A method for constructing a visualization dataset of triaxial magnetic flux leakage signals for pipeline defects

Abstract

The present invention discloses a method for constructing a visualization dataset of three-axis magnetic flux leakage signals of pipeline defects, which belongs to the field of magnetic flux leakage nondestructive testing. The present invention implements the following methods: obtaining three-axis magnetic flux leakage data of the defective portion through defect magnetic flux leakage detection; performing baseline correction and filtering on the pipeline defect channel data based on the baseline estimation and sparse denoising algorithm BEADS; locating the defect data based on the magnetic flux leakage detection data using a rolling standard deviation detection method to obtain the three-axis magnetic flux leakage signal of each defect; and performing baseline correction and filtering on the defect channel data again based on the BEADS algorithm; constructing a pipeline defect magnetic flux leakage simulation model; visualizing the three-axis magnetic flux leakage extended data, and evaluating the accuracy of the three-axis magnetic flux leakage extended data using image evaluation indicators; generalizing all magnetic flux leakage signals by adding Gaussian white noise with different signal-to-noise ratios; constructing a neural network; predicting defects using test data, and quantitatively evaluating defects using the neural network.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic flux leakage nondestructive testing, and relates to a method for constructing a visualization data set of three-axis magnetic flux leakage signals of pipeline defects, and specifically to a method for improving the detection accuracy and efficiency of three-axis magnetic flux leakage signals of pipeline defects based on the visualization data set. Background Art

[0002] Fossil fuels are the primary energy source for global economic activity, with more than half of global energy consumption coming from oil and natural gas. Pipeline transportation is considered the most economical and safest method of transporting oil and gas. However, due to the complex environments and harsh operating conditions in which pipelines operate, corrosion, external interference, and material failure can lead to pipeline failure. A leak can cause significant loss of life and property, as well as environmental pollution. Therefore, regular pipeline inspection and maintenance are crucial to preventing leaks.

[0003] Magnetic flux leakage testing (MFL) is a common internal inspection technique for pipeline nondestructive testing (NDT). To meet the engineering needs of quantitative and high-precision detection of pipeline defects and faults, the rapid development of artificial intelligence (AI) has led to the application of algorithms based on unsupervised and deep learning to MFL testing. Through model training and comparison, these algorithms can improve the accuracy of detecting the length, width, and depth of various pipeline defects. The reliability of these algorithms urgently needs to be verified using large amounts of samples and data. However, due to the sensitivity and cost of actual pipeline MFL data, very few publicly available datasets are available, leaving a long way to go before these algorithms can be applied in real-world projects. Summary of the Invention

[0004] To address the practical application challenges associated with the limited availability of current three-axis magnetic flux leakage (MFL) datasets for pipeline defects, the present invention aims to provide a method for constructing a visualization dataset of three-axis MFL signals from pipeline defects. This method expands upon existing test data to construct a larger and more diverse visualization dataset of three-axis MFL signals. This visualization dataset improves the accuracy and efficiency of detecting the length, width, and depth of pipeline defects.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The present invention discloses a method for constructing a visualization data set of three-axis magnetic flux leakage signals of pipeline defects, comprising the following steps:

[0007] S1: Conduct magnetic flux leakage detection for pipeline defects. The magnetic flux leakage sensors of the detector inside the pipeline are distributed along the circumference to obtain the three-axis magnetic flux leakage data of the defective part.

[0008] S2: Baseline correction and filtering are performed on the pipeline defect channel data based on the baseline estimation and sparse denoising algorithm BEADS to eliminate the baseline drift of each channel sensor caused by vibration, so as to facilitate the normalization processing in the subsequent step S5;

[0009] S3: Defect data is located on the magnetic flux leakage detection data based on the rolling standard deviation detection method, and the three-axis magnetic flux leakage signal of each defect is obtained. The baseline correction and filtering of the defect channel data are performed again based on the BEADS algorithm to further eliminate the baseline drift of each channel sensor caused by vibration, so as to facilitate the normalization processing in the subsequent step S5;

[0010] The defects are regular in shape including rectangle and circle.

[0011] S4: By varying parameters such as defect size, and through experiments and simulations, determining how the magnetic flux leakage signal varies with depth, a magnetic flux leakage simulation model of pipeline defects is constructed. To obtain accurate simulation data, COMSOL simulation software is preferably used as the electromagnetic simulation software.

[0012] S5: Based on the actual three-axis magnetic flux leakage signal, the expanded magnetic flux leakage signal is obtained through interpolation, formula calculation, etc.;

[0013] S6: Visualize the three-axis magnetic flux leakage extension data and evaluate the accuracy of the three-axis magnetic flux leakage extension data through image evaluation indicators such as structural similarity (SSIM), mean square error (MSE) Similarity, and root mean square error (RMSE) Similarity; the visualization methods include grayscale visualization and pseudo-color visualization.

[0014] S7: All magnetic flux leakage signals were generalized by adding Gaussian white noise at varying signal-to-noise ratios. The noise addition ranged from 1dB to 5dB, depending on the actual acquisition environment. All original, expanded, and generalized data were aggregated to generate a visualization dataset of triaxial magnetic flux leakage signals for defects of varying sizes and depths. This resulted in a larger and more diverse triaxial magnetic flux leakage visualization dataset compared to the original in-pipeline detector data.

[0015] S8: Based on the visualization dataset, a neural network is constructed. The input of the neural network is the 3D magnetic flux leakage visualization dataset of the defect. The dataset is used to train and generate the neural network, and the output is the predicted defect length, width, and depth. Defect prediction using a small amount of test data effectively reduces detection costs and improves the accuracy and efficiency of pipeline defect prediction. Furthermore, defect quantification through the neural network can assess the integrity of the pipeline structure, allowing targeted repair and maintenance of problematic pipelines and ensuring safe transportation of oil and gas pipelines.

[0016] Furthermore, in S2, the baseline correction and filtering method for each channel data of pipeline defects based on the baseline estimation and sparse denoising algorithm BEADS is as follows: define Y as the test data, X as the magnetic flux leakage signal, f as the baseline signal, and W as the noise signal. The relationship is expressed as follows:

[0017] Y=X+f+W (1)

[0018] The BEADS algorithm is different from the polynomial approximation method in that it models the magnetic flux leakage signal as a sparse signal and the baseline drift as a low-pass signal. If X does not exist, an estimated value is introduced. Then establish the leakage magnetic signal filtering model, as shown in the following formula:

[0019]

[0020] Where L and H are zero-order uncorrelated recursive filters.

[0021] Formulate a convex optimization problem based on the loss function and establish a (k+1) =argmin x G(X,X (k) ), where k ≥ 0 is the number of iterations. The loss function is F(X), and for any x, G(X, V) ≥ F(X). When X = V, G(X, V) = F(X). A composite sparse derivative model for magnetic flux leakage signals is constructed.

[0022]

[0023]

[0024] in, is the penalty function term, D i X is the i-th order difference operation of X, N i D i The length of X, λ i is the regularization coefficient, increasing λ i Can make D i X is sparser.

[0025] As the iteration proceeds, in order to avoid i When X becomes 0, an error occurs in which the denominator is 0. An asymmetric penalty function is selected, as shown in the following formula:

[0026]

[0027] Among them, r>0, the minimum constant ε approaching 0>0, and the penalty function term is transformed into We further obtain the asymmetric penalty function θ ε (x n; r) of the optimization function g0(x;v).

[0028] The loss function F(X) is expressed as:

[0029]

[0030] where Γ(V) is a diagonal matrix with diagonal elements, as shown below:

[0031]

[0032]

[0033] The minimum iterative optimization target G(X,V) is obtained by the leakage magnetic signal X as shown below:

[0034] X (k+1) =A[Q (k) ](B -1 BA -1 y)-λ0A T b (8)

[0035] Q (k) =B T B+A T M (k) A (9)

[0036]

[0037] Furthermore, in S3, the method based on rolling standard deviation detection is used to locate defects in the magnetic flux leakage detection data and obtain the three-axis magnetic flux leakage signal of each defect. The rolling standard deviation detection is to roll forward a fixed rolling window to count its mean and standard deviation. The signal is judged to be normal within the preset standard deviation range of the mean. The appropriate threshold is set according to the data size. The signal exceeding this threshold is abnormal, thereby obtaining the three-axis magnetic flux leakage signal of each defect. The following formula is used:

[0038]

[0039] Threshold=α·std rolling (12)

[0040]

[0041] Among them, x j is the value of the jth data point in the time series, is the average value of k data points around the i-th data point in the time series, k is the size of the rolling window; α is an adjustable parameter, std rolling is the mean of the rolling standard deviations.

[0042] Furthermore, through experiments and simulations in S4, it was found that the magnetic flux leakage signal of defects with the same length and width changes with depth and satisfies the following rules:

[0043]

[0044]

[0045] Among them, B ji Indicates the j-axis magnetic flux leakage signal size of a defect with a depth of i% of the pipe wall thickness.

[0046] Furthermore, in S5, the expanded magnetic flux leakage signal is derived from the actual three-axis magnetic flux leakage signal through interpolation, formula calculation, and other transformations. Since the magnetic flux leakage signal of each defect varies in magnitude, the magnetic flux leakage signal is normalized to eliminate unnecessary differences between defects, ensuring the effectiveness of feature extraction. This magnetic flux leakage signal normalization includes standardization of units, reference values, and matrix size.

[0047] Furthermore, in S6, the three-axis magnetic flux leakage extended data is visualized and its accuracy is evaluated. Since most current deep learning-based algorithms use magnetic flux leakage data as image data, the three-axis magnetic flux leakage signal is converted into a pseudo-color image and evaluated using image evaluation indicators such as structural similarity (SSIM), mean square error (MSE) Similarity, and root mean square error (RMSE) Similarity. By comparing the pseudo-color image generated by the extended magnetic flux leakage signal with the pseudo-color image generated by the actual defect magnetic leakage signal at the same size, the accuracy of the extended data is evaluated. The following formula is used:

[0048] SSIM(x,y)=[l(x,y)·c(x,y)·s(x,y)] α (16)

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] Among them, l(x, y) is the brightness comparison, c(x, y) is the contrast comparison, and s(x, y) is the structure comparison. x and μ y Represent the average values ​​of x and y, σ x and σ y Represents the standard deviation of x and y, σxy represents the covariance of x and y, α, c1, c2, c3 are constants, is the predicted value, y i is the actual value.

[0055] Beneficial effects:

[0056] 1. The present invention discloses a method for constructing a visualization dataset of three-axis magnetic flux leakage signals of pipeline defects. Based on the BEADS algorithm, the three-axis magnetic flux leakage signals of the defects are subjected to base value correction and filtering preprocessing, eliminating the influence of detection noise and sensor baseline drift. The pipeline defect data is then located based on the rolling standard deviation, achieving accurate extraction of the defect magnetic leakage signals from all detection data.

[0057] 2. This invention discloses a method for constructing a visualization dataset of three-axis magnetic flux leakage signals for pipeline defects. Through experiments and simulations, a formula for how magnetic flux leakage signals vary with depth is derived. Based on the actual three-axis magnetic flux leakage signals, an expanded magnetic flux leakage signal is derived through interpolation and formula calculation. The accuracy of the expanded three-axis magnetic flux leakage data is evaluated using structural similarity, mean square error, and root mean square error to meet engineering requirements. This method effectively addresses the lack of publicly available datasets due to the sensitivity and high cost of actual pipeline magnetic flux leakage inspection data.

[0058] 3. Based on this data set, defects can be quantified by building a neural network, which can reduce detection costs, improve the accuracy and efficiency of pipeline defect prediction, and carry out targeted repair and maintenance of problem pipelines to ensure safe transportation of oil and gas pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a workflow diagram of a method for constructing a visualization data set of three-axis magnetic flux leakage signals of pipeline defects according to the present invention;

[0060] Figure 2 This is a diagram showing the effect of base value correction and filtering preprocessing of defect three-axis magnetic flux leakage data based on the BEADS algorithm of the present invention;

[0061] Figure 3 This is a diagram showing the effect of positioning defect data on magnetic flux leakage detection data using the rolling standard deviation detection method of the present invention;

[0062] Figure 4 This is a graph showing how the magnetic flux leakage signal of a defect of the same length and width varies with depth;

[0063] Figure 5 This is a diagram showing how the simulated magnetic flux leakage signal of a defect of the same length and width varies with depth;

[0064] Figure 6This is a comparison chart of the original experimental three-axis magnetic flux leakage data and the expanded data visualization effect of the same size defect in the present invention. DETAILED DESCRIPTION

[0065] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0066] Example 1:

[0067] like Figure 1 As shown, the present embodiment discloses a method for constructing a visualization dataset of three-axis magnetic flux leakage signals of pipeline defects, including the following steps:

[0068] S1: Implement pipeline defect magnetic flux leakage detection and obtain tri-axis magnetic flux leakage detection data.

[0069] S2: Baseline correction and filtering of the collected 200 channel data based on the BEADS algorithm.

[0070] The output signal of the magnetic flux leakage sensor is affected by vibration interference, etc., which makes it difficult to distinguish the defect signal and is not conducive to defect detection. Therefore, it is necessary to perform baseline correction and filtering on the data of each channel. Figure 2 The figure shows the effect of base value correction and filtering preprocessing of defect three-axis magnetic leakage signal based on BEADS algorithm.

[0071] S3: Defect data is located on the magnetic flux leakage detection data based on the rolling standard deviation detection method, and the three-axis magnetic flux leakage signal of each defect is obtained. Then, baseline correction and filtering are performed on the defect channel data based on the BEADS algorithm.

[0072] like Figure 3 The image below shows the effect of using the rolling standard deviation method to locate defects in magnetic flux leakage test data. This method can pinpoint the location of a specific defect, extract the three-axis magnetic flux leakage signal for each defect, and then perform baseline correction and filtering.

[0073] S4: Through experiments and COMSOL simulations, we found that the leakage magnetic signal changes with depth.

[0074] like Figure 4 、 5 The experimental and simulated magnetic leakage signals of defects with the same length and width vary with depth.

[0075] According to the characteristics of the magnetic flux leakage signals of different axes, different numbers of feature points are selected to compare the magnitude of the magnetic flux leakage signals at different depths. Among them, 4 feature points (Pos1, 2, 3, 4) are selected for the X-axis magnetic flux leakage signal, 2 feature points (Pos5, 6) are selected for the Y-axis magnetic flux leakage signal, and 2 feature points (Pos7, 8) are selected for the Z-axis magnetic flux leakage signal. Figure 4 、5 The experimental and simulated magnetic flux leakage signals of defects of the same length and width are linearly correlated with the depth, satisfying the following formula:

[0076]

[0077]

[0078] Among them, B ji Indicates the j-axis magnetic flux leakage signal size of a defect with a depth of i% of the pipe wall thickness.

[0079] S5: Based on the actual triaxial magnetic flux leakage signal, an expanded magnetic flux leakage signal is derived through interpolation, formula calculation, and other transformations. Since the magnitude of the magnetic flux leakage signal varies from defect to defect, it is necessary to standardize the magnetic flux leakage signal. To this end, 25 channels near the center of each defect's magnetic flux leakage signal and the associated sampling points around it are extracted as the magnetic flux leakage signal for that defect. The data matrix is ​​then unified using cubic spline interpolation to form a standardized defect magnetic flux leakage signal. A formula is then used to calculate the triaxial magnetic flux leakage signal for defects of the same length and width but at different depths.

[0080] S6: Visualize the extended triaxial magnetic flux leakage data and evaluate its accuracy. Commonly used image evaluation metrics, such as SSIM, MSE Similarity, and RMSE Similarity, are used to evaluate the accuracy of the extended data by comparing the SSIM, MSE Similarity, and RMSE Similarity of the pseudo-color image generated by the extended magnetic flux leakage data with the pseudo-color image generated by the measured magnetic flux leakage signal of the defect at that size. The following formula is used:

[0081] SSIM(x,y)=[l(x,y)·c(x,y)·s(x,y)] α (twenty four)

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Among them, l(x, y) is the brightness comparison, c(x, y) is the contrast comparison, and s(x, y) is the structure comparison. x and μ y Represent the average values ​​of x and y, σ x and σ yRepresents the standard deviation of x and y, σ xy represents the covariance of x and y, α, c1, c2, c3 are constants, is the predicted value, y i is the actual value.

[0088] Among them, the SSIM of the extended data of the x-axis is 0.9527, MSE Similarity is 0.9838, RMSESimilarity is 0.8728; the SSIM of the extended data of the y-axis is 0.9765, MSE Similarity is 0.9882, RMSESimilarity is 0.8913; the SSIM of the extended data of the z-axis is 0.9921, MSE Similarity is 0.9979, RMSESimilarity is 0.9539.

[0089] S7: All magnetic flux leakage signals are generalized by adding Gaussian white noise with different signal-to-noise ratios (ranging from 1 dB to 5 dB). All original data, extended data, and generalized data are aggregated to obtain a visualization dataset of triaxial magnetic flux leakage signals of defects of different sizes and depths.

[0090] S8: Based on the visualization dataset, a neural network is constructed. The input of the neural network is the 3D magnetic flux leakage visualization dataset of the defect. The dataset is used to train and generate the neural network, and the output is the predicted defect length, width, and depth. Compared with the original inspection dataset, the prediction accuracy of the defect length, width, and depth increased by 10.51%, reaching a prediction accuracy of 2.17%.

[0091] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing a visualization dataset of pipeline defect triaxial magnetic flux leakage signals, characterized by: The following steps are included: S1: Conduct magnetic flux leakage detection for pipeline defects. The magnetic flux leakage sensors of the detector inside the pipeline are distributed along the circumference to obtain the three-axis magnetic flux leakage data of the defective part. S2: Baseline correction and filtering are performed on the pipeline defect channel data based on the baseline estimation and sparse denoising algorithm BEADS to eliminate the baseline drift of each channel sensor caused by vibration, so as to facilitate the normalization processing in the subsequent step S5; S3: Defect data is located on the magnetic flux leakage detection data based on the rolling standard deviation detection method, and the three-axis magnetic flux leakage signal of each defect is obtained. The baseline correction and filtering of the defect channel data are performed again based on the BEADS algorithm to further eliminate the baseline drift of each channel sensor caused by vibration, so as to facilitate the normalization processing in the subsequent step S5; The defect is a regular shape including a rectangle and a circle; S4: Change the defect size and other parameters, and through experiments and simulations, find out the variation pattern of the magnetic flux leakage signal with depth; build a pipeline defect magnetic flux leakage simulation model; S5: Based on the actual three-axis magnetic flux leakage signal, the expanded magnetic flux leakage signal is obtained through interpolation and formula calculation; S6: Visualize the triaxial magnetic flux leakage extended data and evaluate its accuracy using image evaluation indicators such as structural similarity (SSIM), mean square error (MSE) Similarity, and root mean square error (RMSE) Similarity. S7: Generalize all magnetic flux leakage signals by adding Gaussian white noise with different signal-to-noise ratios. The noise level is determined to be 1dB to 5dB based on the actual acquisition environment. All original inspection data, expanded data, and generalized data are aggregated to obtain a visualization dataset of triaxial magnetic flux leakage signals for defects of different sizes and depths. This constructs a larger and more diverse triaxial magnetic flux leakage signal visualization dataset. S8: Based on the visualization data set, a neural network is constructed, wherein the input of the neural network is the three-dimensional magnetic leakage visualization data set of the defect, and the data set is used to train and generate the neural network, and the output is the predicted defect length, width and depth; the defect prediction is achieved through the test data, thereby improving the prediction accuracy and efficiency of pipeline defects; the defects are quantified through the neural network, the integrity of the pipeline structure is evaluated, and the problem pipeline is repaired and maintained in a targeted manner, thereby achieving safe transportation of oil and gas pipelines.

2. The method for constructing a visualization dataset of pipeline defect triaxial magnetic flux leakage signals according to claim 1, characterized in that: The electromagnetic simulation software is COMSOL simulation software.

3. The method for constructing a visualization dataset of pipeline defect tri-axis magnetic flux leakage signals according to claim 1, characterized in that: The visualization method includes a grayscale visualization method and a pseudo-color image visualization method.

4. The method for constructing a visualization dataset of pipeline defect triaxial magnetic flux leakage signals according to claim 1, characterized in that: In S2, the baseline correction and filtering method for each channel data of pipeline defects based on the baseline estimation and sparse denoising algorithm BEADS is as follows: define Y as the test data, X as the magnetic flux leakage signal, f as the baseline signal, and W as the noise signal. The relationship is expressed as follows: Y=X+f+W (1) The BEADS algorithm is different from the polynomial approximation method. It models the magnetic flux leakage signal as a sparse signal and the baseline drift as a low-pass signal. If X does not exist, an estimated value is introduced. Then establish the leakage magnetic signal filtering model, as shown in the following formula: Where L and H are zero-order uncorrelated recursive filters; Formulate a convex optimization problem based on the loss function and establish a (k+1) =argmin x G(X,X (k) ), k≥0 is the number of iterations; the loss function is F(X), and for any x, it satisfies G(X,V)≥F(X). When X=V, G(X,V)=F(X), and a composite sparse derivative model for magnetic flux leakage signal is constructed; in, is the penalty function term, D i X is the i-th order difference operation of X, N i D i The length of X, λ i is the regularization coefficient, increasing λ i Can make D i X is more sparse; As the iteration proceeds, in order to avoid i When X becomes 0, an error occurs in which the denominator is 0. An asymmetric penalty function is selected, as shown in the following formula: Among them, r>0, the minimum constant ε approaching 0>0, and the penalty function term is transformed into We further obtain the asymmetric penalty function θ ε (x n ; r)’s optimization function g0(x;v); The loss function F(X) is expressed as: where Γ(V) is a diagonal matrix with diagonal elements, as shown below: The minimum iterative optimization target G(X,V) is obtained by the leakage magnetic signal X as shown below: X (k+1) =A[Q (k) ] -1 (B -1 BA -1 y)-λ0A T b (8) Q (k) =B T B+A T M (k) A (9) 5. The method for constructing a visualization dataset of pipeline defect tri-axis magnetic flux leakage signals according to claim 2, characterized in that: In S3, the method based on rolling standard deviation detection is used to locate the defect data of the magnetic flux leakage detection data and obtain the three-axis magnetic flux leakage signal of each defect; The rolling standard deviation test uses a fixed rolling window to roll forward and count its mean and standard deviation. Signals within the preset standard deviation range of the mean are considered normal. A suitable threshold is set according to the data size. Signals exceeding this threshold are considered abnormal. The three-axis magnetic flux leakage signal of each defect is obtained using the following formula: Threshold=αstd rolling (12) Among them, x j is the value of the jth data point in the time series, is the average value of k data points around the i-th data point in the time series, k is the size of the rolling window; α is an adjustable parameter, std rolling is the mean of the rolling standard deviations.

6. The method for constructing a visualization dataset of pipeline defect triaxial magnetic flux leakage signals according to claim 5, characterized in that: Through experiments and simulations in S4, it was found that the magnetic flux leakage signal of defects with the same length and width changes with depth and satisfies the following rules: Among them, B ji Indicates the j-axis magnetic flux leakage signal size of a defect with a depth of i% of the pipe wall thickness.

7. The method for constructing a visualization dataset of pipeline defect tri-axis magnetic flux leakage signals according to claim 6, characterized in that: In S5, an expanded magnetic flux leakage signal is obtained based on the actual three-axis magnetic flux leakage signal through interpolation, formula calculation, and other conversions. Since the magnetic flux leakage signal of each defect is different in size, the magnetic flux leakage signal is standardized to eliminate unnecessary differences between each defect. The magnetic flux leakage signal standardization includes unit unification, reference value unification, and matrix size unification.

8. The method for constructing a visualization dataset of pipeline defect tri-axis magnetic flux leakage signals according to claim 7, characterized in that: In S6, the extended triaxial magnetic flux leakage data is visualized and its accuracy is evaluated. The deep learning-based algorithm uses magnetic flux leakage data as image data, converts the triaxial magnetic flux leakage signal into a pseudo-color image, and uses image evaluation indicators such as structural similarity (SSIM), mean square error (MSE) Similarity, and root mean square error (RMSE) Similarity to evaluate it. The accuracy of the extended data is evaluated by comparing the pseudo-color image generated by the extended magnetic flux leakage signal with the pseudo-color image generated by the measured defect magnetic flux leakage signal at the same size. The following formula is used: SSIM(x,y)=[l(x,y)·c(x,y)·s(x,y)] α (16) Among them, l(x,y) is brightness comparison, c(x,y) is contrast comparison, s(x,y) is structure comparison; μ x and μ y Represent the average values ​​of x and y, σ x and σ y Represents the standard deviation of x and y, σ xy represents the covariance of x and y, α, c1, c2, c3 are constants, is the predicted value, y i is the actual value.

Images