Method and system for detecting the thickness of the insulation layer of a crosslinked insulated cable

Abstract

The application relates to the technical field of cable detection, in particular to a method and system for detecting the thickness of the insulation layer of a cross-linked insulation cable. The method comprises the following steps: obtaining a cable cross-section image and performing region segmentation to identify three topologically connected domains and extract inner and outer boundaries; establishing a physical field model and applying a first type of boundary condition; solving a Laplace equation in the insulation layer region to generate a convergent scalar potential field; performing differential operation on the scalar potential field to obtain a gradient vector field, searching for gradient modulus extreme points on virtual equipotential lines to mark the thinnest and thickest feature points; taking the thinnest feature point and the thickest feature point as starting points, respectively performing streamline tracing along positive and negative gradient directions, and calculating the sum of path lengths to obtain the minimum thickness of the insulation layer and the maximum thickness of the insulation layer respectively. The application eliminates noise by solving the Laplace equation, quickly locates by using the gradient modulus extreme value, and significantly improves the detection accuracy.

Description

Technical Field

[0001] This application relates to the field of cable testing technology. More specifically, this application relates to a method and system for testing the insulation layer thickness of cross-linked insulated cables. Background Technology

[0002] Cross-linked polyethylene (XLPE) insulated cables are widely used in power transmission and distribution due to their excellent electrical and mechanical properties. As the core component of the cable, the uniformity of the insulation layer's thickness directly affects the cable's insulation performance and service life. Accurate measurement of the insulation layer thickness is a crucial step in ensuring product quality during cable production and quality inspection.

[0003] Existing methods for measuring insulation thickness mainly fall into two categories: mechanical contact measurement and image-based measurement. Mechanical contact measurement uses a micrometer or thickness gauge to directly contact the cable cross-section. This method is simple to operate but has limitations such as a limited number of measurement points and inability to cover the entire circumference. Image-based measurement methods acquire images of the cable cross-section, use edge detection algorithms to extract the inner and outer boundaries of the insulation layer, and then calculate the distance between the boundaries to obtain the thickness value. Commonly used edge detection algorithms include the Sobel operator and Canney edge detection. These methods can achieve automated measurement, but they exhibit certain limitations in handling image noise and jagged edges.

[0004] However, in actual cable cross-sectional images, due to limitations in image acquisition equipment resolution, uneven lighting, and uneven cut surfaces, the insulation layer boundaries often appear jagged or locally blurred. Traditional edge detection methods directly sample and calculate distances on the original image boundaries, making them susceptible to edge noise interference and resulting in significant fluctuations in measurement results. Furthermore, for eccentric cables, existing methods typically require dense sampling across the entire circumference to accurately locate the thinnest and thickest points, leading to low computational efficiency. Therefore, there is an urgent need for an insulation layer thickness detection method that can effectively suppress the influence of edge noise, quickly locate extreme thickness points, and achieve high-precision measurement. Summary of the Invention

[0005] The purpose of this application is to propose a method and system for detecting the insulation layer thickness of cross-linked insulated cables, in order to solve the problems of insufficient measurement accuracy caused by noise interference at the insulation layer boundary and low efficiency in locating extreme thickness points in the prior art.

[0006] In a first aspect, the method for detecting the insulation layer thickness of a cross-linked insulated cable provided in this application includes: acquiring a cross-sectional image of the cable; performing region segmentation on the image to identify three topologically connected domains containing at least an inner conductor region, an insulation layer region, and an outer background region; extracting the boundary contour between the inner conductor and the insulation layer as the inner boundary and the boundary contour between the insulation layer and the background as the outer boundary; establishing a physical field model; applying first-type boundary conditions to the inner and outer boundaries respectively to set a potential difference; solving the Laplace equation within the insulation layer region to generate a convergent scalar potential field, the scalar potential field including the potential value of each pixel; and differentiating the scalar potential field. The gradient vector field and gradient magnitude distribution are obtained through calculation. A closed virtual equipotential line is extracted inside the scalar potential field, and the gradient magnitude of each point on the virtual equipotential line is obtained. The maximum and minimum points of the gradient magnitude distribution are searched and marked as the thinnest feature point and the thickest feature point, respectively. Starting from the thinnest and thickest feature points, streamline tracing is performed along the positive and negative gradient directions of the gradient vector field, respectively. The first path length to the inner boundary and the second path length to the outer boundary are calculated. The sum of the first path length and the second path length is taken as the minimum thickness of the insulating layer. The maximum thickness of the insulating layer is obtained from the thickest feature point.

[0007] Based on the physical negative correlation between the scalar potential field gradient magnitude and the insulation layer thickness, this application can quickly locate the thinnest and thickest feature points without dense sampling across the entire circumference. By using the thinnest and thickest feature points as starting points, streamline tracing is performed along the positive and negative gradient directions of the gradient vector field, respectively, to calculate the sum of the path lengths to the inner and outer boundaries. This measurement path is perpendicular to the virtual equipotential lines and geometrically corresponds to the shortest distance, thereby significantly improving the accuracy and efficiency of insulation layer thickness detection.

[0008] Optionally, the region segmentation of the image includes: denoising and smoothing the cable cross-section image; using an image segmentation algorithm to identify the inner conductor region, insulation layer region, and outer background region; and performing morphological processing on each segmented region to fill in internal holes and smooth region boundaries.

[0009] This application establishes a physical field model. This approach gives clear physical meaning to the subsequent solution of the Laplace equation within the insulating layer region, and the generated convergent scalar potential field can adaptively distort and change with the geometry of the insulating layer, laying a theoretical foundation for accurate thickness measurement.

[0010] Optionally, the process of defining the physical field model includes: defining the inner conductor region as a high-potential source region; defining the outer background region as a low-potential ground region; and defining the insulating layer region as the passive physical field region to be solved.

[0011] Optionally, the process of applying the first type of boundary condition includes: fixing the potential value of the inner boundary to a preset high potential constant; and fixing the potential value of the outer boundary to a preset low potential constant or zero potential.

[0012] This application constructs a discrete mesh within the insulation layer region and employs a numerical iterative algorithm to solve for all pixels in the field until the residual index of two adjacent iterations meets a preset convergence condition. This method features fast convergence speed and good parallel computing characteristics, controlling computational overhead while ensuring solution accuracy, making it suitable for real-time processing of high-resolution cable cross-sectional images.

[0013] Optionally, the process of solving the Laplace equation includes: constructing a discrete grid with a preset grid size within the insulating layer region to establish a discrete difference equation system; solving the discrete difference equation system using a numerical iterative algorithm, updating the potential value of each grid node in each iteration, and calculating the residual norm of two adjacent iterations; stopping the iteration and outputting the final scalar potential field when the residual norm is less than a preset convergence threshold.

[0014] This application extracts a closed virtual equipotential line within the scalar potential field instead of sampling on the physical boundary, effectively avoiding the outer boundary region where segmentation errors exist. The virtual equipotential line is extremely smooth and unaffected by the jagged edges of the original image, providing a high-quality data foundation for subsequently obtaining the gradient magnitude of each point on the virtual equipotential line and searching for the maxima and minima of the gradient magnitude distribution.

[0015] Optionally, the extraction process of the virtual equipotential line includes: setting an intermediate potential threshold between the highest and lowest potentials of the scalar potential field; extracting the set of pixels in the scalar potential field whose potential values ​​are equal to the intermediate potential threshold, and connecting them to form a closed curve as the virtual equipotential line, wherein the virtual equipotential line is located inside the insulating layer region and does not coincide with the physical boundary.

[0016] Optionally, the streamline tracing process includes: the streamline tracing is a process of continuously updating the position based on the gradient vector direction of the current position until the boundary is reached; during the position update process, iterative movement is performed using a sub-pixel level step size.

[0017] In the streamline tracing process, this application employs sub-pixel level step size and interpolation algorithms, enabling the acquisition of precise gradient vector directions at non-integer coordinate positions. This high-precision continuous position update method results in sub-pixel level measurement accuracy for the calculated path length, leading to more accurate and stable measurement results compared to methods that directly calculate distances on the pixel grid.

[0018] Optionally, the termination conditions for streamline tracing include: when tracing along the positive gradient direction, if the potential value at the current position reaches or exceeds a preset high potential threshold, then it is determined that the inner boundary has been reached and tracing stops; when tracing along the negative gradient direction, if the potential value at the current position reaches or falls below a preset low potential threshold, then it is determined that the outer boundary has been reached and tracing stops.

[0019] Optionally, the detection method further includes an eccentricity calculation step: calculating the difference between the maximum thickness of the insulation layer and the minimum thickness of the insulation layer, and performing a ratio calculation between the difference and the maximum thickness of the insulation layer to obtain the eccentricity.

[0020] In the second aspect, the insulation layer thickness detection system for cross-linked insulated cables includes:

[0021] processor;

[0022] The memory stores computer instructions for detecting the insulation thickness of cross-linked insulated cables, which, when executed by the processor, cause the system to perform the aforementioned method for detecting the insulation thickness of cross-linked insulated cables.

[0023] The beneficial effects of this application are as follows: By segmenting the image into regions and establishing a physical field model, this application generates a smooth scalar potential field by solving the Laplace equation within the insulating layer region, effectively eliminating noise at the edges of the original image. Based on the physical negative correlation between the gradient magnitude distribution and the insulating layer thickness, the thinnest and thickest feature points can be quickly located. The thickness measurement path achieved by performing streamline tracing along the positive and negative gradient directions of the gradient vector field is perpendicular to the virtual equipotential lines, geometrically corresponding to the shortest distance, thereby significantly improving the accuracy and efficiency of insulating layer thickness detection. Attached Figure Description

[0024] Figure 1 This is a flowchart of a method for detecting the insulation layer thickness of a cross-linked insulated cable according to an embodiment of this application.

[0025] Figure 2 This is an original diagram of a cross-linked insulated cable according to the insulation layer thickness detection method of a cross-linked insulated cable according to an embodiment of this application.

[0026] Figure 3 This is an equipotential line distribution diagram of the insulation layer thickness detection method for cross-linked insulated cables according to an embodiment of this application.

[0027] Figure 4 This is a streamline tracing diagram of the insulation layer thickness detection method for cross-linked insulated cables according to an embodiment of this application.

[0028] Figure 5This is an insulation layer thickness analysis diagram of the cross-linked insulated cable insulation layer thickness detection method according to an embodiment of this application.

[0029] Figure 6 This is a structural block diagram of a cross-linked insulated cable insulation layer thickness detection system according to an embodiment of this application. Detailed Implementation

[0030] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Figure 1 The diagram shown is a flowchart of a method for detecting the insulation layer thickness of a cross-linked insulated cable according to an embodiment of this application.

[0031] S1: Obtain the cross-sectional image of the cable, perform region segmentation, and extract the inner and outer boundaries.

[0032] First, a cross-sectional image of the cable is acquired. The image is then segmented to identify three topologically connected regions, each containing at least an inner conductor region, an insulation layer region, and an outer background region. For example... Figure 2 The image shown is an original cross-linked insulated cable image obtained using the insulation layer thickness detection method for cross-linked insulated cables according to an embodiment of this application. The cable cross-section image is acquired using an industrial camera or microscopic imaging device, with an image resolution set to 1024 pixels by 1024 pixels and a grayscale value range of 0 to 255. During image acquisition, it is necessary to ensure that the cable cross-section is centered in the camera's field of view and adjust the light source angle to obtain uniform illumination conditions, reducing image quality degradation caused by uneven illumination.

[0033] The cable cross-sectional image is denoised and smoothed, and an image segmentation algorithm (such as adaptive thresholding or edge detection) is used to identify and label three topologically connected regions in the image. These three topologically connected regions include an inner conductor region, an insulation layer region, and an outer background region. The inner conductor region corresponds to the metal conductor portion at the center of the cable; the insulation layer region corresponds to the cross-linked polyethylene insulation layer covering the conductor, which is the passive physical field region to be solved in this application; and the outer background region corresponds to the air or other media outside the insulation layer.

[0034] For region segmentation, the grayscale image is first preprocessed with Gaussian filtering. Then, Otsu's method is used to calculate an adaptive threshold, segmenting the image into foreground and background. Morphological processing is then applied to each segmented region to fill internal holes and smooth region boundaries.

[0035] Otsu's method is used to calculate an adaptive threshold, segmenting the image into foreground and background. Otsu's method iterates through all possible grayscale thresholds, calculates the inter-class variance between the foreground and background, and selects the threshold that maximizes the inter-class variance as the optimal segmentation threshold. For cable cross-section images, two thresholding steps are typically required: the first segmentation distinguishes between conductor and non-conductor regions, and the second segmentation distinguishes between insulation and background regions.

[0036] A physical field model is established, and first-type boundary conditions are applied to the inner and outer boundaries to define the potential difference. The specific definition process includes defining the inner conductor region as a high-potential source region, the outer background region as a low-potential ground region, and the insulating layer region as the passive physical field region to be solved. This physical field model ensures that subsequent numerical solutions have clear electrostatic physical meaning. In the electrostatic field model, the potential gradually decreases from the high-potential source to the low-potential ground, forming a smooth potential distribution.

[0037] The boundary contour between the inner conductor and the insulating layer is extracted as the inner boundary, and the boundary contour between the insulating layer and the background is extracted as the outer boundary. Contour extraction employs an edge tracking algorithm to extract a continuous sequence of boundary pixels from the segmented binary image. Both the inner and outer boundaries are closed curves, corresponding to the high-potential and low-potential boundaries of the potential distribution, respectively. The application process of the first type of boundary condition includes: fixing the potential value of the inner boundary to a preset high-potential constant, which is set to 1.0 in this embodiment; and fixing the potential value of the outer boundary to a preset low-potential constant or zero potential, which is set to 0.0 in this embodiment. The formula for setting the boundary conditions is as follows:

[0038] For all points located on the inner boundary; For all points located on the outer boundary, φ represents the potential value, which is dimensionless; x and y represent the pixel coordinates, in pixels. By setting boundary conditions, the boundary constraints for solving the harmonic field are determined, enabling subsequent numerical iterations to converge to a unique solution.

[0039] S2: Solve the Laplace equation within the insulating layer region to generate a convergent scalar potential.

[0040] After completing region segmentation and boundary condition setting, a harmonic field numerical reconstruction is performed based on the Laplace equation to generate a scalar potential field. The process of solving the Laplace equation includes: constructing a discrete grid within the insulating layer region and establishing a set of discrete difference equations. Each pixel corresponds to one grid node. The number of rows and columns of the grid is consistent with the height and width of the image; in this embodiment, it is 1024 times 1024 grid nodes.

[0041] The Laplace equation is the fundamental partial differential equation describing the potential field distribution in a source-free region. In the two-dimensional plane, the continuous form of the Laplace equation is that the sum of the second-order partial derivatives of the potential with respect to the x-coordinate and the second-order partial derivatives with respect to the y-coordinate is zero. A function that satisfies the Laplace equation is called a harmonic function, which has the average value property: the function value at any point is equal to the average of the function values ​​on any circle surrounding that point. This property makes harmonic functions extremely smooth and free of local extrema.

[0042] Discrete difference equations are established based on the Laplace equation. For the discrete grid, a five-point difference scheme is used for discretization, such that the potential value of each grid point is equal to the arithmetic mean of the potential values ​​of its four adjacent points (up, down, left, and right). The discrete difference equations are as follows:

[0043] ;

[0044] in, Represents grid points The potential at that point is dimensionless; and The row and column indices are for the grid points. This difference scheme is a second-order accurate central difference approximation of the Laplace equation, which can effectively approximate the solution of the continuity equation.

[0045] A numerical iterative algorithm is used to solve for all pixels in the field until the residual index of two consecutive iterations meets the preset convergence condition, outputting the final scalar potential field. This embodiment uses either the multigrid method or the red-black Gaussian-Seidel iterative method to solve for all pixels. The red-black Gaussian-Seidel iterative method divides the grid points into two groups: red nodes and black nodes, arranged in a checkerboard pattern. The sum of the row and column indices of red nodes is even, while the sum of the row and column indices of black nodes is odd. In each iteration, the potential values ​​of all red nodes are updated first, followed by the potential values ​​of all black nodes. This grouping update strategy ensures that the updates of nodes within the same group are independent, exhibiting good parallel computing characteristics and fully utilizing the parallel computing capabilities of multi-core processors or graphics processing units to accelerate the solution process.

[0046] The multigrid method is a more efficient iterative solution approach. This method accelerates convergence by alternating solutions at grid levels of different resolutions. First, several iterations are performed on the original fine grid. Then, the residuals are constrained to a coarser grid, where the error correction equation is solved. Finally, the correction is interpolated back to the fine grid for correction. The coarse grid quickly eliminates low-frequency error components, while the fine grid corrects high-frequency details. Through the synergistic effect between multiple grid levels, the multigrid method can achieve convergence in linear time complexity, demonstrating a significant efficiency advantage over single-layer iterative methods.

[0047] This embodiment employs a three-level multi-grid structure, corresponding to three resolutions: 1024x1024, 512x512, and 256x256. Two red-black Gaussian-Seidel iterations are performed at each grid level, followed by inter-grid constraints and interpolation operations. Bilinear interpolation is used for refinement, and full-weight constraints are used for coarsening.

[0048] The convergence criterion is set as follows: the residual norm of two consecutive iterations is less than a preset threshold. The residual is defined as the difference between the current potential value and the theoretical value calculated based on the difference equation. The residual norm is calculated using the L2 norm, which is the square root of the sum of squares of the residuals at all grid points. In this embodiment, the preset threshold is set to 1.0 multiplied by 10 to the power of -6. Iteration stops when the overall potential distribution stabilizes and the convergence criterion is met, resulting in a converged scalar potential field.

[0049] The resulting scalar potential field is physically equivalent to the electrostatic potential distribution within the insulating layer. Due to the average value property of the harmonic function, the generated potential field is extremely smooth, without local fluctuations caused by image noise. The equipotential lines of the potential field automatically twist and adapt to the geometry of the insulating layer, accurately reflecting the true geometric structure of the insulating layer and effectively eliminating jagged noise at the edges of the original image.

[0050] like Figure 3 The figure shows an equipotential line distribution diagram of the insulation layer thickness detection method for cross-linked insulated cables according to an embodiment of this application. The diagram illustrates the scalar potential field distribution generated by harmonic field numerical reconstruction based on the Laplace equation within the insulation layer region. The inner conductor boundary is set as a high-potential source, and the outer insulation layer boundary is set as a low-potential ground. The smooth color gradient and white equipotential lines in the figure demonstrate the distribution characteristics of the harmonic field. This physical field-based method utilizes the average value property of the harmonic function to effectively eliminate jagged noise at the edges of the original image, laying a stable foundation for subsequent high-precision gradient analysis.

[0051] S3: Extract virtual equipotential lines within the scalar potential field and search for the thinnest and thickest feature points.

[0052] After obtaining the converged scalar potential field, the gradient vector field is calculated, and extreme feature points are located on the virtual equipotential lines. The gradient vector field characterizes the rate of change of electric potential in various directions in space and is a vector field derived from the scalar field. A convolution operator is applied to the converged scalar potential field to calculate the gradient vector for each pixel.

[0053] In this embodiment, the Schar operator is used for gradient calculation. The Schar operator is an improved version of the Sobel operator, possessing better rotation invariance and higher accuracy. The Schar operator applies 3x3 convolution kernels in both the horizontal and vertical directions. The weight distribution of the horizontal convolution kernel is as follows: left column: -3, -10, -3; middle column: 0; right column: 3, 10, 3. The weight distribution of the vertical convolution kernel is as follows: top row: -3, -10, -3; middle row: 0; bottom row: 3, 10, 3.

[0054] Convolution operations yield the horizontal and vertical gradient components for each pixel. The horizontal gradient component represents the rate of change of electric potential in the horizontal direction, and the vertical gradient component represents the rate of change of electric potential in the vertical direction. Combining these two components into a two-dimensional gradient vector represents the direction and magnitude of the fastest change in electric potential at that point.

[0055] The magnitude of the gradient vector is calculated to obtain the gradient magnitude distribution of each pixel. The formula for calculating the gradient magnitude is the square root of the sum of the squares of the horizontal gradient components and the squares of the vertical gradient components. The gradient magnitude characterizes the drasticness of the potential change and physically corresponds to the magnitude of the electric field strength. The larger the gradient magnitude, the more drastic the potential change at that location, and the stronger the corresponding electric field strength.

[0056] A potential threshold is set within the scalar potential field, and the closed curve corresponding to this threshold is extracted as a virtual equipotential line. An equipotential line is a set of points with equal potential values, represented as a closed curve on a two-dimensional plane. In this embodiment, the potential threshold is set to 0.05, meaning that equipotential lines with a potential value equal to 0.05 are extracted. This virtual equipotential line is located within the potential field near the outer boundary, but avoids the physical outer boundary where segmentation errors exist.

[0057] The extraction of virtual equipotential lines employs an isoline tracing algorithm. First, all grid cells are traversed to identify cells whose potential values ​​cross a threshold of 0.05. Within each crossing cell, the coordinates of the intersection points between the equipotential line and the cell edge are calculated using linear interpolation. Connecting the intersection points of adjacent cells forms a continuous equipotential line curve. Due to the properties of the harmonic function, the extracted virtual equipotential lines are extremely smooth and unaffected by the jagged edges of the original image.

[0058] Gradient magnitude data of all points on the virtual equipotential line are extracted to construct a one-dimensional distribution sequence. Gradient magnitude values ​​are sampled along the equipotential line at fixed arc length intervals, with one sample point acquired every 1 pixel. The gradient magnitudes of the sampled points are obtained from the gradient magnitude distribution map using bilinear interpolation. The gradient magnitude values ​​of all sampled points are arranged in order of their position on the equipotential line to form a one-dimensional distribution sequence.

[0059] According to the physical principles of electrostatics, electric flux is conserved within an insulating layer. Electric flux equals the product of electric field strength and area. In regions with thinner insulating layers, the same electric flux passes through a smaller cross-sectional area, resulting in a stronger electric field; conversely, in regions with thicker insulating layers, the same electric flux is distributed over a larger cross-sectional area, leading to a weaker electric field. Since the gradient modulus is proportional to the electric field strength, the thinner the insulating layer, the larger the gradient modulus, and the thicker the insulating layer, the smaller the gradient modulus, forming a negative correlation between the gradient modulus and the insulating layer thickness.

[0060] Based on the negative correlation between gradient modulus and insulation layer thickness, the extreme points of the gradient modulus distribution are searched to locate the thinnest and thickest feature points. The global maximum point of the one-dimensional distribution sequence is searched; this point corresponds to the thinnest position of the insulation layer and is marked as the thinnest feature point. The global minimum point of the one-dimensional distribution sequence is searched; this point corresponds to the thickest position of the insulation layer and is marked as the thickest feature point. This extreme point search strategy can quickly locate the physically thinnest and thickest points without requiring dense sampling and thickness measurement along the entire circumference, significantly improving the efficiency of extreme point location. If it is necessary to calculate the average thickness or perform circumferential thickness distribution analysis, several key points can be selected at equal intervals along virtual equipotential lines for subsequent streamline tracing measurements. In this embodiment, 36 equally spaced sampling points can be selected, each corresponding to a 10-degree angular interval, to achieve uniform sampling of the insulation layer thickness.

[0061] like Figure 4 The diagram illustrates the streamline tracing process of the insulation layer thickness detection method for cross-linked insulated cables according to an embodiment of this application. The diagram demonstrates the construction process of the thickness measurement path based on inverse gradient streamline tracing. A virtual equipotential line avoiding boundary segmentation errors is extracted within the reconstructed scalar potential field, and the gradient modulus distribution along this line is calculated. Based on the physical negative correlation between gradient modulus and insulation layer thickness, the point with the largest gradient modulus is quickly located as the thinnest feature point, and the point with the smallest gradient modulus is located as the thickest feature point. Subsequently, starting from these feature points, high-precision streamline tracing is performed along the positive and negative gradient directions of the gradient vector field, respectively, forming the thinnest and thickest measurement paths perpendicular to the equipotential surface.

[0062] S4: Perform gradient streamline tracing and integral to calculate the insulation layer thickness.

[0063] After locating the extreme feature points, gradient streamline tracing is performed and the insulation layer thickness is calculated by integration. Streamline tracing is a process of continuously updating the position based on the gradient vector direction at the current position until the boundary is reached. Streamline tracing employs an iterative stepping method, which has high numerical accuracy and stability. In each iteration, the gradient vector at the current position is first calculated, and the stepping direction is determined after normalization. The normalization operation scales the magnitude of the gradient vector to 1, preserving directional information and ensuring that the distance of each step is determined only by the step size parameter.

[0064] During the position update process, iterative movement is performed with a sub-pixel step size; in this embodiment, the step size is set to 0.1 pixels. A smaller step size ensures the smoothness and accuracy of the tracking path, avoiding path deviation caused by excessively large step sizes. Numerical integration methods, such as the fourth-order Runge-Kutta method, are used to calculate four intermediate slope values ​​in each step cycle. A weighted average is then used to obtain the final position update, which offers higher accuracy compared to the simple Euler method. The iterative update formula is as follows:

[0065] ;

[0066] in, This represents the position coordinates at the k-th iteration, in pixels. This indicates the step size, which is 0.1 pixels in this embodiment; Represents the gradient vector; This represents the gradient magnitude. s is a direction coefficient used to control the tracking direction: when s=1, it indicates tracking along the positive gradient direction of the gradient vector field (i.e., the direction of increasing potential) until reaching the inner boundary of the high potential, thus obtaining the inner path; when s= A value of 1 indicates that the path is traced along the negative gradient direction of the gradient vector field (i.e., the direction of decreasing potential) until the outer boundary of the low potential is reached, thus obtaining the outer path. A negative sign indicates that the path is moved in the opposite direction of the gradient, i.e., from the high potential to the low potential direction.

[0067] After each iteration, it is determined whether the termination condition is met. The termination condition for streamline tracing includes: when tracing along the positive gradient direction, if the potential value at the current position reaches or exceeds a preset high potential threshold (set to 0.95 in this embodiment), then it is determined that the inner boundary has been reached and tracing stops; when tracing along the negative gradient direction, if the potential value at the current position reaches or falls below a preset low potential threshold (set to 0.05 in this embodiment), then it is determined that the outer boundary has been reached and tracing stops. The potential value is also obtained from the scalar potential field through bilinear interpolation.

[0068] During streamline tracing, the path length of each step is accumulated simultaneously. Since the direction vector of each step has been normalized and the step size is fixed at 0.1 pixels, the path length of each step is the step size value of 0.1 pixels. The sum of the path lengths to the inner boundary and the outer boundary is calculated to obtain the total path length from the starting point to the ending point, which is the pixel value of the insulation layer thickness. To eliminate the systematic error caused by threshold truncation, the sum of the path lengths can be divided by the difference in potential thresholds (0.9) for linear compensation, thereby obtaining the physical full thickness of the insulation layer. If it is necessary to convert to physical units, it needs to be multiplied by the pixel size factor of the image, which is determined by the calibration process. Streamline tracing starting from the thinnest feature point yields the minimum thickness of the insulation layer, and streamline tracing starting from the thickest feature point yields the maximum thickness of the insulation layer. This tracing path corresponds to the physical electric field line path. According to electrostatic field theory, electric field lines are always perpendicular to equipotential surfaces. Therefore, the streamline tracing path must be perpendicular to the inner and outer boundaries of the insulation layer, geometrically corresponding to the shortest Euclidean distance between the inner and outer boundaries. This measurement method conforms to the physical definition of insulation thickness, which is the distance perpendicular to the boundary direction.

[0069] The detection method also includes an eccentricity calculation step: calculating the difference between the maximum and minimum insulation layer thickness, and then calculating the eccentricity by ratio of this difference to the maximum insulation layer thickness. Eccentricity is an important indicator for measuring the uniformity of cable insulation layer thickness, directly affecting the cable's insulation performance and operational safety. The formula for calculating eccentricity is as follows:

[0070] ;

[0071] Where E represents the degree of eccentricity, expressed as a percentage; Indicates the maximum thickness of the insulating layer, in pixels or millimeters; This indicates the minimum thickness of the insulation layer, with the same unit as the maximum thickness. Zero eccentricity indicates a completely uniform insulation layer thickness, while higher eccentricity indicates a more uneven thickness distribution. According to cable industry standards, eccentricity typically needs to be controlled within specified limits to ensure the cable's insulation performance meets usage requirements.

[0072] like Figure 5 The diagram illustrates the insulation layer thickness analysis of the cross-linked insulated cable insulation layer thickness detection method according to an embodiment of this application. The diagram visually displays the final insulation layer thickness measurement results. The red solid line represents the minimum measured insulation layer thickness, and the green solid line represents the maximum thickness. These thickness values ​​are obtained through sub-pixel integration along the gradient streamlines, geometrically corresponding precisely to the shortest distance between the inner and outer boundaries. This detection method offers higher noise immunity and measurement accuracy compared to traditional edge detection.

[0073] The system outputs the minimum and maximum thicknesses of the insulation layer, as well as the eccentricity value, as test results. The electric field flow paths at the thinnest and thickest points can be visualized on an image. The test results can be displayed to operators via a human-machine interface and stored in a database for quality traceability and statistical analysis.

[0074] According to a second aspect of this application, this application also provides a system for detecting the insulation layer thickness of cross-linked insulated cables. Figure 6 This is a structural block diagram of an insulation layer thickness detection system for cross-linked insulated cables according to an embodiment of this application. Figure 6 As shown, the system includes a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement the method for detecting the insulation layer thickness of cross-linked insulated cables according to the first aspect of this application. The system also includes other components well-known to those skilled in the art, such as a communication bus and a communication interface. Their configuration and functions are known in the art and will not be described further here.

[0075] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in this application, based on the technical solution and inventive concept of this application, should be within the scope of protection of this application.

Claims

1. A method for detecting the insulation layer thickness of cross-linked insulated cables, characterized in that, The detection method includes: acquiring a cross-sectional image of a cable, performing region segmentation on the image to identify three topologically connected domains that include at least an inner conductor region, an insulation layer region, and an outer background region, and extracting the boundary contour between the inner conductor and the insulation layer as the inner boundary and the boundary contour between the insulation layer and the background as the outer boundary. A physical field model is established, and first-type boundary conditions are applied to the inner and outer boundaries to set the potential difference. The Laplace equation is solved within the insulating layer region to generate a convergent scalar potential field, which includes the potential value of each pixel. The scalar potential field is differentiated to obtain the gradient vector field and gradient magnitude distribution. A closed virtual equipotential line is extracted within the scalar potential field. The gradient magnitude of each point on the virtual equipotential line is obtained. The maximum and minimum points of the gradient magnitude distribution are searched and marked as the thinnest and thickest feature points, respectively. Starting from the thinnest and thickest feature points, streamline tracing is performed along the positive and negative gradient directions of the gradient vector field, respectively. The first path length to the inner boundary and the second path length to the outer boundary are calculated. The sum of the first and second path lengths is taken as the minimum thickness of the insulating layer. The maximum thickness of the insulating layer is obtained from the thickest feature point.

2. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The region segmentation of the image includes: The cable cross-section image is subjected to noise reduction and smoothing processing; An image segmentation algorithm is used to identify the inner conductor region, the insulating layer region, and the outer background region. Morphological processing is performed on each segmented region to fill the internal holes and smooth the region boundaries.

3. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The process of defining the physical field model includes: The inner conductor region is defined as a high potential source region; The external background region is defined as a low-potential ground region; The insulating layer region is defined as the passive physical field region to be solved.

4. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The application process of the first type of boundary condition includes: The potential value of the inner boundary is fixed to a preset high potential constant. The potential value of the outer boundary is fixed to a preset low potential constant or zero potential.

5. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The process of solving the Laplace equation includes: A discrete grid is constructed within the insulating layer region with a preset grid size, and a discrete difference equation system is established. The discrete difference equations are solved using a numerical iterative algorithm. In each iteration, the potential value of each grid node is updated, and the residual norm of the results of two adjacent iterations is calculated. When the residual norm is less than a preset convergence threshold, the iteration stops and the final scalar potential is output.

6. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The process of extracting the virtual equipotential lines includes: An intermediate potential threshold is set between the highest and lowest potentials of the scalar potential field; Extract the set of pixels in the scalar potential field whose potential value is equal to the intermediate potential threshold, and connect them to form a closed curve as the virtual equipotential line. The virtual equipotential line is located inside the insulating layer region and does not coincide with the physical boundary.

7. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The streamline tracing process is a process of continuously updating the position based on the gradient vector direction of the current position until the boundary is reached; During the position update process, iterative movement is performed using sub-pixel level step sizes.

8. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 7, characterized in that, The termination conditions for the streamline tracing include: When tracking along the positive gradient direction, if the potential value at the current position reaches or exceeds the preset high potential threshold, it is determined that the inner boundary has been reached and tracking stops. When tracking along the negative gradient direction, if the potential value at the current position reaches or falls below the preset low potential threshold, it is determined that the outer boundary has been reached and tracking stops.

9. The method for detecting the insulation layer thickness of cross-linked insulated cables according to claim 1, characterized in that, The detection method also includes an eccentricity calculation step: Calculate the difference between the maximum thickness and the minimum thickness of the insulation layer, and then calculate the eccentricity by comparing the difference with the maximum thickness of the insulation layer.

10. A system for detecting the insulation layer thickness of cross-linked insulated cables, characterized in that, include: processor; A memory, wherein a computer program is stored; When the processor is configured to execute the computer program, it implements the method for detecting the insulation layer thickness of a cross-linked insulated cable as described in any one of claims 1 to 9.

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