Cable fault location method and system based on input impedance spectrum real part matrix bundle parameter estimation

Abstract

The application discloses a cable fault positioning method and system based on input impedance spectrum real part matrix pencil parameter estimation, and the method comprises the following steps: S1: obtaining the input impedance spectrum of the cable test end through wide frequency sweep measurement, and obtaining the input impedance real part sequence; S2: performing linear detrending and standardization processing on the input impedance real part sequence; S3: constructing the input impedance real part sequence after detrending and standardization into an exponential signal model superimposed by multiple complex exponential components; S4: constructing two Hankel matrices with a sampling point difference, determining the matrix pencil system matrix, solving the eigenvalue of the system matrix, and obtaining the complex exponential pole set; S5: calculating the distance of the corresponding reflection point from the cable test end according to the phase of each pole, and combining the pole modulus, complex amplitude coefficient, line length constraint and similar distance merging strategy to determine the final candidate reflection point; and S6: marking and removing the end reflection according to the full length of the cable line, and outputting the candidate fault position.

Description

Technical Field

[0001] This invention relates to the field of power cable fault diagnosis and location technology, specifically to a cable fault location method and system based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum. Background Technology

[0002] With the large-scale application of cross-linked polyethylene power cables in urban power distribution and transmission systems, rapid detection and accurate location of cable faults have become crucial technical issues for ensuring the safe operation of the power grid. Since power cables are typically laid underground, the fault location is difficult to observe directly when insulation aging, partial discharge, mechanical damage, sheath damage, grounding faults, or high-resistance faults occur. Therefore, non-destructive or low-destructive testing techniques are needed to determine the fault location.

[0003] Common cable fault location methods include pulse current method, time-domain reflection method, and frequency-domain reflection method. The pulse current method can be used for some high-resistance fault detection, but it usually requires applying a high voltage during the test, posing a risk of secondary damage to the cable insulation, and the on-site test results are easily affected by electromagnetic interference. The time-domain reflection method locates faults by measuring the propagation time difference between the incident pulse and the reflected pulse. Its equipment is relatively simple, but because the high-frequency components in the injected pulse are limited, the signal attenuates and disperses as it propagates over long distances in cables, limiting its location accuracy in long-distance cables, high-resistance faults, and weak reflection fault scenarios.

[0004] Frequency domain reflection methods use a wideband swept-frequency signal as the excitation source and analyze the input impedance spectrum at the cable's beginning to identify and locate faults. This type of method can obtain the cable's impedance response over a wide frequency range. Reflections from the fault point and the end of the line cause distance-related periodic oscillations in the input impedance spectrum, thus containing crucial information about the fault location. Existing input impedance spectrum localization methods often employ Fast Fourier Transform, Inverse Fourier Transform, windowed spectral analysis, improved Z-transform, or peak search to convert the frequency domain impedance spectrum into a distance spectrum or time domain spectrum, and then determine the fault distance through peak positions.

[0005] However, the above methods still have shortcomings. First, the localization resolution of traditional transform-based methods is significantly limited by the sweep bandwidth, frequency step size, and number of sampling points, making it difficult to fully utilize the reflection information in the limited sweep data. Second, spectral leakage, the picket fence effect, and noise interference can cause sidelobes and spurious peaks in the range spectrum, making it difficult to accurately identify weak reflection faults and high-impedance faults. Third, when fault point reflections and line end reflections coexist, multiple reflection components may superimpose, making traditional peak search methods prone to misjudgment. Fourth, the intensity of line end reflections is usually high; without a line end reflection identification strategy, line end reflections are easily misjudged as fault points.

[0006] While some existing high-resolution parameter estimation methods can improve spectral resolution to some extent, they still suffer from problems such as difficulty in determining the model order, insufficient noise immunity, and unclear mapping relationship with fault distance in cable input impedance spectrum applications. Therefore, it is necessary to propose a cable fault location method that can directly utilize the reflection oscillation information of the real part of the input impedance spectrum and extract the reflection poles and fault distance through parameter estimation methods. Summary of the Invention

[0007] The purpose of this invention is to provide a cable fault location method and system based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum, so as to at least solve the problems of limited resolution, large noise interference, difficulty in identifying weak reflection faults, and easy misjudgment of reflection at the end of the line in the prior art.

[0008] To address the aforementioned technical problems, in a first aspect, the present invention provides a cable fault location method based on the estimation of bundle parameters of the real part matrix of the input impedance spectrum, comprising the following steps:

[0009] S1: Obtain the input impedance spectrum of the cable test end by wideband sweep frequency measurement, and obtain the sequence of the real part of the input impedance;

[0010] S2: Perform linear detrending processing on the real part sequence of the input impedance to remove the background trend term that changes slowly with frequency, and perform standardization processing on the detrended real part sequence of the input impedance to obtain a detrended and standardized real part sequence of the input impedance.

[0011] S3: Construct the detrended and normalized sequence of the real part of the input impedance into an exponential signal model with multiple complex exponential components superimposed.

[0012] S4: Construct two Hankel matrices that differ by one sampling point, determine the matrix bundle system matrix through singular value decomposition and adaptive model order determination, and solve for the eigenvalues ​​of the system matrix to obtain the set of complex exponential poles;

[0013] S5: Calculate the distance from the corresponding reflection point to the cable test end based on the phase of each pole, and determine the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and close distance merging strategy;

[0014] S6: Mark and eliminate end reflections based on the total length of the cable line, and output candidate fault locations.

[0015] Furthermore, in step S2, a first-order linear function of the input impedance real part sequence is fitted using the least squares method as a background trend term, and this function is subtracted from the original input impedance real part sequence.

[0016] The expression for the background trend item is:

[0017] ;

[0018] in The linear background trend term; a is the trend slope, b is the trend intercept;

[0019] The parameters a and b are determined using the least squares method, and the expression is:

[0020] ;

[0021] The detrended sequence of the real part of the input impedance is obtained. The expression is:

[0022] ;

[0023] in, The sequence of real parts of the input impedance obtained in step S1. N represents the number of frequency sweep sampling points.

[0024] Further, in step S2, the standardization formula is:

[0025] ;

[0026] in, The mean of the real part sequence of the detrended input impedance is expressed as:

[0027] ;

[0028] The standard deviation of the detrended input impedance real part sequence is expressed as:

[0029] .

[0030] Further, in step S3, the expression for the exponential signal model is:

[0031] ,

[0032] ;

[0033] Where P is the model order, representing the number of exponential components to be estimated; is the amplitude coefficient of the k-th exponential component; This is the pole corresponding to the kth exponential component; This includes noise and unmodeled disturbance terms; The pole magnitude; This represents the pole phase.

[0034] Further, step S4 specifically includes:

[0035] S41: Construct two Hankel matrices that differ by one sampling point. and , Compared to The entire matrix is ​​shifted backward by one sampling point; the Hankel matrix and They are represented as follows:

[0036] ;

[0037] in,

[0038] S42: Yes Perform singular value decomposition:

[0039] ;

[0040] in, and These are the left and right singular vector matrices, respectively. It is a singular value diagonal matrix, and the superscript H denotes the conjugate transpose;

[0041] S43: The model order P is adaptively determined based on the singular value cumulative energy, the relative singular value threshold, and the singular value gap order;

[0042] S44: Extract the first P principal singular values ​​and their corresponding singular vectors to construct the matrix bundle system matrix, resulting in:

[0043] ;

[0044] S45: Solve for the generalized eigenvalues ​​to obtain the set of complex exponential poles { }:

[0045] ;

[0046] in, This is the k-th pole.

[0047] Further, in step S43, adaptively determining the model order P includes:

[0048] S431: Determine the cumulative energy order based on the cumulative energy. The expression is:

[0049] ;

[0050] ;

[0051] in, Let Q be the i-th singular value, Q be the total number of singular values, and m be the order of the candidate model. This represents the cumulative energy percentage of the first m singular values; The energy order is the cumulative energy. Reaching the preset threshold When, the cumulative amount is determined according to the above formula. ;

[0052] S432: Determine the order of the relative singular value threshold based on the relative singular value threshold. The expression is:

[0053] ;

[0054] in, This is the relative singular value threshold; if there is no relative singular value threshold order that satisfies the above condition... Or the relative singularity threshold order obtained from the above conditions. When less than the preset lower limit of order The relative singular value thresholding result is deemed unreliable, and the relative singular value thresholding order is determined to be... Set to the preset upper limit of order ;

[0055] S433: The ratio of adjacent singular values ​​determines the order of the singular value gap. The expression is:

[0056] ;

[0057] S434: Based on the above results, the final model order P is determined as follows:

[0058]

[0059]

[0060] in, It represents the order margin.

[0061] Furthermore, step S4 also includes:

[0062] Construct the Vandermonde matrix The complex amplitude coefficients corresponding to each pole are solved by the least squares method, and the expression is as follows:

[0063] ;

[0064] ;

[0065] in, For complex amplitude coefficient vectors, For matrix The pseudo-inverse matrix, The input impedance real part sequence after detrending and normalization; the magnitude of the complex amplitude coefficients. Used to characterize the strength of the reflection component corresponding to the k-th pole.

[0066] Further, step S5 specifically includes:

[0067] S51: For each pole obtained by the matrix bundle algorithm, calculate its magnitude. and phase And calculate the corresponding reflection distance according to the following formula. :

[0068] ;

[0069] in, The speed at which electromagnetic waves propagate in a cable. The frequency interval for the sweep frequency;

[0070] S52: Solve for the complex amplitude coefficients A corresponding to each pole using the Vandermonde matrix least squares method. k And take its modulus value as the index of reflection intensity. ;

[0071] S53: Perform physical constraint screening on the poles, retaining the poles that simultaneously satisfy the following conditions:

[0072] ,

[0073] ,

[0074] ,

[0075] ;

[0076] in, For the total length of the cable line, For the tolerance at the end of the line;

[0077] S54: Based on the reflection intensity, the selected poles are... Sort from largest to smallest, and merge poles that are close in distance: if two candidate poles are d... i and d j The absolute value of the difference is less than or equal to the distance merging tolerance. If the two are not found, they are merged into the same candidate reflection point. The merged distance is calculated using a weighted average of reflection intensity, and the merged reflection intensity is the sum of the reflection intensities at each pole. The merging tolerance is... The expression is:

[0078] , ;

[0079] in, B represents the theoretical distance resolution, and B represents the sweep bandwidth.

[0080] S55: Normalize the reflection intensity of the merged candidate reflection points to obtain the normalized reflection intensity. , and according to Output candidate reflection points from largest to smallest.

[0081] Furthermore, in step S6, the methods used for marking and removing include:

[0082] The end reflections are individually marked based on the total length of the line. If the candidate distance satisfies:

[0083] ;

[0084] The candidate point is marked as a reflection near the end of the line and is not output as a candidate point for fault. The remaining candidate reflection points are sorted from largest to smallest by reflection intensity and output as candidate locations for fault.

[0085] Secondly, the present invention provides a cable fault location system based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum, comprising:

[0086] The wideband sweep impedance measurement module is used to obtain the input impedance spectrum of the cable test end through wideband sweep measurement, and obtain the real part sequence of the input impedance.

[0087] The trend term elimination module is used to perform linear detrending processing on the input impedance real part sequence to remove the background trend term that changes slowly with frequency, and to standardize the detrended input impedance real part sequence to obtain a detrended and standardized input impedance real part sequence.

[0088] The exponential modeling module is used to construct an exponential signal model by superimposing multiple complex exponential components from the detrended and standardized real part sequence of the input impedance.

[0089] The matrix bundle parameter estimation module is used to construct two Hankel matrices that differ by one sampling point, determine the matrix bundle system matrix through singular value decomposition and adaptive model order determination, and solve the eigenvalues ​​of the system matrix to obtain the set of complex exponential poles.

[0090] The distance conversion and filtering module is used to calculate the distance from the corresponding reflection point to the cable test end based on the phase of each pole, and to determine the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and similar distance merging strategy.

[0091] The end reflection rejection and output module is used to mark and reject end reflections based on the total length of the cable line and output the candidate fault locations.

[0092] The beneficial effects of this invention are as follows: By utilizing the real part sequence of the input impedance measured by wideband sweep frequency measurement, the matrix bundle parameter estimation process only uses the real part sequence of the input impedance, without relying on the impedance phase spectrum and reflection coefficient to participate in pole estimation, thus reducing the complexity of the test equipment and the difficulty of data processing; by constructing a complex exponential signal model and adopting matrix bundle parameter estimation, the resolution capability of multiple close reflection points under limited sweep frequency bandwidth is improved, enabling the differentiation of multiple reflection points that are extremely close together, and eliminating sidelobe interference caused by spectral leakage and picket fence effect; by linearly detrending the real part of the input impedance, the cable distributed parameters and the equivalent impedance at the test end are eliminated. The resulting slow-changing frequency-dependent term makes the input sequence of the subsequent matrix bundle algorithm closer to the ideal exponential superposition model, significantly improving the signal-to-noise ratio of weak reflection signal extraction. Through singular value decomposition and adaptive model order determination, there is no need to manually preset the model order. It can automatically match the optimal order according to the actual signal and noise level, avoiding the problem of false poles caused by excessively high order or the omission of true poles by excessively low order. By combining pole magnitude, complex amplitude coefficient, line length constraint and end reflection removal, it can effectively filter out noise poles and false poles, and fundamentally distinguish fault reflections from strong end reflections, avoiding misjudging the end as a fault point. Attached Figure Description

[0093] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, use the same reference numerals to denote the same or similar parts. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0094] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0095] Figure 2 This is a system principle block diagram of one embodiment of the present invention. Detailed Implementation

[0096] Firstly, such as Figure 1 As shown, this invention discloses a cable fault location method based on the estimation of bundle parameters of the real part matrix of the input impedance spectrum, comprising the following steps:

[0097] S1: Obtain the input impedance spectrum of the cable test end by wideband sweep frequency measurement, and obtain the sequence of the real part of the input impedance;

[0098] S2: Perform linear detrending processing on the real part sequence of the input impedance to remove the background trend term that changes slowly with frequency, and perform standardization processing on the detrended real part sequence of the input impedance to obtain a detrended and standardized real part sequence of the input impedance.

[0099] S3: Construct the detrended and normalized sequence of the real part of the input impedance into an exponential signal model with multiple complex exponential components superimposed.

[0100] S4: Construct two Hankel matrices that differ by one sampling point, determine the matrix bundle system matrix through singular value decomposition and adaptive model order determination, and solve for the eigenvalues ​​of the system matrix to obtain the set of complex exponential poles;

[0101] S5: Calculate the distance from the corresponding reflection point to the cable test end based on the phase of each pole, and determine the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and close distance merging strategy;

[0102] S6: Mark and eliminate end reflections based on the total length of the cable line, and output candidate fault locations.

[0103] This application utilizes the real part sequence of input impedance measured by wideband sweep frequency measurement, eliminating the need to obtain phase spectrum or reflection coefficient spectrum, thus reducing the complexity of test equipment and the difficulty of data processing. By constructing a complex exponential signal model and employing matrix bundle parameter estimation, it overcomes the theoretical limitation of sweep bandwidth on resolution, enabling the differentiation of multiple reflection points that are extremely close together and eliminating sidelobe interference caused by spectral leakage and picket fence effect. By linearly detrending the real part of the input impedance, it eliminates the slow frequency-dependent changes caused by cable distributed parameters and equivalent impedance at the test end, making the input sequence of the subsequent matrix bundle algorithm closer to the ideal exponential superposition model, significantly improving the signal-to-noise ratio of weak reflection signal extraction. Through singular value decomposition and adaptive model order determination, it eliminates the need for manually preset model order, automatically matching the optimal order based on the actual signal and noise levels, avoiding the problems of false poles due to excessively high order or missing true poles due to excessively low order. By combining pole magnitude, complex amplitude coefficient, line length constraints, and end reflection removal, it can effectively filter out noise poles and false poles, and fundamentally distinguish between fault reflections and strong end reflections, avoiding misjudging the end as a fault point.

[0104] According to one embodiment of this application, the formation mechanism of the input impedance spectrum includes:

[0105] According to transmission line theory, power cables cannot be simply equivalent to lumped parameter elements over a wide frequency range. Instead, they should be considered as distributed parameter transmission lines consisting of a continuous distribution of resistance, inductance, conductance, and capacitance per unit length. Let a spatial coordinate x be established along the cable axis, with the test end or power supply end as the origin and the positive direction pointing to the end of the cable. R, L, G, and C represent the resistance, inductance, conductance, and capacitance per unit length of the cable, respectively, ω is the angular frequency, and j is the imaginary unit.

[0106] Under steady-state conditions in the frequency domain, the voltage phasor V̇(x) and current phasor İ(x) at any position x in the cable satisfy the transmission line telegraph equation:

[0107] ,

[0108] ;

[0109] in, Let Γ(x) be the voltage phasor at position x, and İ(x) be the current phasor at position x; R, L, G, and C are the resistance, inductance, conductance, and capacitance per unit length, respectively; ω = 2πf is the angular frequency.

[0110] Differentiating the first-order differential equation above, we obtain the second-order wave equations for voltage and current:

[0111] ,

[0112] ;

[0113] Let the propagation constant γ and characteristic impedance Z0 be respectively:

[0114] ,

[0115] ;

[0116] Where γ is the propagation constant, which can usually be written as γ = α + jβ, where α is the attenuation constant and β is the phase constant; Z0 is the characteristic impedance of the cable;

[0117] As can be seen from the second-order wave equation, the voltage and current at any point on the cable are both composed of the superposition of two traveling wave components with opposite propagation directions. Taking the traveling wave propagating from the test end to the load end and the reflected wave propagating from the load end to the test end as an example, its general solution can be expressed as:

[0118] ,

[0119] ;

[0120] in, This represents the amplitude of the forward voltage wave. The voltage is the amplitude of the reflected voltage wave; the voltage expression has two exponential terms that correspond to the incident wave propagating towards the load and the reflected wave returning to the test end, respectively.

[0121] If we take the load end as the origin of the coordinate system and the x-coordinate represents the distance from the load end, then the above general solution can also be written as:

[0122] ,

[0123] ;

[0124] When x=0, the load terminal voltage and current are respectively:

[0125] ,

[0126] ;

[0127] Let the load impedance be Z. L And satisfying V̇(0) / İ(0)=Z L Then the reflection coefficient Γ at the load end L It can be represented as:

[0128] ;

[0129] Among them, Γ L Z is the reflection coefficient at the load end, representing the amplitude and phase relationship between the reflected wave and the incident wave; L Γ represents the load impedance. If the load is open-circuited, then Γ L =1; if the load is short-circuited, then Γ L =−1.

[0130] The reflection coefficient Γ L Substituting into the general solution, we can obtain the voltage and current at a distance x from the load terminal:

[0131] ,

[0132] ;

[0133] Therefore, the input impedance seen at a distance x from the load terminal is:

[0134] ;

[0135] If the total length of the cable is l, and the test terminal is located at a distance l from the load terminal, then the input impedance spectrum of the test terminal can be written as:

[0136] ;

[0137] Among them, Z l The impedance spectrum is input to the test terminal. Due to γ, Z0, and ΓL Both may vary with frequency, therefore Z l It is a function of frequency f.

[0138] After expanding and simplifying the above equation using Euler's formula, it can be expressed as:

[0139] ;

[0140] in, It is the attenuation constant. Let be the phase constant; under high-frequency conditions, the cable phase constant and frequency satisfy the following relationship:

[0141] ;

[0142] in, Let f be the speed of electromagnetic wave propagation in the cable, and f be the frequency. Since the reflected wave propagates from the test end to the fault point and then returns to the test end, its phase difference is:

[0143] ;

[0144] Therefore, the main oscillatory term in the real part of the input impedance can be expressed as:

[0145] .

[0146] According to one embodiment of this application, step S2 specifically includes:

[0147] As can be seen from the above analysis, the real part of the input impedance It contains a periodic oscillation component related to the fault reflection distance; however, in the actual wideband sweep process, the real part of the input impedance is also affected by the cable body distributed parameters, dielectric loss, conductor loss, equivalent impedance of the test end and frequency-related background response, thus forming a trend term that changes slowly with frequency; this trend term does not directly characterize the local fault location, and if it is directly involved in the matrix bundle parameter estimation, it may reduce the pole extraction stability of the fault reflection oscillation component.

[0148] Therefore, before constructing the matrix bundle model, this invention performs linear detrending processing on the real part of the input impedance; let the sequence of the real part of the input impedance obtained by wideband sweep be:

[0149] ;

[0150] in, This represents the nth sweep frequency point, where N is the number of sweep sampling points.

[0151] The background trend term in the real part of the input impedance is fitted using a first-order linear function:

[0152] ;

[0153] in, The background trend term is linear, where 'a' is the trend slope and 'b' is the trend intercept; parameters 'a' and 'b' are determined using the least squares method.

[0154] ;

[0155] The detrended sequence of the real part of the input impedance is obtained. The expression is:

[0156] ;

[0157] After linear detrending, the slowly changing background term in the real part of the input impedance is weakened, while the cosine-type oscillation characteristic related to the fault distance is highlighted. This processing enables the input sequence of the subsequent matrix bundle algorithm to be closer to the complex exponential component superposition model, which is beneficial to improving the stability of pole estimation and the fault location accuracy.

[0158] According to one embodiment of this application, in step S2, to avoid the magnitude scale of the input impedance real part sequence affecting the singular value decomposition and least squares solution, the detrended input impedance real part sequence is standardized. The standardization formula is as follows:

[0159] ;

[0160] in, The mean of the real part sequence of the detrended input impedance is expressed as:

[0161] ;

[0162] The standard deviation of the detrended input impedance real part sequence is expressed as:

[0163] .

[0164] According to one embodiment of this application, step S3 specifically includes:

[0165] After linear detrending, the sequence of the real part of the input impedance after removing the background trend term is obtained; let this sequence be:

[0166] ;

[0167] in, This represents the real part of the detrending input impedance corresponding to the nth frequency sampling point, where N represents the number of sweep sampling points.

[0168] Because internal fault points in the cable create impedance discontinuities, the reflected signals generated at these locations will form periodic oscillating components in the real part of the input impedance. When multiple reflection points coexist, the detrended sequence of the real part of the input impedance can be expressed as a superposition of multiple exponential components:

[0169] ;

[0170] Where P is the model order, representing the number of exponential components to be estimated; is the amplitude coefficient of the k-th exponential component; This is the pole corresponding to the kth exponential component; This includes noise and unmodeled disturbance terms;

[0171] Among them, the poles It can be represented as:

[0172] ;

[0173] in, The pole magnitude reflects the attenuation characteristics of the reflected component; The pole phase reflects the oscillation frequency characteristics in the real part sequence of the input impedance;

[0174] According to the real part oscillation mechanism of input impedance, the distance to the reflection point and the phase of the pole satisfy the following relationship:

[0175] ;

[0176] in, Let be the distance from the k-th reflection point to the test end. The speed at which electromagnetic waves propagate in a cable. The frequency interval for the sweep frequency;

[0177] Therefore, this invention transforms the cable fault location problem into the problem of estimating the exponential poles in the real part sequence of the detrended input impedance; subsequently, it constructs a matrix bundle and solves for the poles. This allows us to obtain the distance information corresponding to the location of the fault reflection.

[0178] According to one embodiment of this application, step S4 specifically includes:

[0179] After linear detrending and standardization, the input sequence for matrix bundle analysis is obtained:

[0180] ;

[0181] Based on the principle of the matrix bundle algorithm, for a discrete sequence composed of multiple complex exponential components, its pole parameters can be extracted by constructing a Hankel matrix with a shift relationship; this invention constructs two Hankel matrices that differ by one sampling point:

[0182] ;

[0183] Where L is the number of rows in the Hankel matrix; in a preferred embodiment, L is taken as:

[0184] ;

[0185] The two matrices above satisfy a first-order shift relationship. Compared to The entire sequence is shifted backward by one sampling point; this shift relationship contains the pole information of the complex exponential sequence.

[0186] For matrix Perform singular value decomposition:

[0187] ;

[0188] in, and These are the left and right singular vector matrices, respectively. It is a singular value diagonal matrix, and the superscript H denotes the conjugate transpose;

[0189] The model order P is determined based on the magnitude of the singular values; this invention comprehensively uses cumulative energy, relative singular value threshold, and singular value gap to determine the model order; the cumulative energy is defined as:

[0190] ;

[0191] in, For the i-th singular value, for the matrix Performing singular value decomposition yields a sequence of singular values ​​arranged in descending order: Q represents the total number of singular values; m represents the order of the candidate model. This represents the cumulative energy percentage of the first m singular values; when the cumulative energy... Reaching the preset threshold At that time, determine the cumulative energy order. ,in ;

[0192] Relative singular value threshold order Determined according to the following formula:

[0193] ;

[0194] in, The relative singularity threshold is preferably set to 10. -3 When there is no relative singular value threshold order that satisfies the relative singular value threshold condition. Or the relative singularity threshold order obtained from this condition. Less than the preset order lower limit If the relative singular value thresholding result is deemed unreliable, the relative singular value thresholding order is set to the preset upper limit. This is to avoid the effective reflection component being truncated due to an excessively low order.

[0195] Simultaneously, the singular value gap order is determined based on the ratio of adjacent singular values:

[0196] ;

[0197] Based on the above results, the final model order P is determined; that is, in terms of energy order... and relative singularity threshold order Introducing order margin And combined with the order of singular value gaps By constraining the order of the final model, we obtain: And ensure that the model order P satisfies the following constraints: .in, .

[0198] After determining the model order, the first P principal singular values ​​and their corresponding singular vectors are extracted, resulting in:

[0199] ;

[0200] Then construct the matrix bundle system matrix:

[0201] ;

[0202] matrix The eigenvalues ​​are the complex exponential poles to be estimated:

[0203] ;

[0204] in, This is the k-th pole; the phase of this pole reflects the oscillation frequency in the real part sequence of the input impedance, and the pole magnitude reflects the equivalent attenuation characteristics of this component.

[0205] To evaluate the strength of the reflection components corresponding to each pole, this invention further constructs the Vandermonde matrix. :

[0206] ;

[0207] The complex amplitude coefficients corresponding to each pole are then solved using the least squares method.

[0208] ;

[0209] in, For complex amplitude coefficient vectors, Vandermonde matrix The pseudo-inverse matrix, The input impedance real part sequence after detrending and normalization; the magnitude of the complex amplitude coefficients. Used to characterize the strength of the reflection component corresponding to the k-th pole.

[0210] According to one embodiment of this application, step S5 specifically includes:

[0211] After obtaining the complex exponential poles through the matrix bundle algorithm, this invention further calculates the corresponding reflection distance based on the pole phase, and determines the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and close distance merging strategy.

[0212] Suppose the set of poles obtained by the matrix bundle algorithm is:

[0213] ;

[0214] For each pole Calculate its magnitude and phase:

[0215] ;

[0216] in, Let the magnitude of the k-th pole be . The phase of the k-th pole;

[0217] according to The relationship between the real part of the input impedance oscillation term and the reflection distance, and the reflection distance corresponding to the k-th pole. It can be calculated;

[0218] Furthermore, the unit sampling damping factor is calculated based on the pole magnitude:

[0219] ;

[0220] in, This is the unit sampling damping factor corresponding to the k-th pole, used to characterize the equivalent attenuation characteristics of this reflection component;

[0221] To evaluate the strength of the reflection components corresponding to each pole, this invention uses the complex amplitude coefficient A obtained by the aforementioned Vandermonde matrix least squares method. k And take its magnitude as the index of reflection intensity:

[0222] ;

[0223] Among them, A k The complex amplitude coefficient corresponding to the k-th pole is... This is the reflection intensity index corresponding to the kth pole;

[0224] Subsequently, this invention performs physical constraint screening on the original pole set; firstly, it retains a finite number of poles located within the effective range of the circuit:

[0225] ;

[0226] in, Given the total length of the cable line, The tolerance at the end of the line; in a preferred embodiment, the tolerance at the end of the line is taken as:

[0227] ;

[0228] Secondly, poles that clearly do not conform to the damped oscillation model are eliminated based on their pole magnitudes:

[0229] ;

[0230] In a preferred embodiment, the following is taken:

[0231] ;

[0232] At the same time, the reflection intensity index is retained to meet the requirements. The extreme point;

[0233] For the poles that pass the above screening, according to the reflection intensity index... Sort from largest to smallest. Since conjugate poles, repeated poles, or closely spaced reflection components may generate multiple candidate values ​​with close distances, this invention further merges similar distances; let two candidate distances be d. i and d j satisfy:

[0234] ;

[0235] Then the two are merged into the same candidate reflection point; where, The distance merging tolerance is defined as follows: In a preferred embodiment, the distance merging tolerance is taken as:

[0236] ;

[0237] in, The theoretical distance resolution is calculated as follows:

[0238] ;

[0239] Where B is the sweep bandwidth;

[0240] For the merged candidate reflection points, their distances are obtained by weighting the reflection intensity:

[0241] ;

[0242] Where G is the set of poles corresponding to the same candidate reflection point. The candidate reflection distance after merging;

[0243] The combined reflection intensity is:

[0244] ;

[0245] To facilitate comparison of the relative strength of different candidate points, this invention further normalizes the candidate reflection intensity:

[0246] ;

[0247] in, Normalized reflection intensity;

[0248] According to one embodiment of this application, step S6 specifically includes:

[0249] Since the cable end itself is an impedance discontinuity point, end reflections may form candidate points in the matrix bundle results. To avoid misidentifying the cable end as a fault point, this invention marks the end reflections separately based on the entire length of the cable; if the candidate distance satisfies:

[0250] ;

[0251] If the candidate point is not output as a fault candidate point, then it is marked as a reflection near the end of the line; otherwise, it is output as a candidate fault reflection point.

[0252] Finally, according to the normalized reflection intensity Output candidate reflection points from largest to smallest; in a preferred embodiment, output the top K candidate points:

[0253] ;

[0254] Therefore, this invention can obtain candidate fault locations based on matrix bundle pole phase, pole magnitude, complex amplitude coefficient and line physical range constraints without using prior fault distance information, and distinguish line end reflection from fault reflection.

[0255] Secondly, such as Figure 2As shown, this invention discloses a cable fault location system based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum, comprising:

[0256] The wideband sweep impedance measurement module is used to obtain the input impedance spectrum of the cable test end through wideband sweep measurement, and obtain the real part sequence of the input impedance.

[0257] The trend term elimination module is used to perform linear detrending processing on the input impedance real part sequence to remove the background trend term that changes slowly with frequency, and to standardize the detrended input impedance real part sequence to obtain a detrended and standardized input impedance real part sequence.

[0258] The exponential modeling module is used to construct an exponential signal model by superimposing multiple complex exponential components from the detrended and standardized real part sequence of the input impedance.

[0259] The matrix bundle parameter estimation module is used to construct two Hankel matrices that differ by one sampling point, determine the matrix bundle system matrix through singular value decomposition and adaptive model order determination, and solve the eigenvalues ​​of the system matrix to obtain the set of complex exponential poles.

[0260] The distance conversion and filtering module is used to calculate the distance from the corresponding reflection point to the cable test end based on the phase of each pole, and to determine the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and similar distance merging strategy.

[0261] The end reflection rejection and output module is used to mark and reject end reflections based on the total length of the cable line and output the candidate fault locations.

[0262] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A cable fault location method based on the estimation of bundle parameters of the real part matrix of the input impedance spectrum, characterized in that, Includes the following steps: S1: Obtain the input impedance spectrum of the cable test end by wideband sweep frequency measurement, and obtain the sequence of the real part of the input impedance; S2: Perform linear detrending processing on the real part sequence of the input impedance to remove the background trend term that changes slowly with frequency, and perform standardization processing on the detrended real part sequence of the input impedance to obtain a detrended and standardized real part sequence of the input impedance. S3: Construct the detrended and normalized sequence of the real part of the input impedance into an exponential signal model with multiple complex exponential components superimposed. S4: Construct two Hankel matrices that differ by one sampling point, determine the matrix bundle system matrix through singular value decomposition and adaptive model order determination, and solve for the eigenvalues ​​of the system matrix to obtain the set of complex exponential poles; S5: Calculate the distance from the corresponding reflection point to the cable test end based on the phase of each pole, and determine the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and close distance merging strategy; S6: Mark and eliminate end reflections based on the total length of the cable line, and output candidate fault locations.

2. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 1, characterized in that, In step S2, a first-order linear function of the input impedance real part sequence is fitted using the least squares method as a background trend term and then subtracted from the original input impedance real part sequence. The expression for the background trend item is: ； in The background trend term is linear; a is the trend slope, and b is the trend intercept. The parameters a and b are determined using the least squares method, and the expression is: ； The detrended sequence of the real part of the input impedance is obtained. The expression is: ； in, The sequence of real parts of the input impedance obtained in step S1. N represents the number of frequency sweep sampling points.

3. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 2, characterized in that, In step S2, the standardization formula is: ； in, The mean of the real part sequence of the detrended input impedance is expressed as: ； The standard deviation of the detrended input impedance real part sequence is expressed as: 。 4. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 3, characterized in that, In step S3, the expression for the exponential signal model is: ， ； Where P is the model order, representing the number of exponential components to be estimated; is the amplitude coefficient of the k-th exponential component; This is the pole corresponding to the kth exponential component; This includes noise and unmodeled disturbance terms; The pole magnitude; This represents the pole phase.

5. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 4, characterized in that, Step S4 specifically includes: S41: Construct two Hankel matrices that differ by one sampling point. and , Compared to The entire matrix is ​​shifted backward by one sampling point; the Hankel matrix and They are represented as follows: ； in, S42: Yes Perform singular value decomposition: ； in, and These are the left and right singular vector matrices, respectively. It is a singular value diagonal matrix, and the superscript H denotes the conjugate transpose; S43: The model order P is adaptively determined based on the singular value cumulative energy, the relative singular value threshold, and the singular value gap order; S44: Extract the first P principal singular values ​​and their corresponding singular vectors to construct the matrix bundle system matrix, resulting in: ； S45: Solve for the generalized eigenvalues ​​to obtain the set of complex exponential poles { }: ； in, This is the k-th pole.

6. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 5, characterized in that, In step S43, adaptively determining the model order P includes: S431: Determine the cumulative energy order based on the cumulative energy. The expression is: ； ； in, Let Q be the i-th singular value, Q be the total number of singular values, and m be the order of the candidate model. This represents the cumulative energy percentage of the first m singular values; The energy order is the cumulative energy. Reaching the preset threshold When, the cumulative amount is determined according to the above formula. ; S432: Determine the order of the relative singular value threshold based on the relative singular value threshold. The expression is: ； in, This is the relative singular value threshold; if there is no relative singular value threshold order that satisfies the above condition... Or the relative singularity threshold order obtained from the above conditions. When less than the preset lower limit of order The relative singular value thresholding result is deemed unreliable, and the relative singular value thresholding order is determined to be... Set to the preset upper limit of order ; S433: The ratio of adjacent singular values ​​determines the order of the singular value gap. The expression is: ； S434: Based on the above results, the final model order P is determined as follows: in, It represents the order margin.

7. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 6, characterized in that, Step S4 further includes: Construct the Vandermonde matrix The complex amplitude coefficients corresponding to each pole are solved by the least squares method, and the expression is as follows: ； ； in, For complex amplitude coefficient vectors, For matrix The pseudo-inverse matrix, The input impedance real part sequence after detrending and normalization; the magnitude of the complex amplitude coefficients. Used to characterize the strength of the reflection component corresponding to the k-th pole.

8. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 7, characterized in that, Step S5 specifically includes: S51: For each pole obtained by the matrix bundle algorithm, calculate its magnitude. and phase And calculate the corresponding reflection distance according to the following formula. : ； in, The speed at which electromagnetic waves propagate in a cable. The frequency interval is the sweep frequency. S52: Solve for the complex amplitude coefficients A corresponding to each pole using the Vandermonde matrix least squares method. k And take its modulus value as the index of reflection intensity. ; S53: Perform physical constraint screening on the poles, retaining the poles that simultaneously satisfy the following conditions: ， ， ， ； in, For the total length of the cable line, For the tolerance at the end of the line; S54: Based on reflection intensity, the selected poles are... Sort from largest to smallest, and merge poles that are close in distance: if two candidate poles are d... i and d j The absolute value of the difference is less than or equal to the distance merging tolerance. If the two are not found, they are merged into the same candidate reflection point. The merged distance is calculated using a weighted average of reflection intensity, and the merged reflection intensity is the sum of the reflection intensities at each pole. The merging tolerance is... The expression is: ， ； in, B represents the theoretical distance resolution, and B represents the sweep bandwidth. S55: Normalize the reflection intensity of the merged candidate reflection points to obtain the normalized reflection intensity. , and according to Output candidate reflection points from largest to smallest.

9. The cable fault location method based on the estimation of the bundle parameters of the real part matrix of the input impedance spectrum according to claim 8, characterized in that, In step S6, the methods used for marking and removing include: The end reflections are individually marked based on the total length of the line. If the candidate distance satisfies: ； The candidate point is marked as a reflection near the end of the line and is not output as a fault candidate point; the remaining candidate reflection points are sorted by reflection intensity from large to small and output as fault candidate locations.

10. A cable fault location system based on the parameter estimation of the real part matrix of the input impedance spectrum, characterized in that, include: The wideband sweep impedance measurement module is used to obtain the input impedance spectrum of the cable test end through wideband sweep measurement, and obtain the real part sequence of the input impedance. The trend term elimination module is used to perform linear detrending processing on the input impedance real part sequence to remove the background trend term that changes slowly with frequency, and to standardize the detrended input impedance real part sequence to obtain a detrended and standardized input impedance real part sequence. The exponential modeling module is used to construct an exponential signal model by superimposing multiple complex exponential components from the detrended and standardized real part sequence of the input impedance. The matrix bundle parameter estimation module is used to construct two Hankel matrices that differ by one sampling point, determine the matrix bundle system matrix through singular value decomposition and adaptive model order determination, and solve the eigenvalues ​​of the system matrix to obtain the set of complex exponential poles. The distance conversion and filtering module is used to calculate the distance from the corresponding reflection point to the cable test end based on the phase of each pole, and to determine the final candidate reflection point by combining the pole magnitude, complex amplitude coefficient, line length constraint and similar distance merging strategy. The end reflection rejection and output module is used to mark and reject end reflections based on the entire length of the cable line and output candidate fault locations.

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