A method for submarine cable fault location

Abstract

The application provides a submarine cable fault positioning method, and relates to the technical field of fault positioning, comprising: collecting a fault traveling wave signal, and obtaining a plurality of intrinsic mode function components through variational mode decomposition; establishing a frequency-variable group velocity model based on a submarine cable distribution parameter; for the screened components, determining a group velocity matched with a characteristic frequency according to the model; calculating a fault distance according to a wave head arrival time of each component and a corresponding group velocity, and obtaining a final fault distance through weighted fusion. The beneficial effects are: through adaptive decomposition of a wideband signal by variational mode decomposition, and in combination with a frequency-variable group velocity model based on a physical parameter, a corresponding group velocity is matched for each component, dispersion effect is compensated, and positioning accuracy is improved; through multi-component weighted fusion, different frequency information is comprehensively utilized, accidental errors are avoided, and stability and applicability are improved.

Description

Technical Field

[0001] This invention relates to the field of fault location technology, and in particular to a method for locating faults in submarine cables. Background Technology

[0002] Submarine cables, serving as the "main artery" for transoceanic energy and information transmission, undertake crucial tasks such as offshore wind power grid connection, island power supply, and transnational power grid interconnection. Their safe and stable operation directly impacts the reliability and economy of energy supply. Because submarine cables typically contain multiple complex structures, including copper conductors, cross-linked polyethylene insulation, lead sheaths, steel wire armor, and fiber optic units, the significant differences in electrical parameters between these material layers result in a strong frequency dependence in the distributed parameters of submarine cables. This characteristic presents a severe technical challenge to the location of traveling wave faults in submarine cables.

[0003] The existing traveling wave location technology for submarine cable faults mainly has the following problems: First, the ranging error caused by dispersion. The traveling wave signal generated by a fault is not a single frequency, but a broadband pulse containing rich frequency components. During long-distance transmission, due to the frequency-varying characteristics of the distributed parameters of the submarine cable, the propagation characteristics of different frequency components differ significantly: high-frequency components attenuate greatly but propagate quickly, while low-frequency components attenuate less but propagate slowly. This frequency selectivity causes the traveling wave signal to "diffuse" during transmission; that is, the originally steep rising edge of the wavefront gradually becomes gentler as the propagation distance increases, and the wavefront energy is dispersed over a wider time window. This phenomenon makes it difficult to accurately determine the starting time of the wavefront from the gentle waveform when the fault wavefront arrives at the detection end, directly causing errors in the wavefront arrival time calibration, which is the most critical step in traveling wave ranging, and thus affecting the accuracy of fault distance calculation.

[0004] Second, the limitations of fixed wave speeds. Most existing traveling wave positioning methods assume that the traveling wave propagates at a fixed speed, such as a fixed percentage of the speed of light (e.g., v=c / 2) or the power frequency wave speed as a uniform propagation speed. However, the distributed parameters of submarine cables exhibit significant frequency-varying characteristics, causing the actual propagation speed of the traveling wave to change with frequency. Theoretical analysis and measured data both show that the propagation speed difference between different frequency components can reach 1% to 5%. In submarine cable lines spanning hundreds of kilometers, this speed difference directly translates into a positioning error of hundreds of meters. For submarine cable faults, an error of hundreds of meters means a significant increase in the salvage and repair area, requiring the deployment of underwater robots for extensive searches, greatly extending the fault repair time, and increasing the risks and costs of offshore operations and salvage and repair. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for locating submarine cable faults. A traveling wave acquisition device is installed at at least one end of the submarine cable. The method includes: Step S1, the traveling wave acquisition device acquires the traveling wave signal generated after a fault occurs, and uses variational mode decomposition to decompose the fault traveling wave signal into several intrinsic mode function components; Step S2, based on the distributed electrical parameters per unit length of the submarine cable, a frequency-varying group velocity model characterizing the relationship between the traveling wave propagation speed and frequency is established; Step S3, based on the frequency-varying group velocity model, a group velocity matching the characteristic frequency of the intrinsic mode function components is determined; Step S4, based on each intrinsic mode function component and its corresponding group velocity, the corresponding fault distance is calculated, and the fault distances are weighted and fused to obtain the final fault distance.

[0006] Preferably, the variational mode decomposition in step S1 is achieved by transforming the signal decomposition problem into a variational constraint problem. The variational constraint problem is constructed as follows: minimizing the sum of the bandwidths of each intrinsic mode function component under the condition that the sum of all intrinsic mode function components is equal to the original signal.

[0007] Preferably, for the variational constrained problem, by introducing a quadratic penalty factor and Lagrange multipliers, the constrained problem is transformed into an unconstrained problem, and the eigenmode function components and their center frequencies are iteratively updated using the alternating direction multiplier method until convergence is achieved, so as to obtain the final eigenmode function components; the value of the quadratic penalty factor ranges from 1000 to 2500.

[0008] Preferably, before performing step S2, at least one valid intrinsic mode function component is selected from all the intrinsic mode function components for determining the group velocity in step S3. The selection process includes: calculating the normalized kurtosis of each intrinsic mode function component, and selecting the intrinsic mode function components with a normalized kurtosis greater than a preset threshold as valid intrinsic mode function components; the normalized kurtosis is calculated by the ratio of the fourth moment to the square of the second moment of the amplitude of each intrinsic mode function component.

[0009] Preferably, the frequency-varying group velocity model is established through the following steps: determining the frequency-varying series impedance and frequency-varying parallel admittance per unit length of the submarine cable based on the distributed electrical parameters per unit length, wherein the frequency-varying series impedance includes frequency-varying resistance and frequency-varying inductance, and the frequency-varying parallel admittance includes frequency-varying conductance and capacitance; calculating the propagation constant based on the frequency-varying series impedance and frequency-varying parallel admittance, wherein the propagation constant includes the phase shift constant; according to The group velocity was calculated. in, The phase shift constant is For the first Each intrinsic mode function component The corresponding center angular frequency.

[0010] Preferably, the frequency-varying resistor is expressed as: ; in, The skin effect coefficient, The DC resistance of the submarine cable conductor. The permeability of the submarine cable conductor ( ); The frequency-converting inductor is represented as: ; in, The permeability of free space, The outer diameter of the submarine cable insulation layer. Let be the radius of the submarine cable conductor. The frequency coefficient of the internal inductance. The internal inductance of a conductor, External inductor; The expression for the capacitance is: ; in, εr is the vacuum permittivity; εr is the relative permittivity of the insulating material. The expression for the frequency-varying conductance is: ; Wherein, tanδ is the tangent of the dielectric loss angle of the insulating material. It is a capacitor.

[0011] Preferably, in step S3, the characteristic frequency is determined by the following method: performing Hilbert transform on the selected intrinsic mode function components to construct an analytical signal, extracting the instantaneous frequency, and taking the average value of the instantaneous frequencies within a preset range of the fault wavefront as the characteristic frequency of the intrinsic mode function components.

[0012] Preferably, when the traveling wave acquisition device is installed at one end of the submarine cable, the corresponding fault distance is calculated based on the arrival time of the wavefront of each intrinsic mode function component and its corresponding group velocity; the arrival time of the wavefront of each intrinsic mode function component is obtained by detecting the Teager energy operator, and the detection process includes: calculating the corresponding instantaneous energy for each intrinsic mode function component, the calculation formula is as follows: ; in The first derivative of the intrinsic mode function component with respect to time is... The second derivative of the intrinsic mode function component with respect to time is then detected; subsequently, the moment when the instantaneous energy exceeds a preset threshold is taken as the arrival time of the wavefront.

[0013] Preferably, the weights of the weighted fusion are determined based on the normalized kurtosis and signal-to-noise ratio of each intrinsic mode function component; wherein, for each effective intrinsic mode function component, its normalized kurtosis is multiplied by the logarithm of the signal-to-noise ratio to obtain the fusion weight, and then the fusion weights of each effective intrinsic mode function component are normalized to obtain the normalized weights of each effective intrinsic mode function component.

[0014] Preferably, when the traveling wave acquisition device is installed at both ends of the submarine cable, the fault distance corresponding to each intrinsic mode function component is calculated based on the total length of the submarine cable, the group velocity corresponding to the intrinsic mode function component, and the arrival time difference of the intrinsic mode function component at the measurement points at both ends; the final fault distance is the weighted sum of the fault distance corresponding to each intrinsic mode function component and its normalized weight.

[0015] The above technical solution has the following advantages or beneficial effects: 1. Broadband fault traveling wave signals are adaptively decomposed into several intrinsic mode function (EMF) components using variational mode decomposition, each representing a specific narrowband frequency component. Based on this, a frequency-varying group velocity model is established using the physical parameters of the submarine cable. This model accurately reflects the frequency-dependent propagation velocity of the traveling wave energy envelope. By matching the group velocity corresponding to the characteristic frequency of each EMF component, independent calculation and correction of the propagation velocities of different frequency components are achieved. This physically compensates for the velocity differences caused by dispersion effects, significantly improving positioning accuracy.

[0016] 2. For at least one intrinsic mode function component after screening, calculate its wavefront arrival time and corresponding fault distance, and then weight and fuse the fault distances to obtain the final fault distance. This mechanism comprehensively utilizes the positioning information of different frequency components, effectively avoiding the random errors that may be introduced by a single frequency component, making the positioning results more stable and reliable, and applicable to submarine cable scenarios of different sea depths and lengths. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a method for locating submarine cable faults, as described in a preferred embodiment of the present invention. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The present invention is not limited to this embodiment; other embodiments that conform to the spirit of the present invention may also fall within the scope of the present invention.

[0019] In a preferred embodiment of the present invention, based on the above-mentioned problems existing in the prior art, a method for locating submarine cable faults based on VMD and frequency-varying group velocity correction is provided, such as... Figure 1 As shown, the process includes: Step S1, where the traveling wave acquisition device acquires the fault traveling wave signal generated after the fault occurs, and uses variational mode decomposition to decompose the fault traveling wave signal into several intrinsic mode function components; Step S2, based on the distributed electrical parameters per unit length of the submarine cable, a frequency-varying group velocity model characterizing the relationship between the traveling wave propagation speed and frequency is established; Step S3, based on the frequency-varying group velocity model, the group velocity matching the characteristic frequency of the intrinsic mode function component is determined; Step S4, based on each intrinsic mode function component and its corresponding group velocity, the corresponding fault distance is calculated, and the fault distances are weighted and fused to obtain the final fault distance.

[0020] Specifically, in this embodiment, a high-frequency traveling wave acquisition device is first installed at both ends or one end of the submarine cable to acquire transient voltage or current traveling wave signals after a fault occurs, denoted as... The acquired signals undergo denoising preprocessing to eliminate low-frequency background noise caused by wave motion and geomagnetic induction. Subsequently, variational mode decomposition (VMD) is used to decompose the preprocessed signal into... Each of the eigenmode function components represents a specific narrowband frequency component, denoted as _____. Where k = 1, 2, ..., K. Based on this, a frequency-varying group velocity model is established based on the distributed electrical parameters per unit length of the submarine cable. This model can reflect the propagation speed of the traveling wave energy envelope. The frequency-dependent variation pattern. For the selected components containing fault characteristics, the corresponding group velocity is matched from the model based on their frequency characteristics. Finally, the fault distance is calculated by combining the group velocity corresponding to each component, and the final fault distance is obtained by weighted fusion.

[0021] This embodiment effectively eliminates positioning errors caused by dispersion effects and significantly improves positioning accuracy by decomposing the broadband traveling wave signal into multiple narrowband components and matching a precise propagation speed to each component.

[0022] In another preferred embodiment of the present invention, the variational mode decomposition in step S1 is achieved by transforming the signal decomposition problem into a variational constraint problem. The variational constraint problem is constructed as follows: minimizing the sum of the bandwidths of each intrinsic mode function component under the condition that the sum of all intrinsic mode function components is equal to the original signal.

[0023] Specifically, in this embodiment, variational mode decomposition transforms the signal decomposition problem into a variational constraint problem. The mathematical expression of this problem is: under the constraint that the sum of all eigenmode function components equals the original signal... Under the given conditions, minimize the sum of the bandwidths of each component. This variational constraint problem can be specifically expressed as: ; ; in, For each modal component; The center frequency of each mode; It is the Dirac function; This represents the convolution operation; Let be the partial derivative with respect to time.

[0024] The core objective of this problem is to minimize the sum of the bandwidths of each component while ensuring that the sum of all decomposed intrinsic mode function components equals the original signal.

[0025] In this way, variational mode decomposition (VMD) adaptively decomposes the original signal into several narrowband components with sparse characteristics, each distributed around its own center frequency. Compared with traditional wavelet transform, VMD does not require pre-defined basis functions and has stronger adaptability; compared with empirical mode decomposition (EMD), VMD can effectively avoid mode aliasing and endpoint effects. This mathematical construction ensures the accuracy and stability of the decomposition results, laying a solid foundation for subsequent fault feature extraction and velocity correction.

[0026] In another preferred embodiment of the present invention, for the variational constrained problem, by introducing a quadratic penalty factor and Lagrange multipliers, the constrained problem is transformed into an unconstrained problem, and the eigenmode function components and their center frequencies are iteratively updated by the alternating direction multiplier method until convergence is obtained to obtain the final eigenmode function components; the value range of the quadratic penalty factor is 1000 to 2500.

[0027] Specifically, in this embodiment, a quadratic penalty factor is introduced to solve the above variational constraint problem. and Lagrange multipliers This transforms the original constrained problem into an unconstrained problem.

[0028] Among them, the secondary penalty factor The bandwidth used to control each component ranges from 1000 to 2500. This value is determined by combining the center frequency observation method with empirical values, taking into account the wide bandwidth and short-term impact characteristics of the traveling wave signal of submarine cable faults.

[0029] Lagrange multipliers Used to strictly enforce constraints. This ensures that the sum of all decomposed modes equals the original signal, thus preventing information loss.

[0030] Subsequently, the alternating direction multiplier method is used to iteratively update each eigenmode function component and its center frequency until convergence. During the iteration process, the Lagrange multipliers are dynamically updated; in the (n+1)th iteration, The update formula is: ; Where n is the number of iterations; : No. The frequency domain form of the Lagrange multipliers in the next iteration; To update the step size, also known as the noise tolerance parameter; This is the Fourier transform of the original signal x(t); This is the frequency domain representation of the k-th intrinsic mode function component after the (n+1)-th iteration update.

[0031] Update step size Typically, the value is 0 or a small positive number, ranging from [0, 0.1], to achieve a balance between denoising and signal preservation. Through this solution process, variational mode decomposition can efficiently and stably decompose the original signal into multiple physically meaningful narrowband components.

[0032] In another preferred embodiment of the present invention, before performing step S2, at least one valid intrinsic mode function component is selected from all the intrinsic mode function components for determining the group velocity in step S3. The selection process includes: calculating the normalized kurtosis of each intrinsic mode function component, and selecting the intrinsic mode function components with a normalized kurtosis greater than a preset threshold as valid intrinsic mode function components; the normalized kurtosis is calculated by the ratio of the fourth moment to the square of the second moment of the amplitude of each intrinsic mode function component.

[0033] Specifically, in this embodiment, not all eigenmode function components obtained through variational mode decomposition contain valid fault traveling wavefront information; some components may primarily consist of noise. Therefore, it is necessary to filter out the truly valid components that contain fault characteristics from among the numerous components.

[0034] In this embodiment, normalized kurtosis is used as a screening criterion. Kurtosis is a statistical measure that describes the distribution pattern of a signal and can reflect the impulse characteristics in the signal.

[0035] The formula for calculating normalized kurtosis is: ; in, For mathematical expectation operators, For the k-th intrinsic mode function component The mean, This represents the standard deviation of the component. Normalized kurtosis is calculated as the ratio of the fourth moment to the square of the second moment of each component's amplitude. A higher kurtosis indicates a more pronounced impulse characteristic in the signal, meaning a higher probability of containing fault information. A kurtosis threshold is set... (Usually an empirical value of 3.0 is used), and components with normalized kurtosis greater than this threshold are selected as the set of effective intrinsic mode function components. This eliminates the noise-dominated component, improving the accuracy and reliability of subsequent positioning calculations.

[0036] In another preferred embodiment of the present invention, the frequency-varying group velocity model is established through the following steps: determining the frequency-varying series impedance and frequency-varying parallel admittance per unit length of the submarine cable, wherein the frequency-varying series impedance includes frequency-varying resistance and frequency-varying inductance, and the frequency-varying parallel admittance includes frequency-varying conductance and capacitance; calculating the propagation constant based on the frequency-varying series impedance and frequency-varying parallel admittance, wherein the propagation constant includes attenuation constant and phase shift constant; and calculating the group velocity based on the result of differentiating the phase shift constant with respect to frequency.

[0037] Specifically, in this embodiment, the establishment of the frequency-varying group velocity model is one of the core technologies for compensating for dispersion effects in this invention.

[0038] First, determine the frequency-varying series impedance per unit length based on the physical structure of the submarine cable. and frequency-variable parallel admittance Its expression is: ; ; in, Angular frequency, The imaginary unit, For frequency-varying resistors, For frequency-converting inductors, C is the frequency-varying conductivity, and C is the capacitance.

[0039] Frequency-varying series impedance reflects the characteristics of increased resistance and decreased internal inductance of the submarine cable conductor at high frequencies, while frequency-varying parallel admittance reflects the polarization loss of the insulation material at high frequencies. Secondly, according to transmission line theory, the propagation constant γ(ω) is calculated from the series impedance and parallel admittance: ; ; in, The attenuation constant is This is the phase shift constant. Finally, the group velocity... Defined as the propagation speed of the traveling wave energy envelope, its calculation formula is: ; This is the reciprocal of the derivative of the phase shift constant with respect to frequency. Using this model, the accurate propagation speed of traveling wave components at different frequencies can be calculated, fundamentally solving the positioning error problem caused by the fixed wave speed in traditional methods.

[0040] In another preferred embodiment of the present invention, the frequency-varying resistor is expressed as the sum of the DC resistance and the skin effect correction term, which is proportional to the square root of the frequency; the frequency-varying inductor is expressed as the sum of the external inductance and the internal inductance, which is inversely proportional to the square root of the frequency; the frequency-varying conductance is related to the product of the frequency and the capacitance, as well as the tangent of the dielectric loss angle; the capacitance is determined by the dielectric constant of the insulating material and the geometry of the conductor and the shielding layer.

[0041] Specifically, in this embodiment, the parameters in the frequency-variable series impedance and frequency-variable parallel admittance are specifically defined. Frequency-variable resistance Represented as DC resistance The sum of the skin effect correction term and its approximate expression is: ; in, The skin effect coefficient is related to the conductor radius and conductivity. The skin effect correction term is proportional to the square root of the frequency, reflecting the increase in effective resistance caused by current flowing towards the conductor surface at high frequencies. In engineering approximations, it can be expressed as... ,in Where is the conductor radius, is the conductor's conductivity.

[0042] DC resistance of submarine cable conductors ( This value is determined by the cross-sectional area and conductor conductivity of the submarine cable, and can be found directly in the submarine cable manufacturer's specifications.

[0043] : The magnetic permeability of a conductor ( For copper conductors, .

[0044] Frequency conversion inductor Represented as external inductance With internal inductance The sum, its expression is: ; in, Vacuum permeability ; : Outer diameter of submarine cable insulation layer (i.e., inner radius of metal sheath or shielding layer) ); : Radius of the submarine cable conductor ( ); The frequency coefficient of internal inductance is related to the properties of the conductor material; External inductance is mainly determined by the geometry between the conductor and the metal sheath (or armor layer); The internal inductance of a conductor. As the frequency increases, the magnetic flux is repelled out of the conductor, and the internal inductance increases according to... Regular decay.

[0045] The expression for capacitor C is: ; in, Vacuum permittivity ; The relative permittivity of the insulating material (usually XLPE, cross-linked polyethylene). For XLPE, a value typically ranges from... between; Same as above, referring to the radius of the insulation layer and the radius of the conductor, respectively.

[0046] Frequency-varying conductivity The expression is: ; in, : The dielectric loss tangent of the insulating material. For XLPE material in high-voltage submarine cables, this value is usually very small (e.g., However, it cannot be ignored in long-distance transmission and high-frequency computing.

[0047] By using specific expressions for these parameters, the physical parameters and electrical characteristics of submarine cables can be precisely correlated, providing accurate input for calculating group velocity.

[0048] In another preferred embodiment of the present invention, in step S3, the characteristic frequency is determined by the following method: performing Hilbert transform on the selected intrinsic mode function components to construct an analytical signal, extracting the instantaneous frequency, and taking the average value of the instantaneous frequencies within a preset range of the fault wavefront as the characteristic frequency of the intrinsic mode function components.

[0049] Specifically, in this embodiment, for the selected effective intrinsic mode function components... To determine the characteristic frequencies used for velocity matching, we first perform a Hilbert transform on each effective eigenmode function component to construct an analytic signal. The expression for the Hilbert transform is: ; Constructing analytic signals using Hilbert transform : ; Instantaneous frequency can be extracted from the analytic signal. : ; Considering that the frequency components within the preset range of the fault wavefront best reflect the fault characteristics in the fault traveling wave signal, the average value of the instantaneous frequencies within the preset range of the fault wavefront is taken as the characteristic propagation frequency of this component. This characteristic frequency was then substituted into the frequency-varying group velocity model to calculate the precise propagation velocity corresponding to this component. .

[0050] In another preferred embodiment of the present invention, when a traveling wave acquisition device is installed at one end of the submarine cable, the corresponding fault distance is calculated based on the arrival time of the wavefront of each intrinsic mode function component and its corresponding group velocity. The arrival time of the wavefront of each intrinsic mode function component is detected by the Teager energy operator. The detection process includes: calculating the instantaneous energy of each intrinsic mode function component, where the instantaneous energy is equal to the square of the first derivative of the intrinsic mode function component minus the product of the intrinsic mode function component and its second derivative; then detecting the moment when the instantaneous energy exceeds a preset threshold, and taking that moment as the arrival time of the wavefront.

[0051] Specifically, in this embodiment, to address the problem of wavefront flatness and difficulty in accurately determining the wavefront arrival time caused by dispersion effects, the Teager energy operator is used for wavefront detection. The Teager energy operator is a nonlinear operator that can significantly amplify abrupt changes in the signal. For each effective intrinsic mode function component u_i(t), its instantaneous energy is calculated. : ; in, This is the first derivative of the component with respect to time. The second derivative of this component with respect to time. The physical meaning is for the effective eigenmode function components. The calculated sequence of Teager energy operator results. When the traveling wavefront arrives, the signal abruptly changes, and the instantaneous energy exhibits a sharp peak. This is achieved by detecting the instantaneous energy... Once the time exceeds the preset background noise threshold, the arrival time of the wavefront of that frequency band component can be accurately determined. This method can still accurately capture the starting point of a faulty wavefront even when long-distance transmission via submarine cables results in high attenuation and a flattened wavefront, effectively solving the problem of misjudgment caused by a flattened wavefront.

[0052] In another preferred embodiment of the present invention, the weights of the weighted fusion are determined based on the normalized kurtosis and signal-to-noise ratio of each intrinsic mode function component; wherein, for each valid intrinsic mode function component, its normalized kurtosis is multiplied by the logarithm of the signal-to-noise ratio to obtain the fusion weight, and then the fusion weights of each valid intrinsic mode function component are normalized to obtain the normalized weights of each valid intrinsic mode function component.

[0053] Specifically, in this embodiment, since modal components of different frequencies have different characteristics, high-frequency components have high positioning accuracy but large attenuation and low signal-to-noise ratio, while low-frequency components have high signal-to-noise ratio but flat wavefronts. Therefore, it is necessary to assign different weights to each component based on its quality for fusion.

[0054] In this embodiment, the fusion weight comprehensively considers two metrics: normalized kurtosis and signal-to-noise ratio. The formula for calculating the fusion weight is: ; in, Let be the normalized kurtosis of the i-th effective intrinsic mode function component. This represents the signal-to-noise ratio (SNR) of the component within a preset range of wavefront abrupt change points. Normalized kurtosis reflects the severity of impulse features in the signal; the more pronounced the impulse, the steeper the wavefront, and the higher the positioning accuracy. SNR reflects the reliability of the signal; the higher the SNR, the less susceptible to noise interference. Multiplying the normalized kurtosis by the logarithm of the SNR yields the fusion weight, which considers both the component's positioning potential and its reliability. Subsequently, the fusion weights of each effective component are normalized to obtain the normalized weights of each component:

[0055] This weighting mechanism can automatically reduce the weight of modes that are highly susceptible to noise interference or whose wave velocity calculation is inaccurate, making full use of the steepness of high-frequency components and the stability of low-frequency components, thereby improving the robustness of the algorithm.

[0056] In another preferred embodiment of the present invention, when the traveling wave acquisition device is installed at both ends of the submarine cable, the fault distance corresponding to each intrinsic mode function component is calculated based on the total length of the submarine cable, the group velocity corresponding to the intrinsic mode function component, and the arrival time difference of the intrinsic mode function component at the measurement points at both ends; the final fault distance is the weighted sum of the fault distance corresponding to each intrinsic mode function component and its normalized weight.

[0057] Specifically, in this embodiment, the calculation and fusion process of fault distance is illustrated using the two-end ranging method as an example. Let the total length of the submarine cable be... For the i-th valid intrinsic mode function component, the arrival time of this component at the two measurement points is obtained by detecting it using the aforementioned Teager energy operator, and then the arrival time difference is obtained. According to the principle of two-end ranging, the fault distance corresponding to this component is... The calculation formula is: ; in, Let be the group velocity corresponding to this component. Using this formula, a fault distance is calculated for each effective intrinsic mode function component. Since the propagation speeds and arrival time differences of each component are different, the calculated fault distances may have slight variations. The final fault distance is obtained by weighted summation of the fault distances calculated for each component: ; in, This refers to the normalized weights calculated in step nine. Through this weighted fusion, information from each frequency component is comprehensively utilized, further improving positioning accuracy.

[0058] Furthermore, the technical effects of the present invention are verified by taking a 100-kilometer-long 220 kV cross-linked polyethylene insulated three-core optoelectronic composite submarine cable as an example.

[0059] In this embodiment, the submarine cable parameters are first initialized, including the conductor DC resistance. The inductance is 0.098 ohms per kilometer. The capacitance C is calculated based on the cross-sectional data provided by the manufacturer, where the conductor radius... For a certain value, the outer diameter of the insulation layer For a certain value, the relative permittivity of the insulating material Take 2.4, the tangent of the dielectric loss angle. Set the value to 0.0004. The variational mode decomposition parameters are set as follows: number of modes K = 6, quadratic penalty factor α = 2000, update step size τ = 0.

[0060] When the monitoring system detects a breakdown fault in the submarine cable, it activates a dual-end high-speed acquisition device to acquire current traveling wave data within 20 milliseconds after the fault occurs at a sampling rate of 10 MHz. .

[0061] The collected traveling wave data The variational mode decomposition algorithm (VMD) was used to obtain six intrinsic mode function components (IMF components). The normalized kurtosis of each component was calculated. It was found that the low-frequency component IMF1 and the extremely high-frequency noise component IMF6 had relatively low kurtosis, while the mid-to-high-frequency components IMF2, IMF3, and IMF4 had significantly higher kurtosis than the threshold of 3.0, reaching 4.8, 7.2, and 5.6 respectively. Therefore, IMF2, IMF3, and IMF4 were selected as the effective intrinsic mode function components.

[0062] The selected effective component IMF3 was analyzed, and its average instantaneous frequencies at the wavefront were obtained by Hilbert transform as follows: =25 kHz. Substituting these characteristic frequencies into the frequency-varying group velocity model, the corresponding group velocity is calculated as follows: ; Similarly, calculate ( ), ( ).

[0063] The arrival time difference of each component at both ends was detected using the Teager energy operator, and the results are as follows: , , The higher the frequency, the faster the wave velocity and the smaller the time difference. The fault distance corresponding to each component is calculated based on the two-end ranging formula:

[0064]

[0065]

[0066] The three results are very close. Calculating the signal-to-noise ratio (SNR) of each component, IMF3 has the highest SNR, approximately 28 dB, while IMF2 and IMF4 have SNRs of approximately 22 dB and 20 dB, respectively. According to the fusion weight calculation formula, IMF3 has both the highest kurtosis and highest SNR, therefore it is assigned a normalized weight of 0.5, IMF2 is assigned 0.3, and IMF4 is assigned 0.2. The final fault distance is obtained after weighted fusion. .

[0067] The positioning result, verified in this embodiment, is locked at 59.766 kilometers. Compared to the traditional single wave velocity method, which may introduce an error of more than 500 meters, the positioning accuracy of this invention is improved to the meter level. This result fully demonstrates the significant effect of this invention in eliminating dispersion effects and improving positioning accuracy.

[0068] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made using the content of this specification and illustrations should be included within the protection scope of the present invention.

Claims

1. A method for locating submarine cable faults, characterized in that, A traveling wave acquisition device is installed at at least one end of the submarine cable, and the submarine cable fault location method includes: Step S1: The traveling wave acquisition device acquires the fault traveling wave signal generated after the fault occurs, and uses variational mode decomposition to decompose the fault traveling wave signal into several intrinsic mode function components. Step S2: Based on the distributed electrical parameters per unit length of the submarine cable, establish a frequency-varying group velocity model that characterizes the relationship between the propagation speed of traveling waves and the frequency. Step S3: Determine the group velocity that matches the characteristic frequency of the intrinsic mode function component based on the frequency-varying group velocity model; Step S4: Calculate the corresponding fault distance based on each intrinsic mode function component and its corresponding group velocity, and then weight and fuse the fault distances to obtain the final fault distance. Before performing step S2, the normalized kurtosis of each intrinsic mode function component is calculated, and the intrinsic mode function components with a normalized kurtosis greater than a preset threshold are selected as valid intrinsic mode function components. The weights of the weighted fusion are determined based on the normalized kurtosis and signal-to-noise ratio of each intrinsic mode function component. For each valid intrinsic mode function component, its normalized kurtosis is multiplied by the logarithm of the signal-to-noise ratio to obtain the fusion weight. Then, the fusion weights of each valid intrinsic mode function component are normalized to obtain the normalized weights of each valid intrinsic mode function component.

2. The submarine cable fault location method according to claim 1, characterized in that, The variational mode decomposition in step S1 is achieved by transforming the signal decomposition problem into a variational constraint problem. The variational constraint problem is constructed as follows: under the condition that the sum of all intrinsic mode function components is equal to the original signal, minimize the sum of the bandwidths of each intrinsic mode function component.

3. The submarine cable fault location method according to claim 2, characterized in that, For the variational constrained problem, by introducing a quadratic penalty factor and Lagrange multipliers, the constrained problem is transformed into an unconstrained problem. The eigenmode function components and their center frequencies are iteratively updated using the alternating direction multiplier method until convergence is achieved, so as to obtain the final eigenmode function components. The value of the quadratic penalty factor ranges from 1000 to 2500.

4. The submarine cable fault location method according to claim 1, characterized in that, The normalized kurtosis is calculated by the ratio of the fourth moment to the square of the second moment of each intrinsic mode function component amplitude.

5. The submarine cable fault location method according to claim 1, characterized in that, The frequency-varying group velocity model is established through the following steps: The frequency-varying series impedance and frequency-varying parallel admittance per unit length of the submarine cable are determined based on the distributed electrical parameters per unit length, wherein the frequency-varying series impedance includes frequency-varying resistance and frequency-varying inductance, and the frequency-varying parallel admittance includes frequency-varying conductance and capacitance. The propagation constant is calculated based on the frequency-varying series impedance and the frequency-varying parallel admittance, and the propagation constant includes the phase shift constant. according to The group velocity was calculated. in, The phase shift constant is For the first Each intrinsic mode function component The corresponding center angular frequency.

6. The submarine cable fault location method according to claim 5, characterized in that, The frequency-converting resistor is represented as: ； in, The skin effect coefficient, The DC resistance of the submarine cable conductor. Permeability of the submarine cable conductor f is the frequency. Angular frequency; The frequency-converting inductor is represented as: ； in, The permeability of free space, The outer diameter of the submarine cable insulation layer. Let be the radius of the submarine cable conductor. The frequency coefficient of the internal inductance. The internal inductance of a conductor, External inductor; The expression for the capacitance is: ； in, The vacuum permittivity, The relative permittivity of the insulating material; The expression for the frequency-varying conductance is: ； in, This is the tangent of the dielectric loss angle of the insulating material. It is a capacitor.

7. The submarine cable fault location method according to claim 1, characterized in that, In step S3, the characteristic frequency is determined in the following ways: The selected intrinsic mode function components are subjected to Hilbert transform to construct an analytical signal, and the instantaneous frequencies are extracted. The average value of the instantaneous frequencies within a preset range of the fault wavefront is taken as the characteristic frequency of the intrinsic mode function components.

8. The submarine cable fault location method according to claim 1, characterized in that, When the traveling wave acquisition device is installed at one end of the submarine cable, the corresponding fault distance is calculated based on the arrival time of the wavefront of each intrinsic mode function component and its corresponding group velocity. The arrival times of the wavefronts of each intrinsic mode function component are obtained by detecting the Teager energy operator. The detection process includes: The instantaneous energy corresponding to each intrinsic mode function component is calculated using the following formula: ； in The first derivative of the intrinsic mode function component with respect to time is... The second derivative of the intrinsic mode function component with respect to time is given by . The moment when the instantaneous energy exceeds a preset threshold is then detected and taken as the arrival time of the wavefront.

9. The method according to claim 1, characterized in that, When the traveling wave acquisition device is installed at both ends of the submarine cable, the fault distance corresponding to each intrinsic mode function component is calculated based on the total length of the submarine cable, the group velocity corresponding to the intrinsic mode function component, and the arrival time difference of the intrinsic mode function component at the two measurement points. The final fault distance is the weighted sum of the fault distances corresponding to each intrinsic mode function component and their normalized weights.

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