Guided wave frequency dispersion compensation method and device based on Fourier-based CAE (Computer Aided Engineering) network

Abstract

The invention relates to the technical field of ultrasonic guided wave processing, in particular to a guided wave frequency dispersion compensation method and device based on a Fourier-based CAE network, and the method comprises the following steps: collecting an ultrasonic guided wave signal; constructing a convolutional self-encoding network model based on a Fourier basis; substituting the ultrasonic guided wave signal data into the convolutional self-encoding network model for training until the convolutional self-encoding network model tends to be stable; inputting the acquired ultrasonic guided wave signal data into the trained convolutional self-encoding network model, and outputting a coordinate with a maximum value; and taking a maximum value coordinate, converting the maximum value coordinate to a time domain again, combining the excitation signal, and performing frequency dispersion compensation on the ultrasonic guided wave signal to obtain a guided wave signal without frequency dispersion. According to the method, the Fourier basis is introduced into the auto-encoder, and a path for performing time-frequency information extraction by using the Fourier basis is added, so that the converted data has two characteristics of time and frequency, signal frequency dispersion compensation under the condition of multiple wave packets can be realized, and the effect is relatively good.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic guided wave processing technology, and in particular to a guided wave dispersion compensation method and apparatus based on Fourier basis CAE networks. Background Technology

[0002] Ultrasonic guided waves are widely used in nondestructive testing (NDT) and structural health monitoring (SHM) due to their advantages such as low propagation attenuation, long detection distance, high detection efficiency, and low detection cost. Ultrasonic guided waves propagating in waveguide media exhibit dispersion and multimodal characteristics. The dispersion characteristic of guided waves refers to the change in phase velocity and group velocity with frequency during propagation. This dispersion causes inconsistent propagation speeds of guided waves at different frequencies, resulting in guided wave echoes with the same structural features not arriving at the transducer simultaneously. Due to the difference in wave velocity, the echo wave packet gradually widens in the time domain with increasing propagation distance, dispersing acoustic energy in the time-space domain. This reduces the signal-to-noise ratio and sensitivity of the detection signal, and also reduces the temporal resolution of the Lamb wave, affecting damage localization and imaging results. Therefore, dispersion elimination or compensation is essential for efficient guided wave applications.

[0003] Over the past few decades, several methods have been proposed for dispersion compensation, such as optimized excitation waveform design, signal domain transformation, linearization mapping, frequency distortion transformation, and time reversal. Typically, narrowband excitation signals can significantly reduce dispersion in the frequency domain because the fluctuations in the phase velocity and group velocity of guided waves are small within this frequency range, and the reduced bandwidth weakens the dispersion effect. However, in the time domain, this makes signals more prone to overlap, thus reducing time resolution. Liu and Yuan, based on the Taylor wavenumber linear approximation, proposed a linear mapping method for single-mode Lamb wave dispersion removal, verifying its effectiveness using A0-mode Lamb wave signals from an aluminum plate. Wilcox proposed an effective dispersion compensation method called the time-distance mapping method, which maps the single-mode Lamb wave signal from the time domain to the distance domain. Backpropagation is also a very effective signal processing tool in dispersion compensation; for example, the time reversal method reverses the dispersion signal in the time domain, retransmitting it from the sensor position to the actuator position. Hua performs dispersion compensation by applying time reversal to the excitation signal at a given distance. De Marchi et al. proposed a dispersion compensation method using warped frequency transformation. However, due to the nonlinearity of the warped function, the compensated signal still exhibits distortion compared to the excitation.

[0004] Due to their powerful ability to extract nonlinear features, neural networks are widely used in the study of guided wave signals. Most researchers process the guided wave data first, then use a network model to learn the features. Liao developed a super-resolution deconvolutional neural network applicable to all Lamb wave modes based on the dispersion relationship of Lamb wave modes, capable of acquiring sub-wavelength defect images of layered structures. Chen obtained defect image data from the extracted defect echo signals using a total focusing method, and then trained the data samples using a fast region convolutional neural network model to quantitatively assess the defect location. Fakih proposed a novel structural health monitoring method that uses a small number of sensors to achieve damage detection, localization, and assessment. This method establishes a six-parameter Bayesian inference for damage degree and location, thereby enabling damage detection, localization, and assessment in different materials. Shao used a one-dimensional convolutional neural network to deeply mine the damage features of complex Lamb wave signals with multiple modes and multiple boundary reflections. A three-level damage classification multi-task cascaded one-dimensional convolutional neural network architecture was established, corresponding to different structural health monitoring levels. Rautela et al. proposed a joint training model of convolutional neural network and long short-term memory network for damage detection and localization in a supervised environment, and then verified the stability of the network in a real-world scenario.

[0005] Existing guided wave dispersion compensation methods perform well when dealing with a single wave packet, but their performance is poor when dealing with more than one wave packet. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a guided wave dispersion compensation method and apparatus based on Fourier basis CAE network, which can realize signal dispersion compensation in the case of multiple wave packets, and the effect is good.

[0007] The present invention solves the above-mentioned technical problems through the following technical means:

[0008] In a first aspect, embodiments of the present invention provide a waveguide dispersion compensation method based on a Fourier basis CAE network, comprising the following steps:

[0009] Acquire ultrasonic guided wave signals;

[0010] Construct a convolutional autoencoder network model based on Fourier basis;

[0011] The ultrasonic guided wave signal data is substituted into the convolutional autoencoder network model for training until the convolutional autoencoder network model tends to stabilize.

[0012] The collected ultrasonic guided wave signal data is input into the trained convolutional autoencoder network model, and the output value is the coordinate of the maximum value.

[0013] The maximum value coordinates are taken and transformed back to the time domain. Combined with the excitation signal, and the ultrasonic guided wave signal is subjected to dispersion compensation to obtain the guided wave signal with dispersion removed.

[0014] The guided wave dispersion compensation method based on Fourier basis CAE network of the present invention introduces Fourier basis into the autoencoder CAE model and adds a path for extracting time and frequency information using Fourier basis, so that the transformed data has both time and frequency characteristics. Due to the frequency dependence of guided wave signal, the features with time and frequency characteristics can be used more effectively for training network model.

[0015] The guided wave dispersion compensation method based on Fourier basis CAE networks of this invention learns the Time-of-Flight (TOF) of the signal through a Fourier basis-based convolutional autoencoder network model, thereby reconstructing a non-dispersion guided wave signal. This provides a new solution to the problem of insufficient datasets in current guided wave research. The guided wave dispersion compensation method based on Fourier basis CAE networks of this invention can achieve dispersion compensation in multiple wave packet scenarios with good results.

[0016] This invention presents a guided wave dispersion compensation method based on a Fourier-based CAE network. By adding a Fourier-based convolution module to the CAE network, the model can simultaneously learn the time-domain and frequency-domain characteristics of the signal. Regarding the parameter selection of the Fourier convolution layer, the performance of the Fourier-based convolutional autoencoder (FCE) was compared under different numbers and lengths of convolutional kernels. Increasing the number of convolutional kernels initially improves the model's performance, then worsens it, while longer kernel lengths generally improve performance. Experimental tests compared the Fourier-based FCE with the original convolutional autoencoder in numerical simulation, modeling, and experimental aspects. The results show that the Fourier-based FCE generally performs better. Finally, dispersion compensation for both simulated and experimental signals was implemented and applied to DAS defect imaging.

[0017] In a second aspect, the present invention also provides a guided wave dispersion compensation device based on a Fourier basis CAE network, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described in the first aspect above.

[0018] Thirdly, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in the first aspect above.

[0019] It is understood that the beneficial effects of the second and third aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here. Attached Figure Description

[0020] Figure 1This is a flowchart of a waveguide dispersion compensation method based on Fourier basis CAE networks;

[0021] Figure 2 This is the overall flowchart of learning Time of Flow using a Fourier basis-based convolutional autoencoder;

[0022] Figure 3 This is a flowchart of the setup process for a Fourier basis convolutional autoencoder model;

[0023] Figure 4 It is a dispersion curve of the aluminum plate;

[0024] Figure 5 This is a sample image from dataset 1;

[0025] Figure 6 This is a sample image from dataset 2;

[0026] Figure 7 This is a 3-sample image of the dataset;

[0027] Figure 8 This is the result image after training dataset 1;

[0028] Figure 9 This is the result image after training dataset 2;

[0029] Figure 10 This is the result image after training dataset 3;

[0030] Figure 11 This is a graph showing the experimental results for dataset 3 under different convolutional kernel sizes;

[0031] Figure 12 It represents the accuracy for different kernel lengths;

[0032] Figure 13 These are the experimental results for dataset 3 under different numbers of convolutional kernels;

[0033] Figure 14 It represents the accuracy under different numbers of convolutional kernels;

[0034] Figure 15 This is an example image of a simulated dataset from a simulation verification experiment for defect imaging;

[0035] Figure 16 This is a training result image of the simulated dataset in the simulation verification experiment of defect imaging;

[0036] Figure 17 These are the timing diagrams of six sets of simulated signals from the simulation verification experiment for defect imaging;

[0037] Figure 18 This is a signal image obtained from a simulation verification experiment of defect imaging after removing dispersion;

[0038] Figure 19 This is the final defect detection image obtained in the simulation verification experiment of defect imaging;

[0039] Figure 20 This is an example image of the experimental dataset used in the experimental verification experiment for defect imaging;

[0040] Figure 21 This is a diagram showing the training results of the experimental dataset in the experimental verification experiment for defect imaging;

[0041] Figure 22 This is a timeline diagram from the experimental verification experiment of defect imaging;

[0042] Figure 23 This is a signal image obtained from the experimental verification experiment of defect imaging after removing dispersion;

[0043] Figure 24 This is the final defect detection image obtained in the experimental verification experiment of defect imaging. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0045] The terms "first" and "second," etc., used in the specification and claims herein are used to distinguish different objects, not to describe a specific order of objects. In the description of embodiments of this application, unless otherwise stated, "a plurality of" means two or more, for example, "a plurality of processing units" means two or more processing units, "a plurality of elements" means two or more elements, etc.

[0046] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0047] Traditional autoencoders are widely used in feature learning, noise reduction, and other fields. The input signal undergoes multiple convolution operations to learn its main features, and then deconvolution is the reverse process, i.e., the operation of restoring the signal from the features. Generally, it is desirable for the input and output signals to have a high degree of similarity. However, the goal of this application is to learn the Time of Flight (TOF) of the signal for dispersion compensation. Considering the frequency correlation of the guided wave signal, Fourier basis is introduced into the CAE model, enabling the network model to learn both time-domain and frequency-domain features simultaneously.

[0048] Please refer to Figure 1 This application discloses a waveguide dispersion compensation method based on Fourier basis CAE networks, comprising the following steps:

[0049] Step S100: Acquire ultrasonic guided wave signals.

[0050] Step S200: Construct a convolutional autoencoder network model based on Fourier basis, namely the FCAE model.

[0051] Step S300: Substitute the ultrasonic guided wave signal data into the convolutional autoencoder network model for training until the convolutional autoencoder network model tends to stabilize.

[0052] Step S400: Input the collected ultrasonic guided wave signal data into the trained convolutional autoencoder network model, and take the coordinates of the maximum value of the output value.

[0053] In step S500, the maximum value coordinates are taken and transformed back to the time domain. Combined with the excitation signal, the ultrasonic guided wave signal is subjected to dispersion compensation to obtain a guided wave signal with dispersion removed.

[0054] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0055] First, let's understand the dispersion compensation principle of this application. When the wavenumber and frequency are linearly related, the signal dispersion only manifests as a phase shift and does not affect the propagation time or the signal packet width. This is the basic principle of dispersion compensation. The signal that has propagated over a specific distance x0 is given by the following equation (1):

[0056] (1)

[0057] Where j represents the imaginary sign and t represents time. The derivative representing frequency, It is an excitation signal The Fourier transform of the waveguide, where k is the frequency of a specific guided wave mode. The wavenumber under the given conditions, based on the Fourier transform, can be expressed as:

[0058] (2)

[0059] In equation (2), , It is a signal Fourier transform. It will not cause dispersion, so we can obtain:

[0060] (3)

[0061] Can be Interpolation is performed to obtain the distance traveled by a velocity c. non-dispersion signal It can be represented as:

[0062] (4)

[0063] As can be seen from equation (4), the dispersion compensation of the signal is only related to a time delay. This time delay, namely TOF, is learned through the network, and then combined with equation (4) to obtain the non-dispersion signal.

[0064] The above is the basic principle of dispersion compensation.

[0065] The acquired ultrasonic guided wave signals can originate from fields such as non-destructive testing and structural health monitoring. Due to the complexity of guided wave signals, Time-of-Flight (TOF) analysis obtained solely from time-domain features is susceptible to interference between signal wave packets. Therefore, a Fourier-based convolutional layer is added to extract the frequency-domain features of the signal, enabling TOF learning from multiple perspectives.

[0066] To extract frequency information, the first layer is set as a custom layer to implement the Fourier transform of the input data. In fact, since the Fourier basis of the first layer is usually set to be smaller than the length of the input data, this transform can be regarded as a short-time Fourier transform, which can balance frequency and time information.

[0067] The convolution kernel of a Fourier convolutional layer references the Discrete Fourier Transform:

[0068] (5)

[0069] in , It is a time-domain signal sequence, where N is the signal length, k represents the frequency sampling point, and j represents the imaginary sign. Using the relationship between trigonometric functions and the exponent e, equation (5) can be rewritten as:

[0070] (6)

[0071] In formula (6), i represents the imaginary number symbol.

[0072] The result of the discrete Fourier transform of a real number signal is a set of complex numbers. Since the amplitude is the key, while the phase information is not used, and for the convenience of network model calculation, the cosine basis and sine basis are calculated separately, and then the amplitude of the two components is calculated to realize the setting of the Fourier basis convolution kernel.

[0073] To improve efficiency, convolution and deconvolution operations are introduced to form an encoder-decoder structure. Convolutional structures are also introduced to reduce the number of weights and connections. Finally, a neural network form of the CAE is formed. In the CAE used in this application, in addition to the Fourier base convolutional layers and the last convolutional layer, each convolutional layer is followed by a batch normalization layer and an activation layer, which enables both feature extraction and efficient model training. In this stage, the input signal is z, and the learned features... It can be represented as:

[0074] (7)

[0075] in, The weights represent the convolutional kernels that connect the input and hidden layers. It's a bias. It is batch normalization that makes the learning process more stable. It is a non-linear activation function used to mitigate the vanishing or spiking gradient problem. The decoder uses compressed features from the encoder to generate a sequence containing Time-of-Flight (TOF) sequences, which includes deconvolution layers, batch normalization (BN) layers, and activation function layers. High-level features are upsampled through deconvolution operations and decompressed into TOF sequences, generating the output... It can be represented as:

[0076] (8)

[0077] in, The weights represent the decoder weights. This is the bias. The mean squared error (MSE) is used as the loss function to optimize the parameters, while also optimizing the parameters by minimizing the following error between the decoded output and the given label. The labels and loss functions are set as shown in Equations (9) and (10), respectively:

[0078] (9)

[0079] (10)

[0080] In the above formula, This is the decoded output of the model, where t represents time. j Representing time, A j Represents signal amplitude. This represents the unit of the impact signal. By adjusting the parameters to minimize the error, accurate compensation for the Time-of-Flight (TOF) of the dispersive signal can be achieved.

[0081] The overall process of learning Time-of-Flight (TOF) using a Fourier-based convolutional autoencoder is as follows: Figure 2 As shown, the required dispersion curve is first calculated using software, then the required dataset is generated, the dataset is divided into training and testing sets, and then substituted into the network model for training. Finally, the accuracy of the model is verified in the test data.

[0082] Figure 3 The diagram shows the setup of the FCAE network model. Because the kernel length of the Fourier basis convolutional layers is larger than that of typical convolutional kernels, the signal length after two rounds of convolution is not strictly equal to 250, but this makes the model architecture easier to understand. Compared to the original CAE model, a path for extracting time-frequency information using Fourier basis is added. The original model can only utilize time-domain information, while FCAE references both time-domain and frequency-domain information, allowing it to identify more feature information.

[0083] The Fourier basis-based convolutional autoencoder consists of a custom convolutional layer and a subsequent convolutional autoencoder. The custom convolutional layer first generates multiple cosine and sine functions of selected frequencies, then convolves the data with the cosine and sine bases respectively, and performs a square root operation by squaring and summing the two results to achieve the Fourier basis convolution operation on the data.

[0084] Because the convolution process of a neural network is highly similar to the short-time Fourier transform, the features obtained by convolving the Fourier basis convolution kernel with the signal also possess certain temporal information. Since the sine and cosine bases are of finite length, this process can be analogized to performing a short-time Fourier transform on the data, resulting in the transformed data exhibiting both time- and frequency-related characteristics. Due to the frequency dependence of guided wave signals, features with time- and frequency characteristics can be more effectively used for training the network model.

[0085] The waveguide dispersion compensation method based on Fourier basis CAE network proposed in this application will be numerically simulated, modeled, and experimentally tested to fully understand the beneficial effects achieved by the waveguide dispersion compensation method based on Fourier basis CAE network proposed in this application.

[0086] I. Numerical Simulation

[0087] (1) Dataset creation

[0088] To verify the effectiveness of the guided wave dispersion compensation method based on Fourier basis CAE networks proposed in this application, a 1mm thick aluminum alloy 1100 plate was selected as the material plate, and the dispersion information and wavenumbers of the A0 and S0 modes were calculated. and speed A sinusoidal signal modulated by a 3-cycle Hanning window with a center frequency of 100kHz was used as the excitation, and the propagation distance was from 0 to 1m, uniformly divided into 5000 points. The sampling frequency was set to... Hz, time sampling number is set to 500, and data amplitude in the dataset is set to 1.

[0089] In the simulated data experiments, three datasets were generated. The first dataset (dataset 1) contained only one wave packet, generated by either the A0 or S0 mode, with 5000 data points generated for each mode. The second dataset (dataset 2) contained two wave packets, adding a wave packet from another mode with a random propagation distance to the first dataset. The third dataset (dataset 3) contained three wave packets, adding a wave packet from a random mode to the second dataset. The datasets were randomly divided into a training set of 9000 data samples and a test set of 1000 data samples. The generated signals were normalized, and the sample data and dispersion information used in the datasets are as follows: Figures 4-7 As shown, at a frequency of 100 kHz, the wavenumber of the A0 mode changes rapidly, exhibiting a significant dispersion effect, while the wavenumber of the S0 mode is nearly linear, with a weak dispersion phenomenon. As the excitation signal propagates a certain distance, the dispersion phenomenon becomes more pronounced.

[0090] This dispersion causes the guided wave packet to broaden in the time domain, extending the waveform over time. The result is a reduction in signal resolution, making it difficult to distinguish specific features, especially when multiple wave packets overlap. In this situation, the various components of the signal become intricately intertwined, making it difficult to separate and differentiate their individual characteristics.

[0091] (2) Dataset performance comparison

[0092] The CAE model consists of two convolutional modules and two deconvolutional modules. Except for the last deconvolutional module, which lacks a batch normalization (BN) layer, each convolutional module (or deconvolutional module) consists of one convolutional layer (or deconvolution), one BN layer, and one ReLU activation function layer. The FCAE model, besides adding a Fourier basis convolutional layer and one convolutional module, which are then connected to the two convolutional modules of the original CAE model, has a similar network structure to CAE, differing only slightly in the convolutional kernel size. The FCAE model uses 10 frequency components, uniformly distributed from 95kHz to 105kHz. Table 1 shows the model's structural settings when the kernel length for each frequency is 30. Once the Fourier basis is set, no further parameter updates are performed; parameter settings will be described later.

[0093]

[0094] Table 1

[0095] Experiments were conducted on both CAE and FCAE models. The optimizer for both models was adam, the learning rate was set to 1e-3, the batch size was set to 64, MSE was used as the loss metric, and the number of iterations was set to 500.

[0096] The results after training on dataset 1 are as follows Figure 8 As shown, Figure 8 In the table, (a) represents CAE loss, (b) represents FCAE loss, (c) represents CAE accuracy, and (d) represents FCAE accuracy. Figure 8 It can be seen that both CAE and FCAE models have good learning capabilities, with accuracies of 0.967 and 0.974, respectively. The data structure is relatively simple, containing only a single wave packet, allowing for the learning of many features solely from the time domain. Due to the time-frequency resolution limitations of Fourier convolution, frequency domain features also have certain limitations; therefore, the performance of the two models is similar.

[0097] The results after training on dataset 2 are as follows Figure 9 As shown, Figure 9 In the table, (a) represents CAE loss, (b) represents FCAE loss, (c) represents CAE accuracy, and (d) represents FCAE accuracy. Figure 9 It can be seen that the differences between the CAE and FCAE models are quite significant, especially when predicting the flight time of the second wave packet. The accuracies of CAE and FCAE on the first wave packet are 0.908 and 0.933 respectively, with the performance difference still within an acceptable range. However, on the second wave packet, the accuracy difference between the CAE and FCAE models reaches 0.11, with CAE achieving 0.81 and FCAE 0.923. This is certainly related to the fluctuating accuracy of the CAE model on the test machine during training, but overall, the FCAE model shows better performance. At this point, the data structure becomes more complex, with some wave packets overlapping, affecting the accuracy improvement. Features learned solely from the time domain are affected by interference between wave packets, while frequency domain features do not have this problem, hence the better performance of the FCAE model. Furthermore, under the same parameters, the FCAE model's test set accuracy is more stable, while CAE fluctuates significantly over a wider range. Interference between wave packets makes it difficult to distinguish between two wave packets in the time domain. The added Fourier convolutional layer enables the model to distinguish wave packets in the time and frequency domains, thus increasing the model's stability.

[0098] The results after training on dataset 3 are as follows Figure 10 As shown, Figure 10In the table, (a) represents CAE loss, (b) represents FCAE loss, (c) represents CAE accuracy, and (d) represents FCAE accuracy. Figure 10 As can be seen, the interference between different wave packets is more severe in this data, leading to a further difference in performance between the CAE and FCAE models. The difference between the two models is quite significant, especially when predicting the time of flight of the second wave packet. The accuracy of CAE and FCAE on the first wave packet is 0.906 and 0.918, respectively. This is because the first wave packet is usually an S0 mode wave packet, with a certain interval from the other two wave packets, resulting in higher accuracy. However, on the second wave packet, the accuracy of CAE and FCAE models is 0.758 and 0.800, respectively, and on the third wave packet, the accuracy is 0.797 and 0.828, respectively. Compared to the first wave packet, the accuracy of the latter two wave packets is significantly lower. The data structure is more complex now, with some wave packets overlapping significantly, which greatly affects the accuracy improvement. Features learned only from the time domain are more affected by the interference between wave packets compared to dataset 2, while learning both time and frequency domain features simultaneously reduces this effect, thus the FCAE model performs better.

[0099] Similar to the training results of dataset 2, under the same parameters, the FCAE model exhibits more stable test set accuracy, while the CAE model fluctuates significantly over a wider range. The training and test set accuracies for wave packet 1 tend to be consistent because the S0 mode wave packet contained in the signal is temporally separated from the other two wave packets, thus allowing both models to achieve similar accuracies. However, for overlapping wave packets, it is difficult to distinguish between the two wave packets in the temporal domain; the added Fourier convolutional layer increases the discriminative power of the signal components.

[0100] The performance of the CAE and FCAE models on the three datasets is shown in Table 2:

[0101]

[0102] Table 2

[0103] The data in Table 2 shows that the FCAE model has a higher accuracy than the CAE model. With a single wave packet, the signal structure is simple, and similar results can be obtained from both time-domain and time-frequency-domain characteristics. When there are two or more wave packets, the resolving power of the signal's time-domain characteristics decreases, and frequency-domain information is needed to effectively distinguish multiple wave packets.

[0104] (3) Setting the kernel size and number of Fourier bases

[0105] The added Fourier basis module serves two purposes. First, because the set Fourier basis size is much smaller than the signal length, this convolution is similar to the short-time Fourier transform, meaning the extracted features have time-frequency characteristics, which can better distinguish Lamb wave signals. Second, the Fourier basis treats the truncated signal segment as a stable periodic signal, thus achieving better noise suppression.

[0106] However, the features extracted using Fourier basis methods also bring some negative effects to the network. This convolutional form loses frequency information at the end of the model, and the frequency information collected is also related to the convolution length. Therefore, the size of the convolution kernel has a certain impact on the model's accuracy. Similarly, the number of convolution kernels, i.e., how many frequency points are collected, also affects the model's performance. The following section will delve into the impact of Fourier basis kernel size and the number of convolution kernels on the model.

[0107] (I) Influence of kernel size

[0108] Dataset 3 best reflects the model's performance, therefore, it was chosen for the experiments. At a center frequency of 100 kHz, one sine wave period is approximately 5 time steps. Therefore, 5 time steps were chosen as the basic growth unit. The convolutional size was gradually increased from 5, with each increase being 5 units, for a total of 10 experiments. The frequency of the convolutional kernel was set to a frequency sampling point divided into ten equal parts from 95 kHz to 105 kHz. The optimizer was the Adam optimizer, with a learning rate of 1e-3, a batch size of 64, MSE as the loss metric, and 200 iterations. The Fourier basis convolutional layers were not involved in parameter updates.

[0109] Figure 11 Training results are presented for the FCAE model excluding the model with a kernel size of 30. When the kernel size is small, the test results for the second and third wave packets fluctuate significantly, and the accuracy is also low. As the kernel size increases, the training and test results become largely consistent, and the accuracy improves. When the kernel size increases to 35 or higher, the FCAE model in this application exhibits some degree of overfitting, and the accuracy tends to stabilize.

[0110] The accuracy of FCAE models with different kernel sizes after 200 training iterations is shown in Table 3:

[0111]

[0112] Table 3

[0113] When the kernel size is less than 15, the FCAE model has a high recognition rate for the first wave packet, but its recognition rate for the second and third wave packets is significantly lower than that of models with other kernel sizes, resulting in poor overall performance. This indicates that the efficiency of frequency feature extraction is low at this kernel size. Ignoring some fluctuations during the iteration process, the overall performance of the model increases with the increase of the kernel size. With a 3-period excitation signal, due to the dispersion effect, the wave packets of the signal become longer, thus requiring a longer kernel length to extract the signal frequency. However, an excessively long kernel will cause multiple wave packets to participate in the convolution process at the same location, introducing some unfavorable constraints to feature recognition.

[0114] The recognition rate of the third wave packet is most significantly affected by the kernel size. Although the third wave packet, like the first, is located at the edge, it propagates for the longest time, exhibits more severe dispersion, and has stronger interference with the second wave packet, resulting in a lower recognition rate than the first. Increasing the kernel size expands the features the model can learn, thus having the greatest impact on the third wave packet.

[0115] like Figure 12 As shown, the overall performance of the FCAE model increases with the increase of convolutional kernel size. The model's recognition rate is consistently higher for the first wave packet than for the other two wave packets, because the first wave packet experiences less interference with the other wave packets. The training accuracy for the third wave packet is generally in the middle, while the accuracy for the second wave packet is the lowest, reflecting that the second wave packet experiences the most severe inter-packet interference.

[0116] (II) The influence of the number of convolution kernels

[0117] At a center frequency of 100 kHz, the frequency range of 95 kHz to 105 kHz constitutes the majority of the signal energy. Therefore, this range was divided into ten equal groups of sampling frequencies, with the number of groups ranging from 1 to 10. The convolution kernel length for each frequency was set to 30, and the rest were set up using the same numerical simulation experiments as dataset 3.

[0118] Figure 13 Training results are presented for models other than the FCAE model with 10 convolutional kernels. With fewer convolutional kernels, the accuracy on the training set and the test set remain consistent, indicating that the FCAE model can fully learn the signal features. As the number of convolutional kernels increases, the accuracy on the training set is higher than the accuracy on the test set for the two packets other than the first packet, with a difference of approximately 0.02. This indicates a slight overfitting phenomenon; the model learns more features, but this is also somewhat affected.

[0119] The accuracy of FCAE models with different numbers of convolutional kernels after 300 training iterations is shown in Table 4:

[0120]

[0121] Table 4

[0122] The overall performance of the FCAE model reaches its peak when the number of convolutional kernels is 5. At this number, the FCAE model can effectively learn frequency features without overfitting. When the number of convolutional kernels is less than 5, the FCAE model learns insufficient features; when it is greater than 5, it learns too many features and cannot effectively extract them. Too many input features lead to an increase in the number of parameters in the FCAE model. However, since only the parameters of the first Fourier convolutional layer change, the rest of the structure remains unchanged. Therefore, the model cannot effectively utilize the features output by the Fourier convolutional layers, easily leading to overfitting.

[0123] like Figure 14 As shown, the overall performance of the FCAE model first increases and then decreases with the increase of the number of convolutional kernels. When the number of convolutional kernels is 5, the recognition rate of the three wave packets of the FCAE model is relatively high, and then the performance of the FCAE model gradually declines.

[0124] II. Simulation Verification of Defect Imaging

[0125] Six sets of simulation data obtained using the ABAQUS simulation software cannot be directly used in deep learning. After simulating the propagation signal, it is substituted into the FCAE model for training. Based on the time interval of the simulation data, the sampling frequency is calculated to be 1129575 Hz. The Abaqus simulation experiment still uses an aluminum plate. Based on the corresponding dispersion curve, a simulated signal is generated using a 3-cycle Hanning window modulation signal with a center frequency of 100 kHz as the excitation. The propagation distance is from 0 to 1 m, uniformly divided into 5000 points, with 500 time points sampled, and all amplitudes set to 1. Since the scattered wave in the Abaqus simulation data contains only one wave packet, a dataset containing only one wave packet is generated. The wave packet is generated from either the A0 or S0 mode, with 5000 data points generated for each mode. The generated data samples are as follows: Figure 15 As shown, compared to dataset 1, the sampling frequencies of the two datasets are different, resulting in different generated signals.

[0126] The basic settings of the model are the same as those in the experiment conducted on dataset 1 above. After 500 iterations, the FCAE model tends to stabilize. The training results are shown in [link to training results]. Figure 16 , Figure 16In the table, (a) represents the CAE loss, (b) represents the FCAE loss, (c) represents the CAE accuracy, and (d) represents the FCAE accuracy. The CAE accuracy reaches 0.872, while the FCAE model achieves 0.929. On this dataset, the accuracy is lower compared to dataset 1. The comparison reveals that different data frequencies also lead to changes in signal characteristics. The time-domain features extracted by the CAE model ignore this frequency variation, while the FCAE model, due to its performance limitations, suffers from overfitting and loses some accuracy.

[0127] After training, the six sets of data obtained from the simulation are input into the model, and the output value is the coordinate of the maximum value. The time sequence diagrams of the six sets of simulated signals are as follows. Figure 17 As shown, due to the symmetry of the path, the data sets are pairwise approximate, resulting in severe data dispersion and a loss of signal energy concentration. The output results after training are shown in Table 5.

[0128]

[0129] Table 5

[0130] The data in Table 5 show that the CAE and FCAE models have similar results, with significant differences only in signals 2 and 5. At this point, the signal dispersion is most severe, and the energy of the wave packet is most dispersed; therefore, the model's signal recognition rate will decrease. By transforming the maximum value coordinates back to the time domain and combining them with the excitation signal, dispersion compensation is performed on the signal according to formula (4), resulting in a dispersion-removed signal as shown below. Figure 18 As shown, Figure 18 In the diagram, (a) is the CAE model and (b) is the FCAE model. Compared to the original signal, the signal after dispersion compensation achieves energy reconcentration.

[0131] Combining the DAS imaging algorithm, the final defect detection results are as follows: Figure 19 As shown, Figure 19 In the image, (a) is the CAE model and (b) is the FCAE model. Figure 19 In the diagram, black squares represent the location of defects, and white circles represent the locations of sensors. The CAE model does not accurately represent the location of damage, while the FCAE model does.

[0132] III. Experimental Verification of Defect Imaging

[0133] Similar to simulation verification experiments, simulation data was generated and then fed into the network model for training. Based on the time interval of the collected data, the sampling frequency was calculated to be 1.5 MHz. 304 stainless steel plates were used in the experiment. Based on the corresponding dispersion curve, a simulated signal was generated using a 3-cycle Hanning window modulation signal with a center frequency of 100 kHz as the excitation. The propagation distance ranged from 0 to 0.5 m, uniformly divided into 5000 points, with 500 time points sampled, and all amplitudes set to 1. Since the scattered waves in the experimental data contained three wave packets, a dataset containing three wave packets was generated using the method described in Dataset 3. Wave packets were generated from either the A0 or S0 mode, with 5000 data points generated for each mode each time. The dispersion curve and data samples used in the experiment are shown below. Figure 20 As shown, Figure 20 In the diagram, (a) shows the dispersion curve, and (b) shows the sample data. At a center frequency of 100 kHz, the variation of the A0 mode is still greater than that of the S0 mode, therefore the wave generated by the A0 mode contains more obvious dispersion.

[0134] The model settings were the same as those used in the experiments on dataset 3 of the numerical simulation section. After 500 iterations, the model stabilized. The training results are shown below. Figure 21 , Figure 21 In the dataset, (a) represents the CAE loss, (b) represents the FCAE loss, (c) represents the CAE accuracy, and (d) represents the FCAE accuracy. The accuracies for the three wave packets of the CAE model are 0.707, 0.415, and 0.406, respectively, while the accuracies of the FCAE model are 0.753, 0.556, and 0.629. Because the maximum propagation distance of the signal is only 0.5m, less than the 1m set in dataset 3, there is severe interference between wave packets, resulting in lower model accuracy. Both the CAE and FCAE models can only achieve stable recognition of the first wave packet; the recognition rates for the other two wave packets fluctuate significantly. However, overall, the FCAE model performs better.

[0135] After training, the six sets of experimental data were input into the model, and the output value was the coordinate of the maximum value. The time series diagrams of the six sets of experimental signals are shown below. Figure 22 As shown, the signal contains high noise, and subsequent wave packets are submerged in noise, with only the first wave packet being relatively clear. Taking the three maximum coordinates (see Table 6 for maximum coordinates), we retransform the signal to the time domain and perform dispersion compensation, obtaining the dispersion-removed signal as shown below. Figure 23 , Figure 23 In the table, (a) represents CAE loss and (b) represents FCAE loss.

[0136]

[0137] Table 6

[0138] from Figure 23It can be seen that, except for the first wave packet, the recognition rates of the remaining wave packets are relatively low. Therefore, the first wave packet was selected for defect imaging experiments. Combined with the DAS imaging algorithm, the final defect detection results are as follows: Figure 24 , Figure 24 In the image, (a) is the CAE model and (b) is the FCAE model. Figure 24 In the diagram, black squares represent the location of defects, and white circles represent the location of sensors. Both CAE and FCAE models indicate the defect location around the actual defect location, but the FCAE model shows the location more clearly.

[0139] Another embodiment of this application provides a guided wave dispersion compensation device based on a Fourier basis CAE network, including: a processor, a memory, and a computer program stored in the memory and executable on the processor, such as a guided wave dispersion compensation method program based on a Fourier basis CAE network. When the processor executes the computer program, it implements the steps in the above-described embodiments of the guided wave dispersion compensation method based on a Fourier basis CAE network. Figure 1 The steps.

[0140] For example, the above-mentioned computer program can be divided into one or more modules / units, which are stored in memory and executed by a processor to complete the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing specific functions. These instruction segments describe the execution process of the computer program in a waveguide dispersion compensation device based on Fourier basis CAE networks. For example, the computer program can be divided into a data acquisition module, a model building module, a model training module, a data output module, and a dispersion compensation module. The specific functions of each module are as follows:

[0141] The data acquisition module is used to acquire ultrasonic guided wave signals. The model building module is used to construct a convolutional autoencoder (CA) network model based on Fourier basis. The model training module is used to train the CA model by substituting the ultrasonic guided wave signal data into the CA model until the CA model tends to stabilize. The data output module is used to input the acquired ultrasonic guided wave signal data into the trained CA model, and the output value is the coordinate of the maximum value. The dispersion compensation module is used to convert the maximum value coordinates back to the time domain, combine them with the excitation signal, and perform dispersion compensation on the ultrasonic guided wave signal to obtain a dispersion-removed guided wave signal.

[0142] Waveguide dispersion compensation devices based on Fourier basis CAE networks can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. These devices may include, but are not limited to, processors and memory; for example, they may also include output devices, network access devices, and buses.

[0143] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the waveguide dispersion compensation device based on Fourier basis CAE networks, connecting various parts of the entire waveguide dispersion compensation device using various interfaces and lines.

[0144] The memory can be used to store computer programs and / or modules. The processor implements various functions of the guided wave dispersion compensation device based on Fourier basis CAE network by running or executing the computer programs and / or modules stored in the memory, and by calling the data stored in the memory.

[0145] If the integrated module / unit of the guided wave dispersion compensation device based on Fourier basis CAE network is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various embodiments of the guided wave dispersion compensation method based on Fourier basis CAE network described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0146] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention. Technical aspects, shapes, and structures not described in detail in this invention are all well-known technologies.

Claims

1. A waveguide dispersion compensation method based on Fourier-based CAE network, characterized by, The method comprises the following steps: Collecting ultrasonic guided wave signals; Building a convolutional auto-encoding network model based on Fourier basis; Training the convolutional auto-encoding network model by inputting the ultrasonic guided wave signal data into the model until the model tends to be stable; Inputting the collected ultrasonic guided wave signal data into the trained convolutional auto-encoding network model, and taking the coordinate of the maximum value of the output value; Converting the maximum value coordinate back to the time domain, combining the excitation signal, and performing frequency dispersion compensation on the ultrasonic guided wave signal to obtain a guided wave signal with dispersion removed.

2. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 1, wherein, The step of building a convolutional auto-encoding network model based on Fourier basis comprises the following steps: Setting a Fourier basis convolution kernel to form a Fourier basis convolution layer; Introducing convolution and deconvolution operations to form an encoder-decoder structure, and introducing a convolution structure to form a convolutional auto-encoding network model based on Fourier basis.

3. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 2, wherein, The step of setting a Fourier basis convolution kernel to form a Fourier basis convolution layer comprises the following steps: The first layer of the convolutional auto-encoding network model is set as a custom layer to realize Fourier transform of the input data, and the Fourier basis convolution kernel is transformed as follows: ； wherein , is a time-domain signal sequence, N is the length of the signal, k denotes the frequency sample point, and j denotes the imaginary symbol; Through the relationship between trigonometric functions and e exponentials, we get: ； Where i represents the imaginary symbol.

4. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 3, wherein, The length of the Fourier basis convolution kernel is 25-35, and the number is 5-10.

5. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 4, wherein, The length of the Fourier basis convolution kernel is 30, and the number is 10.

6. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 3, wherein, The introduction of convolution and deconvolution operations forms an encoder-decoder structure, while introducing a convolution structure forms a convolutional auto-encoding network model based on Fourier bases. In the step of forming a convolutional auto-encoding network model based on Fourier bases, the input signal is z, and the learned features are is represented as: ； wherein, is a weight representing a convolution kernel connecting the input layer and the hidden layer, is a bias, is a batch normalization, is a nonlinear activation function for mitigating the problem of vanishing or exploding gradients; The generated output is represented as follows: ； wherein, represents the weight of the decoder, is a bias; The parameters are optimized by minimizing the following error between the decoding output and the given label, and the settings of the label and the loss function are as follows: ； ； wherein, is the decoded output of the model, t represents time, t j represents time, A j represents signal amplitude, represents a unit impulse signal.

7. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 6, wherein, In the convolutional auto-encoding network model based on Fourier basis, a batch normalization layer and an activation layer are set after each convolutional layer except the Fourier basis convolution layer and the last convolutional layer.

8. The Fourier-based CAE network-based guided wave dispersion compensation method of claim 1, wherein, The step of dispersion compensating the ultrasonic guided wave signal, where a signal having a velocity c propagates a distance of a non-dispersive signal is represented as follows: ； wherein represents a non-dispersive signal, is a Fourier transform of the excitation signal , k is a wave number at a specific guided wave mode frequency , j represents an imaginary number symbol, and t represents time.

9. A waveguide dispersion compensation device based on Fourier-based CAE network, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program is executed by the processor to realize the steps of the method according to any one of claims 1-8.

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