S0 Lamb wave scattering sound field solving method based on physical constraint enhanced TransUNet

Abstract

The invention discloses an S0 Lamb wave scattering sound field solving method based on physical constraint enhanced TransUNet. The method comprises the following steps: acquiring a global scattering sound field in an out-of-plane direction after an S0 Lamb wave passes through an irregular defect; performing data processing on the global scattering sound field, and establishing a scattering sound field data set; constructing an S0 Lamb wave scattering sound field prediction model adopting a TransUNet network, dividing a scattering sound field data set into a training set and a test set, and sequentially performing data driving training and physical constraint training on the S0 Lamb wave scattering sound field prediction model by utilizing the training set until training is completed; and inputting thickness distribution of a to-be-tested plate structure containing defects in the test set into the trained S0 Lamb wave scattering sound field prediction model to obtain a predicted scattering sound field with irregular defects, further obtaining a scattering time domain signal and a scattering far field amplitude result, and completing solving of the scattering sound field of the S0 Lamb waves. The invention provides an innovative method for solving the scattering sound field of the irregular defect S0 Lamb wave in the plate.

Description

Technical Field

[0001] The present invention relates to the technical field of guided wave nondestructive testing and structural health monitoring, and in particular to a method for solving the S0 Lamb wave scattering acoustic field. Background Art

[0002] In guided wave nondestructive testing research, scattering refers to the process by which the propagation path and characteristics of guided waves change when they encounter discontinuities, defects, or changes in geometric features in a structure. It is a crucial research topic in nondestructive testing. By analyzing scattered waves, key information about structural defects, material properties, and stress distribution can be obtained, thereby enabling health monitoring and safety assessment of the structure. Guided wave scattering research has significant advantages in the field of nondestructive testing, especially in the inspection of large and complex structures. These advantages include strong penetration, high sensitivity, strong adaptability, the ability to provide global structural information, high defect location accuracy, and high detection efficiency. Solving the guided wave scattered acoustic field can provide a more accurate theoretical basis and practical guidance for structural reliability assessment.

[0003] Solving the scattered acoustic field caused by the interaction between guided waves and defects has always been a difficult problem in the field of guided wave research. To solve the scattering problem in plate-like structures, scholars have successively developed analytical methods, numerical methods, and deep learning-based methods. The analytical method is to use Bessel functions to expand the wave field of guided waves (Lamb waves and SH waves) in the plate. Through projection, the diffusion coefficient is solved using boundary conditions such as stress and displacement. In addition, scholars have studied plate theory as an alternative method for solving scattering under low-frequency thick product conditions, using Poisson theory and Kirchhoff theory (or Mindlin theory) to approximate the propagation of Lamb waves and SH waves in plates, respectively. Other scholars have proposed the "Complex Mode Expansion of Vector Projection (CMEP)" method to solve the scattering problem of Lamb waves in plates. This method projects the stress boundary condition onto the conjugate of the displacement, and simultaneously projects the displacement boundary condition onto the conjugate of the stress, to achieve faster convergence. Although accurate and effective, the above analytical methods are too complex to be applied to regular defects such as through holes, blind holes, and steps in simple structures. They mainly focus on analyzing the amplitude of the scattered far-field signal and cannot obtain the scattered sound field including the time domain signal.

[0004] In addition to analytical methods, numerical methods such as finite element methods, boundary element methods, and hybrid methods combining finite element methods and modal expansions are also widely used in the study of scattering problems due to their ability to handle complex scatterers. However, these numerical methods all require meshing the solution domain, and there is an unavoidable trade-off between solution accuracy and computational effort. High-frequency and high-dimensional problems inevitably increase the number of meshes, making these methods more difficult to solve.

[0005] With the continuous advancement of artificial intelligence methods, deep learning has also been widely used to solve scattering problems. However, data-driven neural networks rely heavily on training datasets. A small dataset or an imbalance in the number of datasets with different labels can significantly impact the network's performance. In theory, the amount of training data required for accurate predictions increases exponentially with the dimensionality of the parameter model input. However, acquiring large datasets in real life is not always easy, which, to a certain extent, limits the application of data-driven neural networks in practical engineering problems.

[0006] In recent years, physically embedded neural networks (PINNs) and their various variants have rapidly become a research hotspot in many fields due to their outstanding performance, becoming, to a certain extent, an alternative to data-driven neural networks. PINNs combine physical constraints with data-driven approaches. Their core concept is to explicitly introduce physical constraints, such as governing equations and boundary conditions, into the neural network's loss function. This allows the network to not only fit the data but also automatically satisfy the physical constraints during training. However, there is currently a significant lack of research using this concept to solve Lamb wave scattering acoustic fields. Summary of the Invention

[0007] In response to the technical problems of existing methods such as large computational complexity, limitation to regular defects of simple structures, and over-reliance on large-scale labeled data training, the present invention combines the advantages of data-driven and physical constraints, and proposes a S0 Lamb wave scattering sound field solution method based on physics-enhanced TransUNet (PTUNet). This method combines the local feature extraction capability of UNet and the global modeling capability of Transformer, and improves the learning and prediction ability of the S0 Lamb wave scattering sound field prediction model for the spatial distribution characteristics of the scattered sound field. By introducing physical constraints, the dependence on large-scale labeled data is reduced, while ensuring that the prediction results conform to physical laws, avoiding non-physical solutions, and improving the generalization ability of the S0 Lamb wave scattering sound field prediction model, so that the scattered sound field information of irregular defects can be more accurately predicted.

[0008] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0009] A method for solving the S0 Lamb wave scattering acoustic field based on physical constraint enhanced TransUNet includes the following steps:

[0010] S1. Based on the thickness distribution of the plate structure containing irregular defects, the global scattered sound field in the off-plane direction of the S0 Lamb wave after passing through the irregular defects is obtained through forward calculation;

[0011] S2, performing spatial and temporal truncation processing on the global scattered sound field obtained in step S1, and then performing downsampling to obtain the scattered sound field, and establishing a scattered sound field dataset;

[0012] S3. Constructing an S0 Lamb wave scattered sound field prediction model, wherein the S0 Lamb wave scattered sound field prediction model adopts a TransUNet network, wherein the TransUNet network includes an encoder, a decoder, and a skip connection, wherein the skip connection is provided between the encoder and the decoder;

[0013] S4. Divide the scattered sound field data set into a training set and a test set, and use the training set to perform data-driven training and physical constraint training on the S0 Lamb wave scattered sound field prediction model in sequence to obtain a trained S0 Lamb wave scattered sound field prediction model;

[0014] S5. Inputting the thickness distribution of the defective plate structure to be tested in the test set into the trained S0 Lamb wave scattered sound field prediction model to obtain the predicted scattered sound field of the irregular defect;

[0015] S6. Based on the predicted scattered acoustic field of the irregular defect, the scattered time domain signal and the scattered far-field amplitude results are obtained, and the scattered acoustic field solution of the S0 Lamb wave is completed.

[0016] Furthermore, the method for obtaining the global scattered sound field of the S0 Lamb wave in the off-plane direction after passing through the irregular defects through forward calculation based on the thickness distribution of the plate structure containing irregular defects is as follows: a perfectly matched layer is set around the plate containing irregular defects, the plate containing irregular defects is excited by a dual-sensor symmetrical excitation method, and based on the thickness distribution of the plate structure containing irregular defects, the Kirchhoff-Love plate theory is used to solve the global scattered sound field of the S0 Lamb wave in the off-plane direction, thereby obtaining the global scattered sound field of the S0 Lamb wave in the off-plane direction after passing through the irregular defects.

[0017] Furthermore, the method for solving the global scattered sound field of the S0 Lamb wave in the off-plane direction using the Kirchhoff-Love plate theory is:

[0018] A plane rectangular coordinate system is established with the surface of the plate containing irregular defects as a reference;

[0019] The governing equations of the Kirchhoff-Love plate theory for an isotropic uniform thin plate under free vibration are expressed as:

[0020]

[0021] Where ρ is the density of the plate, h is the thickness of the plate, and D is the bending stiffness matrix of the plate. is a biharmonic operator;

[0022]

[0023] u(x,y,t) represents the out-of-plane displacement at coordinate (x,y) at time t; E represents Young's modulus, and v represents Poisson's ratio. After transformation, the intermediate parameter ζ is:

[0024]

[0025] The transformed control equation is expressed as:

[0026]

[0027] The transformed governing equations are solved to obtain the global scattering acoustic field of the S0 Lamb wave in the off-plane direction after passing through the irregular defect.

[0028] Furthermore, the method for establishing the scattered sound field data set is:

[0029] The global scattered sound field obtained in step S1 is truncated in space and time:

[0030] In terms of time, intercept t0-t e The scattered sound field inside, t0 is the time when the S0 Lamb wave reaches the irregular defect area, t e is the time when the S0 Lamb wave leaves the irregular defect area;

[0031] In space, since from t0 to t e During the propagation time, the scattered information occurs in the region of the x-coordinate range x1 to x2 and the y-coordinate range y1 to y2. Therefore, in space, the scattered sound field in the region of the x-coordinate range x1 to x2 and the y-coordinate range y1 to y2 is intercepted.

[0032] Next, let the step size in the x direction be Δx, the step size in the y direction be Δy, and the time step be Δt, and perform downsampling to obtain the scattered sound field;

[0033] Several forward calculations of random irregular defects are performed, and the global scattered sound fields obtained are truncated and downsampled. The thickness distribution of the plate structure containing irregular defects and all the scattered sound fields obtained constitute the scattered sound field data set.

[0034] Furthermore, the encoder and decoder are symmetrically connected. The encoder is composed of four identical sub-encoders connected in series, and the sub-encoder is composed of a convolutional layer I, a convolutional layer II, a Transformer block containing a multi-head attention mechanism, and a 2×2 maximum pooling layer connected in sequence; the decoder is composed of four identical sub-decoders connected in series, and the sub-decoder is composed of a 2×2 convolution upsampling layer, a cascade layer, a convolutional layer III, and a convolutional layer IV connected in sequence;

[0035] Among them, the convolution kernel size of convolution layer I, convolution layer II, convolution layer III and convolution layer IV is 3×3, and LeakyReLU is used as the activation function;

[0036] The skip connection is provided between the sub-encoder and the sub-decoder.

[0037] Furthermore, the steps of sequentially performing data-driven training and physical constraint training on the S0 Lamb wave scattering sound field prediction model using the training set include:

[0038] Setting the network parameters of the TransUNet network, including setting the thresholds I and II in the number of iterations, the learning rate, the batch size, and the weighting parameters in the composite loss function; wherein the threshold II is greater than the threshold I;

[0039] The thickness distribution of the plate structure with irregular defects in the training set is input into the S0 Lamb wave scattering acoustic field prediction model. For the thickness distribution of the i-th input, u(x i ,y i ,t i ) represents the real scattered sound field obtained by forward modeling, and u * (x i ,y i ,t i ) represents the predicted scattered sound field obtained by output;

[0040] S4.1. Determine a data-driven error. When the number of iterations does not reach a set threshold value I, iteratively train the S0 Lamb wave scattering sound field prediction model based on the data-driven error to obtain the S0 Lamb wave scattering sound field prediction model to be optimized.

[0041] S4.2. When the number of iterations reaches the set threshold I, the physical constraints corresponding to the Kirchhoff-Love plate theory are obtained using finite differences, the physical driving error is determined, and the data-driven error and the physical driving error are weighted and superimposed to train the S0 Lamb wave scattering acoustic field prediction model to be optimized;

[0042] S4.3. When the number of iterations reaches the set threshold II, stop training, save all model parameters, and obtain the trained S0Lamb wave scattering sound field prediction model.

[0043] Furthermore, the calculation expression of the data-driven error is:

[0044]

[0045] in, is the data-driven error, N D Expressed as the calculated data-driven error The space-time sampling points on the solution domain are randomly selected.

[0046] Furthermore, the calculation expression of the physical driving error is:

[0047]

[0048] Among them, N P To calculate the physical drive error The space-time sampling points on the solution domain are randomly selected.

[0049] Furthermore, for each randomly selected spatiotemporal sampling point N P , the partial derivatives are first solved by the following formula:

[0050]

[0051] Next, the physical driving error is obtained by substituting it into the calculation expression of the physical driving error.

[0052] Furthermore, when the data-driven error and the physical-driven error are weighted and superimposed, the composite loss function is expressed as:

[0053]

[0054] Where λ represents the weighting parameter.

[0055] Compared with the existing technology, the present invention has the following advantages: the present invention provides an innovative method for solving the scattered acoustic field of S0 Lamb waves caused by irregular defects in plates; the present invention fully integrates the advantages of data-driven and physical constraints, uses finite difference technology to embed the Kirchhoff-Love plate theory as a physical constraint into the network framework, and uses the Kirchhoff-Love plate theory to guide the learning process, thereby enhancing the S0 Lamb wave scattered acoustic field prediction model's ability to model the scattering mechanism and solve the scattered acoustic field of irregular defects. Compared with analytical methods, the present invention does not require complex and tedious matrix operations and has strong applicability; compared with numerical methods, the present invention eliminates the need for grid division, avoiding the dilemma between accuracy and computational complexity; compared with purely data-driven methods, the introduction of physical constraints can effectively reduce the reliance on large-scale labeled data while ensuring that the prediction results conform to the laws of physics. In addition, the embedding of physical constraints can also improve the generalization ability of the model, enabling it to more accurately predict the scattered acoustic field distribution of different defects. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 It is a flow chart of the method of the present invention.

[0058] Figure 2 It is a diagram of the plate structure parameter settings during forward modeling in an embodiment of the present invention.

[0059] Figure 3 This is a network framework and workflow diagram of the physical constraint enhanced TransUNet in one embodiment of the present invention.

[0060] Figure 4 1 is a diagram of a training loss curve and a physical constraint enhancement verification result in one embodiment of the present invention.

[0061] Figure 5 It is a random defect thickness distribution diagram on the test set in one embodiment of the present invention.

[0062] Figure 6 1 is a diagram showing the solution results of the scattered sound field in one embodiment of the present invention.

[0063] Figure 7 This is a comparison diagram of the scattered time domain signal solution and far field amplitude in one embodiment of the present invention.

[0064] Figure 8This is a diagram of the experimental platform construction in one embodiment of the present invention.

[0065] Figure 9 This is a diagram showing the experimental scattered sound field solution results in one embodiment of the present invention.

[0066] Figure 10 This is a comparison diagram of the experimental scattering time domain signal solution and the scattering far-field amplitude in one embodiment of the present invention. DETAILED DESCRIPTION

[0067] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0068] like Figure 1 As shown in the figure, a method for solving the S0 Lamb wave scattering sound field based on physical constraint enhanced TransUNet (PTUNet) is proposed. According to the thickness distribution of the plate structure with irregular defects, forward calculation is performed to obtain the global scattering sound field corresponding to the irregular defects; data processing is performed on the global scattering sound field obtained by forward modeling to establish a scattering sound field dataset; network parameters are set; when the number of iterations does not reach the set threshold I, only the data constraints are used to train the S0 Lamb wave scattering sound field prediction model; otherwise, when the number of iterations reaches the set threshold I, the physical constraints corresponding to the Kirchhoff-Love plate theory are obtained by finite differences, and the S0 Lamb wave scattering sound field prediction model is trained using the weighted superposition of data constraints and physical constraints; when the number of iterations reaches the set threshold II, the training is stopped and all model parameters are saved; otherwise, when the number of iterations does not reach the set threshold II, the weighted superposition of data constraints and physical constraints is continued to be used to train the S0 Lamb wave scattering sound field prediction model. The Lamb wave scattering acoustic field prediction model is trained. After training, the thickness distribution of the defective plate structure to be tested is input into the trained S0 Lamb wave scattering acoustic field prediction model to obtain the predicted S0 Lamb wave scattering acoustic field corresponding to the irregular defect. The predicted scattered acoustic field is processed to obtain the scattered time domain signal and the scattered far field amplitude results. The specific steps are as follows:

[0069] S1. Based on the thickness distribution of the plate structure containing irregular defects, the global scattered acoustic field in the off-plane direction after the S0 Lamb wave passes through the irregular defects is obtained through forward calculation.

[0070] In this embodiment, when performing forward calculation, the parameters of the plate structure containing irregular defects are set as follows: Figure 2 As shown, the density ρ of the aluminum plate is 2700 kg / m3 , Young's modulus E is 70.7 GPa, and Poisson's ratio ν is 0.33.

[0071] A rectangular coordinate system is established based on the surface of the aluminum plate. The center of the irregularly shaped defect with varying depths is located at (200, 400), and any boundary of the defect does not extend beyond a square with a side length of 70 mm. Different defects have different geometric shapes and remaining thickness information. For each specific defect, the remaining thickness is fixed, and the remaining thickness of all defects ranges from 0.3 mm to 1 mm.

[0072] To eliminate the effects of boundary reflections during forward modeling, a perfectly matched layer (PML) of a certain thickness is placed around the aluminum plate to absorb boundary reflections. If the PML thickness is too large, the computational complexity increases; if the PML thickness is too small, it is insufficient to completely absorb boundary reflections. In this example, a 200mm wide PML is placed around the aluminum plate to eliminate the effects of boundary reflections.

[0073] To minimize the generation of Lamb waves in other modes (A0) during excitation, this embodiment employs a dual-sensor symmetrical excitation method. To comply with the far-field assumption and reduce boundary reflections, a first piezoelectric sensor with a center frequency of 100 kHz is placed on the front of the aluminum plate at coordinates (600, 400). A second piezoelectric sensor with a center frequency of 100 kHz is placed on the back of the aluminum plate, corresponding to the front coordinates (600, 400). The first and second piezoelectric sensors are symmetrical with respect to the aluminum plate. The excitation signal with a center frequency of 100 kHz is a sine function with a Hanning window and five cycles. The time step is 1e-7 seconds, the total duration is 2.5e-4 seconds, and the grid size is 5 mm.

[0074] For plate structures containing irregular defects, the Kirchhoff-Love plate theory is used to solve the global scattered acoustic field of the S0 Lamb wave in the off-plane direction. The Kirchhoff-Love plate theory assumes that the plate maintains a constant thickness during deformation, and any line initially perpendicular to the mid-surface remains straight and vertical after deformation. The Kirchhoff-Love plate theory captures the bending behavior of the plate under small lateral loads and provides a basis for analyzing the propagation of bending waves within the structure. Because the main component of the scattered acoustic field when the S0 Lamb wave is incident on the defect and scattered, the Kirchhoff-Love plate theory can be used as a physical constraint. The governing equation of the Kirchhoff-Love plate theory for isotropic uniform thin plates under free vibration is expressed as:

[0075]

[0076] Where ρ is the density of the plate, h is the thickness of the plate, and D is the bending stiffness matrix of the plate. is a biharmonic operator;

[0077]

[0078] u(x,y,t) represents the out-of-plane displacement at coordinate (x,y) at time t; E represents Young's modulus, and v represents Poisson's ratio. After transformation, the intermediate parameter ζ is:

[0079]

[0080] Then formula (1) can be expressed as:

[0081]

[0082] By solving equation (5), we can obtain the global scattered sound field of the S0 Lamb wave in the off-plane direction after passing through the irregular defect.

[0083] S2. The global scattered sound field obtained in step S1 is truncated in space and time, and then downsampled to obtain the scattered sound field, and a scattered sound field data set is established.

[0084] After step S1, the global scattered sound field within the range of 800 mm×800 mm and the time of 250 μs is obtained.

[0085] In order to better capture useful scattering characteristics, reduce the amount of calculation, and thus solve the scattering more efficiently, the global scattered sound field data is truncated in space and time.

[0086] Specifically, in terms of time, intercept t0-t e The scattered sound field inside, t0 is the time when the S0 Lamb wave reaches the irregular defect area, t e is the time it takes for the S0 Lamb wave to leave the irregular defect area. In this embodiment, according to the dispersion curve of the guided wave in the aluminum plate, the time it takes for the S0 Lamb wave to reach the irregular defect area is 75 μs, and it leaves the irregular defect area at 175 μs. Therefore, the scattered sound field within 75 μs to 175 μs is intercepted.

[0087] From the global sound field results obtained by forward calculation, it can be seen that within the propagation time of 75μs to 175μs, the scattered information mainly occurs in the square area with the x-coordinate range of 0 to 400mm and the y-coordinate range of 200 to 600mm. Therefore, in space, the scattered sound field within the square area with the x-coordinate range of 0 to 400mm and the y-coordinate range of 200 to 600mm is intercepted.

[0088] Downsampling is then performed to reduce the amount of data, taking Δx = Δy = 4 mm, Δt = 1 μs, where Δx is the step size in the x direction, Δy is the step size in the y direction, and Δt is the time step. The final dimension of the scattered sound field data is 101 × 101 × 101, corresponding to the x, y, and t dimensions, respectively.

[0089] In this embodiment, a total of 400 forward calculations of random irregular defects are performed, and the obtained global scattered sound fields are truncated and downsampled. The thickness distribution of the plate structure containing irregular defects and all the obtained scattered sound fields constitute the scattered sound field data set.

[0090] S3. Construct an S0 Lamb wave scattered sound field prediction model, wherein the S0 Lamb wave scattered sound field prediction model adopts a TransUNet network, and the TransUNet network includes an encoder, a decoder and a jump connection.

[0091] The encoder extracts image features by gradually reducing the spatial dimensions of the input image. As the S0 Lamb wave scattering acoustic field prediction model deepens, the extracted features become more advanced and abstract. The encoder captures image features by gradually reducing the image size and increasing the number of channels.

[0092] The decoder gradually increases the size of the feature map to restore it to the spatial dimensions of the original input image. The decoder utilizes skip connections to combine low-level features from the encoder with its own high-level features, restoring image details and generating the final output. By concatenating or pixel-by-pixel adding low-level features from the encoder to high-level features from the decoder, skip connections help capture multi-scale information and improve network performance. They also mitigate the vanishing gradient problem, enhancing the training of the S0 Lamb wave scattering sound field prediction model.

[0093] like Figure 3 As shown in Figure 2, the TransUNet network combines the complementary strengths of the UNet and Transformer models to better address the multi-scale challenges in solving guided wave scattering acoustic fields. As a classic encoder-decoder architecture, the UNet excels in image segmentation and feature extraction, making it well-suited for complex wavefield reconstruction. Furthermore, the Transformer model and its self-attention mechanism effectively capture global dependencies, offering significant advantages in modeling scattered signals and enhancing the representation capabilities of guided wave scattering fields.

[0094] The present invention utilizes the local recognition capability of UNet to learn the S0 Lamb wave scattering characteristics caused by defects, and utilizes the global modeling capability of Transformer to solve the propagation of S0 Lamb waves.

[0095] like Figure 3-As shown in (a), the encoder and decoder are symmetrically connected. The encoder is composed of four identical sub-encoders connected in series. The sub-encoders are composed of convolutional layer I, convolutional layer II, a Transformer block containing a multi-head attention mechanism, and a 2×2 maximum pooling layer connected in sequence.

[0096] The decoder consists of four identical sub-decoders connected in series. Each sub-decoder consists of a 2×2 convolution upsampling layer, a cascade layer, a convolution layer III, and a convolution layer IV. The convolution kernel size of Convolution Layers I, II, III, and IV is 3×3, and LeakyReLU is used as the activation function.

[0097] Skip connections are set between the sub-encoder and sub-decoder to preserve high-resolution scatter features.

[0098] The Transformer block is able to capture the relationship between scattered features across spatiotemporal coordinates. By adding a Transformer block with a multi-head attention mechanism in the encoder, the prediction of the scattered sound field is enhanced.

[0099] S4. Divide the scattered sound field dataset into a training set and a test set in a ratio of 7:1. Use the training set to perform data-driven training and physical constraint training on the S0 Lamb wave scattered sound field prediction model in sequence to obtain a trained S0 Lamb wave scattered sound field prediction model.

[0100] like Figure 3 As shown in (b), the steps of sequentially performing data-driven training and physical constraint training on the S0 Lamb wave scattering sound field prediction model using the training set include:

[0101] The network parameters of the TransUNet network are set, including setting thresholds I and II in the number of iterations, a learning rate, a batch size, and a weighting parameter λ in the composite loss function; the threshold II is greater than the threshold I.

[0102] The thickness of the defective plate structure with a dimension of 101×101 in the training set is input into the S0 Lamb wave scattering acoustic field prediction model. After being processed by the S0 Lamb wave scattering acoustic field prediction model, a scattered acoustic field with a dimension of 101×101×101 is generated, which is represented in a square spatial domain of 400mm×400mm, with a time span of 75μs to 175μs, a spatial resolution of 4mm, and a time resolution of 1μs. For the thickness distribution of the i-th input, u(x i ,y i ,t i ) represents the real scattered sound field obtained by forward modeling, and u * (x i ,y i ,ti ) represents the predicted scattered sound field obtained by output.

[0103] S4.1. Determine the data-driven error. When the number of iterations does not reach the set threshold I, iteratively train the S0 Lamb wave scattering sound field prediction model based on the data-driven error to obtain the S0 Lamb wave scattering sound field prediction model to be optimized.

[0104] In this embodiment, the threshold value I is set to 300 times.

[0105] The calculation expression of the data-driven error is:

[0106]

[0107] in, is the data-driven error, which represents the pure data error between the predicted and actual scattered sound fields. D To calculate the data driven error The random 101×101×101 time-space sampling points on the solution domain are used. In this embodiment, all time-space sampling points in the solution domain are used to perform data-driven error Calculation.

[0108] Purely data-driven network models rely heavily on the dataset and may produce predictions that violate the laws of physics. Therefore, introducing the constraints of the Kirchhoff-Love governing equations not only retains the core advantages of data-driven learning, but also uses physical constraints as a correction to the prediction results.

[0109] S4.2. When the number of iterations reaches the set threshold I, the physical constraints corresponding to the Kirchhoff-Love plate theory are obtained using finite differences, the physical driving error is determined, and the data-driven error and the physical driving error are weighted and superimposed to train the S0 Lamb wave scattering acoustic field prediction model to be optimized.

[0110] The physical drive error The calculation expression is:

[0111]

[0112] Among them, N P For calculation The randomly selected 101×101×101 time-space sampling points in the solution domain are randomly selected. In this embodiment, 2000 points are randomly selected for each time-domain snapshot for calculation. The partial derivatives in the control equations are calculated by central finite differences, and are:

[0113]

[0114]

[0115] For each randomly selected spatiotemporal sampling point N P , the partial derivatives are solved through formulas (8) to (11), and the physical driving error is obtained by substituting them into formula (7). Then, the data driving error and the physical driving error are weighted and superimposed to train the optimized S0Lamb wave scattering sound field prediction model.

[0116] Composite loss function Expressed as:

[0117]

[0118] Here, λ represents a weighting parameter used to balance the relative magnitudes of data-driven error and physical-driven error. It should be flexibly adjusted and selected based on specific results, and the optimal value should be determined through repeated experiments. In this embodiment, the weighting parameter λ = 0.01.

[0119] S4.2. When the number of iterations reaches the set threshold II, stop training, save all model parameters, and obtain the trained S0Lamb wave scattering sound field prediction model.

[0120] In this embodiment, the threshold II is set to 800 times.

[0121] like Figure 4 The following figure shows the training loss curve and the physical constraint enhancement verification result in this embodiment. In order to evaluate the enhancement effect of physical constraints on solving the scattered sound field, the training loss and test results with and without the introduction of physical constraints are compared. Figure 4 -(a) shows the training loss curve, with a learning rate of 0.0001 and a batch size of 1. In the first 300 iterations, only data constraints are used for training. As training progresses, the loss curve begins to stabilize at the 300th iteration. At this time, 2000 points are randomly selected for each time domain snapshot to calculate the physical constraints, and a mixed loss function is formed by adding the weight of 0.01 to the data constraints, and the network training continues. Figure 4 -(a) shows that the embedding of physical constraints effectively accelerates the training process and reduces the overall training error. The training error after adding physical constraints is lower than the training error of pure data constraints.

[0122] In order to further evaluate the generalization ability of the proposed method, the relative 2-norm error l2 of the network with or without physical constraints on the test set is compared.

[0123] The relative 2-norm error l2 is calculated as follows:

[0124]

[0125] For each sample in the test set, there are 101 time-domain snapshots of the scattered sound field. The average value of the relative 2-norm error l2 of each sample over all time steps is calculated, and the result is as follows: Figure 4 (b) The test results of the TransUNet network with the added physical constraints consistently show lower errors, better scattered sound field calculation performance on the test data, and stronger generalization ability. This further verifies the effectiveness of introducing physical constraints. It not only guides the S0Lamb wave scattered sound field prediction model to adhere to physical laws and accelerate convergence, but also reduces dependence on the training dataset.

[0126] S5. Input the thickness distribution of the defective plate structure to be tested in the test set into the trained S0 Lamb wave scattered sound field prediction model to obtain the predicted scattered sound field of the irregular defect.

[0127] like Figure 5 As shown in the figure, it is a random defect thickness distribution diagram on the test set in this embodiment. After the training is completed, all model parameters are saved and Figure 5 The thickness distribution diagram shown is input into the trained S0 Lamb wave scattering acoustic field prediction model to obtain the predicted S0 Lamb wave scattering acoustic field corresponding to the irregular defect.

[0128] Select snapshots of four moments in the scattered sound field and compare the predicted scattered sound field with the actual scattered sound field obtained by forward calculation. The results are as follows: Figure 6 As shown. Figure 6 In , (a1) to (a4) are the scattered sound fields obtained by forward modeling, which are recorded as true solutions. Figure 6 In the figure, (b1) to (b4) and (c1) to (c4) are the predicted scattered sound fields obtained by the trained S0 Lamb wave scattered sound field prediction model, and the error distribution of the predicted scattered sound fields relative to the true solution. In order to fully capture the information of S0 Lamb wave propagation and scattering, the wave fields at four different times of 95μs, 115μs, 135μs and 155μs are studied. Figure 6 As shown in (a1), at 95μs, the S0 Lamb wave reaches the defect and the scattered wave (S0-A0) begins to appear. By 115μs, the S0 Lamb wave continues to propagate, while the scattered wave radiates outward from the defect. At this stage, another wave appears on the right side of the domain, corresponding to the A0 Lamb wave generated during the excitation process. At 135μs, as shown in Figure 6As shown in (a3), the S0 Lamb wave is about to leave the computational domain, while the scattered wave has already begun to interact with the A0 Lamb wave, resulting in interference. By 155 μs, the initially excited S0 Lamb wave has completely left the computational domain, leaving only the scattered wave and the propagating A0 Lamb wave. The A0 Lamb wave will then interact with the defect and generate a secondary scattered wave (A0-A0), further increasing the complexity of the wavefield.

[0129] It is noteworthy that the amplitude of the excited S0 Lamb wave gradually decays as the wave propagates. In contrast, the scattered wave undergoes a gradual increase in amplitude, initially increasing and then gradually decreasing as it propagates. Furthermore, the wave field exhibits anisotropic amplitude variations at different propagation angles, reflecting the influence of the defect's asymmetry on the scattering properties. It is precisely this inherent correlation between the defect and the scattered acoustic field that makes defect inversion possible through scattering analysis.

[0130] The comparison between the real solution and the predicted solution shows that the present invention effectively captures the scattered acoustic field characteristics, and the obtained guided wave propagation information is relatively consistent with the real guided wave propagation information. The differences are mainly concentrated in the defect area and around the guided wave interference area. In addition, with the propagation of the guided wave, the error in the far field area tends to increase. This shows that during the training process of the S0 Lamb wave scattered acoustic field prediction model, the prediction accuracy of the scattered acoustic field with a longer propagation time is reduced. This is because the scattered acoustic field caused by the defect is too complex, and it is difficult to capture all the complex details and it is impossible to completely reconstruct all the fine features. Despite these local errors, Figure 6 The results show that the present invention can solve the scattered sound field of irregular defects, has reasonable generalization ability, and is an effective method for guided wave scattering analysis of complex structures.

[0131] S6. Based on the predicted scattered acoustic field of the irregular defect, the scattered time domain signal and the scattered far-field amplitude results are obtained, and the scattered acoustic field solution of the S0 Lamb wave is completed.

[0132] After obtaining the scattered sound field of the irregular defect, the time domain signal at any coordinate position can be further extracted. Assuming that 360 receiving points are evenly arranged on a circle with a radius of 160 mm and a coordinate of (200, 400) (the center of the calculation domain) as the origin, the time domain signal at these 360 receiving points can be obtained. Figure 7As shown in Figure 1-(a), time domain signals at 12 angles are displayed at 30° intervals. As the angle increases, the propagation distance of the S0 Lamb wave increases symmetrically around 180°, initially gradually increasing and then decreasing, resulting in an arc-shaped distribution of the time domain signal centered at 180°. When the S0 Lamb wave reaches the defect, it generates a scattered A0 Lamb wave (S0-A0), which propagates outward from the defect. Because the propagation paths of scattered A0 Lamb waves at different angles to the receiving point are nearly identical, the scattered A0 Lamb waves appear at roughly the same locations on the time domain signal. Figure 7 -The results in (a) confirm this result and further verify the physical consistency of the scattering process. Overall, the scattered time-domain signal predicted by the present invention is in good agreement with the true solution. In the S0 Lamb wave region where scattering has not yet occurred, the results predicted by the present invention are almost completely consistent with the true solution, proving that the S0 Lamb wave scattering acoustic field prediction model can accurately capture the propagation of undisturbed S0 Lamb waves. After approximately 135μs, when the scattered A0 Lamb wave reaches the receiving point, a slight amplitude difference appears between the predicted and true results, but the overall propagation trend remains consistent.

[0133] In order to further study the scattering characteristics, the peak amplitudes of the scattered A0 Lamb waves at different angles were extracted and obtained. Figure 7 -(b) shows the scattered far-field amplitude results. The results show that the scattered far-field amplitude distribution predicted by the present invention is consistent with the true solution, which further confirms the generalization ability of the present invention. It is worth noting that in the area where the scattering characteristics show obvious changes, such as Figure 7 The present invention still accurately predicts these scattering characteristics near 90° and 270° in (b). While some differences are observed within specific angle ranges, such as between 150° and 180°, the overall trend remains consistent with the true solution. Overall, the present invention demonstrates good predictive ability in predicting the propagation characteristics of scattered waves.

[0134] In order to further verify the performance of the present invention in solving the scattered sound field, a sound field scanning experiment was carried out using a Polytec Laser Doppler Vibrometer (SLDV). Figure 8 As shown. A 6061 aluminum plate of 800mm×800mm×1.5mm is fixed on the optical table. In order to minimize boundary reflections, damping clay is arranged on the four edges of the aluminum plate. The clay is shaped into a wedge shape, and the thickness gradually tapers from the edge to the center of the plate, as shown in FIG. Figure 8 -(b). This design effectively reduces the secondary reflection caused by the interaction between the wave and the damping material during propagation. Figure 8As shown in Figure 1-(c), an irregular defect with a remaining thickness of 0.5 mm was precisely machined into an aluminum plate. The spatial coordinates of the defect were consistent with those used in the forward modeling. Two identical 100 kHz piezoelectric transducers were symmetrically placed on the aluminum plate, 400 mm from the defect center, to excite a relatively pure S0 Lamb wave. A sinusoidal excitation signal with a frequency of 100 kHz, an amplitude of 4 Vpp, and 5 cycles was generated by a signal generator. This sinusoidal excitation signal was amplified 20 times by an Aigtek ATA-2022B dual-channel power amplifier and then applied to both transducers. The SLDV probe was carefully adjusted to ensure that the emitted laser beam was as perpendicular as possible to the plate surface. To enhance the SLDV probe's ability to capture minute vibrations, reflective paper was applied to the defect surface. The scanning area was defined as a 100 mm × 100 mm square centered on the defect. The SLDV sampling frequency was 6.25 MHz, the number of acquisition points was set to 5000, and the bandpass filter range was set to 80 kHz to 120 kHz.

[0135] The thickness distribution of the defective aluminum plate to be tested in the experiment is input into the trained S0 Lamb wave scattering sound field prediction model to obtain the predicted scattering sound field, and the predicted scattering sound field is compared with the actual result of the forward calculation. Figure 9 As shown in the figure, the present invention accurately captures the propagation of the S0 Lamb wave and the scattering behavior after interacting with the defect, which is in good agreement with the actual results.

[0136] Through SLDV scanning, the scattered acoustic field information of the defect to be tested in the experiment can be obtained. Similarly, assuming that 360 receiving points are evenly distributed on a circle with a radius of 100mm centered on the defect, Figure 10 (a) shows the time domain signals at 12 receiving points evenly spaced at 30° intervals. The wave structure characteristics of the S0 Lamb wave and the A0 Lamb wave indicate that the S0 Lamb wave has a relatively small out-of-plane displacement, while the A0 Lamb wave has a relatively large out-of-plane displacement. Therefore, the SLDV is unable to detect the S0 Lamb wave. However, the scattered A0 Lamb wave, generated by the interaction between the S0 Lamb wave and the defect, appears around 135μs and can be clearly discerned. The A0 Lamb wave, generated by excitation and appearing around 240μs, exhibits its maximum amplitude.

[0137] The scattered far-field amplitude results obtained using the time domain signal are as follows: Figure 10-(b). Although the geometry of the defect is relatively smooth and simple, the scattered acoustic field exhibits significant complexity, as evidenced by the complex amplitude variations in the scattering results. The prediction results of the present invention are relatively consistent with the true solution, effectively and comprehensively capturing the complex scattering characteristics. The present invention successfully reconstructs most of the scattering information, highlighting the modeling capability of the interaction between S0 Lamb waves and irregular defects. Although there are differences between the experimental scanning results and the true solution, the overall trend remains consistent. Taking into account factors such as the S0 Lamb wave off-plane displacement being too small to be effectively collected, inevitable boundary reflections, defect processing errors, and various experimental noises, it can be considered that the prediction results of the present invention are reasonably consistent with the SLDV experimental results and the true solution.

[0138] In summary, simulation and experimental results demonstrate that the present invention is a powerful and efficient framework for guided wave scattering analysis, which has significant advantages in solving the S0 Lamb wave scattering acoustic field of irregular defects and provides a promising solution for nondestructive testing and structural health monitoring applications.

[0139] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for solving the S0 Lamb wave scattering sound field based on physical constraint enhanced TransUNet, characterized in that: The following steps are involved: S1. Based on the thickness distribution of the plate structure containing irregular defects, the global scattered sound field in the off-plane direction of the S0 Lamb wave after passing through the irregular defects is obtained through forward calculation; S2, performing spatial and temporal truncation processing on the global scattered sound field obtained in step S1, and then performing downsampling to obtain the scattered sound field, and establishing a scattered sound field dataset; S3. Constructing an S0 Lamb wave scattered sound field prediction model, wherein the S0 Lamb wave scattered sound field prediction model adopts a TransUNet network, wherein the TransUNet network includes an encoder, a decoder, and a skip connection, wherein the skip connection is provided between the encoder and the decoder; S4. Divide the scattered sound field data set into a training set and a test set, and use the training set to perform data-driven training and physical constraint training on the S0 Lamb wave scattered sound field prediction model in sequence to obtain a trained S0 Lamb wave scattered sound field prediction model; S5. Inputting the thickness distribution of the defective plate structure to be tested in the test set into the trained S0 Lamb wave scattered sound field prediction model to obtain the predicted scattered sound field of the irregular defect; S6. Based on the predicted scattered acoustic field of the irregular defect, the scattered time domain signal and the scattered far-field amplitude results are obtained, and the scattered acoustic field solution of the S0 Lamb wave is completed.

2. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 1 is characterized in that: The method for obtaining the global scattered sound field of the S0 Lamb wave in the off-plane direction after passing through the irregular defect by forward calculation based on the thickness distribution of the plate structure containing the irregular defect is as follows: perfectly matched layers are set around the plate containing the irregular defect, the plate containing the irregular defect is excited by a dual-sensor symmetrical excitation method, and the Kirchhoff-Love plate theory is used to solve the global scattered sound field of the S0 Lamb wave in the off-plane direction based on the thickness distribution of the plate structure containing the irregular defect, thereby obtaining the global scattered sound field of the S0 Lamb wave in the off-plane direction after passing through the irregular defect.

3. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 2 is characterized in that: The method for solving the global scattered sound field of the S0 Lamb wave in the off-plane direction using the Kirchhoff-Love plate theory is: A plane rectangular coordinate system is established with the surface of the plate containing irregular defects as a reference; The governing equations of the Kirchhoff-Love plate theory for an isotropic uniform thin plate under free vibration are expressed as: Where ρ is the density of the plate, h is the thickness of the plate, and D is the bending stiffness matrix of the plate. is a biharmonic operator; u(x,y,t) represents the out-of-plane displacement at coordinate (x,y) at time t; E represents Young's modulus, and v represents Poisson's ratio; After transformation, the intermediate parameter ζ is recorded as: The transformed control equation is expressed as: The transformed governing equations are solved to obtain the global scattering acoustic field of the S0 Lamb wave in the off-plane direction after passing through the irregular defect.

4. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 1 or 3, characterized in that: The method for establishing the scattered sound field data set is: The global scattered sound field obtained in step S1 is truncated in space and time: In terms of time, intercept t0-t e The scattered sound field inside, t0 is the time when the S0 Lamb wave reaches the irregular defect area, t e is the time when the S0Lamb wave leaves the irregular defect area; In space, since from t0 to t e During the propagation time, the scattered information occurs in the region of the x-coordinate range x1 to x2 and the y-coordinate range y1 to y2. Therefore, in space, the scattered sound field in the region of the x-coordinate range x1 to x2 and the y-coordinate range y1 to y2 is intercepted. Next, let the step size in the x direction be Δx, the step size in the y direction be Δy, and the time step be Δt, and perform downsampling to obtain the scattered sound field; Several forward calculations of random irregular defects are performed, and the global scattered sound fields obtained are truncated and downsampled. The thickness distribution of the plate structure containing irregular defects and all the scattered sound fields obtained constitute the scattered sound field data set.

5. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 4 is characterized in that: The encoder and decoder are connected symmetrically. The encoder is composed of four identical sub-encoders connected in series. The sub-encoder is composed of a convolutional layer I, a convolutional layer II, a Transformer block containing a multi-head attention mechanism, and a 2×2 maximum pooling layer connected in sequence. The decoder is composed of four identical sub-decoders connected in series. The sub-decoder is composed of a 2×2 convolution upsampling layer, a cascade layer, a convolutional layer III, and a convolutional layer IV connected in sequence. Among them, the convolution kernel size of convolution layer I, convolution layer II, convolution layer III and convolution layer IV is 3×3, and LeakyReLU is used as the activation function; The skip connection is provided between the sub-encoder and the sub-decoder.

6. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 5, characterized in that: The steps of sequentially performing data-driven training and physical constraint training on the S0 Lamb wave scattering sound field prediction model using the training set include: Setting the network parameters of the TransUNet network, including setting the thresholds I and II in the number of iterations, the learning rate, the batch size, and the weighting parameters in the composite loss function; wherein the threshold II is greater than the threshold I; The thickness distribution of the plate structure with irregular defects in the training set is input into the S0 Lamb wave scattering acoustic field prediction model. For the thickness distribution of the i-th input, u(x i ,y i ,t i ) represents the real scattered sound field obtained by forward modeling, and u * (x i ,y i ,t i ) represents the predicted scattered sound field obtained by output; S4.

1. Determine a data-driven error. When the number of iterations does not reach a set threshold value I, iteratively train the S0 Lamb wave scattering sound field prediction model based on the data-driven error to obtain the S0 Lamb wave scattering sound field prediction model to be optimized. S4.

2. When the number of iterations reaches the set threshold I, the physical constraints corresponding to the Kirchhoff-Love plate theory are obtained using finite differences, the physical driving error is determined, and the data-driven error and the physical driving error are weighted and superimposed to train the S0Lamb wave scattering sound field prediction model to be optimized; S4.

3. When the number of iterations reaches the set threshold II, stop training, save all model parameters, and obtain the trained S0Lamb wave scattering sound field prediction model.

7. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 6, characterized in that: The calculation expression of the data-driven error is: in, is the data-driven error, N D Expressed as the calculated data-driven error The space-time sampling points on the solution domain are randomly selected.

8. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 6, characterized in that: The calculation expression of the physical driving error is: Among them, N P To calculate the physical drive error The space-time sampling points on the solution domain are randomly selected.

9. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 6, characterized in that: For each randomly selected spatiotemporal sampling point N P , the partial derivatives are first solved by the following formula: Next, the physical driving error is obtained by substituting it into the calculation expression of the physical driving error.

10. The method for solving the SO Lamb wave scattered sound field based on physical constraint enhanced TransUNet according to claim 6, characterized in that: When the data-driven error and the physical-driven error are weighted and superimposed, the composite loss function is expressed as: Where λ represents the weighting parameter.

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