A full waveform inversion guided wave tomography method based on a recurrent neural network

Abstract

The application discloses a guided wave tomography method based on full waveform inversion of a recurrent neural network, comprising the following steps: step 1, time series forward modeling based on the acoustic formula of the finite difference method is realized by using sequence calculation of the recurrent neural network, and an initial model is obtained; step 2, the wave field value of each time step at each excitation position is calculated in turn, and a simulation value is generated; step 3, after actual observation values are processed, a least square target equation of the simulation value and the observation value is generated; step 4, the least square target equation is iteratively minimized by an inversion part, including an automatic differentiation method and an Adam algorithm, which are respectively responsible for gradient calculation of the target equation and iterative updating of a velocity model and a UNet weight; step 5, the updated velocity model is subjected to depth image prior UNet regularization; and step 6, steps 1 to 5 are repeated, and the next iteration calculation is performed until the target equation is lower than a specified threshold value, so that a final velocity model is obtained, and the final velocity model is converted into a thickness model by using a dispersion relation.

Description

Technical Field

[0001] This invention relates to the field of industrial nondestructive testing, and specifically to a full-waveform inversion guided wave tomography method based on a recurrent neural network. Background Technology

[0002] Quantitative corrosion detection of plates or plate-like structures is a key and complex topic in industrial nondestructive testing (NDT) research, as it determines the remaining life of materials. Plates or plate-like components are widely used in the aircraft, automotive, shipbuilding, and petroleum industries. During use, due to mechanical and chemical effects, defects gradually form inside the plates. The propagation of these defects can lead to fatigue failure of the structure, resulting in production safety accidents. Therefore, plate damage detection and quantification of the remaining life of materials are of paramount importance.

[0003] As a traditional non-destructive testing (NDT) technique, guided wave ultrasound (TWME) is widely used to detect internal defects in plate-shaped components. This method is characterized by low equipment requirements, non-invasive testing, speed and efficiency, high precision, low cost, and no pollution. Currently, the academic community has conducted extensive research on guided wave tomography algorithms, including travel-time imaging, diffraction imaging, and other advanced algorithms that consider more physical principles, such as robust breast ultrasound computed tomography (HARBUT) or improved hybrid algorithms like the HARBUT series, full waveform inversion (FWI), and fast inversion tomography. However, all of these algorithms have certain drawbacks, limiting the practical application of guided wave tomography.

[0004] Compared to other methods (X-ray, magnetic particle, eddy current), ultrasonic guided wave tomography (AWT) offers advantages such as non-invasiveness, speed, efficiency, high precision, and low cost. Among various WFT algorithms, travel-time or diffraction algorithms can image defect corrosion, but their accuracy is low and they are greatly affected by noise. While the FWI algorithm can reconstruct damage images with relatively high precision, it requires a relatively accurate initial model, has low robustness, and there is still room for improvement in convergence speed and imaging resolution. Summary of the Invention

[0005] This invention is made to solve the above-mentioned problems, and aims to provide a full-waveform inversion guided wave tomography method based on recurrent neural networks.

[0006] This invention provides a full-waveform inversion guided wave tomography method based on recurrent neural networks, characterized by the following steps: Step 1, using the sequence computation of a recurrent neural network (CNN) to achieve time-series forward modeling of the acoustic wave formula based on the finite difference method, obtaining an initial model; Step 2, based on the initial model, sequentially calculating the wave field value at each time step at each excitation position to generate simulated values; Step 3, after signal processing of the actual observed values, generating a least-squares objective equation between the simulated values ​​and the observed values; Step 4, the inversion part iteratively minimizes the least-squares objective equation, including an automatic differentiation method and the Adam algorithm. The automatic differentiation method is responsible for calculating the gradient of the objective equation, and the Adam algorithm is responsible for iteratively updating the velocity model and UNet weights, finally generating an updated velocity model; Step 5, applying Depth Image Prior (DIP) UNet regularization to the updated velocity model to generate the initial model for the next iteration; Step 6, repeating steps 1 to 5 for the next iterative calculation until the objective equation is below a specified threshold, obtaining the final velocity model, and converting the final velocity model into a thickness model using dispersion relations.

[0007] The full-waveform inversion guided wave tomography method based on recurrent neural networks provided in this invention may also have the following feature: In step 1, forward modeling is the process of numerically propagating the wave source in the model and recording the wave field at the location of the receiving transducer. Specifically, the two-dimensional acoustic wave formula in a constant-density medium is expressed as:

[0008]

[0009] p t =ξ(s t (2)

[0010] In the formula, p(r,t) is the wave field, s(r,t) is the wave source, r represents a 2-D or 3-D spatial vector, t is time, and v(r) is the ultrasonic wave velocity. ξ is the spatial Laplace operator, and ξ is the forward operator. Equation (1) is calculated and discretized using the finite difference method, and the wave field is calculated at the finite difference grid points. The second-order finite difference is defined as:

[0011]

[0012] In the formula, Δt is the unit step time. By simultaneously solving the above equations, the following result is obtained:

[0013]

[0014] Equation (4) is the forward modeling formula for FWI. The wave field values ​​at all times can be obtained by calculating equation (4).

[0015] The full-waveform inversion guided wave tomography method based on recurrent neural networks provided in this invention may also have the following feature: In step 4, the Adam algorithm is used to update the weight parameters of the CNN.

[0016] m (k+1) =m (k) -a (k) g′ (k) (5)

[0017] In the formula, a is the iteration update step size, k is the number of iteration steps, and g is the gradient.

[0018] The full-waveform inversion guided wave tomography method based on recurrent neural networks provided in this invention may also have the following feature: In step 4, the least squares objective equation is rewritten as:

[0019]

[0020] In the formula, N is the neural network, z is a random matrix, and w is the weight of the neural network.

[0021] The full-waveform inversion guided wave tomography method based on recurrent neural networks provided by this invention may also have the following feature: In step 5, the detailed parameter information of the DIP-UNet structure is shown in the table below, including but not limited to the parameter settings in the table:

[0022]

[0023] The full-waveform inversion guided wave tomography method based on recurrent neural networks provided by this invention may also have the following feature: in step 5, the output of UNet is directly combined with the updated velocity model as the velocity map parameter update for the next FWI cycle.

[0024] The role and effect of invention

[0025] According to the full-waveform inversion guided wave tomography method based on recurrent neural networks of the present invention, the specific process is as follows: Step 1, using the sequence calculation of CNN to realize the time series forward modeling of the acoustic wave formula based on the finite difference method, to obtain an initial model; Step 2, according to the initial model, the wave field value at each time step at each excitation position is calculated cyclically to generate simulated values; Step 3, after signal processing of the actual observed values, the least squares objective equation of the simulated values ​​and the observed values ​​is generated; Step 4, the inversion part iteratively minimizes the least squares objective equation. The inversion part includes an automatic differentiation method and the Adam algorithm. The automatic differentiation method is responsible for calculating the gradient of the objective equation, and the Adam algorithm is responsible for iteratively updating the velocity model and UNet weights, finally generating an updated velocity model; Step 5, the updated velocity model is regularized by DIP-UNet to generate the initial model for the next iteration; Step 6, steps 1 to 5 are repeated to perform the next iteration calculation until the objective equation is lower than a specified threshold, to obtain the final velocity model, and the final velocity model is transformed into a thickness model using the dispersion relation.

[0026] Therefore, the full-waveform inversion guided wave tomography method based on recurrent neural networks provided by this invention has better performance in terms of convergence speed, initial model requirements, robustness, and accuracy.

[0027] Furthermore, the RNN temporal structure enables computation at each time point of the forward computation, and the automatic differentiation method replaces the adjoint state method to calculate the gradient of the objective function in the inversion. These two aspects provide the foundation for introducing deep learning into FWI. RNN-FWI uses the Adam mini-batch global optimization algorithm to update model parameters, which does not require the computation of the Hessian matrix, thus resulting in faster convergence and less memory requirements, replacing the traditional quasi-Newton method.

[0028] Finally, deep learning RNNs provide a solution to address the shortcomings of traditional FWI. The Adam optimization algorithm avoids the calculation of the Hessian matrix, quickly explores the descent space with small batches of data, accelerates convergence, and reduces memory requirements; the automatic differentiation method avoids explicit gradient calculation and avoids the systematic errors of the adjoint state method; the CNN-based DIP regularization method can enhance the robustness of the algorithm, alleviate the periodic jump phenomenon, and does not require subjectively set parameters. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the experimental apparatus for guided wave tomography in an embodiment of the present invention;

[0030] Figure 2 This is a flowchart of the full waveform inversion guided wave tomography method based on recurrent neural networks in an embodiment of the present invention;

[0031] Figure 3 This is a structural diagram of RNN-FWI in an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram of a single computing unit of an RNN-FWI with PML in an embodiment of the present invention;

[0033] Figure 5 This is a UNet structure diagram of RNN-FWI in an embodiment of the present invention;

[0034] Figure 6 This is a diagram of the experimental apparatus in an embodiment of the present invention;

[0035] Figure 7 These are simulation experiment settings and excitation waveform diagrams in embodiments of the present invention, wherein... Figure 7 (a) Setting up the simulation experiment diagram, Figure 7 (b) is the excitation waveform function diagram;

[0036] Figure 8 This is a group velocity dispersion curve of the aluminum plate in an embodiment of the present invention;

[0037] Figure 9 This is a comparison diagram of the filtered windowed waveform and the simulated waveform in an embodiment of the present invention, wherein...

[0038] Figure 9 (a) is a waveform diagram of the filtered and windowed waveform. Figure 9 (b) is a simulation waveform diagram;

[0039] Figure 10 These are comparison figures of the velocity field reconstruction results of embodiments and comparative examples of the present invention, wherein Figure 10(a) is the actual model. Figure 10 (b) is the traditional FWI. Figure 10 (c) is an RNN-FWIAdam;

[0040] Figure 11 These are comparison diagrams showing magnified central defects in embodiments and comparative examples of the present invention, wherein... Figure 11 (a) is the real model. Figure 11 (b) is the traditional FWI. Figure 11 (c) is an RNN-FWIAdam;

[0041] Figure 12 These are cross-sectional position diagrams along the X and Y axes of an embodiment of the present invention;

[0042] Figure 13 This is a cross-sectional comparison of the results of five epochs for the embodiments and comparative examples of the present invention, wherein... Figure 13 (a) is a result diagram of the embodiment. Figure 13 (b) is a comparative comparison chart;

[0043] Figure 14 This is a comparison chart of the loss functions of embodiments and comparative examples of the present invention;

[0044] Figure 15 This is a comparison chart of the calculation results of real experimental data from embodiments and comparative examples of the present invention, wherein... Figure 15 (a) is a result diagram of the embodiment. Figure 15 (b) is a comparative comparison chart;

[0045] Figure 16 These are cross-sectional comparison diagrams of the reconstruction results of embodiments and comparative examples of the present invention, wherein... Figure 16 (a) is a result diagram of the embodiment. Figure 16 (b) is a comparative result graph. Detailed Implementation

[0046] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate a full-waveform inversion guided wave tomography method based on a recurrent neural network.

[0047] Example

[0048] In this embodiment, a full-waveform inversion guided wave tomography method based on recurrent neural networks is provided.

[0049] Figure 1 This is a schematic diagram of the experimental apparatus for guided wave tomography in an embodiment of the present invention.

[0050] like Figure 1 As shown, the experimental setup 100 in this embodiment is conducted on an isotropic plate 10 with a central defect. The plate 10 has a circular transducer array 20 on its surface, where each transducer sequentially generates ultrasonic waves while all other transducers receive the waveforms. The experimental setup 100 also includes a source 30 and a defect 40.

[0051] Full waveform inversion (FWI) is based on the wave equation and utilizes wave travel time and amplitude information to model parameters. It calculates the difference between simulated and observed data and uses optimization algorithms to continuously reduce this difference, thereby minimizing the objective functional and updating the parameters. FWI consists of forward propagation of the wave field and backward propagation of the residuals. This process is very similar to the backpropagation (BP) algorithm in artificial neural networks, where backpropagation also involves forward feedforward and then error backpropagation. Both algorithms iteratively calculate gradients and update parameters. Therefore, FWI can be introduced into deep learning, allowing various optimization techniques and advantages of deep learning to further improve the performance of conventional FWI.

[0052] The structure of RNN-FWI is basically the same as that of traditional methods, including forward and inverse parts. It utilizes the sequential computation of a recurrent neural network to achieve time-series forward modeling of the acoustic wave formula based on the finite difference method. It iteratively calculates the wave field value at each time step for each excitation location. After signal processing, the actual observed values ​​generate a least-squares objective equation between the simulated and observed values. The inverse part includes automatic differentiation and the Adam algorithm, responsible for calculating the gradient of the objective equation and iteratively updating the velocity model and UNet weights, respectively. After generating the initial velocity model, it enters the UNet-based DIP for regularization, generating the initial model velocity parameters for the next iteration. Then, the next iteration is performed until the objective equation falls below a specified threshold.

[0053] Figure 2 This is a flowchart of the full waveform inversion guided wave tomography method based on a recurrent neural network in an embodiment of the present invention.

[0054] like Figure 2 As shown, the full-waveform inversion guided wave tomography method based on recurrent neural networks involved in this embodiment includes the following steps:

[0055] Step S1: Use the sequence calculation of the recurrent neural network to realize the time series forward modeling of the acoustic wave formula based on the finite difference method, and obtain the initial model.

[0056] FWI forward modeling is the process of numerically propagating a wave source in a model and recording the wave field at the location of the receiving transducer. The formula for two-dimensional acoustic waves in a constant-density medium can be expressed as:

[0057]

[0058] p t =ξ(s t (2)

[0059] Where p(r,t) is the wave field, s(r,t) is the wave source, r represents a 2-D or 3-D spatial vector, t is time, and v(r) is the ultrasonic wave velocity. It is the spatial Laplace operator, and ξ is the forward operator. A common method for solving differential equations is to first discretize the spatiotemporal coordinates of the equation, and then solve it in the form of numerical differentiation. Equation (1) can be calculated and discretized using the finite difference method, and the wave field can be calculated at the finite difference grid points. The second-order finite difference is defined as:

[0060]

[0061] Where Δt is the unit step time. By simultaneously solving the above equations, we can obtain the following result:

[0062]

[0063] The above is the forward modeling formula for FWI. Thus, the wave field values ​​at all times can be obtained by calculating equation (4). Similarly, the waveform at the transducer responsible for receiving can also be obtained. To compensate for and absorb boundary reflections, the Perfectly Matched Layer (PML) approximates the finite-size model to an infinite-size model by setting damping and absorption layers at the boundaries.

[0064] Recurrent Neural Networks (RNNs) are a type of artificial neural network in which layers are connected by a series of directed graphs. RNNs use their internal cascaded units to process input sequences, making them suitable for time series signal processing tasks. Due to the temporal directionality of wave propagation—that is, the wave field at the current time is only affected by the wave fields of the past two time periods and not by its future state—directed-undirected circular graph RNNs are suitable for sound wave simulation.

[0065] Step S2: Based on the initial model, calculate the wave field value at each time step at each excitation position in a sequential loop to generate simulated values.

[0066] Step S3: After signal processing, the actual observed values ​​generate a least-squares objective equation between the simulated values ​​and the observed values.

[0067] Step S4: The inversion part iteratively minimizes the least squares objective equation. The inversion part includes the automatic differentiation method and the Adam algorithm. The automatic differentiation method is responsible for calculating the gradient of the objective equation, and the Adam algorithm is responsible for iteratively updating the velocity model and UNet weights, finally generating the updated velocity model.

[0068] Figure 3 This is a structural diagram of RNN-FWI in an embodiment of the present invention.

[0069] Figure 4 This is a schematic diagram of a single computing unit of an RNN-FWI with PML in an embodiment of the present invention.

[0070] To construct an RNN architecture that supports full waveform inversion, each RNN unit contains the same operations, and forward modeling can be achieved by repeatedly applying forward modeling operations in each unit. In this case, the trainable variables are the velocity model parameters. Figures 3-4 As shown, the relevant directed acyclic graph of the RNN architecture is displayed in a compact form. Figure 3 In the text, the extended form is also displayed. Figure 4 middle.

[0071] m (k+1) =m (k) -a (k) g′ (k) (5)

[0072] Where a is the iteration update step size, k is the number of iterations, and g is the gradient adaptive moment (Adam) algorithm is used to update the weight parameters of the neural network. Unlike the Newton method or quasi-Newton method of traditional FWI, the Adam algorithm adopts the idea of ​​mini-batch data processing, which can not only quickly explore the descent space to accelerate convergence, but also does not require all data to participate in a single iteration, and has lower memory consumption.

[0073] Deep Image Prior (DIP) is a CNN architecture that can be used as a prior without pre-training and has significant effects on denoising and super-resolution. For neural networks with convolutional layers, the convolutional kernels applied across domains exhibit self-similarity and spatial correlation. Therefore, reparameterizing the speed model parameters with a CNN naturally introduces regularization for FWI. The objective function can be rewritten as:

[0074]

[0075] Where N is the neural network, z is a random matrix, and w is the weights of the neural network. We can use a CNN architecture to represent the velocity model, which naturally introduces spatial correlation as a regularization into the velocity model, thereby suppressing noise in the gradient and mitigating local minima, and significantly improving inversion in the presence of noise. Furthermore, not all image priors must be learned from the data; instead, the convolutional structure captures a large amount of image statistics, so DIP does not require additional training data and optimization training.

[0076] Step S5: Apply depth image prior UNet regularization to the updated velocity model to generate the initial model for the next iteration.

[0077] UNet+ResNet, which includes skip connection layers, was initially applied to medical image segmentation. Its simple structure allows it to acquire features at different scales to a certain extent. Based on the UNet structure, it can combine low-level and high-level information. The low-resolution information after multiple downsampling can provide contextual information about defects in the entire image; this can be understood as a feature reflecting the relationship between prior erosion information and the velocity map. After the stitching operation, high-resolution information is directly transmitted from the encoder to the decoder at the same level. Skip connections serve to supplement information, adding image details at higher levels.

[0078] Figure 5 This is a UNet structure diagram of RNN-FWI in an embodiment of the present invention, including but not limited to the parameter settings in the table.

[0079] Therefore, this embodiment designs a DIP-UNet that uses UNet to implement FWI regularization. The structure diagram is as follows. Figure 5As shown in Table 1, detailed parameter information for UNet is presented. This embodiment constructs a UNet with a series of pooling layers, convolutional layers, velocity model layers, copying and connection layers, and upsampling operations to convert a random matrix into a velocity model. In FWI, this embodiment directly combines the output of UNet with the velocity model updated by the RNN as the velocity map parameter update for the next FWI cycle; therefore, the neural network is trained to predict the velocity model update.

[0080] Table 1 shows the DIP-UNet structure of RNN-FWI.

[0081] Table 1

[0082]

[0083] Step S6: Repeat steps S1 to S5 for the next iteration calculation until the target equation is below the specified threshold to obtain the final velocity model. Then, use the dispersion relation to transform the final velocity model into a thickness model.

[0084] Figure 6 This is a diagram of the experimental apparatus in an embodiment of the present invention.

[0085] Figure 7 This is a simulation experiment setup and excitation waveform diagram in an embodiment of the present invention. Figure 7 (a) is the setup diagram for the simulation experiment. Figure 7 (b) is the excitation waveform function graph.

[0086] like Figure 6 As shown, the experiment in this embodiment was conducted on a 1000*1000*10mm 6061 (aluminum grade) aluminum plate with a material density of 2.9g / cm³. 3 The Young's modulus E = 71 GPa, Poisson's ratio 0.33, and a rotating platform underneath facilitates operation and measurement. The corrosion of the plate consists of a series of irregular defects with depths of 1 mm, 0.5 mm, and 0.25 mm, with the deepest defect reaching half the plate thickness. The defect walls form a 30° angle with the plate surface, preventing the conversion from A0 mode to S0 mode. The corrosion was designed using CAD and engraved using CNC, ensuring a high degree of consistency with the numerical simulation model. A 700 mm diameter circular transducer array surrounds the corrosion on the metal plate surface, comprising 60 PZT-5 transducers with a center frequency of approximately 50 kHz, all uniformly bonded to the aluminum plate with epoxy resin. All PZT transducers can transmit and receive ultrasound. The excitation waveform function is a five-cycle sinusoidal burst signal with a Hanning window, a center frequency of 50 kHz, and a 15 dB bandwidth of 35–65 kHz. Figure 7 As shown on the right. The simulation experiment setup is as follows. Figure 7 As shown in the left figure, all physical parameters are consistent with the actual experiment. The dark dots are the excitation points, and the light dots are the receiving points.

[0087] Figure 8 This is a group velocity dispersion curve of the aluminum plate in an embodiment of the present invention.

[0088] from Figure 8 It can be seen that the dispersion curve is very sensitive to changes in thickness and is not affected by other guided wave modes.

[0089] The Lamb wave transmission signal was generated by an Agilent 33220A arbitrary waveform generator and amplified by an AG SeriesAmplifier 1011 (T&C Power Conversion, Inc.) RF power amplifier. The PZT signal was acquired by an Agilent MSO6052A mixed-signal oscilloscope. The FWI calculations were performed by a computer with an i7 9700k CPU, 16GB DDR4 memory, and an Nvidia GTX 1080ti 11GB GPU.

[0090] Figure 9 This is a comparison diagram of the filtered windowed waveform and the simulated waveform in an embodiment of the present invention.

[0091] in Figure 9 (a) is a waveform diagram of the filtered and windowed waveform. Figure 9 (b) is a simulation waveform diagram.

[0092] Each PZT transducer acquires 0.5ms of waveform information, which is then divided into 1000 points for storage. After data acquisition, the actual raw waveforms are compared with numerical simulations. Figure 9 As shown in Figure (a), the phase difference between the two signals is essentially nonexistent. It is necessary to limit the bandwidth of the acquired signal to remove clutter frequencies outside the 45-65 Hz range; therefore, a third-order Butterworth bandpass filter is used to filter the signal. Then, the first arriving A0 packet and the defect scattering wave are gated to block boundary echoes and other clutter interference. In this embodiment, a flat-top Hamming window is used for gating, which effectively prevents spectral leakage. Signal processing can be performed simply by adding different delays to such a window and multiplying the processed signals. Figure 9 (b) is a comparison between the processed signal and the analog signal extracted from the two transducers at relative positions. It can be seen that the actual experiment and the simulation experiment highly overlap.

[0093] Comparative Example

[0094] In this comparative example, a conventional FWI method combining the adjoint state method and L-BFGS-B is provided, along with the RNN-FWI method described in the above embodiment, in combination with Adam for reconstruction. Figure 7 A two-dimensional model was constructed. Different combinations of algorithms were used to verify the feasibility and superiority of the algorithms in the above embodiments.

[0095] The purpose of this comparative study is to compare the inversion accuracy and speed of different algorithms. The experiments were run for a uniform 5 epochs. To facilitate comparison, the observed values ​​used are simulated values ​​from numerical simulations rather than actual experimental data.

[0096] Figure 10 This is a comparison diagram of the velocity field reconstruction results of embodiments and comparative examples of the present invention, wherein... Figure 10 (a) is the real model. Figure 10 (b) is the traditional FWI. Figure 10 (c) is RNN-FWI Adam.

[0097] Figure 11 These are comparison diagrams showing magnified central defects in embodiments and comparative examples of the present invention, wherein... Figure 11 (a) is the real model. Figure 11 (b) is the traditional FWI. Figure 11 (c) is RNN-FWI Adam.

[0098] Figure 12 This is a cross-sectional view of the X-axis and Y-axis of an embodiment of the present invention.

[0099] Figure 13 This is a cross-sectional comparison of the results of five epochs for the embodiments and comparative examples of the present invention, wherein... Figure 13 (a) is a result diagram of the embodiment. Figure 13 (b) is a comparative result graph.

[0100] Figure 14 This is a comparison chart of the loss functions of embodiments and comparative examples of the present invention.

[0101] from Figures 10-14 As can be seen, the RNN-FWI (Adam) in the embodiments of this invention achieves excellent reconstruction results for erosion edges and slopes. The convergence plot shows that Adam+RNN-FWI converges the fastest, consistent with previous assumptions. Optimization algorithms with adaptive momentum gradient step size updates and mini-batch datasets can significantly accelerate convergence, requiring only about two epochs. Although the final loss value on the convergence plot is very close between Adam and L-BFGS-B, it can be seen that the conventional FWI depth reconstruction in the comparative example is still insufficient compared to RNN-FWI (Adam).

[0102] Regarding computation time costs, the addition of GPUs has improved computation speed. Timing stops when the objective function reaches a predetermined threshold.

[0103] Table 2 shows the computation time for convergence of the two algorithms.

[0104] Table 2 Time Consumption of Various Algorithms

[0105]

[0106] In this comparative example, experiments were also conducted using the experimental configuration of an embodiment of the present invention. The difference was that the observed values ​​used actual acquired waveforms and underwent certain signal processing. The velocity model was reconstructed using RNN-FWI (Adam+UNet) and traditional FWI (L-BFGS-B+TV). The initial model was an undamaged aluminum plate model with uniform thickness.

[0107] Figure 15 This is a comparison chart of the calculation results of real experimental data from embodiments and comparative examples of the present invention, wherein... Figure 15 (a) is a result diagram of the embodiment. Figure 15 (b) is a comparative result graph.

[0108] like Figure 15 As shown, the comparison chart in the figure shows the results of RNN-FWI using Adam and UNet in the embodiment of the present invention, and the results of traditional FWI using TV regularization and L-BFGS-B in this comparison example.

[0109] Figure 16 These are cross-sectional comparison diagrams of the reconstruction results of embodiments and comparative examples of the present invention, wherein... Figure 16 (a) is a result diagram of the embodiment. Figure 16 (b) is a comparative result graph.

[0110] like Figure 16 As shown, however Figure 12 The imaging accuracy was observed by performing a cross-sectional view at the indicated location. We used 10 epochs for the inversion.

[0111] The observation results show that the algorithm proposed in the embodiments of the present invention uses actual experimental data as observation data. Although the filtering window filters out the echo signal, the RNN-FWI of the embodiments of the present invention still realistically depicts the shape of the erosion. At some thinner defect locations, the inverted depth is not as reliable as the true depth value, but compared with traditional algorithms, the improvement in accuracy and robustness is significant.

[0112] The role and effect of the embodiments

[0113] According to the full-waveform inversion guided wave tomography method based on recurrent neural networks involved in this embodiment, the specific process is as follows: Step 1, the time series forward modeling based on the acoustic wave formula of the finite difference method is realized by using the sequence calculation of CNN to obtain the initial model; Step 2, according to the initial model, the wave field value at each time step at each excitation position is calculated in turn to generate the simulated value; Step 3, after signal processing, the actual observed value generates the least squares objective equation of the simulated value and the observed value; Step 4, the inversion part iteratively minimizes the least squares objective equation. The inversion part includes automatic differentiation and Adam algorithm. Automatic differentiation is responsible for calculating the gradient of the objective equation, and Adam algorithm is responsible for iteratively updating the velocity model and UNet weights, and finally generating the updated velocity model; Step 5, the updated velocity model is regularized by DIP-UNet to generate the initial model for the next iteration; Step 6, Steps 1 to 5 are repeated to perform the next iteration calculation until the objective equation is lower than the specified threshold to obtain the final velocity model, and the final velocity model is converted into a thickness model using the dispersion relation.

[0114] Therefore, the full-waveform inversion guided wave tomography method based on recurrent neural networks provided in this embodiment has better performance in terms of convergence speed, initial model requirements, robustness, and accuracy.

[0115] Furthermore, the RNN temporal structure enables computation at each time point of the forward computation, and the automatic differentiation method replaces the adjoint state method to calculate the gradient of the objective function in the inversion. These two aspects provide the foundation for introducing deep learning into FWI. RNN-FWI uses the Adam mini-batch global optimization algorithm to update model parameters, which does not require the computation of the Hessian matrix, thus resulting in faster convergence and less memory requirements, replacing the traditional quasi-Newton method.

[0116] Furthermore, deep learning RNNs provide a solution to address the shortcomings of traditional FWI. The Adam optimization algorithm avoids the calculation of the Hessian matrix, quickly explores the descent space with small batches of data, accelerates convergence, and reduces memory requirements; the automatic differentiation method avoids explicit gradient calculation and avoids the systematic errors of the adjoint state method; the CNN-based DIP regularization method can enhance the robustness of the algorithm, alleviate the periodic jump phenomenon, and does not require subjectively set parameters.

[0117] Finally, this embodiment and the comparative example compare and analyze the performance of RNN-FWI with several optimization algorithms such as Adam and conventional FWI in experiments. Through numerical simulation and actual experiments, it is concluded that RNN-FWI avoids the situation of getting trapped in local minima to a certain extent. The regularization tool based on UNet enhances robustness and gets rid of the high dependence on the initial velocity model. The Adam optimization algorithm speeds up the convergence speed and reduces memory usage.

[0118] The above embodiments are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention.

Claims

1. A guided wave tomography method based on full waveform inversion using a recurrent neural network, characterized in that, Includes the following steps: Step 1: Use the sequence calculation of the recurrent neural network to realize the time series forward modeling of the acoustic wave formula based on the finite difference method, and obtain the initial model; Step 2: Based on the initial model, calculate the wave field value at each time step at each excitation position in a sequential loop to generate simulated values; Step 3: After signal processing, the actual observed values ​​are used to generate the least squares objective equations of the simulated and observed values. Step 4: The inversion part iteratively minimizes the least squares objective equation. This inversion part includes automatic differentiation and the Adam algorithm. The automatic differentiation method is responsible for calculating the gradient of the objective equation, and the Adam algorithm is responsible for iteratively updating the velocity model and UNet weights, finally generating an updated velocity model. The Adam algorithm is used to update the weight parameters of the recurrent neural network: （5） In the formula, It is an iterative update step size. It is the number of iterations. It is the gradient. The least squares objective equation is rewritten as: （6） In the formula, It's a neural network. It is a random matrix. These are the weights of the neural network; Step 5: Apply depth image prior UNet regularization to the updated velocity model to generate the initial model for the next iteration; Step 6: Repeat steps 1 to 5 for the next iteration calculation until the target equation is below the specified threshold to obtain the final velocity model. Then, use the dispersion relation to transform the final velocity model into a thickness model.

2. The guided wave tomography method based on full waveform inversion using a recurrent neural network according to claim 1, characterized in that: in, In step 1, the forward modeling is the process of numerically propagating the wave source in the model and recording the wave field at the location of the receiving transducer. The specific process is as follows: The formula for two-dimensional acoustic waves in a constant-density medium is expressed as: (1) (2) In the formula It's a Tron field. It is a wave source. Represents a 2D or 3D spatial vector. It is time. It is the speed of ultrasonic waves. It is the space Laplace operator. Forward operator, Equation (1) is calculated and discretized using the finite difference method, and the wave field is calculated at the finite difference grid points. The second-order finite difference is defined as: (3) In the formula It is the unit step time. By solving the above equations simultaneously, we obtain the following result: (4) Equation (4) is the forward modeling formula for full waveform inversion. The wave field values ​​at all times can be obtained by calculating Equation (4).

3. The guided wave tomography method based on full waveform inversion using a recurrent neural network according to claim 1, characterized in that: in, In step 5, the detailed structural parameters of the depth image prior UNet regularization are shown in the following table: 。 4. The guided wave tomography method based on full waveform inversion using a recurrent neural network according to claim 1, characterized in that: in, In step 5, the output of UNet is directly combined with the updated velocity model as the velocity map parameter update for the next full waveform inversion loop.

Images