Local wave number estimation damage optimal imaging method based on strong constraint Bayesian optimization

Abstract

The invention discloses a local wave number estimation damage optimal imaging method based on strong constraint Bayesian optimization, and relates to the technical field of material structure health monitoring, and the technical scheme is characterized in that the method comprises the following steps: obtaining a three-dimensional guided wave signal of the surface of a thin-wall structure, converting the three-dimensional guided wave signal to a frequency-wave number domain through multi-dimensional Fourier transform, and obtaining a three-dimensional guided wave signal of the surface of the thin-wall structure; a filtered Fourier spectrum is obtained; adaptively extracting a target modal filtering local wave number from the filtered Fourier spectrum to obtain a local wave number estimation value; and obtaining an imaging quality evaluation index and a constraint frequency band, introducing a strong constraint Bayesian optimization method to carry out optimal frequency search on a local wave number estimation value, and outputting a stable damage imaging result. According to the frequency selection and imaging optimization method disclosed by the invention, an optimization problem of changing depending on manual frequency selection into data driving, strong constraint, noise resistance and efficient sample is solved, the imaging quality and robustness of local wave number estimation method imaging in complex structure damage detection are improved, and an efficient frequency selection and imaging optimization method is constructed.

Description

Technical Field

[0001] This invention relates to the field of material structure health monitoring technology, and more specifically, to a local wavenumber estimation damage optimal imaging method based on strongly constrained Bayesian optimization. Background Technology

[0002] Thin-walled metal and composite material structures are widely used in aerospace, energy, and transportation infrastructure. During service, these structures are susceptible to damage from multiple sources, including fatigue, impact, corrosion, and delamination. Failure to identify and locate these damages promptly and accurately directly threatens structural safety and lifespan management. Therefore, high-resolution non-destructive testing and structural health monitoring technologies for large-scale, complex shapes and in-service conditions have become core requirements in engineering applications. Ultrasonic guided waves, due to their advantages such as long-distance propagation, sensitivity to minute defects, and flexible sensor deployment, are widely used for damage visualization and assessment of such structures.

[0003] Among numerous guided wave imaging methods, local wavenumber estimation can directly characterize the spatial frequency features of the guided wave field, highlighting wavenumber anomalies at the damage site. It boasts advantages such as high resolution and adaptability to full-field measurements, making it suitable for configurations like thin plates, stiffened plates, and laminated plates. However, local wavenumber imaging is highly sensitive to center frequency and bandwidth: modal composition, dispersion, and attenuation differ significantly at different frequencies, and even slight errors can introduce artifacts, leading to blurred images or positioning deviations. Under complex geometries, anisotropic materials, and noise interference, this sensitivity is further amplified, resulting in large fluctuations in image quality and insufficient repeatability and consistency.

[0004] Current frequency setting methods largely rely on manual experience or simple screening based on dispersion curves, lacking unified criteria and systematic processes. This often results in imaging results with significant uncertainty and low resolution. Furthermore, narrowband filtering and modal separation frequently require multiple trials, incurring high computational costs and heavy operator dependence. Additionally, the difficulty in integrating high-confidence frequency bands, spectral characteristics, and noise resistance constraints into a unified decision-making process makes frequency selection and imaging optimization prone to local, accidental, and unstable factors, failing to meet the high-precision, high-reliability, and batch processing requirements of engineering scenarios. Therefore, there is an urgent need for a data-driven, information-based frequency selection and imaging optimization method that explicitly incorporates physical priors and constraints. This method should organically combine modal reachability and spectral feature reliability in the frequency-wavenumber domain, balancing global search and local fine-tuning, and consistently obtain high-resolution, low-artifact local wavenumber imaging results even with limited samples and noise disturbances. This would improve the accuracy, stability, and engineering applicability of damage detection in complex structures.

[0005] In view of this, the present invention proposes a local wavenumber estimation method for optimal damage imaging based on strongly constrained Bayesian optimization. Summary of the Invention

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution: The first aspect of this invention provides a local wavenumber estimation-based optimal imaging method for damage (SCBO-AMFLW) based on strongly constrained Bayesian optimization, comprising the following steps: The three-dimensional guided wave signal on the surface of the thin-walled structure is acquired, and it is converted to the frequency-wavenumber domain by multidimensional Fourier transform to obtain the filtered Fourier spectrum. Adaptively extract the local wavenumber of the target mode filter from the filtered Fourier spectrum to obtain the local wavenumber estimate; The imaging quality evaluation index and constraint frequency band are obtained. A strongly constrained Bayesian optimization method is introduced to search for the optimal frequency of the local wavenumber estimate and output the damage detection image.

[0007] In conjunction with the first aspect, the present invention is further configured such that the formula for converting it to the frequency-wavenumber domain through multidimensional Fourier transform is: ; in, and These are the projections of the space wavenumber K onto the x-axis and y-axis, respectively. f For frequency.

[0008] In conjunction with the first aspect, the present invention is further configured such that: the adaptive extraction of the target mode filtering local wavenumber from the filtered Fourier spectrum to obtain the local wavenumber estimate includes: first, automatically identifying the target mode center wave value from the filtered Fourier spectrum; second, performing target mode wavenumber filtering; and finally, using wavelet transform to extract the local wavenumber estimate, wherein the target mode is the A0 mode.

[0009] In conjunction with the first aspect, the present invention is further configured such that: the method for obtaining the imaging quality evaluation index is as follows: cropping the edge noise of the damaged image, determining the threshold of the damaged area and the non-damaged area, generating a binary mask accordingly, dividing the damaged and non-damaged area sets, and calculating the image quality evaluation index with the mean difference contrast.

[0010] In conjunction with the first aspect, the present invention is further configured such that: the method for obtaining the constraint frequency band is: based on the magnitude distribution of the dispersion curve and the establishment of a Gaussian prior distribution of the frequency, combined with the likelihood function constructed by the target mode energy concentration and the coherent signal-to-noise ratio, the posterior probability distribution is obtained through Bayes' theorem, thereby obtaining a constraint frequency band with high confidence.

[0011] In conjunction with the first aspect, the present invention is further configured as follows: the step of acquiring imaging quality evaluation indicators and constraint frequency bands, introducing a strongly constrained Bayesian optimization method to perform optimal frequency search on local wavenumber estimates, and outputting a damage detection image includes the following steps: The initial sampling frequency points are generated using the optimal Latin hypercube design method across the entire frequency band. For each initial sampling frequency, local wavenumber imaging is performed, and a mask-based image contrast index is calculated to establish an initial sample database. A surrogate model between frequency and image quality is established using Gaussian process regression. Construct an AVEI / SC acquisition function with constraint term R to balance global exploration and local mining, and suppress infeasible frequency bands; Maximize the acquisition function within the candidate frequency range to determine a new sampling frequency point, perform local wavenumber imaging and image quality assessment at that point, and update the sample database. Update the proxy model and collection function parameters based on the new samples, and proceed to the next iteration; Determine if the termination condition is met (such as the maximum number of iterations or the improvement rate being lower than a threshold). If not, continue iterating. When the termination condition is met, the optimal frequency is output, and the optimal damage detection image is obtained.

[0012] In conjunction with the first aspect, the present invention is further configured such that the AVEI / SC acquisition function is: ; in, , These represent the expected value and uncertainty of the image quality predicted by the Gaussian process, respectively. The target value parameter for each iteration; To control the weighting coefficients of the two items before and after.

[0013] A second aspect of the present invention also provides an apparatus / device / system for optimal damage imaging based on local wavenumber estimation using strongly constrained Bayesian optimization, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0014] A third aspect of the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0015] A fourth aspect of the present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the above-described method.

[0016] In summary, the present invention has the following beneficial effects: 1) Damage imaging is performed by selecting frequencies through intelligent optimization algorithms, which avoids the subjectivity and uncertainty caused by traditional frequency selection based on human experience, and improves the clarity and repeatability of damage imaging results.

[0017] (2) The prior and posterior probability models constructed using dispersion features and spectral domain features, as well as the automatic identification method of target modes, enable the optimization process to have strong adaptability under different boundary conditions, complex structures and noise interference, ensuring the consistency and stability of damage detection results.

[0018] (3)SCBO-AMFLW can quickly converge to the optimal narrow-band center frequency within a finite number of iterations, and shows strong stability and robustness to the found global optimal frequency value.

[0019] (4) Using indicators with clear physical meanings, such as damaged image contrast, as optimization targets makes the relationship between frequency selection and imaging effect more intuitive and clear.

[0020] (5) The SCBO-AMFLW algorithm has less dependence on parameter selection in operation, and the process is easy to integrate, which has strong promotion value and application prospects. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the pre-damaged aluminum plate structure and the laser scanning area in Embodiment 2 of the present invention; Figure 2 This is a flowchart of the local wavenumber estimation damage optimal frequency imaging method based on strongly constrained Bayesian optimization in embodiments 1, 2 and 3 of the present invention. Figure 3 These are the top 200 high-confidence frequency points of the posterior probability distribution in Embodiment 2 of the present invention; Figure 4 These are flowcharts of the strongly constrained Bayesian optimization algorithms in embodiments 1, 2, and 3 of this invention. Figure 5 These are the optimal value evolution curves of the SCBO-AMFLW algorithm in embodiments 1, 2, and 3 of this invention; Figure 6 This is the optimal narrow-band full-mode two-dimensional wavenumber spectrum in Embodiment 2 of the present invention; Figure 7 This is the smoothed radial average energy spectrum in Embodiment 2 of the present invention; Figure 8 This is the two-dimensional wavenumber spectrum of the optimal frequency band A0 mode in Embodiment 2 of the present invention; Figure 9 This is the optimal damaged image after 5% edge cropping in Embodiment 2 of the present invention; Figure 10This is a flowchart of the overall process of a local wavenumber estimation damage optimal imaging method based on strong constraint Bayesian optimization in Embodiment 3 of the present invention. Detailed Implementation

[0022] 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.

[0023] Example 1: A local wavenumber estimation method for optimal damage imaging based on strongly constrained Bayesian optimization includes the following steps: Step 1: Perform laser ultrasonic testing on the surface of the thin-walled structure to obtain the three-dimensional guided wave signal w(x,y,t) in the time-space domain of the tested area, and convert it to the frequency-wavenumber domain through multidimensional Fourier transform. : in, and These are the projections of the space wavenumber K onto the x-axis and y-axis, respectively. f For frequency.

[0024] Set the filter frequency range and obtain the starting frequency index, that is, select a narrow frequency band within the given frequency wavenumber domain. , making , and These represent the upper and lower filtering ranges of the intercepted frequency, respectively.

[0025] A frequency domain filtering window function is generated for filtering to reduce spectral leakage caused by truncation effects. The Tukey window function is used for filtering, and its mathematical expression is as follows: in, These are parameters of the Tukey window, used to control the size of the smoothing area; It refers to the frequency range being intercepted.

[0026] By By performing a dot product operation between the function and the Tukey window function, the narrow-band frequency-wavenumber domain of the frequency filtering is obtained, as shown in the following formula: Step 2: For adaptive extraction of target mode filtering local wavenumbers, the first step is to automatically identify the center wave value of the target mode, then perform target mode wavenumber filtering, and finally use wavelet transform to extract local wavenumber estimates. The A0 mode is defined as the target mode. The specific process for adaptive extraction of target mode filtering local wavenumbers is as follows: (1) For a wavenumber spectrum containing multiple modes, polar coordinate processing is performed and its radial distribution is projected into a one-dimensional vector form. This simplifies the characterization of the multimodal ring energy distribution while preserving the physical information of the central wavenumber position.

[0027] (2) Binning statistics are performed on the one-dimensional radial distribution of the multimodal wavenumber spectrum, and the energy level of the interval is approximated by the mathematical expectation value. Specifically, the one-dimensional wavenumber spectrum is divided into N equal-width statistical intervals, and the energy mean is calculated in each interval to obtain the radial wavenumber average energy spectrum. Its expression is: in, Let j be the number of samples in the j-th interval. Let j be the set of data indices that fall within the j-th interval. To smooth the operator, For vectorization operations, Radial wave number, For the first Radial wavenumber at each point.

[0028] (3) For a radial wavenumber average energy spectrum sequence Define the main energy peak The screening criteria are shown in the following formula: in, For peak prominence, and These are the minimum values ​​(valleys) between the left and right sides of the peak and the next point (or signal boundary) above this peak. For salience threshold factor, for The maximum value in This is the index number of the location of the main energy peak.

[0029] Among all the peaks obtained through salience screening, the main energy peak with the largest wavenumber is the A0 mode energy peak. The wavenumber value corresponding to half the amplitude of the A0 mode energy peak is used as the half-height standard to select the lower boundary of the A0 mode wavenumber filter, and twice the wavenumber value corresponding to the peak A0 mode energy peak is used as the upper boundary of the filter, which can cover the overflow part of the energy tail.

[0030] (4) Based on the determined upper and lower boundary values ​​of the A0 mode wavenumber filtering, the narrow-band frequency-wavenumber domain can be obtained by using the Tukey window function to perform A0 mode wavenumber bandpass filtering on the narrow-band frequency-wavenumber domain. : Where R is the filter weight matrix, and These are the wavenumber domain matrices in and Discrete index position of direction.

[0031] (5) When estimating the local wavenumber of narrow-band single-mode wavenumber domain data after frequency and wavenumber filtering, a two-dimensional Mexican hat (Mexh) wavelet function based on the second derivative of the Gaussian function is selected as the kernel function. In the specific implementation, the local continuous wavelet transform (CWT) coefficients are obtained by convolving the wavenumber domain wavefield data with the wavenumber domain Mexh wavelet kernel function. These CWT coefficients reflect the local response of the wavefield under different scale factors and spatial locations. Furthermore, among the CWT coefficient moduli obtained under different scale factors, the scale factor corresponding to the maximum value is taken as the local scale factor estimate. By utilizing the mapping relationship between the local scale factor and the local wavenumber, the local wavenumber estimate of the measured area can be obtained, and damage imaging can be realized accordingly.

[0032] The scaling factor in the frequency-wavenumber domain is Two-dimensional wavelet kernel function : CWT coefficients in the frequency-wavenumber domain : in, Indicates the position of the wavelet kernel function translation, superscript Represents complex conjugation CWT coefficient modulus and : Local scale factor estimate : Local wavenumber estimates Conversion relationship with local scale factor: Step 3: After cropping the edges of the damaged image, calculate its contrast as an imaging quality evaluation index. Since the boundary envelope of the actually acquired guided wave signal is often discontinuous, Fourier transforming it introduces edge noise. Therefore, cropping the edge noise of the damaged image can effectively reduce its impact. The Otsu method is used to determine the thresholds between the damaged and non-damaged areas. (That is, the threshold that maximizes the inter-class variance) is used to generate a binary mask to divide the damaged and non-damaged regions. Based on this, the mean difference contrast is calculated and used as an image quality evaluation index.

[0033] Binary mask BW: Damage area collection : Collection of non-damaged regions : Mean difference contrast : in, Local wavenumber estimate The normalized value, and They are respectively Element indexing in both vertical and horizontal directions.

[0034] Step 4: The constraint conditions are based on the magnitude distribution of the dispersion curve and the established Gaussian prior distribution of the frequency. The likelihood function is constructed by combining the energy concentration of the target mode and the coherent signal-to-noise ratio. The posterior probability distribution is obtained through Bayes' theorem, thereby determining the constraint frequency band with high confidence.

[0035] Gaussian prior distribution: in, and The statistical mean and variance are determined by the magnitude of the dispersion curve and the variance, respectively.

[0036] The formula for updating the posterior probability after introducing exponential weighting is as follows: in, The posterior probability is the probability from the previous time step; for the first update, This is the initial prior probability; Let be the constructed likelihood function; It is the normalization factor that sums up all frequencies. This is a smoothing factor.

[0037] Step 5: After obtaining the imaging quality evaluation indicators and constraint frequency bands, a strongly constrained Bayesian optimization method is introduced to search for the optimal frequency. This method is based on the (AVEI) acquisition function and adaptively sets the target value and dynamically balances global exploration and local mining during the iteration process, focusing sampling on potentially high-yield frequency bands. Simultaneously, a strongly constrained (SC) mechanism incorporates the posterior high-confidence frequency band into the acquisition function, ensuring that the physical constraints such as modal separability and spectral characteristics are met throughout the search process. This allows the optimization to efficiently converge to the optimal narrow-band center frequency and output stable damage imaging results. The specific process is as follows: (1): The initial sampling frequency points are generated using the optimal Latin hypercube design method across the entire frequency band.

[0038] (2): For each initial sampling frequency, perform local wavenumber imaging and calculate the image contrast index based on the mask to establish an initial sample database.

[0039] (3): A surrogate model between frequency and imaging quality is established by Gaussian process regression.

[0040] (4): Construct a strongly constrained adaptive mutation expectation improvement (AVEI / SC) acquisition function to balance global exploration and local mining, and suppress infeasible frequency bands.

[0041] Constraint R: in, P Let N be the posterior probability of the frequency, and N be the number of high-confidence frequency points selected. Let C be a set of frequencies, where C is a large value.

[0042] Strongly constrained adaptive mutation expectation improves the acquisition function : in, , These represent the expected value and uncertainty of the image quality predicted by the Gaussian process, respectively. is the target value parameter for each iteration; w is the weight coefficient that controls the weights of the preceding and following items. In the first iteration, w is set to 0.5, and in the (k+1)th iteration, w will be adjusted according to the feedback information.

[0043] (5): Maximize the acquisition function within the candidate frequency range, determine the new sampling frequency point, perform local wavenumber imaging and image quality assessment at the point, and update the sample database.

[0044] (6): Update the proxy model and collection function parameters based on the new samples, and proceed to the next iteration.

[0045] (7): Determine whether the termination condition is met. If not, continue iterating.

[0046] (8): When the termination condition is met, output the optimal frequency and obtain the optimal damage detection image.

[0047] Example 2: Taking a pre-damaged aluminum plate as an example, the technical solution of the present invention will be explained in detail.

[0048] Taking a pre-damaged aluminum plate structure with dimensions of 300 x 300 x 0.6 mm as an example, a laser ultrasonic system is used for C-scan inspection. An acoustic emission sensor is placed on the back of the specimen, and a laser ultrasonic scanning area is selected on the surface of the specimen. The location, size, sensor position, and laser scanning area of ​​the specimen are as follows: Figure 1 As shown. The signal sampling rate is 2.5MHz, the number of sampling points is 2000, the spatial sampling rate is 0.5mm, and the laser energy factor is 150.

[0049] The operation process mainly includes the following steps: Step 1: Acquire laser ultrasonic guided wave signal data and convert it to the frequency-wavenumber domain using multidimensional Fourier transform. Step 2: Within the A0 modal bandwidth, based on the spectral domain characteristics such as the cumulative energy distribution, energy concentration, and coherent signal-to-noise ratio of the dispersion curve, combined with Bayesian statistics, the posterior distribution of the frequency is obtained; Step 3: Within the entire frequency band, generate the initial sampling frequency point using the optimal Latin hypercube design method, and use it as the center frequency of the frequency filter.

[0050] Step 4: For each initial sampling frequency, set the narrow bandwidth to ±20kHz, perform frequency filtering using the Tukey window function, and obtain the smoothed radial average energy spectrum through adaptive mode identification. Select the A0 mode wavenumber bandpass range according to the main energy peak screening criterion and perform wavenumber filtering to obtain the narrow-band single-mode wavenumber domain wavefield.

[0051] Step 5: Perform local wavenumber estimation imaging on the narrow-band single-mode wavenumber domain wavefield, calculate the wavenumber image contrast imaging quality index based on binary mask, and establish an initial sample database.

[0052] Step 6: Using image contrast as the objective function value, and the top 200 high-confidence frequency points of the frequency posterior distribution as physical constraints in the optimization process, the distribution of which is as follows: Figure 3 As shown. Finally, the center frequency value of the narrow band is optimized using a strongly constrained Bayesian optimization algorithm, as shown. Figure 4As shown. Using the acquired guided wave data, setting the initial sampling narrowband center frequency to 20, and optimizing the iteration count to 50, the optimal narrowband center frequency value for damage imaging is obtained. The optimal value evolution curve of the algorithm is shown below. Figure 5 As shown. The wavenumber spectrum after performing frequency filtering on the optimal narrow-band center frequency value is as follows. Figure 6 As shown, the smoothed radial average energy spectrum obtained by performing adaptive A0 mode identification is as follows: Figure 7 As shown, the wavenumber spectrum after adaptive filtering of the A0 mode is as follows: Figure 8 As shown, the optimal damage image obtained by performing local wavenumber estimation is as follows: Figure 9 As shown.

[0053] Example 3: A local wavenumber estimation method for optimal damage imaging based on strongly constrained Bayesian optimization, such as... Figure 10 As shown, it includes the following steps: S100. Acquire the three-dimensional guided wave signal on the surface of the thin-walled structure, and convert it to the frequency-wavenumber domain through multidimensional Fourier transform to obtain the filtered Fourier spectrum. S200. Adaptively extract the local wavenumber of the target mode filter from the filtered Fourier spectrum to obtain the local wavenumber estimate; S300. Obtain imaging quality evaluation indicators and constraint frequency bands, introduce a strongly constrained Bayesian optimization method to search for the optimal frequency of local wavenumber estimates, and output stable damage imaging results.

[0054] In this embodiment S100, the formula for converting it to the frequency-wavenumber domain using multidimensional Fourier transform is as follows: ; in, and These are the projections of the space wavenumber K onto the x-axis and y-axis, respectively. f For frequency.

[0055] In this embodiment S200, adaptive extraction of the target mode filtering local wavenumber is performed on the filtered Fourier spectrum to obtain the local wavenumber estimate. This includes: first, automatically identifying the target mode center wave value on the filtered Fourier spectrum; second, performing target mode wavenumber filtering; and finally, using wavelet transform to extract the local wavenumber estimate. The target mode is the A0 mode.

[0056] The specific process of adaptively extracting the local wavenumber of the target mode filter is as follows: (1) For a wavenumber spectrum containing multiple modes, polar coordinate processing is performed and its radial distribution is projected into a one-dimensional vector form. This simplifies the characterization of the multimodal ring energy distribution while preserving the physical information of the central wavenumber position.

[0057] (2) Binning statistics are performed on the one-dimensional radial distribution of the multimodal wavenumber spectrum, and the energy level of the interval is approximated by the mathematical expectation value. Specifically, the one-dimensional wavenumber spectrum is divided into N equal-width statistical intervals, and the energy mean is calculated in each interval to obtain the radial wavenumber average energy spectrum, which is then smoothed. The expression is as follows: in, Let j be the number of samples in the j-th interval. Let j be the set of data indices that fall within the j-th interval. To smooth the operator, For vectorization operations, Radial wave number, For the first Radial wavenumber at each point.

[0058] (3) For a radial wavenumber average energy spectrum sequence The selection criteria for the main energy peak are defined as follows: in, For peak prominence, and These are the minimum values ​​(valleys) between the left and right sides of the peak and the next point (or signal boundary) above this peak. For salience threshold factor, for The maximum value in This is the index number of the location of the main energy peak.

[0059] Due to its low group velocity, the A0 mode typically has a high wavenumber. Therefore, among all the peaks obtained through salience screening, the main energy peak with the highest wavenumber is the A0 mode energy peak. The wavenumber value corresponding to half the amplitude of the A0 mode energy peak is used as the half-height standard to select the lower boundary of the A0 mode wavenumber filter, and twice the wavenumber value corresponding to the peak energy value of the A0 mode is used as the upper boundary of the filter. This covers the energy tail and the energy spillover caused by damage, stray energy, and other effects.

[0060] (4) Based on the determined upper and lower boundary values ​​of the A0 mode wavenumber filtering, the narrow-band frequency-wavenumber domain can be obtained by using the Tukey window function to perform A0 mode wavenumber bandpass filtering on the narrow-band frequency-wavenumber domain. : Where R is the filter weight matrix, and These are the wavenumber domain matrices in and Discrete index position of direction.

[0061] (5) When estimating the local wavenumber of narrow-band single-mode wavenumber domain data after frequency and wavenumber filtering, a two-dimensional Mexican Hat (Mexh) wavelet function based on the second derivative of the Gaussian function is selected as the kernel function. This wavelet is sensitive to signal edges and local abrupt changes, and can highlight the energy concentration effect of the target mode in the local wavenumber neighborhood, thus enhancing the significance of local wavenumber features. In the specific implementation process, the local continuous wavelet transform (CWT) coefficients are obtained by convolving the wavenumber domain wavefield data with the wavenumber domain Mexh wavelet kernel function. The CWT coefficients reflect the local response of the wavefield under different scale factors and spatial locations. Furthermore, among the CWT coefficient moduli obtained under different scale factors, the scale factor corresponding to the maximum value is taken as the local scale factor estimate. By utilizing the mapping relationship between the local scale factor and the local wavenumber, the local wavenumber estimate of the measured area can be obtained, and damage imaging can be realized accordingly.

[0062] The scaling factor in the frequency-wavenumber domain is Two-dimensional wavelet kernel function: CWT coefficients in the frequency-wavenumber domain: in, Indicates the position of the wavelet kernel function translation, superscript Represents complex conjugation CWT coefficient modulus sum: Local scale factor estimates: Local wavenumber estimates Conversion relationship with local scale factor: .

[0063] In this embodiment S300, the method for obtaining the imaging quality evaluation index is as follows: cropping the edge noise of the damaged image, determining the threshold of the damaged area and the non-damaged area, generating a binary mask accordingly, dividing the damaged and non-damaged area sets, and calculating the image quality evaluation index with the mean difference contrast.

[0064] In this embodiment S300, the method for obtaining the constraint frequency band is as follows: based on the magnitude distribution of the dispersion curve and the establishment of the frequency Gaussian prior distribution, combined with the likelihood function constructed by the target mode energy concentration and coherent signal-to-noise ratio, the posterior probability distribution is obtained through Bayes' theorem, and a high-confidence constraint frequency band is obtained.

[0065] In this embodiment S300, the imaging quality evaluation index and constraint frequency band are obtained, and a strongly constrained Bayesian optimization method is introduced to search for the optimal frequency of the local wavenumber estimate, outputting a stable damage imaging result, including the following steps: (1): The initial sampling frequency points are generated using the optimal Latin hypercube design method across the entire frequency band; (2): For each initial sampling frequency, perform local wavenumber imaging and calculate the image contrast index based on the mask to establish an initial sample database; (3): A surrogate model between frequency and imaging quality is established using Gaussian process regression. (4): Construct an AVEI / SC acquisition function with constraint term R to balance global exploration and local mining, and suppress infeasible frequency bands; (5): Maximize the acquisition function within the candidate frequency range, determine the new sampling frequency point, perform local wavenumber imaging and image quality assessment at the point, and update the sample database; (6): Update the proxy model and collection function parameters based on the new samples, and proceed to the next iteration; (7): Determine whether the termination condition is met (such as the maximum number of iterations or the improvement is lower than the threshold). If not, continue iterating. (8): When the termination condition is met, output the optimal frequency and obtain the optimal damage detection image.

[0066] In this embodiment, the AVEI / SC acquisition function is: ; in, , These represent the expected value and uncertainty of the image quality predicted by the Gaussian process, respectively. The target value parameter for each iteration; To control the weighting coefficients of the two items before and after.

[0067] The present invention also provides an apparatus / device / system for optimal damage imaging based on local wavenumber estimation using strongly constrained Bayesian optimization, comprising a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the above method.

[0068] The present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0069] The present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the above-described method.

[0070] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. 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. A local wavenumber estimation method for optimal damage imaging based on strongly constrained Bayesian optimization, characterized by: Includes the following steps: The three-dimensional guided wave signal on the surface of the thin-walled structure is acquired, and it is converted to the frequency-wavenumber domain by multidimensional Fourier transform to obtain the filtered Fourier spectrum. Adaptively extract the local wavenumber of the target mode filter from the filtered Fourier spectrum to obtain the local wavenumber estimate; The imaging quality evaluation index and constraint frequency band are obtained. A strongly constrained Bayesian optimization method is introduced to search for the optimal frequency of the local wavenumber estimate and output the damage detection image.

2. The local wavenumber estimation damage optimal imaging method according to claim 1, characterized in that: The formula for converting it to the frequency-wavenumber domain using multidimensional Fourier transform is as follows: ； in, and These are the projections of the space wavenumber K onto the x-axis and y-axis, respectively. f For frequency.

3. The local wavenumber estimation damage optimal imaging method according to claim 1, characterized in that: The adaptive extraction of the target mode filtering local wavenumber from the filtered Fourier spectrum to obtain the local wavenumber estimate includes: first, automatically identifying the center wave value of the target mode from the filtered Fourier spectrum; second, performing target mode wavenumber filtering; and finally, using wavelet transform to extract the local wavenumber estimate, wherein the target mode is the A0 mode.

4. The local wavenumber estimation damage optimal imaging method according to claim 1, characterized in that: The method for obtaining the imaging quality evaluation index is as follows: cropping the edge noise of the damaged image, determining the threshold of the damaged area and the non-damaged area, generating a binary mask accordingly, dividing the damaged and non-damaged areas into sets, calculating the mean difference contrast, and using the mean difference contrast as the imaging quality evaluation index.

5. The local wavenumber estimation damage optimal imaging method according to claim 1, characterized in that: The method for obtaining the constrained frequency band is as follows: based on the magnitude distribution of the dispersion curve and the establishment of the frequency Gaussian prior distribution, combined with the likelihood function constructed by the target mode energy concentration and coherent signal-to-noise ratio, the posterior probability distribution is obtained through Bayes' theorem, thereby obtaining the constrained frequency band with high confidence.

6. The local wavenumber estimation damage optimal imaging method according to claim 1, characterized in that: The process of acquiring imaging quality evaluation indicators and constrained frequency bands, introducing a strongly constrained Bayesian optimization method to search for the optimal narrow-band center frequency of the local wavenumber estimate, and outputting a damage detection image includes the following steps: The initial sampling frequency points are generated using the optimal Latin hypercube design method across the entire frequency band. For each initial sampling frequency, local wavenumber imaging is performed, and a mask-based image contrast index is calculated to establish an initial sample database. A surrogate model between frequency and image quality is established using Gaussian process regression. A strongly constrained adaptive mutation expectation improvement (AVEI / SC) acquisition function is constructed to balance global exploration and local mining, and to suppress infeasible frequency bands; Maximize the acquisition function within the candidate frequency range to determine a new sampling frequency point, perform local wavenumber imaging and image quality assessment at that point, and update the sample database. Update the proxy model and collection function parameters based on the new samples, and proceed to the next iteration; Determine if the termination condition is met; if not, continue iterating. When the termination condition is met, the optimal frequency is output, and the optimal damage detection image is obtained.

7. The local wavenumber estimation damage optimal imaging method according to claim 6, characterized in that: The AVEI / SC acquisition function is: ； in, , These represent the expected value and uncertainty of the image quality predicted by the Gaussian process, respectively. The target value parameter for each iteration; To control the weighting coefficients of the two items before and after.

8. A device / equipment / system for optimal damage imaging based on local wavenumber estimation using strongly constrained Bayesian optimization, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1-7.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1-7.

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