Cable fault identification method based on variational mode decomposition
The cable reflected signal is decomposed into an eigenmode function through the variational modal decomposition method, which solves the problem of noise and modal aliasing in the traditional method and realizes high-precision identification of cable faults.
Patent Information
- Application Number
- CN202510803442.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-17
- Publication Date
- 2025-07-25
AI Technical Summary
Traditional cable fault recognition methods rely on wavelet transformation to be susceptible to basis function selection and noise, and there is a modal aliasing problem in empirical modal decomposition, resulting in inaccurate fault recognition results.
The variational modal decomposition method is used to decompose the reflected signal at the end of the cable into multiple eigenmodulo functions. By observing the image of the eigenmodulo function, a variational model is constructed and the augmented Lagrangian function is iteratively solved by using the alternating direction multiplier method to optimize the decomposition process.
High-precision cable fault recognition is realized, modal aliasing and noise interference are avoided, and the accuracy and stability of fault recognition are improved.
Smart Images
Figure CN120370095A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of cable fault identification, and particularly to a cable fault identification method based on variational mode decomposition. Background Art
[0002] With the further development of urban construction, overhead transmission lines have gradually been replaced by power cables, and their proportion in the power supply network has gradually increased, becoming an important part of the power system. In the distribution network, cables are the main medium for carrying electrical energy transfer, and whether they are faulty directly determines the safety and economy of the entire power system. With the widespread use of power cables, the number of cable faults has gradually increased. Since most cables are buried underground and affected by conditions such as temperature and humidity, it is difficult to identify cable faults.
[0003] Traditional identification methods rely on wavelet transform and empirical mode decomposition. However, wavelet transform depends on the selection of basis functions and is easily affected by noise, and empirical mode decomposition has the problem of mode mixing. The decomposed mode components are prone to deviate from the actual physical characteristics, affecting the fault identification results. Summary of the Invention
[0004] In view of the deficiencies of the prior art, the present invention proposes a cable fault identification method based on variational mode decomposition to achieve accurate judgment of cable faults.
[0005] To achieve the above object, the present invention provides a cable fault identification method based on variational mode decomposition, and the specific steps are as follows: S1: Transmit a fault detection signal to the head end of the cable, and then receive the reflected signal at the end of the cable; S2: Perform variational mode decomposition on the reflected signal received at the end of the cable to decompose it into multiple intrinsic mode functions; S3: Observe the images of the intrinsic mode functions to determine whether there is a fault.
[0006] Preferably, the construction of the variational model: Objective: Decompose the original reflected signal f(t) at the end into K modal components , and each component satisfies the following conditions: Amplitude modulation - frequency modulation characteristic: , where represents the amplitude, represents the phase, represents the modal component number, and the value is an integer in the range of [1, K]; Bandwidth minimization: The sum of the bandwidths of the analytic signals of each mode is minimized after Hilbert transform; Reconstruction constraint: .
[0007] Preferably, the construction of the variational model further includes setting an optimization function: wherein, represents the partial differential operator of t, represents the modal component, represents the center frequency, and j represents the imaginary unit.
[0008] Preferably, to handle the constraint conditions and the optimization function, an augmented Lagrangian function is constructed: wherein, ɑ represents the penalty factor, which balances the bandwidth and the reconstruction error, represents the Lagrange multiplier.
[0009] Preferably, the augmented Lagrangian function is iteratively solved by the alternating direction method of multipliers, and the specific method is as follows: Initialize the parameters, including the mode , the center frequency , the Lagrange multiplier λ, the number of decomposed modes , the penalty factor , the maximum number of iterations , the convergence threshold ε, and the step size τ; Iteratively update, for each mode , solve in the Fourier domain: Calculate the center frequency of each mode: Update the Lagrange multiplier: Convergence judgment: , if the convergence condition is satisfied, stop the iteration, otherwise continue the above iteration process until the maximum number of iterations , and sequentially obtain the modal components .
[0010] Preferably, observe whether the extrema exist simultaneously in the images of the obtained intrinsic mode function and the reflection signal. If so, it is determined that a fault exists.
[0011] The beneficial effects of the present invention compared with the prior art are as follows: (1) The present invention is based on variational mode decomposition. The reflected signal at the end of the cable received is decomposed into a series of intrinsic mode functions. By observing the images of the intrinsic mode functions, it is determined whether the cable is faulty. Variational mode decomposition decomposes the signal into multiple intrinsic mode functions through preset parameters, which can effectively avoid the mode mixing problem existing in traditional empirical mode decomposition, making the decomposed mode components more in line with actual physical characteristics and being conducive to suppressing noise interference, significantly reducing the impact of noise on the detection of traveling wave fronts.
[0012] (2) The present invention adaptively decomposes the signal by presetting the characteristics of the intrinsic mode functions, and the process of decomposing the signal is more stable, which is conducive to avoiding the problem that wavelet transform is vulnerable to noise influence, and the fault phase recognition accuracy is higher. Brief Description of the Drawings
[0013] Figure 1 is the flowchart of the present invention, Figure 2 is the waveform diagram of the transmission signal at the head end of the cable, Figure 3 is the waveform diagram of the reflected signal at the end of the cable, Figure 4 is the intrinsic mode function obtained by variational mode decomposition in an embodiment of the present invention waveform diagram, Figure 5 is the intrinsic mode function obtained by variational mode decomposition in an embodiment of the present invention waveform diagram, Figure 6 is the intrinsic mode function obtained by variational mode decomposition in an embodiment of the present invention waveform diagram. Detailed Embodiment
[0014] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0015] As Figures 1 to 6 shown, the embodiment of the present invention discloses a cable fault identification method based on variational mode decomposition, including the following steps: S1: Transmit a fault detection signal to the head end of the cable and receive the reflected signal at the end of the cable; S2: Perform variational mode decomposition on the reflected signal received at the end of the cable to decompose it into multiple intrinsic mode functions; S3: Observe the image of the intrinsic mode function to determine whether there is a fault.
[0016] The specific steps of the present invention are as follows: Transmit a fault detection signal to the head end of the cable, as Figure 2 shown.
[0017] Receive the reflected signal at the end of the cable, as Figure 3 shown.
[0018] Perform variational mode decomposition on the reflected signal received at the end of the cable; Variational mode decomposition: A signal processing method based on the variational principle, mainly used to decompose complex signals into multiple intrinsic mode functions (IMFs) with different characteristics. Its core idea is to construct a variational model to decompose the original signal into several intrinsic mode function components with limited bandwidth and different center frequencies , so as to extract the intrinsic characteristics of the signal.
[0019] Set the characteristics of the intrinsic mode function: (1) Amplitude modulation - frequency modulation characteristic: , where represents the amplitude, represents the phase; (2) Bandwidth minimization: The sum of the bandwidths of the analytical signals (after Hilbert transform) of each mode is minimized; (3) Reconstruction constraint: .
[0020] Construct a variational model, set the optimization function and constraint conditions: , Variational mode decomposition needs to optimize the variational problem, that is, minimize this function.
[0021] Constraint conditions: .
[0022] To handle the constraint conditions and enhance the robustness, construct an augmented Lagrangian function: where, ɑ represents the penalty factor, balancing the bandwidth and the reconstruction error, represents the Lagrange multiplier.
[0023] Use the alternating direction method of multipliers to solve the variational model, and update each mode component by alternately optimizing and iterating , , λ: Initialize the parameters: Initialize each mode , Initialize the center frequency , Initialize the Lagrange multiplier , Set the penalty factor ɑ = 2000, Set the maximum number of iterations = 1500, Set the convergence threshold , Set the step size , Iteratively update. For each mode k, solve in the Fourier domain: Calculate the center frequency of each mode: Update the Lagrange multiplier: Convergence judgment: , If the convergence condition is satisfied, stop the iteration; otherwise, continue the above iteration process until the maximum number of iterations = 1500, Successively obtain the intrinsic mode functions , , , respectively, as shown in Figure 4 , Figure 5 , Figure 6 .
[0024] It is observed that both the images of the intrinsic mode functions and the end reflection signals have maxima at the position, indicating that there is a fault in the cable.
Claims
1. A cable fault identification method based on variational mode decomposition, characterized in that It includes the following steps: S1: Transmit a fault detection signal to the head end of the cable, and then receive the reflected signal at the end of the cable; S2: Perform variational mode decomposition on the reflected signal received at the end of the cable to decompose it into multiple intrinsic mode functions; S3: Observe the images of the intrinsic mode functions to determine whether there is a fault.
2. The cable fault identification method based on variational mode decomposition according to claim 1, characterized in that: Variational model construction: Objective: Decompose the original end reflection signal f(t) into K modal components , and each component satisfies the following conditions: Amplitude - Frequency Modulation Characteristics: , where represents the amplitude, represents the phase, represents the modal component number, and the value is an integer in the range of [1, K]; Bandwidth minimization: The sum of the bandwidths of the analytical signals of each mode is minimized after Hilbert transform; Reconstruction constraints: .
3. The cable fault identification method based on variational mode decomposition according to claim 2, characterized in that: The construction of the variational model further includes setting an optimization function: Among them, represents the partial differential operator of t, represents the modal component, represents the center frequency, and j represents the imaginary unit.
4. The cable fault identification method based on variational mode decomposition according to claim 3, characterized in that: To handle the constraint conditions and the optimization function, construct an augmented Lagrangian function: Among them, ɑ represents the penalty factor, which balances the bandwidth and the reconstruction error, represents the Lagrange multiplier.
5. The cable fault identification method based on variational mode decomposition according to claim 4, characterized in that: Iteratively solve the augmented Lagrangian function by the alternating direction method of multipliers. The specific method is as follows: Initialize parameters, including mode , center frequency , Lagrange multiplier λ, number of decomposed modes , penalty factor , maximum number of iterations , convergence threshold ε, step size τ; Iteratively update for each modality , and solve in the Fourier domain: Calculate the central frequency of each mode: Update the Lagrange multiplier: Convergence judgment: , stop the iteration if the convergence condition is met, otherwise continue the above iteration process until the maximum number of iterations , and obtain the modal components in sequence .
6. The cable fault identification method based on variational mode decomposition according to claim 7, characterized in that: Observed intrinsic mode function and the image of the reflected signal have simultaneous extreme values. If so, it is determined that there is a fault.