Cable partial discharge signal denoising method based on RSVD and improved wavelet packet threshold method

Abstract

The invention discloses a cable partial discharge signal denoising method based on RSVD and an improved wavelet packet threshold method. The cable partial discharge signal denoising method comprises the following steps: decomposing a noisy partial discharge PD signal into K IMF components through CEEMDAN; constructing Hankel matrixes for the IMF components one by one, decomposing the Hankel matrixes through random singular value decomposition RSVD, then performing zero setting on singular value abrupt change components, and eliminating narrowband interference; by calculating and comparing cross correlation coefficients of the IMF components, selecting a proper feature component closest to an original signal; and reconstructing the feature components obtained by screening, and eliminating the residual white noise in the superposed signal by adopting a wavelet packet threshold function method of an improved threshold function to obtain a new partial discharge PD signal. According to the method, the effects of extracting the signal-to-noise ratio and the waveform reduction degree of partial discharge PD are good, and the calculation efficiency is better than that of a singular value decomposition SVD algorithm.

Description

Technical Field

[0001] This invention relates to the field of partial discharge signal technology, and specifically to a method for denoising cable partial discharge signals based on RSVD and an improved wavelet packet thresholding method. Background Technology

[0002] In the early stages of power distribution network construction, overhead lines were commonly used as the primary transmission method. With the continuous advancement of power technology, power cables, due to their underground installation, superior aesthetics, and operational reliability, have gradually gained widespread application. However, improper handling during cable transportation and installation, coupled with the long-term exposure to the damp, high-electric-field underground environment, can gradually degrade the performance of the cable's insulation. The partial discharge signal generated during this insulation degradation is a crucial basis for determining the cable's operating status and fault type. Partial discharge typically occurs in the early stages of insulation defects, and the resulting high-frequency current signal attenuates significantly as it propagates along the cable, resulting in a low signal-to-noise ratio and susceptibility to background noise interference. Therefore, effectively extracting and reconstructing the true waveform of partial discharge from complex noise has become a key link and core challenge in achieving accurate cable fault diagnosis and location.

[0003] In recent years, research on denoising methods for partial discharge signals has mainly focused on improvements or superpositions of methods such as empirical mode decomposition (EMD), variational mode decomposition (VMD), singular value decomposition (SVD), and wavelet transform. Some studies employ improved ensemble empirical mode decomposition (EEMD) to process partial discharge signals. This method first uses EEMD and Fourier transform for preliminary signal processing, and then uses local weighted regression scatter smoothing to achieve noise suppression. Although this approach alleviates the mode aliasing phenomenon in traditional EMD, it still suffers from significant white noise residue and heavy computational burden. Other researchers have proposed an adaptive singular value denoising strategy. This method is based on the analysis of the effective order of singular values ​​of noisy partial discharge signals under different noise backgrounds, and adaptively determines the order to suppress mixed noise interference. This strategy overcomes the complexity of threshold setting in traditional SSVD; however, due to its cumbersome global decomposition process and the additional computational load introduced by adaptive threshold selection, its operating efficiency drops sharply when processing large-scale data. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for denoising cable partial discharge signals based on RSVD and an improved wavelet packet thresholding method. This method achieves better signal-to-noise ratio and waveform restoration of partial discharge PDs, and has a greater advantage in computational efficiency than the Singular Value Decomposition (SVD) algorithm.

[0005] The technical solution adopted in this invention is as follows: A method for denoising cable partial discharge signals based on RSVD and an improved wavelet packet thresholding method includes the following steps: Step 1: Decompose the noisy partial discharge (PD) signal into K IMF components using CEEMDAN; Step 2: Construct Hankel matrices for each IMF component, decompose them using random singular value decomposition (RSVD), and then set the singular value mutation components to zero to remove narrowband interference. Step 3: By calculating and comparing the cross-correlation coefficients of each IMF component, select the feature component that is closest to the original signal and is suitable. Step 4: Reconstruct the selected feature components and remove the remaining white noise in the superimposed signal by using the wavelet packet threshold function method with an improved threshold function to obtain a new partial discharge PD signal.

[0006] Step 1 includes the following steps: S1.1: In the original signal x ( t Gaussian white noise is added to the signal to obtain a new signal. x ( t )+ δ 0 n i ( t In the formula, δ 0 is the noise figure. n i ( t ) is the added auxiliary white noise.

[0007] The noisy signal is decomposed using EMD. I The components are then decomposed, and the summation and averaging are performed to obtain the first IMF component: (1); In formula (1): This is the first intrinsic mode function obtained from EMD decomposition; It is the highest frequency intrinsic mode component obtained from the original partial discharge signal through EMD decomposition, containing detailed features and noise. i =1,2,3,…, I .

[0008] Remove IMF 1( t The first residual component obtained: (2); In formula (2): The residual signal obtained after removing the first IMF component from the original signal; S1.2: Will F j Defined as the first EMD jEach modal component, for the noise-added signal Decompose it. This is the second-order noise figure; Indicates to i The Gaussian white noise sequence added later After performing EMD decomposition, its first IMF component is obtained; The second IMF component was obtained: (3); In formula (3): This represents the second intrinsic mode function component obtained through EMD decomposition.

[0009] S1.3: This can be deduced from S1.1. k Residual components of order: (4); In equation (4): To remove the first from the original signal k The residual signal obtained after one IMF component; To remove the first from the original signal k-1 The residual signal obtained after one IMF component; The first one obtained from EMD decomposition k One intrinsic mode function k =2,3,4,…, K , K This represents the total number of IMF components obtained throughout the entire EM decomposition process; For the k Noise signal Perform EMD decomposition. Let be the noise figure of order k. Through calculation Determined by the standard deviation; Indicates to i The Gaussian white noise sequence added later After performing EMD decomposition, its first... k One IMF component; By analogy with S1.2, we can obtain the... k +1 IMF component: (5); In formula (5): No. k +1 intrinsic mode function component; S1.4: Repeat the above operation. When the residual components become monotonic, stop the decomposition and obtain all K IMF components. At this point, the original signal can be represented as: (6); In formula (6): Indicates the final residual component; Adaptive Fully Empirical Mode Decomposition via Noise Figure δ k Adaptive adjustment of the added Gaussian white noise effectively improves the problems existing in CEEMD.

[0010] Step 2 includes the following steps: S2.1: Let the one-dimensional noisy PD signal be: To achieve RSVD decomposition, Constructing a Hankel matrix: (7); In equation (7): It is a one-dimensional signal x Constructed m × l 3D Hankel matrix; Represents a one-dimensional signal x The first sampling point; Represents a one-dimensional signal x The second sampling point; Represents a one-dimensional signal x The third sampling point; Represents a one-dimensional signal x The m One sampling point; Represents a one-dimensional signal x The m+1 One sampling point; Represents a one-dimensional signal x The l One sampling point; Represents a one-dimensional signal x The l+1 One sampling point; Represents a one-dimensional signal x The last sampling point, m = n -l+1, take l= n / 3.

[0011] S2.2: The algorithm flow for random singular value decomposition based on random projection is as follows: Step 1: α = randn ( m , r + s ); Step 2: A = Hα ; Step 3:Q = orth ( A ); Step 4: B = QTH ; Step 5: [ U , S , V ]= svd ( B ); First, through randn The function randomly generates a m OK k + s Standard matrix of columns α ,in, r for H rank of a matrix s For oversampling parameters; H Matrix multiplied by a random matrix α We obtain matrix A; then, we orthogonally normalize matrix A using the orth function to obtain matrix A. Q ; to matrix Q transpose multiplied by H matrix to matrix B Finally, through svd Functions on matrices B Perform singular value decomposition; where the singular value matrix S = diag ( σ 1, σ 2, σ 3, , σp ), σ 1, σ 2, σ 3, , σp These are the singular values ​​of matrix B, which are the elements on the diagonal of the singular matrix. p =min( l , m ), p The total number of singular values ​​in matrix B. l Let H be the row number of the Hanke matrix. m Let H be the column number of the Hankel matrix H; RSVD generates random matrices. α High-level H The matrix is ​​decomposed into two low-rank matrices: H = QB.

[0012] S2.3: Narrowband interference in the signal is removed by setting the abrupt singular value components to zero. (8); In equation (8): This indicates the first [th] after improved threshold processing. i One singular value; This indicates the first [th] after improved threshold processing. i-1 One singular value; This indicates the first [th] after improved threshold processing. i-2 One singular value; Indicates the increment coefficient. i =1,2,3,…, p , p This represents the total number of singular values.

[0013] In step 3, after narrowband interference suppression of the PD signal is completed, the correlation between each IMF component and the original PD signal is quantified by the cross-correlation coefficient, thereby screening out the effective mode components: Equation (9) can be used to calculate the cross-correlation coefficients between the original PD signal and each IMF component: (9); In equation (9): No. i Cross-correlation coefficients between each IMF component and the original PD signal; This indicates that the original PD signal Y(t) is in i The values ​​of each sampling point; and These represent the original signals respectively. and intrinsic modal components The average value; Indicates the length of the signal; In step 4, an improved threshold function is proposed: (10); In formula (10): This represents the k-th wavelet coefficient in the j-th layer of the wavelet packet decomposition; This represents the coefficient after thresholding. Indicates the first j The threshold of the layer; This is a sign function, its function is to preserve the sign of the original wavelet coefficients; Represents the natural exponential function; When | When |→∞, we have: (11); When | |→ λ j At that time, there were: (12); In equation (12): It is a natural constant e The value of 0 raised to the power of 1 is 1.

[0014] After all the above steps, the new partial discharge PD signal is finally obtained by reconstructing all the filtered and processed IMF components. : (13); In equation (13): express k One intrinsic mode function component that has undergone double denoising processing; This represents the set of valid components that have been filtered out. This new signal has a higher signal-to-noise ratio, a clearer discharge pulse pattern, and most of the noise and interference has been effectively suppressed compared to the original signal.

[0015] This invention provides a method for denoising cable partial discharge signals based on RSVD and an improved wavelet packet thresholding method, with the following technical advantages: 1) Highly efficient noise reduction and strong waveform restoration capabilities: This method combines RSVD with an improved wavelet packet thresholding method, effectively suppressing narrowband interference and white noise. The signal-to-noise ratio (SNR) is improved by an average of 37.02%, the waveform correlation coefficient (NCC) is improved by an average of 43.18%, and the transform trend parameter (VTP) is improved by an average of 33.44%, which is significantly better than the existing CEEMD-wavelet thresholding method and ASVD-EWT method.

[0016] 2) Significantly improved computational efficiency: By replacing traditional SVD with random singular value decomposition (RSVD), the problem of mode aliasing is solved, narrowband interference in the signal is effectively suppressed, and high efficiency is maintained even when the data length continues to increase. The efficiency is improved by about 1.5–4.1 times when processing long sequence data, making it suitable for large-scale, real-time signal processing needs in engineering field.

[0017] 3) Highly adaptable and widely applicable: Through CEEMDAN adaptive decomposition and cross-correlation coefficient screening, it effectively avoids mode aliasing, adapts to different noise environments and signal characteristics, and is suitable for various cable partial discharge monitoring scenarios such as medium-voltage cabinets, switch cabinets, and ring main units.

[0018] 4) Signal preprocessing and component optimization strategies: In the feature component screening step, cross-correlation coefficients are selected first. ρ ( iThe top N largest IMF components are reconstructed to further improve the signal-to-noise ratio while preserving the signal characteristics.

[0019] The intensity coefficient of the adaptive Gaussian white noise added during the CEEMDAN decomposition process δ k The standard deviation of the previous residual component determines the decomposition effect, thereby reducing noise residue and mode mixing.

[0020] 5) Optimization of the specific implementation of the RSVD method: When constructing the Hankel matrix, its number of columns l is preferably set to one-third of the signal length n (i.e., l = n / 3) to achieve the best balance between preserving the signal structure and computational efficiency.

[0021] The number of columns in the random matrix α should be greater than the estimated rank r of matrix H and include an oversampling parameter s (e.g., r+s) to ensure the accuracy of the low-rank approximation. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a flowchart of the noise reduction algorithm.

[0023] Figure 2 This is a curve showing the amplitude characteristics of singular values.

[0024] Figure 3 This is a comparison chart of threshold functions.

[0025] Figure 4(a) shows the simulated waveform of the partial discharge signal; Figure 4(b) shows the simulated waveform of the noisy partial discharge signal.

[0026] Figure 5 This is the result of the intrinsic mode component decomposition.

[0027] Figure 6 This is a curve showing the variation of singular values ​​with narrowband interference.

[0028] Figure 7 Time-domain plots of each modal component after removing narrowband interference.

[0029] Figure 8 This is a graph of the IMF3 curve.

[0030] Figure 9 The denoising results for IMF1-3.

[0031] Figure 10 for Figure 9 A magnified view of point A.

[0032] Figure 11(a) shows the denoising results of the method of the present invention; Figure 11(b) shows the denoising results of CEEMD-wavelet thresholding method.

[0033] Figure 11(c) shows the denoising results of the ASVD-EWT method.

[0034] Figure 12 A comparison chart showing the time required for the RSVD and ASVD algorithms at different data lengths.

[0035] Figure 13 This is a comparison chart of the RSVD and ASVD algorithms at different processing rates.

[0036] Figure 14 This is a comparison image of the noise reduction method of the present invention before and after.

[0037] Figure 15 This is a diagram of the acquired PD signal.

[0038] Figure 16 The image shows the measured signal with added noise.

[0039] Figure 17 This is a comparison chart of the denoising of the measured signals.

[0040] Figure 18 This is a practical application scenario for noise reduction methods. Detailed Implementation

[0041] A cable PD signal denoising method based on random singular value decomposition combined with an improved wavelet packet thresholding method is proposed. First, the noisy PD signal is decomposed into several IMFs using adaptive full empirical mode decomposition. Then, components containing narrowband interference are removed using random singular value decomposition. Subsequently, the signal after the first round of screening is further filtered by calculating and comparing its cross-correlation coefficients to remove useless components with low correlation to the original signal, and these components are then superimposed. Finally, residual white noise is filtered out using a wavelet packet thresholding method with an improved threshold function. Simulation results show that the proposed method achieves better signal-to-noise ratio and waveform restoration accuracy in PD signal extraction, and has a computational efficiency advantage over the SVD algorithm.

[0042] S1: Decompose the noisy PD signal into K IMF components using CEEMDAN; S2: Construct Hankel matrices for each IMF component, decompose them using RSVD, and then set the singular value mutation components to zero to remove narrowband interference; S3: By calculating and comparing the cross-correlation coefficients of each IMF component, select the feature component that is closest to the original signal and is suitable. S4: Reconstruct the selected feature components and remove the remaining white noise in the superimposed signal by using the wavelet packet threshold function method with an improved threshold function to obtain a new PD signal.

[0043] The specific process of the algorithm is as follows: Figure 1 As shown.

[0044] 1. CEEMDAN Algorithm Principle: Adaptive Fully Empirical Mode Decomposition (CEEMD) is an optimization of CEEMD. By adding adaptive white Gaussian noise to the original signal, it improves the problems of high computational cost and difficulty in quantizing the number of decomposed modes. The specific process is as follows: (1) In the original signal x ( t Gaussian white noise is added to the signal to obtain a new signal. x ( t )+ δ 0 n i ( t In the formula, δ 0 is the noise figure. n i ( t The added white noise is called auxiliary white noise. The noisy signal is decomposed I times using EMD decomposition, and then the decomposed signals are superimposed and averaged to obtain the first IMF component. (1); In the formula, i =1,2,3,…, I .

[0045] Remove IMF 1( t The first residual component obtained: (2); (2) F j Defined as the first EMD j One modal component. For the noisy signal. Decomposition yields the second IMF component: (3); (3) By analogy from step (1), we can obtain k Residual components of order: (4); In the formula, k =2,3,4,…, K .

[0046] For the k Noise signal EMD decomposition is performed, and by analogy from step (2), the first step can be obtained. k +1 IMF component: (5); In the formula, δ k It is determined by calculating the standard deviation of rk(t).

[0047] (4) Repeat the above operation. When the residual components become monotonic, stop the decomposition and obtain all K IMF components. At this point, the original signal can be represented as: (6); Adaptive Fully Empirical Mode Decomposition via Noise Figure δ k Adaptive adjustment of the added Gaussian white noise effectively improves the problems existing in CEEMD.

[0048] 2. Removal of narrowband interference based on RSVD: Random Singular Value Decomposition (RSVD) is an improved algorithm compared to traditional SVD. RSVD significantly reduces computation by decomposing a high-order matrix into two orthogonal low-order matrices. The specific process is as follows: (1) Assume a one-dimensional noisy PD signal is: To achieve RSVD decomposition, Constructing a Hankel matrix: (7); In the formula, m = n -l+1, take l= n / 3.

[0049] (2) The algorithm flow of random singular value decomposition based on random projection algorithm is as follows: Step 1: α = randn ( m , r + s ); Step 2: A = Hα ; Step 3: Q = orth ( A ); Step 4: B = QTH ; Step 5: [ U , S , V ]= svd ( B ); First, through randnThe function randomly generates a m OK k + s Standard matrix of columns α ,in r for H rank of a matrix s These are the oversampling parameters. H Matrix multiplied by a random matrix α Obtain matrix A, and then use the orth function to... A Matrix orthogonal normalization yields the matrix Q . Matrix Q transpose multiplied by H matrix to matrix B Finally passed svd Functions on matrices B Perform singular value decomposition. Where the singular value matrix S = diag ( σ 1, σ 2, σ 3, , σp ), p =min( l , m ).

[0050] RSVD generates higher-order random matrices. H The matrix is ​​decomposed into two low-rank matrices: H = QB ,matrix B Since the rank is low and the number of rows is small, singular value decomposition of it is much more efficient than decomposition of the matrix. H Perform singular value decomposition directly.

[0051] (3) According to research, for a noise-free PD signal, after singular value decomposition, the original PD signal exhibits low-rank characteristics, and the narrowband interference also exhibits low-rank characteristics, but its distribution differs from the original PD signal. White noise, however, exhibits full-rank characteristics. Further analysis of the singular value characteristics of these three signals is conducted through simulation in this invention, such as... Figure 2 As shown, the three signals exhibit significant differences in singular value amplitudes. The singular value amplitude characteristic curves of the ideal PD signal and the PD signal containing white noise basically overlap, but the curve containing narrowband interference shows abrupt changes at the first few singular value points. Therefore, narrowband interference in the signal can be removed by setting the abruptly changed singular value components to zero.

[0052] Use equation (8) to set the mutation component to zero: (8); In the formula, It is the incremental coefficient.i =1,2,3,…, p ; 3. Selecting feature components based on cross-correlation coefficients: After completing the narrowband interference suppression of the PD signal, the selection of characteristic components becomes crucial. Therefore, the correlation between each IMF component and the original PD signal is quantified using cross-correlation coefficients to select effective modal components for further analysis.

[0053] Equation (9) can be used to calculate the cross-correlation coefficients between the original PD signal and each IMF component: (9); In the formula, and These are the original signal Y(i) and the intrinsic mode components, respectively. IMFk ( i The average value of ) n It is the length of the signal.

[0054] In practical research, the cross-correlation coefficient between the original PD signal and the PD signal containing white noise is inversely proportional to the intensity of the white noise; that is, the stronger the energy of the white noise, the smaller the cross-correlation coefficient between the two signals, and vice versa. Definition ρ ( i ) is the first i The cross-correlation coefficient between each IMF component and the original signal. It is generally believed that the absolute value of the cross-correlation coefficient is between [0.8, 1], indicating a high degree of correlation, but it should be discussed based on the actual situation.

[0055] 4. Improved wavelet packet thresholding method for noise reduction: Wavelet Packet Decomposition (WPD) is an improvement on traditional wavelet decomposition. Wavelet decomposition only decomposes the low-frequency part of the signal, so it has a good processing effect on signals that are dominated by low-frequency components. However, PD signals are mainly concentrated in the high-frequency band between 300KHz and 100MHz. Therefore, wavelet packet decomposition, which can decompose and reconstruct both the high-frequency and low-frequency parts of the signal, is more beneficial for denoising and restoring PD signals.

[0056] Wavelet packet denoising typically consists of four parts: wavelet packet decomposition, determining the wavelet packet basis, threshold quantization, and wavelet packet reconstruction. Threshold quantization is crucial in determining the fit between the denoised signal and the original signal. Therefore, selecting a high-performance threshold function is essential. Traditional hard thresholding and soft thresholding functions suffer from poor continuity and constant bias, respectively. With ongoing research, new threshold functions have been proposed. To preserve the integrity of the original signal as much as possible, this invention proposes an improved threshold function: (10); In the formula, dj,k is the k-th wavelet coefficient of the j-th layer in the wavelet packet decomposition. λj is the coefficient after thresholding, and λj is the threshold point.

[0057] As |dj,k|→∞, we have: (11); When | d j,k |→ λ j At that time, there were: (12); From equations (11) and (12) and Figure 3 It can be proven that the improved threshold function proposed in this invention effectively improves the problems of discontinuity in hard threshold functions and bias in soft threshold functions. Figure 3 As can be seen, compared with the two mainstream improved threshold functions currently available, the improved threshold function proposed in this invention has advantages in... converges to DJ , k During the process, the convergence speed is faster. Therefore, the improved threshold function proposed in this invention has superior performance.

[0058] 5. Improved wavelet packet thresholding method for noise reduction: 5.1: Simulation of Noisy Partial Discharge Signal: According to existing research, partial discharge signals can usually be represented by two mathematical models: a single exponential decay oscillation model and a double exponential decay oscillation model.

[0059] (1) Single exponential decaying oscillation model: (13); (2) Double exponential decaying oscillation model: (14); In the formula, A is the signal amplitude, and in this invention, A1 = 1mV and A2 = 3.5mV are taken respectively; τ is the attenuation coefficient, and τ1 = 0.5μs and τ2 = 0.8μs are taken respectively; fc is the oscillation frequency, and is taken as 50MHz; the sampling frequency is taken as 1000MHz. In order to make the waveform of the partial discharge signal closer to the actual situation, the parameters of the second waveform are set differently from those of the first waveform. The time domain diagrams of its simulation signal are shown in Figure 4(a) and Figure 4(b).

[0060] Gaussian white noise with a signal-to-noise ratio of -8dB is added to the partial discharge simulation signal to simulate actual white noise interference. Based on the waveform and frequency of narrowband interference in reality, this invention uses three superimposed sine waves with frequencies of 1.2MHz, 12MHz, and 98MHz for simulation. The noisy partial discharge signal is shown in Figure 4(a) and Figure 4(b).

[0061] 5.2: Noise Reduction Simulation Experiment: Based on the noise reduction strategy adopted in this study, the initial step is to use adaptive fully empirical mode decomposition (EFD) to decompose the disturbed partial discharge signal into several intrinsic mode components. In this process, the introduced random noise intensity parameter is set to 0.2 standard deviations, and the number of iterations for mode decomposition is determined to be 100. The decomposition results are as follows: Figure 5 As shown.

[0062] After CEEMDAN decomposes the PD signal into 10 IMFs, a Hankel matrix is ​​constructed for each intrinsic mode component, and then each component is decomposed one by one using stochastic singular value decomposition. The singular value curves of each IMF are shown below. Figure 6 As shown. It can be found that the singular values ​​of each IMF exhibit amplitude abrupt changes, and the amplitude change factor is about 3-11 times. Therefore, the increment coefficient in equation (8) is set to 3, and the abrupt component is set to zero through equation (8) to remove narrowband interference. The signal after removing narrowband interference is reconstructed, and its time domain diagram is shown. Figure 7 As shown.

[0063] To preserve the original PD signal characteristics to the greatest extent possible, after eliminating narrowband interference, this invention calculates the cross-correlation coefficients between each IMF component and the original partial discharge signal, and then selects representative characteristic components, as shown in Table 1.

[0064]

[0065] Based on the calculated cross-correlation coefficients, it can be found that the first three intrinsic mode components have the largest cross-correlation coefficients. Furthermore, by removing narrowband interference from the IMF3 image, its similarity to the original partial discharge signal can be more intuitively observed. Figure 8 As shown, the main part of the PD signal is in IMF1-3. Therefore, this invention uses an improved threshold function wavelet packet decomposition method to remove white noise from the first three reconstructed IMFs.

[0066] Observation of the denoised IMF1-3 reveals that Gaussian white noise is significantly suppressed, but slight glitches still exist in the signal. Figure 9 , Figure 10 As shown.

[0067] To further demonstrate the feasibility and superior performance of the proposed method in denoising, denoising simulations were performed using the method of this invention, the CEEMD-wavelet thresholding method, and the ASVD-EWT denoising method. The results are shown in Figures 11(a) to 11(c). Using the improved wavelet packet thresholding method proposed in this invention to remove white noise, it can be seen that both types of noise are basically eliminated, and there is no visible waveform distortion, as shown in Figure 11(a). Although the CEEMD-wavelet thresholding method effectively suppresses narrowband interference, it still leaves slight white noise, and the signal energy is also damaged, as shown in Figure 11(b). The ASVD-EWT method cannot effectively remove narrowband interference and also leaves a large amount of white noise, resulting in poor denoising performance, as shown in Figure 11(c).

[0068] 5.3: Analysis of Noise Reduction Simulation Effect: To further verify the effectiveness of the method of this invention, the present invention uses three parameters for further analysis: signal-to-noise ratio (SNR), normalized correlation coefficient (NCC), and variation trend parameter (VTP). This invention defines the original PD signal as... s ( r The denoised PD signal is defined as follows: h ( r ).

[0069] (1) Signal-to-noise ratio (SNR) refers to the comparison between the signal power and noise power before denoising. The larger the SNR value, the better the denoising effect. The calculation formula is as follows: (16); (2) The waveform correlation coefficient refers to the similarity between the waveforms before and after signal denoising. The closer the NCC value is to 1, the higher the similarity between the two signal waveforms. The calculation formula is as follows: (17); (3) The transformation trend parameter refers to the similarity of the waveforms before and after denoising in terms of rising and falling trends. The closer the VTP value is to 1, the higher the similarity of the changing trends of the two signal waveforms. VTP is divided into rising transformation trend parameter (RVPT) and falling transformation trend parameter (FVPT), ​​and its calculation formula is as follows: (18); In the formula: h ( r )> h ( r -1), s (r )> s ( r -1); (19); In the formula: h ( r )< h ( r -1), s ( r )< s ( r -1); (20); The three evaluation parameters for the three denoising methods are calculated sequentially according to equations (16), (17), and (20), and the results are shown in Table 2. In Table 2, a, b, and c represent the three methods, respectively.

[0070]

[0071] Through analysis Figure 8 Based on the three evaluation parameters in Table 2, it can be seen that the method proposed in this invention outperforms the other two methods in terms of waveform similarity, signal-to-noise ratio, and energy loss.

[0072] To verify the superiority of the RSVD algorithm proposed in this invention in terms of data processing speed, this invention is compared with the ASVD algorithm under the same conditions. The time required by the two algorithms for different data lengths is calculated, such as... Figure 12 As shown.

[0073] according to Figure 12 It can be seen that when the data length is short (below 6000), the time consumption of the two methods is relatively similar; however, when the data length is long (above 6000), the time consumption of ASVD increases rapidly, while RSVD can still maintain high processing efficiency. According to Figure 13 It can be more clearly observed that when the data length is short, the processing speed of ASVD is slightly higher than that of RSVD, but when the data length is long, the speed of RSVD is much higher than that of ASVD. This shows that RSVD has a clear advantage in data processing speed.

[0074] To analyze the advantages and disadvantages of the method of this invention in more depth, the waveforms before and after denoising are superimposed and compared, such as... Figure 14 As shown in the comparison image, a magnified view reveals that the denoising algorithm based on RSVD-improved wavelet packet thresholding has a good effect on suppressing narrowband interference and white noise in PD signals, with high waveform restoration accuracy. However, there is energy loss and some distortion at lower waveform amplitudes.

[0075] 6. Experimental Results and Analysis: To further verify the effectiveness of the proposed method for actual PD signals in real substation environments, this method was used to denoise the measured PD signal of a 10kV switchgear in a certain switch station. This invention involves installing a high-frequency current transformer at the grounding wire of the cable terminal to collect partial discharge signals. The obtained signals are transmitted to a sampling circuit, processed by a microcontroller, and finally output as measured PD signal waveforms on an oscilloscope.

[0076] The acquired PD signal is as follows Figure 15 As shown in the figure. Since the noise intensity of the PD signal measured under this environment is low, to fully verify the noise suppression capability of the method of this invention, narrowband interference with an amplitude of 1 and frequencies of 0.06MHz, 18MHz, and 60MHz were added to the measured signal. The measured signal with added noise is shown in the figure. Figure 16 As shown.

[0077] Since noise-free PD signals cannot be obtained through actual measurements, this invention compares the denoised measured signal with the measured PD signal, such as... Figure 17 As shown. Noise suppression using the algorithm of this invention results in minimal waveform distortion and significant denoising effect, but there is some energy loss.

[0078] The denoising algorithm proposed in this invention can be widely applied in engineering practice to signal preprocessing for cable partial discharge monitoring in various scenarios such as medium-voltage switchgear, switch cabinets, and ring main units, significantly improving the accuracy of PD signal monitoring and positioning. For example... Figure 18 As shown, in practical applications, high-frequency current sensors are usually installed on the grounding wire of the cable. The measured current signal is then denoised and converted by a partial discharge acquisition device. Finally, the partial discharge status information is transmitted to a computer for monitoring via optical fiber or network cable.

[0079] 7. Conclusion: To address the issues of unsatisfactory noise suppression performance in current PD signal denoising methods and a sharp drop in efficiency when processing long signals, this invention proposes a cable partial discharge signal denoising method based on RSVD-improved wavelet packet thresholding, based on an analysis of the characteristics of narrowband interference that differ from white noise and the original signal. Through simulation and analysis, the following three conclusions are drawn: 1) RSVD is used to process the IMF after CEEMDAN decomposition, which not only solves the problem of mode aliasing, but also effectively suppresses narrowband interference in the signal. It can still maintain high efficiency as the data length continues to increase, and the efficiency is improved by about 1.5-4.1 times when the data length is long.

[0080] 2) Improved wavelet packet thresholding method: Based on soft and hard thresholding functions, a new improved thresholding function is proposed. While retaining the advantages of the continuity of the soft thresholding function and the small deviation of the hard thresholding function, the convergence speed is improved compared with the mainstream thresholding function.

[0081] 3) The method proposed in this invention can effectively extract the original PD signal from the noisy PD signal and maintain the integrity of the waveform to a large extent. Compared with other proposed methods, the signal-to-noise ratio, waveform correlation coefficient and transformation trend parameter are improved by an average of 37.02%, 43.18% and 33.44%, respectively, and the minimum improvements are 6.07%, 25.53% and 31.75%, respectively. It can be applied to the identification and localization of PD signals.

Claims

1. A method for denoising cable partial discharge signals based on RSVD and an improved wavelet packet thresholding method, characterized in that... Includes the following steps: Step 1: Decompose the noisy partial discharge (PD) signal into K IMF components using CEEMDAN; Step 2: Construct Hankel matrices for each IMF component, decompose them using random singular value decomposition (RSVD), and then set the singular value mutation components to zero. Step 3: By calculating and comparing the cross-correlation coefficients of each IMF component, select the feature component that is closest to the original signal and is suitable. Step 4: Reconstruct the selected feature components and remove the remaining white noise in the superimposed signal by using the wavelet packet threshold function method with an improved threshold function to obtain a new partial discharge PD signal.

2. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 1, characterized in that: Step 1 includes the following steps: S1.1: In the original signal x ( t Gaussian white noise is added to the signal to obtain a new signal. x ( t )+ δ 0 n i ( t In the formula, δ 0 is the noise figure. n i ( t ) is the added auxiliary white noise; The noisy signal is decomposed using EMD. I The components are then decomposed, and the summation and averaging are performed to obtain the first IMF component: （1）； In formula (1): This is the first intrinsic mode function obtained from EMD decomposition; It is the highest frequency intrinsic mode component obtained from the original partial discharge signal through EMD decomposition, containing detailed features and noise. i =1,2,3,…, I ; Remove IMF 1( t The first residual component obtained: （2）； In formula (2): The residual signal obtained after removing the first IMF component from the original signal; S1.2: Will F j Defined as the first EMD j Each modal component, for the noise-added signal Decompose it. This is the second-order noise figure; Indicates to i The Gaussian white noise sequence added later After performing EMD decomposition, its first IMF component is obtained; The second IMF component was obtained: （3）； In formula (3): This represents the second intrinsic mode function component obtained through EMD decomposition; S1.3: This can be deduced from S1.

1. k Order residual components: （4）； In equation (4): To remove the first from the original signal k The residual signal obtained after one IMF component; To remove the first from the original signal k-1 The residual signal obtained after one IMF component; The first one obtained from EMD decomposition k One intrinsic mode function k =2,3,4,…, K , K This represents the total number of IMF components obtained throughout the entire EM decomposition process; For the k Noise signal Perform EMD decomposition. The noise figure is the k-th order. Indicates to i The Gaussian white noise sequence added later After performing EMD decomposition, its first... k One IMF component; By analogy with S1.2, we can obtain the... k +1 IMF component: （5）； In formula (5): No. k +1 intrinsic mode function component; S1.4: Repeat the above operation. When the residual components become monotonic, stop the decomposition and obtain all K IMF components. At this point, the original signal can be represented as: （6）； In formula (6): This represents the final residual component.

3. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 2, characterized in that: In step 2: Let the one-dimensional noisy PD signal be: To achieve RSVD decomposition, Constructing a Hankel matrix: （7）； In equation (7): It is a one-dimensional signal x Constructed m × l 3D Hankel matrix; Represents a one-dimensional signal x The first sampling point; Represents a one-dimensional signal x The second sampling point; Represents a one-dimensional signal x The third sampling point; Represents a one-dimensional signal x The m One sampling point; Represents a one-dimensional signal x The m+1 One sampling point; Represents a one-dimensional signal x The l One sampling point; Represents a one-dimensional signal x The l+1 One sampling point; Represents a one-dimensional signal x The last sampling point.

4. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 3, characterized in that: The algorithm flow for random singular value decomposition based on random projection is as follows: First, through randn The function randomly generates a m OK k + s Standard matrix of columns α ,in, r for H rank of a matrix s For oversampling parameters; H Matrix multiplied by a random matrix α We obtain matrix A; then, we orthogonally normalize matrix A using the orth function to obtain matrix A. Q ; to matrix Q transpose multiplied by H matrix to matrix B Finally, through svd Functions on matrices B Perform singular value decomposition; where the singular value matrix S = diag ( σ 1, σ 2, σ 3, , σp ), σ 1, σ 2, σ 3, , σp These are the singular values ​​of matrix B, which are the elements on the diagonal of the singular matrix. p =min( l , m ), p The total number of singular values ​​in matrix B. l Let H be the row number of the Hanke matrix. m Let H be the column number of the Hankel matrix H; RSVD generates random matrices α High-level H The matrix is ​​decomposed into two low-rank matrices: H = QB .

5. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 4, characterized in that: Narrowband interference in the signal is removed by setting the abrupt singular value components to zero. （8）； In equation (8): This indicates the first [th] after improved threshold processing. i One singular value; This indicates the first [th] after improved threshold processing. i-1 One singular value; This indicates the first [th] after improved threshold processing. i-2 One singular value; Indicates the increment coefficient. i =1,2,3,…, p , p This represents the total number of singular values.

6. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 5, characterized in that: In step 3, after narrowband interference suppression of the PD signal is completed, the correlation between each IMF component and the original PD signal is quantified by the cross-correlation coefficient, thereby screening out the effective mode components: Equation (9) can be used to calculate the cross-correlation coefficients between the original PD signal and each IMF component: （9）； In equation (9): No. i Cross-correlation coefficients between each IMF component and the original PD signal; This indicates that the original PD signal Y(t) is in i The value of each sampling point; and Representing the original signals respectively and intrinsic modal components The average value; Indicates the length of the signal.

7. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 6, characterized in that: In step 4, an improved threshold function is proposed: （10）； In formula (10): This represents the k-th wavelet coefficient in the j-th layer of the wavelet packet decomposition; This represents the coefficient after thresholding. Indicates the first j The threshold of the layer; This is a sign function, its function is to preserve the sign of the original wavelet coefficients; This represents the natural exponential function.

8. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 7, characterized in that: When | When |→∞, we have: （11）； When | |→ λ j At that time, there were: （12）； In equation (12): It is a natural constant e The value of 0 raised to the power of 1 is 1.

9. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 8, characterized in that: By reconstructing all the filtered and processed IMF components, a new partial discharge PD signal is obtained. : （13）； In equation (13): express k One intrinsic mode function component that has undergone double denoising processing; This represents the set of valid components that have been filtered out.

10. The method for denoising cable partial discharge signals based on RSVD and improved wavelet packet thresholding as described in claim 9, characterized in that: Define the original PD signal as s ( r The denoised PD signal is defined as follows: h ( r ); (1) Signal-to-noise ratio (SNR) refers to the comparison between the signal power and noise power before denoising. The larger the SNR value, the better the denoising effect. The calculation formula is as follows: （16）； (2) The waveform correlation coefficient refers to the similarity between the waveforms before and after signal denoising. The closer the NCC value is to 1, the higher the similarity between the two signal waveforms. The calculation formula is as follows: （17）； (3) The transformation trend parameter refers to the similarity of the waveforms before and after denoising in terms of rising and falling trends. The closer the VTP value is to 1, the higher the similarity of the changing trends of the two signal waveforms. VTP is divided into rising transformation trend parameter (RVPT) and falling transformation trend parameter (FVPT), ​​and its calculation formula is as follows: （18）； In the formula: h ( r )> h ( r -1), s ( r )> s ( r -1); （19）； In the formula: h ( r )< h ( r -1), s ( r )< s ( r -1); （20）。

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