Ultrasonic defect identification method based on gradient sparse non-negative matrix factorization

Abstract

The invention provides a composite material ultrasonic defect detection method based on gradient sparse non-negative matrix factorization, aiming at the non-visual display of ultrasonic defect detection. Belongs to the field of nondestructive testing of internal defects of carbon fiber composite materials. The invention develops a gradient sparse NMF-based dimension reduction mode, and the method comprises the steps: firstly, employing a standardization method to carry out the preprocessing of defect ultrasonic data, and eliminating the mutual influence between defect echoes; after preprocessing, clustering and dimensionality reduction are carried out on the ultrasonic data; carrying out clustering trend judgment according to an elbow principle, and carrying out gradient sparse dimensionality reduction; and finally, reconstructing the data into an image with an original size, and carrying out visual evaluation. According to the method, a model is established for defect processing in the actual ultrasonic nondestructive testing process, deep data information is fully obtained, and visual display of defect detection is achieved.

Description

Technical Field

[0001] The invention belongs to the field of nondestructive detection of internal defects of carbon fiber composite materials, and in particular relates to an ultrasonic defect recognition method based on gradient sparse non-negative matrix decomposition. Background Art

[0002] Composite materials are composite manufactured materials composed of two or more different substances, arranged together in the right way, but separated by interfaces, and their properties are very different from the properties of the original phases used alone. Among them, carbon fiber composite materials (Carbon Fiber Reinforced Polymer, CFRP) are one of the most widely used and influential composite materials. They have the advantages of low density, good formability, high specific strength, good corrosion resistance, good seismic performance, strong designability, good fatigue resistance, etc., and their mechanical properties and overall material are very good.

[0003] However, during the CFRP manufacturing stage and even during the operation of the product, various defects are inevitably generated due to imperfect theories or improper human operations. Even if it operates under normal conditions, these defects will hinder its performance and eventually lead to its failure, thus limiting its service life. First, understand the types of defects that may occur in fiber composite materials. The main types of invisible defects include fiber breakage, voids, cracks, delamination, interface debonding, etc. Among them, the most common invisible defects are interface debonding and delamination. Interface debonding usually refers to the separation between the composite material panel and the honeycomb core reinforcement layer of the sandwich panel, and delamination refers to the separation between the layers of the composite laminate. These defects will affect the comprehensive properties of the material, reduce the material's bearing capacity, and have a great impact on product quality. Therefore, composite materials must be effectively defect-detected. Because destructive testing will cause damage to the workpiece or material, destructive testing is generally not adopted, and non-destructive testing is used.

[0004] Ultrasonic nondestructive testing is a commonly used defect detection method, but its display of defect detection is not intuitive, and both qualitative and quantitative analysis of defects are difficult. The visualization of ultrasonic data has always lacked an intuitive method. Currently, a composite material ultrasonic defect identification detection method is needed to determine the shape, size, depth and other information of the defects.

[0005] To solve the above problems, the present invention proposes a method for ultrasonic defect detection of composite materials based on Ultrasonic Gradient Sparse Non-negative Matrix Factorization (UGSNMF). First, the defect ultrasonic data is preprocessed by a standardized method to eliminate the mutual influence between defect echoes. After preprocessing, the ultrasonic data is clustered and dimensionally reduced. The clustering trend is judged based on the elbow principle, and gradient sparse (Non-negative Matrix Factorization, NMF) is used for dimensionality reduction. Finally, the data is reconstructed into an image of the original size for visual evaluation. Contents of the invention

[0006] In view of the fact that the display of ultrasonic defect detection is not intuitive, the present invention proposes a method for ultrasonic defect detection of composite materials based on gradient sparse non-negative matrix decomposition. First, a gradient sparse NMF dimensionality reduction method is developed, which can explore the deeper relationship between defect depth and shape, and improve the current image processing algorithm to display the detection results more intuitively. This method establishes a model for defect processing in the actual ultrasonic non-destructive testing process, fully obtains deep data information, and realizes the intuitive display of defect detection.

[0007] The technical solution adopted by the present invention to solve its technical problem is:

[0008] An ultrasonic defect recognition method based on gradient sparse non-negative matrix decomposition, the method comprising the following steps:

[0009] (1) Obtaining CFRP internal defect detection dataset

[0010] Ultrasonic phased array detection technology is used to transmit continuous fixed-interval ultrasonic pulses to the CFRP defect sample, capturing the ultrasonic echo before and after the interface reflection. Finally, the acquired ultrasonic detection data is saved as a three-dimensional matrix and recorded.

[0011] (2) Defect ultrasonic data preprocessing

[0012] Ultrasonic images collected by ultrasonic phased array detectors have significant redundancy. A robust standardized preprocessing step is introduced to standardize the expanded data matrix to reduce ultrasonic data noise and improve data performance.

[0013] (3) Determination of defect quantity

[0014] The number of clusters is determined by the elbow principle combined with actual conditions. When the degree of distortion decreases the most with the increase of the number of clusters, the best clustering performance can usually be obtained by using the corresponding number of clusters as the clustering number.

[0015] (4) Gradient sparse non-negative matrix factorization

[0016] In order to obtain the sequential features of ultrasonic data, it is necessary to decompose the input matrix X. The feature matrix W and coefficient matrix H of ultrasonic data are updated by the gradient method, one column at a time.

[0017] (5) Defect recognition performance evaluation

[0018] Reconstruct the W matrix into the original size image n x ×n y Perform a visual qualitative assessment and visualize the H matrix to quantitatively assess the depth of the defect.

[0019] Further, the process of (2) is as follows:

[0020] Step 2.1: Convert the recorded three-dimensional ultrasound matrix into a two-dimensional matrix to facilitate preprocessing operations.

[0021] Step 2.2: The ultrasonic images collected by the ultrasonic phased array detector have significant redundancy. A robust standardization preprocessing step is introduced to standardize the expanded data matrix to reduce ultrasonic data noise and improve the data performance. Each row vector x i (i=1,…,n x ×n y ) as sampling points, the sample size is n x ×n y ×n h The calculation formula is:

[0022]

[0023] Where x' i is the sample point after preprocessing, x i is the sample point in the data set; q is the median of the sample; IQR is the interquartile range of the sample.

[0024] Further, the process of (3) is as follows:

[0025] The elbow principle in the clustering algorithm is used to determine the number of defects, thereby determining the rank of the matrix in the matrix decomposition. The square sum error (SSE) between the points under each cluster number and the corresponding cluster center is calculated. When the loss of SSE decreases the most, the loss change tends to be flat. Using the value c as the cluster number can often bring excellent clustering performance and is regarded as an effective parameter selection. The number determined by the elbow principle includes the background, that is, the entire area is divided into c areas, so the number of defects r is equal to c-1. The calculation formula is as follows:

[0026]

[0027] Where j is the observed value, c i is the predicted value.

[0028] Further, the process of (4) is as follows:

[0029] Step 4.1: Initialize the matrix factors. The matrix update rule is designed to update the parameters C and G of the model to minimize the loss function or achieve other optimization goals. Its expression is as follows:

[0030] C=-XH T +WHH T

[0031] G=HH T

[0032] Step 4.2: Determine the rank of the matrix and the number of corresponding defects according to the elbow principle. For each column of eigenvector W j (j=1,…,r) adopts the strategy of updating one column at a time, and keeps updating alternately. According to the matrix update rule, each time there is a corresponding vector U j :

[0033] U j =C j -W j G jj

[0034] The matrix vector needs to be projected onto the sparsity constraint, j Sort by decreasing value, so suppose there exists a=sort(b) and a matrix of length m such that for all i, j, there exists a mapping π such that a i =π(b i ) and a j ≥a j+1 , b i is a matrix vector, a i Yes i After the projection, sort(·) sorts the elements from large to small. In order to find the closest vector that satisfies the required sparsity constraint, for the transition point p in (k 2 ,m), calculate the Lagrangian parameters λ(p) and μ(p):

[0035]

[0036] Where k is the ratio of the L1 / L2 norm of the feature matrix W.

[0037] According to the matrix update strategy, set the formula:

[0038]

[0039] Among them, p * =m.

[0040] The closest vector y that satisfies the required sparsity constraint can be obtained, where y = π(x i ).

[0041] Then update vectors C and W j , where C' is the updated vector.

[0042]

[0043] W j =y

[0044] Step 4.3: Use multiplication update to alternately update the feature matrix W and the coefficient matrix H until convergence, where H' and W' are the updated matrices:

[0045]

[0046] Where ⊙ represents element-by-element multiplication (Hadamard Product).

[0047] Further, the process of (5) is as follows:

[0048] After UGSNMF training, the original ultrasonic data is decomposed into a feature matrix W and a coefficient matrix H. The i-th column of the W matrix is ​​reconstructed into an image of size x×y for visualization, and the j-th row of the H matrix is ​​visualized to extract depth information, and finally 3D visualization can be performed. The obtained basis matrix W shows the shape of the ultrasonic defect, and the coefficient matrix H shows the depth of the ultrasonic defect. In terms of visualization quality, sequential gradient decomposition has a competitive advantage. The basis matrix is ​​reconstructed into the size of an ultrasonic image to show the shape of the ultrasonic defect, and the coefficient matrix shows the depth of the ultrasonic defect, achieving the purpose of corresponding shape and depth relationship of defect visualization, and characterizing the 3D characteristics of ultrasonic defects, and the defect information is complete.

[0049] The present invention uses the elbow principle method to determine the number of defects and improve the clustering effect; and uses non-negative matrix decomposition to update the matrix through gradients, extract the potential features of the data, and solve the weight matrix and coefficient matrix of the ultrasonic data. It ensures that the depth and position information of the defects correspond, and visualizes the shape and depth information of the material defects.

[0050] The beneficial effects of the present invention are mainly manifested in: establishing a model for defect processing in the actual ultrasonic non-destructive testing process, improving the current image processing algorithm, and improving the algorithm efficiency; by visualizing the feature matrix and the coefficient matrix, the defect shape and depth are matched one by one, which can effectively separate the shape and depth of the defect, and display the defect information quickly, intuitively and accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a schematic diagram of the method of the present invention;

[0052] Figure 2 Schematic diagram of CFRP defects;

[0053] Figure 3 It is the ultrasound echogram of different positions;

[0054] Figure 4 is the intra-cluster error sum of squares graph;

[0055] Figure 5 Visualize UGSNMF for defective samples;

[0056] Figure 6 Visualize the defect sample coefficient matrix H;

[0057] Figure 7 This is the defect area assessment diagram. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings.

[0059] Reference Figure 1 to Figure 7 , an ultrasonic defect recognition method based on gradient sparse non-negative matrix decomposition, the method comprising the following steps:

[0060] (1) Obtaining ultrasonic detection data of CFRP internal defects. The process is as follows:

[0061] The CFRP specimens were prepared by vacuum assisted resin infusion (VARTM) molding process, and six invisible defects were artificially prefabricated. The specimens were made of 78 layers of carbon fiber as the substrate, with a size of 241.0 mm × 44.5 mm. Six Teflon tapes were buried in the designated positions of the carbon fiber sheet, such as Figure 2 As shown. Each Teflon tape has an area of ​​400mm 2 , with a thickness of 0.5mm, are all square, numbered h1 to h6 from left to right, and in order from light to dark they are: h3, h6, h2, h5, h1, h4.

[0062] The data set obtained in ultrasonic testing is usually a 3D matrix, and the displayed ultrasonic echo maps the plane projection of the test piece at different depths. To obtain the ultrasonic signal image within a specific depth range, set n h The acquisition range of each frame. x ×n y The pixel structure ensures the image is detailed and clear. It is converted into a two-dimensional matrix X for storage, where M, N and T represent its length, width and number of images respectively. The experiment collected 500 ultrasound imaging scans of two samples, such as Figure 3 As shown, in these images, a serious uneven background can be observed, making defect detection difficult. For the defect sample scan image, its size is 57×241, so the total number of pixels can be calculated by the product of the number of rows and the number of columns, which is 13737 pixels.

[0063] (2) Data preprocessing

[0064] The ultrasonic images collected by the ultrasonic phased array detector have significant redundancy. The original ultrasonic echo data is preprocessed to eliminate the mutual influence between defect echoes.

[0065] Step 2.1: Convert the recorded three-dimensional ultrasound matrix into a two-dimensional matrix to facilitate preprocessing operations.

[0066] Step 2.2: The ultrasonic images collected by the ultrasonic phased array detector have significant redundancy. A robust standardization preprocessing step is introduced to standardize the expanded data matrix to reduce ultrasonic data noise and improve the data performance. Each row vector x i (i=1,…,n x ×n y ) as sampling points, the sample size is n x ×n y ×n h The calculation formula is:

[0067]

[0068] Where x i ' is the sample point after preprocessing, x i is the sample point in the data set; q is the median of the sample; IQR is the interquartile range of the sample.

[0069] (3) Determination of defect quantity

[0070] The elbow principle in the clustering algorithm is used to determine the number of defects, thereby determining the rank of the matrix in the matrix decomposition. Figure 4 , calculate the square sum error (SSE) between each cluster number and the corresponding cluster center. When the loss of SSE decreases the most, the loss changes gradually. Using the value c as the cluster number can often bring excellent clustering performance and is considered an effective parameter selection. The number determined by the elbow principle includes the background, that is, the entire area is divided into c areas, so the number of defects r is equal to c-1. The calculation formula is as follows:

[0071]

[0072] Where j is the observed value, c i is the predicted value, therefore, the number of clusters is selected as 6 in this experiment.

[0073] (4) UGSNMF training

[0074] In order to obtain the sequential features of ultrasonic data, it is necessary to decompose the input matrix X. The feature matrix W and coefficient matrix H of ultrasonic data are updated by the gradient method, one column at a time.

[0075] Step 4.1: Initialize the matrix factors. The matrix update rule is designed to update the parameters C and G of the model to minimize the loss function or achieve other optimization goals. Its expression is as follows:

[0076] C=-XH T +WHH T

[0077] G=HH T ;

[0078] Step 4.2: Determine the rank of the matrix and the number of corresponding defects according to the elbow principle. For each column of eigenvector W j (j=1,…,r) adopts the strategy of updating one column at a time, and keeps updating alternately. According to the matrix update rule, each time there is a corresponding vector U j :

[0079] U j =C j -W j G jj

[0080] The matrix vector needs to be projected onto the sparsity constraint, j Sort by decreasing value, so suppose there exists a=sort(b) and a matrix of length m such that for all i, j, there exists a mapping π such that a i =π(b i ) and a j ≥a j+1 , b i is a matrix vector, a i Yes i After the projection, sort(·) sorts the elements from large to small. In order to find the closest vector that satisfies the required sparsity constraint, for the transition point p in (k 2 ,m), calculate the Lagrangian parameters λ(p) and μ(p):

[0081]

[0082] Where k is the ratio of the L1 / L2 norm of the feature matrix W.

[0083] According to the matrix update strategy, set the formula:

[0084]

[0085] Among them, p * =m.

[0086] The closest vector y that satisfies the required sparsity constraint can be obtained, where y = π(x i ).

[0087] Then update vectors C and W j , where C' is the updated vector.

[0088]

[0089] W j =y;

[0090] Step 4.3: Use multiplication update to alternately update the feature matrix W and the coefficient matrix H until convergence, where H' and W' are the updated matrices:

[0091]

[0092] Where ⊙ represents element-by-element multiplication (Hadamard Product).

[0093] (5) Defect recognition performance evaluation

[0094] After UGSNMF training, the original ultrasonic data is decomposed into a feature matrix W and a coefficient matrix H. The i-th column of the W matrix is ​​reconstructed into an x×y image for visualization, and the j-th row of the H matrix is ​​visualized to extract depth information. The visualization results are shown in Figure 5 and Figure 6 Finally, 3D visualization can be performed. The obtained basis matrix W shows the shape of the ultrasonic defect, and the coefficient matrix H shows the depth of the ultrasonic defect. In terms of visualization quality, sequential gradient decomposition has a competitive advantage. The basis matrix is ​​reconstructed into the size of the ultrasonic image to show the shape of the ultrasonic defect, and the coefficient matrix shows the depth of the ultrasonic defect, achieving the purpose of the corresponding relationship between the shape and depth of the defect visualization, and characterizing the 3D characteristics of the ultrasonic defect, and the defect information is complete.

[0095] As shown in the table and figure. Overall, the error of the UGNF method in depth and area prediction is relatively small, which shows its accuracy and reliability in defect detection. Some defects will have certain defects due to manufacturing or other reasons, such as defects, so their area will have a certain deviation from the true value. Overall, the performance of UGNF is better than that of general methods. It can not only capture the location of defects more accurately, but also predict the depth and area of ​​defects more accurately, and the location and depth correspond one to one, which provides strong support for subsequent defect analysis.

[0096] Table 1 Defect depth evaluation

[0097]

Claims

1. An ultrasonic defect recognition method based on gradient sparse non-negative matrix decomposition, characterized by: The method comprises the following steps: (1) Obtaining a dataset for internal defect detection of carbon fiber composite materials Use ultrasonic phased array detection technology to emit continuous fixed-interval ultrasonic pulses to defective carbon fiber composite material CFRP samples, capture ultrasonic echoes before and after interface reflection; and save the acquired ultrasonic detection data as a three-dimensional matrix. (2) Defect ultrasonic data preprocessing A robust normalization preprocessing step was introduced to normalize the extended data matrix to reduce the ultrasonic data noise and improve the data representation capability; (3) Determination of defect quantity The number of clusters is determined by combining the elbow principle with the actual situation. When the degree of distortion decreases the most with the increase of the number of clusters, the corresponding number of clusters is taken as the number of defects. (4) Gradient sparse non-negative matrix factorization Decompose the input matrix X, and update the characteristic matrix W and coefficient matrix H of the ultrasonic data by the gradient method, one column at a time; (5) Defect recognition performance evaluation Reconstruct the W matrix into the original size image n x ×n y Perform a visual qualitative assessment and visualize the H matrix to quantitatively assess the depth of the defect.

2. The method of claim 1, wherein: In (3), the elbow principle in the clustering algorithm is used to determine the number of defects, thereby determining the rank of the matrix in the matrix decomposition. The process is: 1) Calculate the sum of squared errors (SSE) between the points and the corresponding cluster centers under each cluster number, and use the value c as the cluster number; 2) The entire data area is divided into c areas, and the number of defects r is equal to c-1, and its calculation formula is as follows: Where j is the observed value, c i is the predicted value.

3. The gradient sparse non-negative matrix factorization according to claim 1, characterized in that: In (4), the solved characteristic matrix W shows the shape of the ultrasonic defect, and the solved coefficient matrix H shows the depth of the ultrasonic defect, and the shape of the defect has a one-to-one correspondence with the depth. The process of step (4) is: Step 4.1: Initialize the matrix factors and design the matrix update rule to update the parameters C and G of the ultrasonic gradient sparse non-negative matrix factorization model to achieve the optimization goal. The expression is as follows: C=-XH T +WHH T G=HH T ; Step 4.2: Determine the rank of the matrix and the number of corresponding defects according to the elbow principle. For each column of eigenvector W j (j=1,…,r) adopts the strategy of updating one column at a time, and updates alternately; according to the matrix update rule, there is a corresponding vector U each time j : U j =C j -W j G jj The matrix vector needs to be projected onto the sparsity constraint, j Sort by descending value. Suppose there exists a=sort(b) and a matrix of length m such that for all i, j, there exists a mapping π such that a i =π(b i ) and a j ≥a j+1 , b i is a matrix vector, a i Yes i After the projection, sort(·) sorts the elements from large to small; in order to find the closest vector that satisfies the required sparsity constraint, for the transition point p in (k 2 ,m), calculate the Lagrangian parameters λ(p) and μ(p): Where k is the ratio of the L1 / L2 norm of the feature matrix W; According to the matrix update strategy, set the formula: where a = sort(b), p * = m, sort(·) is used to sort the elements from small to large; The closest vector y that satisfies the required sparsity constraint can be obtained, where y = π(x i ); then update vectors C and W j , where C' is the updated vector: W j =y; Step 4.3: Use multiplication update to alternately update the feature matrix W and the coefficient matrix H until convergence, where H' and W' are the updated matrices: Here, ⊙ represents element-by-element multiplication.

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