An aviation part crack detection and repair method

Abstract

This invention relates to the field of industrial vision technology, specifically to a method for detecting and repairing cracks in aerospace components. The method includes the following steps: acquiring optical images of the aerospace component at a reference time point and optical images of the aerospace component at the time point to be tested. In this invention, by performing logarithmic polar coordinate transformation on images at different time points and extracting rotation, scaling, and translation parameters, an image registration relationship is established, enhancing the structural consistency of the time-series images in local regions. Furthermore, a structural tensor is constructed for the neighborhood of each pixel, and the change characteristics of the bi-temporal tensor are compared to generate a saliency map of structural changes, enabling sensitive capture of areas with minute deformations and improving the response capability to initial cracks. Then, through adaptive threshold segmentation and skeleton extraction, the crack propagation range is further refined into the main crack path. Combined with the tip contour information of the crack geometric boundary, the sharpness of the crack tip is calculated, providing quantitative support for the crack's severity.

Description

Technical Field

[0001] This invention relates to the field of industrial vision technology, and in particular to a method for detecting and repairing cracks in aerospace components. Background Technology

[0002] Industrial vision systems are automated devices based on image recognition technology. They are mainly used for quality inspection, processing and assembly control, and process monitoring in industrial production, covering fields such as automobile manufacturing, electronic assembly, and food processing.

[0003] Existing industrial vision systems rely on pattern matching and edge detection mechanisms from static images for quality control and defect identification. However, when dealing with the evolution of micro-scale structures like aerospace components, they struggle to accurately identify minute crack growth trends. Furthermore, they fail to quantify and analyze local structural tension changes and geometric evolution paths, making them prone to misjudgment or missed detection on highly complex material surfaces. For example, before a crack expands into a visible defect, its contrast in a grayscale image is extremely low, making it difficult for traditional edge operators to respond effectively, thus missing the optimal window for early intervention. Therefore, improvements are needed. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a method for detecting and repairing cracks in aerospace components.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for detecting and repairing cracks in aerospace components, comprising the following steps:

[0006] Acquire optical images of aerospace components at a reference time point and optical images of aerospace components at the time point to be measured. Perform logarithmic polar coordinate transformation on the optical images to estimate rotation and scaling parameters, and generate subpixel registered image pairs.

[0007] Based on the subpixel registered image pair, the gradient distribution is calculated in the neighborhood of each pixel, and independent structure tensors are constructed for the reference image and the image to be tested, respectively, to obtain a dual-temporal structure tensor field. A saliency map of structural changes is generated based on the dual-temporal structure tensor field.

[0008] Based on the structural change saliency map, an adaptive segmentation threshold is set, and points with pixel values ​​greater than the adaptive segmentation threshold are set as foreground and the rest are set as background to obtain the crack propagation binarized region. The skeleton of the crack propagation binarized region is extracted to generate the crack tip contour curve.

[0009] Based on the crack tip profile curve, the tip sharpness quantification value is calculated. At the same time, the number and distribution density of microcracks around the crack tip in the stress concentration area of ​​the aerospace component are statistically analyzed, and the crack propagation tendency index is calculated.

[0010] Preferably, the step of obtaining the sub-pixel registered image pair is as follows:

[0011] Load the optical images of the aerospace components at the reference time point and the optical images of the aerospace components at the time point to be measured, unify the bit depth and pixel spacing, crop the common field of view of the two images, construct a logarithmic polar coordinate grid, resample according to the angle sequence and radius sequence, and statistically analyze the angular peak position and radial ratio to generate rotation and scaling parameters;

[0012] Based on the rotation and scaling parameters, the optical image of the aviation component at the time point to be measured is corrected to the coordinate system of the optical image of the aviation component at the reference time point according to the angle and scale. The spectral conjugate product of the two corrected images is calculated and the amplitude is normalized and the main peak is searched. The integer and subpixel deviations of row offset and column offset are located and the translation amount is generated.

[0013] Based on the translation amount, the optical image of the aerospace component at the time point to be tested is geometrically corrected according to the rotation and scaling parameters, and subpixel-level interpolation displacement is performed according to the translation amount. The image is then aligned to the pixel grid of the optical image of the aerospace component at the reference time point, and the overlapping areas and holes are trimmed to generate a subpixel registered image pair.

[0014] Preferably, the steps for obtaining the dual-temporal structure tensor field are as follows:

[0015] Based on the subpixel registered image pair, fixed square neighborhoods are extracted on the reference image and the image to be tested, the horizontal gradient and vertical gradient are calculated, the square of the gradient and the product of the gradient are summed item by item in the neighborhood and smoothed with a uniform scale, and symmetric second-order matrices are assembled at the corresponding pixel positions and correspond one-to-one to generate a dual-temporal structure tensor field.

[0016] Preferably, the step of obtaining the saliency map of structural changes is as follows:

[0017] Based on the dual-temporal structure tensor field, the structural change metric is calculated to form a structural change metric matrix.

[0018] Based on the structural change metric matrix, the global minimum and global maximum metric values ​​are extracted, linearly stretched and mapped, and the output intensity is written according to the pixel position, keeping the size and coordinates consistent with the reference image to form a structural change saliency map.

[0019] Preferably, the step of obtaining the crack propagation binarized region is as follows:

[0020] Based on the structural change saliency map, the pixel value histogram is statistically analyzed at fixed intervals and the count of each segment is recorded. The difference between adjacent counts is compared to determine the initial value of the adaptive segmentation threshold. The adaptive segmentation threshold is corrected according to the difference between the mean and median of the pixel neighborhood. The pixel is compared with the adaptive segmentation threshold and the foreground is merged with four neighbor connections to obtain the crack propagation binarized region.

[0021] Preferably, the step of obtaining the crack tip profile curve is as follows:

[0022] Based on the crack propagation binarized region, refine it round by round according to the eight neighborhoods while keeping the endpoints and intersections. Delete edge pixels that meet the redundancy conditions to shrink to a single pixel width. Traverse along the longest connected chain and count the degree of each node. Filter out the unique pixel with a degree of one that is located at the end to obtain the end point of the main crack path.

[0023] Based on the end point of the main crack path, an equidistant annular sampling zone with the end point of the main crack path as the center is constructed and limited to the boundary of the crack propagation binarized region. The boundary coordinates between the sampling zone and the background are scanned in polar angle order and discontinuous coordinates are eliminated. Adjacent coordinates are connected to form a closed curve and the jagged edges are smoothed to generate the crack tip contour curve.

[0024] Preferably, the step of obtaining the tip sharpness quantification value is as follows:

[0025] Based on the crack tip profile curve, boundary coordinate points are extracted at fixed intervals on both sides of the vertex, the local arc is reconstructed and the arc radius is calculated. The reciprocal of the arc radius is used as the quantization value to obtain the tip sharpness quantization value.

[0026] Preferably, the step of obtaining the crack propagation tendency index is as follows:

[0027] Based on the vertex position of the crack tip contour curve, a fixed circular region with the vertex as the center and radius R is set. All crack pixels in the region are filtered for connectivity. The microcrack endpoints are marked one by one and the number of endpoints is counted. The ratio of the number of endpoints to the area of ​​the fixed circular region is calculated to obtain the microcrack density.

[0028] The crack propagation tendency index is calculated based on the tip sharpness quantification and the microcrack density.

[0029] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0030] In this invention, by performing logarithmic polar coordinate transformation on images at different time points and extracting rotation, scaling, and translation parameters, image registration relationships are established, enhancing the structural consistency of time-series images in local regions. Furthermore, a structural tensor is constructed for the neighborhood of each pixel, and the change characteristics of the bi-temporal tensor are compared to generate a saliency map of structural changes, enabling sensitive capture of micro-deformation regions and improving the response capability to initial cracks. Then, through adaptive threshold segmentation and skeleton extraction, the crack propagation range is further refined into the main crack path. Combined with the tip contour information of the crack geometric boundary, the crack tip sharpness is calculated, providing quantitative support for the crack hazard level. Moreover, by statistically analyzing the micro-crack density in a circular region with fixed stress concentration, the propagation risk of the crack tip can be dynamically reflected, providing data support and response priority judgment for subsequent repair measures. This enables continuous monitoring of the entire process of crack generation, propagation, and trend assessment, improving the efficiency of crack repair for aerospace components. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0033] Please see Figure 1 This invention provides a technical solution: a method for detecting and repairing cracks in aerospace components, comprising the following steps:

[0034] Acquire optical images of aerospace components at a reference time point and optical images of aerospace components at the time point to be measured. Perform logarithmic polar coordinate transformation on the optical images to estimate rotation and scaling parameters, and generate subpixel registered image pairs.

[0035] Based on the subpixel registered image pairs, the gradient distribution is calculated in the neighborhood of each pixel. Independent structure tensors are constructed for the reference image and the image to be tested, respectively, to obtain a dual-temporal structure tensor field. A saliency map of structural changes is generated based on the dual-temporal structure tensor field.

[0036] Based on the saliency map of structural changes, an adaptive segmentation threshold is set. Points with pixel values ​​greater than the adaptive segmentation threshold are set as foreground and the rest are set as background to obtain the crack propagation binarized region. The skeleton of the crack propagation binarized region is extracted to generate the crack tip contour curve.

[0037] Based on the crack tip profile curve, the tip sharpness quantification value is calculated. At the same time, the number and distribution density of microcracks around the crack tip in the stress concentration area of ​​aerospace components are statistically analyzed, and the crack propagation tendency index is calculated.

[0038] The steps for obtaining subpixel registered image pairs are as follows:

[0039] Load the optical images of the aerospace components at the reference time point and the optical images of the aerospace components at the time point to be measured, unify the bit depth and pixel spacing, crop the common field of view of the two images, construct a logarithmic polar coordinate grid, resample according to the angle sequence and radius sequence, and statistically analyze the angular peak position and radial ratio to generate rotation and scaling parameters;

[0040] Based on rotation and scaling parameters, the optical images of the aviation components at the time point to be measured are corrected to the coordinate system of the optical images of the aviation components at the reference time point according to the angle and scale. The spectral conjugate product of the two corrected images is calculated and the amplitude is normalized and the main peak is searched. The integer and sub-pixel deviations of row offset and column offset are located and the translation amount is generated.

[0041] Based on the translation amount, the optical images of the aerospace components at the time point to be measured are geometrically corrected according to the rotation and scaling parameters, and then subpixel-level interpolation displacement is performed according to the translation amount. The images are aligned to the pixel grid of the optical images of the aerospace components at the reference time point, and the overlapping areas and holes are trimmed to generate subpixel registered image pairs.

[0042] Specifically, after loading the optical images of the aerospace components at the reference time point and the optical images of the aerospace components at the test time point, the metadata of the two images is first parsed. The bit depth of the images is then read and unified. For example, if the reference image is an 8-bit unsigned integer grayscale image and the test image is 16-bit, the pixel values ​​of the test image are converted to 8-bit depth through a linear mapping: new pixel value = (original pixel value / 65535)*255. At the same time, the pixel spacing is unified. Based on the physical resolution information recorded in the image file header, such as the number of pixels per millimeter, one of the images is resampled so that the physical size represented by its pixels is consistent with that of the other image. The two images are completely identical. To eliminate interference from non-interesting regions, an automatic feature matching method is used to determine the common viewing range of the two images. Specifically, the Speeded Robust Feature (SURF) algorithm is used to detect hundreds of feature points in each of the two images. By calculating the Euclidean distance between feature descriptors, the best matching point pairs with a distance less than a preset matching threshold are selected. This matching threshold is set by calculating the average and standard deviation of the distances of all matching pairs, with the threshold set to the average plus 1.5 times the standard deviation. Based on at least four pairs of matching points selected, the Random Sample Consensus (RANSAC) algorithm is used to estimate the single-view distance between the two images. An adaptive transformation matrix is ​​used to transform the coordinates of the four corner points of the test image to the coordinate system of the reference image. The intersection of the bounding boxes of the two images is calculated, forming the largest inscribed rectangular region as the common viewing range. The two images are then cropped. Next, to convert rotation and scaling transformations into translation transformations for subsequent processing, a logarithmic polar coordinate grid is constructed for the cropped images. This grid has its origin at the image center, with an angle sequence from 0 to 360 degrees divided into 720 angular steps, and a radius sequence from 1 pixel to half the length of the image diagonal divided into 512 radius steps on a logarithmic scale. Bilinear interpolation is then used to... The algorithm calculates the corresponding pixel value in the original Cartesian coordinate image for each sampling point on the log-polar coordinate grid, completes resampling, and obtains two log-polar coordinate images. On these two images, the phase correlation method is used to statistically determine the angular peak position and radial ratio, that is, to perform Fourier transform on them, calculate their cross power spectral density, and then perform inverse Fourier transform. In the obtained phase correlation matrix, the position (Δθ, Δρ) of the peak point corresponds to the angular offset and radius offset of the two images in the log-polar coordinate space, where the angular peak position represents the rotation angle and the radial ratio represents the scaling factor. Finally, the rotation and scaling parameters required for subsequent steps are generated.

[0043] Based on the rotation and scaling parameters generated in the previous step, the optical image of the aerospace component at the test time point is initially corrected. Specifically, an affine transformation matrix is ​​constructed, containing the rotation angle calculated based on the angular peak position and the scaling factor calculated based on the radial scale. This transformation matrix is ​​applied to each pixel coordinate of the test image, and the pixel grayscale value at the new coordinates is calculated using bicubic interpolation. This generates a corrected image aligned with the optical image of the aerospace component at the reference time point in terms of angle and scale. Next, to accurately calculate the translation, a phase correlation method is used. First, a two-dimensional Fast Fourier Transform (FFT) is performed on both the reference image and this corrected test image to obtain their frequency domain representation F. base (u,v) and F test′ (u,v) is used to calculate the cross-power spectrum of the two images. The calculation involves multiplying the frequency domain representation of the reference image by the complex conjugate of the frequency domain representation of the image under test, and then normalizing the result. The calculation formula is as follows: Where C(u,v) is the normalized cross-power spectrum. The normalization step is the complex conjugate of the frequency domain representation of the corrected image under test. This normalization step enhances phase information and suppresses the influence of amplitude information. Subsequently, a two-dimensional inverse fast Fourier transform (IFFT) is performed on the normalized cross-power spectrum C(u,v) to obtain a spatial domain impulse response matrix. Theoretically, there exists a unique peak in this matrix, whose position coordinates correspond to the integer pixel translation between the two images. By traversing the entire impulse response matrix, the pixel coordinates (x,v) with the maximum value are searched and recorded. int ,y int This coordinate is the integer part of the row offset and column offset. To achieve sub-pixel level precise positioning, a 3x3 neighborhood window is taken around the found integer peak point. Using the 9 response values ​​within this window, a two-dimensional quadratic polynomial surface is fitted using the least squares method to find the precise peak point coordinates of the fitted surface. The offset of this precise peak point relative to the center of the window (x) sub ,y sub This is the subpixel offset. Finally, the integer offset is added to the subpixel offset, i.e., the total row offset = y_int + y_sub and the total column offset = x_int + x_sub, to generate the high-precision translation amount used for subsequent image registration.

[0044] Based on the translation amount, which includes integer and sub-pixel deviations, calculated in the previous step, and combined with the earlier generated rotation and scaling parameters, these three sets of transformation parameters (rotation, scaling, and translation) are integrated into a single affine transformation matrix. This matrix can complete the entire geometric correction of the optical image of the aerospace component at the test time point in one step. This integrated affine transformation matrix is ​​applied to each pixel coordinate of the image under test to calculate its new coordinates in the coordinate system of the aerospace component optical image at the reference time point. Since the calculated new coordinates are usually non-integer, sub-pixel level interpolation displacement is required. Here, the Lanczos interpolation algorithm is used. This algorithm uses an interpolation kernel based on the Sinc function to perform a weighted average of the pixel values ​​in the 8x8 neighborhood around each point to be calculated in the source image, calculating the precise grayscale value on the target pixel grid. This method can complete image resampling and displacement while maintaining image details and edge sharpness, thereby aligning the pixel grid of the image under test with the pixel grid of the aerospace component optical image at the reference time point. After geometric correction and alignment, the image boundaries need to be trimmed because rotation and translation operations can cause invalid data areas (usually displayed as black) to appear on the corrected image boundaries. By comparing the valid data range of the corrected test image with the boundary of the reference image, the maximum rectangular overlap area shared by the two is calculated, and both images are cropped into this common area. In addition, for tiny holes that may be generated inside the image during the transformation process (e.g., pixel loss due to nonlinear distortion correction), a hole filling operation is performed. Specifically, all pixels with a value of 0 are detected, and their eight neighboring pixels are checked. If the number of non-zero pixels in the eight neighboring pixels of a hole pixel exceeds a set threshold (e.g., set to 5), the value of the hole pixel is set to the average of all its non-zero neighboring pixels. This process is iterated until there are no more holes in the image that meet the filling conditions. Through the above processing, a pair of reference and test images that are precisely aligned at both the pixel and sub-pixel levels are finally generated, i.e., a sub-pixel registered image pair.

[0045] The steps for obtaining the two-phase structure tensor field are as follows:

[0046] Based on the subpixel registered image pairs, fixed square neighborhoods are extracted on the reference image and the image to be tested. The horizontal and vertical gradients are calculated, and the squares of the gradients and the product of the gradients are summed item by item in the neighborhood and smoothed with a uniform scale. Symmetric second-order matrices are assembled at the corresponding pixel positions and correspond one-to-one to generate a dual-temporal structure tensor field.

[0047] Specifically, based on the subpixel-registered image pairs, each pixel in the reference image and the image to be tested is traversed. A square neighborhood of a fixed size is extracted with the current pixel as the center. The size of this neighborhood is set to 7x7 pixels. This size is determined by performing Fourier transform analysis on sample images containing typical microcracks, observing the spatial scale corresponding to their main frequency components, and considering computational efficiency. This effectively captures the local structural features of the cracks while smoothing out isolated noise points. Then, within each 7x7 neighborhood, a 3x3 Sobel operator is applied to calculate the horizontal and vertical gradients of the center pixel. Specifically, the horizontal Sobel kernel [[-1,0,1],[-2,0,2],[-1,0,1]] and the vertical Sobel kernel [[-1,-2,-1],[0,0,0],[1,2,1]] are convolved with the pixel values ​​in the neighborhood to obtain the horizontal gradient component I. x and vertical gradient component I y Next, in order to construct the structure tensor, it is necessary to calculate the three combined terms of the gradient components: the square of the horizontal gradient. Square of vertical gradient And the product of the horizontal gradient and the vertical gradient, I x I y These three values ​​initially describe the gradient information at that pixel. To make the description of the structure tensor more robust and stable, it is necessary to perform a local weighted average (i.e., smoothing) on ​​these gradient combinations, using a Gaussian kernel with a standard deviation of 1.5 pixels across the entire image. and I x I y The component images are smoothed by convolution. This uniform smoothing scale ensures that the structural information of all pixels is integrated to the same extent. The smoothed component is denoted as J. xx J yy and J xy Finally, at each corresponding pixel location in the reference image and the image under test, the smoothed gradient components are assembled into a symmetric second-order matrix, namely the structure tensor matrix. Since the same operation was performed on both the reference image and the image under test, two one-to-one structural tensor matrices were obtained at each pixel location. These two sets of matrices together constitute the biphase structural tensor field required for subsequent analysis.

[0048] The steps to obtain the saliency map of structural changes are as follows:

[0049] Based on the dual-temporal structure tensor field, the structural change metric is calculated, forming the structural change metric matrix. The calculation formula is as follows:

[0050]

[0051] Among them, Em (p) is a measure of the structural change of pixel p, J u (p) is the structure tensor matrix of the reference image at pixel p, J v (p) is the structure tensor matrix of the image to be tested at pixel p, tr(J u (p)) is J u The trace of (p), tr(J) v (p)) is J v (p) trace, e u,1 (p) is J u (p) The unit eigenvector corresponding to the largest eigenvalue, e v,1 (p) is J v (p) The unit eigenvector corresponding to the largest eigenvalue, e u,1 (p)·e v,1 (p) is the dot product of the two unit feature vectors at pixel p, β is the scalar coefficient, and p is the current pixel coordinate;

[0052] Based on the structural change metric matrix, the global minimum and global maximum metric values ​​are extracted, linearly stretched and mapped, and the output intensity is written according to the pixel position, keeping the size and coordinates consistent with the reference image to form a structural change saliency map.

[0053] Specifically, the formula: The intensity and orientation changes of local image structures between two time points are quantified. The first term of the formula (tr(J) u (p))-tr(J v (p))) 2 The changes in structural strength are captured because the trace of the structural tensor is proportional to the magnitude of the local gradient energy, and the square of the difference amplifies the differences in strength. The second term quantifies the changes in structural orientation, where (e u,1 (p)·e v,1 (p)) 2 This represents the square of the dot product of the principal direction vectors. A value close to 1 indicates that the direction remains unchanged, while a value close to 0 indicates that the direction has deflected by nearly 90 degrees. Therefore, 1-(e u,1 (p)·e v,1 (p)) 2 This measure, which quantifies the degree of directional change, is also multiplied by a weighting factor. In this way, higher weight is given to directional changes in areas where the structure itself is strong (such as clear edges or cracks), while the influence of directional changes is suppressed in flat or noisy areas. The scalar coefficient β is used to balance the contributions of both strength and directional changes.

[0054] J u(p) is the structure tensor matrix of the reference image at pixel p. It is a 2x2 symmetric matrix obtained by assembling the matrix after calculating the gradient in the neighborhood of pixel p and smoothing the product of the gradient components using Gaussian smoothing. This matrix describes the local image structure around pixel p. For example, in a pixel p with a clear vertical crack edge, the horizontal gradient in its neighborhood is much greater than the vertical gradient. After calculation and smoothing, the resulting reference image structure tensor matrix might be:

[0055] J v (p) is the structure tensor matrix of the image under test at pixel p, and its acquisition method is the same as that of J. u (p) is exactly the same, except that the calculation is based on the optical image at the time point to be measured. This matrix describes the local image structure of the same physical location at the time point to be measured. If the crack at that location expands, causing its edges to become more complex or its direction to be slightly deflected, its structure tensor will also change accordingly. For example, the structure tensor matrix of the image under test at the same point p may become

[0056] tr(J u (p)) is J u The trace (p) represents the local structure intensity of the reference image at pixel p. It is obtained by adding the elements on the main diagonal of the matrix and reflects the sum of gradient energy in the neighborhood of that point. A higher trace value indicates the presence of strong edges, corners, or textures in that region. Based on the previously obtained J... u (p), the calculation process of its trace is: tr(J u (p))=150.8+5.3=156.1.

[0057] tr(J v (p)) is J v The trace (p) represents the local structure intensity of the image under test at pixel p. The calculation method is the same as above, by comparing tr(J) u (p)) and tr(J v (p) can determine whether the strength of the local structure has changed, based on the previously obtained J. v (p), the calculation process of its trace is: tr(J v (p))=165.4+8.9=174.3.

[0058] e u,1 (p) is J u (p) The unit eigenvector corresponding to the largest eigenvalue indicates the direction of the most dramatic gradient change in the reference image at pixel p, i.e., the principal direction of the local structure. First, J needs to be calculated. u The eigenvalues ​​of (p) are obtained by solving the characteristic equation det(J).u (p)-λI)=0 that is (150.8-λ)(5.3-λ)-10.2 2 =0, and the two eigenvalues ​​are λ. u,1 =151.5 and λ u,2 =4.6, take the largest eigenvalue λ u,1 =151.5, then solve the system of linear equations (J) u (p)-λ u,1 I) x = 0, obtain the corresponding eigenvector, then normalize it, and finally obtain

[0059] e v,1 (p) is J v (p) The unit eigenvector corresponding to the largest eigenvalue is obtained in the same way as e. u,1 (p) is the same, indicating the main direction of the structure of the image under test at pixel p. First, J is calculated. v The eigenvalues ​​of (p) are obtained by solving the characteristic equation det(J). v (p)-λI)=0 that is (165.4-λ)(8.9-λ)-25.7 2 =0, and the two eigenvalues ​​are λ. v,1 =167.3 and λ v,2 =7.0, take the largest eigenvalue λ v,1 =167.3, calculate its corresponding unit eigenvector, and obtain

[0060] β is a scalar coefficient used to balance the relative importance of structural strength and structural orientation variations. Its value is determined by analyzing a large number of sample image pairs containing both actual crack propagation and non-crack variations (such as illumination variations), with the goal of maximizing the E value of the crack variation region. m (p) value, while minimizing E in the non-crack variation region. m The (p) value is determined by calculating the intensity term in the formula on the sample data. and direction terms The mean of , the initial value of β is set to For example, if the sample analysis shows that the mean of the intensity term is 80,000 and the mean of the direction term is 25,000, then β is set to 80,000 / 25,000 = 3.2.

[0061] Calculations based on parameters:

[0062] Substitute all the parameter values ​​obtained from the previous example into the formula:

[0063] J u The trace tr(J) of (p) u(p))=156.1;

[0064] J v The trace tr(J) of (p) v (p))=174.3;

[0065] e u,1 (p)·e v,1 (p)=0.997·0.988+0.070·0.155=0.985+0.011=0.996;

[0066] β = 3.2;

[0067]

[0068]

[0069] The results show that at pixel p, the structural change metric is 32.09. This value comprehensively reflects the degree of change in the local structure at that point in terms of both intensity and direction. By performing the same calculation on all pixels in the image, a complete structural change metric matrix can be obtained. Each element in the matrix represents the magnitude of change in the corresponding pixel. The higher the value, the greater the likelihood of structural changes occurring at that pixel, such as crack formation, propagation, or reversal. Thresholding will be performed based on this matrix to extract regions with significant changes.

[0070] Based on the structural change metric matrix generated in the previous step, it is first necessary to traverse all elements of the matrix to determine the global minimum and maximum metric values. This process involves initializing two variables, one for the maximum and the other for the minimum, and then comparing each metric value in the matrix and updating these two variables one by one until the traversal is complete, obtaining the global dynamic range of metric values ​​[E_min, E_max]. Next, in order to convert these floating-point metric values ​​into an 8-bit grayscale image (pixel value range 0 to 255) suitable for display and subsequent processing, the metric value E for each pixel is... m (p) Apply linear stretching mapping. Specifically, create a new blank image with the exact same size as the reference image and an 8-bit unsigned integer data type. Then, iterate through each position (x, y) of the structure change metric matrix again and read its metric value E. m(p), and calculates the corresponding integer intensity value between 0 and 255 according to the formula = round(((E_m(p)-E_min) / (E_max-E_min))*255), where the round function represents rounding to the nearest integer. This linear stretching process uniformly maps the entire dynamic range of the original metric value to the gray level of 0 to 255, thereby maximizing the visual contrast of the change area, so that even small structural changes can be clearly observed in the generated image. Each calculated output intensity value is written one by one to the corresponding (x,y) pixel position in the newly created blank image. Since the creation size and writing position of the new image strictly refer to the coordinate system of the reference image, the generated image is consistent with the reference image in terms of size and spatial coordinates. Finally, after the intensity values ​​of all pixels have been calculated and written, this newly generated grayscale image is the saliency map of structural changes.

[0071] The steps for obtaining the binary region of crack propagation are as follows:

[0072] Based on the saliency map of structural changes, the pixel value histogram is statistically analyzed at fixed intervals and the count of each segment is recorded. The difference between adjacent counts is compared to determine the initial value of the adaptive segmentation threshold. The adaptive segmentation threshold is corrected according to the difference between the mean and median of the pixel neighborhood. The pixel is compared with the adaptive segmentation threshold and the foreground is merged with four-neighbor connectivity to obtain the crack propagation binarized region.

[0073] Specifically, based on the structural change saliency map, the pixel values ​​from 0 to 255 are first divided into 16 intervals at fixed intervals of 16 gray levels. The number of pixels falling into each interval is counted, generating a pixel value histogram containing 16 count values. Then, to determine a robust initial segmentation threshold, the histogram is Gaussian smoothed to eliminate small fluctuations, and the main valleys in the histogram are identified. Specifically, the first-order difference of the smoothed histogram is calculated, and the positions where the difference value changes from negative to positive are found. These positions correspond to local minima, i.e., valleys. From these valleys, the most robust segmentation thresholds are selected. Select the deepest valley between the two maximum peaks, and set the starting value of the gray value range corresponding to this valley as 112. For example, if the valley is located in the gray value range [112, 127], then set 112 as the initial value of the adaptive segmentation threshold. Then, in order to make the threshold adapt to the local characteristics of the image, this initial value is modified. Traverse each pixel of the structural change saliency map, take a 21x21 neighborhood centered on that pixel, and calculate the mean and median of the gray values ​​of all pixels in the neighborhood. The difference between these two values ​​reflects the degree of skewness of the gray value distribution in the neighborhood. The domain typically has a high degree of skewness. The correction is calculated by multiplying the difference by a correction coefficient. This correction coefficient is set based on an empirical value derived from the analysis of a large number of sample images, for example, 0.2. The final adaptive segmentation threshold is the initial value + 0.2 * (neighborhood mean - neighborhood median). After calculating the adaptive segmentation threshold, the entire structural change saliency map is traversed again, and the gray value of each pixel is compared with the adaptive segmentation threshold calculated for it. If the pixel value is greater than the threshold, the pixel is set to 255 (foreground) in the newly generated binary image; otherwise... Then set it to 0 (background). Finally, merge the foreground regions of the obtained preliminary binary image. Use a queue-based four-neighbor connected component labeling algorithm to scan the image. When an unlabeled foreground pixel is encountered, it is used as the seed of a new component, and its four adjacent foreground pixels (up, down, left, right) are added to the queue. Process the pixels in the queue in turn until the queue is empty, thus completing the labeling of a connected region. Repeat this process until all foreground pixels are labeled, thereby merging the discrete foreground pixels into a continuous region and obtaining the crack propagation binarized region.

[0074] The steps for obtaining the crack tip profile curve are as follows:

[0075] Based on the crack propagation binarized region, refine it round by round according to the eight neighborhoods while keeping the endpoints and intersections. Delete edge pixels that meet the redundancy conditions to shrink to a single pixel width. Traverse along the longest connected chain and count the degree of each node. Filter out the unique pixel with a degree of one that is located at the end to obtain the end point of the main crack path.

[0076] Based on the end point of the main crack path, an equidistant annular sampling zone with the end point of the main crack path as the center is constructed and limited to the boundary of the crack propagation binarized region. The boundary coordinates between the sampling zone and the background are scanned in polar angle order and discontinuous coordinates are removed. Adjacent coordinates are connected to form a closed curve and the jagged edges are smoothed to generate the crack tip contour curve.

[0077] Specifically, based on the binary region of crack propagation, an iterative parallel thinning algorithm is used to process it. This algorithm executes in two sub-steps in each iteration. In the first sub-step, each foreground pixel is checked. If it simultaneously meets the following four conditions: 1. The number of foreground pixels in its eight-neighborhood is between 2 and 6; 2. When its eight-neighborhood pixels are arranged in clockwise order, the number of mode transitions from background to foreground is 1; 3. At least one of its top, right, and bottom neighbors is a background pixel; 4. At least one of its left, right, and bottom neighbors is a background pixel. If a pixel is a background pixel, it is marked as a pixel to be deleted. After all pixels have been checked in the first sub-step, all marked pixels are deleted. In the second sub-step, all foreground pixels are checked again, but conditions 3 and 4 are replaced with: 3a, at least one of its top, right, and left neighbors is a background pixel; 4b, at least one of its top, left, and bottom neighbors is a background pixel. If all conditions are met, the pixel is marked as a pixel to be deleted, and all pixels are deleted after the check is completed. These two sub-steps constitute a complete round of refinement. Multiple rounds of refinement are repeated until no pixels are found. The process continues until any pixel can be deleted, shrinking the crack region to a single pixel width while preserving the original region's topology, particularly endpoints and intersections, resulting in the crack's skeleton. Next, the skeleton is treated as an undirected graph where each foreground pixel is a node, and an edge exists between adjacent foreground pixels in their eight-neighborhood. All nodes are traversed, and the number of neighbors (degree) of each node is counted. Then, to find the main crack path, the longest connected chain in the skeleton needs to be identified. Starting from each endpoint with a degree of 1, a depth-first search algorithm is used to traverse all possible paths until another endpoint or intersection (a node with a degree greater than 2) is encountered. The length of each path (the number of pixels it contains) is recorded. The lengths of all paths are compared, and the longest is chosen as the main path. Finally, the endpoints of this longest connected chain are selected as the crack tip's endpoint. This can typically be determined based on the crack's growth direction or coordinate position; for example, the endpoint with the largest y-coordinate value can be chosen as the endpoint of the final main crack path.

[0078] Based on the endpoint of the main crack path, a ring-shaped sampling region, or sampling band, is first constructed using the pixel coordinates of this endpoint as the center. The inner and outer radii of this sampling band are pre-set according to the material properties and imaging resolution of the aerospace components. For example, the inner radius is set to 5 pixels and the outer radius to 25 pixels. This setting avoids the potential morphological singularities of the endpoint itself while fully capturing the contour features of the crack tip. Then, this ring-shaped sampling band is logically ANDed with the previously obtained crack propagation binarized region (unrefined) to obtain a ring-shaped binary image containing only the crack tip. Next, starting from the center, a scan is performed with a step size of 0.5 degrees, from 0 degrees to 360 degrees according to the polar angle. In each angular direction, the search starts from the inner radius and moves outwards, recording the coordinates of the first point that changes from a foreground pixel (crack region) to a background pixel. This point is the boundary point of the crack region in that angular direction. All the scanned boundary point coordinates are then sorted according to their corresponding polar angles. The coordinates are stored sequentially to form an ordered list. To eliminate isolated outliers caused by noise or digitization effects, a continuity check is performed on this list. The Euclidean distance between any two adjacent coordinates in the list is calculated. If a distance exceeds a preset distance threshold (e.g., set to 5 pixels, which is approximately 1.5 times the average crack width), the next point is considered a discontinuity and is removed from the list. After removal, the remaining adjacent coordinates in the list are connected sequentially with straight line segments to form a closed polyline. This polyline initially outlines the contour of the crack tip. However, due to the discreteness of pixels, there may be jagged edges on the contour line. Finally, to obtain a smooth contour curve, a moving average filter with a window size of 5 is applied to the coordinates of each vertex on the polyline. That is, the coordinates of each point are updated using the average of the coordinates of each point and the two points before and after it. This smoothing process is iterated twice, ultimately generating a crack tip contour curve that can accurately describe the crack geometry.

[0079] The steps for obtaining the tip sharpness quantification are as follows:

[0080] Based on the crack tip profile curve, boundary coordinate points are extracted at fixed intervals on both sides of the apex. The local arc is reconstructed and the arc radius is calculated. The reciprocal of the arc radius is used as the quantization value to obtain the tip sharpness quantization value.

[0081] Specifically, based on the crack tip profile curve, the first step is to determine the vertex on the curve. This vertex is the point with the greatest curvature on the curve, representing the sharpest position of the crack tip. The vertex is located by calculating the curvature of each point on the curve. Specifically, for each point on the curve, take 10 points before and after it to form a small line segment. Fit this line segment with a quadratic polynomial and calculate the first and second derivatives of the polynomial at that point. Calculate the curvature at that point using the curvature formula K=|y”| / (1+(y’)^2)^(3 / 2). Traverse the entire curve, and the point with the largest curvature value is the vertex. After determining the vertex, move a fixed arc length distance along the profile curve to both sides of the vertex. This distance is set to 15 pixels, which is determined based on the empirical value of the plastic zone size of a typical crack tip. Extract the boundary coordinates located at these two distance points, denoted as P1 and P2, and add the vertex P. v This yields three non-collinear points P1, P2, P3, P4, P5, P6, P7, P v Points P1, P2, and P3 are used to reconstruct an arc that approximates the local geometry of the tip. The center (x_c, y_c) and radius R_arc of the arc are determined by solving the equations that these three points are concyclic. This is achieved by solving the system of equations (x_1-x_c)^2+(y_1-y_c)^2=R_arc^2, (x_v-x_c)^2+(y_v-y_c)^2=R_arc^2, and (x_2-x_c)^2+(y_2-y_c)^2=R_arc^2. The radius of the arc, R_arc, reflects the degree of blunting at the crack tip. The smaller the radius, the sharper the tip. Finally, to obtain a dimensionless quantization value that is positively correlated with sharpness, the reciprocal of the arc radius (i.e., curvature) is calculated and multiplied by a feature length for normalization. This feature length is the radius R of the fixed circular region used in subsequent steps to calculate the microcrack density (e.g., R = 50 pixels). The calculation formula is (1 / R_arc)*R, and the resulting value is the tip sharpness quantization value.

[0082] The steps to obtain the crack propagation tendency index are as follows:

[0083] Based on the vertex position of the crack tip profile curve, a fixed circular region with the vertex as the center and radius R is set. All crack pixels in the region are filtered for connectivity. The microcrack endpoints are marked one by one and the number of endpoints is counted. The ratio of the number of endpoints to the area of ​​the fixed circular region is calculated to obtain the microcrack density.

[0084] Based on the quantified value of the crack tip sharpness and the microcrack density, the crack propagation tendency index is calculated using the following formula:

[0085]

[0086] Among them, P iS is the crack propagation tendency index. a D is the quantification of the sharpness of the tip. m D represents the microcrack density. cr denoted as the critical microcrack density, and k is the dimensionless material damage coefficient.

[0087] Specifically, based on the vertex position of the crack tip contour curve, a fixed circular region with radius R is first defined, centered on the vertex pixel coordinates. The value of radius R needs to be determined according to the damage mechanism of the aerospace component material being studied, and is usually set as the characteristic size of the critical damage zone of the material. For example, for a certain aluminum alloy, based on its fracture toughness experimental data, R can be set to 50 pixels, which corresponds to a physical size of approximately 0.5 mm. Then, this circular region is used as a mask, and a logical AND operation is performed with the previously obtained crack propagation binarized region to extract all crack pixels located within the circular region. These extracted crack pixels are then subjected to connectivity filtering. Using an eight-neighbor connected component labeling algorithm, all interconnected crack pixels are divided into different connected regions. For each connected region, if its area is less than a preset area threshold (e.g., ...), ... For example, if the limit is set to 20 pixels to exclude isolated noise points, these will be removed from the analysis. What remains is the set of microcracks distributed around the tip of the main crack. Then, the connected domain of each retained microcrack is skeletonized to obtain a microcrack skeleton with a width of one pixel. Each pixel on these skeletons is traversed, and the number of foreground pixels in its eight-neighborhood is calculated, i.e., the degree of the node. Pixels with a degree of 1 are identified as endpoints of microcracks. The total number of endpoints of all microcracks is marked and counted, denoted as N_endpoints. Finally, the ratio of this total number of endpoints to the area of ​​the fixed circular region is calculated. This ratio is the microcrack density, and the calculation formula is microcrack density = N_endpoints / (π*R^2). This density value quantifies the degree of damage to the material near the tip of the main crack, thus obtaining the microcrack density.

[0088] formula: By combining the geometrical sharpness of the crack tip with the microscopic damage state of the material near the tip, the influence of microcrack density on propagation tendency is amplified through an exponential function. Crack propagation depends not only on the stress concentration at the tip (quantitatively determined by the dimensionless tip sharpness quantification S) but also on the stress concentration at the tip. a Characterization is also influenced by the evolution of the material's internal microstructure. The formation and convergence of microcracks are precursors to the propagation of the main crack. Therefore, the microcrack density D m Relative to a critical value D cr The ratio can be seen as a measure of the material's damage state, with the exponential term being... The physical process of crack instability propagation that increases sharply when micro-damage accumulates to near a critical state was simulated. The material damage coefficient k modulates the rate of this growth and reflects the differences in the sensitivity of different materials to micro-damage.

[0089] S a The sharpness quantification is a modified dimensionless index that describes the relative sharpness of the crack tip geometry. It is calculated by first determining the curvature of the local profile at the crack tip (i.e., the radius R of the locally fitted circular arc). arc The reciprocal of the value is then used, and the curvature is normalized using a characteristic length, i.e., the radius R of the circular region used for microcrack density analysis. The calculation formula is S. a =(1 / R) arc )·R, the sharper the tip, the better. arc The smaller S a The larger the value, the more severe the relative stress concentration. For example, by analyzing the tip of a crack, the local arc radius is calculated to be 2.9 pixels, and the radius R of the region used for microcrack analysis is 50 pixels. Then the tip sharpness quantification value is (1 / 2.9)*50≈17.24.

[0090] D m The microcrack density, calculated through the aforementioned steps, quantifies the degree of microscopic damage to the material within a certain region near the tip of the main crack. It is obtained by counting the number of microcrack endpoints within a fixed circular region centered on the crack tip and then dividing by the area of ​​that circular region. The unit is microcracks per pixel. 2 A high microcrack density indicates the presence of numerous microscopic damages within the material. These microcracks may connect, accelerating the propagation of the main crack. For example, within a circular region with a radius of 50 pixels, image analysis reveals 18 microcrack endpoints. Therefore, the microcrack density is calculated as 18 / (π*50^2)=18 / 7854≈0.00229 microcracks / pixel. 2 .

[0091] D cr The critical microcrack density is a material constant that represents the point at which the material will undergo macroscopic instability and fracture. Its unit is D. m Same, per pixel 2This value is obtained by conducting a series of fatigue crack propagation experiments on specific aerospace component materials. During the experiments, the crack tip region is observed in situ using a high-magnification microscope, and the number of load cycles and the generation and evolution of microcracks are recorded simultaneously. When the main crack propagates rapidly and uncontrollably, the microcrack density at the tip region is recorded at this moment. The average value of multiple experimental results is taken to obtain the critical microcrack density of the material. For example, for 7075-T6 aluminum alloy, the average critical microcrack density obtained through 10 sets of fatigue experiments is 0.015 cracks / pixel. 2 .

[0092] k is a dimensionless material damage coefficient, which reflects the material's sensitivity to the accumulation of microcrack damage, or in other words, the degree to which an increase in microcrack density leads to a faster crack propagation rate. Its value also needs to be calibrated through material experiments. In the fatigue crack propagation experiment described above, the microcrack density D was recorded under different load cycles. m And the corresponding crack propagation rate da / dN, then, based on the fracture mechanics model, the crack propagation tendency index P i Correlation with crack propagation rate was achieved by fitting experimental data da / dN vs. D. m The value of k is determined by the relationship curve, so that the trend predicted by the formula matches the experimental results best. For materials with good toughness, the value of k is small, which means that the cumulative effect of micro-damage on crack propagation is relatively mild. For brittle materials, the value of k is large. For example, for 7075-T6 aluminum alloy, the material damage coefficient k obtained by data fitting is 2.5.

[0093] Calculations based on parameters:

[0094] Substitute all the parameter values ​​obtained from the previous example into the formula:

[0095] S a =17.24;

[0096] D m =0.00229;

[0097] D cr =0.015;

[0098] k = 2.5;

[0099]

[0100] P i =17.24·exp(2.5·0.1527);

[0101] P i =17.24·exp(0.3818);

[0102] P i =17.24·1.4649;

[0103] P i ≈25.25;

[0104] The results indicate that the crack propagation tendency index is 25.25 under the current conditions, reflecting the risk of the crack continuing to propagate under the current load and material conditions. By setting a risk threshold based on material experiments and safety margins, such as 30, the calculated index is compared with this threshold. If the calculated value is less than the threshold, such as 25.25 in this example, the crack condition is considered to be of high risk and requires enhanced monitoring. If the calculated value is greater than or equal to the threshold, it indicates that the crack has a high risk of propagation and requires immediate repair or replacement of the component.

[0105] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. An aircraft part crack detection and repair method, characterized by, Includes the following steps: Acquire optical images of aerospace components at a reference time point and optical images of aerospace components at the time point to be measured. Perform logarithmic polar coordinate transformation on the optical images to estimate rotation and scaling parameters, and generate subpixel registered image pairs. Based on the subpixel registered image pair, the gradient distribution is calculated in the neighborhood of each pixel, and independent structure tensors are constructed for the reference image and the image to be tested, respectively, to obtain a dual-temporal structure tensor field. A saliency map of structural changes is generated based on the dual-temporal structure tensor field. Based on the structural change saliency map, an adaptive segmentation threshold is set, and points with pixel values ​​greater than the adaptive segmentation threshold are set as foreground and the rest are set as background to obtain the crack propagation binarized region. The skeleton of the crack propagation binarized region is extracted to generate the crack tip contour curve. Based on the crack tip profile curve, calculate the tip sharpness quantification value, and simultaneously count the number and distribution density of microcracks around the crack tip in the stress concentration area of ​​the aerospace component to calculate the crack propagation tendency index. The steps for obtaining the sub-pixel registered image pairs are as follows: Load the optical images of the aerospace components at the reference time point and the optical images of the aerospace components at the time point to be measured, unify the bit depth and pixel spacing, crop the common field of view of the two images, construct a logarithmic polar coordinate grid, resample according to the angle sequence and radius sequence, and statistically analyze the angular peak position and radial ratio to generate rotation and scaling parameters; Based on the rotation and scaling parameters, the optical image of the aviation component at the time point to be measured is corrected to the coordinate system of the optical image of the aviation component at the reference time point according to the angle and scale. The spectral conjugate product of the two corrected images is calculated and the amplitude is normalized and the main peak is searched. The integer and subpixel deviations of row offset and column offset are located and the translation amount is generated. Based on the translation amount, the optical image of the aviation component at the time point to be measured is geometrically corrected according to the rotation and scaling parameters and then subpixel-level interpolation displacement is performed according to the translation amount. The image is aligned to the pixel grid of the optical image of the aviation component at the reference time point, and the overlapping area and hole filling are trimmed to generate a subpixel registered image pair. The steps for obtaining the dual-temporal structure tensor field are as follows: Based on the subpixel registered image pair, fixed square neighborhoods are extracted on the reference image and the image to be tested, the horizontal gradient and vertical gradient are calculated, the square of the gradient and the product of the gradient are summed item by item in the neighborhood and smoothed with a uniform scale, and symmetric second-order matrices are assembled at the corresponding pixel positions and correspond one-to-one to generate a dual-temporal structure tensor field.

2. The method of claim 1, wherein, The steps for obtaining the saliency map of structural changes are as follows: Based on the dual-temporal structure tensor field, the structural change metric is calculated to form a structural change metric matrix. Based on the structural change metric matrix, the global minimum and global maximum metric values ​​are extracted, linearly stretched and mapped, and the output intensity is written according to the pixel position, keeping the size and coordinates consistent with the reference image to form a structural change saliency map.

3. The method of claim 1, wherein, The steps for obtaining the binary region of crack propagation are as follows: Based on the structural change saliency map, the pixel value histogram is statistically analyzed at fixed intervals and the count of each segment is recorded. The difference between adjacent counts is compared to determine the initial value of the adaptive segmentation threshold. The adaptive segmentation threshold is corrected according to the difference between the mean and median of the pixel neighborhood. The pixel is compared with the adaptive segmentation threshold and the foreground is merged with four neighbor connections to obtain the crack propagation binarized region.

4. The method for detecting and repairing cracks in aerospace components according to claim 1, characterized in that, The steps for obtaining the crack tip profile curve are as follows: Based on the crack propagation binarized region, refine it round by round according to the eight neighborhoods while keeping the endpoints and intersections. Delete edge pixels that meet the redundancy conditions to shrink to a single pixel width. Traverse along the longest connected chain and count the degree of each node. Filter out the unique pixel with a degree of one that is located at the end to obtain the end point of the main crack path. Based on the end point of the main crack path, an equidistant annular sampling zone with the end point of the main crack path as the center is constructed and limited to the boundary of the crack propagation binarized region. The boundary coordinates between the sampling zone and the background are scanned in polar angle order and discontinuous coordinates are eliminated. Adjacent coordinates are connected to form a closed curve and the jagged edges are smoothed to generate the crack tip contour curve.

5. The method of claim 1, wherein, The steps for obtaining the tip sharpness quantification are as follows: Based on the crack tip profile curve, boundary coordinate points are extracted at fixed intervals on both sides of the vertex, the local arc is reconstructed and the arc radius is calculated. The reciprocal of the arc radius is used as the quantization value to obtain the tip sharpness quantization value.

6. The method of claim 1, wherein, The steps for obtaining the crack propagation tendency index are as follows: Based on the vertex position of the crack tip contour curve, a fixed circular region with the vertex as the center and radius R is set. All crack pixels in the region are filtered for connectivity. The microcrack endpoints are marked one by one and the number of endpoints is counted. The ratio of the number of endpoints to the area of ​​the fixed circular region is calculated to obtain the microcrack density.

7. The method of claim 6, wherein, The step of obtaining the crack propagation tendency index further includes: calculating the crack propagation tendency index based on the tip sharpness quantification value and the microcrack density.

8. The method of claim 7, wherein, The formula for calculating the crack propagation tendency index is as follows: ； in, This is a crack propagation tendency index. This is a quantification of the sharpness of the tip. Microcrack density, The critical microcrack density. is the dimensionless material damage coefficient.

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