High-positioning-precision power cable fault detection method based on time-frequency domain reflection method

Abstract

The invention relates to a high-positioning-precision power cable fault detection method based on a time-frequency domain reflection method, and aims to solve the technical problems of insufficient positioning precision and weak anti-interference capability of a traditional fault detection method. The method comprises the following steps: firstly, enabling a power cable to be equivalent to a uniform transmission line distribution parameter model, and generating a Gaussian envelope linear frequency modulation incident signal meeting a detection requirement by utilizing a time-frequency domain reflection method and fusing the technical advantages of a time domain reflection method and a frequency domain reflection method, and injecting the Gaussian envelope linear frequency modulation incident signal into a target cable; the method comprises the following steps: performing smooth pseudo Wigner-Ville distribution time-frequency transformation on a cable reflection signal to obtain a time-frequency domain image; aiming at the problem of shape distortion caused by elliptic features presented by GELC signals after SPWVD transformation and noise interference, a Hough transformation ellipse detection algorithm is adopted, ellipse feature parameters are accumulated and counted in a parameter space through preprocessing steps of image graying, threshold segmentation, contour extraction and the like, an ellipse center corresponding to a time-frequency correlation peak is accurately positioned, and a time-frequency correlation curve is obtained. And determining the position of a cable fault point. The method effectively overcomes the limitation of a single-domain reflection method and the influence of noise interference, remarkably improves the precision and reliability of power cable fault positioning, and is suitable for fault detection scenes of open circuit, short circuit, impedance mismatching and the like of various power cables.

Description

Technical Field

[0001] This invention relates to the field of power cable fault detection technology, and specifically to a power cable fault detection method based on time-frequency domain reflection with high positioning accuracy. Background Technology

[0002] As the core equipment for power transmission in a power system, the operating status of power cables directly affects the stability and reliability of the power system. With the continuous increase in the length of power cables laid, they are susceptible to environmental corrosion, mechanical damage, insulation aging, and other factors during long-term operation, leading to faults such as open circuits, short circuits, or impedance mismatches. Quickly and accurately locating the fault point is crucial to ensuring the rapid restoration of power supply and minimizing economic losses.

[0003] Currently, the main methods for locating power cable faults include Time Domain Reflectometry (TDR), Frequency Domain Reflectometry (FDR), and Traveling Wave Method. Among these, TDR involves injecting a step signal or narrow pulse signal into the cable and calculating the fault location based on the time difference between the reflected and incident signals. Its advantages include strong real-time performance and simple operation, making it suitable for short-distance cable fault detection. However, it has significant disadvantages: firstly, low time-frequency resolution, as the bandwidth of the step signal is limited, resulting in insufficient sensitivity to minute impedance changes such as early insulation aging and slight joint loosening, easily leading to missed detections; secondly, weak anti-interference capability, as electromagnetic noise in the field environment, such as power frequency interference and pulse noise, easily drowns out the weak reflected signal, leading to increased location errors, typically ranging from 5% to 10%. Its advantages are strong real-time performance and simple operation, making it suitable for short-distance cable fault detection; however, it has significant disadvantages: First, low time-frequency resolution, limited bandwidth of step signals, and insufficient sensitivity to minute impedance changes such as early insulation aging and slight joint loosening, leading to easy missed detections; second, weak anti-interference capability, electromagnetic noise in the field environment such as power frequency interference and pulse noise easily drown out weak reflected signals, resulting in increased positioning errors, typically 5%-10%; third, the existence of a "measurement blind zone," due to the transition time of the signal rise edge, faults within 0-5m of the signal injection end are difficult to detect accurately. Frequency Domain Reflectometry (FDR): By injecting a swept frequency signal into the cable, the frequency domain response of the cable, such as the transmission coefficient and reflection coefficient, is measured. Fourier transform is then used to convert the frequency domain information into time domain information to achieve fault location. Its advantages include high frequency domain resolution and the ability to capture minute impedance changes; however, its disadvantages are: first, it is difficult to accurately obtain time domain information, as the time domain waveform of the swept frequency signal is not intuitive and requires complex reconstruction, which easily introduces calculation errors; second, it has weak anti-interference capability, as frequency-selective noise during the sweep process will directly distort the frequency domain response curve, leading to location failure; and third, it has slow detection speed, typically requiring several seconds to tens of seconds to complete a full sweep covering 1kHz-100MHz, making it unsuitable for emergency fault repair scenarios. Traveling wave method: This method locates the fault by detecting naturally occurring transient traveling waves such as those from lightning strikes, short circuits, or artificially injected traveling wave signals, based on the time difference between the arrival times of the traveling waves at both ends. Its advantages include high positioning accuracy, with an error typically within 10m, making it suitable for long-distance high-voltage cables. However, its disadvantages are: 1. It relies on transient signals; the generation of natural traveling waves is random, and artificially injecting traveling waves requires complex high-voltage pulse generators, resulting in high costs and operational risks. 2. It has poor anti-interference capability; the transient traveling wave signal has small amplitude and short duration, making it susceptible to interference from system harmonics, grounding currents, etc., and difficult to accurately identify. 3. It lacks the ability to distinguish multiple fault points; if the cable has multiple impedance discontinuities, the traveling wave will reflect and superimpose multiple times, leading to signal distortion and making it impossible to distinguish the fault location. 4. It has a "measurement blind zone"; due to the transition time at the signal rise edge, faults within 0-5m of the signal injection end are difficult to detect accurately.

[0004] Furthermore, traditional fault detection methods are ineffective in handling noise interference. When impulse noise is mixed into the cable reflection signal, the time-frequency characteristics of the signal are distorted, making fault feature extraction difficult. For example, after using smooth pseudo-Wigner-Ville distribution (SPWVD) for time-frequency transformation, the GELC signal in an ideal state would present a standard elliptical shape, but under noise interference, the elliptical shape becomes irregular, directly affecting the accuracy of fault location.

[0005] Therefore, how to effectively integrate time and frequency domain information, suppress noise interference, and accurately extract fault features has become a key technical challenge in improving the fault location accuracy of power cables. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a high-precision power cable fault detection method based on the time-frequency domain reflection method. This method integrates the technical advantages of the time-frequency domain reflection method and combines it with the Hough transform ellipse detection algorithm to achieve accurate fault location.

[0007] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0008] This invention provides a high-precision power cable fault detection method based on time-frequency domain reflection, comprising the following steps:

[0009] S1 establishes a uniform transmission line distribution parameter model for power cables. In the model, the resistance, inductance, capacitance, and conductance of the cable are uniformly distributed along the line. When the cable length is much greater than the wavelength of the electromagnetic wave being propagated, the cable is treated as a long line.

[0010] S2 designs and generates a Gaussian envelope linear frequency modulation (GELC) incident signal, the transmission parameters of which are determined based on the cable and coupler channel transmission characteristics measured by a vector network analyzer.

[0011] S3 injects the GELC incident signal into the target power cable and simultaneously receives the reflected signal after being reflected by the cable fault point or impedance discontinuity point.

[0012] S4 performs a smooth pseudo-Wigner-Ville distribution (SPWVD) time-frequency transform on the reflected signal to obtain a time-frequency domain image containing fault feature information. The ideal feature shape of the GELC signal in the time-frequency domain image is a standard ellipse.

[0013] S5 performs grayscale processing, threshold segmentation, and contour extraction preprocessing on the time-frequency domain image in sequence to remove image noise and enhance the elliptical feature contour.

[0014] S6 uses the Hough transform ellipse detection algorithm to analyze the preprocessed image. By establishing an ellipse parameterization equation, the elliptical features in the image space are transformed to the parameter space. The cumulative statistical results in the parameter space are used to locate the center of the ellipse, which corresponds to the peak-to-peak position of the time-frequency correlation. Based on the time-frequency coordinate information of the ellipse center and the propagation speed of electromagnetic waves in the cable, the precise location of the power cable fault point is calculated. Preferably, the design process of the GELC incident signal in step 2 includes: testing the channel transmission attenuation characteristics and impedance matching characteristics of the power cable and coupler using a vector network analyzer; optimizing the center frequency, bandwidth, and envelope parameters of the signal based on the test results to ensure that the signal meets the penetration and resolution requirements of cable fault detection; wherein, the optimized center frequency range is 10-100MHz, the optimized bandwidth range is 10-80MHz, and the attenuation coefficient α of the Gaussian envelope ranges from 0.1-10.

[0015] Preferably, the SPWVD time-frequency transformation in step 4 is used to preserve the joint time-frequency characteristics of the reflected signal. The transformation process suppresses cross-term interference in the following way: a Hanning window, Hamming window, or Blackman window is used as a smoothing window function to weight the kernel function of the Wigner-Ville distribution. The window length ranges from 64 to 512 points to balance the time-frequency resolution and the cross-term suppression effect. When the signal noise intensity is greater than 20dB, an adaptive filtering algorithm is introduced to preprocess the reflected signal to further reduce noise interference.

[0016] Preferably, the implementation process of the Hough transform ellipse detection algorithm in step 6 includes:

[0017] (1) Establish the parametric equation of the ellipse in polar coordinates, the equation of which is:

[0018]

[0019] Where (ρ,θ) are polar coordinate parameters, (a,b) are the coordinates of the ellipse center, and r is the equivalent radius of the ellipse, which maps the pixels in the image space to the parameter space;

[0020] (2) Accumulate the count of feature points in the parameter space, set the cumulative threshold to 60%-80% of the maximum value of the parameter space, and form a cumulative peak. The parameter corresponding to the cumulative peak is the feature parameter of the ellipse.

[0021] (3) Determine the coordinates of the center of the ellipse according to the ellipse feature parameters. The coordinates correspond one-to-one with the time-frequency correlation peak-to-peak value of the reflected signal, and the coordinate positioning error is controlled within 1 pixel.

[0022] Preferably, the ellipse parameterization equation is established based on the point-line duality principle, which converts any point on the ellipse in the image space into a curve in the parameter space, and the intersection of all curves is the feature parameter of the ellipse; in the parameter space mapping process, a step-by-step search strategy is adopted to first determine the coordinate range of the ellipse center, and then optimize the major axis, minor axis and rotation angle parameters to reduce the computational complexity.

[0023] Preferably, the method for calculating the location of the fault point in step 7 is as follows: Where L is the distance from the fault point to the signal injection end, in meters; v is the propagation speed of electromagnetic waves in the cable, in meters per second; and t is the time difference between the incident signal and the reflected signal, in seconds. The time difference is determined by the time-domain coordinates of the ellipse center, and the conversion factor between the time-domain coordinates and the actual time is determined based on the signal sampling rate.

[0024] Preferably, the electromagnetic wave propagation speed v is calculated using the following formula: Where μ is the high-frequency relative permeability of the medium surrounding the cable core, with a value ranging from 1 to 1.5; ε is the high-frequency relative permittivity of the medium surrounding the cable core, with a value of 2.3-3.0 for cross-linked polyethylene insulated cables and 3.0-4.0 for polyvinyl chloride insulated cables; c0 is the propagation speed of electromagnetic waves in a vacuum; the values ​​of μ and ε need to be corrected according to the actual type of insulation material of the cable during calculation.

[0025] Preferably, the faults include open-circuit faults, short-circuit faults, and impedance mismatch faults at the joints. When an open-circuit fault occurs, the reflection coefficient is 1, and the reflected signal amplitude remains unchanged; when a short-circuit fault occurs, the reflection coefficient is -1, and the reflected signal amplitude is reversed; when an impedance mismatch fault occurs, the reflection coefficient is determined according to the impedance Z at the fault point. f The ratio of the characteristic impedance Z0 of the cable is determined by the following formula: in L0 is the inductance per unit length of the cable, and C0 is the capacitance per unit length of the cable.

[0026] Preferably, in step 3, the received reflected signal uses a high-speed data acquisition module with a sampling rate ranging from 500 MSps to 2 GSps, a sampling bit depth of 12-16 bits, and an acquisition duration determined based on the cable length. The calculation formula is as follows: Its L max v is the maximum length of the cable. min T is the minimum propagation speed of electromagnetic waves. s The duration of the signal is used to ensure complete acquisition of the reflected signal.

[0027] Preferably, in step 5, the threshold segmentation adopts an adaptive thresholding algorithm, which determines the segmentation threshold by calculating the bimodal threshold of the image grayscale histogram or based on the maximum inter-class variance method, and the threshold adjustment step size is 1-5 gray levels; the contour extraction adopts the Canny edge detection algorithm, with the high threshold value ranging from 100 to 200 and the low threshold value being 1 / 2 to 2 / 3 of the high threshold, to ensure complete extraction of the elliptical edge contour.

[0028] The beneficial effects of this invention are as follows:

[0029] This invention combines the technical advantages of TDR and FDR methods, and uses TFDR for fault detection. It not only preserves the time difference information of the time domain signal, but also utilizes the high resolution characteristics of the frequency domain signal, effectively improving the detection sensitivity of small reflection signals.

[0030] To address the elliptical characteristics of GELC signals after SPWVD time-frequency transformation, a Hough transform ellipse detection algorithm is introduced. This algorithm is robust to noise interference and target shape distortion, and can accurately locate the center of the ellipse in complex noise environments, avoiding the positioning errors caused by signal distortion in traditional methods.

[0031] By optimizing the GELC incident signal parameters using a vector network analyzer and combining this with image preprocessing steps, noise interference was further suppressed, fault characteristics were enhanced, and high accuracy and reliability of fault location were ensured.

[0032] This invention is applicable to the detection of open circuit, short circuit and impedance mismatch faults in various types of power cables. It has a wide range of applications, is easy to operate, and has good engineering practicality and promotional value. Attached Figure Description

[0033] Figure 1 A diagram showing the distributed parameter model of a power cable transmission line;

[0034] In the diagram: R0 is the resistance per unit length, L0 is the inductance per unit length, and C0 is the capacitance per unit length;

[0035] Figure 2 Here is a flowchart of the Hough transform ellipse detection process;

[0036] The process includes: time-frequency domain image input → edge extraction → parameter space mapping → cumulative matrix initialization → edge point sampling → parameter space accumulation → peak detection → ellipse center output;

[0037] Figure 3 This is a schematic diagram of the Cartesian coordinate system and the parametric coordinate system under the Hough transform;

[0038] The left image is a time-frequency domain image in a rectangular coordinate system, containing elliptical features; the right image is the parameter space (a,b plane), where each edge point on the ellipse corresponds to a curve, and the intersection of these curves is the center of the ellipse (a...b plane). max b max );

[0039] Figure 4 This is the dual graph of parameter space and image space in polar coordinates;

[0040] The figure illustrates the duality between the edge points of the ellipse in image space and the corresponding curves in parameter space. All curves intersect at a single point, which is the center parameter of the ellipse. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described clearly and completely below in conjunction with specific embodiments.

[0042] The solution for this implementation is achieved as follows:

[0043] A high-precision power cable fault detection method based on time-frequency domain reflection includes the following steps: S1: Establishing a uniform transmission line distributed parameter model.

[0044] Under ideal operating conditions, a power cable can be considered a uniform transmission line, with its resistance R0, inductance L0, capacitance C0, and conductance G0 uniformly distributed along the line. When the cable length L is much larger than the wavelength of the propagated electromagnetic wave, the cable is equivalent to a long line. In this case, the voltage and current not only change with time but are also related to the transmission line length, providing a theoretical model basis for subsequent signal transmission analysis and fault location.

[0045] S2: Design and generate the GELC incident signal

[0046] The channel transmission characteristics of the target power cable and coupler were tested using a vector network analyzer, including transmission attenuation and impedance matching. Based on the test results, parameters such as the center frequency, bandwidth, and envelope shape of the GELC signal were optimized to ensure good signal penetration and resolution, effectively exciting reflected signals from cable fault points. The mathematical expression for the GELC signal is:

[0047] Where α determines the width of the reference signal and is inversely proportional to the pulse width; β determines the frequency bandwidth of the reference signal and is linearly related to the bandwidth; ω0 is the center angular frequency, and t0 is the center time of the signal.

[0048] S3: Signal Injection and Reflection Signal Reception

[0049] The designed GELC incident signal is injected into the target power cable. At the same time, the reflected signal after reflection from the cable fault point or impedance discontinuity point is collected in real time through the signal receiving module, and the reflected signal is stored in the data buffer unit to prepare for subsequent time-frequency transformation and feature extraction.

[0050] S4: SPWVD Time-Frequency Transform Processing

[0051] The received reflected signal undergoes a smooth pseudo-SPWVD time-frequency transform, converting the one-dimensional time-domain signal into a two-dimensional time-frequency domain image. SPWVD suppresses cross-term interference from the traditional Wigner-Ville distribution by introducing a smoothing window function, preserving the joint time-frequency characteristics of the reflected signal while maintaining time-frequency resolution. Ideally, the GELC signal presents a standard elliptical shape in the time-frequency domain image, with the ellipse's position and shape related to the fault location information. The calculation formula for the SPWVD transform is as follows:

[0052]

[0053] Where ω is the frequency; h(t) and g(t) are smoothing window functions in the time and frequency domains, respectively.

[0054] S5: Time-frequency domain image preprocessing

[0055] The time-frequency domain image after SPWVD transformation is sequentially processed by grayscale conversion, thresholding, and contour extraction. Grayscale conversion converts the color image to grayscale, simplifying data processing; thresholding separates the target region from the background region by setting a reasonable grayscale threshold, removing some noise; contour extraction enhances the edge information of elliptical features, providing a clear target contour for subsequent ellipse detection.

[0056] S6: Hough Transform Ellipse Detection

[0057] The Hough transform ellipse detection algorithm is used to analyze the preprocessed image. The specific process is as follows: An ellipse parameterization equation in polar coordinates is established. Based on the point-line duality principle of the Hough transform, any pixel on the ellipse in the image space is mapped to the parameter space, with each pixel corresponding to a curve in the parameter space. The curves in the parameter space are accumulated and counted. When multiple curves intersect at the same parameter point, a cumulative peak is formed. The parameters corresponding to this peak are the characteristic parameters of the ellipse, including the ellipse center coordinates, major axis, minor axis, and rotation angle. The ellipse center coordinates are determined based on the ellipse characteristic parameters. These coordinates correspond one-to-one with the time-frequency correlation peak-peak value of the reflected signal, thereby accurately locating the fault feature in the time-frequency domain.

[0058] S7: Fault Location Calculation. Based on the time-domain coordinates of the ellipse center, the time difference t between the GELC incident and reflected signals is determined. Combined with the electromagnetic wave propagation speed v in the cable, the location is calculated using the formula... Calculate the distance L from the fault point to the signal injection end. The electromagnetic wave propagation speed v is determined by the cable dielectric properties, and is obtained through a common... The calculation is performed, where μ is the high-frequency relative permeability of the medium surrounding the cable core, and ε is the high-frequency relative permittivity of the medium surrounding the cable core.

[0059] Example 1: Fault Detection of 10kV Cross-linked Polyethylene Insulated Cable

[0060] 1.1 Experimental Conditions

[0061] Cable parameters: 10kV XLPE insulated cable, length 3km, core material is copper ρc=1.72×10 -8 Ω·m, cable core radius r c =5mm, inner radius r of shielding layer s =15mm, relative permittivity ε of insulating material r =2.3, relative permeability μ r =1;

[0062] Fault setting: Set an open circuit fault 375m away from the signal injection end, the cable core is cut off, and the insulation layer is intact;

[0063] Environmental conditions: Indoor laboratory environment, temperature 25℃, humidity 50%, no obvious electromagnetic interference, SNR≈30dB;

[0064] Testing equipment: Vector network analyzer, FPGA signal generation module, high-speed data acquisition card, capacitive coupler, industrial computer.

[0065] 1.2 Experimental Procedure

[0066] 1.2.1 Establishing a distributed parameter model:

[0067] Theoretical calculated distributed parameters: R0 = 0.02Ω / m, L0 = 0.5μH / m, C0 = 100pF / m, G0 = 1nS / m; Vector network analyzer test correction: Measured reflection coefficient in the 1-100MHz frequency band, fitted to obtain actual parameters: R0 = 0.022Ω / m, L0 = 0.48μH / m, C0 = 102pF / m, G0 = 1.2nS / m, characteristic impedance

[0068]

[0069] 1.2.2 GELC Signal Design and Generation:

[0070] Channel characteristics test: The cable's transmission attenuation at a center frequency of 50MHz is 4.2dB, impedance matching error is <3%, and dispersion effect is weak; Parameter optimization: center frequency f0 = 50MHz, bandwidth B = 40MHz, Gaussian envelope coefficient α = 0.5×10 14 s -2 The corresponding time domain pulse width

[0071] Signal generation: The FPGA generates a GELC signal, which is converted from D / A and amplified to 5V by an amplifier, and then injected into the cable through a capacitive coupler.

[0072] 1.2.3 Reflected signal reception and preprocessing:

[0073] Data Acquisition: A high-speed data acquisition card acquires the reflected signal, with an acquisition time of 10μs and a data storage capacity of approximately 10MB.

[0074] SPWVD time-frequency transformation: Using Hanning window (window length 256 points) and Hamming window (window length 128 points), a time-frequency domain image of 1024×1024 pixels is obtained. The incident signal ellipse and the reflected signal ellipse are clearly visible in the image.

[0075] Image preprocessing: After grayscale conversion, Otsu's algorithm is used for segmentation, with a threshold T. opt =128, Canny edge detection, high threshold 150, low threshold 75, to obtain an elliptical contour image.

[0076] 1.2.4 Hough Transform Ellipse Detection:

[0077] Parameter space settings: values ​​of a and b range from 0 to 1024 pixels, and the cumulative matrix step size is 1 pixel;

[0078] Edge point sampling: Sample 200 edge points from the contour image;

[0079] Cumulative peak detection: Maximum cumulative value H of the cumulative matrix max =185, threshold T=0.7×185=129.5, the ellipse center coordinates corresponding to the detected cumulative peak are (512, 384) pixels;

[0080] Time difference conversion: With a sampling rate of 1 GSps, the time difference corresponding to 384 pixels in the time domain is t = 384 × 1 ns = 3.84 μs.

[0081] 1.2.5 Fault location calculation: Electromagnetic wave propagation speed:

[0082]

[0083] Distance from the fault point

[0084] 1.3 Experimental Results

[0085] The actual fault location was 375m, and the positioning error of this invention was 1.32m, with an error rate of 0.35%, which is far superior to traditional TDR and existing TFDR technologies. Simultaneously, the fault type was accurately identified as an "open circuit fault" using elliptical grayscale features. Although the invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features; however, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this invention.

Claims

1. A high-precision power cable fault detection method based on time-frequency domain reflection, characterized in that, Includes the following steps: S1 establishes a uniform transmission line distribution parameter model for power cables. In the model, the resistance, inductance, capacitance, and conductance of the cable are uniformly distributed along the line. When the cable length is much greater than the wavelength of the electromagnetic wave being propagated, the cable is treated as a long line. S2 designs and generates a Gaussian envelope linear frequency modulated incident signal, the transmission parameters of which are determined based on the cable and coupler channel transmission characteristics measured by a vector network analyzer. S3 injects the GELC incident signal into the target power cable and simultaneously receives the reflected signal after being reflected by the cable fault point or impedance discontinuity point. S4 performs a smooth pseudo-Wigner-Ville distribution (SPWVD) time-frequency transform on the reflected signal to obtain a time-frequency domain image containing fault feature information. The ideal feature shape of the GELC signal in the time-frequency domain image is a standard ellipse. S5 performs grayscale processing, threshold segmentation, and contour extraction preprocessing on the time-frequency domain image in sequence to remove image noise and enhance the elliptical feature contour. S6 uses the Hough transform ellipse detection algorithm to analyze the preprocessed image. By establishing the ellipse parameterization equation, the ellipse features in the image space are transformed into the parameter space. The cumulative statistical results of the parameter space are used to locate the center of the ellipse, which corresponds to the peak position of the time-frequency correlation. Based on the time-frequency coordinates of the center of the ellipse and the propagation speed of electromagnetic waves in the cable, the precise location of the power cable fault point is calculated.

2. The method according to claim 1, characterized in that, The design process of the GELC incident signal in step 2 includes: testing the channel transmission attenuation characteristics and impedance matching characteristics of the power cable and coupler using a vector network analyzer; optimizing the center frequency, bandwidth, and envelope parameters of the signal based on the test results to ensure that the signal meets the penetration and resolution requirements for cable fault detection; wherein, the center frequency optimization range is 10-100MHz, the bandwidth optimization range is 10-80MHz, and the attenuation coefficient α of the Gaussian envelope ranges from 0.1 to 10.

3. The method according to claim 1, characterized in that, The SPWVD time-frequency transformation described in step 4 is used to preserve the joint time-frequency characteristics of the reflected signal. The transformation process suppresses cross-term interference in the following ways: a Hanning window, Hamming window, or Blackman window is used as a smoothing window function to weight the kernel function of the Wigner-Ville distribution. The window length ranges from 64 to 512 points to balance the time-frequency resolution and the cross-term suppression effect. When the signal noise intensity is greater than 20dB, an adaptive filtering algorithm is introduced to preprocess the reflected signal to further reduce noise interference.

4. The method according to claim 1, characterized in that, The implementation process of the Hough transform ellipse detection algorithm in step 6 includes: (1) Establish the parametric equation of the ellipse in polar coordinates, the equation of which is: Where (ρ,θ) are polar coordinate parameters, (a,b) are the coordinates of the ellipse center, and r is the equivalent radius of the ellipse, which maps the pixels in the image space to the parameter space; (2) Accumulate the count of feature points in the parameter space, set the cumulative threshold to 60%-80% of the maximum value of the parameter space, and form a cumulative peak. The parameter corresponding to the cumulative peak is the feature parameter of the ellipse. (3) Determine the coordinates of the center of the ellipse according to the ellipse feature parameters. The coordinates correspond one-to-one with the time-frequency correlation peak-to-peak value of the reflected signal, and the coordinate positioning error is controlled within 1 pixel.

5. The method according to claim 4, characterized in that, The ellipse parameterization equation is established based on the point-line duality principle, which transforms any point on the ellipse in the image space into a curve in the parameter space. The intersection of all curves is the feature parameter of the ellipse. In the parameter space mapping process, a step-by-step search strategy is adopted. First, the coordinate range of the ellipse center is determined, and then the major axis, minor axis and rotation angle parameters are optimized to reduce the computational complexity.

6. The method according to claim 1, characterized in that, The method for calculating the location of the fault point in step 7 is as follows: Where L is the distance from the fault point to the signal injection end, in meters; v is the propagation speed of electromagnetic waves in the cable, in meters per second; and t is the time difference between the incident signal and the reflected signal, in seconds. The time difference is determined by the time-domain coordinates of the ellipse center, and the conversion factor between the time-domain coordinates and the actual time is determined based on the signal sampling rate.

7. The method according to claim 6, characterized in that, The propagation speed v of the electromagnetic wave is calculated using the following formula: Where μ is the high-frequency relative permeability of the medium surrounding the cable core, with a value ranging from 1 to 1.5; ε is the high-frequency relative permittivity of the medium surrounding the cable core, with a value of 2.3-3.0 for cross-linked polyethylene insulated cables and 3.0-4.0 for polyvinyl chloride insulated cables; c0 is the propagation speed of electromagnetic waves in a vacuum; the values ​​of μ and ε need to be corrected according to the actual type of insulation material of the cable during calculation.

8. The method according to claim 1, characterized in that, The faults include open-circuit faults, short-circuit faults, and impedance mismatch faults at the joints. When an open-circuit fault occurs, the reflection coefficient is 1, and the reflected signal amplitude remains unchanged; when a short-circuit fault occurs, the reflection coefficient is -1, and the reflected signal amplitude is reversed; when an impedance mismatch fault occurs, the reflection coefficient is determined according to the impedance Z at the fault point. f The ratio of the characteristic impedance Z0 of the cable is determined by the following formula: in L0 is the inductance per unit length of the cable, and C0 is the capacitance per unit length of the cable.

9. The method according to claim 1, characterized in that, In step 3, the reflected signal is received using a high-speed data acquisition module with a sampling rate ranging from 500 MSps to 2 GSps and a sampling bit depth of 12-16 bits. The acquisition time is determined based on the cable length, and the calculation formula is as follows: Its L max v is the maximum length of the cable. min T is the minimum propagation speed of electromagnetic waves. s The duration of the signal is used to ensure complete acquisition of the reflected signal.

10. The method according to claim 1, characterized in that, In step 5, the threshold segmentation adopts an adaptive thresholding algorithm, which determines the segmentation threshold by calculating the bimodal threshold of the image grayscale histogram or based on the maximum inter-class variance method. The threshold adjustment step size is 1-5 gray levels. The contour extraction adopts the Canny edge detection algorithm, with the high threshold value ranging from 100 to 200 and the low threshold value being 1 / 2 to 2 / 3 of the high threshold, to ensure complete extraction of the elliptical edge contour.

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