Cable fault identification method based on empirical mode decomposition remodeling and wavelet transformation
By combining empirical mode decomposition and wavelet transform, and assigning different weights to the center frequencies of IMF components for weighted averaging, the problem of inaccurate cable fault location in existing technologies is solved, and precise and stable cable fault location is achieved.
Patent Information
- Application Number
- CN202511856484.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-10
- Publication Date
- 2026-02-06
AI Technical Summary
Existing cable fault location methods ignore the information contained in each IMF component, resulting in the loss of signal detail information and affecting the accuracy and stability of the location.
A method based on empirical mode decomposition and wavelet transform is adopted. The wavelet transform function is obtained through the Gaussian kernel function. Different weights are assigned according to the center frequency of the IMF component, and a weighted average is performed to achieve accurate location of cable faults.
By making full use of the fault characteristic information of each component in different frequency bands, environmental noise interference is suppressed, and the accuracy and stability of fault location are improved.
Smart Images
Figure CN121476835A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of computer defect positioning, and particularly relates to a cable fault identification method based on empirical mode decomposition remodeling and wavelet transformation. BACKGROUND
[0002] With the further development of urban construction, overhead transmission lines are gradually replaced by power cables, and the proportion of power cables in power supply networks is gradually increasing, and power cables become an important part of power systems. In the distribution network, the cable is the main medium for transferring electric energy, and its failure directly determines the safety and economy of the entire power system. With the widespread use of power cables, the number of power cable faults is gradually increasing. Since the cable is mostly buried underground and is affected by temperature, humidity and other conditions, when the cable is fault located, signal instability is prone to occur, and misjudgment is thus caused.
[0003] The existing method is to obtain a judgment signal by remodeling after various transformation processing of the IMF component obtained by empirical mode decomposition; this processing method ignores the information contained in each IMF component, and the signal obtained by remodeling is only the result of superposition of all IMF components, and the detailed information is completely lost, which is extremely unfavorable for cable fault positioning.
[0004] The present application studies the cable defect diagnosis method, uses empirical mode decomposition and wavelet transformation, and proposes a cable fault positioning method based on empirical mode decomposition and wavelet transformation. SUMMARY
[0005] The purpose of the present application is to provide a cable fault identification method based on empirical mode decomposition remodeling and wavelet transformation, to obtain a wavelet transformation function by a Gaussian kernel function for the IMF component, to give different weights according to the size of the center frequency of the IMF component, and to realize accurate positioning of the cable defect by weighted average.
[0006] To achieve the above purpose, the present application provides a cable fault identification method based on empirical mode decomposition remodeling and wavelet transformation, comprising the following steps: S1, transmitting a fault detection signal to the end of the cable, and receiving a reflected signal at the end of the cable; S2, performing empirical mode decomposition on the reflected signal received at the end of the cable to obtain a plurality of intrinsic mode functions and a residual component; S3, performing wavelet transformation on the intrinsic mode function to obtain a series of wavelet transformation functions; S4, performing weighted average on the maximum value points of the wavelet transformation function image and their weights to obtain the cable fault position.
[0007] Preferably, in S2, the number of extreme points and zero points of the obtained intrinsic modulus function is equal or differs by one over the entire data length, and the average value of the envelope function of the maximum and minimum points is zero; the obtained residual component is monotonically decreasing or monotonically increasing over the entire data length.
[0008] Preferably, in S2, the specific process of empirical mode decomposition is as follows: For the reflected signal respectively Cubic spline interpolation is performed on the maxima and minima to obtain the envelope function of the maxima. envelope function of local minimum points ; The mean function is obtained by taking the mean of the envelope functions at their maxima and minima. ,make ;use Alternative Repeat the above process until... If the intrinsic modulus function is satisfied, then ; make ,right Then perform intrinsic mode decomposition, and we have The intrinsic mode functions after mode decomposition are obtained. until the residual component function When it becomes a monotonic function, the decomposition stops.
[0009] Preferably, cubic spline interpolation is used to construct a smooth piecewise cubic function given a set of data points. To fit these data points, specifically: Given Data points ,in ,and cubic spline interpolation function It is a piecewise function, in each interval ,in superior, ; The interpolation conditions for cubic spline interpolation are as follows: ; ; ; .
[0010] The preferred cubic spline interpolation solution process is as follows: set up Then in the interval Above, to Linear interpolation, there are: ; Will In the interval Integrate twice, get: ; Using interpolation conditions And Simplify, there are: ; ; ; .
[0011] Preferably, the process of solving cubic spline interpolation also includes: Will In the interval Integrate once, get: ; Using the continuous condition of the derivative function, that is , record: ; ; ; Get: , that is: .
[0012] Preferably, the process of solving cubic spline interpolation also includes using Gauss-Seidel method to solve linear equations, the specific process is as follows: For matrix equation , the coefficient matrix Decomposed into , where Is the diagonal matrix composed of the main diagonal elements of , Is the lower triangular matrix composed of the strict lower triangular part of , Is the upper triangular matrix composed of the strict upper triangular part of , Gauss-Seidel iterative formula is: ; The vector sequence Converges to the exact solution .
[0013] Preferably, in S3, the mother wavelet function Wavelet transform is performed on all the eigenmode functions to obtain wavelet transform functions of all the eigenmode functions: ; wherein, denotes a scale factor, denotes a translation factor, denotes a wavelet mother function, denotes a complex conjugate of the wavelet mother function.
[0014] Preferably, the wavelet mother function is composed of a Gaussian function and a complex exponential function, and is defined as follows: ; and the wavelet mother function satisfies the following admissibility condition: ; If , the wavelet function is said to have order vanishing moments.
[0015] Preferably, in S4, all the wavelet-transformed eigenmode functions have maximum points, and the functions with the maximum points are respectively denoted as , wherein, ; the maximum points are denoted as ; The weight of any maximum point is , and the cable fault position is: .
[0016] Therefore, the cable fault recognition method based on the empirical mode decomposition reshaping and wavelet transform has the following beneficial effects: (1) The wavelet transform is performed on each IMF component, and the fault feature information contained in each component in different frequency bands is fully utilized, especially the high-frequency details reflecting the fault abrupt change points, so that more complete feature basis is provided for accurate positioning.
[0017] (2) The weighted average is performed according to the different weights of the IMF component center frequencies, the contribution of the low-frequency signals containing the main fault features is highlighted, and the detailed information of the high-frequency signals is reasonably utilized, the influence of environmental noise and signal interference is effectively suppressed, the fault positioning result is more stable and reliable, and the complex field working conditions are adapted.
[0018] The technical solutions of the present application are further described in detail below with reference to the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS
[0019] Figure 1 is the overall flow chart of the cable fault recognition method embodiment of the present application based on empirical mode decomposition remodeling and wavelet transform. DETAILED DESCRIPTION
[0020] The technical solutions of the present application are further described below by means of the accompanying drawings and examples.
[0021] Unless otherwise defined, the technical terms or scientific terms used in the present application shall be understood as the usual meanings understood by those skilled in the art to which the present application belongs.
[0022] As shown in the figure, the cable fault recognition method based on empirical mode decomposition remodeling (EMD) and wavelet transform (WT) includes the following steps: Figure 1 S1, transmitting a fault detection signal to the end of the cable, and receiving a reflected signal from the end of the cable. S2, performing empirical mode decomposition on the reflected signal received by the end of the cable to obtain a plurality of intrinsic mode functions and a residual component.
[0023] The intrinsic mode function obtained by empirical mode decomposition has equal number of extreme points and zero points or a difference of one in the entire data length, and the average value of the envelope function of the maximum value point and the minimum value point is zero; the residual component obtained is monotonically decreasing or monotonically increasing in the entire data length.
[0024] The specific process of empirical mode decomposition of the present application is as follows:
[0025] Firstly, cubic spline interpolation is performed on the maximum value points and the minimum value points of the reflected signal respectively to obtain the envelope function of the maximum value points and the envelope function of the minimum value points . The cubic spline interpolation of the present application is used to construct a smooth piecewise cubic function
[0026] to fit the data points under the condition of given data points, specifically as follows: Given data points , where , and , the cubic spline interpolation function is a piecewise function on each interval , where . .
[0027] The cubic spline interpolation interpolation condition is as follows: ; ; ; .
[0028] The present application adopts the following method for cubic spline interpolation solution, in particular: Let , then on the interval , the linear interpolation is made to , and there is: .
[0029] The is integrated twice on the interval , and the following is obtained: .
[0030] The interpolation condition and are simplified, and there is: ; ; ; .
[0031] The cubic spline interpolation solution process of the present application further includes: The is integrated once on the interval , and the following is obtained: .
[0032] The derivative function continuity condition, i.e. , is used, and the following is recorded: ; ; .
[0033] After arrangement, the following is obtained: , that is: .
[0034] In addition, the cubic spline interpolation solution process further includes solving the linear equation set by using the Gauss-Seidel method, and the specific process is as follows: For the matrix equation , the coefficient matrix is decomposed into ,in yes A diagonal matrix composed of elements along the main diagonal. yes A lower triangular matrix consisting of the strict lower triangular portion (elements below the main diagonal). yes The upper triangular matrix formed by the strict upper triangular portion (elements above the main diagonal) is given by the Gauss-Seidel method iteration formula: ; This method yields a vector sequence Converging to the exact solution .
[0035] The envelope function at the maximum point is The envelope function of the local minimum point The mean value is obtained by deriving the mean function. .
[0036] Let the original function Subtract the mean function ,get ; Use the obtained Replace the original reflected signal Repeat the above process until... If the intrinsic modulus function is satisfied, then .
[0037] make Repeat the above search The process, for Then perform intrinsic mode decomposition, and we have The intrinsic mode functions after mode decomposition are obtained. until the residual component function If it becomes a monotonic function, the decomposition stops. Clearly, the result obtained according to the empirical mode decomposition process... They are arranged in ascending order of center frequency.
[0038] After the empirical mode decomposition is completed, .
[0039] S3. Obtain a series of wavelet transform functions by applying wavelet transform to the intrinsic modulus functions.
[0040] This step selects the wavelet mother function. Wavelet transform is performed on all intrinsic mode functions, and the wavelet mother function in this invention is... It consists of a Gaussian function and a complex exponential function, and is defined as follows: .
[0041] and the mother wavelet function satisfy the following admissibility condition: .
[0042] If , the wavelet function is said to have order vanishing moments.
[0043] The wavelet transform function of all eigenmode functions is obtained: ; wherein denotes a scale factor, denotes a translation factor, denotes the mother wavelet function, and denotes the complex conjugate of the mother wavelet function.
[0044] S4, the maximum points of the wavelet transform function image and their weights are weightedly averaged to obtain the cable fault location.
[0045] All wavelet-transformed eigenmode functions are arranged in ascending order according to the subscript to obtain a set of wavelet-transformed eigenmode functions .
[0046] All wavelet-transformed eigenmode functions , the functions having maximum points are respectively denoted as , wherein ; and the maximum points thereof are denoted as .
[0047] The low-frequency signal contains the overall information of the signal, and the high-frequency signal contains the detailed information of the signal; the input signal of the cable fault recognition is a sine wave function, and the reflected signal obtained through reflection is still dominated by the sine signal; therefore, a greater weight should be given to the low-frequency signal, and a smaller weight should be given to the high-frequency signal.
[0048] Suppose that the weight of any maximum point is , the maximum point and its weight are weightedly averaged to obtain the cable fault location: .
[0049] The weight of low frequency signal is larger, which ensures the restoration of the original signal; meanwhile, the weight of high frequency signal is smaller, which retains the detail information of the signal, and greatly improves the accuracy of cable fault positioning.
[0050] Therefore, the cable fault recognition method based on EMD and wavelet transform is adopted, the fine extraction and accurate positioning of the cable fault characteristics are realized through the organic combination of EMD and wavelet transform, and reliable technical support is provided for the safe operation of the power cable.
[0051] Therefore, the cable fault recognition method based on EMD and wavelet transform is adopted, the fine extraction and accurate positioning of the cable fault characteristics are realized through the organic combination of EMD and wavelet transform, and reliable technical support is provided for the safe operation of the power cable.
[0052] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application rather than limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by the equivalent, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.
Claims
1. A cable fault identification method based on empirical mode decomposition reshaping and wavelet transform, characterized in that, Includes the following steps: S1. Transmit a fault detection signal to the end of the cable and receive the reflected signal from the end of the cable; S2. Perform empirical mode decomposition on the reflected signal received at the end of the cable to obtain several intrinsic mode functions and a residual component; S3. Obtain a series of wavelet transform functions by applying wavelet transform to the intrinsic mode functions; S4. Take a weighted average of the maximum points and their weights in the wavelet transform function image to obtain the cable fault location.
2. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 1, characterized in that, In S2, the number of extreme points and zero points of the obtained intrinsic modulus function is equal or differs by one over the entire data length, and the average value of the envelope function of the maximum and minimum points is zero; the obtained residual components are monotonically decreasing or monotonically increasing over the entire data length.
3. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 2, characterized in that, In S2, the specific process of empirical mode decomposition is as follows: For the reflected signal respectively Cubic spline interpolation is performed on the maxima and minima to obtain the envelope function of the maxima. envelope function of local minimum points ; The mean function is obtained by taking the mean of the envelope functions at their maxima and minima. ,make ;use Alternative Repeat the above process until... If the intrinsic modulus function is satisfied, then ; make ,right Then perform intrinsic mode decomposition, and we have The intrinsic mode functions after mode decomposition are obtained. until the residual component function When it becomes a monotonic function, the decomposition stops.
4. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 3, characterized in that, Cubic spline interpolation is used to construct a smooth piecewise cubic function given a set of data points. To fit these data points, specifically: Given Data points ,in ,and cubic spline interpolation function It is a piecewise function, in each interval ,in superior, ; The interpolation conditions for cubic spline interpolation are as follows: ； ； ； 。 5. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 4, characterized in that, The specific process of cubic spline interpolation is as follows: set up Then in the interval Above, to For linear interpolation, we have: ； Will In the interval Integrating twice, we get: ； Using interpolation conditions and Simplifying, we have: ； ； ； 。 6. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 5, characterized in that, The cubic spline interpolation process also includes: Will In the interval Integrating once, we get: ； Using the continuity condition of the derivative, i.e. ,remember: ； ； ； The results were: ,Right now: 。 7. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 6, characterized in that, The cubic spline interpolation process also includes solving the linear equation system using the Gauss-Seidel method, as detailed below: For matrix equations , the coefficient matrix Decomposed into ,in yes A diagonal matrix composed of elements along the main diagonal. yes A lower triangular matrix composed of the strictly lower triangular parts. yes The upper triangular matrix formed by the strictly upper triangular parts is given by the Gauss-Seidel method iteration formula as follows: ； The resulting vector sequence Converging to the exact solution .
8. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 2, characterized in that, In S3, the wavelet mother function is selected. Performing wavelet transform on all eigenmode functions yields the wavelet transform functions for all eigenmode functions: ； in, Indicates the scale factor. Indicates the translation factor. Describes the wavelet mother function. This represents the complex conjugate of the wavelet mother function.
9. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 8, characterized in that, wavelet mother function It consists of a Gaussian function and a complex exponential function, and is defined as follows: ； And wavelet mother function The following allowable conditions must be met: ； like Then it is called a wavelet function. have Vanishing moment of order.
10. The cable fault identification method based on empirical mode decomposition and wavelet transform according to claim 9, characterized in that, In S4, for all eigenmode functions after wavelet transform... The functions with maximum points are denoted as follows: ,in, Its maximum point is denoted as ; arbitrary maximum point The weight is The location of the cable fault is: 。