Unidirectional CFRP ultrasonic field prediction method based on physical informed neural network

Abstract

The invention discloses a one-way CFRP ultrasonic wave field prediction method based on a physical informed neural network, so as to realize non-gridding wave field simulation and prediction. The method comprises the following steps: firstly, deriving a longitudinal wave and transverse wave component field expression by utilizing a two-dimensional elastic wave fluctuation differential equation and a Helmholtz decomposition theory of an isotropic surface or an anisotropic surface of a unidirectional stacked carbon fiber reinforced resin matrix composite (CFRP); secondly, constructing two physical informed neural networks based on a full-connection neural network, introducing a two-dimensional elastic wave fluctuation differential equation of a composite material and two longitudinal and transverse wave component fields at early moments as loss items of the physical informed neural networks (PINNs), and respectively predicting ultrasonic wave fields at different moments; verification is carried out through finite element simulation, the result shows that the PINNs wave field prediction result is consistent with the finite element simulation result, and the error does not exceed 1.5 * 10 <-3 >.

Description

Technical Field

[0001] The present invention relates to the field of ultrasonic testing of carbon fiber composite materials, and particularly to a method for predicting ultrasonic wave fields of unidirectional carbon fiber reinforced polymer (CFRP) based on physics-informed neural networks. Background Art

[0002] Traditional machine learning processes are mainly data-driven, and their models rely on a large amount of high-quality data. However, in practical applications, problems such as scarce data or noise in the data are often encountered. In such cases, it is not accurate enough to only use data-driven models to obtain accurate and reliable prediction results.

[0003] Physics-informed neural networks (PINNs) introduce physical knowledge as prior knowledge, aiming to overcome the limitation of insufficient data. In the case of limited data, PINNs can use physical laws to provide predictions with physical intuition. 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 introduce the equation and boundary conditions into the loss function. For example, Shukla et al. used PINNs based on the acoustic wave equation to estimate the sound speed of a metal plate. Then, they determined the location of the fracture of the metal plate by analyzing the position where the sound speed decreased, 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 the wave fields in various complex medium models. The results showed that PINNs can predict the wave fields at arbitrary spatio-temporal points without calculating the entire wave field, thus greatly shortening the time required for numerical simulation. PINNs can also predict the acoustic wave fields of anisotropic media and complex structures.

[0004] In summary, trained PINNs have shown high efficiency and accuracy in predicting acoustic wave propagation. However, composite materials are anisotropic media, and the propagation of elastic waves is affected by five independent elastic constants, which increases the complexity. The main challenges of physics-informed neural networks in predicting the CFRP wave field are: on the one hand, ultrasonic waves in solids include longitudinal waves and transverse waves. However, due to the anisotropy of carbon fiber composite materials, it is difficult to embed the physical laws of longitudinal wave and transverse wave propagation into PINNs to predict the wave fields of these two waves. On the other hand, due to the small wavelength of high-frequency ultrasonic waves, it increases the model complexity and training time of PINNs. Summary of the Invention

[0005] An object of the present application is to solve one of the above problems, and provides an improved method for predicting the ultrasonic wave field of unidirectional CFRP.

[0006] To achieve the above object, some embodiments of the present invention provide a method for predicting the ultrasonic field of unidirectional CFRP based on a physics-informed neural network. For the 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: Place an ultrasonic piezoelectric transducer at a preset position on the surface of the unidirectional CFRP laminate, and collect actual ultrasonic field data at a preset first time and second time; Establish a first elastic stiffness matrix including five independent elastic constants for the isotropic plane of the unidirectional CFRP composite plate; Define the xy plane of the unidirectional CFRP laminate as the isotropic plane, and define the two-dimensional elastic wave wave differential equation of 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, use the 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): Thus, express the scalar displacement field U(x, y, t) at a certain moment as: For the xy plane, construct a first physics-informed neural network (PINNs) and a second physics-informed neural network based on a fully connected feedforward neural network. Both the first physics-informed neural network and the second physics-informed neural network take the coordinates (x, y) and the time variable t on the xy plane as inputs, and the outputs are u x (x, y, t) and u y (x, y, t); In the first physics-informed neural network and the second physics-informed neural network, the output result of the l-th layer is expressed as: H(x l-1 ) = σ(w l x l-1 + b l ), where σ is the activation function: and They respectively represent the weights and biases of the l-th layer, and there are no weights and biases in the input layer; the first two-dimensional elastic wave differential equation and the first initial condition are used to calculate the first residual term, the second residual term, and the third residual term in the loss functions of the first physics-informed neural network and the second physics-informed neural network: the first residual term, the second residual term, and the third residual term are combined with the products of the weight coefficients of the respective residual terms to obtain the isotropic total loss function Loss1, and the deviation between the neural network prediction value and the true solution is measured based on this isotropic total loss function Loss1; the isotropic total loss function Loss1 is minimized by updating the respective weight coefficients and the deviation 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, so as to obtain 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:

[0008]

[0009] where the subscript "o" represents the actual displacement field or the measured signal, and the subscript "p" represents the first prediction result obtained through the first physics-informed neural network and the second physics-informed neural network; among them, the first residual term C1 is derived from the first two-dimensional elastic wave differential equation; the second residual term C2 is derived based on the longitudinal wave component field P o (x, y, t) at the first early time t1 and the second early time t2 determined by finite element simulation; the third residual term C3 is derived based on the transverse wave component field S o (x, y, t) at the first early time t1 and the second early time t2.

[0010] In some embodiments, the second two-dimensional elastic wave differential equation is: according to the root mean square error (MSE), combined with the respective residual terms to obtain the isotropic total loss function Loss1, and the deviation between the prediction value of the physics-informed neural network and the true solution is measured based on the isotropic total loss function Loss1, where the total loss function Loss1 = λ PDE1 MSE PDE + λ PW1 MSE PW + λ SW1 MSE SW , where λ PDE1 is the weight coefficient of the first residual quantity; λ PW2 is the weight coefficient of the second residual quantity; λ SW3 is the weight coefficient of the third residual quantity.

[0011] In some embodiments, the preset position of the transducer that emits ultrasonic waves is T(a s ,0), where a s is the abscissa of the center position of the transducer.

[0012] In some embodiments, the unidirectional CFRP composite plate is a transversely isotropic medium, and is represented by the first elastic stiffness matrix C with 5 independent elastic constants (C 11 , C 13 , C 33 , C 44 and C 66 ) in Voigt.

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

[0014] The beneficial effects of the present invention include: on the one hand, the present invention proposes a meshless ultrasonic field simulation and prediction method for the forward problem of ultrasonic wave propagation in unidirectional carbon fiber composite laminates. On the other hand, the present invention separates the wave field by using the Helmholtz decomposition theory, improving the efficiency of the physics-informed neural network in predicting the wave field. Description of the Drawings

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

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

[0017] Figure 2a is the transducer reception signal diagram of the isotropic plane according to an embodiment of the present application;

[0018] Figure 2b is the first transducer reception signal diagram of the isotropic plane according to an embodiment of the present application;

[0019] Figure 2c is the wave field snapshot diagram at t = 0.5 μs;

[0020] Figure 3 is a schematic diagram of the change of the loss function with the increase of the number of training times in the case of the isotropic plane according to an embodiment of the present application;

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

[0022] Figure 4b is Figure 4aSchematic diagram of comparison results;

[0023] Figure 5a Received signal diagram of all anisotropic planar transducers according to an embodiment of the present application;

[0024] Figure 5b Received signal diagram of the first transducer of the anisotropic plane according to an embodiment of the present application;

[0025] Figure 5c Snapshot diagram of the wave field at t = 0.5 μs;

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

[0027] Figure 6b For Figure 6a Comparison result diagram in

[0028] Figure 7 Flow chart of the unidirectional CFRP ultrasonic wave field prediction method based on physics-informed neural network according to an embodiment of the present application. Detailed implementation manners

[0029] The technical solutions in the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0030] The present invention provides a unidirectional CFRP ultrasonic wave field prediction method based on physics-informed neural network (PINNs). To make the objectives, technical solutions and effects of the present invention clearer and more definite, the method of the present invention is further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0031] Embodiment 1: Anisotropic CFRP ultrasonic wave field prediction method based on physics-informed neural network.

[0032] According to an embodiment of the present application, the unidirectional CFRP ultrasonic wave field prediction method based on physics-informed neural network is as 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 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; placing an ultrasonic piezoelectric transducer at a preset position on the surface of the unidirectional CFRP laminate, collecting actual ultrasonic field data at a preset first time and second time; establishing a first elastic stiffness matrix of the isotropic plane of the unidirectional CFRP composite plate including a plurality of independent elastic constants; defining the xy plane of the unidirectional CFRP laminate as the isotropic plane, and defining a two-dimensional elastic wave wave differential equation of 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 the 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): Thus, the scalar displacement field U(x, y, t) at a certain moment is expressed as:

[0033] For the xy plane, constructing a first physics-informed neural network (PINNs) and a second physics-informed neural network based on a fully connected feedforward neural network, both the first physics-informed neural network and the second physics-informed neural network take the coordinates (x, y) and the time variable t on the xy plane as inputs, and the outputs are u x (x, y, t) and u y (x, y, t);

[0034] In the first physics-informed neural network and the second physics-informed neural network, the output result of the l-th layer is expressed as: H(x l-1 ) = σ(w l x l-1 + b l ), where σ is the activation function: and respectively represent the weight and bias of the l-th layer, and the input layer has no weight and bias;

[0035] Using the first two-dimensional elastic wave wave differential equation and the first initial condition to calculate the first residual term, the second residual term and the third residual term in the loss functions of the first physics-informed neural network and the second physics-informed neural network:

[0036]

[0037] Among them, the subscript "o" represents the actual displacement field or measurement signal, and the subscript "p" represents the first prediction result obtained by the first physics-informed neural network and the second physics-informed neural network; among them, the first residual term C1 is derived from the first two-dimensional elastic wave wave differential equation; the second residual term C2 is derived from the longitudinal wave component field P o (x, y, t) at the first early time t1 and the second early time t2 determined by finite element simulation; the third residual term C3 is derived from the transverse wave component field S o (x, y, t) at the first early time t1 and the second early time t2;

[0038] Combining the first residual term, the second residual term, and the third residual term with the product of the weight coefficients of each residual term to obtain the isotropic total loss function Loss1, and measuring the deviation between the neural network prediction value and the true solution based on the isotropic total loss function Loss1;

[0039] Minimize the isotropic total loss function Loss1 by updating the weight coefficients and the deviation at each iteration; before the loss error is less than the threshold or the number of iterations exceeds the set value, terminate the training of PINNs by minimizing the isotropic loss function, so as to obtain various output results.

[0040] In the above method, the root mean square error (MSE) can be combined with each residual term to obtain the isotropic total loss function Loss1, and the deviation between the predicted value of the physics-informed neural network and the true solution is measured based on the isotropic total loss function Loss1, where the total loss function Loss1 = λ PDE1 MSE PDE + λ PW1 MSE PW + λ SW1 MSE SW , where the first elastic differential equation residual loss term λ PDE1 is the weight coefficient of the first residual quantity; the transverse wave wavelength snapshot residual loss term λ PW2 is the weight coefficient of the second residual quantity; the longitudinal wave wavelength snapshot residual loss term λ SW3 is the weight coefficient of the third residual quantity.

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

[0042] In the above method, the transverse isotropy performance of the unidirectional CFRP composite plate is represented by 5 independent elastic constants (C 11 , C 13, C 33 , C 44 and C 66 )'s first elastic stiffness matrix C is expressed as a 6×6 matrix as follows:

[0043]

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

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

[0046] Step 1: For a unidirectional CFRP laminate, define the x-axis of the coordinate system 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 plate is H and the density is ρ; place an ultrasonic piezoelectric transducer on the surface of the unidirectional CFRP laminate, and its position is T(a s , 0); the unidirectional CFRP composite material has a longitudinal second elastic stiffness matrix.

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

[0048]

[0049] where u y and u z are displacement vectors.

[0050] Step 2: For the body waves of the elastic waves, two waveforms, qP wave (quasi-longitudinal wave) and qSV wave (quasi-transverse wave), are shown on the two-dimensional plane; according to the Helmholtz decomposition theory, use the curl and divergence operators to separate the vector wave field of the elastic waves 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 physics-informed neural network and a second physics-informed neural network based on a fully connected feedforward neural network. Both the first physics-informed neural network and the second physics-informed neural network take the yz coordinates (y, z) and the time variable t as inputs, and the outputs are u y(y, z, t) and u z (y, z, t);

[0053] In the first physics-informed neural network and the second physics-informed neural network, the output result of the l-th layer can be expressed as: H(x l-1 ) = σ(w l x l-1 + b l ); where σ is the activation function: and represent the weight and bias of the l-th layer respectively, and the input layer has no weight and bias;

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

[0055]

[0056] where 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 wave differential equation; the fifth residual term C5 is composed of the longitudinal wave component fields P o (y, z, t) at the first early time t1 and the second early time t2 determined by finite element simulation; the sixth residual term C6 is composed of the transverse wave component fields S o (y, z, t) at the first early time t1 and the second early time t2;

[0057] Combine the product of the fourth residual term, the fifth residual term, and the sixth residual term with the weight coefficients of the respective residual terms to obtain the anisotropic total loss function Loss2, and measure the deviation between the predicted value and the true solution based on this anisotropic total loss function Loss2;

[0058] Minimize the anisotropic loss function Loss2 by updating the respective weight coefficients and the deviation at each iteration; before the loss error is less than the threshold or the number of iterations exceeds the set value, terminate the training of PINNs by minimizing the anisotropic loss function to obtain various output results.

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

[0060] Experimental example:

[0061] The unidirectional carbon fiber composite laminate model in this embodiment is as follows: Using the solid mechanics module in COMSOL Multiphysics 5.6, a two-dimensional plane strain finite element model of a unidirectional CFRP plate was established. As Figure 1a , Figure 1b shown, 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 the direction along the thickness of the laminate, and the z-axis is the direction parallel to the carbon fiber. A linear sensor array consisting of N sensor elements is placed on the surface of the CFRP plate with a thickness of H. These sensor elements are arranged at equal intervals with a spacing of d. The central coordinates of the sensor elements are R i (a i , 0) {i = 1, 2, 3, …, N}, where one sensor element T(a s , 0) is the transmitting and receiving sensor, where a s is the abscissa of the center position of this sensor element (i.e., transducer). This transmitting and receiving sensor acts as a transmitting transducer to emit ultrasonic signals into the CFRP laminate, and the N sensor elements act as receivers to receive 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 / m 3 . Thus, an isotropic plane model of CFRP, i.e., the xy plane model, is established, as shown in the model of Figure 1a , and an anisotropic plane model, i.e., the yz plane model, as shown in the model of Figure 1b .

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

[0063]

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

[0065]

[0066] In the above finite element simulation, a matching layer with a width of 5 mm can be set near each model boundary to reduce the influence of ultrasonic wave reflection at the model boundary. It is assumed that the adjacent layers of the carbon fiber composite laminate are completely bonded at the interface. Transient pressure boundary conditions are applied in the thickness direction to simulate the excitation of ultrasonic signals. The ultrasonic signals are emitted by a linear array of sensors, as shown in Table 1. The linear array of sensors consists of 16 sensor elements along the upper boundary of the CFRP. Transient pressure boundary conditions are applied in the thickness direction to simulate the excitation of ultrasonic signals. The signal is a Hann window modulated signal with a center frequency of 5 MHz and a period of 2.5. The center position of the sensor element for emission is (2.4 mm, 0 mm).

[0067] Table 1: Parameters of the linear array.

[0068]

[0069] The total acquisition time of the longitudinal displacement component 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 shown in Figure 2a while the signal received by the first receiving transducer (R1) is as shown in Figure 2b This indicates that two waveforms are received. Since the carbon fiber laminate is 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 unchanged as the propagation direction changes. Therefore, as shown in Figure 2c at t = 0.5 μs, the wave field distribution is circular.

[0070] Two PINNs are used for wave field prediction. The coefficients of each loss term are the differential equation residual loss term λ PDE = 0.1, the longitudinal wave field snapshot residual loss term λ PW = 1, and the transverse wave field snapshot residual loss term λ 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 four hidden layers in each fully connected feedforward neural network contains 50 neurons. Figure 3 For the change of the loss term error in the first elastic differential equation with the increase of the number of training epochs, after 80,000 training epochs, the error gradually becomes constant, where PDE1 represents R PDE1 and PDE2 represents R PDE2, PW1 represents R PW1 , PW2 represents R PW2 . The qP wave fields at three moments obtained by simulation and the wave field results predicted by PINNs are as shown in Figure 4a 、 Figure 4b . Their root mean square errors (MSE) are 3.12×10 -4 、3.10×10 -4 and 1.10×10 -3 .

[0071] For forward wave propagation in the yz plane, the second elastic stiffness matrix is input into COMSOL, which is similar to the steps in the xy plane case described previously. The longitudinal displacement signals received at the central positions of 16 receiving sensors are as shown in Figure 5a . Figure 5b is the first array element, and the signal received by T9 - R1. It can be seen that qP wave and qSV wave signals are received. Different from the qP wave field in the xy plane in Figure 2c , the separation of qP wave and qSV wave components in the yz plane in Figure 5c is not fully achieved. The waveform profile is similar to an ellipse, indicating that the sound speed distribution varies with the propagation direction.

[0072] The network structure and the weights of each loss term provided are the same as those in the above - mentioned xy plane. At this time, the true values and predicted values of the wave field and their errors are as shown in Figure 6a 、 Figure 6b . Compared with the prediction results in the xy plane, due to the influence of anisotropy on ultrasonic waves, the effect of separating qP waves and qSV waves using Helmholtz decomposition theory is not good, increasing the difficulty of deep learning. Their mean square errors are 9.01×10 -4 、8.49×10 -4 and 1.5×10 -3 .

[0073] Therefore, using a method for predicting the unidirectional CFRP ultrasonic wave field based on a physics - informed neural network proposed by the present invention, mesh - free wave field calculation can be realized. By constructing a fully - connected feed - forward neural network, after deep learning, the weights and biases of the network structure can be transferred by migration learning to large - scale structures, thus greatly improving the efficiency of wave field calculation.

[0074] Parts not described in the present invention can be implemented by adopting or referring to existing technologies. Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions, or substitutions made by those skilled in the art within the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A unidirectional CFRP ultrasonic field prediction method based on a physics-informed neural network, wherein the unidirectional carbon fiber reinforced resin-based 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 comprises the following steps: placing an ultrasonic piezoelectric transducer at a preset position on the surface of the unidirectional CFRP laminate, and collecting actual ultrasonic field data at a preset first time and a preset second time; Establishing a first elastic stiffness matrix including five independent elastic constants of an isotropic plane of the unidirectional CFRP composite plate; defining an xy plane of the unidirectional CFRP laminate as the isotropic plane, and defining a two-dimensional elastic wave differential equation of the isotropic plane based on the first elastic stiffness matrix and the displacement vector in the xy plane as a first two-dimensional elastic wave differential equation; According to the Helmholtz decomposition theory, the curl and divergence operators are used to separate the vector wave field of elastic waves 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 is expressed as: For the xy plane, a first physical information neural network (PINNs) and a second physical information neural network based on a fully connected feedforward neural network are constructed. The first physical information neural network and the second physical information neural network both take the coordinates (x, y) on the xy plane and the time variable t as input, and the outputs are u 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 result of the lth layer is expressed as: H(x l-1 )=σ(w l x l-1 +b l ), where σ is the activation function: and Represent the weight and bias of the lth layer respectively, while the input layer has no weight and bias; The first two-dimensional elastic wave differential equation and the first initial condition are used to calculate the first residual term C1, the second residual term C2 and the third residual term C3 in the loss function of the first physical information neural network and the second physical information neural network: Combining the first residual term C1, the second residual term C2 and the third residual term C3 with the product of the weight coefficients of the residual terms to obtain an isotropic total loss function Loss1, and measuring the deviation between the neural network prediction value and the true solution based on the isotropic total loss function Loss1; The isotropic total loss function Loss1 is minimized by updating the weight coefficients and the deviations of 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.

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: Wherein, the subscript "o" represents the actual displacement field or the measurement signal, and the subscript "p" represents the first prediction result obtained by 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 at the first early time t1 and the second early time t2 determined by finite element simulation o (x, y, t); 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: according to the root mean square error (MSE) combined with each residual term to obtain the isotropic total loss function Loss1, based on the isotropic total loss function Loss1 to measure the deviation between the predicted value of the physical information neural network and the true solution, wherein the total loss function Loss1 = λ PDE1 MSE PDE +λ PW1 MSE PW +λ SW1 MSE SW , where λ PDE1 is the weight coefficient of the first residual; PW2 is the weight coefficient of the second residual; SW3 is the weight coefficient of the third residual.

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

5. The method according to claim 1, characterized in that The unidirectional CFRP composite plate is a transversely isotropic medium, and the Voigt method has five independent elastic constants (C 11 , C 13 , C 33 , C 44 and C 66 ) is represented by the first elastic stiffness matrix C, which is expressed 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 unidirectional CFRP ultrasonic field prediction method based on a physically informed neural network, characterized in that: The following steps are involved: 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 plate is H, and the density is ρ; An ultrasonic piezoelectric transducer is placed at a preset position on the surface of the unidirectional CFRP laminate, and its position is T(a s ,0), collect actual ultrasonic field data at the preset first time and second time; Establishing a second elastic stiffness matrix including five independent elastic constants in the anisotropic plane of the unidirectional CFRP composite plate; 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, and the second two-dimensional elastic wave differential equation is: where u y and u z is the displacement vector; 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 by using the 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. The first physical information neural network and the second physical information neural network both take the yz coordinate (y, z) and the time variable t as input, and the outputs are u y (y,z,t) and u z (y,z,t); In the first physical information neural network and the second physical information neural network, the output result of the lth layer can be expressed as: H(x l-1 )=σ(w l x l-1 +b l ), where σ is the activation function: and Represent the weight and bias of the lth layer respectively, while the input layer has no weight and bias; 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 the measurement signal, "p" represents the prediction result obtained by 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 at the first early time t1 and the second early time t2 determined by the finite element simulation o (y, z, t); the sixth residual term C6 is the shear wave component field S of the first early time t1 and the second early time t2 o (y,z,t); Combining the fourth residual term C4, the fifth residual term C5 and the sixth residual term C5 with the product of the weight coefficients of the residual terms to obtain an anisotropic total loss function Loss2, and measuring the deviation between the predicted value and the true solution based on the anisotropic total loss function Loss2; The anisotropic loss function Loss2 is minimized by updating the weight coefficients and the deviations of 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 anisotropic loss function, thereby obtaining various output results.

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