An iterative quantitative imaging method based on nonlinear lamb wave mixing acoustic field

Abstract

The application provides an iterative quantitative imaging method based on a nonlinear Lamb wave mixing sound field, and steps are as follows: a finite element model of a metal plate containing a complex mode early damage is established; a mixing fundamental wave mode pair and a working frequency are determined; mixing sound field signals in a non-damage state and a damage state are obtained through finite element simulation, and a frequency domain sound field matrix of a difference frequency, a sum frequency and a fundamental frequency is extracted; ray tomography positioning representation is carried out by using the frequency domain sound field matrix of the difference frequency, first imaging is realized, the first imaging is fused with the fundamental frequency sound field feature to strengthen positioning representation, and an initial velocity model of iterative quantitative imaging is established; an offline training data set is constructed, a nonlinear mapping model of sound field changes and model changes is learned based on a conjugate gradient method, online inversion based on the optimal nonlinear mapping model is carried out, and second imaging is realized; and the application extracts the sum frequency and the difference frequency component, keeps high sensitivity of the nonlinear ultrasonic to microscopic and mesoscopic damage, and significantly improves detection reliability.

Description

Technical Field

[0001] This invention relates to the technical field of nondestructive testing and structural health monitoring, and in particular to an iterative quantitative imaging method based on a nonlinear Lamb wave mixing sound field. Background Technology

[0002] In industries such as nuclear power, hydrogen storage and transportation, and petrochemicals, critical metal equipment operates under harsh conditions of high temperature, high pressure, and heavy load for extended periods. This makes their internal structures prone to early damage characterized by microcracks, voids, and localized performance degradation. These types of damage are minute in scale and develop covertly, making them difficult to identify effectively by conventional testing methods for most of the component's service life. However, they can continue to evolve and eventually lead to sudden failure, seriously threatening the overall safety of the equipment. Especially in environments involving reactive media such as hydrogen, media atoms easily penetrate the metal lattice, inducing changes in the microstructure and further exacerbating the initiation and propagation of damage. With modern industry placing increasingly higher demands on the safety, reliability, and service life of equipment, developing a non-destructive testing technology capable of highly sensitive and reliable detection of early damage to metal components has become a critical technical challenge that urgently needs to be overcome.

[0003] Currently, conventional nondestructive testing methods such as ultrasound, electromagnetic, and X-ray have limitations in terms of detection sensitivity, spatial resolution, and applicability to various operating conditions, making it difficult to accurately detect and characterize microscopic damage within components online and in service. Nonlinear ultrasonic testing technology, by capturing waveform distortion phenomena (such as higher harmonics and mixing responses) caused by the propagation of elastic waves with finite amplitude in materials, can sensitively reflect the evolution of the material's microstructure, thus providing a new technical approach for early damage identification and service life prediction. Further integration with guided wave tomography technology allows for simultaneous rapid scanning of large-scale structures and high-resolution detection of microscopic damage, making it a research hotspot in the field of early material damage assessment.

[0004] However, under complex actual working conditions, metal components often exhibit spatial gradient distributions of mechanical properties and diverse and complex damage morphologies, leading to complex propagation paths and significant changes in dispersion characteristics of sound waves, posing a severe challenge to the quantitative characterization of damage. In the prior art, Chinese patent document CN109085244A discloses a nonlinear Lamb wave structural fatigue damage tomography method based on a piezoelectric array. This method uses the variation of the second harmonic of the Lamb wave as a damage characteristic parameter and employs a damage probability detection reconstruction algorithm (RAPID) to locate and image early damage such as microcracks and fatigue. However, the detection signals of such traditional nonlinear detection methods based on fixed-order harmonics are highly susceptible to interference from the nonlinear response of the detection system itself, affecting the accuracy and reliability of the measurement.

[0005] Another Chinese patent document, CN117825526A, discloses a method for reconstructing icing characteristics and shape based on ultrasonic full-waveform inversion. This method achieves subwavelength resolution by considering features such as group velocity changes caused by diffraction and multiple scattering, and has the potential for quantitative reconstruction of damage. However, because its reconstruction process requires iteratively finding the optimal solution by calculating the Hessian matrix, the computational cost is extremely high, making it difficult to meet the timeliness requirements of practical engineering applications. Furthermore, this method fails to fully utilize the deep quantitative correlation between the complex morphology of the damage and the resulting nonlinear acoustic field response. Therefore, the existing technology still suffers from limitations such as strong system interference, low computational efficiency, and insufficient utilization of acoustic field information.

[0006] Therefore, there is an urgent need to develop a new rapid guided wave tomography method that can integrate multi-dimensional nonlinear acoustic parameters and possess intelligent processing capabilities. This method should be able to significantly reduce the uncertainty of the reconstruction process by deeply mining and effectively utilizing the nonlinear response information in the acoustic field, thereby ultimately achieving rapid and accurate quantitative characterization of early damage of various complex forms, meeting the urgent need for highly sensitive and efficient nondestructive testing technology in industrial settings. Summary of the Invention

[0007] To address the technical problems of existing nonlinear ultrasonic guided wave detection methods being susceptible to interference from inherent nonlinear noise in the system, and the high computational cost and difficulty in fully utilizing multi-dimensional acoustic field information in full waveform inversion methods, this invention proposes an iterative quantitative imaging method based on nonlinear Lamb wave mixing acoustic field, which can achieve high sensitivity, low artifacts, and rapid quantitative imaging of early damage with complex morphology.

[0008] To achieve the above objectives, the technical solution of this invention is as follows: an iterative quantitative imaging method based on a nonlinear Lamb wave mixing sound field, comprising the following steps:

[0009] Step 1: Establish a finite element model of a metal plate with complex early damage, and set up the transducer array and excitation receiving method;

[0010] Step 2: Calculate and plot the phase velocity dispersion curves of the Lamb wave fundamental frequency and the nonlinear harmonics using the global matrix method to determine the mixing fundamental mode pair and operating frequency.

[0011] Step 3: Obtain the mixing sound field signals under undamaged and damaged conditions through finite element simulation, and extract the frequency domain sound field matrix of difference frequency, sum frequency and fundamental frequency;

[0012] Step 4: Use the frequency domain acoustic field matrix of the difference frequency to perform X-ray tomography localization characterization to achieve the first imaging;

[0013] Step 5: Intensify the localization characterization by fusing the fundamental frequency acoustic field features from the first imaging and establish an initial velocity model for iterative quantitative imaging;

[0014] Step 6: Construct an offline training dataset and learn a nonlinear mapping model between sound field changes and model changes based on the conjugate gradient method;

[0015] Step 7: Achieve a second imaging by online inversion based on the optimal nonlinear mapping model.

[0016] Preferably, the finite element model incorporates third-order elastic constants, and also includes Lamé constant and density, and adopts Murnaghan hyperelastic constitutive model; a boundary absorption layer is set around the finite element model, and a transducer array is arranged on the surface of the metal plate, the transducer array is located within the boundary absorption layer, and the transducer array uses n-channel piezoelectric ceramic transducers arranged at equal intervals around it;

[0017] The transducer array employs a full-matrix acquisition mode of "sequential excitation of single elements and simultaneous reception of all elements," with the excitation signal being a 10-cycle sine wave pulse modulated by a Hanning window; the fundamental frequency f is used. a and fundamental frequency f b The difference frequency (f) a -f b ) and frequency (f a + f b ) incentive, and f a > f b .

[0018] Preferably, in the finite element model, early damage is simulated by locally modifying the material parameters in the scanning domain of the transducer array: a grayscale image reflecting the spatial distribution of damage is generated, which can present early damage features of any complex form, and the grayscale image is embedded into the finite element model; based on the principle of monotonically negative correlation, the pixel values ​​of the grayscale image are linearly mapped to the range of multiples of the third elastic constant relative to the base value, and the mapping range is set to [3, 10], while the Lamé constant and density remain unchanged.

[0019] Preferably, the method for determining the fundamental mode pair and operating frequency of the mixing frequency is as follows: using the Lamé constant, density, and thickness d of the metal sheet as input, the phase velocity dispersion curve of the fundamental Lamb wave is plotted, and the phase velocity dispersion curve of the second harmonic mode of the Lamb wave is plotted simultaneously. Utilizing the phase matching and non-zero energy flow transfer conditions of the nonlinear harmonics of the Lamb wave, the excitation mode pair S0-s0 and S1-s2 of the nonlinear Lamb wave are selected, and they are defined as the difference frequency (f) under the second-order nonlinear effect. a -f b ) and frequency (f a + f bThe excitation point of the harmonic is used to excite the nonlinear Lamb wave; where S represents the fundamental frequency symmetric mode and s represents the second harmonic symmetric mode.

[0020] By selecting fundamental mode pairs that can generate strong nonlinear energy flow accumulation effects through phase matching and non-zero energy flow conditions.

[0021] Preferably, the method for extracting the frequency domain sound field matrix of difference frequency, sum frequency, and fundamental frequency is as follows: calculate the baseline sound field signal under the undamaged state, collect the time domain signals of all channel pairs of the transducer array as the baseline signal, introduce an early damage region into the finite element model, repeat the simulation, and calculate the sound field signal with damage; perform Fourier transform on the baseline signal and the sound field signal to obtain the frequency signal, and extract the difference frequency component, sum frequency component, and fundamental frequency f from the frequency domain signal. a The amplitude information of the components is used to construct a frequency domain sound field matrix with dimensions n × n, where n is the number of transducer channels.

[0022] Preferably, the method for implementing the X-ray tomography localization characterization is as follows: Tomographic imaging reconstruction is performed based on a probabilistic defect detection and reconstruction algorithm: the signal amplitude covariance of each channel pair in the frequency domain acoustic field matrix of the difference frequency between the acoustic field signal in the damaged state and the baseline signal is calculated, and the value of the signal amplitude covariance is used as the damage feature quantity of the corresponding channel pair; then, an elliptical region is defined with the position of the transmitting and receiving transducers in each channel pair as the vertices of the major axis. The weight of the major axis of the ellipse is positively correlated with the magnitude of the covariance and decreases as the distance from the major axis to both sides of the ellipse increases; the weight distributions of the major axes of all channel pairs are superimposed to obtain a probability distribution map of damage localization, which is the first imaging, describing the approximate location and distribution range of the damage;

[0023] The method for establishing the initial velocity model is as follows: extract the fundamental frequency f with early damage. a The amplitude attenuation matrix of the sound field signal is obtained, and the fundamental frequency localization characterization result is obtained based on the probabilistic defect detection and reconstruction algorithm. The first imaging and the fundamental frequency localization characterization result are fused into a multimodal image using weighted average fusion. The region within the localization extraction threshold in the fusion result is extracted, and the phase is inverted within the localization extraction threshold range to obtain the initial velocity model describing the spatial distribution of the damage.

[0024] Preferably, the method for constructing the nonlinear mapping model is as follows: select various damage morphologies including different sizes and degrees of hydrogen embrittlement and degradation combinations as training samples, randomly generate multiple location distributions for each damage morphology, and obtain offline training examples; repeat steps three to five for each example to obtain the initial velocity model and multi-dimensional frequency domain sound field matrix;

[0025] The sound field change ΔP is defined as the element-wise difference between the sum-frequency sound field matrix and the difference-frequency sound field matrix, and the model change ΔQ is defined as the element-wise difference between the initial velocity model and the reference model. With the core objective of learning the nonlinear mapping relationship from the sound field change ΔP to the model change ΔQ, the conjugate gradient method is used to iteratively optimize the offline training examples. By minimizing the global error between the mapped predicted value and the true value, the optimal nonlinear mapping model is constructed. .

[0026] Preferably, the loss function for the iterative optimization training is the sum of the 2-norm errors between the predicted and actual values ​​of the model changes for all offline training examples;

[0027] The conjugate gradient method iterative optimization is as follows: The partial derivative of the loss function with respect to the mapping model F is used to obtain the gradient ∇R. The negative gradient direction −∇R is used as the initial search direction. The conjugate coefficients are calculated using the Fletcher-Reeves formula, and the conjugate search direction for subsequent iterations is updated. The optimal step size for each iteration is solved through a one-dimensional line search, continuously updating the parameters of the mapping model F. When the loss function value is less than a preset threshold or gradient norm... Stop iterating when the value is less than the convergence threshold.

[0028] Preferably, the initial velocity model obtained for the actual detection object is used. The optimal nonlinear mapping model is obtained by directly inputting the sound field change ∆p, which represents the sum frequency and difference frequency of the sound field, as a test example. The model change Δq for the test case is obtained, and the model change Δq for the test case is compared with the initial velocity model. Element-level superposition operations are performed to obtain the final quantitative imaging model q for early damage morphology; the signal difference coefficients of the final quantitative imaging model q for early damage morphology are then uniformly mapped to the initial velocity model. Within the same signal difference coefficient range, quantitative reconstruction visualization results of the early damage morphology of the test case were obtained, which are the results of the second imaging.

[0029] Preferably, the weights of the weighted average fusion are set according to the differences in the sensitivity of each feature parameter to damage, with the first imaging having a weight of 0.75 and the fundamental frequency localization characterization result having a weight of 0.25.

[0030] The location extraction threshold is the top 20% of the signals with the highest signal difference coefficient values;

[0031] The reference model is a standard model established using the actual geometric parameters of the finite element model. The signal difference coefficient of the reference model is mapped to the same signal difference coefficient range as the initial velocity model.

[0032] The beneficial effects of this invention are as follows: This invention constructs an iterative imaging framework of "difference frequency tomography localization—fundamental frequency characterization enhancement—sum frequency inversion quantification," realizing progressive imaging from initial localization of early damage to quantitative morphological reconstruction. By extracting sum and difference frequency mixing components, this invention effectively avoids system nonlinear noise interference while maintaining the high sensitivity of nonlinear ultrasound to microscopic and mesoscopic damage, significantly improving detection reliability. Compared with existing full-waveform inversion methods, this invention uses the conjugate gradient method to transfer the main computational task to the offline training stage. Online inversion only requires one forward calculation, avoiding the high computational cost of repeatedly solving the Hessian matrix and greatly improving imaging efficiency. Simultaneously, this invention integrates multiple acoustic field feature parameters such as difference frequency, fundamental frequency, and sum frequency, effectively overcoming the limitations of incomplete information from a single acoustic parameter, achieving accurate quantitative characterization of early damage with complex morphologies, and providing an effective technical means for in-service nondestructive testing of key metal components in fields such as nuclear power, hydrogen energy storage and transportation, and petrochemicals. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart of the present invention.

[0035] Figure 2 This is a finite element model for an embodiment of the present invention.

[0036] Figure 3 The diagram shows the Lamb wave dispersion curves of an embodiment of the present invention, where (a) is the phase velocity dispersion curve and (b) is the group velocity dispersion curve. In the diagram, A represents the fundamental frequency antisymmetric mode, S represents the fundamental frequency symmetric mode, and s represents the second harmonic symmetric mode. Each mode is labeled sequentially along the positive horizontal axis as 0, 1, 2…, such as A0, S1, s2, etc. The fundamental-harmonic mode pairs used to excite the second harmonic are identified using the "fundamental mode-harmonic mode" method, such as the S1-s2 mode pair.

[0037] Figure 4 The above is a signal diagram collected by a transducer according to an embodiment of the present invention, wherein (a) is a time-domain signal diagram and (b) is a frequency-domain signal diagram.

[0038] Figure 5 This is a tomographic localization characterization diagram based on the difference frequency sound field in an embodiment of the present invention, wherein (a) is the frequency domain sound field matrix of the difference frequency signal, and (b) is the damage localization probability distribution diagram reconstructed based on the probabilistic defect detection algorithm.

[0039] Figure 6 This is a schematic diagram of the initial model establishment for iterative quantitative imaging in an embodiment of the present invention, wherein (a) is the probabilistic defect detection and localization reconstruction result based on the fundamental frequency signal, and (b) is the result of reconstructing the difference frequency localization result ( Figure 5 (b) and the fundamental frequency positioning results ( Figure 6 (a) is the result of the tomographic representation after fusion, and (c) is the initial model established by extracting high-probability regions from the superposition result by setting a threshold and mapping them to the velocity model.

[0040] Figure 7 This is a schematic diagram of the sound field difference between the sum frequency and difference frequency in an embodiment of the present invention.

[0041] Figure 8 The images show the iterative quantitative imaging results and comparisons of embodiments of the present invention, where (a) is the iterative quantitative imaging result and (b) is the reference model established based on the real geometric parameters of the finite element model.

[0042] In the figure, 1 is the boundary absorption layer of the finite element model, 2 is the transducer array, and 3 is the early damage of the complex shape. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] like Figure 1As shown, an iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field is proposed to improve the detection sensitivity and quantitative characterization accuracy of guided wave tomography for early damage (such as hydrogen embrittlement, degradation, and microcracks) in metal components, effectively overcoming the inherent limitations of traditional methods in terms of resolution, real-time performance, and resistance to nonlinear interference from electronic systems. This invention utilizes the mixing effect (sum frequency and difference frequency) generated by the coupling of the Lamb wave fundamental frequency signal in the damaged region to develop a frequency domain sound field matrix extraction and multi-feature parameter fusion method. An offline training dataset for iterative quantitative imaging is constructed, and an iterative imaging method of "difference frequency tomography localization—fundamental frequency characterization enhancement—sum frequency inversion quantification" is proposed. This invention can achieve high-sensitivity, low-artifact, and rapid quantitative imaging of early damage with complex morphologies. In this invention, X-ray tomography based on difference-frequency sound field is used for initial damage localization (first imaging), providing an initial model for subsequent imaging. Based on this, multi-dimensional feature parameters such as the fundamental frequency sound field attenuation coefficient are fused to enhance the localization characterization and optimize the initial model. The nonlinear mapping relationship between sound field changes and model changes, constructed through offline training using the sum-frequency sound field combined with the conjugate gradient method, is utilized to achieve a second imaging step (quantitative reconstruction of damage morphology), thereby completing the accurate quantitative characterization of early-stage damage. The specific steps of this invention are as follows:

[0045] Step 1: Establish a finite element model of a metal plate with complex early damage, and set up the transducer array and excitation receiving method.

[0046] like Figure 2 As shown, a finite element model of a metal plate containing early damage of complex morphology is established. Given that this invention detects early damage based on the nonlinear Lamb wave mixing effect, its physical essence lies in utilizing the mixing components (sum frequency and difference frequency) generated by the nonlinear interaction between ultrasonic guided waves and the material's microstructure. However, traditional linear elastic constitutive models only contain second-order elastic constants and cannot describe waveform distortion and harmonic generation phenomena during guided wave propagation. Therefore, to accurately simulate the nonlinear elastic behavior of materials under finite deformation and establish a quantitative correlation between microscopic damage and macroscopic acoustic field response, this finite element model introduces third-order elastic constants and adopts the Murnaghan hyperelastic constitutive model. The model's geometric dimensions are 1000 mm × 1000 mm × 10 mm, and the elastic constants of its aluminum alloy are set as: Lamé constants λ = 54.9 GPa and μ = 26.5 GPa, density ρ = 2.8 g / mm². 2The third-order elastic constants are υ1 = -205.8 GPa, υ2 = -149.3 GPa, and υ3 = -87.8 GPa. A boundary absorption layer 1 is set around the finite element model to eliminate the interference of boundary reflections on the sound field signal. A transducer array 2 is arranged on the surface of the plate, using n channels (n is the number of transducer channels, n = 32 in this embodiment) of piezoelectric ceramic transducers (center frequency adjustable, model PZT-5H) arranged at equal intervals, with an array diameter of 800 mm and each array element diameter of 10 mm. The transducer array is arranged inside the boundary absorption layer, and the area defined by the boundary absorption layer is the sound field calculation area for finite element simulation analysis. When the sound wave propagates to the boundary, it is completely absorbed by the absorption layer, thereby effectively suppressing boundary reflections, reducing clutter interference, and ensuring the purity of the sound field signal. Transducer array 2 employs a full-matrix acquisition mode of "sequential excitation of single elements and simultaneous reception of all elements," with the excitation signal being a 10-cycle sinusoidal pulse modulated by a Hanning window. Full-matrix acquisition aims to acquire a complete sound field encompassing all transmit and receive combinations. This sound field contains n×n independent propagation paths, providing a rich information foundation for subsequent steps to construct a high-dimensional frequency domain sound field matrix and extract difference and sum frequency components, thus improving the spatial resolution and inversion accuracy of damage imaging. The sidelobe suppression effect of the Hanning window concentrates energy highly at the center frequency, effectively suppressing the dispersion effect of Lamb waves and ensuring a pure excitation mode. The moderately wide pulse characteristics control the nonlinear noise introduced by system electronic equipment (such as power amplifiers and the transducer itself) away from the mixing components (sum and difference frequencies) in the frequency domain, significantly reducing interference from inherent nonlinearities. Furthermore, sufficient energy flow is transferred from the fundamental frequency to the nonlinear harmonics, ensuring a sufficient signal-to-noise ratio for the nonlinear harmonics and preventing them from being overwhelmed by background noise. By adjusting the fundamental excitation frequency f... a and f b (f) a > f b ), using the difference frequency f of the excitation a -f b and frequency f a +f b This enables collinear beam mixing configuration.

[0047] Figure 1The constitutive relation of the hyperelastic model is set, and the early damage set morphology is defined. First, a grayscale image reflecting the spatial distribution of damage is generated using MATLAB. This grayscale image can present early damage features of arbitrarily complex shapes and is embedded into the finite element model. Based on the principle of monotonically negative correlation, the pixel values ​​of the grayscale image are linearly mapped to the multiple range of the third-order elastic constants υ1, υ2, and υ3 relative to the base values. The mapping range is set to [3, 10]: that is, the lower the grayscale value (the more severe the damage), the higher the corresponding multiple, thereby establishing a quantitative correlation between the damage geometry and the nonlinear parameters of the material. In the finite element model, early damage is simulated by locally modifying the material parameters in the scanning domain of transducer array 2. Within the damage region, the third-order elastic constants υ1, υ2, and υ3 are adjusted to 3 to 10 times the base values, while the Lamé constant and density remain unchanged, to simulate the changes in mechanical properties caused by early damage such as material degradation and hydrogen embrittlement.

[0048] Step 2: Calculate and plot the phase velocity dispersion curves of the Lamb wave fundamental frequency and the nonlinear harmonics using the global matrix method to determine the mixing fundamental mode pair and operating frequency.

[0049] The Lamb wave dispersion characteristics of the metal sheet were calculated using the global matrix method. Using the material parameters of 6061 aluminum alloy (Lame constants λ and μ, density ρ) and the sheet thickness d as input, the phase velocity dispersion curve of the fundamental frequency Lamb wave was plotted, as shown below. Figure 3 As shown in (a), the two mode pairs are drawn with gray circles. The figure also plots the phase velocity dispersion curves of the Lamb wave second harmonic mode, with the horizontal axes of the two dispersion curves representing the product of the fundamental frequency and the second harmonic frequency (fd and 2fd), respectively. Subsequently, using the phase matching and non-zero energy flow transfer conditions of the Lamb wave nonlinear harmonics, the excitation mode pairs S0-s0 and S1-s2 of the nonlinear Lamb wave were selected, and they were defined as the difference frequency (fd) under the second-order nonlinear effect. a -f b ) and frequency (f a + f b The excitation point of the harmonic is used to excite the nonlinear Lamb wave.

[0050] In this embodiment, a fundamental mode pair capable of generating a strong nonlinear energy flow accumulation effect is selected through wave structure analysis, and the selection is made based on phase matching and non-zero energy flow conditions. The sum-frequency product (fd) is 3.5 MHz·mm, and the difference frequency is 0.5 MHz·mm. Since the aluminum plate thickness is 10 mm, the excitation fundamental frequency f is set... a = 0.2 MHz, f b = 0.15 MHz.

[0051] Step 3: Obtain the mixing sound field signals under undamaged and damaged conditions through finite element simulation, and extract the frequency domain sound field matrix of difference frequency, sum frequency and fundamental frequency.

[0052] In ABAQUS software, the finite element model described in step one is established, and the Murnaghan hyperelastic constitutive relation is defined using the subroutine VUMAT. First, the baseline acoustic field signal under undamaged conditions is calculated by acquiring the time-domain signals of all channel pairs in transducer array 2. A sound field acquisition is performed using finite element simulation under undamaged conditions, and the acquired signal serves as the baseline signal. The baseline signal provides a reference standard for the acoustic field under undamaged conditions. By comparing it with the signal under damaged conditions, changes in the acoustic field caused by early damage (such as amplitude attenuation, phase shift, and nonlinear harmonic components) are extracted, thereby eliminating inherent system noise and environmental interference, and highlighting the impact of damage on the acoustic field. Subsequently, an early damage region is introduced into the finite element model, and the simulation is repeated to calculate the acoustic field signal under damaged conditions.

[0053] Based on the dispersion equation and numerical differentiation method, the fundamental frequency of the Lamb wave is converted from phase velocity to group velocity to obtain the group velocity dispersion curve, such as... Figure 3 As shown in (b), the fundamental frequency f can be obtained. b Group velocities c in A0 and S0 modes at location g The values ​​are 2.45 mm / μs and 5.20 mm / μs, respectively, with a fundamental frequency f. a The group velocities for modes A0, A1, and S0 at the location are 3.01 mm / μs, 2.95 mm / μs, and 3.10 mm / μs, respectively. Taking a propagation distance of 800 mm transducer array diameter as an example, the time-domain signal acquired by the transducer on the opposite side is as follows: Figure 4 As shown in (a), a Fourier transform is performed on the time-domain signal to obtain the frequency signal as shown in (a). Figure 4 As shown in (b), the difference frequency component (center frequency 0.05 MHz), the sum frequency component (center frequency 0.35 MHz), and the fundamental frequency f are extracted from the frequency domain signal. a The amplitude information of the component (center frequency 0.2 MHz) is used to construct a frequency domain sound field matrix of dimension n × n (n is the number of transducer channels, n = 32 in this embodiment). The sound field matrix in the undamaged state is used as the baseline signal. Figure 5 (a) shows the frequency domain acoustic field matrix of the difference frequency signal collected in this embodiment, which will be used first for X-ray tomography localization characterization.

[0054] Step 4: Use the difference frequency sound field for X-ray tomography localization characterization to achieve the first imaging (preliminary damage localization).

[0055] Differential frequency harmonics have the characteristics of low frequency, small attenuation and long propagation distance, and their attenuation coefficient is more sensitive to the distribution of microscopic damage. Therefore, this embodiment uses the differential frequency sound field (the frequency domain sound field matrix of the differential frequency) for damage localization.

[0056] A reconstruction algorithm based on probabilistic defect detection is used for tomographic imaging reconstruction. First, the signal amplitude covariance of each channel pair in the frequency domain acoustic field matrix containing the damage state and the baseline signal is calculated, and this covariance value is used as the damage feature quantity for the corresponding channel pair. Then, an elliptical region is defined with the positions of the transmitting and receiving transducers in each channel pair as the vertices of the major axis. The weight of the major axis of the ellipse is positively correlated with the magnitude of the covariance and decreases as the distance from the major axis to the sides of the ellipse increases. By superimposing the elliptical weight distributions of all channel pairs, a probability distribution map of damage localization can be obtained. Figure 5 As shown in (b). This result is the first imaging output, which can describe the approximate location and distribution range of the damage, but the boundaries are blurred and the quantitative accuracy is limited.

[0057] Step 5: Integrate the fundamental frequency sound field features from the first imaging to enhance the localization characterization and establish an initial velocity model for iterative quantitative imaging.

[0058] Building upon difference frequency tomography localization, the multidimensional characteristic parameters of the fundamental frequency sound field are further utilized to enhance the accuracy of damage characterization. In this embodiment, the fundamental frequency component with a higher center frequency (f0) is selected. a = 0.2 MHz) is used as the analysis object because its shorter wavelength and higher spatial resolution can effectively capture damage details. By extracting multi-dimensional characteristic parameters such as the attenuation coefficient and scattering coefficient of this fundamental frequency, the accuracy of damage characterization is enhanced. The baseline signal without damage and the fundamental frequency signal with early damage are simulated using a finite element model. The obtained time-domain signals are then analyzed in the frequency domain to obtain the frequency domain amplitude between each channel, forming a frequency-domain sound field matrix. In this embodiment, the amplitude attenuation matrix of the fundamental frequency sound field is extracted, which is the attenuation caused by the amplitude decrease after the defect occurs, representing the fundamental frequency f before and after the defect. a The frequency domain acoustic field difference in mode A0 is also analyzed using the probabilistic defect detection and reconstruction algorithm from step four to obtain the fundamental frequency localization characterization result, such as... Figure 6 As shown in (a).

[0059] The difference frequency localization characterization results ( Figure 6 (b) and the fundamental frequency localization characterization results ( Figure 6 Multimodal image fusion is performed in (a) of this embodiment. A weighted average fusion strategy is used, with weights set according to the differences in the sensitivity of each feature parameter (including fundamental frequency attenuation and difference frequency) to damage (difference frequency weight 0.75, fundamental frequency weight 0.25). The tomographic characterization results after fusion are as follows: Figure 6 As shown in (b), the damage boundary is clearer and the positioning accuracy is significantly improved.

[0060] The top 20% of regions with high signal difference coefficients in the fusion results are extracted and their locations are inverted within the current signal difference coefficient range [1.652, 1.724] to reverse the grayscale values ​​representing the defects, thus more clearly describing the early damage localization and obtaining an initial velocity model describing the spatial distribution of the damage. Figure 6 As shown in (c), this initial velocity model will serve as a priori input for the subsequent second imaging (quantitative imaging).

[0061] Step 6: Construct an offline training dataset and learn a nonlinear mapping model between sound field changes and model changes based on the conjugate gradient method.

[0062] In this embodiment, 64 different damage morphologies (including combinations of hydrogen embrittlement and degradation of different sizes and degrees) were selected as training samples. Eight location distributions were randomly generated for each damage morphology, resulting in a total of 512 offline training examples. Steps three to five were repeated for each example to obtain the initial velocity model and the multi-dimensional frequency domain acoustic field matrix. The initial velocity model was a damage velocity model established after fundamental frequency / difference frequency multi-feature fusion localization characterization. The multi-dimensional frequency domain acoustic field matrix included the sum frequency domain acoustic field matrix, difference frequency domain acoustic field matrix, and fundamental frequency domain acoustic field matrix under the damage state. The dimension of each matrix was n×n (n is the number of transducer channels; in this embodiment, n = 32).

[0063] The sound field variation ΔP is defined as the element-wise difference between the sum-frequency sound field matrix and the difference-frequency sound field matrix, thus characterizing the nonlinear response of the mixing sound field to early damage in metal components. Figure 7 As shown; the model variation ΔQ is defined as the element level difference between the initial velocity model and the reference model, where the reference model is a standard model established using the actual geometric parameters of the finite element model. Its signal difference coefficient is mapped to the same signal difference coefficient interval as the initial velocity model, thus characterizing the spatial difference between the model reconstruction value and the actual damage characteristics. The reference model is generated when an arbitrary-shaped defect is embedded into the finite element model from the real model.

[0064] This step focuses on learning the nonlinear mapping relationship ΔQ = F(ΔP) from the sound field change ΔP to the model change ΔQ. It uses the conjugate gradient method to iteratively optimize 512 offline training examples, constructing the optimal nonlinear mapping model by minimizing the global error between the predicted and actual values. The specific training process and parameter settings are as follows:

[0065] First, construct the target loss function. Define the global loss function as the sum of the 2-norm errors between the predicted and actual values ​​of the model changes for all offline training examples. This quantifies the fitting accuracy of the mapping relationship. The loss function is:

[0066] (1);

[0067] In the formula, N is the number of training samples (N = 512 in this embodiment), ΔP i ΔQ i These represent the sound field changes and model changes for the i-th training example, respectively. Let R be the 2-norm of the matrix. The optimization objective of the training is to find the mapping model that minimizes the loss function R, i.e. .

[0068] Secondly, iterative optimization using the conjugate gradient method is employed. The partial derivative of the loss function R with respect to the mapping model F is used to obtain the gradient ∇R. The negative gradient direction −∇R is used as the initial search direction. The Fletcher-Reeves formula is used to calculate the conjugate coefficients and update the conjugate search direction for subsequent iterations. The optimal step size for each iteration is solved through a one-dimensional line search, continuously updating the parameters of the mapping model F. A dual convergence criterion is set during the iteration process. In this embodiment, when the loss function value is less than a preset threshold γ = 5 × 10⁻⁶, the convergence criterion is determined. −6 or gradient norm Less than the convergence threshold ε = 5 × 10 −4 When the iteration stops, the learning of the nonlinear mapping relationship is complete.

[0069] The offline training process in this embodiment is performed on a workstation equipped with an NVIDIA Tesla V100 GPU, using MATLAB R2023a as the runtime environment. To balance training efficiency and fitting accuracy, the maximum number of iterations k = 10 is set, and the solution accuracy σ for the one-dimensional line search is set to 3 × 10⁻⁶. −6 The optimal nonlinear mapping model was obtained after iterative optimization. This model can achieve accurate and rapid mapping from sound field change ΔP to model change ΔQ, providing core model support for subsequent online inversion.

[0070] Step 7: Based on the online inversion of the optimal nonlinear mapping model, a second imaging (quantitative reconstruction of damage morphology) is achieved.

[0071] The initial velocity model obtained in steps three through five for the actual detection object ( The changes in the sound field matrix (∆p) of sum frequency and difference frequency are used as test examples, based on the optimal nonlinear mapping model obtained in step six. The model variation is directly solved by the change in sound field, and the online quantitative inversion of the early damage morphology of metal components is completed, realizing the second imaging. The specific execution process and result analysis are as follows:

[0072] First, the test case model is changed. The sound field change Δp (the frequency domain matrix difference between the sum frequency and the difference frequency) of the test case is input into the optimal nonlinear mapping model obtained through offline training. In the above, the model change Δq of the test case is obtained directly through the nonlinear mapping relationship. The calculation formula is as follows:

[0073] (2);

[0074] This parameter is the initial velocity model for the test case iteration. The precise correction amount can reflect the spatial deviation distribution between the initial model and the actual damage morphology.

[0075] Secondly, the early damage morphology is quantitatively reconstructed. The model change Δq of the test case is compared with the initial velocity model. Element-level superposition operations are performed to correct spatial biases in the initial velocity model, resulting in the final quantitative imaging model q for early damage morphology. The calculation formula is as follows:

[0076] (3);

[0077] In the formula, q represents the result model of quantitative reconstruction of damage morphology. The initial velocity model obtained by fusing fundamental frequency and difference frequency features for the test case uses the signal difference coefficient as a characterization quantity, which can accurately reflect the spatial distribution, geometric contour, size and degree of damage.

[0078] The signal difference coefficients of the final quantitative imaging model q are uniformly mapped to the same signal difference coefficient range of the initial model to obtain the quantitative reconstruction visualization result of the early damage morphology of the test case, which is the second imaging result of this invention. Figure 8 As shown in (a), the results indicate that the reconstructed damage morphology is clear, the boundaries are accurate, and there is no obvious artifact interference. A reference model (such as...) was established based on the actual geometric parameters and damage characteristics of the finite element model. Figure 8 Based on (b), a quantitative accuracy analysis of the imaging results was performed. The root mean square error of the damage morphology reconstruction in this invention was calculated to be 8.47 × 10⁻⁶. -3 The localization characterization Pearson coefficient reached 0.85, and the overall time for a single iteration of imaging was about 9 seconds, indicating that the method has excellent computational efficiency while ensuring high reconstruction accuracy, and can meet the needs of rapid and accurate quantitative detection of early damage in practical engineering.

[0079] The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field proposed in this invention achieves direct and rapid solution from sound field changes to model changes through multi-sound field parameter fusion of difference frequency tomography localization, fundamental frequency characterization enhancement and sum frequency inversion quantification, combined with the optimal nonlinear mapping model. It does not require additional sound field forward modeling and complex matrix operations, effectively improving the timeliness and accuracy of imaging, and providing a brand-new technical solution for in-service nondestructive testing of metal components under harsh working conditions.

[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An iterative quantitative imaging method based on a nonlinear Lamb wave mixing sound field, characterized in that, The steps are as follows: Step 1: Establish a finite element model of a metal plate with complex early damage, and set up the transducer array and excitation receiving method; Step 2: Calculate and plot the phase velocity dispersion curves of the Lamb wave fundamental frequency and the nonlinear harmonics using the global matrix method to determine the mixing fundamental mode pair and operating frequency. Step 3: Obtain the mixing sound field signals under undamaged and damaged conditions through finite element simulation, and extract the frequency domain sound field matrix of difference frequency, sum frequency and fundamental frequency; Step 4: Use the frequency domain acoustic field matrix of the difference frequency to perform X-ray tomography localization characterization to achieve the first imaging; Step 5: Intensify the localization characterization by fusing the fundamental frequency acoustic field features from the first imaging and establish an initial velocity model for iterative quantitative imaging; Step 6: Construct an offline training dataset and learn a nonlinear mapping model between sound field changes and model changes based on the conjugate gradient method; Step 7: Achieve a second imaging by online inversion based on the optimal nonlinear mapping model.

2. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 1, characterized in that, The finite element model incorporates third-order elastic constants, including Lamé constant and density, and adopts Murnaghan hyperelastic constitutive model. A boundary absorption layer is set around the finite element model, and a transducer array is arranged on the surface of the metal plate. The transducer array is located within the boundary absorption layer, and the transducer array uses n-channel piezoelectric ceramic transducers arranged at equal intervals. The transducer array employs a full-matrix acquisition mode of "sequential excitation of single elements and simultaneous reception of all elements," with the excitation signal being a 10-cycle sine wave pulse modulated by a Hanning window; the fundamental frequency f is used. a and fundamental frequency f b The difference frequency (f) a -f b ) and frequency (f a + f b ) incentive, and f a > f b .

3. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 2, characterized in that, In the finite element model, early damage is simulated by locally modifying the material parameters in the scanning domain of the transducer array: a grayscale image reflecting the spatial distribution of damage is generated, which can present early damage features of any complex form. The grayscale image is embedded into the finite element model. Based on the principle of monotonically negative correlation, the pixel values ​​of the grayscale image are linearly mapped to the range of multiples of the third elastic constant relative to the base value. The mapping range is set to [3, 10], while the Lamé constant and density remain unchanged.

4. The iterative quantitative imaging method based on a nonlinear Lamb wave mixing sound field according to claim 2 or 3, characterized in that, The method for determining the fundamental mode pair and operating frequency of the mixing frequency is as follows: using the Lamé constant, density, and plate thickness d of the metal sheet as input, the phase velocity dispersion curve of the fundamental frequency Lamb wave is plotted, and the phase velocity dispersion curve of the second harmonic mode of the Lamb wave is plotted simultaneously. Utilizing the phase matching and non-zero energy flow transfer conditions of the nonlinear harmonics of the Lamb wave, the excitation mode pair S0-s0 and S1-s2 of the nonlinear Lamb wave are selected, and they are defined as the difference frequency (f) under the second-order nonlinear effect. a -f b ) and frequency (f a + f b The excitation point of the harmonic is used to excite the nonlinear Lamb wave; where S represents the fundamental frequency symmetric mode and s represents the second harmonic symmetric mode. By selecting fundamental mode pairs that can generate strong nonlinear energy flow accumulation effects through phase matching and non-zero energy flow conditions.

5. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 4, characterized in that, The method for extracting the frequency domain sound field matrix of difference frequency, sum frequency, and fundamental frequency is as follows: Calculate the baseline sound field signal under undamaged conditions; collect the time-domain signals of all channel pairs of the transducer array as the baseline signal; introduce an early damage region into the finite element model; repeat the simulation; calculate the sound field signal under damaged conditions; perform Fourier transform on the baseline signal and the sound field signal to obtain the frequency signal; extract the difference frequency component, sum frequency component, and fundamental frequency f from the frequency domain signal. a The amplitude information of the components is used to construct a frequency domain sound field matrix with dimensions n × n, where n is the number of transducer channels.

6. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 5, characterized in that, The method for implementing the X-ray tomography localization characterization is as follows: Tomographic imaging reconstruction is performed based on a probabilistic defect detection and reconstruction algorithm: the frequency domain acoustic field matrix of the difference frequency between the acoustic field signal in the damaged state and the baseline signal is calculated, and the signal amplitude covariance of each channel pair is used as the damage feature quantity of the corresponding channel pair; then, an elliptical region is defined with the positions of the transmitting and receiving transducers in each channel pair as the vertices of the major axis. The weight of the major axis of the ellipse is positively correlated with the magnitude of the covariance and decreases as the distance from the major axis to both sides of the ellipse increases; the weight distributions of the major axes of all channel pairs are superimposed to obtain a probability distribution map of damage localization, which is the first imaging, describing the approximate location and distribution range of the damage; The method for establishing the initial velocity model is as follows: extract the fundamental frequency f with early damage. a The amplitude attenuation matrix of the sound field signal is obtained, and the fundamental frequency localization characterization result is obtained based on the probabilistic defect detection and reconstruction algorithm. The first imaging and the fundamental frequency localization characterization result are fused into a multimodal image using weighted average fusion. The region within the localization extraction threshold in the fusion result is extracted, and the phase is inverted within the localization extraction threshold range to obtain the initial velocity model describing the spatial distribution of the damage.

7. The iterative quantitative imaging method based on a nonlinear Lamb wave mixing sound field according to claim 5 or 6, characterized in that, The method for constructing the nonlinear mapping model is as follows: select various damage morphologies including different sizes and degrees of hydrogen embrittlement and degradation combinations as training samples, randomly generate multiple location distributions for each damage morphology, and obtain offline training examples; repeat steps three to five for each example to obtain the initial velocity model and multi-dimensional frequency domain sound field matrix. The sound field change ΔP is defined as the element-level difference between the sum-frequency sound field matrix and the difference-frequency sound field matrix, and the model change ΔQ is defined as the element-level difference between the initial velocity model and the reference model. With the core objective of learning the nonlinear mapping relationship between sound field change ΔP and model change ΔQ, the conjugate gradient method is used to iteratively optimize offline training examples. By minimizing the global error between the mapped predicted value and the true value, the optimal nonlinear mapping model is constructed. .

8. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 7, characterized in that, The loss function for the iterative optimization training is the sum of the 2-norm errors between the predicted and actual values ​​of the model changes for all offline training examples. The conjugate gradient method iterative optimization is as follows: The partial derivative of the loss function with respect to the mapping model F is used to obtain the gradient ∇R. The negative gradient direction −∇R is used as the initial search direction. The conjugate coefficients are calculated using the Fletcher-Reeves formula, and the conjugate search direction for subsequent iterations is updated. The optimal step size for each iteration is solved through a one-dimensional line search, continuously updating the parameters of the mapping model F. When the loss function value is less than a preset threshold or gradient norm... Stop iterating when the value is less than the convergence threshold.

9. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 8, characterized in that, The initial velocity model obtained for the actual detection object The optimal nonlinear mapping model is obtained by directly inputting the sound field change ∆p, which represents the sum frequency and difference frequency of the sound field, as a test example. The model change Δq for the test case is obtained, and the model change Δq for the test case is compared with the initial velocity model. Element-level superposition operations are performed to obtain the final quantitative imaging model q for early damage morphology; the signal difference coefficients of the final quantitative imaging model q for early damage morphology are then uniformly mapped to the initial velocity model. Within the same signal difference coefficient range, quantitative reconstruction visualization results of the early damage morphology of the test case were obtained, which are the results of the second imaging.

10. The iterative quantitative imaging method based on nonlinear Lamb wave mixing sound field according to claim 1, characterized in that, The weights of the weighted average fusion are set according to the differences in the sensitivity of each feature parameter to damage. The first imaging is given a weight of 0.75, and the fundamental frequency localization characterization result is given a weight of 0.

25. The location extraction threshold is the top 20% of the signals with the highest signal difference coefficient values; The reference model is a standard model established using the actual geometric parameters of the finite element model. The signal difference coefficient of the reference model is mapped to the same signal difference coefficient range as the initial velocity model.

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