A method for locating micro-defects of power cable based on CFI-Z algorithm

Abstract

This invention discloses a method for locating minor defects in power cables based on the CFI-Z algorithm. It obtains the reflection coefficient vector at the beginning of the power cable from a multi-frequency swept signal, and then, based on the continuously frequency-enhanced Z-transform matrix, acquires the minimum norm least squares solution and the closed-form solution of the power cable fault location factor. Furthermore, it obtains the sparsity intensity of the minimum norm least squares solution and the closed-form solution to arrive at the final solution of the power cable fault location factor. Finally, it obtains the location of the power cable defect based on the time-domain sequence of the reflection at the beginning of the power cable, thus completing the location of early-stage defects in the cable. This invention solves the problems of insufficient high-frequency components and bandwidth limitations in the injected pulse, resulting in high sensitivity and strong noise resistance for power cable defect location. Especially in the case of long cables or cables with minor defects, the location error is small, and it has a good effect on locating early-stage minor defects.

Description

Technical Field

[0001] This invention relates to the field of cable defect location technology, and in particular to a method for locating minute defects in power cables based on the CFI-Z algorithm. Background Technology

[0002] Early minor defects in power cables refer to small damage to the cable insulation or conductor surface. These defects typically have a limited impact on overall performance and safety. Specific criteria for minor defects include: scratches on the cable body with a length less than 5 cm, a depth less than 1 mm, and a capacitance change at the defect location less than 5%. Although early minor defects do not lead to complete electrical failure, they can easily cause localized insulation aging or current concentration during prolonged high-load operation or under extreme conditions.

[0003] Cable defects typically manifest as changes in location characteristic impedance, making the traveling wave method effective for defect detection. Currently, the main location methods include Time Domain Reflectometry (TDR), Frequency Domain Reflectometry (FDR), and Time-Frequency Domain Reflectometry (TFDR), all based on traveling wave theory. Among these, TDR and TFDR are widely used in field testing due to their simple principles and convenient calculations. However, both methods suffer from insufficient high-frequency components in the injected pulse, resulting in low defect location sensitivity and poor noise immunity. Therefore, in the case of long cables or cables with small defects, the location error is relatively large. Furthermore, due to signal noise and bandwidth limitations, their effectiveness in locating early-stage small defects is less than ideal. Summary of the Invention

[0004] This invention discloses a method for locating minute defects in power cables based on the CFI-Z algorithm, in order to overcome the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for locating minute defects in power cables based on the CFI-Z algorithm includes the following steps:

[0007] S1: Establish a reflection coefficient acquisition instrument for measuring the reflection coefficient of the beginning of a power cable to obtain N reflection coefficient vectors of the beginning of the power cable; the reflection coefficient vectors of the beginning of the power cable include the reflection coefficients of the beginning of the power cable obtained based on frequency sweep signals of multiple frequencies; where N represents the total number of reflection coefficient vectors of the beginning of the power cable.

[0008] S2: Based on the N power cable head reflection coefficient vectors, obtain M sampling points, where M < N, based on the CFI-Z algorithm to obtain a continuous frequency increasing Z-transform matrix, i.e., the CFI-Z matrix; where M represents the total number of sampling points;

[0009] S3: Based on the continuous frequency increasing Z-transform matrix and the power cable head reflection coefficient vectors, establish a minimized quadratic difference equation, and obtain the least squares solution with minimum norm of the power cable fault location factor based on the least squares method with minimum norm, and obtain the closed-form solution of the power cable fault location factor based on the closed-form solution method;

[0010] S4: Based on the least squares solution with minimum norm of the power cable fault location factor and the closed-form solution of the power cable fault location factor, obtain the sparsity intensity of the least squares solution with minimum norm of the power cable fault location factor and the sparsity intensity of the closed-form solution of the power cable fault location factor;

[0011] S5: Based on the sparsity intensity of the least squares solution with minimum norm of the power cable fault location factor and the sparsity intensity of the closed-form solution of the power cable fault location factor, obtain the final solution of the power cable fault location factor, and based on the minimized quadratic difference equation, obtain the head reflection time domain sequence of the power cable;

[0012] S6: Based on the head reflection time domain sequence of the power cable, obtain the location of the power cable defect to complete the location of the early defect of the cable.

[0013] Further, the formulas for obtaining the sparsity intensity of the least squares solution with minimum norm of the power cable fault location factor and the sparsity intensity of the closed-form solution of the power cable fault location factor are as follows:

[0014]

[0015]

[0016] In the formula, represents the sparsity intensity of the location factor; i represents the row index of the location factor matrix; j' represents the column index of the location factor matrix; I represents the total number of rows of the location factor matrix; J represents the total number of columns of the location factor matrix; is the indicator function; represents the element in the i-th row and j'-th column of the location factor matrix.

[0017] Further, the method for obtaining the final solution of the power cable fault location factor is as follows:

[0018] If the sparsity strength of the least norm least squares solution of the power cable fault location factor is greater than the sparsity strength of the closed solution of the power cable fault location factor, then the final solution of the power cable fault location factor is the least norm least squares solution of the power cable fault location factor.

[0019] Otherwise, the final solution of the power cable fault location factor is a closed solution of the power cable fault location factor.

[0020] Furthermore, the formula for calculating the location of the power cable defect is as follows:

[0021] L = x × V

[0022] In the formula: L is the distance from the beginning of the power cable; V represents the signal propagation speed of the power cable.

[0023] Furthermore, the reflection coefficient acquisition instrument includes: a frequency sweep signal generation module, a reflection signal extraction module, and a receiver module;

[0024] The frequency sweep signal generation module is used to acquire frequency sweep signals at the beginning of the power cable at multiple frequencies, so as to generate a reflected signal when there is a defect in the power cable; at this time, both the frequency sweep signal and the reflected signal exist at the beginning of the power cable.

[0025] The signal separation module is used to extract reflected signals at the beginning of the power cable when there is a defect in the power cable;

[0026] The receiver module is used to obtain the reflection coefficient of the power cable head end based on the reflected signal.

[0027] Furthermore, the reflected signal extraction module includes a first resistor R1, a second resistor R2, a third resistor R3, a fourth resistor R4, a fifth resistor R5, a sixth resistor R6, a seventh resistor R7, a first capacitor C1, a second capacitor C2, a third capacitor C3, a fourth capacitor C4, a fifth capacitor C5, a sixth capacitor C6, a seventh capacitor C7, an eighth capacitor C8, a ninth capacitor C9, a power cable SMA connector, an N-type transistor Q1, a feedthrough capacitor filter; a first inductor L1, a second inductor L2, a third inductor L3, an operational amplifier module U2, and a differential operational amplifier module U1;

[0028] The SMA connector of the power cable is connected to the beginning end of the power cable.

[0029] Pin 5 of the SMA connector of the power cable is connected to the sweep frequency signal generation module; pins 1 and 4 of the SMA connector of the power cable are grounded; pin 2 of the SMA connector of the power cable is connected to one end of the fourth resistor R4; pin 3 of the SMA connector of the power cable is connected to the output terminal of the feedthrough capacitor filter.

[0030] The input terminal and the feedback terminal of the feedthrough capacitor filter are both connected to the other end of the fourth resistor R4.

[0031] One end of the third resistor R3 and one end of the first resistor R1 are both connected to the connection point between the input terminal of the feedthrough capacitor filter and the fourth resistor R4.

[0032] The other end of the third resistor R3 is connected to pin 5 of the SMA connector of the power cable.

[0033] One end of the second resistor R2 is connected to pin 5 of the SMA connector of the power cable;

[0034] The other end of the first resistor R1 and the other end of the second resistor R2 are both connected to the emitter of the N-type transistor Q1;

[0035] The base of the N-type transistor Q1 is connected to the connection point between the input terminal of the feedthrough capacitor filter and the fourth resistor R4.

[0036] The collector of the N-type transistor Q1 is connected to the first capacitor C1;

[0037] The other end of the first capacitor C1 is connected to one end of the second capacitor C2; the other end of the second capacitor C2 is connected to one end of the third capacitor C3.

[0038] The first inductor L1, the second inductor L2, and the third inductor L3 are connected in parallel with the first capacitor C1, the second capacitor C2, and the third capacitor C3, respectively.

[0039] One end of the fourth capacitor C4 is connected to the junction of the collector of the N-type transistor Q1 and the first capacitor C1; one end of the fifth capacitor C5 is connected to the junction of the first capacitor C1 and the second capacitor C2; one end of the sixth capacitor C6 is connected to the junction of the second capacitor C2 and the third capacitor C3; one end of the seventh capacitor C7 is connected to the other end of the third capacitor C3; the other ends of the fourth capacitor C4, the fifth capacitor C5, the sixth capacitor C6, and the seventh capacitor C7 are all grounded;

[0040] The other end of the third capacitor C3 is connected to pin 3 of the operational amplifier module U2;

[0041] The two ends of the fifth resistor R5 are connected to pin 1 and pin 2 of the operational amplifier module U2, respectively;

[0042] One end of the sixth resistor R6 is connected to pin 2 of the operational amplifier module U2, and the other end is grounded;

[0043] One end of the eighth capacitor C8 is connected to the junction of the second resistor R2 and the third resistor R3, and the other end is connected to pin 8 of the differential operational amplifier module U1.

[0044] Pin 1 of the differential operational amplifier module U1 is connected to one end of the ninth capacitor C9; the other end of the ninth capacitor C9 is connected to the feedback terminal of the feedthrough capacitor filter; pin 4 of the differential operational amplifier module U1 is grounded; pin 6 of the differential operational amplifier module U1 is connected to one end of the seventh resistor R7, the other end of the seventh resistor R7 can be connected to the eighth resistor R8, and the other end of the eighth resistor R8 is grounded.

[0045] Pin 5 of the differential operational amplifier module U1 is connected to the connection point of the seventh resistor R7 and the eighth resistor R8;

[0046] Pin 6 of the differential operational amplifier module U1 is connected to the receiver module.

[0047] Furthermore, the formula used to obtain the continuously frequency-enhanced Z-transform matrix is ​​as follows:

[0048]

[0049] In the formula, C represents the continuously increasing frequency Z-transform matrix, i.e., the CFI-Z matrix; R0 is the starting radius of the sampling path of the reflection coefficient vector at the beginning of the power cable in the Z plane; j represents the imaginary unit of the complex number; θ0 represents the starting phase angle of the sampling path of the reflection coefficient vector at the beginning of the power cable in the Z plane; n represents the index number of the reflection coefficient vector at the beginning of the cable, n = 0, 1, 2, ..., N-1; N represents the total number of reflection coefficient vectors at the beginning of the cable. F0 represents the angular frequency difference between two adjacent sampling points on the sampling path of the reflection coefficient vector at the beginning of the power cable in the Z-plane; F0 represents the elongation of the helix; m represents the number of the sampling point in the Z-plane, m = 0, 1, 2, ..., M-1; M represents the total number of sampling points in the Z-plane, and M-1 <N。

[0050] Furthermore, the equation for minimizing the quadratic difference is established as follows:

[0051]

[0052] In the formula: Indicates the fault location factor for power cables; Let Cx-X be the L2 norm; arg be the objective function to be minimized; x be the time-domain sequence of reflections at the beginning of the power cable; X be the vector sequence of reflection coefficients at the beginning of the power cable, i.e., the frequency-domain sequence of reflections at the beginning of the power cable; and C be the continuously increasing frequency Z-transform matrix.

[0053] Furthermore, the closed-form solution of the power cable fault location factor is obtained as follows:

[0054]

[0055] In the formula: This represents the closed-form solution of the fault location factor for power cables.

[0056] Furthermore, the minimum norm least squares solution of the power cable fault location factor is obtained as follows:

[0057]

[0058] In the formula: The least-norm least-squares solution represents the fault location factor of a power cable.

[0059] Beneficial Effects: This invention provides a method for locating minor defects in power cables based on the CFI-Z algorithm. Using a constructed reflection coefficient acquisition instrument, it obtains a vector of reflection coefficients at the beginning of the power cable, composed of reflection coefficients from multiple frequency sweep signals. Based on a continuously increasing frequency Z-transform matrix, it acquires the minimum norm least squares solution and the closed-form solution of the power cable fault location factor. Furthermore, it obtains the sparsity intensity of the minimum norm least squares solution and the closed-form solution to obtain the final solution of the power cable fault location factor. Finally, based on the time-domain sequence of the reflection at the beginning of the power cable, it obtains the location of the power cable defect, thus completing the location of early-stage defects in the cable. Because the reflection coefficient acquisition instrument of this invention obtains the reflection coefficient vector at the beginning of the power cable based on multiple frequency sweep signals, it solves the problems of insufficient high-frequency components and bandwidth limitations in the injected pulse. This results in high sensitivity and strong noise resistance for power cable defect location, especially in the case of long cables or cables with minor defects, where the location error is small, and it has a good effect on locating early-stage minor defects. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0061] Figure 1 This is a flowchart of the method for locating minute defects in power cables based on the CFI-Z algorithm of the present invention;

[0062] Figure 2 This is a block diagram of the overall design of the reflection coefficient acquisition instrument in an embodiment of the present invention;

[0063] Figure 3 This is a schematic diagram of the signal separation module circuit in an embodiment of the present invention;

[0064] Figure 4 This is a schematic diagram of the AD9854 and its peripheral circuits in an embodiment of the present invention;

[0065] Figure 5 This is a schematic diagram of the gain phase detection circuit in an embodiment of the present invention;

[0066] Figure 6a This is a schematic diagram of the power cable defect location spectrum under DFT transformation in an embodiment of the present invention;

[0067] Figure 6b This is a schematic diagram of the power cable defect location spectrum under CFI-Z transformation in an embodiment of the present invention;

[0068] Figure 7a This is a schematic diagram of the experimental results under the DFT transformation of sample #2 in this embodiment of the invention;

[0069] Figure 7b This is a schematic diagram of the experimental results under the DFT transformation of sample #3 in this embodiment of the invention;

[0070] Figure 7c This is a schematic diagram of the experimental results under the DFT transformation of sample #4 in this embodiment of the invention;

[0071] Figure 8a This is a schematic diagram of the experimental results under CFI-Z transform for sample #2 in this embodiment of the invention;

[0072] Figure 8b This is a schematic diagram of the experimental results under CFI-Z transform for sample #3 in this embodiment of the invention;

[0073] Figure 8c This is a schematic diagram of the experimental results under the CFI-Z transform of sample #4 in this embodiment of the invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] This embodiment introduces a method for locating minute defects in power cables based on the CFI-Z algorithm, such as... Figure 1 As shown,

[0076] S1: Establish a reflection coefficient acquisition instrument for measuring the reflection coefficient at the beginning of a power cable to obtain N reflection coefficient vectors at the beginning of the power cable; the reflection coefficient vectors at the beginning of the power cable include the reflection coefficients at the beginning of the power cable obtained based on multiple scanning frequencies;

[0077] Preferably, the reflection coefficient acquisition instrument includes: a frequency sweep signal generation module, a reflection signal extraction module, and a receiver module;

[0078] The frequency sweep signal generation module is used to acquire frequency sweep signals at the beginning of the power cable at multiple frequencies, so as to generate a reflected signal when there is a defect in the power cable; at this time, both the frequency sweep signal and the reflected signal exist at the beginning of the power cable.

[0079] The signal separation module is used to extract reflected signals at the beginning of the power cable when there is a defect in the power cable;

[0080] The receiver module is used to obtain the reflection coefficient of the power cable head end based on the reflected signal.

[0081] Specifically, it also includes a power supply module and a main control module. The power supply module provides power to the sweep frequency signal generation module, the reflection signal extraction module, and the receiver module. The main control module controls the sweep frequency of the sweep frequency signal generation module and transmits the reflection coefficient of the power cable end obtained by the receiver module to the host computer. In this embodiment, the main control module also controls the relevant configuration of the ADC module in the receiver module and configures the output voltage value of the gain and phase module, such as... Figure 2 As shown, the system uses the STM32F407 as the main control module. This chip is based on the ARM Cortex-M4 architecture, with a main frequency of up to 168MHz and a computing power of 120DMIPS, which can meet the real-time and computational performance requirements of the reflectance coefficient acquisition instrument. A system power supply module is also provided to ensure stable operation of the device.

[0082] Specifically, the reflection coefficient acquisition instrument in this embodiment is mainly used to measure the reflection coefficient at the cable head end and transmit the data to the host computer for processing. The core of the device includes two sweep frequency signal sources generated by DDS, and uses a transmission signal extraction module to separate the incident and reflected signals at the cable head end. The reflected signals generated by the defect location of the power cable are then output as the amplitude and phase of the reflection coefficient through an amplitude and phase discrimination circuit.

[0083] Specifically, the sweep frequency signal generation module in this embodiment mainly consists of a DDS chip and its peripheral circuits, a low-pass filter circuit, and an amplifier circuit. The AD9854 is a highly integrated digital synthesizer capable of generating four programmable sine waves (frequency, phase, and amplitude), each with a 90° phase difference, and one square wave signal. This paper selects the AD9854 as the DDS chip to meet the requirements of a test frequency range of 150kHz to 100MHz. The schematic diagram of the AD9854 and its peripheral circuits is shown below. Figure 4 As shown.

[0084] Preferably, the reflected signal extraction module includes a first resistor R1, a second resistor R2, a third resistor R3, a fourth resistor R4, a fifth resistor R5, a sixth resistor R6, a seventh resistor R7, a first capacitor C1, a second capacitor C2, a third capacitor C3, a fourth capacitor C4, a fifth capacitor C5, a sixth capacitor C6, a seventh capacitor C7, an eighth capacitor C8, a ninth capacitor C9, a power cable SMA connector, an N-type transistor Q1, a feedthrough capacitor filter; a first inductor L1, a second inductor L2, a third inductor L3, an operational amplifier module U2, and a differential operational amplifier module U1.

[0085] The SMA connector of the power cable is connected to the beginning end of the power cable.

[0086] Pin 5 of the SMA connector of the power cable is connected to the sweep frequency signal generation module; pins 1 and 4 of the SMA connector of the power cable are grounded; pin 2 of the SMA connector of the power cable is connected to one end of the fourth resistor R4; pin 3 of the SMA connector of the power cable is connected to the output terminal of the feedthrough capacitor filter.

[0087] The input terminal and the feedback terminal of the feedthrough capacitor filter are both connected to the other end of the fourth resistor R4.

[0088] One end of the third resistor R3 and one end of the first resistor R1 are both connected to the connection point between the input terminal of the feedthrough capacitor filter and the fourth resistor R4.

[0089] The other end of the third resistor R3 is connected to pin 5 of the SMA connector of the power cable.

[0090] One end of the second resistor R2 is connected to pin 5 of the SMA connector of the power cable;

[0091] The other end of the first resistor R1 and the other end of the second resistor R2 are both connected to the emitter of the N-type transistor Q1;

[0092] The base of the N-type transistor Q1 is connected to the connection point between the input terminal of the feedthrough capacitor filter and the fourth resistor R4.

[0093] The collector of the N-type transistor Q1 is connected to the first capacitor C1;

[0094] The other end of the first capacitor C1 is connected to one end of the second capacitor C2; the other end of the second capacitor C2 is connected to one end of the third capacitor C3.

[0095] The first inductor L1, the second inductor L2, and the third inductor L3 are connected in parallel with the first capacitor C1, the second capacitor C2, and the third capacitor C3, respectively.

[0096] One end of the fourth capacitor C4 is connected to the junction of the collector of the N-type transistor Q1 and the first capacitor C1; one end of the fifth capacitor C5 is connected to the junction of the first capacitor C1 and the second capacitor C2; one end of the sixth capacitor C6 is connected to the junction of the second capacitor C2 and the third capacitor C3; one end of the seventh capacitor C7 is connected to the other end of the third capacitor C3; the other ends of the fourth capacitor C4, the fifth capacitor C5, the sixth capacitor C6, and the seventh capacitor C7 are all grounded;

[0097] The other end of the third capacitor C3 is connected to pin 3 of the operational amplifier module U2;

[0098] The two ends of the fifth resistor R5 are connected to pin 1 and pin 2 of the operational amplifier module U2, respectively;

[0099] One end of the sixth resistor R6 is connected to pin 2 of the operational amplifier module U2, and the other end is grounded;

[0100] One end of the eighth capacitor C8 is connected to the junction of the second resistor R2 and the third resistor R3, and the other end is connected to pin 8 of the differential operational amplifier module U1.

[0101] Pin 1 of the differential operational amplifier module U1 is connected to one end of the ninth capacitor C9; the other end of the ninth capacitor C9 is connected to the feedback terminal of the feedthrough capacitor filter; pin 4 of the differential operational amplifier module U1 is grounded; pin 6 of the differential operational amplifier module U1 is connected to one end of the seventh resistor R7, the other end of the seventh resistor R7 can be connected to the eighth resistor R8, and the other end of the eighth resistor R8 is grounded.

[0102] Pin 5 of the differential operational amplifier module U1 is connected to the connection point of the seventh resistor R7 and the eighth resistor R8;

[0103] Pin 6 of the differential operational amplifier module U1 is connected to the receiver module.

[0104] Specifically, both the differential operational amplifier module U1 and the operational amplifier module U2 are connected to the power supply, which is a standard technique and will not be described in detail here.

[0105] Specifically, when measuring the reflection coefficient of a cable, it is necessary to obtain the amplitude and phase of the reflected signal at the cable's head end. When a signal source inputs a signal to the cable's head end, the incident signal will be reflected when it encounters a fault point. Therefore, both the incident and reflected signals will appear simultaneously at the cable's head end, requiring the use of a reflection signal extraction module to extract the reflected signal. This embodiment uses a reflection signal extraction module to extract the reflected signal, such as... Figure 3 As shown, the incident signal IOUT enters the SMA interface (cable head end) through the signal conditioning circuit. The differential voltage signal output from its two ends is filtered out by the feedthrough capacitor to remove the DC component, and then the reflected signal V_REF is output by the differential operational amplifier.

[0106] Specifically, Figure 5 This is a schematic diagram of the gain and phase detection circuit in the receiver module of this embodiment. The chip is powered by a single 5V power supply. V_REF is the reflected signal from the cable end, V_INC is the incident signal, and VMAG and VPHS output amplitude ratio and phase difference analog signals for ADC processing.

[0107] S2: Obtain M sampling points based on the CFI-Z algorithm, and obtain the CFI-Z matrix, i.e., the continuously frequency-enhanced Z-transform matrix. The formula used is as follows:

[0108] Specifically, similar to the Discrete Fourier Transform, the continuously frequency-enhanced Z-transform matrix can also be represented in matrix form:

[0109] X = Cx (1)

[0110] In the formula: C represents the continuously increasing frequency Z-transform matrix, i.e., the CFI-Z matrix, with a size of M×N; x represents the time-domain sequence of reflection at the beginning of the power cable; X represents the vector sequence of reflection coefficients at the beginning of the power cable, i.e., the frequency-domain sequence of reflection at the beginning of the power cable.

[0111] Specifically, in this embodiment, the reflection coefficient acquisition instrument transmits a swept frequency signal. The reflection coefficient vector sequence X at the beginning of the power cable is in the form of a frequency domain signal matrix and is obtained by the reflection coefficient acquisition instrument in this embodiment. x is the time domain sequence of the reflection at the beginning of the power cable, which is also in matrix form. C is the CFI-Z matrix.

[0112]

[0113] Wherein, R0 is the starting radius of the sampling path of the reflection coefficient vector at the head end of the power cable in the Z plane; j represents the imaginary unit of a complex number; θ0 represents the starting phase angle of the sampling path of the reflection coefficient vector at the head end of the power cable in the Z plane; n represents the index number of the reflection coefficient vector at the cable head end, n = 0, 1, 2, …, N - 1; N represents the total number of reflection coefficient vectors at the cable head end; represents the angular frequency difference between two adjacent sampling points on the sampling path of the reflection coefficient vector at the head end of the power cable in the Z plane; F0 represents the stretch rate of the helix; m represents the number of sampling points in the Z plane, m = 0, 1, 2, …, M - 1; M represents the total number of sampling points in the Z plane, and M < N.

[0114] Specifically, the Z plane is a basic concept in control theory. In this embodiment, the horizontal axis of the Z plane represents the magnitude of the reflection coefficient, and the vertical axis represents the frequency. Among them, the sparse sampling path is a path for arranging sampling points on the complex frequency plane defined in CFI-Z. It samples by selecting specific complex frequency values and following certain rules to achieve high-resolution analysis of the signal in a specific frequency region. Specifically, the sampling path usually changes in the form of a helix or arc in the complex frequency plane, which can flexibly focus on the frequency band of interest of the signal, achieve non-uniform and dense frequency sampling, and thus capture the subtle changes and characteristics of the signal.

[0115] Then the inverse expression is as shown in Equation (3), that is, mapping the frequency-domain signal X to the time-domain signal x.

[0116] x = C -1 X (3)

[0117] [[ID=!However, for a general CFI-Z matrix, that is, M < N. Using a general matrix will lead to inverse ill-posedness, that is, problems of no solution, non-unique solution, or extremely sensitive solution to the input.

[0118] S3: According to the continuous frequency increase Z-transform matrix and the reflection coefficient vector at the head end of the power cable, establish a minimized quadratic difference equation, and obtain the least squares solution of the minimum norm of the power cable fault location factor based on the least squares method of minimum norm, and obtain the closed-form solution of the power cable fault location factor based on the closed-form solution method;

[0119] Specifically, this embodiment regards such an inverse problem as a minimization problem, that is, seeking to minimize the quadratic difference between Cx and X.

[0120] Preferably, the minimized quadratic difference equation is established as follows:

[0121]

[0122] In the formula: [[ID=![]] Indicates the fault location factor for power cables; Denote the L2 norm of Cx-X;

[0123] Specifically, in this embodiment, the minimum norm least squares solution of the power cable fault location factor is obtained based on the minimum quadratic difference method, and the closed solution of the location factor is obtained based on the closed form solution method. The methods used are all conventional techniques in the field and will not be elaborated here.

[0124] Preferably, the closed-form solution of the power cable fault location factor is obtained as follows:

[0125]

[0126] In the formula: This represents the closed-form solution of the fault location factor for power cables.

[0127] Preferably, the least-norm least-squares solution of the power cable fault location factor is obtained as follows:

[0128]

[0129] In the formula: The least-norm least-squares solution representing the fault location factor of a power cable;

[0130] S4: Based on the minimum norm least squares solution and the closed solution of the power cable fault location factor, and based on the zero element calculation formula of the location factor, obtain the sparsity strength of the minimum norm least squares solution and the sparsity strength of the closed solution of the power cable fault location factor, respectively.

[0131] Specifically, this embodiment can obtain the number of zero elements in the least squares solution of the minimum norm of the fault location factor and the number of zero elements in the closed solution of the fault location factor of the power cable based on the zero element calculation formula of the location factor.

[0132] Specifically, considering the problem of minute reflections along the cable, assumptions are made about the time-domain sequence x of reflections at the beginning of the power cable. These assumptions are called priors and are used to regulate ill-posed inverse problems, meaning that multiple solutions exist in the case of an underdetermined inverse problem. One of the prior conditions is the sparsity of the weak signal; a signal is considered sparse when it has a large number of zero elements. Therefore, the minimum solution with non-zero elements, i.e., the weakest location factor, can be determined using the following method.

[0133] Specifically, in this embodiment, the minimum norm least squares solution and the closed-form solution of the power cable fault location factor are used to count the number of zero elements using the following formula for calculating the zero elements of the location factor:

[0134]

[0135] In the formula, The sparseness of the location factors is represented by ; i represents the row index of the location factor matrix; j′ represents the column index of the location factor matrix; I represents the total number of rows in the location factor matrix; J represents the total number of columns in the location factor matrix. It is an indicator function; This represents the element in the i-th row and j′-th column of the matrix representing the location factors.

[0136] Specifically, the minimum norm least squares solution and the closed solution of the power cable fault location factor are substituted into the zero element calculation formula of the location factor to obtain the sparsity strength of the minimum norm least squares solution and the sparsity strength of the closed solution of the power cable fault location factor.

[0137] S5: Based on the sparsity strength of the least squares solution of the minimum norm of the power cable fault location factor and the sparsity strength of the closed solution of the power cable fault location factor, obtain the final solution of the power cable fault location factor, and obtain the time-domain sequence of the first-end reflection of the power cable according to the minimum quadratic difference equation.

[0138] Preferably, the final solution for the power cable fault location factor is obtained as follows:

[0139] If the sparsity strength of the least norm least squares solution of the power cable fault location factor is greater than the sparsity strength of the closed solution of the power cable fault location factor, then the final solution of the power cable fault location factor is the least norm least squares solution of the power cable fault location factor.

[0140] Otherwise, the final solution of the power cable fault location factor is a closed solution of the power cable fault location factor.

[0141] Specifically, by substituting the final solution of the power cable fault location factor into the minimization quadratic difference equation, the time-domain sequence x of the power cable head-end reflection can be obtained.

[0142] S6: Based on the time-domain sequence of reflections at the beginning of the power cable, the location of the power cable defect is obtained to complete the localization of early defects in the cable.

[0143] Preferably, the formula for calculating the location of the power cable defect is as follows:

[0144] L = x × V

[0145] In the formula: L is the distance from the beginning of the power cable; V represents the signal propagation speed of the power cable.

[0146] A specific embodiment of the present invention is as follows:

[0147] To verify the effectiveness of the proposed method in locating early-stage minute defects in power cables, multiple sets of defect samples were prepared for verification. Related experiments were conducted on 200m and 400m power cables to verify the feasibility of the proposed method. Sample parameters are shown in Table 1 below.

[0148] Table 1 Sample of defects in power cables

[0149]

[0150] The reflection coefficient acquisition instrument built in this embodiment is set with a frequency range of 150KHz to 100MHz, which meets the experimental requirements.

[0151] The testing procedure is as follows: First, use a reflectance coefficient acquisition instrument to measure S. 11 The parameters are calculated, and their real parts are extracted. Next, the collected data undergoes sparse reconstruction CFI-Z transform or DFT transform processing to obtain a preliminary localization spectrum. Finally, the preliminary localization spectrum is subjected to Gaussian and Savitzky-Golay iterative filtering to obtain the localization spectrum of early-stage minor defects in the power cable.

[0152] Experimental Results and Analysis:

[0153] The real part of the reflection coefficient at the beginning of sample #1 was processed using DFT and sparse reconstruction CFI-Z, respectively, followed by iterative filtering to obtain the local defect location spectrum of the power cable. Both transformations resulted in a clear peak at 200m, indicating accurate location of the cable end. Figure 6a It can be seen that the localization map obtained by using DFT exhibits a certain symmetrical distribution, most of the information is redundant, and the sensitivity for early small defect identification is too low, causing misjudgment and making it impossible to identify early small defects. Figure 6b The peak of the mid-range localization spectrum at 100m indicates the location of the defect point, identifying early minor defects. Comparison shows that using sparse reconstruction CFI-Z transform can effectively improve the resolution of cable defect localization, reduce redundancy, reduce the influence of interference peaks, and improve the sensitivity of early minor defect localization.

[0154] After processing the head-end reflection coefficients of samples #2, #3, and #4 using DFT transform, the cable defect location spectrum is obtained through iterative filtering, as shown below. Figures 7a-7c As shown in the figure. Experimental results show that DFT cannot identify early, minute defects, but it can identify cable ends.

[0155] After processing the head-end reflection coefficients of samples #2, #3, and #4 using the sparse reconstruction CFI-Z transform, the cable defect location spectrum is obtained through iterative filtering, as shown below. Figures 8a-8c As shown in the figure. Experimental results show that the sparse reconstruction CFI-Z transform can achieve the identification of early, small defects.

[0156] This embodiment of the power cable micro-defect localization method based on the CFI-Z algorithm uses a constructed reflection coefficient acquisition instrument to obtain a power cable head-end reflection coefficient vector composed of reflection coefficients obtained from sweep signals based on multiple frequencies. Then, based on the continuously increasing frequency Z-transform matrix, the minimum norm least squares solution and closed-form solution of the power cable fault location factor are obtained. Furthermore, the sparsity intensity of the minimum norm least squares solution and closed-form solution is obtained to arrive at the final solution of the power cable fault location factor. Finally, based on the power cable head-end reflection time-domain sequence, the location of the power cable defect is obtained to complete the localization of early-stage cable defects. Since the power cable head-end reflection coefficient vector obtained by the reflection coefficient acquisition instrument of this invention is based on sweep signals of multiple frequencies, it solves the problems of insufficient high-frequency components and bandwidth limitations in the injected pulse. This results in high sensitivity and strong noise resistance for power cable defect localization, especially in the case of long cables or cables with micro-defects, where the localization error is small, and it has a good effect in locating early-stage micro-defects.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating minute defects in power cables based on the CFI-Z algorithm, characterized in that, Includes the following steps: S1: Based on the reflection coefficient acquisition instrument used to measure the reflection coefficient at the beginning of the power cable, obtain... N A vector of reflection coefficients at the beginning of a power cable; the vector of reflection coefficients at the beginning of the power cable includes reflection coefficients at the beginning of the power cable obtained based on a frequency sweep signal of multiple frequencies; wherein... N This represents the total number of reflection coefficient vectors at the beginning of the power cable; S2: According to N Given a vector of reflection coefficients at the beginning of a power cable, obtain the result based on the CFI-Z algorithm. M One sampling point, M < N To obtain the continuously frequency-enhanced Z-transform matrix, i.e., the CFI-Z matrix; where, M Indicates the total number of sampling points; The formula used to obtain the continuously frequency-enhanced Z-transform matrix is ​​as follows: In the formula, C This represents the continuously frequency-enhanced Z-transform matrix, i.e., the CFI-Z matrix; The starting radius of the sampling path for the reflection coefficient vector at the beginning of the power cable on the Z-plane; j The imaginary unit that represents complex numbers; This represents the starting phase angle of the sampling path of the reflection coefficient vector at the beginning of the power cable in the Z-plane; n This indicates the index number of the reflection coefficient vector at the beginning of the power cable. n =0,1,2,…, N -1; N This represents the total number of reflection coefficient vectors at the beginning of the power cable; This represents the angular frequency difference between two adjacent sampling points on the sampling path of the reflection coefficient vector at the beginning of the power cable in the Z plane; F 0 represents the elongation of the spiral; m Indicates the number of the sampling point on the Z-plane. m =0,1,2,…, M -1; M This represents the total number of sampling points on the Z-plane, and M < N ; S3: Based on the continuously increasing frequency Z-transform matrix and the reflection coefficient vector at the beginning of the power cable, establish a minimum quadratic difference equation, obtain the minimum norm least squares solution of the power cable fault location factor based on the minimum norm least squares method, and obtain the closed solution of the power cable fault location factor based on the closed form solution method. The equation for minimizing the quadratic difference is established as follows: In the formula: Indicates the fault location factor for power cables; express The L2 norm; arg min represents the parameter that minimizes the objective function; x Represents the time-domain sequence of reflections at the beginning of a power cable; X This represents the vector sequence of reflection coefficients at the beginning of a power cable, i.e., the frequency domain sequence of reflections at the beginning of a power cable. C Represents the continuously increasing frequency Z-transform matrix; S4: Based on the minimum norm least squares solution and the closed solution of the power cable fault location factor, obtain the sparsity strength of the minimum norm least squares solution and the sparsity strength of the closed solution of the power cable fault location factor. S5: Based on the sparsity strength of the least squares solution of the minimum norm of the power cable fault location factor and the sparsity strength of the closed solution of the power cable fault location factor, obtain the final solution of the power cable fault location factor, and obtain the time-domain sequence of the first-end reflection of the power cable according to the minimum quadratic difference equation. S6: Based on the time-domain sequence of reflections at the beginning of the power cable, the location of the power cable defect is obtained to complete the localization of early defects in the cable.

2. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that, The formulas used to obtain the sparsity strength of the minimum norm least squares solution and the sparsity strength of the closed-form solution of the power cable fault location factor are as follows: In the formula, This indicates the sparsity intensity of the location factor; Represents the row index of the positioning factor matrix; Represents the column index of the positioning factor matrix; This represents the total number of rows in the positioning factor matrix; J This represents the total number of columns in the positioning factor matrix; It is an indicator function; The matrix representing the positioning factors, the first... i Line number The elements of the column.

3. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that, The final solution for the power cable fault location factor is obtained as follows: If the sparsity strength of the least norm least squares solution of the power cable fault location factor is greater than the sparsity strength of the closed solution of the power cable fault location factor, then the final solution of the power cable fault location factor is the least norm least squares solution of the power cable fault location factor. Otherwise, the final solution of the power cable fault location factor is a closed solution of the power cable fault location factor.

4. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that, The formula for calculating the location of the power cable defect is as follows: In the formula: L This refers to the distance from the location of the defect on the power cable to the beginning of the power cable. V This indicates the speed at which signals propagate through power cables.

5. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that, The reflection coefficient acquisition instrument includes: a frequency sweep signal generation module, a reflection signal extraction module, and a receiver module; The frequency sweep signal generation module is used to acquire frequency sweep signals at the beginning of the power cable at multiple frequencies, so as to generate a reflected signal when there is a defect in the power cable; at this time, both the frequency sweep signal and the reflected signal exist at the beginning of the power cable. The reflected signal extraction module is used to extract reflected signals at the beginning of the power cable when there is a defect in the power cable; The receiver module is used to obtain the reflection coefficient of the power cable head end based on the reflected signal.

6. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 5, characterized in that, The reflected signal extraction module includes a first resistor R1, a second resistor R2, a third resistor R3, a fourth resistor R4, a fifth resistor R5, a sixth resistor R6, a seventh resistor R7, an eighth resistor R8, a first capacitor C1, a second capacitor C2, a third capacitor C3, a fourth capacitor C4, a fifth capacitor C5, a sixth capacitor C6, a seventh capacitor C7, an eighth capacitor C8, a ninth capacitor C9, a power cable SMA connector, an N-type transistor Q1, a feedthrough capacitor filter; a first inductor L1, a second inductor L2, a third inductor L3, an operational amplifier module U2, and a differential operational amplifier module U1; The SMA connector of the power cable is connected to the beginning end of the power cable. Pin 5 of the SMA connector of the power cable is connected to the sweep frequency signal generation module; pins 1 and 4 of the SMA connector of the power cable are grounded; pin 2 of the SMA connector of the power cable is connected to one end of the fourth resistor R4; pin 3 of the SMA connector of the power cable is connected to the output terminal of the feedthrough capacitor filter. The input terminal and the feedback terminal of the feedthrough capacitor filter are both connected to the other end of the fourth resistor R4. One end of the third resistor R3 and one end of the first resistor R1 are both connected to the connection point between the input terminal of the feedthrough capacitor filter and the fourth resistor R4. The other end of the third resistor R3 is connected to pin 5 of the SMA connector of the power cable. One end of the second resistor R2 is connected to pin 5 of the SMA connector of the power cable; The other end of the first resistor R1 and the other end of the second resistor R2 are both connected to the emitter of the N-type transistor Q1; The base of the N-type transistor Q1 is connected to the connection point between the input terminal of the feedthrough capacitor filter and the fourth resistor R4. The collector of the N-type transistor Q1 is connected to the first capacitor C1; The other end of the first capacitor C1 is connected to one end of the second capacitor C2; the other end of the second capacitor C2 is connected to one end of the third capacitor C3. The first inductor L1, the second inductor L2, and the third inductor L3 are connected in parallel with the first capacitor C1, the second capacitor C2, and the third capacitor C3, respectively. One end of the fourth capacitor C4 is connected to the junction of the collector of the N-type transistor Q1 and the first capacitor C1; one end of the fifth capacitor C5 is connected to the junction of the first capacitor C1 and the second capacitor C2; one end of the sixth capacitor C6 is connected to the junction of the second capacitor C2 and the third capacitor C3; one end of the seventh capacitor C7 is connected to the other end of the third capacitor C3; the other ends of the fourth capacitor C4, the fifth capacitor C5, the sixth capacitor C6, and the seventh capacitor C7 are all grounded; The other end of the third capacitor C3 is connected to pin 3 of the operational amplifier module U2; The two ends of the fifth resistor R5 are connected to pin 1 and pin 2 of the operational amplifier module U2, respectively; One end of the sixth resistor R6 is connected to pin 2 of the operational amplifier module U2, and the other end is grounded; One end of the eighth capacitor C8 is connected to the junction of the second resistor R2 and the third resistor R3, and the other end is connected to pin 8 of the differential operational amplifier module U1. Pin 1 of the differential operational amplifier module U1 is connected to one end of the ninth capacitor C9; the other end of the ninth capacitor C9 is connected to the feedback terminal of the feedthrough capacitor filter; pin 4 of the differential operational amplifier module U1 is grounded; pin 6 of the differential operational amplifier module U1 is connected to one end of the seventh resistor R7, the other end of the seventh resistor R7 can be connected to the eighth resistor R8, and the other end of the eighth resistor R8 is grounded. Pin 5 of the differential operational amplifier module U1 is connected to the connection point of the seventh resistor R7 and the eighth resistor R8; Pin 6 of the differential operational amplifier module U1 is connected to the receiver module.

7. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that, The closed-form solution of the power cable fault location factor is obtained as follows: In the formula: This represents the closed-form solution of the fault location factor for power cables.

8. The method for locating minute defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that, The minimum norm least squares solution of the power cable fault location factor is obtained as follows: In the formula: The least-norm least-squares solution represents the fault location factor of a power cable.

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