Cable treeing defect severity classification method and system based on reflection coefficient spectrum and SDP

Abstract

The application discloses a cable branch defect severity classification method and system based on a reflection coefficient spectrum and an SDP, and comprises the following steps: seven types of cable models are constructed through simulation; reflection coefficient spectrum data sets corresponding to the cable models are obtained; the generated reflection coefficient spectrum data sets are subjected to EMD data feature extraction and input into an SDP model to generate SDP images; the generated SDP images are input into a Resnet model for model training, and a confusion matrix is output to evaluate the classification performance of the Resnet model; reflection coefficient spectrum data of a to-be-tested cable are obtained, the reflection coefficient spectrum data are subjected to EMD data feature extraction, the extracted features are introduced into the SDP model, SDP images of the to-be-tested cable are generated, and the generated feature images are introduced into the trained Resnet model, and a cable defect classification result is output. The application realizes automatic and accurate classification of normal cables, cables containing slight branch defects, cables containing moderate branch defects and cables containing severe branch defects, and effectively overcomes the efficiency bottleneck of manual detection.

Description

Technical Field

[0001] This invention relates to the field of power cable condition detection and fault diagnosis technology, specifically to a method for classifying the severity of dendritic defects in cables based on Reflection Coefficient Spectrum (RCS) combined with Symmetric Point Pattern (SDP) and deep learning, used to distinguish between normal cables, cables with slight dendritic defects, cables with moderate dendritic defects, and cables with severe dendritic defects. Background Technology

[0002] Cross-linked polyethylene (XLPE) cables, due to their excellent electrical insulation, mechanical strength, and laying flexibility, have become a core infrastructure of modern high-voltage power transmission and urban distribution networks. However, under the combined effects of manufacturing defects, moisture intrusion, mechanical damage, and long-term electrothermal aging, the XLPE insulation layer is highly susceptible to two typical dendritic defects: water trees and electrical trees. These defects are the core factors leading to cable insulation breakdown, and their deterioration exhibits a significant staged evolution pattern.

[0003] Accurate classification of the severity of dendritic defects has significant engineering application implications. By distinguishing between four cable grades—normal, minor, moderate, and severe—the insulation health level and remaining service life of cables can be accurately assessed. Furthermore, the classification results can provide a scientific basis for power grid operation and maintenance decisions, promoting a shift in cable operation and maintenance from reactive repair to condition-based maintenance, avoiding resource waste caused by indiscriminate cable replacement, and significantly reducing the probability of sudden power outages caused by insulation failure.

[0004] Cross-linked polyethylene (XLPE) cables, as the core of power transmission, are primarily affected by dendritic defects (such as water trees and electrical trees) that emerge within their insulation layer. In humid environments, water trees slowly degrade insulation performance, and under strong electric fields, they easily evolve into destructive electrical trees. These defects progress from microscopic carbonization channels to fully conductive pathways, signifying a gradual escalation of insulation risk.

[0005] Existing research has employed partial discharge, dielectric loss, and signal processing techniques combined with deep learning to identify cable defects. However, in practical engineering applications, common challenges include weak early-stage defect characteristic signals, overlapping defect characteristics of varying severity, and insufficient identification sensitivity due to complex background noise interference. Furthermore, existing research primarily focuses on binary classification of cable defects, lacking a refined hierarchical assessment of the complete degradation cycle from initial defect initiation to eventual breakdown. Therefore, accurately distinguishing between normal conditions and minor, moderate, and severe dendritic defects through technical means, and achieving hierarchical identification throughout the entire degradation cycle, can enable the development of differentiated operation and maintenance strategies for cables. This will promote the transformation of cable operation and maintenance from reactive repair to condition-based maintenance, effectively reducing power grid operation and maintenance costs and improving power system operational stability, demonstrating significant engineering application value.

[0006] In the existing field of cable defect detection, the reflection coefficient spectrum, as a key characterization method in the frequency domain reflection method, has been widely used in defect spatial localization due to its high sensitivity to impedance mismatch. However, this technique is primarily used for defect spatial localization, and research on the correlation between reflection coefficient spectrum characteristics and the degree of dendritic defect evolution is insufficient, making it difficult to achieve precise differentiation from early-stage degradation to late-stage defects. Summary of the Invention

[0007] To address the technical challenge of low correlation between signal characteristics and insulation degradation in existing cable defect identification technologies, this invention proposes a method for classifying the severity of dendritic defects in cables by integrating reflection coefficient spectrum, symmetric point patterns, and deep learning. This method uses the reflection coefficient spectrum as the core signal representation carrier, leveraging its high sensitivity to impedance mismatch to capture waveform variations in reflected signals induced by cable defects. Subsequently, Empirical Mode Decomposition (EMD) is introduced to extract features and reconstruct the one-dimensional spectral signal through noise reduction. SDP transformation is then used to map the reconstructed feature sequence into a two-dimensional fingerprint image with rich texture and geometric symmetry, effectively highlighting subtle feature differences caused by minor defects. Finally, by constructing a ResNet for end-to-end feature self-learning, automated and accurate classification of dendritic defects at four levels—normal, minor, moderate, and severe—is achieved, overcoming the shortcomings of existing research in refined grading and assessment of defects throughout their entire lifecycle.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP includes the following steps: Step 1: Based on the differentiated impact of dendritic defects of varying severity on cable insulation properties, multiple cable models are constructed through simulation; through simulation calculations, the reflection coefficient spectrum dataset corresponding to each cable model is obtained. Step 2: Extract EMD data features from the reflectance coefficient spectrum dataset generated in Step 1, and input the extracted EMD data features into the SDP model to generate an SDP image; Step 3: Input the SDP image generated in Step 2 into the ResNet model for model training, and output the confusion matrix to evaluate the classification performance of the ResNet model; Step 4: Obtain the reflection coefficient spectrum data of the cable under test, extract data features and import them into the SDP model to obtain feature maps. Import the generated feature maps into the trained ResNet model and output the cable defect classification results.

[0009] In step 1, various cable models are used, including a normal cable model, a cable model with slight electrical tree defects, a cable model with moderate electrical tree defects, a cable model with severe electrical tree defects, a cable model with slight water tree defects, a cable model with moderate water tree defects, and a cable model with severe water tree defects.

[0010] Step 1 includes the following steps: 1.1: A three-layer cable model consisting of a conductor layer, an insulation layer, and a shielding layer is constructed through simulation, and the reflection coefficient spectrum is used as the basic data for defect characterization; Dendritic defects of varying severity exhibit significant differences in defect morphology, dielectric parameter disturbance amplitude, and spatial distribution range. These differences lead to distinguishable characteristic variations in the amplitude, phase, and frequency domain details of the reflection coefficient spectrum. This invention establishes a high-precision cable transmission line model to quantitatively characterize the signal transmission characteristics of defective cables. Simultaneously, it introduces feature extraction and image representation methods based on the reflection coefficient spectrum to achieve intelligent identification and classification of cable defect severity.

[0011] Figure 2 It is an equivalent model of a cable containing local abnormal sections, used to simulate the changes in electromagnetic properties of the cable caused by abnormal structural or material parameters.

[0012] exist Figure 2 In the model shown, the cable head end To the beginning of the abnormal section This is the normal section of the cable, with standard distributed electrical parameters.

[0013] abnormal section start point To the abnormal section terminal This is the defect-affected zone, where the electrical distribution parameters change depending on the defect state.

[0014] Abnormal section terminal To cable terminal For the normal section after the defect, the electrical parameters of the cable are restored to the standard state.

[0015] Figure 3 This is an equivalent schematic diagram of a cable local defect detection system based on the reflection method. The system consists of a data acquisition and control unit and the cable under test. The data acquisition and control unit includes a host computer and a network analyzer. The cable under test includes a cable core, insulation layer, and shielding layer. It can realize the complete process of signal injection, transmission, and reflection signal acquisition. After the detection signal is injected into the cable under test, when the incident wave propagates to the defect location, the impedance and propagation constant of the defect region change abruptly, triggering electromagnetic wave reflection and refraction phenomena. The reflected wave is collected by the network analyzer to generate reflection coefficient spectrum data. The refracted wave continues to propagate towards the cable end, and its energy and phase changes can be used to assist in verifying the existence and location of the defect.

[0016] Based on this, this invention uses EMD to extract features from the collected reflectance coefficient spectrum data, decomposing the reflectance coefficient spectrum into multi-order intrinsic mode components to construct feature sequences characterizing different defect levels. SDP images are generated using EMD features according to a preset mapping rule, realizing the conversion from one-dimensional spectral data to two-dimensional texture images, thereby enhancing the differential representation between cables with slight dendritic defects, severe dendritic defects, and normal cables. The generated SDP images are input into an image classification model based on a ResNet residual network for training and inference, outputting cable state categories to achieve accurate differentiation between normal cables, cables with slight dendritic defects, and cables with severe dendritic defects.

[0017] Dendritic defects inside the insulation layer are used to simulate the actual growth morphology and spatial distribution characteristics of electrical or water trees. By adjusting the equivalent dielectric constant and equivalent conductivity in the defect-affected area, the difference in electromagnetic propagation characteristics between defective and intact insulation media is characterized. The difference in defect degree is mapped to the reflection coefficient spectrum and its EMD-SDP image features, providing a learnable discrimination basis for ResNet classification.

[0018] 1.2: The phase-field method is used to simulate the evolution process of dendritic defects in cable insulation. This method drives the dielectric to spontaneously form an equivalent conductive channel in the high electric field region by coupling the electric field and the damage field, thereby realizing the simulation of the growth and expansion of dendritic breakdown defects. Damage field using scalar variables Characterizing the degree of media degradation, where: Indicates a good medium. This indicates complete damage, and it dynamically evolves from 1 to 0 over time under the influence of electric field energy. Figure 4(a) shows a simulation model of a defect-free and intact cable with a complete cable insulation structure.

[0019] Figure 4(b) shows a model of a slight dendritic defect, where the defect begins to grow but its influence is small.

[0020] Figure 4(c) shows a model of moderate defects.

[0021] Figure 4(d) shows a severe dendritic defect, which is close to a through-breakdown, and the cable is approaching a failure state.

[0022] In the three-layer cable model shown in Figure 4(a), a high potential is applied to the core conductor as a high-voltage electric field source, and a grounded low-potential boundary is set in the shielding layer, forming a radial electric field from the conductor to the shielding layer inside the insulation layer. The normal cable model does not have any defective structures.

[0023] 1.3: Calculate the cable's resistance, inductance, conductance, capacitance, and characteristic impedance using the electrical parameter calculation formulas: (1); (2); (3); (4); (5); In the formula: The resistance per unit length of the cable; Permeability of free space; Angular frequency; , These are the cable core radius and the inner radius of the shielding layer, respectively. , These are the resistivity of the cable core and the resistivity of the shielding layer, respectively. Inductance per unit length of cable; Capacitance per unit length of cable; is the dielectric constant of the dielectric. The electrical conductivity per unit length of the cable; The conductivity of the dielectric. This is the characteristic impedance of the cable; It is the imaginary unit.

[0024] 1.4: According to transmission line theory, the key electromagnetic parameters such as dielectric constant and conductivity in the defective region of the cable's electrical tree are significantly different from those in the intact insulation medium, resulting in a significant difference in the reflection coefficient spectrum characteristics of the defective cable and the normal cable. After calculating the electrical parameters and characteristic impedance of the normal and defective sections of the cable using formulas (1) to (5), the reflection coefficient spectrum of the defective cable is then solved using the following characteristic impedance and reflection coefficient correlation formulas (6) to (10). : (6); (7); (8); (9); (10); (11); In the formula: , and These are the distances from the first section of the cable. , and Input impedance at the location; , and These are the distances from the first section of the cable. , and Reflectance coefficient at that location; and These are the propagation constants for the normal segment and the defective segment, respectively; The characteristic impedance of the defective section of the cable. This is the characteristic impedance of a normal cable; This is the characteristic impedance of a normal cable. Indicates the total length of the cable.

[0025] 1.5: By adjusting the dielectric constant and conductivity parameters of the medium in the defect region, the electromagnetic characteristics of electrical tree defects and water tree defects in the cable are simulated respectively, while the insulation medium parameters of the normal cable model remain unchanged; Figure 5(a) shows the electric field distribution of a cable containing electrical tree defects. Figure 5(b) shows the electric field distribution of a cable containing water tree defects.

[0026] Based on the established water-tree cable model, electric tree cable model, and normal cable model, the resistance, conductance, inductance, capacitance, and characteristic impedance of the three types of cable models are calculated according to formulas (1) to (5); then, the reflection coefficient spectrum of the three types of cables is calculated using formulas (6) to (11). Finally, a structured reflection coefficient spectrum dataset is constructed and stored.

[0027] Step 2 includes the following steps: Step 2.1: Import the reflection coefficient spectrum data of normal cables, cables with slight dendritic defects, and cables with severe dendritic defects from the reflection coefficient spectrum dataset into the processing flow. The reflection coefficient spectrum data is a complex sequence obtained from actual measurement or simulation, and its amplitude spectrum can be used as the input signal for subsequent feature extraction; Step 2.2: Perform EMD feature extraction, standardization preprocessing, and SDP image generation on the reflectance coefficient spectrum data in sequence.

[0028] Step 2.2 specifically includes: Step 2.2.1: Analyze and preprocess the complex signal of the reflection coefficient spectrum, extract the reflection coefficient amplitude sequence as a one-dimensional input signal, and unify the one-dimensional input signal to a fixed length. If the length exceeds the limit, the excess part will be truncated to ensure that all sample data have the same dimension. Step 2.2.2: Subsequently, EMD is performed on the one-dimensional input signal to decompose the signal into several intrinsic mode function (IMF) components and residual terms. The specific decomposition formula is as follows: (12); In the formula: The input signal is one-dimensional. The first decomposition obtained Each intrinsic mode function component (IMF) represents a local characteristic oscillation component of the signal in different frequency bands, from high to low. The residual term represents the overall trend of the signal or the DC bias baseline; This represents the total number of IMF components obtained from the decomposition.

[0029] The first few IMF components are selected and summed for reconstruction, which enhances the core oscillation characteristics of the signal while reducing noise interference, resulting in the characteristic signal of the reflection coefficient spectrum. The reconstruction formula is as follows: (13); In the formula: The reconstructed discrete feature signal sequence; The number of reconstructed components is preset, and satisfies the following conditions: Since the core fault pulses and discontinuity oscillations in the reflected signal are mainly concentrated in the first few high-frequency IMF components, while random noise and baseline drift are usually distributed in the remaining low-frequency components or residual terms, by limiting the extraction of the first few components... By superimposing and reconstructing the core components, background noise can be effectively filtered out, highlighting the reflection anomalies caused by faults.

[0030] Step 2.2.3: Perform mean removal and normalization on the reconstructed feature signal, and map it to... The interval, used as the input sequence for SDP generation, is reconstructed using the following specific formula: (14); (15); In the formula, For the mean-removed signal; For normalized feature sequences; This represents the total number of sample points in the characteristic signal sequence. and These are mean-reduced signal sequences. Maximum and minimum values Step 2.2.4: Input the normalized feature sequence into the SDP image generation module, based on the preset number of symmetry planes. Angular magnification factor Delay parameters Once the SDP parameters have completed the data transformation, the one-dimensional feature sequence is converted into a two-dimensional SDP image. For the normalized feature sequence... , its first Each sampling point and its time delay Subsequent sampling points In polar coordinates, this is mapped to symmetrical pairs of coordinate points. and The formulas for calculating its polar radius and polar angle are as follows: (16); (17); (18); In the formula: The polar radius directly reflects the signal amplitude at the current position; and respectively along the first The polar angles of the clockwise and counterclockwise expansion on both sides of the axis of symmetry; This is a delay parameter used to capture the temporal correlation characteristics of the signal; Let be the angular magnification factor, satisfying ; For the first The initial deflection angle of each symmetric plane.

[0031] Since there are significant differences between slight and severe dendritic defects in the detailed structure and oscillation characteristics of the reflection coefficient spectrum, these differences are further highlighted after EMD reconstruction. The generated SDP image exhibits distinguishable image features in terms of texture density, symmetry structure, and energy distribution, providing stable input for subsequent deep network classification.

[0032] Step 3 includes the following steps: Step 3.1: Store the SDP images corresponding to each cable model generated in Step 2 according to seven preset categories: normal, slight electrical tree defects, moderate electrical tree defects, severe electrical tree defects, slight water tree defects, moderate water tree defects, and severe water tree defects, and construct the corresponding image dataset, using the folder to which the image belongs as the source of the category label; randomly divide the image dataset to obtain the training set for model training and the validation set for performance verification.

[0033] Step 3.2: Adjust the size of the SDP image uniformly and perform channel expansion processing on the single-channel grayscale image. The single-channel grayscale image generated by the one-dimensional feature sequence is copied and superimposed in the channel dimension, and the single-channel feature matrix is ​​expanded into a three-channel pseudo-color image matrix, so that the expanded red (R), green (G), and blue (B) channels have the same numerical distribution of pixel intensity to meet the input requirements of the ResNet model.

[0034] Step 3.3: Select the ResNet model as the base model for image classification and adaptively adjust its output layer structure by replacing the fully connected layer and classification layer at the end of the network to make the number of output categories of the model consistent with the target classification task.

[0035] Step 3.4: During the model training phase, iteratively correct the network's internal parameters based on the gradient descent optimization algorithm; The expanded three-channel image is input into the network for forward propagation. The original scores for each defect category are output through the last fully connected layer of the network. A focus loss function is introduced to calculate the loss value between the network output and the true label. This is to force the model to focus on learning the misclassified samples that are difficult to classify by adjusting the dynamic weights. The formula for calculating the loss function is as follows: (19); In the formula: The size of the current training batch; The category weight coefficient is dynamically calculated based on the reciprocal of the number of samples in each category, and is used to counteract the imbalance in the number of normal cable samples and defective samples. The focus parameter is used to reduce the loss contribution weight of easily classified samples; This represents the probability value that the model predicts the defect to be of the true defect category. Subsequently, the gradient of the loss value with respect to the weights and bias parameters of each layer in the network is calculated using the backpropagation algorithm, and the internal parameters of the network are iteratively corrected using an adaptive matrix estimation optimization algorithm. The parameter update formula is as follows: (20); In the formula: These are the network weights or bias parameters for the current round; This is the learning rate for the current iteration, and the learning rate is dynamically adjusted using a cosine annealing algorithm. and These are the adaptive estimates of the first and second moments of the gradient after bias correction, respectively; This is the weight decay coefficient, used to prevent network overfitting; To prevent smooth terms with a denominator of zero; The Softmax function outputs the probability of each category, and its specific calculation formula is as follows: (twenty one); In the formula: In this embodiment, the preset total number of categories is used. ; The first output of the fully connected layer at the end of the network The original unnormalized scores for each defect category; The input image obtained after mapping by the Softmax function belongs to the first... The normalized probability values ​​of each preset category, and satisfying The network will eventually output probability values. The largest corresponding defect category is used as the final identification result to achieve classification and identification of SDP images of cables in different states; Step 3.5: After training, evaluate the classification performance of the ResNet model based on the validation set, and output the classification accuracy and confusion matrix. The classification accuracy is used to evaluate the model's overall accuracy in identifying cable states, and its calculation formula is as follows: ; In the formula: To verify the total number of cable SDP images correctly classified by the ResNet model in the set, The total number of samples in the validation set; The confusion matrix is ​​a matrix of size [size missing]. (Right now A two-dimensional statistical matrix, where any element in the matrix... Indicates the true category is the first Class, but predicted by the ResNet model as the first Number of cable sample images of class; where: when In this case, the elements on the main diagonal of the matrix represent the number of correctly identified defects of each category, while the elements outside the diagonal represent the distribution of misclassifications among different defect severity levels or different defect types. This is used to quantitatively evaluate the model's fine-grained identification performance among normal conditions, electrical tree defects, and water tree defects, in order to obtain a ResNet model for cable defect identification.

[0036] In step 4, the reflection coefficient spectrum of the cable under test is measured using a network analyzer. and the reflection coefficient spectrum The data is transmitted to the host computer, EMD and SDP are imported, corresponding SDP images are generated, and then the SDP images are input into the trained ResNet module to obtain the classification results of the severity of cable defects.

[0037] This invention provides a method and system for classifying the severity of dendritic defects in cables based on reflection coefficient spectrum and SDP, which has the following technical advantages: 1) This invention innovatively introduces EMD and SDP imagery methods to transform one-dimensional cable reflection coefficient spectrum data into two-dimensional SDP images with rich texture features. This method can intuitively present the subtle impedance changes caused by minor dendritic defects through the symmetrical structure and point density distribution of the SDP image, effectively highlighting the characteristic differences between different defect degrees, and solving the technical problem of insignificant and difficult-to-distinguish features in the early identification of minor defects in traditional one-dimensional spectrum analysis.

[0038] 2) This invention utilizes ResNet to construct an end-to-end image classification model, achieving automated and precise classification of normal cables, cables with minor dendritic defects, cables with moderate dendritic defects, and cables with severe dendritic defects. Unlike traditional methods that can only distinguish between normal operation and fault states, this invention can accurately identify the development stage of defects. Maintenance personnel can formulate maintenance strategies in the early stages of defect development, effectively avoiding sudden cable breakdown accidents caused by missed diagnoses of severe defects, and significantly improving diagnostic efficiency and the reliability of power grid operation.

[0039] 3) This invention designs and constructs a highly integrated visual diagnostic interactive interface, enhancing the on-site adaptability and human-machine operation convenience of the detection system. The interface integrates underlying signal analysis and deep learning computation processes, simultaneously and graphically displaying two-dimensional feature images of the cable's original spectral data and defect level judgment conclusions. The visual operation mode reduces the data analysis difficulty for on-site personnel; staff do not need to be familiar with the algorithm's internal principles to quickly obtain cable operating status assessment conclusions, thus promoting the application of theoretical algorithms to actual power operation and maintenance scenarios. Attached Figure Description

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the process of the present invention.

[0041] Figure 2 This is an equivalent model for a cable transmission line containing local defects.

[0042] Figure 3 This is an equivalent schematic diagram of a cable local defect detection system based on the reflection method.

[0043] Figure 4(a) is a schematic diagram of the finite element simulation model containing a normal cable; Figure 4(b) is a schematic diagram of the finite element simulation model of a cable with slight dendritic defects; Figure 4(c) is a schematic diagram of the finite element simulation model of a cable with moderate dendritic defects; Figure 4(d) is a schematic diagram of the finite element simulation model of a cable with severe dendritic defects.

[0044] Figure 5(a) shows the electric field diagram of a cable containing electrical tree defects; Figure 5(b) shows the electric field diagram of a cable containing water tree defects.

[0045] Figure 6(a) shows the confusion matrix of the ResNet model characterizing the classification performance of cables with electrical tree defects; Figure 6(b) shows the accuracy of the ResNet model in characterizing the severity classification performance of cables with electrical tree defects.

[0046] Figure 7(a) shows the confusion matrix of the ResNet model characterizing the classification performance of cables with water tree defects. Figure 7(b) shows the accuracy of the ResNet model in characterizing the severity classification performance of cables with water tree defects.

[0047] Figure 8 The confusion matrix is ​​used to characterize the classification performance of ResNet models for the severity of cables with electrical tree and water tree defects.

[0048] Figure 9 This is the user interface for cable state classification software based on a trained ResNet model. Detailed Implementation

[0049] Example 1: The cable dendritic defect severity classification system based on reflection coefficient spectrum and SDP consists of two main parts: a data acquisition and control unit and the cable under test. The data acquisition and control unit is composed of a network analyzer and a host computer.

[0050] The network analyzer is a vector network analyzer. Its test port is connected to the beginning of the cable under test via a measurement cable. It injects a swept-frequency detection signal into the cable and simultaneously receives reflected signals from points of impedance discontinuity within the cable. After processing the reflected signals, the network analyzer generates reflection coefficient spectrum data for the cable under test. The network analyzer's data communication interface connects to a host computer, transmitting the reflection coefficient spectrum data to the host computer in real time.

[0051] The host computer is equipped with an Empirical Mode Decomposition (EMD) module, a Symmetric Point Pattern (SDP) image generation module, and a trained ResNet model. After receiving the reflection coefficient spectrum data, the host computer first extracts the reflection coefficient amplitude sequence and performs EMD, selects the main intrinsic mode function components to reconstruct the feature signal, and then performs mean removal and normalization processing. Subsequently, the processed feature sequence is input into the Symmetric Point Pattern (SDP) image generation module, which transforms the one-dimensional feature sequence into a two-dimensional SDP image with texture and geometric symmetry features through symmetry mapping in polar coordinates. Finally, the SDP image is input into the trained ResNet model, and the ResNet model outputs the defect severity classification result of the tested cable.

[0052] The cable under test is a cross-linked polyethylene (XLPE) cable, which consists of a three-layer structure: a core, an insulation layer, and a shielding layer. The dendritic defect regions inside the cable caused by aging or damage will cause changes in the local characteristic impedance and propagation constant, which in turn will lead to characteristic differences in the amplitude, phase, and frequency domain details of the reflection coefficient spectrum corresponding to the severity of the defect.

[0053] This system achieves automated output from the original reflection coefficient spectrum to the defect level determination result through the entire process of signal injection, reflection acquisition, spectrum transformation, image mapping and deep learning inference, effectively overcoming the efficiency bottleneck of manual inspection.

[0054] A method for classifying the severity of dendritic defects in cables based on reflection coefficient spectrum and SDP (Self-Depth Difference) is proposed. This method utilizes cable reflection coefficient spectrum data, extracts effective signals using EMD (Effective Microscopy) to suppress noise interference, and maps the one-dimensional spectral signal to a two-dimensional SDP image with rich texture features through SDP transformation. A ResNet model is then trained based on this image. By leveraging the geometric shape and pixel distribution features of images corresponding to different defect severity levels in the SDP image, the model can deeply mine subtle differences hidden in the data, thereby achieving high-precision automated classification and identification of insulation defect severity.

[0055] To clearly illustrate the aforementioned technical principles and engineering application value, this invention provides four progressively layered embodiments: Embodiments 2 to 4 aim to verify the model's diagnostic capabilities for different single and complex defects, detailing the severity classification process for electrical tree defects, water tree defects, and mixed electrical and water tree defects; Embodiment 5 focuses on practical engineering applications, introducing the classification application of this method on actual cables, and highlighting the accompanying visual diagnostic software and interactive interface developed to assist maintenance personnel. These four embodiments, progressing from single defects to complex defects, and extending from the core algorithm to practical software applications, fully demonstrate the complete technical loop of this invention from theoretical model to engineering site.

[0056] Example 2: a1: Construct a cable simulation model and obtain reflection coefficient spectrum data.

[0057] Based on the influence of electrical treeing at different development stages on insulation properties, simulation models for four types of cables were established, and the corresponding reflection coefficient spectra were solved. The steps include: a1.1: A finite element simulation model of the XLPE cable, consistent with the actual structure, was constructed. This model consists of a conductor layer, an insulation layer, and a shielding layer, as shown in Figure 4(a), completely reproducing the key structural layers of the cable. In the model, the conductor layer serves as the high-voltage electrode, simulating the actual function of the cable core, and its outer diameter is set to 20.8 mm. The insulation layer uses cross-linked polyethylene material, possessing nonlinear properties, and its thickness is set to 20.5 mm, corresponding to the main insulation part of the cable. The shielding layer serves as the grounding electrode, with a thickness of 4 mm. Figure 4(a) visually shows the spatial arrangement of this three-layer structure.

[0058] a1.2: The phase-field method is used to dynamically simulate the generation process of cable insulation defects. This method, based on the interaction mechanism between electric field strength and material damage, can reproduce the development process of dendritic defects from slight to severe. In the simulation, when the electric field in a local area of ​​the cable exceeds the critical threshold, the insulation material gradually evolves from an intact state to a breakdown state, spontaneously forming dendritic conductive channels. The dendritic defects extend from the high-field-strength conductor region to the low-field-strength shielding region until they penetrate the entire insulation structure.

[0059] To quantify the severity of defects, this simulation categorizes them based on the proportion of dendritic defect length to the total insulation thickness: less than 20% is defined as a minor defect, 20% to 60% as a moderate defect, and greater than 60% as a severe defect. For electrical treeing defects, the generated tree channels are filled with air, which has a dielectric constant of 1 and a conductivity of 100 S / m, to simulate actual physical characteristics; the normal cable model does not include any treeing defects.

[0060] a1.3: Establish 50 normal cable models, 50 cable models with slight electrical tree defects, 50 cable models with moderate electrical tree defects, and 50 models with severe electrical tree defects, and calculate the corresponding reflection coefficient spectrum data.

[0061] a2: A feature extraction and image representation method based on empirical mode decomposition and symmetric point patterns.

[0062] To effectively identify and classify the severity of cable insulation defects, this invention proposes a feature extraction and image representation method for EMD and SDP. This method takes the reflection coefficient amplitude sequence as input and, through adaptive signal decomposition and pattern mapping, transforms the one-dimensional signal into discriminative two-dimensional image features. Specifically, it includes the following steps: a2.1: Reflection Eigendecomposition and Reconstruction Based on Empirical Mode Decomposition First, the measured complex-form reflectance coefficient data are preprocessed to extract the amplitude sequence of the reflectance coefficients as the analysis object. To eliminate length differences between different samples, the amplitude sequence is truncated or zero-padding is used to make its length uniform.

[0063] Subsequently, the reflection coefficient amplitude sequence is adaptively decomposed using an empirical mode decomposition algorithm, resulting in several intrinsic mode functions (IMFs) arranged from high frequency to low frequency. Each IMF component characterizes the oscillation characteristics of the signal at different time scales.

[0064] Based on the characteristic that defect information is mainly concentrated in high-frequency and mid-frequency components, the first few IMF components are selected for superposition and reconstruction to obtain a reconstructed signal containing the main defect features. To avoid the influence of DC components on subsequent image generation, the reconstructed signal is subjected to mean removal processing and further normalized to a preset interval, thereby obtaining a stable and scale-uniform feature sequence.

[0065] a2.2: Feature Image Representation Based on Symmetric Point Patterns The normalized feature sequence obtained in step a2.1 is used as input to the symmetric point pattern generator. The symmetric point pattern generator maps the one-dimensional feature sequence into a two-dimensional point lattice structure by introducing a multi-plane symmetric mapping mechanism in the polar coordinate system.

[0066] Specifically, based on the set number of symmetry planes, angle magnification factor, and time delay parameter, the amplitude at different times in the feature sequence is geometrically mapped and symmetrically projected to generate a two-dimensional image with repeatability, symmetry, and texture structure. The differences in reflection characteristics corresponding to different degrees of cable insulation defects will be manifested in the SDP image as significantly different point distribution patterns and texture features.

[0067] In this way, one-dimensional signal features that are originally difficult to distinguish directly are transformed into two-dimensional image representations with high separability, thereby providing effective input for subsequent image-based pattern recognition.

[0068] a2.3: Construction of SDP Feature Image Dataset.

[0069] Repeat steps a2.1 and a2.2 for all samples to be analyzed to generate corresponding SDP feature images. Based on the actual detection results or preset standards of cable insulation defects, label the severity of defects in the generated SDP images and store and manage them according to categories: normal, minor, moderate, and severe. Construct an image dataset for defect identification and classification.

[0070] This dataset can be directly used for subsequent training and testing of machine learning or deep learning models, thereby enabling automatic identification and classification of the severity of cable insulation defects.

[0071] a3: SDP Image Classification and Model Validation Based on Deep Residual Networks

[0072] After generating the SDP feature image as described in step a2, a ResNet image classification model is built to automatically identify and classify the severity of cable insulation defects. The defect levels include four categories: normal, minor, moderate, and severe.

[0073] a3.1: Construction and partitioning of the SDP image dataset.

[0074] The SDP feature images generated in step a2 are stored in corresponding category folders according to the severity of defects. The folder names correspond to four defect level labels: "Normal," "Minor," "Moderate," and "Severe." The main directory and its subdirectories are recursively read through an image data reading mechanism, and the folder names are used as image category labels to achieve automatic association between image samples and category labels.

[0075] Subsequently, the entire SDP image dataset was randomly divided into a training set and a validation set, with the training set accounting for 80% and the validation set accounting for 20%, for performance evaluation and generalization capability verification during model training.

[0076] a3.2: Construction and training of ResNet-18 classification model.

[0077] A ResNet-18 deep residual convolutional neural network was selected as the defect severity classification model. Given that SDP images primarily exhibit geometric symmetry and local texture features, the feature extraction capabilities of ResNet-18 are sufficient to meet the requirements. Furthermore, it effectively avoids overfitting on a limited sample set due to excessive model complexity, thus improving the model's generalization performance and training efficiency. In this embodiment, the ResNet-18 network is initialized without pre-trained weights, allowing the model parameters to be trained end-to-end entirely based on the SDP image dataset.

[0078] For the four-class classification task, the terminal structure of the ResNet-18 network is adaptively adjusted: while keeping the structure and connection relationships of the other layers of the network unchanged, the last fully connected layer of the original network is replaced so that the number of output nodes is consistent with the number of defect categories, and the classification output layer is replaced at the same time, thereby constructing a deep residual network model suitable for the four-class classification tasks of normal, mild, moderate and severe.

[0079] a3.3: Input image preprocessing and channel adaptation.

[0080] The SDP images in both the training and validation sets are uniformly adjusted to the input size required by the ResNet-18 network. Since SDP images are usually single-channel grayscale images, in order to meet the network's three-channel input requirement, the grayscale images are subjected to channel expansion processing to convert them into a three-channel format, thereby ensuring the consistency of the network's input dimensions.

[0081] a3.4: Model training strategy.

[0082] The ResNet-18 network was trained using the Stochastic Gradient Descent Momentum (SGDM) optimization algorithm. During training, a fixed mini-batch sample input method was used, with the sample order randomly shuffled in each training epoch. A maximum number of training epochs and an initial learning rate were set, and a validation set was periodically introduced during training to verify performance and monitor the model's convergence and generalization ability. After training, a cable insulation defect severity identification model based on SDP images was obtained.

[0083] a3.5: Model Validation and Classification Performance Analysis.

[0084] The trained model was used to perform classification predictions on the test set. The consistency rate between the predicted and true classes was calculated as the classification accuracy evaluation index. The recognition effect among the four states was visualized and analyzed using a confusion matrix to evaluate the model's ability to distinguish different defect severity levels. Figure 6(a) shows the confusion matrix representing the classification performance of the ResNet model on cables with dendritic defects, and Figure 6(b) shows the test set accuracy evaluation results of the model.

[0085] As shown in Figure 6(a), the model proposed in this invention achieved excellent quantitative results in the identification of various features: a total of 42 intact cable samples and 20 samples with severe electrical tree defects were identified, with an accuracy rate of 100% for both types of samples, with no misclassifications or omissions. For early and mid-stage defects with small feature differences and easy confusion, the model still maintained extremely high sensitivity and classification level. Among the 20 samples with moderate electrical tree defects, 18 samples were correctly identified, with a classification accuracy rate of 90%; and among the 20 samples with slight electrical tree defects, 19 samples were correctly identified, with a classification accuracy rate of 95%. Combined with the quantitative evaluation results in Figure 6(b), the final comprehensive classification accuracy of the model on the entire test set reached 97.06%. The above detailed quantitative diagnostic data fully demonstrates that the classification method based on reflectance coefficient spectrum and SDP image combined with ResNet can accurately extract and amplify the subtle feature differences between different defect degrees, providing strong support for the feasibility and effectiveness of this method in the refined classification and diagnosis of actual cable defects.

[0086] Example 3: This embodiment aims to solve the technical problem of the difficulty in quantitatively assessing the degree of water tree aging in cross-linked polyethylene cables, and proposes a cable defect detection scheme that integrates signal mode decomposition and visual perception technologies.

[0087] b1: Establish a water tree aging simulation model and generate a sample library.

[0088] Given that water trees are microporous structures formed by water and ions penetrating an insulating layer under the influence of an electric field, their dielectric constant is significantly higher than that of normal insulating materials. This step simulates this change in physical properties using finite element simulation, and the specific steps are as follows: b1.1: Physical field modeling.

[0089] A three-dimensional electromagnetic simulation model of the XLPE cable was established, with the geometric parameters of the model set to be the same as those of the cable containing electrical tree defects. b1.2: The phase field method is used to dynamically simulate the generation of cable insulation.

[0090] Based on the coupling mechanism between electric field and material damage, the phase-field method was used to dynamically simulate the complete evolution process of water trees in cable insulation. Simulation results show that when the local electric field strength of the cable exceeds the critical threshold, dendritic conductive channels will spontaneously emerge inside the insulation medium. The defect structure gradually extends from the high-field-strength conductor region to the low-field-strength shielding region, eventually penetrating the entire insulation structure and causing insulation breakdown faults.

[0091] b1.3: Defect Classification and Data Generation: Based on the percentage of water tree erosion depth to insulation layer thickness, the simulation categorizes defect severity into three levels according to the proportion of tree branch length: minor (<20%), moderate (20%-60%), and severe (>60%). For water tree defects, the generated tree channels are filled with materials having a dielectric constant of 5 and a conductivity of 1×10⁻⁶. -11 The water medium with a reflectance ratio of S / m was used to simulate actual physical properties. Fifty simulation models were generated for each of the four states: normal, slight, moderate, and severe. The corresponding reflectance coefficient spectrum data were calculated using a frequency domain solver to form the original sample library.

[0092] b2: Signal enhancement and multidimensional visualization transformation based on EMD-SDP.

[0093] To address the nonlinear and non-stationary characteristics of reflected signals, the following strategy is employed to transform them into image features recognizable by machine vision: b2.1: Extract features using EMD.

[0094] The reflection coefficient is preprocessed to extract the amplitude sequence relative to the characteristic impedance, and length alignment is achieved through truncation or zero-padding. Subsequently, EMD is used to adaptively decompose the sequence into a set of IMFs arranged from high frequency to low frequency. Finally, high- and mid-frequency IMF components rich in defect information are selected for signal reconstruction, and after mean removal and normalization, the influence of DC components is eliminated and the scale is unified to extract a stable feature sequence.

[0095] b2.2: Feature image representation based on SDP.

[0096] The normalized sequence extracted in step S2.1 is input into the SDP generator. Utilizing a multi-plane symmetry mapping mechanism in polar coordinates, the one-dimensional time-domain features are transformed into a two-dimensional spatial lattice structure. By optimizing key parameters such as the number of symmetry planes, angular amplification factor, and time delay, the signal amplitude is mapped in a geometric projection form to a two-dimensional image with significant texture and symmetry. The severity of cable insulation defects will be intuitively reflected in the differences in lattice distribution and texture morphology in the SDP image, thus achieving the conversion of one-dimensional features into highly separable two-dimensional features.

[0097] b2.3: ​​Construction of SDP feature image dataset.

[0098] The above process is executed across all samples to generate corresponding SDP images in batches. Based on the detection standards, the images are divided into four levels: normal, minor, moderate, and severe, and labeled accordingly, constructing a structured defect identification dataset. This dataset can directly support the training and validation of subsequent machine learning or deep learning models, providing a data foundation for the intelligent and automatic grading of cable insulation conditions.

[0099] b3: SDP image classification and model validation based on deep residual networks.

[0100] This stage utilizes the Resnet-18 network to automatically identify the generated images, achieving accurate classification of cable insulation defects. The classification categories include four types: intact, minor, moderate, and severe.

[0101] b3.1: Dataset construction and preprocessing.

[0102] Defect labels are automatically associated by recursively reading subdirectory names. The dataset is randomly divided into training and validation sets in an 8:2 ratio to ensure good generalization ability of the model. Generated images are uniformly scaled to the network's standard size. For single-channel grayscale images, channel expansion techniques are used to convert them into a three-channel format to meet the input dimension requirements of ResNet-18.

[0103] b3.2: ResNet-18 model construction and training strategy.

[0104] The ResNet-18 architecture was chosen. Its residual structure effectively avoids gradient vanishing while maintaining feature extraction depth, and its moderate model complexity prevents overfitting on finite SDP sample sets. The pre-defined convolutional layers were retained, and the terminal fully connected layers and classification layers were modified to have four output nodes to achieve a four-class classification task. For specific settings, refer to the electrical tree implementation example.

[0105] b3.3: Classification Validation and Effectiveness Evaluation.

[0106] The model's recognition accuracy is evaluated by calculating the prediction accuracy on the validation set. A confusion matrix is ​​introduced to visualize and analyze the false positives and false negatives between different levels, providing an in-depth analysis of the model's ability to identify defects of different severity. Figure 7(a) shows the confusion matrix representing the ResNet model's performance in classifying the severity of cables containing water tree dendritic defects, clearly showing which defect types were misclassified. Figure 7(b) shows the accuracy of the ResNet model in classifying the severity of cables containing water tree dendritic defects, demonstrating an accuracy rate of 92.16%.

[0107] Example 4: This embodiment addresses the common electrical tree and water tree defects in cross-linked polyethylene cables by classifying the cable insulation status into seven categories: normal cable, slightly electrical tree aged cable, moderately electrical tree aged cable, severely electrical tree aged cable, slightly water tree aged cable, moderately water tree aged cable, and severely water tree aged cable, thereby achieving accurate classification and identification of multiple insulation statuses.

[0108] c1: Establish simulation model and generate sample library.

[0109] Electrical tree defects and water tree defects within the cable insulation layer are both microporous deterioration structures formed by the intrusion of moisture and charged ions into the insulating medium under the influence of an electric field. The dielectric parameters and electrical properties of the defective regions differ significantly from those of intact insulation material. This embodiment reproduces the physical property variation patterns of these two types of defects using finite element simulation. The specific steps are as follows: c1.1: Physics Field Modeling A three-dimensional electromagnetic simulation model of the XLPE cable was established. The geometric parameters of the model were set according to the actual cable dimensions: copper conductor diameter 20.8 mm, XLPE insulation layer thickness 20.5 mm, and outer shielding layer thickness 4 mm.

[0110] c1.2: The phase field method is used to dynamically simulate the generation of cable insulation.

[0111] Based on the coupling mechanism between electric field and material damage, the phase-field method was used to dynamically simulate the entire evolution process of electrical treeing in cable insulation. The results show that when the local electric field strength of the cable exceeds the critical threshold, dendritic conductive channels spontaneously form inside the insulation medium. The defect structure gradually extends from the high field strength conductor region to the low field strength shielding region, and after completely penetrating the insulation layer, it will cause cable insulation breakdown fault.

[0112] c1.3: Defect Classification and Data Generation The severity of defects is classified into three levels: minor, moderate, and severe, based on the proportion of dendritic defect erosion depth to the overall thickness of the insulation layer. The defect level determination criteria, simulation modeling methods, and methods for generating reflection coefficient spectrum data are all consistent with the aforementioned simulation implementation method for electrical tree defects. Simulation models corresponding to seven insulation states are constructed, and the reflection coefficient spectrum data of each model are solved in batches to build a multi-category composite defect sample library.

[0113] c2: Signal enhancement and multidimensional visualization transformation based on EMD-SDP.

[0114] To address the inherent nonlinear and nonstationary characteristics of cable reflection signals, signal optimization processing and geometric mapping transformation are used to convert one-dimensional time-domain signals into highly discriminative two-dimensional image features that can be recognized by machine vision. The specific processing flow is as follows: c2.1: Extract features using EMD.

[0115] The reflection coefficient is preprocessed to extract the amplitude sequence relative to the characteristic impedance, and length alignment is achieved through truncation or zero-padding. Subsequently, EMD is used to adaptively decompose the sequence into a set of IMFs arranged from high frequency to low frequency. Finally, high- and mid-frequency IMF components rich in defect information are selected for signal reconstruction, and after mean removal and normalization, the influence of DC components is eliminated and the scale is unified to extract a stable feature sequence.

[0116] c2.2: Feature image representation based on SDP.

[0117] The normalized sequence extracted in step S2.1 is input into the SDP generator. Utilizing a multi-plane symmetry mapping mechanism in polar coordinates, the one-dimensional time-domain features are transformed into a two-dimensional spatial lattice structure. By optimizing key parameters such as the number of symmetry planes, angular amplification factor, and time delay, the signal amplitude is mapped in a geometric projection form to a two-dimensional image with significant texture and symmetry. The severity of cable insulation defects will be intuitively reflected in the differences in lattice distribution and texture morphology in the SDP image, thus achieving the conversion of one-dimensional features into highly separable two-dimensional features.

[0118] C3: Construction of SDP Feature Image Dataset.

[0119] The above process is executed on all samples to generate corresponding SDP images in batches. Image category labeling is completed based on cable insulation defect judgment standards, covering seven types: intact condition, minor electrical tree defects, moderate electrical tree defects, severe electrical tree defects, minor water tree defects, moderate water tree defects, and severe water tree defects. A structured dataset adapted for multi-category composite defect identification is constructed, which can be directly used for subsequent deep learning model training and validation, providing data support for intelligent automatic classification of cable composite insulation defects.

[0120] C3: SDP Image Classification and Model Validation Based on Deep Residual Networks

[0121] This stage utilizes the Resnet-18 network to automatically identify the generated images, achieving accurate classification and identification of seven insulation aging states of cables.

[0122] C3.1: Dataset Construction and Preprocessing.

[0123] Defect labels are automatically associated by recursively reading subdirectory names. The dataset is randomly divided into training and validation sets in an 8:2 ratio to ensure good generalization ability of the model. Generated images are uniformly scaled to the network's standard size. For single-channel grayscale images, channel expansion techniques are used to convert them into a three-channel format to meet the input dimension requirements of ResNet-18.

[0124] C3.2: ResNet-18 model construction and training strategies.

[0125] This scheme uses ResNet-18 as the core architecture of the classification network. By introducing a residual connection mechanism, this model effectively alleviates the vanishing gradient problem during training while maintaining the representational power of deep networks. The number of nodes in the fully connected layers and the classification output layer at the network's end is adjusted to adapt to the classification task of seven insulation aging states of cables. The remaining training parameters and configurations of the model are the same as those in the aforementioned example of electrical tree defect identification.

[0126] C3.3: Classification Validation and Effectiveness Evaluation.

[0127] The model's recognition accuracy is evaluated by calculating the prediction accuracy on the validation set. A confusion matrix is ​​introduced to visualize and analyze the false positives and false negatives at each level, providing an in-depth analysis of the model's ability to identify defects of varying severity. Figure 8 The confusion matrix characterizes the classification performance of the ResNet model for cables with dendritic defects, from... Figure 8 The system clearly shows which defect types were misjudged and which were accurately identified, with an accuracy rate of 92.35%.

[0128] In summary, through comprehensive experimental verification of Examples 2 to 4, the classification method proposed in this invention demonstrates extremely high accuracy in diagnosing electrical treeing defects, water treeing defects, and mixed defects of both. Experimental results show that the ResNet model can not only accurately extract key features in the evolution process of a single defect, but also effectively isolate weak interference signals by analyzing the pixel distribution patterns of the SDP image when facing complex mixed electrical-water treeing defects, achieving precise anchoring of the insulation degradation stage. The above three levels of verification fully demonstrate the universal applicability and high reliability of the EMD noise reduction-SDP feature mapping-ResNet automatic identification technique in dealing with diverse and complex cable defects.

[0129] Example 5: To further demonstrate the applicability of this method in actual industrial settings, this embodiment provides a physical platform construction method for a local defect detection system based on physical cables and a corresponding visualization software application scheme.

[0130] In this embodiment, a YJQ41 type 110 kV cross-linked polyethylene cable is selected. The network analyzer used is a SIGLENT SHA851A vector network analyzer (VNA), with its scan frequency range set to 10. 5 Hz to 3×10 8 Hz, with 801 frequency sampling points.

[0131] d1: For example Figure 3 As shown, a cable defect detection experimental platform is constructed. To ensure the accuracy and repeatability of the cable defect detection results, the experimental platform must be built and key measuring equipment must be rigorously calibrated before conducting formal testing. The main steps are as follows: d1.1: The experimental platform was built with the core principle of improving measurement accuracy. Standard load devices, short-circuit devices and open-circuit devices were used to perform single-port calibration on the vector network analyzer, establish a high-precision measurement benchmark, and eliminate the interference of equipment system errors on the test data.

[0132] d1.2: Connect the cross-linked polyethylene cable sample to be tested to a calibrated vector network analyzer to collect raw data of the single-port reflection coefficient spectrum of the cable. The collected signal data is transmitted to the host computer in real time through a standard communication interface, providing raw data support for subsequent intelligent classification of the severity of dendritic defects in the cable.

[0133] d2: Automated classification and visual diagnosis based on pre-trained ResNet models. To adapt to the operational needs of rapid inspection and efficient maintenance in industrial settings, this system adopts a working mode combining offline model training with online real-time diagnosis, eliminating the complex process of on-site model training and significantly improving on-site detection efficiency. For example... Figure 9 As shown, this invention is accompanied by a highly integrated cable status classification visualization software. The software interface has a scientifically designed layout, transforming the black-box deep learning inference process into intuitive charts and data. It is mainly divided into three functional modules: d2.1: Operation Console Module: This module embeds the underlying PyTorch framework and a pre-trained high-precision ResNet-18 classification model. The background displays the model architecture's running status and data alignment status in real time. On-site maintenance personnel do not need to write any code or adjust algorithm parameters; they can simply use the built-in data import and diagnostic function buttons to batch import the feature image data transmitted from the host computer, complete model forward inference and automatic classification, significantly reducing the operational threshold and adapting to the needs of frontline maintenance personnel.

[0134] d2.2: Statistical Visualization Area Module: This module is used to intuitively display cable defect diagnosis results from multiple dimensions. For example... Figure 9 The test set statistics page shown automatically generates a classification confusion matrix based on the model's inference results. The matrix uses a blue gradient for visualization, intuitively presenting the true and predicted class distributions of four types of samples: intact, minor electrical tree defects, moderate electrical tree defects, and severe electrical tree defects. This function clearly displays the clustering characteristics of correctly classified samples, while highlighting subtle identification biases between different adjacent defect levels, facilitating staff's intuitive assessment of the model's classification effectiveness and the cable insulation degradation status.

[0135] d2.3: Test Set Evaluation and Log Module: This area provides core quantitative indicators and detailed traceability functions. The top of the module displays the overall recognition accuracy of the test set; in this embodiment, the overall model recognition accuracy reaches 97.06%, providing maintenance personnel with a precise overall health assessment conclusion. The bottom of the module contains a misjudgment log statistics function, which can accurately record and list the specific filenames (e.g., 67.jpeg) of misjudged samples and their classification deviations (e.g., True: Medium electrical tree -> False: Severe electrical tree). This fault tracing mechanism effectively improves the interpretability of diagnostic results, facilitating secondary verification and in-depth analysis of edge samples by technical personnel, further ensuring the accuracy and reliability of cable defect classification diagnosis.

Claims

1. A method for classifying the severity of dendritic defects in cables based on reflection coefficient spectrum and SDP, characterized in that, Includes the following steps: Step 1: Based on the differentiated impact of dendritic defects of varying severity on cable insulation properties, multiple cable models are constructed through simulation; through simulation calculations, the reflection coefficient spectrum dataset corresponding to each cable model is obtained. Step 2: Extract EMD data features from the reflectance coefficient spectrum dataset generated in Step 1, and input the extracted EMD data features into the SDP model to generate an SDP image; Step 3: Input the SDP image generated in Step 2 into the ResNet model for model training, and output the confusion matrix to evaluate the classification performance of the ResNet model; Step 4: Obtain the reflection coefficient spectrum data of the cable under test, extract data features and import them into the SDP model to obtain feature maps. Import the generated feature maps into the trained ResNet model and output the cable defect classification results.

2. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 1, characterized in that: In step 1, various cable models are used, including a normal cable model, a cable model with slight electrical tree defects, a cable model with moderate electrical tree defects, a cable model with severe electrical tree defects, a cable model with slight water tree defects, a cable model with moderate water tree defects, and a cable model with severe water tree defects.

3. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 1, characterized in that: Step 1 Includes the following steps: 1.1: A three-layer cable model consisting of a conductor layer, an insulation layer, and a shielding layer is constructed through simulation, and the reflection coefficient spectrum is used as the basic data for defect characterization; 1.2: The phase-field method is used to simulate the evolution process of dendritic defects in cable insulation. This method drives the dielectric to spontaneously form equivalent conductive channels in the high electric field region by coupling the electric field and the damage field, thereby realizing the simulation of the growth and expansion of dendritic breakdown defects. Damage field using scalar variables Characterizing the degree of medium degradation, wherein: Indicates a good medium. This indicates complete damage, and it dynamically evolves from 1 to 0 over time under the influence of electric field energy. 1.3: Calculate the cable's resistance, inductance, conductance, capacitance, and characteristic impedance using the electrical parameter calculation formulas for the cable: （1）； （2）； （3）； （4）； （5）； In the formula: The resistance per unit length of the cable; Permeability of free space; Angular frequency; , These are the cable core radius and the inner radius of the shielding layer, respectively. , These are the resistivity of the cable core and the resistivity of the shielding layer, respectively. Inductance per unit length of cable; Capacitance per unit length of cable; is the dielectric constant of the dielectric; The electrical conductivity per unit length of the cable; The conductivity of the dielectric. This is the characteristic impedance of the cable; The imaginary unit; 1.4: After calculating the electrical parameters and characteristic impedance of the normal and defective sections of the cable using formulas (1) to (5), the reflection coefficient spectrum of the defective cable is then solved using the following formulas (6) to (10) relating characteristic impedance and reflection coefficient. : （6）； （7）； （8）； （9）； （10）； （11）； In the formula: , and These are the distances from the first section of the cable. , and Input impedance at the location; , and These are the distances from the first section of the cable. , and Reflectance coefficient at that location; and These are the propagation constants for the normal segment and the defective segment, respectively; The characteristic impedance of the defective section of the cable. This is the characteristic impedance of a normal cable; This is the characteristic impedance of a normal cable. Indicates the total length of the cable; 1.5: By adjusting the dielectric constant and conductivity parameters of the medium in the defect region, the electromagnetic characteristics of electrical tree defects and water tree defects in the cable are simulated respectively, while the insulation medium parameters of the normal cable model remain unchanged; Based on the established water-tree cable model, electric tree cable model, and normal cable model, the resistance, conductance, inductance, capacitance, and characteristic impedance of the three types of cable models are calculated according to formulas (1) to (5); then, the reflection coefficient spectrum of the three types of cables is calculated using formulas (6) to (11). Finally, a structured reflection coefficient spectrum dataset is constructed and stored.

4. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 1, characterized in that: Step 2 includes the following steps: Step 2.1: Import the reflection coefficient spectrum data of normal cables, cables with slight dendritic defects, and cables with severe dendritic defects from the reflection coefficient spectrum dataset into the processing flow. The reflection coefficient spectrum data is a complex sequence obtained from actual measurement or simulation, and its amplitude spectrum can be used as the input signal for subsequent feature extraction; Step 2.2: Perform EMD feature extraction, standardization preprocessing, and SDP image generation on the reflectance coefficient spectrum data in sequence.

5. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 4, characterized in that: Step 2.2 specifically includes: The complex signal of the reflection coefficient spectrum is analyzed and preprocessed to extract the reflection coefficient amplitude sequence as a one-dimensional input signal, and the one-dimensional input signal is then unified into a fixed length. If the length exceeds the limit, the excess part will be truncated to ensure that all sample data have the same dimension. Subsequently, EMD is performed on the one-dimensional input signal to decompose it into several intrinsic mode function (IMF) components and residual terms. The specific decomposition formula is as follows: （12）； In the formula: The input signal is one-dimensional. The first decomposition obtained Each intrinsic mode function component (IMF) represents a local characteristic oscillation component of the signal in different frequency bands, from high to low. The residual term represents the overall trend of the signal or the DC bias baseline; The total number of IMF components obtained from the decomposition; The first few IMF components are selected and summed for reconstruction, which enhances the core oscillation characteristics of the signal while reducing noise interference, resulting in the characteristic signal of the reflection coefficient spectrum. The reconstruction formula is as follows: （13）； In the formula: The reconstructed discrete feature signal sequence; The number of reconstructed components is preset, and satisfies the following conditions: .

6. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 5, characterized in that: Step 2.2 also includes: The reconstructed feature signal is subjected to mean removal and normalization, and then mapped to... The interval, used as the input sequence for SDP generation, is reconstructed using the following specific formula: （14）； （15）； In the formula: For the mean-removed signal; For normalized feature sequences; This represents the total number of sample points in the characteristic signal sequence. and These are mean-reduced signal sequences. The maximum and minimum values ​​in; The normalized feature sequence is input into the SDP image generation module, based on the preset number of symmetry planes. Angular magnification factor Delay parameters The data transformation is completed, converting the one-dimensional feature sequence into a two-dimensional SDP image. For the normalized feature sequence... , its first Each sampling point and its time delay Subsequent sampling points In polar coordinates, this is mapped to symmetrical pairs of coordinate points. and The formulas for calculating its polar radius and polar angle are as follows: （16）； （17）； （18）； In the formula: The polar radius directly reflects the signal amplitude at the current position; and respectively along the first The polar angles of the clockwise and counterclockwise expansion on both sides of the axis of symmetry; This is a delay parameter used to capture the temporal correlation characteristics of the signal; Let be the angular magnification factor, satisfying ; For the first The initial deflection angle of each symmetric plane.

7. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: Store the SDP images corresponding to each cable model generated in Step 2 according to seven preset categories: normal, slight electrical tree defects, moderate electrical tree defects, severe electrical tree defects, slight water tree defects, moderate water tree defects, and severe water tree defects, and construct the corresponding image dataset, using the folder to which the image belongs as the source of the category label; randomly divide the image dataset to obtain the training set for model training and the validation set for performance verification. Step 3.2: Adjust the size of the SDP image uniformly and perform channel expansion processing on the single-channel grayscale image. Copy and superimpose the single-channel grayscale image generated by the one-dimensional feature sequence in the channel dimension, and expand the single-channel feature matrix into a three-channel pseudo-color image matrix, so that the expanded red (R), green (G), and blue (B) channels have the same numerical distribution of pixel intensity to meet the input requirements of the ResNet model. Step 3.3: Select the ResNet model as the base model for image classification and adaptively adjust its output layer structure by replacing the fully connected layer and classification layer at the end of the network to make the number of output categories of the model consistent with the target classification task. Step 3.4: During the model training phase, iteratively correct the network's internal parameters based on the gradient descent optimization algorithm; The expanded three-channel image is input into the network for forward propagation. The original scores of each defect category are output through the last fully connected layer of the network. A focus loss function is introduced to calculate the loss value between the network output and the true label. By adjusting the dynamic weights, the model is forced to focus on learning the misclassified samples that are difficult to classify. Subsequently, the gradient of the loss value with respect to the weights and bias parameters of each layer in the network is calculated using the backpropagation algorithm, and the internal parameters of the network are iteratively corrected using an adaptive matrix estimation optimization algorithm. The parameter update formula is as follows: （20）； In the formula: These are the network weights or bias parameters for the current round; This is the learning rate for the current iteration, and the learning rate is dynamically adjusted using a cosine annealing algorithm. and These are the adaptive estimates of the first and second moments of the gradient after bias correction, respectively; This is the weight decay coefficient, used to prevent network overfitting; To prevent smooth terms with a denominator of zero; The Softmax function outputs the probability corresponding to each category. Step 3.5: After training, evaluate the classification performance of the ResNet model based on the validation set, and output the classification accuracy and confusion matrix. The classification accuracy is used to evaluate the model's overall accuracy in identifying cable states, and its calculation formula is as follows: ； In the formula: To verify the total number of cable SDP images correctly classified by the ResNet model in the set, The total number of samples in the validation set; The confusion matrix is ​​a matrix of size ... (Right now A two-dimensional statistical matrix, where any element in the matrix... Indicates the true category is the first Class, but predicted by the ResNet model as the first Number of cable sample images of class; where, when In this case, the elements on the main diagonal of the matrix represent the number of correctly identified defects of each category, while the elements outside the diagonal represent the distribution of misclassifications among different defect severity levels or different defect types. This is used to quantitatively evaluate the model's fine-grained identification performance among normal conditions, electrical tree defects, and water tree defects, in order to obtain a ResNet model for cable defect identification.

8. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 7, characterized in that: In step 3.4, the probability corresponding to each category is output through the Softmax function, and its specific calculation formula is as follows: （21）； In the formula: In this embodiment, the preset total number of categories is used. ; The first output of the fully connected layer at the network end The original unnormalized scores for each defect category; The input image obtained after mapping by the Softmax function belongs to the first... The normalized probability values ​​of each preset category, and satisfying The network will eventually output probability values. The largest corresponding defect category is used as the final identification result to achieve classification and identification of SDP images of cables in different states.

9. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 7, characterized in that: In step 3.4, the formula for calculating the focus loss function is as follows: （19）； In the formula: The size of the current training batch; The category weight coefficient is dynamically calculated based on the reciprocal of the number of samples in each category, and is used to counteract the imbalance in the number of normal cable samples and defective samples. The focus parameter is used to reduce the loss contribution weight of easily classified samples; This represents the probability value that the model predicts the defect to be of the true defect category.

10. The method for classifying the severity of cable dendritic defects based on reflection coefficient spectrum and SDP according to claim 1, characterized in that: In step 4, the reflection coefficient spectrum of the cable under test is measured using a network analyzer. and the reflection coefficient spectrum The data is transmitted to the host computer, EMD and SDP are imported, corresponding SDP images are generated, and then the SDP images are input into the trained ResNet module to obtain the classification results of the severity of cable defects.

Images