A method for detecting a saggar defect

Abstract

The application discloses a kind of sagger defect detection methods, it includes the following steps: step S1, sagger image is collected, sagger image is detected to crack defect, and crack identification result is obtained;Step S2, the length and width determination of sagger crack identified are judged whether the length and width determination of crack exceed alarm value, and prewarning is carried out if exceeding alarm value.The application provides a kind of sagger defect detection method, based on artificial intelligence and neural network innovation technology, realize the automatic detection of sagger cracking defect.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of sagger defect detection methods, belong to sagger detection technical field. BACKGROUND

[0002] At present, lithium battery material sintering process is one of the key steps for preparing high-performance lithium ion batteries. The purpose of sintering is to make solid-phase reaction between active material particles in the positive electrode material, so as to achieve the purpose of crystallization, activation and improvement of material electrochemical performance.

[0003] The existing lithium battery material sintering process is roughly as follows: into saggar, sintering, out saggar, saggar, sweep saggar, saggar, into saggar, and so on. However, the saggar used for lithium battery material sintering will cause saggar peeling, slag dropping, cracking and finally scrap due to high temperature and strong corrosion of lithium battery positive and negative materials during sintering. In addition to causing positive and negative material pollution and performance damage, the cracking of the through-type saggar will also cause positive and negative material leakage, thereby polluting the kiln, and even causing the kiln to stop production, resulting in serious economic losses.

[0004] Therefore, it is necessary to detect the cracking defect of the saggar in time during sintering to ensure the normal operation of the lithium battery material sintering process. SUMMARY

[0005] The technical problem to be solved by the present application is to overcome the shortcomings of the prior art and provide a saggar defect detection method based on artificial intelligence and neural network innovation technology to realize automatic detection of saggar cracking defects.

[0006] To solve the above technical problems, the technical scheme of the present application is as follows:

[0007] A saggar defect detection method, comprising the following steps:

[0008] Step S1, collecting saggar images, detecting crack defects of the saggar images, and obtaining crack recognition results;

[0009] Step S2, determining the length and width of the recognized saggar cracks, and determining whether the length and width of the cracks exceed the alarm value, and if the alarm value is exceeded, a warning is given.

[0010] Further, in step S1, the saggar is subjected to crack defect detection, and crack recognition results are obtained, which specifically includes the following steps:

[0011] Step S11, constructing a crack data set of saggar images;

[0012] Step S12, performing crack detection and segmentation of saggar images;

[0013] Step S13, according to the defect characteristics of the sagger, the style transfer-based data augmentation technology is used to optimize and improve the segmentation network and the defect segmentation loss function.

[0014] Further, in the step S11, the crack data set of the sagger image is constructed, specifically including the following steps:

[0015] According to the sagger image sample, the defect data labeling work is completed, and a defect data set is established.

[0016] The defect image model training label is made using a deep learning labeling tool, and the defect label required by the defect segmentation model is obtained, which is a binary image.

[0017] The defect sample is placed in the folder corresponding to the defect name, and the folder name is used as the label of the defect classification sample.

[0018] Further, in the step S12, the crack detection and segmentation of the sagger image are performed, specifically including the following steps:

[0019] An image segmentation algorithm based on a deep neural network is used to realize the crack detection and segmentation of the product sagger photo.

[0020] Based on the deep neural network, an encoding and decoding structure is adopted, and the overall network structure includes an encoder and a decoder. The encoder and the decoder structure are completely symmetrical, and the same dimension features are obtained after layer-by-layer encoding and decoding.

[0021] A feature superposition module is added in each encoding and decoding process, which fuses the features before and after each encoding and decoding process.

[0022] Based on the CBAM attention module, the results of the spatial attention and the channel attention in series and parallel are superimposed.

[0023] A hybrid loss function of binary cross entropy and Dice is used to focus on data features from the foreground and background.

[0024] Further, in the step S13, according to the defect characteristics of the sagger, the style transfer-based data augmentation technology is used to optimize and improve the segmentation network and the defect segmentation loss function, specifically including the following steps:

[0025] Step S131, the public crack data set is migrated to the sagger image background through the label-guided style transfer network, and then an augmented sample data set is constructed.

[0026] Step S132, the semantic segmentation network is trained using the real sagger image and the augmented sample data set generated by the style transfer network, and the trained semantic segmentation network is used to segment the sagger image background in the test phase.

[0027] Further, the style transfer network in the step S131 specifically includes the following steps for performing style transfer:

[0028] An initial image of pixel adjustment of the network is an initial image of random initialization white noise image, a loss function is calculated through the feature extraction network, and then each pixel value of the generated image is fine-tuned, and the network is iterated to a given number of times to output the generated image.

[0029] Further, the establishment process of the total loss function of the style transfer network is as follows:

[0030] Step S1311, establishing a style loss function;

[0031] Step S1312, establishing a content loss function;

[0032] Step S1313, loss function fusion and network optimization.

[0033] Further, in the step S2, the length of the identified saggar crack is measured, specifically including the following steps:

[0034] The crack is skeletonized, the unit pixels of the crack are connected into a curve, the actual lengths corresponding to the unit pixels are added according to the actual lengths corresponding to the unit pixels, and the length of the saggar crack is obtained.

[0035] Further, in the step S2, the width of the identified saggar crack is measured, specifically including the following steps:

[0036] The pixel point perpendicular of the crack skeleton intersects with the crack contour, the line segment intersecting with the contour is obtained as the width of the crack, and the width of the crack is finally calculated according to the calculation of the pixel points of the line segment; all the crack widths are obtained by calculating the crack widths of all the pixel points on the skeleton, and the maximum width of the crack is obtained.

[0037] By adopting the above technical scheme, the application relies on the phased array detection sensor with high precision and high reliability, and through the real-time processing and analysis of the obtained saggar detection image data by using artificial intelligence and neural network innovation technology, the saggar is continuously self-learned, automatically analyzed, and automatically judged, the crack of the saggar is automatically detected, and it is determined whether to send an alarm signal according to the parameter threshold. The safety of enterprise production is ensured, and the production efficiency of the enterprise is improved. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 A flowchart of a saggar defect detection method of the application;

[0039] Figure 2 A hardware structure diagram of a saggar defect detection of the application;

[0040] Figure 3 The main frame diagram of the segmentation algorithm of the coding and decoding structure of the application;

[0041] Figure 4 The flow chart of the style transfer task of the application;

[0042] Figure 5 The flow chart of the crack segmentation strategy based on style transfer data augmentation of the application;

[0043] Figure 6 The flow chart of the traditional style transfer network of the application;

[0044] Figure 7 The schematic diagram of crack skeletonization and crack length calculation of the application;

[0045] Figure 8 The schematic diagram of crack skeletonization and crack width calculation of the application. DETAILED DESCRIPTION

[0046] In order to make the content of the application more easily understood, the application will be further described in detail below according to specific embodiments and in conjunction with the accompanying drawings.

[0047] As shown in Figure 1 , the present embodiment provides a saggar defect detection method, which comprises the following steps:

[0048] Step S1, collecting saggar images, detecting crack defects of the saggar images, and obtaining crack recognition results. As shown in Figure 2 , the signal transmitter 3 emits an irradiation signal to the saggar 2, and the signal receiver 1 simultaneously generates and receives an imaging signal. The software system collects saggar imaging data from the signal receiver's collection port, and the software system converts and synthesizes the imaging data into an image file. Then the software system synchronously analyzes and identifies whether there is a crack.

[0049] Step S2, measuring the length and width of the identified saggar cracks, determining whether the length and width measurement values of the cracks exceed the alarm value, and if the length and width measurement values exceed the alarm value, a pre-warning is performed. If the minimum width of the detected crack is greater than or equal to 0.5mm (the alarm width parameter can be set by oneself), an NG signal (or an audible and light alarm) is emitted or a PLC-recognizable rejection signal is given.

[0050] In step S1 of the present embodiment, the saggar is subjected to crack defect detection, and crack recognition results are obtained, which specifically comprises the following steps:

[0051] Step S11, constructing a crack data set of the saggar image;

[0052] Step S12, performing crack detection and segmentation of the saggar image;

[0053] Step S13, according to the defect characteristics of the specific saggar, further optimize the segmentation network and defect segmentation loss function based on the data augmentation technology of style transfer, at the same time, in order to ensure that the defect detection model can have high accuracy, consider introducing the image augmentation technology based on style transfer to generate more training samples, at the same time optimize the defect detection model, enhance the generalization ability of the defect detection model (i.e. reduce the difference between training samples and real test environment), improve the detection accuracy of the model.

[0054] In step S11 of the embodiment, a crack data set of saggar images is constructed, specifically including the following steps:

[0055] In the initial stage of project implementation, defect data labeling is completed according to the saggar image samples, and a defect data set is established; in order to ensure the accuracy of the inspection algorithm and the classification algorithm, the defect data set ensures 1000+ defect image data files;

[0056] Use the deep learning labeling tool to make defect image model training labels, obtain the defect labels required by the defect segmentation model, and the defect labels are binary images, in which the pixel value of 1 represents the background pixel, and the black pixel of 0 represents the defect pixel;

[0057] Put the defect samples into the folder corresponding to the defect name, and use the folder name as the label of the defect classification sample.

[0058] In step S12 of the embodiment, crack detection and segmentation of saggar images are performed, specifically including the following steps:

[0059] In this embodiment, an image segmentation algorithm based on deep neural network is used to realize crack detection and segmentation of product saggar photos.

[0060] Based on deep neural network, an encoding and decoding structure is adopted, and the overall network structure includes an encoder and a decoder. The encoder and the decoder structure are completely symmetrical, and the same dimension features are obtained after layer-by-layer encoding and decoding, which is convenient for information fusion.

[0061] In each encoding and decoding process, a feature superposition module is added, which fuses the features before and after each encoding and decoding process. The features related to cracks can be retained with greater probability.

[0062] Based on the CBAM attention module, the results of the spatial attention and the channel attention in series and parallel are superimposed, which retains the crack-related detail features to a greater extent and suppresses irrelevant background features.

[0063] To solve the problem of uneven pixel distribution in balanced crack image samples, a hybrid loss function of binary cross-entropy and Dice is used to focus on data features from the foreground and background, respectively, to avoid background data guiding model training.

[0064] The segmentation algorithm takes the surface crack image of the electronic commutator as the experimental object and achieves excellent segmentation results.

[0065] As shown in Figure 3 The segmentation algorithm of the encoding-decoding structure involved in the foregoing includes:

[0066] 1. Encoder

[0067] The encoder extracts features through multiple convolution pooling and is composed of convolution layers, BN layers, ReLU activation layers and down-sampling. Let the input of the encoding end be x i =x b×h×w×c , where b, h, w and c represent the training batch number, height, width and channel number of the input image, respectively; the following down-sampling operation is the limit, the encoder has four encodings and three down-samplings, and let the encoding layer be l e (1≤l e ≤4); after any convolution calculation of the encoder, a BN layer and a ReLU activation layer are followed to form a convolution process, which is expressed as:

[0068] C k×k (x i )=Relu(BN(Conv k×k (x i )));

[0069] where ReLu, BN and Conv represent ReLu activation, batch normalization and convolution calculation, respectively, where k is the size of the convolution kernel, and in this algorithm, the convolution kernel of the channel integration layer is 1×1, and the convolution kernels of the other layers are all 3×3. The change of the channel integration is expressed as:

[0070] T=C 1×1 (x i );

[0071] With the change of the encoding / decoding layer, the channel number of the feature map after channel integration also changes, and the change of the channel is:

[0072] c={c1,c2,c3,c4,c5}={64,128,256,512,3};

[0073] In the algorithm, the encoder and the decoder have three consecutive encoding / decoding blocks to implement the encoding / decoding process, and the process in the encoder is expressed as:

[0074]

[0075] Down-sampling operation is achieved by max-pooling between each encoding layer in the encoding process, and the symbol represents the down-sampling operation at the beginning of the le-th layer, and the encoder can be represented as:

[0076]

[0077] 2、Decoder

[0078] The decoder design is symmetrical to the encoder design. In the decoder, the number of decoding layers is denoted as l d and 1≤l d ≤4, l d is symmetrical to the l e of the encoder. The encoding process is from top to bottom with the increase of l e , and the encoding degree is stronger. The decoding process is from bottom to top with the decrease of l d , and the decoding degree is stronger. In the decoder, the method of inverse pooling is used to achieve up-sampling to restore the scale of the feature map, and the up-sampling process is denoted as Compared with the encoder, the decoder adds a segmentation layer, and the segmentation layer realizes the segmentation of the decoding result through a sigmoid function, wherein the sigmoid function is represented as:

[0079]

[0080] In the formula, e is a constant, x represents the input of the function, and the decoding block in the decoder is represented as:

[0081]

[0082] The decoder can be represented as:

[0083]

[0084] 3、Loss function

[0085] Through the segmentation algorithm, the probability of whether each pixel point on the image is background or crack is obtained, and the segmentation is realized through the probability. Therefore, this problem is essentially a binary classification problem. Binary cross-entropy loss function is a loss function commonly used in binary classification problems in deep learning, and the function is defined as:

[0086]

[0087] Where y i represents the label of the i-th input sample, and y irepresents the predicted value of the i-th sample, the cross-entropy loss function is often used with the Sigmoid activation function in the classification task to obtain the output probability of each class, and the closer the prediction result is to the label, the smaller the loss is, and vice versa. For each image sample, it is composed of N pixels. After the loss function predicts and evaluates each pixel point of the entire image sample, the average is obtained, so all the pixel points in the image sample are learned evenly, but when the pixel number distribution in the sample is uneven, the loss is easily guided by the majority of samples, resulting in insufficient attention to small pixel feature areas (cracks).

[0088] To solve the problem of binary cross-entropy loss function, the Dice coefficient is used to calculate the loss in the segmentation field. The Dice coefficient can evaluate the similarity of two samples, the higher the similarity, the larger the value, and vice versa. It is defined as:

[0089]

[0090] Where |y∩y′| represents the number of intersection of sample label and prediction result, |y| and |y′| represent the number of label and prediction result respectively. Since there are only two values of 0 and 1 in segmentation, |y∩y′| can be regarded as the multiplication of label and prediction result, and all misclassified pixel values can be cleared to zero. |y| and |y′| are approximately equal to the sum of the number of pixels of the label and the output. The Dice loss function can be represented as:

[0091]

[0092] To solve the problem of small cracks and small sample area pixels, this chapter uses a hybrid loss function of binary cross-entropy and Dice as the loss function of the model, and the model loss function is defined as:

[0093] L bce+dice =λ0L bce +λ1L dice ;

[0094] Where λ0, λ1 are the loss function weights.

[0095] The segmentation algorithm takes the surface crack image of the electronic commutator as the experimental object and achieves excellent segmentation results. It can be seen that the cracks can be basically segmented out, so under the premise that the image shooting accuracy (i.e. imaging accuracy is higher than ≥0.5mm) is guaranteed, the scheme can complete the detection of cracks with high accuracy of ≥0.5mm and above.

[0096] In step S13 of this embodiment, according to the defect characteristics of the specific saggar, the segmentation network and the defect segmentation loss function are further optimized based on the data augmentation technology of style transfer. At the same time, in order to ensure that the defect detection model has high accuracy, the image augmentation technology based on style transfer is introduced to generate more training samples, and the defect detection model is optimized to enhance the generalization ability of the model (i.e. reduce the difference between training samples and real test environment samples), and improve the detection accuracy of the model. Specifically, the following steps are included:

[0097] By migrating the crack features of the disclosed crack dataset (source domain) to the saggar image background (target domain), more crack samples with saggar image background can be obtained for data augmentation. In this scheme, the disclosed crack dataset is regarded as "content", and the saggar image background is regarded as "style". By style transfer, the cracks of the disclosed crack dataset can be migrated to the style background to obtain data augmented crack samples, as shown in Figure 4 .

[0098] The saggar image crack segmentation strategy based on style transfer data augmentation mainly includes crack migration and semantic segmentation algorithm training and testing. The specific strategy structure is shown in Figure 5 .

[0099] Step S131, crack migration is to migrate the crack features of the disclosed crack dataset (source domain) to the saggar image background (target domain) through the label guided style transfer network, and then construct the augmented sample dataset.

[0100] Step S132, the semantic segmentation training and testing part is to train the semantic segmentation network using real saggar images and augmented sample datasets generated by the style transfer network. In the testing stage, the trained semantic segmentation network is used to segment the cracks in the saggar image background (target domain).

[0101] The style transfer network in step S131 of this embodiment includes the following steps:

[0102] As shown in Figure 6 , a random initial white noise image is used as the initial image for pixel adjustment of the network. The loss function is calculated through the feature extraction network, and then each pixel value of the generated image is fine-tuned. The network is iterated for a given number of times and outputs the generated image.

[0103] The migration effect of the style transfer network is greatly affected by its loss function. How to constrain and optimize the result image generated by the network through the loss function is the key of the style transfer network. The loss function is designed in two parts, one for constraining the style of the network and the other for constraining the content of the network. The establishment process of the total loss function of the style transfer network is as follows:

[0104] Step S1311, establishing a style loss function:

[0105] The feature map F extracted by the image through the VGG16 is w x h x c in size, and each channel of the feature map is a feature. The deeper the network, the more complex the extracted features. For a pixel region, there may be or may not be correlation between the features after encoding. To calculate whether there is correlation between the channels, each channel of the feature map is converted into a vector in order, and then there are c w x h vectors. The formula of the feature of a certain channel after conversion is as follows:

[0106]

[0107] When the entire feature map is represented by a vector, the feature map F is represented as:

[0108]

[0109] Where each row of F represents the feature map of each channel. To determine whether there is correlation between the channels, the dot product is calculated, and if there is correlation, the calculation result of the dot product is larger, and if there is no correlation, the calculation result is smaller. The dot product of all channels is calculated, that is, the Gram matrix is used to measure the co-occurrence correlation between features. However, the calculation result of the Gram matrix is only related to the data between the channels, and is not related to the order in the same channel. Therefore, the Gram matrix can be used to measure the "style" of an image. The calculation of the Gram matrix is as follows:

[0110] G=MM T ;

[0111] Therefore, the style loss function of the lth layer is defined as:

[0112]

[0113] Where the feature map of the style map of the lth layer is constant, that is, is constant, and only the Gram matrix of the generated image needs to be optimized to reduce the style loss. Therefore, the total style loss function is:

[0114]

[0115] The high-level neural network can capture more texture information, and the low-level neural network can obtain color information. Therefore, the features of multiple layers in the network need to be considered to determine the style of the network.

[0116] Step S1312, establishing a content loss function

[0117] The content loss function is to measure the difference between the content image and the generated image, but the loss function of the content image is to measure the similarity of the features of the two images at a certain layer in the network. The input content image and the output generated image in the network are in one-to-one correspondence, and the input content image remains unchanged, and the output generated image is updated with the iteration of the network, so the content loss function is designed as:

[0118]

[0119] Where F represents the current feature map of the generated image, and P represents the current feature map of the content image. For the content image feature P, a content image is constant, that is, a constant. Through network optimization of the initial image, the closer the features extracted by the generated image and the features extracted by the content image, the smaller the content loss function.

[0120] The VGG network has multiple feature extraction layers. As the number of network layers increases, the pixel information in the spatial scale gradually loses, and the semantic information gradually increases, so the use of the features of the first few layers is better when reconstructing the content. In this paper, the third layer feature is used for content loss calculation.

[0121] Step S1313, loss function fusion and network optimization

[0122] The total loss function of the network is:

[0123] L(p,a,x)=αL Content (p,x)+βL Style (a,x);

[0124] Where α and β are the weights of the content loss function and the style loss function, respectively.

[0125] In step S2 of this embodiment, the length and width of the identified saggar cracks are measured, specifically including the following steps:

[0126] After obtaining the detection and recognition results of the crack defects, in order to measure the length of the crack, the skeletonization processing is used in this design. Skeletonization refers to the process of changing a crack with a certain width into a single-pixel wide crack. After skeletonization, the topological structure of the crack can be described intuitively, and the center pixel contour of the crack defect on the image can also be extracted, which can clearly show the information of the crack.

[0127] As shown in Figure 7 The specific algorithm flow of crack length measurement is as follows:

[0128] Skeletonize the crack to connect the unit pixels of the crack into a curve. According to the actual length corresponding to the unit pixel, the actual lengths corresponding to multiple unit pixels are added to obtain the length of the saggar crack.

[0129] As Figure 8 shown, the specific algorithm flow of the crack length measurement is as follows:

[0130] The pixel point vertical line of the crack skeleton is intersected with the crack contour, the line segment intersected with the contour is obtained as the width of the crack, and the width of the crack is finally calculated according to the calculation of the pixel points of the line segment. All crack widths are obtained by calculating the crack width of all pixel points on the skeleton, and the maximum width of the crack is obtained.

[0131] The above-described specific embodiments further illustrate the technical problems solved by the present application, technical solutions and beneficial effects. It should be understood that the above-described is only a specific embodiment of the present application and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for detecting defects in saggers, characterized in that, It includes the following steps: Step S1: Acquire images of the sagger, perform crack defect detection on the sagger images, and obtain crack identification results; Step S2: Measure the length and width of the identified crucible cracks, and determine whether the measured values ​​of the crack length and width exceed the alarm value. If they exceed the alarm value, issue an early warning. In step S1, crack defect detection is performed on the sagger, and crack identification results are obtained. This specifically includes the following steps: Step S11: Construct a crack dataset of sagger images; Step S12: Perform crack detection and segmentation on the sagger image; Step S13: Based on the defect characteristics of the cassette, optimize and improve the segmentation network and defect segmentation loss function using data augmentation techniques based on style transfer; In step S12, crack detection and segmentation of the sagger image are performed, specifically including the following steps: A deep neural network-based image segmentation algorithm is used to detect and segment cracks in product sagger photographs. Based on deep neural networks, an encoding and decoding structure is adopted. The overall network structure includes two parts: an encoder and a decoder. The encoder and decoder are completely symmetrical in structure, and features of the same dimension are obtained after layer-by-layer encoding and decoding. A feature overlay module is added to each encoding and decoding process, which fuses the features before and after each encoding and decoding process; Based on the CBAM attention module, the results of the serial and parallel connection of spatial attention and channel attention are superimposed. We use a hybrid loss function of binary cross-entropy and Dice to focus on data features from the foreground and background perspectives, respectively.

2. The method for detecting defects in a sagger according to claim 1, characterized in that, In step S11, constructing the crack dataset of the sagger image specifically includes the following steps: Based on the sample images of the crucible, complete the defect data labeling work and establish a defect dataset; Using deep learning annotation tools, defect image model training labels are created to obtain the defect labels required by the defect segmentation model. The defect labels are binary images. Place the defect samples into folders with the corresponding defect names, and use the folder names as labels for the defect classification samples.

3. The method for detecting defects in a sagger according to claim 1, characterized in that, In step S13, based on the defect characteristics of the sagger, the segmentation network and the defect segmentation loss function are optimized and improved using style transfer data augmentation techniques, specifically including the following steps: Step S131: Transfer the crack features from the publicly available crack dataset to the background of the cassette image using a label-guided style transfer network, and then construct an augmented sample dataset. Step S132: Train the semantic segmentation network using real sagger images and augmented sample datasets generated by the style transfer network. In the testing phase, use the trained semantic segmentation network to segment the cracks in the background of the sagger image.

4. The method for detecting defects in a sagger according to claim 3, characterized in that, The style transfer network in step S131 specifically includes the following steps for style transfer: A random initial white noise image is used as the initial image for pixel adjustment by the network. The loss function is calculated by the feature extraction network, and then the pixel value of each pixel in the generated image is fine-tuned. After the network iterates to a given number of times, it outputs the generated image.

5. The method for detecting defects in a sagger according to claim 4, characterized in that, The process of establishing the total loss function of the style transfer network is as follows: Step S1311: Establish the style loss function; Step S1312: Establish the content loss function; Step S1313: Perform loss function fusion and network optimization.

6. The method for detecting defects in a sagger according to claim 1, characterized in that, In step S2, the length of the identified crucible crack is measured, which specifically includes the following steps: The crack is skeletonized by connecting the unit pixels of the crack into curves. Based on the actual length corresponding to the unit pixel, the actual lengths corresponding to multiple unit pixels are added together to obtain the length of the crack in the sagger.

7. The method for detecting defects in a sagger according to claim 1, characterized in that, In step S2, the width of the identified crucible crack is measured, which specifically includes the following steps: The vertical lines of the pixels in the crack skeleton intersect the crack outline. The line segment intersecting the outline is the width of the crack. The width of the crack is finally calculated based on the pixels of this line segment. By calculating the crack width of all pixels on the skeleton, all crack widths are obtained, and the maximum crack width is obtained from them.

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