Cable partial discharge signal denoising method based on CEEMDAN

Abstract

The invention belongs to the technical field of cable partial discharge signal processing, and discloses a CEEMDAN-based cable partial discharge signal denoising method, which comprises the following steps: acquiring a high-frequency current signal on a cable shielding layer grounding wire through a sensor as an original noisy signal; performing adaptive decomposition on the signal by using a CEEMDAN algorithm to obtain a plurality of intrinsic mode function components and a residual component; calculating a correlation coefficient between each IMF component and an original signal in a frequency domain, and carrying out moderate attenuation on the component of which the correlation coefficient is lower than a set threshold by adopting a continuous threshold function; calculating an energy spectrum of each IMF component in a time domain, enhancing an energy concentration area through rectangular window convolution, setting an energy threshold value based on median absolute deviation, and extracting an effective signal interval; and finally, reconstructing the processed IMF component into a de-noised signal. The method is high in anti-interference capability, good in adaptability, high in calculation efficiency and suitable for cable partial discharge signal extraction under the condition of low signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of cable partial discharge signal processing technology, and particularly relates to a method for denoising cable partial discharge signals based on CEEMDAN. Background Technology

[0002] Partial discharge (PD) refers to the localized discharge phenomenon occurring within the insulation layer of high-voltage power equipment. This discharge lacks penetrability and therefore does not form a conductive path, typically occurring in areas where the electric field strength exceeds the normal range. In power cable systems, partial discharge often originates from aging and damage to the insulation layer at a certain location on the cable, leading to the formation of an equivalent capacitance structure in this area. When a significant potential difference exists between the internal conductor and the external metallic shielding layer of the cable, charge gradually accumulates in this area until it reaches the discharge threshold, triggering a discharge. Due to the presence of the external metallic shielding layer, its excellent shielding effectiveness effectively hinders the radiation and propagation of electromagnetic waves generated during the discharge process, making it extremely difficult to directly capture these electromagnetic wave signals from the outside. To effectively monitor partial discharge activity inside the cable, a common method is to detect the high-frequency current signal generated by the discharge on the grounding wire of the shielding layer. However, the main interference encountered in the implementation of this method comes from Gaussian white noise induced by the thermal effect of the shielding layer metal. The discharge process is often accompanied by a sudden increase in temperature, and this temperature change significantly enhances the power level of the white noise. Therefore, Gaussian white noise signals constitute the main source of interference in the extraction of partial discharge signals within the insulation layer.

[0003] Frequent partial discharges can gradually degrade insulation performance, potentially leading to equipment failure. Detecting weak partial discharge signals allows for timely detection of internal insulation problems, preventing further deterioration and avoiding serious equipment malfunctions. Therefore, noise reduction of weak partial discharge signals is crucial for preventing equipment damage due to insulation failure and extending its service life.

[0004] In existing technologies, wavelet transform is a commonly used method for processing non-stationary partial discharge signals. However, its performance is heavily dependent on the selection of wavelet basis functions, and the optimal basis functions vary depending on the signal, resulting in insufficient adaptability. Empirical mode decomposition (EMD), while possessing adaptability, suffers from mode aliasing. Variational mode decomposition (VMD) can alleviate mode aliasing, but it requires presetting parameters such as the number of decomposition layers, leading to high computational cost and low efficiency. Patent CN120910403A discloses a method for denoising cable joint discharge signals combining CEEMDAN and Singular Spectral Analysis (SSA). Although it exhibits strong adaptability when processing complex signals, the computational complexity of SSA increases quadratically or cubically with increasing sequence length during embedding dimension and eigenvalue decomposition. The required Hankle matrix embedding dimension, reconstruction order, and singular value selection lack unified criteria, requiring repeated adjustments based on signal characteristics. Furthermore, the frequency resolution achieved by SSA is very limited, making it ineffective for separating tightly coupled modes. Summary of the Invention

[0005] The purpose of this invention is to provide a method for denoising cable partial discharge signals based on CEEMDAN, so as to solve the above-mentioned technical problems.

[0006] To address the aforementioned technical problems, this invention provides a cable partial discharge signal denoising technique based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). This technique can adaptively process signals and exhibits excellent denoising performance and high engineering application efficiency under low signal-to-noise ratio conditions. The specific technical solution is as follows:

[0007] A method for denoising cable partial discharge signals based on CEEMDAN includes the following steps:

[0008] Step 1: Signal Acquisition: The high-frequency current signal on the grounding wire of the cable shield is acquired by a sensor as the raw noisy signal;

[0009] Step 2: Signal decomposition: The acquired original noisy signal is adaptively decomposed using the fully adaptive noise set empirical mode decomposition (CEEMDAN) algorithm to obtain a series of intrinsic mode function components and a residual component.

[0010] Step 3: Frequency domain filtering: After calculating the correlation coefficient between each IMF component and the original noisy signal, a continuous threshold function is used to moderately attenuate the components with correlation coefficients lower than the set threshold.

[0011] Step 4: Time-domain filtering: In the signal processing, the time-domain energy spectrum of each IMF component is first calculated, and a rectangular window function of predetermined length is used to perform convolution operation on the time-domain energy spectrum to enhance the significance of the energy concentration region; then, the standard deviation of the median (MAD) is used as a statistic to set the energy threshold, and the energy range exceeding the threshold is extracted accordingly to achieve accurate separation of effective signal and noise in the time domain.

[0012] Step 5: Signal reconstruction: The IMF components after time-frequency domain filtering are superimposed and reconstructed to obtain a clean partial discharge denoising signal.

[0013] Furthermore, the method is specifically designed to process high-frequency current signals collected from the grounding wire of the power cable shield, wherein the interference source in the noisy signal is Gaussian white noise induced by the thermal effect of the conductor.

[0014] Furthermore, step 2 includes the following steps:

[0015] Step 2.1: Generate a noisy signal group:

[0016] x i (t)=x(t)+ε0w i (t) (1)

[0017] Step 2.2: Perform EMD on each signal and extract the first-order IMF:

[0018] IMF1 i (t)=E1(x i (t)) (2)

[0019] Step 2.3: Integral averaging yields the first-order IMF of CEEMDAN:

[0020]

[0021] Step 2.4: Calculate the first-order residual:

[0022] r1(t) = x(t) - IMF1(t). (4)

[0023] Furthermore, the iteration in step 2 stops when the residual signal is a monotonic function or contains fewer than two extreme points.

[0024] Solving this, we obtain a series of IMF components arranged from high frequency to low frequency, and the final signal reconstruction is as follows:

[0025]

[0026] Furthermore, the continuous threshold function in step 3 is expressed as:

[0027]

[0028] Furthermore, the formula for calculating the standard deviation (MAD) of the median in step 4 is as follows:

[0029]

[0030] Where IMF is the signal sequence to be processed; the energy threshold is set to K times MAD, where K is a predefined constant.

[0031] The cable partial discharge signal denoising method based on CEEMDAN of the present invention has the following advantages:

[0032] Strong anti-interference capability: It makes full use of the characteristics that the partial discharge signal has concentrated energy in the time and frequency domain while the white noise has dispersed energy, and can still effectively extract the signal under low signal-to-noise ratio. Its performance is significantly better than the traditional wavelet thresholding method.

[0033] Good adaptability: Compared with the traditional wavelet thresholding method, the present invention uses CEEMDAN for signal decomposition, which does not require preset basis functions or decomposition layers, and is adaptable to partial discharge signals with different waveform characteristics.

[0034] Low computational cost: In response to the shortcomings of the patent CN120910403A scheme, this invention utilizes CEEMDAN's efficient time-frequency decomposition and statistical parameters to achieve higher filtering performance at low signal-to-noise ratios with less computational cost. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the overall process of the method of the present invention.

[0036] Figure 2 The waveform of the pure partial discharge signal in the simulation experiment is shown in the time domain.

[0037] Figure 3 This is the time-domain waveform of the noisy partial discharge signal in the simulation experiment.

[0038] Figure 4 This is the S-transform result of the noisy signal.

[0039] Figure 5 This is a time-domain diagram of the signal after denoising using the method of this invention.

[0040] Figure 6 The graph shows a comparison of the denoising performance of the method of the present invention and the wavelet thresholding method under different signal-to-noise ratios.

[0041] Figure 7 This is the measured partial discharge sampling signal.

[0042] Figure 8 The figures show the results of applying the method of this invention to the measured signals.

[0043] Figure 9 The graphs show the results of applying the wavelet thresholding method to the measured signals. Detailed Implementation

[0044] To better understand the purpose, structure, and function of this invention, the following detailed description of a cable partial discharge signal denoising method based on CEEMDAN, in conjunction with the accompanying drawings, is provided.

[0045] The present invention provides a method for denoising cable partial discharge signals based on CEEMDAN, comprising the following steps:

[0046] Step 1: Signal Acquisition: The high-frequency current signal on the grounding wire of the cable shield is acquired by a sensor as the raw noisy signal.

[0047] Step 2: Signal decomposition: The acquired original noisy signal is adaptively decomposed using the Fully Adaptive Empirical Mode Decomposition (CEEMDAN) algorithm to obtain a series of intrinsic mode function components and a residual component.

[0048] Step 2.1: Generate a noisy signal group:

[0049] x i (t)=x(t)+ε0w i (t) (1)

[0050] Step 2.2: Perform EMD on each signal and extract the first-order IMF:

[0051] IMF1 i (t)=E1(x i (t)) (2)

[0052] Step 2.3: Integral averaging yields the first-order IMF of CEEMDAN:

[0053]

[0054] Step 2.4: Calculate the first-order residual:

[0055] r1(t)=x(t)-IMF1(t) (4)

[0056] The above process iterates until the residual signal is a monotonic function or contains fewer than two extrema, at which point the decomposition stops. This yields a series of IMF components arranged from high to low frequency, and the final signal can be accurately reconstructed as follows:

[0057]

[0058] Step 3: Frequency domain filtering: After calculating the correlation coefficient between each IMF component and the original noisy signal, a continuous threshold function is used to moderately attenuate the components with correlation coefficients lower than the set threshold, instead of completely eliminating them using a hard threshold.

[0059]

[0060] The core advantage of this "attenuation" processing method lies in its smoothing characteristic: by retaining the contribution of components that have low correlation with the effective signal but still contain some effective information, it can effectively avoid the introduction of Gibbs phenomenon or reconstruction distortion due to the sudden and complete loss of certain IMF components during signal reconstruction. Especially in the analysis of weak discharge signals, this gradual attenuation strategy can better preserve signal edges and transient characteristics, maintain the integrity of the signal waveform, and thus ensure the accuracy and reliability of subsequent analysis.

[0061] Step 4: Time-Domain Filtering: In the signal processing, the time-domain energy spectrum of each IMF component is first calculated, and then a rectangular window function of predetermined length is used to convolve the time-domain energy spectrum to enhance the significance of energy concentration regions. Subsequently, the standard deviation based on the median (MAD) is used as a statistic to set an energy threshold, and the energy range exceeding the threshold is extracted accordingly, achieving accurate separation of effective signals and noise in the time domain.

[0062]

[0063] Wherein IMF is the signal sequence to be processed; the energy threshold is set to K times MAD, where K is a predefined constant.

[0064] The reason for choosing MAD instead of the traditional mean standard deviation is that MAD is not sensitive to energy changes in the pulsed partial discharge signal itself, effectively avoiding threshold estimation errors caused by the discharge pulse; however, it is extremely sensitive to sudden energy fluctuations caused by random noise. Therefore, the threshold set based on MAD can more accurately capture brief discharge pulses from complex background noise, exhibiting stronger anti-interference capability and robustness. Frequency domain filtering (correlation coefficient) and time domain filtering (MAD energy) complement each other. Frequency domain filtering performs preliminary "coarse screening" and attenuation based on the frequency characteristics of the entire component, while time domain filtering, on this basis, performs "fine screening" in the time dimension to locate the effective signal range with concentrated energy. This two-stage filtering strategy of "frequency domain first, then time domain" and "overall first, then local" constitutes a complete and complementary denoising system.

[0065] Step 5: Signal reconstruction: The IMF components after time-frequency domain filtering are superimposed and reconstructed to obtain a clean partial discharge denoising signal.

[0066] Example

[0067] (1) Simulation signal denoising

[0068] The present invention will now be further analyzed with reference to the accompanying drawings.

[0069] The detailed steps are shown in the flowchart below. Figure 1 As shown:

[0070] S1. Signal Acquisition: Partial discharge signals have distinct characteristics, exhibiting a rapid and steep rising edge, a short duration, and a gradually weakening pulse waveform. This can be simulated using single-exponential and double-exponential oscillation decay models.

[0071]

[0072] Table 1 Simulation parameter settings

[0073]

[0074] The parameters used in the simulation are shown in Table 1 above. The continuous signal was discretized at a sampling frequency of 200MHz to obtain 6000 data points, thus yielding the sampled voltage waveform of the partial discharge current signal, as shown below. Figure 2 As shown. Gaussian white noise with a standard deviation of 0.1mV was added to this ideal partial discharge signal, and its time-domain waveform is shown in... Figure 3 The S-transform was used to perform time-frequency analysis on the mixed signal, and the results are shown in the figure below. Figure 4 As shown in the figure, black and white represent the energy levels. Comparing it with the time-domain plot of the pure signal, it can be seen that the energy of the partial discharge signal in the time-frequency domain is more concentrated than that of white noise, with higher energy at the beginning and middle of the signal, while the white noise signal covers almost the entire time-frequency domain.

[0075] S2. Signal decomposition: Perform CEEMDAN decomposition on the original signal to obtain 13 IMF components and one residual component. The component signals are effectively separated into different frequency bands.

[0076] S3. Frequency Domain Filtering: Calculate the correlation coefficient between each IMF and the original signal, set a threshold of 0.1, and retain components with correlation coefficients higher than this value.

[0077] S4. Time-Domain Filtering: Calculate the time-domain energy spectrum of each IMF component after frequency-domain filtering. Convolve the energy spectrum using a rectangular window of length 50 to enhance energy concentration features. Calculate the MAD value of the energy spectrum for each component and set an energy threshold of twice the MAD. Extract the signal time periods where the energy exceeds this threshold.

[0078] S5. Signal Reconstruction: All processed IMF components are superimposed to reconstruct the denoised partial discharge signal, as shown below. Figure 5 As shown.

[0079] To effectively evaluate the denoising effect and the error between the processed signal and the ideal true signal, this invention uses the Normalized Correlation Coefficient (NCC) as a quantitative indicator to evaluate the correlation between two signals. The closer the coefficient value is to 1, the higher the similarity between the signals before and after processing, thus reflecting better denoising performance.

[0080]

[0081] To verify the effectiveness, the same signal was simultaneously processed using the traditional wavelet thresholding method (Db8 wavelet, heuristic soft thresholding). The denoising performance of this technique and the wavelet thresholding method was compared under different signal-to-noise ratios. Figure 6 As shown, when the signal-to-noise ratio (SNR) is greater than 1.597 dB, both methods achieve ideal denoising effects, with waveform similarity coefficients exceeding 0.9. When the SNR is lower, the effectiveness of both methods is attenuated to varying degrees, with the attenuation of the method in this invention being significantly less than that of the wavelet thresholding method. With a waveform similarity coefficient of 0.9 as a limit, the lower the SNR at this value, the stronger the anti-interference denoising capability of the method. The lowest SNR for the wavelet thresholding method is 1.597 dB, while the lowest SNR for this technique is -1.9248 dB. This means that when the SNR is below 1.597 dB, the signal denoising effect of this method is significantly better than that of the wavelet thresholding method.

[0082] (2) Noise reduction of measured signal

[0083] S1. Signal Acquisition: An oscillating wave is applied to a cable with a certain insulation defect for testing. A partial discharge monitoring terminal is used on the grounding wire of the shield layer of the defective cable to collect the high-frequency current signal generated by partial discharge. The collected partial discharge current sensing sampling signal data is filtered. Figure 7 The time-domain waveform of the partial discharge signal is shown, with a sampling frequency of 125MHz and the signal amplitude having been normalized. The periodic signal is an uncorrelated signal of the measuring device itself, while the remaining signals are cable partial discharge signals. Three partial discharges occurred within the cable during the 35µs sampling time, which can be used to measure the intensity of the discharge.

[0084] S2. Signal decomposition: Perform CEEMDAN decomposition on the signal to obtain the IMF component and a residual component.

[0085] S3. Frequency Domain Filtering: Calculate the correlation coefficient between each IMF and the original signal, set the threshold to 0.1, and use the continuous threshold function mentioned above to attenuate the components with correlation coefficients lower than this value.

[0086] S4. Time-Domain Filtering: Calculate the time-domain energy spectrum of each IMF component after frequency-domain filtering. Convolve the energy spectrum using a rectangular window of length 50 to enhance energy concentration features. Calculate the MAD value of the energy spectrum for each component and set an energy threshold of twice the MAD. Extract the signal time periods where the energy exceeds this threshold.

[0087] S5. Signal Reconstruction: Superimpose all processed IMF components to reconstruct the denoised partial discharge signal.

[0088] To verify the effect, the signal was also processed using the traditional wavelet thresholding method (Db8 wavelet, heuristic soft thresholding). The denoising effects of this technique and the wavelet thresholding method were obtained as follows: Figure 8 and Figure 9 As shown in the figure, the details reveal that, compared to the wavelet thresholding method, the processing result of this technique preserves more details of the partial discharge signal.

[0089] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for denoising cable partial discharge signals based on CEEMDAN, characterized in that, The method comprises the following steps: Step 1: signal acquisition: collecting the high-frequency current signal on the cable shielding layer ground wire as the original noisy signal through a sensor; Step 2: signal decomposition: performing adaptive decomposition on the collected original noisy signal by using a complete self-adaptive noise ensemble empirical mode decomposition (CEEMDAN) algorithm to obtain a series of intrinsic mode function (IMF) components and a residual component; Step 3: frequency domain filtering: after calculating the correlation coefficients of each IMF component and the original noisy signal, a continuous threshold function is used to moderately attenuate the components with correlation coefficients lower than a set threshold value; Step 4: time domain filtering: in the signal processing process, first, the time energy spectrum of each IMF component is calculated, and a predetermined length of a rectangular window function is used to perform convolution operation on the time energy spectrum to enhance the saliency of the energy concentration area; Then, the median-based standard deviation (MAD) is used as a statistical quantity to set an energy threshold, and the energy interval exceeding the threshold is extracted to realize accurate separation of effective signals and noise in the time domain. Step 5: signal reconstruction: superimposing and reconstructing the IMF components after time-frequency domain filtering processing to obtain a pure partial discharge denoising signal.

2. The CEEMDAN-based cable partial discharge signal denoising method according to claim 1, characterized in that, The method is specially used for processing high-frequency current signals collected from the shielding layer ground wire of a power cable, and the interference source in the noisy signal is Gaussian white noise induced by conductor thermal effect.

3. The CEEMDAN-based cable partial discharge signal denoising method according to claim 1, characterized in that, The step 2 comprises the following steps: Step 2.1: generating a noisy signal group: x i (t) = x(t) + e0w i (t) (1) Step 2.2: performing EMD on each signal to extract the first-order IMF: IMF1 i (t) = E1(x i (t)) (2) Step 2.3: integrating and averaging to obtain the first-order IMF of CEEMDAN: Step 2.4: calculating the first-order residual: r1(t)=x(t)-IMF1(t) (4).

4. The CEEMDAN-based cable partial discharge signal denoising method according to claim 3, characterized in that, The step 2 iterates until the residual signal is a monotonic function or contains less than 2 extreme points to stop decomposition, obtaining a series of IMF components arranged from high frequency to low frequency, and finally reconstructing the signal as:

5. The CEEMDAN-based cable partial discharge signal denoising method according to claim 1, characterized in that, The continuous threshold function of the step 3 is represented as:

6. The CEEMDAN-based denoising method for partial discharge signals of power cables according to claim 1, characterized in that, The calculation formula of the median-based standard deviation (MAD) of the step 4 is: Where IMF is the signal sequence to be processed; the energy threshold is set as K times of MAD, where K is a predefined constant.

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