A one-way CFRP ultrasonic wave field prediction method based on a physically informed neural network

Abstract

The application discloses a one-way CFRP ultrasonic wave field prediction method based on a physically informed neural network, so as to realize meshless wave field simulation and prediction. First, the two-dimensional elastic wave differential equation of the isotropic plane or anisotropic plane of the one-way stacked carbon fiber reinforced resin matrix composite (CFRP) and the Helmholtz decomposition theory are used to derive the longitudinal wave and transverse wave component field expression. Secondly, two physically informed neural networks based on a full connection neural network are constructed, the two-dimensional elastic wave differential equation of the composite material and the longitudinal and transverse wave component fields at two early time points are introduced as loss terms of the physically informed neural network (PINN), and are used for predicting ultrasonic wave fields at different time points, respectively. The application is verified through finite element simulation, and the result shows that the PINN predicted wave field result is consistent with the finite element simulation result, and the error is not more than 1.5*10 ‑3 .

Description

Technical Field

[0001] This invention relates to the field of ultrasonic testing of carbon fiber composites, and in particular to a method for predicting the ultrasonic field of unidirectional carbon fiber reinforced polymer (CFRP) based on a physical-informed neural network. Background Technology

[0002] Traditional machine learning processes are primarily data-driven, with models relying on large amounts of high-quality data. However, in practical applications, problems such as data scarcity or noise within the data are frequently encountered. In such cases, simply using data-driven models to obtain accurate and reliable predictions is insufficient.

[0003] Physical Information Neural Networks (PINNs) incorporate physical knowledge as prior knowledge to overcome the limitations of insufficient data. In situations with limited data, PINNs can provide physically intuitive predictions using physical laws. Most studies have shown that using PINNs to solve partial differential equations can improve the efficiency of solving differential equations. Its basic principle is to incorporate the equations and boundary conditions into the loss function. For example, Shukla et al. used PINNs based on acoustic wave equations to estimate the sound velocity of a metal plate. They then determined the location of the plate fracture by analyzing the location of the sound velocity reduction and used an adaptive activation function to accelerate the convergence speed. For wave equations with multi-scale propagation and oscillation characteristics, Moseley et al. used PINNs to solve wave fields in various complex medium models. The results show that PINNs can predict wave fields at arbitrary points in space and time without calculating the entire wave field, thus significantly reducing the time required for numerical simulations. PINNs can also predict acoustic wave fields in anisotropic media and complex structures.

[0004] In summary, trained PINNs demonstrate high efficiency and accuracy in predicting acoustic wave propagation. However, composite materials are anisotropic media, and the propagation of elastic waves is influenced by five independent elastic constants, increasing complexity. The main challenges of physically-informed neural networks in predicting CFRP wave fields are: firstly, ultrasound in solids includes both longitudinal and transverse waves. However, due to the anisotropy of carbon fiber composites, it is difficult to embed the physical laws governing the propagation of longitudinal and transverse waves into PINNs to predict the wave fields of both types of waves. Secondly, the relatively short length of high-frequency ultrasound waves increases the model complexity and training time of PINNs. Summary of the Invention

[0005] The purpose of this application is to solve one of the above problems by providing an improved method for predicting unidirectional CFRP ultrasonic fields.

[0006] To achieve the above objectives, some embodiments of the present invention provide a method for predicting the ultrasonic field of unidirectional CFRP based on a physically informed neural network. The unidirectional carbon fiber reinforced resin matrix composite (CFRP) laminate is defined with the x-axis of the coordinate system defined as perpendicular to the carbon fibers; the y-axis as along the thickness of the laminate; and the z-axis as parallel to the carbon fibers. The thickness of the unidirectional CFRP laminate is H, and its density is ρ. The method includes the following steps: placing an ultrasonic piezoelectric transducer at a preset position on the surface of the unidirectional CFRP laminate, and collecting data at preset first and second time intervals. The data includes ultrasonic field data; a first elastic stiffness matrix comprising five independent elastic constants is established for the isotropic plane of the unidirectional CFRP composite plate; the xy plane of the unidirectional CFRP laminate is defined as the isotropic plane, and a two-dimensional elastic wave differential equation for the isotropic plane is defined based on the first elastic stiffness matrix and the displacement vector in the xy plane, serving as the first two-dimensional elastic wave differential equation; according to Helmholtz decomposition theory, the vector wave field of the elastic wave is separated using curl and divergence operators to obtain the longitudinal wave field P(x,y,t) and the transverse wave field S(x,y,t): Therefore, the scalar displacement field U(x,y,t) at a certain moment can be expressed as: For the xy plane, a first physical information neural network (PINNs) and a second physical information neural network are constructed based on a fully connected feedforward neural network. Both the first and second physical information neural networks take the coordinates (x, y) on the xy plane and the time variable t as inputs, and their outputs are u, respectively. x (x,y,t) and u y (x,y,t); In the first physical information neural network and the second physical information neural network, the output of the l-th layer is represented as: H(x l-1 )=σ(w l x l-1 +b l ), where σ is the activation function: and Let represent the weights and biases of the l-th layer, respectively, while the input layer has no weights and biases. The first two-dimensional elastic wave differential equation and the first initial condition are used to calculate the first, second, and third residual terms in the loss functions of the first and second physical information neural networks. The first, second, and third residual terms are combined with the products of the weight coefficients of each residual term to obtain the isotropic total loss function Loss1. Based on this isotropic total loss function Loss1, the deviation between the neural network's predicted value and the true solution is measured. The isotropic total loss function Loss1 is minimized by updating the weight coefficients and the deviation in each iteration. Before the loss error is less than a threshold or the number of iterations exceeds a set value, the training of the first and second PINNs is terminated by minimizing the isotropic loss function, thereby obtaining various output results.

[0007] In some embodiments, the first residual term C1, the second residual term C2, and the third residual term C3 are defined as follows:

[0008]

[0009] Wherein, the subscript "o" represents the actual displacement field or measurement signal, and the subscript "p" represents the first prediction result obtained through the first physical information neural network and the second physical information neural network; wherein, the first residual term C1 is derived from the first two-dimensional elastic wave differential equation; the second residual term C2 is based on the longitudinal wave component field P determined by the first early time t1 and the second early time t2 in finite element simulation. o (x,y,t) is derived; the third residual term C3 is based on the shear wave component field S of the first early time t1 and the second early time t2. o (x,y,t) is derived.

[0010] In some embodiments, the second two-dimensional elastic wave differential equation is: an isotropic total loss function Loss1 is obtained by combining the root mean square error (MSE) with each residual term; the deviation between the predicted value and the true solution of the physical information neural network is measured based on the isotropic total loss function Loss1, wherein the total loss function Loss1 = λ PDE1 MSE PDE +λ PW1 MSE PW +λ SW1 MSE SW , where λ PDE1 λ is the weighting coefficient for the first residual; PW2 λ is the weighting coefficient for the second residual. SW3 The weighting coefficient for the third residual is given.

[0011] In some embodiments, the transducer that emits ultrasonic waves is positioned at a preset location T(a). s ,0), where a s The x-coordinate represents the center position of the transducer.

[0012] In some embodiments, the unidirectional CFRP composite plate is a transversely isotropic medium, which has five independent elastic constants (Ci, C ...) in Voigt. 11 C 13 C 33 C 44 and C 66 The first elastic stiffness matrix C is represented by ).

[0013] In some embodiments, the first initial condition is a transient pressure boundary condition.

[0014] The beneficial effects of this invention include: firstly, it proposes a meshless ultrasonic field simulation and prediction method for the forward modeling problem of ultrasonic wave propagation in unidirectional carbon fiber composite laminates; secondly, it improves the efficiency of physically informed neural networks in predicting wave fields by utilizing Helmholtz decomposition theory to separate the wave field. Attached Figure Description

[0015] Figure 1a This is a schematic diagram of a unidirectional CFRP isotropic plane according to an embodiment of this application;

[0016] Figure 1b This is a schematic diagram of a unidirectional CFRP anisotropic plane according to an embodiment of this application;

[0017] Figure 2a A diagram showing the received signals of the transducer in an isotropic plane according to an embodiment of this application;

[0018] Figure 2b A diagram showing the signal received by a first transducer in an isotropic plane according to an embodiment of this application;

[0019] Figure 2c This is a snapshot of the wavefield at t = 0.5 μs;

[0020] Figure 3 This is a schematic diagram illustrating the change of the loss function with increasing training iterations in the case of an isotropic plane according to an embodiment of the application;

[0021] Figure 4a A comparison diagram of the actual wave field of the isotropic plane and the predicted wave field of PINNs according to an embodiment of this application;

[0022] Figure 4b for Figure 4aA schematic diagram of the comparison results;

[0023] Figure 5a A diagram showing the received signals of all transducers in an anisotropic plane according to an embodiment of this application;

[0024] Figure 5b A diagram showing the signal received by a first transducer in an anisotropic plane according to an embodiment of this application;

[0025] Figure 5c This is a snapshot of the wavefield at t = 0.5 μs;

[0026] Figure 6a A comparison diagram of the actual wave field of an anisotropic plane and the predicted wave field of PINNs according to an embodiment of this application;

[0027] Figure 6b for Figure 6a Comparison results in the figure.

[0028] Figure 7 This is a flowchart of a unidirectional CFRP ultrasonic field prediction method based on a physically informed neural network according to an embodiment of this application. Detailed Implementation

[0029] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0030] This invention provides a unidirectional CFRP ultrasonic field prediction method based on Physically Informed Neural Networks (PINNs). To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the method of this invention is further described in detail below. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0031] Example 1: An anisotropic CFRP ultrasonic field prediction method based on a physically informed neural network.

[0032] According to one embodiment of this application, the unidirectional CFRP ultrasonic field prediction method based on a physically informed neural network is as follows: Figure 7As shown, the method includes the following steps: defining the unidirectional carbon fiber reinforced resin matrix composite (CFRP) laminate, defining the x-axis of the coordinate system as the direction perpendicular to the carbon fiber; the y-axis as the direction along the thickness of the laminate, and the z-axis as the direction parallel to the carbon fiber; the thickness of the unidirectional CFRP laminate is H, and the density is ρ; placing an ultrasonic piezoelectric transducer at a preset position on the surface of the unidirectional CFRP laminate, and acquiring actual ultrasonic field data at preset first and second times; establishing a first elastic stiffness matrix including multiple independent elastic constants for the isotropic plane of the unidirectional CFRP composite plate; defining the xy plane of the unidirectional CFRP laminate as the isotropic plane, and defining a two-dimensional elastic wave wave differential equation for the isotropic plane based on the first elastic stiffness matrix and the displacement vector in the xy plane, as the first two-dimensional elastic wave wave differential equation; according to the Helmholtz decomposition theory, using curl and divergence operators to separate the vector wave field of the elastic wave to obtain the longitudinal wave field P(x,y,t) and the transverse wave field S(x,y,t): Therefore, the scalar displacement field U(x,y,t) at a certain moment can be expressed as:

[0033] For the xy plane, a first physical information neural network (PINNs) and a second physical information neural network are constructed based on a fully connected feedforward neural network. Both the first and second physical information neural networks take the coordinates (x, y) on the xy plane and the time variable t as inputs, and their outputs are u, respectively. x (x,y,t) and u y (x,y,t);

[0034] In the first physical information neural network and the second physical information neural network, the output of the l-th layer is represented as: H(x) l-1 )=σ(w l x l-1 +b l ), where σ is the activation function: and These represent the weights and biases of the l-th layer, respectively, while the input layer has no weights and biases.

[0035] The first two-dimensional elastic wave differential equation and the first initial conditions are used to calculate the first residual term, the second residual term, and the third residual term in the loss function of the first physical information neural network and the second physical information neural network:

[0036]

[0037] Wherein, the subscript "o" represents the actual displacement field or measurement signal, and the subscript "p" represents the first prediction result obtained through the first physical information neural network and the second physical information neural network; wherein, the first residual term C1 is derived from the first two-dimensional elastic wave differential equation; the second residual term C2 is based on the longitudinal wave component field P determined by the first early time t1 and the second early time t2 in finite element simulation. o (x,y,t) is derived; the third residual term C3 is based on the shear wave component field S of the first early time t1 and the second early time t2. o (x,y,t) is derived;

[0038] The isotropic total loss function Loss1 is obtained by combining the products of the first residual term, the second residual term, and the third residual term with the weight coefficients of each residual term. Based on this isotropic total loss function Loss1, the deviation between the neural network prediction value and the true solution is measured.

[0039] The isotropic total loss function Loss1 is minimized by updating the weight coefficients and the bias in each iteration; before the loss error is less than the threshold or the number of iterations exceeds the set value, the training of PINNs is terminated by minimizing the isotropic loss function, thereby obtaining various output results.

[0040] In the above method, the isotropic total loss function Loss1 can be obtained by combining the root mean square error (MSE) with each residual term. Based on the isotropic total loss function Loss1, the deviation between the predicted value and the true solution of the physical information neural network is measured, where the total loss function Loss1 = λ. PDE1 MSE PDE +λ PW1 MSE PW +λ SW1 MSE SW Among them, the residual loss term λ in the first elastic differential equation PDE1 The weighting coefficient for the first residual; the shear wave wavelength snapshot residual loss term λ PW2 The weighting coefficient for the second residual; the longitudinal wave wavelength snapshot residual loss term λ SW3 The weighting coefficient for the third residual is given.

[0041] In the above method, the preset position is T(a) s ,0), where a s for.

[0042] In the above method, the transverse isotropic properties of the unidirectional CFRP composite plate are represented by five independent elastic constants (Ci, Ci, Ci) in Voigt. 11 C 13C 33 C 44 and C 66 The first elastic stiffness matrix C is represented as 6×6, as shown below:

[0043]

[0044] In the above method, the first initial condition is a transient pressure boundary condition.

[0045] Example 2: An anisotropic CFRP ultrasonic field prediction method based on a physically-informed neural network. Another embodiment of this application proposes a unidirectional CFRP ultrasonic field prediction method based on a physically-informed neural network, including the following steps:

[0046] Step 1: For a unidirectional CFRP laminate, define the x-axis of the coordinate system as perpendicular to the carbon fibers. The y-axis is along the thickness of the laminate, and the z-axis is parallel to the carbon fibers; the thickness of the unidirectional CFRP laminate is H, and the density is ρ; place an ultrasonic piezoelectric transducer on the surface of the unidirectional CFRP laminate at position T(a). s ,0); Unidirectional CFRP composites have a second elastic stiffness matrix in the longitudinal direction.

[0047] The yz plane of a unidirectional CFRP laminate is an anisotropic plane. The two-dimensional elastic wave differential equation for the yz plane is defined as the second two-dimensional elastic wave differential equation, which is:

[0048]

[0049] Where u y and u z It is a displacement vector.

[0050] Step 2: For the body wave of the elastic wave, two waveforms, qP wave (quasi-longitudinal wave) and qSV wave (quasi-transverse wave), are displayed on a two-dimensional plane; according to the Helmholtz decomposition theory, the vector wave field of the elastic wave is separated using curl and divergence operators to obtain the longitudinal wave field P(x,y,t) and the transverse wave field S(x,y,t):

[0051] The scalar displacement field U(x,y,t) at a certain moment can be expressed as:

[0052] Step 3: For the yz plane, construct a first physical information neural network and a second physical information neural network based on a fully connected feedforward neural network. Both the first and second physical information neural networks take the yz coordinates (y,z) and the time variable t as inputs, and their outputs are u, respectively. y(y,z,t) and u z (y,z,t);

[0053] In the first physical information neural network and the second physical information neural network, the output of the l-th layer can be represented as: H(x) l-1 )=σ(w l x l-1 +b l ); where σ is the activation function: and These represent the weights and biases of the l-th layer, respectively, while the input layer has no weights and biases.

[0054] Step 4: Transform the fourth residual term C4, the fifth residual term C5, and the sixth residual term C6 in the second two-dimensional elastic wave differential equation and the second initial condition PINNs loss function:

[0055]

[0056] Wherein, the subscript "o" represents the actual displacement field or measurement signal, and "p" represents the prediction result obtained through the first PINNs and the second PINNs; the fourth residual term C4 is derived from the second elastic wave differential equation; the fifth residual term C5 is the longitudinal wave component field P determined by the first early time t1 and the second early time t2 in finite element simulation. o (y,z,t) constitutes the sixth residual term C6, which is the shear wave component field S at the first early time t1 and the second early time t2. o Composed of (y,z,t);

[0057] The anisotropic total loss function Loss2 is obtained by combining the fourth, fifth, and sixth residual terms with the weight coefficients of each residual term. The deviation between the predicted value and the true solution is measured based on the anisotropic total loss function Loss2.

[0058] The anisotropic loss function Loss2 is minimized by updating the weight coefficients and the bias in each iteration; the training of PINNs is terminated by minimizing the anisotropic loss function before the loss error is less than the threshold or the number of iterations exceeds the set value, thereby obtaining various output results.

[0059] In this embodiment, the second elastic stiffness matrix of the yz plane is obtained by performing a Bond transformation.

[0060] Experimental example:

[0061] The unidirectional carbon fiber composite laminate model in this embodiment is as follows: A two-dimensional plane strain finite element model of the unidirectional CFRP plate was established using the solid mechanics module in COMSOL Multiphysics 5.6. For example... Figure 1a , Figure 1b As shown, for a unidirectional CFRP laminate, the x-axis of the coordinate system is defined as perpendicular to the carbon fiber. The y-axis is along the thickness of the laminate, and the z-axis is parallel to the carbon fiber. A linear array of sensors consisting of N sensor elements is placed on the surface of a CFRP laminate of thickness H. These sensor elements are arranged at equal intervals of d. The center coordinates of the sensor elements are R. i (a i ,0){i=1,2,3,…,N}, where one of the sensor array elements T(a s (0) are the transmitting and receiving sensors, where a s This represents the x-coordinate of the center position of the sensor element (i.e., the transducer). This transmitting and receiving sensor acts as a transmitting transducer, emitting ultrasonic signals into the CFRP laminate, while N sensor elements act as receivers, receiving the signals. The CFRP laminate consists of eight layers, with a width of 5 mm, a thickness of 0.2 mm, and a density of 1494 kg / m³. 3 Therefore, an isotropic plane model of CFRP, i.e., an xy-plane model, was established, as follows: Figure 1a The model shown is an anisotropic plane model, i.e., the yz plane model, as shown below. Figure 1b The model is shown.

[0062] For an isotropic plane, i.e., an xy-plane model, the first elastic stiffness matrix in the material properties of a two-dimensional model input into COMSOL Multiphysics 5.6 (COMSOL for short) for finite element simulation is:

[0063]

[0064] For an anisotropic plane, i.e., the yz plane model, due to the observation coordinates (x, z) of the two-dimensional plane in COMSOL... c ,y c Since there is a difference between the constitutive coordinates (y, z), the Bond transformation method can be used to transform the second elastic stiffness matrix in the yz plane, and then the yz plane model can be simulated using finite element methods. The second elastic stiffness matrix in the longitudinal direction is as follows:

[0065]

[0066] In the above finite element simulation, a 5mm wide matching layer can be placed near each model boundary to reduce the influence of ultrasonic wave reflection from the model boundary. It is assumed that adjacent layers of the carbon fiber composite laminate are fully bonded at the interface. Transient pressure boundary conditions are applied in the thickness direction to simulate ultrasonic signal excitation. The ultrasonic signal is emitted by a linear sensor array (see Table 1), which consists of 16 sensor elements along the upper boundary of the CFRP. A transient pressure boundary condition is applied in the thickness direction to simulate ultrasonic signal excitation. This signal is a Hanning window modulated signal with a center frequency of 5MHz and a period of 2.5. The center position of the emitting sensor element is (2.4mm, 0mm).

[0067] Table 1: Parameters of linear arrays.

[0068]

[0069] The total acquisition time for the longitudinal displacement components obtained through the solid mechanics module in COMSOL is 2 μs. When the 9th transducer (T9) is used as the transmitting transducer, the signals received by all transducers are as follows: Figure 2a As shown, the signal received by the first receiving transducer (R1) is as follows: Figure 2b As shown. This indicates that two waveforms were received. Since the carbon fiber laminates are unidirectionally stacked, there is no structural noise caused by interlayer reflection and refraction, and the qP wave group velocity in the xy plane (isotropic plane) remains constant as the propagation direction changes. Therefore, as... Figure 2c As shown, at t = 0.5 μs, the wave field distribution is circular.

[0070] Wavefield prediction is performed using two PINNs, with the coefficients of each loss term being the residual loss term λ of the differential equation. PDE =0.1, residual loss term λ of P-wave field snapshot PW =1, residual loss term λ of shear wave field snapshot SW =0. The Adam optimizer is an improved version of stochastic gradient descent with a learning rate of 10. -4 In this network structure, the elastic constants in the first elastic stiffness matrix Cxy are introduced into the first elastic wave wave differential equation, and only two fully connected feedforward neural networks are constructed, namely the first fully connected feedforward neural network N1(w1,b1) and the second fully connected feedforward neural network N2(w2,b2), without using observation data. Each of the fully connected feedforward neural networks has four hidden layers containing 50 neurons. Figure 3 The error in the loss term of the first elastic differential equation changes with the number of training cycles. After 80,000 training cycles, the error gradually becomes constant, where PDE1 represents R. PDE1 PDE2 represents R PDE2PW1 represents R PW1 PW2 represents R PW2 The simulated qP wavefield at three time points and the wavefield predicted by PINNs are shown below. Figure 4a , Figure 4b As shown. Their root mean square errors (MSE) are 3.12 × 10⁻⁶. -4 3.10×10 -4 and 1.10×10 -3 .

[0071] For positive wave propagation in the yz plane, the second elastic stiffness matrix is ​​input into COMSOL, similar to the steps described earlier for the xy plane case. The longitudinal displacement signal received at the center position of the 16 receiving sensors is as follows: Figure 5a As shown. Figure 5b The first array element is shown in the center. The signal received by T9-R1 shows both qP and qSV waves. Figure 2c The qP wave field in the xy plane is different. Figure 5c The separation of the qP and qSV wave components in the mid-yz plane is not fully achieved. The waveform profile resembles an ellipse, indicating that the sound velocity distribution varies with the propagation direction.

[0072] The provided network structure and weights for each loss term are the same as those in the xy-plane described above. At this point, the true and predicted values ​​of the wavefield and their errors are as follows: Figure 6a , Figure 6b As shown, compared to the prediction results in the xy plane, the anisotropy of ultrasound makes the separation of qP and qSV waves using Helmholtz decomposition theory less effective, increasing the difficulty of deep learning. Their mean square errors are 9.01 × 10⁻⁶. -4 8.49×10 -4 and 1.5×10 -3 .

[0073] Therefore, the proposed unidirectional CFRP ultrasonic field prediction method based on a physically informed neural network can achieve meshless wavefield calculation. By constructing a fully connected feedforward neural network and performing deep learning, the weights and offsets of the network structure can be transferred to large structures, thereby greatly improving the efficiency of wavefield calculation.

[0074] For any parts not described in this invention, existing technologies can be used or referenced. Of course, the above description is not intended to limit the invention, nor is it limited to the examples given above. Any changes, modifications, additions, or substitutions made by those skilled in the art within the scope of this invention should also be considered within the protection scope of this invention.

Claims

1. A method for predicting the ultrasonic field of unidirectional CFRP based on a physical-informed neural network, wherein the unidirectional CFRP is a unidirectional carbon fiber reinforced resin matrix composite (CFRP) laminate, the x-axis of the coordinate system is defined as the direction perpendicular to the carbon fiber; the y-axis is the direction along the thickness of the laminate, and the z-axis is the direction parallel to the carbon fiber; the thickness of the unidirectional CFRP laminate is H, and the density is ρ; the method includes the following steps: An ultrasonic piezoelectric transducer is placed at a preset position on the surface of the unidirectional CFRP laminate, and actual ultrasonic field data are collected at a preset first time and a preset second time. Establish a first elastic stiffness matrix comprising five independent elastic constants in the isotropic plane of the unidirectional CFRP laminate; The xy plane of the unidirectional CFRP laminate is defined as the isotropic plane. Based on the first elastic stiffness matrix and the displacement vector in the xy plane, a two-dimensional elastic wave wave differential equation for the isotropic plane is defined as the first two-dimensional elastic wave wave differential equation. According to the Helmholtz decomposition theory, the vector wave field of the elastic wave is separated using curl and divergence operators to obtain the longitudinal wave field P(x, y, t) and the transverse wave field S(x, y, t): ； Therefore, the scalar displacement field U(x, y, t) at a certain moment can be expressed as: ; For the xy plane, a first physical information neural network (PINNs) and a second physical information neural network are constructed based on a fully connected feedforward neural network. Both the first and second physical information neural networks take the coordinates (x, y) on the xy plane and the time variable t as inputs, and their outputs are respectively... and ; In the first physical information neural network and the second physical information neural network, the output of the l-th layer is represented as follows: ,in For activation function: , and These represent the weights and biases of the l-th layer, respectively, while the input layer has no weights and biases. The first two-dimensional elastic wave differential equation and the first initial conditions are used to calculate the first residual term C1, the second residual term C2, and the third residual term C3 in the loss functions of the first physical information neural network and the second physical information neural network: The isotropic total loss function Loss1 is obtained by combining the product of the first residual term C1, the second residual term C2 and the third residual term C3 with the weight coefficient of each residual term. Based on this isotropic total loss function Loss1, the deviation between the neural network prediction value and the true solution is measured. The isotropic total loss function Loss1 is minimized by updating the weight coefficients and the bias in each iteration; before the loss error is less than the threshold or the number of iterations exceeds the set value, the training of the first and second PINNs is terminated by minimizing the isotropic loss function, thereby obtaining various output results.

2. The method according to claim 1, characterized in that, The first residual term C1, the second residual term C2, and the third residual term C3 are defined as follows: ； Wherein, the subscript "o" represents the actual displacement field or measurement signal, and the subscript "p" represents the first prediction result obtained through the first physical information neural network and the second physical information neural network; wherein, the first residual term C1 is derived from the first two-dimensional elastic wave wave differential equation; the second residual term C2 is based on the longitudinal wave component field P determined by the first early time t1 and the second early time t2 in finite element simulation. o (x, y, t) is derived; the third residual term C3 is based on the shear wave component field S of the first early time t1 and the second early time t2. o (x, y, t) is derived.

3. The method according to claim 1, characterized in that, The second two-dimensional elastic wave differential equation is as follows: Based on the root mean square error (MSE) and each residual term, an isotropic total loss function Loss1 is obtained. Based on this isotropic total loss function Loss1, the deviation between the predicted value and the true solution of the physical information neural network is measured. The total loss function... ,in, The weighting coefficient of the first residual term; The weighting coefficient for the second residual term; The weighting coefficient for the third residual term.

4. The method according to claim 1, characterized in that, The transducer that emits ultrasonic waves is preset to a position T(a). s ,0), where a s The x-coordinate represents the center position of the transducer.

5. The method according to claim 1, characterized in that, The unidirectional CFRP laminate is a transversely isotropic medium, and its elastic constants (Ci, C ...) are defined by five independent elastic constants in Voigt. 11 C 13 C 33 C 44 and C 66 The first elastic stiffness matrix C of the matrix is ​​represented as 6×6, as shown below: 。 6. The method according to claim 1, characterized in that, The first initial condition is a transient pressure boundary condition.

7. A method for predicting unidirectional CFRP ultrasonic fields based on a physically-informed neural network, characterized in that: Includes the following steps: For a unidirectional CFRP laminate, the x-axis of the coordinate system is defined as the direction perpendicular to the carbon fiber; the y-axis is along the thickness of the laminate; and the z-axis is parallel to the carbon fiber. The thickness of the unidirectional CFRP laminate is H, and the density is ρ. An ultrasonic piezoelectric transducer is placed at a predetermined position on the surface of the unidirectional CFRP laminate, the position being T(a). s ,0), collect actual ultrasonic field data at the preset first and second time; Establish a second elastic stiffness matrix comprising five independent elastic constants for the anisotropic plane of the unidirectional CFRP laminate; The yz plane of the unidirectional CFRP laminate is defined as the anisotropic plane, and the two-dimensional elastic wave differential equation of the yz plane is defined as the second two-dimensional elastic wave differential equation, which is: in and It is a displacement vector; For the body wave of the elastic wave, two waveforms are displayed on a two-dimensional plane: qP wave (quasi-longitudinal wave) and qSV wave (quasi-transverse wave). According to the Helmholtz decomposition theory, the vector wave field of the elastic wave is separated using curl and divergence operators to obtain the longitudinal wave field P(y, z, t) and the transverse wave field S(y, z, t): ; The scalar displacement field U(y, z, t) at a certain moment can be expressed as: ; For the yz plane, a first physical information neural network and a second physical information neural network based on a fully connected feedforward neural network are constructed. Both the first and second physical information neural networks take the yz coordinates (y, z) and the time variable t as inputs, and their outputs are respectively... and ; In the first physical information neural network and the second physical information neural network, the output of the l-th layer can be represented as: ,in For activation function: , and These represent the weights and biases of the l-th layer, respectively, while the input layer has no weights and biases. The fourth residual term C4, the fifth residual term C5, and the sixth residual term C6 in the second two-dimensional elastic wave differential equation and the second initial condition PINNs loss function are: ; ; ； Wherein, the subscript "o" represents the actual displacement field or measurement signal, and "p" represents the prediction result obtained through the first PINNs and the second PINNs; the fourth residual term C4 is derived from the second two-dimensional elastic wave differential equation; the fifth residual term C5 is the longitudinal wave component field P determined by the first early time t1 and the second early time t2 in finite element simulation. o (y, z, t) constitutes the sixth residual term C6, which is the shear wave component field S at the first early time t1 and the second early time t2. o It is composed of (y, z, t); The anisotropic total loss function Loss2 is obtained by combining the fourth residual term C4, the fifth residual term C5, and the sixth residual term C5 with the weight coefficients of each residual term. The deviation between the predicted value and the true solution is measured based on the anisotropic total loss function Loss2. The anisotropic loss function Loss2 is minimized by updating the weight coefficients and the bias in each iteration; before the loss error is less than the threshold or the number of iterations exceeds the set value, the training of the first and second PINNs is terminated by minimizing the anisotropic loss function, thereby obtaining various output results.

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