic modulus matrix, and M is the cumulative mass matrix;

[0076] Step 14: The overall control equation is used to study the elastic modulus of the composite material through the elastic modulus matrix, and is numerically solved to construct a theoretical phase velocity dispersion curve of the multilayer composite material at each frequency and a data set for deep neural network training.

[0077] The deep neural network of this embodiment includes three convolutional neural layer CNN blocks and a fully connected layer FCN block, each CNN block contains several one-dimensional convolutional neural layers 1D-CNN and a maximum pooling layer Max pooling, and the FCN block contains several FCN layers. After the maximum pooling layer is added to the 1D-CNN layer, it contains three functions: reducing feature size, reducing feature invariance and preventing overfitting, which will significantly reduce the number of parameters in the neural network, thereby reducing training time. Then, after the feature extraction is completed by 1D-CNN, FCN is used for regression, which simulates the relationship between the extracted features and the label set (i.e., the elastic modulus of the material). Therefore, FCN takes into account the features extracted from the guided wave dispersion curve and outputs the elastic modulus of the material. This process is called the training phase of the neural network, which will obtain a well-trained neural network model to predict the elastic modulus of the material by inputting experimentally reconstructed dispersion curve samples A0 and S0. The process of training the deep neural network in step 40 includes that the FCN block will identify all the guided wave dispersion curve features extracted by the CNN block after the flattening operation, and output the required elastic modulus. The CNN block has only one convolutional layer. The CNN block selects three types of convolution kernels with sizes of 3×3, 5×5, and 7×7. Such a multi-scale set also enhances the robustness of the neural network to environmental noise. The number of filters of the CNN block is set to 16, 32, and 64. The first layer of the FCN block has 64 kernels, followed by activations of LReLU and Dropout. The second layer with 9 kernels and linear activation is used to output the target elastic modulus.

[0078] A finite element (FE) model of the composite structure was established in COMSOL to verify the feasibility of the method of this embodiment. Each layer of the composite laminate was connected together using a two-dimensional plane strain model, and each layer was modeled separately.

[0079]

[0080] Table 1

[0081] Table 1 shows the elastic modulus and density of the composite laminate used (real values). The model is used to simulate the generation of two signals received from the deployed piezoelectric actuator. The piezoelectric elements are connected to the composite laminate through linear elastic thin layer conditions. Each piezoelectric element is 5 mm long, 250 μm thick and made of PZT-5A. In general, the accuracy of the numerical model depends on the temporal and spatial resolution of the analysis. The node spacing in the composite laminate model is set to ensure that there are at least 10 nodes on the minimum wavelength and the element growth rate is 1.25. For the time step resolution, the highest frequency is set to at least 20 points per cycle.

[0082] The mean square loss function (MSE) is used as the loss function, and R 2 Coefficient is used to evaluate the performance of the neural network algorithm. The smaller the loss, the better the R 2 The closer the value of the coefficient is to 1, the better the performance of the neural network algorithm. In addition, Adam with adaptive learning rate is used for optimization, which is a small batch stochastic gradient descent optimization algorithm based on first-order gradient. The hyperparameters of Adam are set to: α = 0.001, β1 = 0.9, β2 = 0.999. We use the semi-analytical finite element method to generate 6000 samples, and the results of training the neural network are as follows Figure 4 As shown in Figure 2, it is found that after sufficient training, the closer the loss value is to 0, the smaller the R 2 The closer the coefficient is to 1, the better the performance of the established neural network model. The test results of composite materials using this neural network are as follows: Figure 5 As shown, the predicted value of the elastic modulus of the composite laminate obtained by using the neural network is very close to the true value, which shows that the result is satisfactory.

[0083] The above specific implementation methods are only for illustrating the technical concept and structural features of the present invention, and the purpose is to enable relevant persons familiar with this technology to implement it. However, the above content does not limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for monitoring elastic modulus of composite materials based on deep learning, characterized in that: The steps include: Step 10: Based on the elastic properties of the composite material, including density, thickness, orientation of reinforcing fibers, number of stacked layers, and elastic constants, a data set suitable for deep neural network training is constructed using the semi-analytical finite element method. The specific steps are as follows: Step 11: Model the composite material to be tested and establish a global Cartesian coordinate system, where the axis x is parallel to the thickness direction and the reinforcing fibers are set at an angle θ relative to the axis z. Assume that the elastic modulus is independent of the frequency variable and viscoelasticity is not considered here. Since the direction of each layer is described as a rotation angle θ relative to the axis z, the elastic modulus is in s=sin(θ), c=cos(θ), C 12 =C 21 ,C 13 =C 31 ,C 23 =C 32 Step 12: Introduce the arbitrary propagation angle of the guided wave into the guided wave number vector k, Where k represents the wave number, β represents the wave propagation angle, and represents the direction unit vector, Introducing a one-dimensional spectral element, the displacement u at a point (x, y, z) within the unit is written as: in is the finite element shape function, d (e) is the nodal displacement, ω is the angular frequency, e is the element label, Thus, the strain tensor ε in the unit is obtained, ε=[B1-jk y B2-jk z B3]d (e) exp[j(ωt+ksin(β)y-kcos(β)z)] Where: B1 = L x N x ,B2=L y N,B3=L z N, N x is the derivative of N in the x direction, k y , k z represents the components of the wave number in the y and z directions, and n is the number of nodes in the unit; Step 13: Element elastic modulus matrix and the element mass matrix m e Respectively expressed as: me e =∫ρN T Ndx Where ρ represents the material density, Rewrite the overall governing equation into linear form: [A-γB]V=0 in V=[d γd] T Where γ = jk, s′ = sin(β), c′ = cos(β), K is the cumulative elastic modulus matrix, and M is the cumulative mass matrix; Step 14: The overall control equation is used to study the elastic modulus of the composite material through the elastic modulus matrix, and numerically solves it to construct a theoretical phase velocity dispersion curve of the multilayer composite material at each frequency and a data set for deep neural network training; Step 20: In the composite material structure to be tested, an actuator and a sensor are arranged to transmit and receive the guided wave signal; Step 30: reconstruct the waveguide signals transmitted and received in step 20 by using a two-dimensional Fourier transform (2D-FFT) to obtain a waveguide dispersion curve of the composite material to be tested; Step 40: Train a deep neural network using the data set described in step 10; Step 50: Input the waveguide dispersion curve reconstructed in step 30 into the deep neural network trained in step 40 to obtain the elastic modulus of the material to be tested.

2. The method for monitoring elastic modulus of composite materials based on deep learning according to claim 1, characterized in that: The deep neural network includes several convolutional neural layer CNN blocks and a fully connected layer FCN block. The number of CNN blocks depends on the size of the data set. Each CNN block contains multiple one-dimensional convolutional neural layers 1D-CNN and a maximum pooling layer, and the FCN block contains multiple FCN layers.

3. The method for monitoring elastic modulus of composite materials based on deep learning according to claim 2, characterized in that: The process of training the deep neural network in step 40 includes the FCN block identifying all the guided wave dispersion curve features extracted by the CNN block after the flattening operation, and outputting the required elastic modulus.

4. The method for monitoring elastic modulus of composite materials based on deep learning according to claim 3, characterized in that: The deep neural network structure includes three CNN blocks and one FCN block. The CNN block has only one convolutional layer. The CNN block selects three types of convolution kernels with sizes of 3×3, 5×5 and 7×7, respectively. The number of filters of the CNN block is set to 16, 32 and 64, and the first layer of the FCN block has 64 kernels.

Images