Power cable tiny defect positioning method based on CFI-Z algorithm

Abstract

The invention discloses a power cable tiny defect positioning method based on a CFI-Z algorithm, and the method comprises the steps: obtaining a reflection coefficient vector of a head end of a power cable obtained through sweep frequency signals based on multiple frequencies, and obtaining a minimum norm least square solution and a closed solution of a power cable fault positioning factor according to a continuous frequency-increasing Z transformation matrix; and obtaining the sparse intensity of the minimum norm least square solution and the closed solution to obtain the final solution of the power cable fault positioning factor, and finally obtaining the position of the power cable defect according to the head end reflection time domain sequence of the power cable to complete the positioning of the early defect of the cable. According to the invention, the problems of insufficient high-frequency components and bandwidth limitation in the injected pulse are solved, so that the defect positioning sensitivity of the power cable is high, the anti-noise capability is strong, the positioning error is small especially under the condition of a long cable or a cable with small defects, and the method has a good effect in early-stage small defect positioning.

Description

Technical Field

[0001] The present invention relates to the technical field of cable defect positioning, and in particular to a method for positioning tiny defects of a power cable based on a CFI-Z algorithm. Background Art

[0002] Early minor defects in power cables refer to small damages on the cable insulation layer or conductor surface, which usually have limited impact on overall performance and safety. The specific standards for minor defects are: the length of the scratch on the cable body is less than 5cm, the depth is less than 1mm, and the capacitance change at the defect is less than 5%. Although early minor defects will not lead to comprehensive electrical failure, they are very likely to cause local insulation aging or current concentration under long-term high-load operation or extreme environments.

[0003] Cable defects usually manifest as changes in the characteristic impedance of the position, so the traveling wave method has a good effect in defect detection. At present, the main positioning methods include time domain reflectometry (TDR), frequency domain reflectometry (FDR) and time-frequency domain reflectometry (TFDR) based on traveling wave theory. Among them, TDR and TFDR are widely used in field tests because of their simple principles and convenient calculations. However, these two methods lack high-frequency components in the injected pulse, resulting in low defect location sensitivity and poor noise resistance. Therefore, in the case of long cables or cables with tiny defects, the positioning error is large. At the same time, due to the influence of signal noise and bandwidth limitations, the effect is not ideal when locating early tiny defects. Summary of the invention

[0004] The invention discloses a method for locating tiny defects of a power cable based on a CFI-Z algorithm, so as to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

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

[0007] S1: Establish a reflection coefficient acquisition instrument for measuring the reflection coefficient of the head end of a power cable to obtain N reflection coefficient vectors of the head end of the power cable; the reflection coefficient vector of the head end of the power cable includes the reflection coefficient of the head end of the power cable obtained based on a sweep frequency signal of multiple frequencies; wherein N represents the total number of reflection coefficient vectors of the head end of the power cable;

[0008] S2: Based on the N power cable head reflection coefficient vectors, obtain M, M < N sampling points 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 the minimum norm of the power cable fault location factor based on the least squares method with the 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 the 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 the 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 the 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 time-domain reflection sequence at the power cable head;

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

[0013] Further, the formulas for obtaining the sparsity intensity of the least squares solution with the 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 sparseness intensity of the minimum norm least squares solution of the power cable fault location factor is greater than the sparseness intensity of the closed solution of the power cable fault location factor, then the final solution of the power cable fault location factor is the minimum norm least squares solution of the power cable fault location factor;

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

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

[0021] L=x×V

[0022] Where: L is the distance from the head end of the power cable; V represents the propagation speed of the power cable signal.

[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 sweep frequency signal generating module is used to obtain sweep frequency signals of multiple frequencies at the head end of the power cable to generate a reflection signal when there is a defect in the power cable; at this time, the sweep frequency signal and the reflection signal exist at the head end of the power cable at the same time;

[0025] The signal separation module is used to extract the reflected signal at the head end 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 according to the reflection signal.

[0027] Further, 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, and a feed-through 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 power cable SMA connector is connected to the first end of the power cable;

[0029] Pin 5 of the power cable SMA connector is connected to the sweep signal generating module; Pin 1 and Pin 4 of the power cable SMA connector are grounded; Pin 2 of the power cable SMA connector is connected to one end of the fourth resistor R4; Pin 3 of the power cable SMA connector is connected to the output end of the feed-through capacitor filter;

[0030] The input end of the feed-through capacitor filter and the feedback end of the feed-through 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 between the input end of the feed-through capacitor filter and the fourth resistor R4;

[0032] The other end of the third resistor R3 is connected to the 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 between the input end of the feed-through 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 respectively connected in parallel with the first capacitor C1, the second capacitor C2, and the third capacitor C3;

[0039] One end of the fourth capacitor C4 is connected to the connection between the collector of the N-type transistor Q1 and the first capacitor C1; one end of the fifth capacitor C5 is connected to the connection between the first capacitor C1 and the second capacitor C2; one end of the sixth capacitor C6 is connected to the connection between 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 end of the fourth capacitor C4, the other end of the fifth capacitor C5, the other end of the sixth capacitor C6, and the other end of 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] Two ends of the fifth resistor R5 are respectively connected to pin 1 and pin 2 of the operational amplifier module U2;

[0042] One end of the sixth resistor R6 is connected to the 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 connection point between the second resistor R2 and the third resistor R3, and the other end is connected to the 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 end 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 between 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 continuous frequency increase Z transform matrix is ​​as follows:

[0048]

[0049] Where C represents the continuous frequency increment Z transform matrix, namely CFI-Z matrix; R 0 is the starting radius of the sampling path of the reflection coefficient vector at the head end of the power cable on the Z plane; j represents the imaginary unit of the complex number; θ 0 Represents the starting phase angle of the sampling path of the reflection coefficient vector at the head end of the power cable on the Z plane; n represents the index number of the reflection coefficient vector at the head end of the cable, n = 0, 1, 2, ..., N-1; N represents the total number of reflection coefficient vectors at the head end of the cable; represents the angular frequency difference between two adjacent sampling points on the sampling path of the reflection coefficient vector of the head end of the power cable on the Z plane; F 0 represents the stretch rate of the spiral; m represents the number of the sampling points on the Z plane, m = 0, 1, 2, ..., M-1; M represents the total number of sampling points on the Z plane, and M <N。

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

[0051]

[0052] Where: represents the power cable fault location factor; represents the binary norm of Cx-X; arg represents the minimization objective function; x represents the time domain sequence of the reflection at the head end of the power cable; X represents the reflection coefficient vector sequence at the head end of the power cable, that is, the frequency domain sequence of the reflection at the head end of the power cable; C represents the continuous frequency-increasing Z-transform matrix.

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

[0054]

[0055] Where: It represents the closed solution of the power cable fault location factor.

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

[0057]

[0058] Where: Represents the minimum norm least squares solution of the power cable fault location factor.

[0059] Beneficial effect: A method for locating small defects in power cables based on the CFI-Z algorithm of the present invention obtains the power cable head end reflection coefficient vector composed of the power cable head end reflection coefficient obtained based on the swept frequency signal of multiple frequencies through the constructed reflection coefficient acquisition instrument, and obtains the minimum norm least squares solution and closed solution of the power cable fault location factor according to the continuous frequency increase Z transform matrix; and then obtains the sparse strength of the minimum norm least squares solution and the closed solution to obtain the final solution of the power cable fault location factor, and finally obtains the position of the power cable defect according to the time domain sequence of the power cable head end reflection to complete the positioning of the early defects of the cable. Since the power cable head end reflection coefficient vector obtained by the reflection coefficient acquisition instrument of the present invention is obtained based on the swept frequency signal of multiple frequencies, the problem of insufficient high frequency components and bandwidth limitation in the injected pulse is solved, so that the power cable defect positioning sensitivity is high and the anti-noise ability is strong, especially in the case of long cables or cables with small defects, the positioning error is small, and it has a better effect in locating early small defects. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0061] Figure 1 It is a flow chart of the method for locating small defects in power cables based on the CFI-Z algorithm of the present invention;

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

[0063] Figure 3 Schematic diagram of the circuit principle of the signal separation module in an embodiment of the present invention;

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

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

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

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

[0068] Figure 7a Schematic diagram of experimental results of DFT transformation of sample #2 in an embodiment of the present invention;

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

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

[0071] Figure 8a Schematic diagram of experimental results of sample #2 under CFI-Z transformation in an embodiment of the present invention;

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

[0073] Figure 8c Schematic diagram of the experimental results of sample #4 under CFI-Z transformation in an embodiment of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0076] S1: Establishing a reflection coefficient acquisition instrument for measuring the reflection coefficient of the head end of a power cable to obtain N reflection coefficient vectors of the head end of the power cable; the reflection coefficient vector of the head end of the power cable includes the reflection coefficient of the head end of the power cable obtained based on multiple scanning frequencies;

[0077] Preferably, the reflection coefficient acquisition instrument comprises: a frequency sweep signal generating module, a reflection signal extracting module, and a receiver module;

[0078] The sweep frequency signal generating module is used to obtain sweep frequency signals of multiple frequencies at the head end of the power cable to generate a reflection signal when there is a defect in the power cable; at this time, the sweep frequency signal and the reflection signal exist at the head end of the power cable at the same time;

[0079] The signal separation module is used to extract the reflected signal at the head end 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 according to the reflection signal.

[0081] Specifically, it also includes a power module and a main control module; the power module is used to provide power to the sweep signal generation module, the reflection signal extraction module, the receiver module, etc., and the main control module is used to control the sweep frequency of the sweep signal generation module, and transmit the reflection coefficient of the power cable head end obtained by the receiver module to the host computer. At the same time, the main control module of this embodiment is also used to control the relevant configuration of the ADC module in the receiver module, and configure the output voltage value of the gain phase module, such as Figure 2 As shown in the figure, the system uses STM32F407 as the main control module. The 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 requirements of the reflection coefficient collector for real-time and computing performance. It is also equipped with a system power module to ensure the stable operation of the equipment.

[0082] Specifically, the reflection coefficient acquisition instrument of this embodiment is mainly used to measure the reflection coefficient of the cable head end and transmit the data to the host computer for processing. The core of the device includes two swept frequency signal sources generated by DDS, and uses a transmission signal extraction module to separate the input reflection signal of the cable head end, and outputs the amplitude and phase of the reflection coefficient of the reflection signal generated by the defective position of the power cable through an amplitude and phase detection circuit.

[0083] Specifically, the frequency sweep signal generation module of this embodiment is mainly composed of a DDS chip and its peripheral circuits, a low-pass filter circuit and an amplifier circuit. Among them, AD9854 is a highly integrated digital synthesizer that can generate four sinusoidal signals with programmable frequency, phase and amplitude, each with a phase difference of 90°, and one square wave signal. This article selects AD9854 as the DDS chip to meet the requirements of the test frequency range of 150kHz to 100MHz. The schematic diagram of AD9854 and its peripheral circuits is shown in the figure. Figure 4 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, and a feed-through capacitor filter; a first inductor L1, a second inductor L2, a third inductor L3, an operational amplifier module U2, a differential operational amplifier module U1,

[0085] The power cable SMA connector is connected to the first end of the power cable;

[0086] Pin 5 of the power cable SMA connector is connected to the sweep signal generating module; Pin 1 and Pin 4 of the power cable SMA connector are grounded; Pin 2 of the power cable SMA connector is connected to one end of the fourth resistor R4; Pin 3 of the power cable SMA connector is connected to the output end of the feed-through capacitor filter;

[0087] The input end of the feed-through capacitor filter and the feedback end of the feed-through 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 between the input end of the feed-through capacitor filter and the fourth resistor R4;

[0089] The other end of the third resistor R3 is connected to the 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 between the input end of the feed-through 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 respectively connected in parallel with the first capacitor C1, the second capacitor C2, and the third capacitor C3;

[0096] One end of the fourth capacitor C4 is connected to the connection between the collector of the N-type transistor Q1 and the first capacitor C1; one end of the fifth capacitor C5 is connected to the connection between the first capacitor C1 and the second capacitor C2; one end of the sixth capacitor C6 is connected to the connection between 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 end of the fourth capacitor C4, the other end of the fifth capacitor C5, the other end of the sixth capacitor C6, and the other end of 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] Two ends of the fifth resistor R5 are respectively connected to pin 1 and pin 2 of the operational amplifier module U2;

[0099] One end of the sixth resistor R6 is connected to the 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 connection point between the second resistor R2 and the third resistor R3, and the other end is connected to the 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 end 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 between 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, the differential operational amplifier module U1 and the operational amplifier module U2 are both connected to a power supply, which belongs to conventional technology and will not be described in detail here.

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

[0106] Specifically, Figure 5 This is the schematic diagram of the gain phase detection circuit in the receiver module in this embodiment. The chip is powered by a single 5V power supply, V_REF is the reflected signal at the head end of the cable, 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, that is, the continuous frequency increment Z transform matrix. The formula used is as follows:

[0108] Specifically, similar to the discrete Fourier transform, the continuous frequency-increasing Z transform matrix can also be expressed in the form of a matrix:

[0109] X=Cx (1)

[0110] Where: C represents the continuous frequency increment Z transform matrix, i.e., CFI-Z matrix, with a size of M×N; x represents the time domain sequence of the reflection at the head end of the power cable; X represents the reflection coefficient vector sequence at the head end of the power cable, i.e., the frequency domain sequence of the reflection at the head end of the power cable;

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

[0112]

[0113] In the formula, R 0 is the starting radius of the sampling path of the reflection coefficient vector at the head end of the power cable on the Z plane; j represents the imaginary unit of the complex number; θ 0represents 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 head end of the cable, n = 0, 1, 2, …, N - 1; N represents the total number of the reflection coefficient vectors at the head end of the cable; 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; F 0 represents the stretch ratio of the helix; m represents the number of the sampling points in the Z-plane, m = 0, 1, 2, …, M - 1; M represents the total number of the 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 realizes high-resolution analysis of signals in a specific frequency region by selecting specific complex frequency values and sampling according to certain rules. Specifically, the sampling path usually changes in the form of a helix or an arc in the complex frequency plane, which can flexibly focus on the frequency band of interest of the signal, realize non-uniform and dense frequency sampling, so as to 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] However, for a general CFI-Z matrix, that is, M < N. Using a general matrix will lead to an ill-posed inverse problem, that is, problems such as no solution, non-unique solution, or a solution that is extremely sensitive to the input.

[0118] S3: According to the continuous frequency-increasing 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 with the minimum norm of the power cable fault location factor based on the least squares method with the 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: represents the power cable fault location factor; represents the two-norm of Cx - X;

[0123] Specifically, in this embodiment, according to the minimization of quadratic differences method, the minimum norm least squares solution of the power cable fault location factor is obtained based on the minimum norm least squares method, and the closed form solution of the location factor of the power cable fault location factor is obtained based on the closed form solution method. The methods adopted are all conventional technologies in the field and will not be described in detail here.

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

[0125]

[0126] Where: It represents the closed solution of the power cable fault location factor.

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

[0128]

[0129] Where: represents the minimum norm least squares solution of the power cable fault location factor;

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

[0131] Specifically, according to the calculation formula of zero elements of the locating factor, this embodiment can obtain the number of zero elements in the minimum norm least squares solution of the power cable fault locating factor and the number of zero elements in the closed solution of the power cable fault locating factor;

[0132] Specifically, considering the problem of small reflections along the cable, an assumption is made about the reflection time series x at the head end of the power cable. This assumption is called a priori and is used to standardize the ill-posed inverse problem, that is, in the case of an underdetermined inverse problem, there are multiple solutions. One of the prior conditions is the sparsity of weak signals. When a signal has many zero elements, it is considered to be sparse. Therefore, the minimum non-zero element solution, that is, the weakest positioning factor, can be determined by the following method:

[0133] Specifically, this embodiment uses the following locating factor zero element calculation formula to count the number of zero elements in the minimum norm least squares solution of the power cable fault locating factor and the closed solution of the power cable fault locating factor:

[0134]

[0135] In the formula, represents the sparse strength of the positioning factor; i represents the row index of the positioning factor matrix; j′ represents the column index of the positioning factor matrix; I represents the total number of rows of the positioning factor matrix; J represents the total number of columns of the positioning factor matrix; is the indicator function; The element in the i-th row and j′th column of the matrix representing the positioning factor.

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

[0137] S5: obtaining a final solution of the power cable fault location factor according to the sparse intensity of the minimum norm least squares solution of the power cable fault location factor and the sparse intensity of the closed solution of the power cable fault location factor, so as to obtain a reflection time domain sequence of the power cable head end according to the minimized quadratic difference equation;

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

[0139] If the sparseness intensity of the minimum norm least squares solution of the power cable fault location factor is greater than the sparseness intensity of the closed solution of the power cable fault location factor, then the final solution of the power cable fault location factor is the minimum norm least squares solution of the power cable fault location factor;

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

[0141] Specifically, the final solution of the power cable fault location factor is brought into the minimization quadratic difference equation, which can obtain the reflection time domain sequence x at the head end of the power cable;

[0142] S6: According to the reflection time domain sequence at the head end of the power cable, the position of the power cable defect is obtained to locate the early defects of the cable.

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

[0144] L=x×V

[0145] Where: L is the distance from the head end of the power cable; V represents the propagation speed of the power cable signal.

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

[0147] In order to verify the effectiveness of the method proposed in this embodiment in locating early minor defects in power cables, multiple groups of defective samples were prepared for verification, and relevant experiments were carried out on 200m and 400m power cables to verify the feasibility of the method proposed in the present invention. The sample parameters are shown in Table 1 below.

[0148] Table 1 Power cable defect samples

[0149]

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

[0151] The test process is as follows: First, use the reflection coefficient acquisition instrument to measure S 11 Parameters and extract their real part. Then, the collected data is processed by sparse reconstruction CFI-Z transform or DFT transform to obtain a preliminary positioning spectrum. Finally, the preliminary positioning spectrum is subjected to Gaussian and Savitzky-Golay iterative filtering to obtain the positioning spectrum of early minor defects in power cables.

[0152] Experimental results and analysis:

[0153] The real part of the reflection coefficient of the head end of sample #1 was processed by DFT and sparse reconstruction CFI-Z respectively, and then iterative filtering was performed to obtain the local defect location spectrum of the power cable. Among them, the location spectra obtained by the two transformations both showed obvious peaks at 200m, and the ends of the cables were accurately located. Figure 6a It can be seen that the positioning map obtained by using DFT presents a certain symmetrical distribution, most of the information is redundant, and the sensitivity for early-stage micro-defect recognition is too low, resulting in misjudgment and inability to achieve early-stage micro-defect recognition. Figure 6b The peak of the middle positioning spectrum at 100m is the location of the defect point, and early tiny defects are identified. By comparison, the use of sparse reconstruction CFI-Z transform can effectively improve the resolution of cable defect positioning, reduce redundancy, reduce the impact of interference peaks, and improve the sensitivity of early tiny defect positioning.

[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, such as Figure 7a-7c The experimental results show that DFT cannot identify small defects at an early stage, but can identify the end of the cable.

[0155] After processing the head-end reflection coefficients of samples #2, #3, and #4 using sparse reconstruction CFI-Z transform, the cable defect location spectrum is obtained through iterative filtering, as shown in Figure 8a-8cThe experimental results show that sparse reconstruction CFI-Z transform can realize the early recognition of small defects.

[0156] The method for locating small defects of power cables based on the CFI-Z algorithm of this embodiment obtains the reflection coefficient vector of the power cable head end composed of the reflection coefficient of the power cable head end obtained based on the swept frequency signal of multiple frequencies through the constructed reflection coefficient acquisition instrument, and obtains the minimum norm least squares solution and closed solution of the power cable fault location factor according to the continuous frequency increase Z transform matrix; and then obtains the sparse strength of the minimum norm least squares solution and the closed solution to obtain the final solution of the power cable fault location factor, and finally obtains the position of the power cable defect according to the time domain sequence of the reflection of the power cable head end to complete the positioning of the early defects of the cable. Since the reflection coefficient vector of the power cable head end obtained by the reflection coefficient acquisition instrument of the present invention is obtained based on the swept frequency signal of multiple frequencies, the problem of insufficient high-frequency components and bandwidth limitation in the injected pulse is solved, so that the defect location sensitivity of the power cable is high and the anti-noise ability is strong, especially in the case of long cables or cables with small defects, the positioning error is small, and it has a better effect in locating early small defects.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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 small defects in power cables based on CFI-Z algorithm, characterized in that: Including the following steps: S1: Establish a reflection coefficient acquisition instrument for measuring the reflection coefficient at the head end of a power cable to obtain N reflection coefficient vectors at the head end of the power cable; the reflection coefficient vector at the head end of the power cable includes the reflection coefficient at the head end of the power cable obtained based on sweep signals of multiple frequencies; where N represents the total number of reflection coefficient vectors at the head end of the power cable; S2: According to the N reflection coefficient vectors at the head end of the power cable, obtain M, M < N sampling points based on the CFI-Z algorithm to obtain a continuous frequency-increasing Z-transform matrix, that is, a CFI-Z matrix; where M represents the total number of sampling points; S3: According to the continuous frequency-increasing 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 with the minimum norm of the power cable fault location factor based on the least squares method with the minimum norm, and obtain the closed-form solution of the power cable fault location factor based on the closed-form solution method; S4: According to the least squares solution with the minimum norm of the power cable fault location factor and the closed-form solution of the power cable fault location factor, obtain the sparse intensity of the least squares solution with the minimum norm of the power cable fault location factor and the sparse intensity of the closed-form solution of the power cable fault location factor; S5: According to the sparse intensity of the least squares solution with the minimum norm of the power cable fault location factor and the sparse 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 reflection time domain sequence at the head end of the power cable; S6: According to the reflection time domain sequence at the head end of the power cable, obtain the location of the power cable defect to complete the location of the early defect of the cable.

2. According to claim 1, a method for locating small defects in power cables based on the CFI-Z algorithm is characterized in that: The formulas for obtaining the sparse intensity of the least squares solution with the minimum norm of the power cable fault location factor and the sparse intensity of the closed-form solution of the power cable fault location factor are as follows: Wherein, θ represents the sparse strength of the positioning factor; i represents the row index of the positioning factor matrix; j′ represents the column index of the positioning factor matrix; I represents the total number of rows of the positioning factor matrix; J represents the total number of columns of the positioning factor matrix; is the indicator function; The element in the i-th row and j′th column of the matrix representing the positioning factor.

3. A method for locating minute defects of a power cable based on the CFI-Z algorithm according to claim 1, characterized in that The method for obtaining the final solution of the power cable fault location factor is as follows: If the sparse intensity of the least squares solution with the minimum norm of the power cable fault location factor is greater than the sparse intensity of the closed-form solution of the power cable fault location factor, then the final solution of the power cable fault location factor is the least squares solution with the minimum norm of the power cable fault location factor; Otherwise, the final solution of the power cable fault location factor is the closed-form solution of the power cable fault location factor.

4. The method for locating small defects in power cables based on the CFI-Z algorithm according to claim 1 is characterized in that: The formula for calculating the location of the power cable defect is as follows: L = x × V In the formula: L is the distance from the head end of the power cable on the power cable; V represents the signal propagation speed of the power cable.

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

6. A method for locating small 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, and a feed-through 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 power cable SMA connector is connected to the first end of the power cable; Pin 5 of the power cable SMA connector is connected to the sweep signal generating module; Pin 1 and Pin 4 of the power cable SMA connector are grounded; Pin 2 of the power cable SMA connector is connected to one end of the fourth resistor R4; Pin 3 of the power cable SMA connector is connected to the output end of the feed-through capacitor filter; The input end of the feed-through capacitor filter and the feedback end of the feed-through 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 between the input end of the feed-through capacitor filter and the fourth resistor R4; The other end of the third resistor R3 is connected to the 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 between the input end of the feed-through 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 respectively connected in parallel with the first capacitor C1, the second capacitor C2, and the third capacitor C3; One end of the fourth capacitor C4 is connected to the connection between the collector of the N-type transistor Q1 and the first capacitor C1; one end of the fifth capacitor C5 is connected to the connection between the first capacitor C1 and the second capacitor C2; one end of the sixth capacitor C6 is connected to the connection between 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 end of the fourth capacitor C4, the other end of the fifth capacitor C5, the other end of the sixth capacitor C6, and the other end of 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; Two ends of the fifth resistor R5 are respectively connected to pin 1 and pin 2 of the operational amplifier module U2; One end of the sixth resistor R6 is connected to the 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 connection point between the second resistor R2 and the third resistor R3, and the other end is connected to the 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 end 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 between 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 small defects in power cables based on the CFI-Z algorithm according to claim 1 is characterized in that: The formula used to obtain the continuous frequency-increasing Z-transform matrix is ​​as follows: Where, C represents the continuous frequency increment Z transform matrix, namely CFI-Z matrix; R0 is the starting radius of the sampling path of the reflection coefficient vector at the head end of the power cable on 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 head end of the power cable on the Z plane; n represents the index number of the reflection coefficient vector at the head end of the cable, n=0,1,2,…,N-1; N represents the total number of reflection coefficient vectors at the head end of the cable; Represents the angular frequency difference between two adjacent sampling points on the sampling path of the reflection coefficient vector of the head end of the power cable on the Z plane; F0 represents the extension rate of the spiral line; m represents the number of the sampling points on the Z plane, m = 0, 1, 2, ..., M-1; M represents the total number of sampling points on the Z plane, and M <N。 8. The method for locating small defects in power cables based on the CFI-Z algorithm according to claim 1 is characterized in that: The minimization quadratic difference equation is established as follows: Where: represents the power cable fault location factor; represents the binary norm of Cx-X; arg represents the minimization objective function; x represents the time domain sequence of the reflection at the head end of the power cable; X represents the reflection coefficient vector sequence at the head end of the power cable, that is, the frequency domain sequence of the reflection at the head end of the power cable; C represents the continuous frequency-increasing Z-transform matrix.

9. The method for locating small defects in power cables based on the CFI-Z algorithm according to claim 1, characterized in that: The closed solution of the power cable fault location factor is obtained as follows: Where: It represents the closed solution of the power cable fault location factor.

10. The method for locating small 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: Where: Represents the minimum norm least squares solution of the power cable fault location factor.

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