A partial discharge signal denoising system and method based on an improved wavelet threshold algorithm

Abstract

The present application relates to the technical field of discharge signal processing, and particularly relates to a partial discharge signal denoising system and method based on an improved wavelet threshold algorithm, which specifically comprises the following steps: collecting and preprocessing the original partial discharge signal of power equipment; performing singular value decomposition with spectrum constraint, determining the constraint condition according to the spectrum entropy distribution, and suppressing narrowband interference; performing multi-scale wavelet decomposition; establishing scale correlation confidence distribution based on the normalized cross-correlation coefficient of adjacent scale detail coefficients; solving the threshold field energy functional extreme value to generate a continuous threshold field; processing the detail coefficients by using a single continuous threshold function with confidence adaptive modulation; obtaining the denoised signal by wavelet inverse transformation, and iteratively correcting the confidence distribution by the energy distribution of the processed coefficients to form a closed loop. The present application realizes the cooperative suppression of narrowband interference and white noise, significantly improves the detection sensitivity, and effectively solves the contradiction between edge preservation and noise suppression through iterative optimization of the closed loop.

Description

Technical Field

[0001] This invention relates to the field of discharge signal processing technology, specifically to a partial discharge signal denoising system and method based on an improved wavelet threshold algorithm. Background Technology

[0002] Power equipment is a core component of the power grid, and partial discharge is a significant sign of insulation aging. Timely detection and monitoring of partial discharge are crucial for preventing equipment failures and ensuring power grid safety. Many power equipment systems are now equipped with online monitoring systems that can collect partial discharge signals in real time during equipment operation.

[0003] However, the signals collected on-site were very weak and subject to strong interference. There were two main types of interference: narrowband interference, such as mobile phone and radio signals, which are concentrated in frequency and have high energy, making them difficult to separate from partial discharge signals; and white noise, which has a wide frequency distribution and high randomness, resulting in a very low signal-to-noise ratio. Existing denoising methods have several problems: wavelet thresholding methods have fixed thresholds and cannot adapt to signal changes; hard thresholding produces spikes, while soft thresholding blurs signal edges; methods such as empirical mode decomposition lack a solid theoretical foundation and easily mix different signals together; ordinary singular value decomposition can remove narrowband interference but is ineffective against white noise and does not consider the characteristics of partial discharge signals. Moreover, existing methods are mostly open-loop processing, with each stage operating independently and unable to automatically adjust based on the processing results, resulting in limited denoising effectiveness.

[0004] Therefore, a denoising method is needed that can simultaneously remove narrowband interference and white noise and automatically adapt to the characteristics of partial discharge signals, so as to provide reliable data for equipment condition assessment. Summary of the Invention

[0005] In view of the above-mentioned shortcomings of the prior art, the present invention provides a partial discharge signal denoising system and method based on an improved wavelet threshold algorithm, which can effectively solve the problems mentioned in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for denoising partial discharge signals based on an improved wavelet thresholding algorithm, the specific steps of which include: S100: Acquire the original partial discharge signal of the power equipment, preprocess the original signal to obtain a digital signal; S200. Perform spectral-constrained singular value decomposition on the digitized signal. The spectral constraints are determined based on the spectral entropy distribution of the digitized signal, so that the singular vectors obtained by decomposition are orthogonal to the narrowband interference frequency range indicated by the spectral entropy in the frequency domain. After setting the singular values ​​that satisfy the orthogonality condition to zero, the signal is reconstructed to obtain the narrowband interference suppression signal. S300. Perform multi-scale wavelet decomposition on the narrowband interference suppression signal to obtain the approximation coefficients and detail coefficients at each scale. S400. Establish scale correlation confidence distribution based on normalized cross-correlation coefficients of detail coefficients between adjacent scales; S500. Determine the initial threshold distribution based on the noise statistical characteristics of the detail coefficients at each scale, and use the scale-related confidence distribution as the boundary constraint condition. Generate a continuous threshold field distribution by solving the extremum problem of the threshold field energy functional. S600. A single continuous threshold function is used to process the detail coefficients. The shrinkage characteristics of the threshold function are continuously modulated by the local threshold of the continuous threshold field distribution and the local confidence of the scale-related confidence distribution to obtain the processed detail coefficients and the energy distribution of the processed detail coefficients. S700: Based on the processed detail coefficients and approximation coefficients, perform inverse wavelet transform to obtain the denoised partial discharge signal; The scale-related confidence distribution is iteratively corrected based on the coefficient energy distribution processed by the single continuous threshold function in S600, forming an iterative optimization closed loop.

[0007] Furthermore, the spectrally constrained singular value decomposition includes: The digitized signal is constructed into a Hankel matrix; Calculate the spectral entropy distribution of the digitized signal and identify the narrowband frequency range corresponding to the local minimum of the spectral entropy; Construct a spectral constraint matrix, wherein the column space of the spectral constraint matrix is ​​orthogonal to the frequency domain subspace corresponding to the narrowband frequency range; Solve the generalized singular value decomposition problem with orthogonality constraints to obtain singular vectors orthogonal to the frequency domain of narrowband interference under the spectral constraints; Set the singular values ​​corresponding to non-orthogonal singular vectors to zero, and retain the singular values ​​corresponding to orthogonal singular vectors for signal reconstruction.

[0008] Furthermore, the generation of the scale-related confidence distribution includes: Calculate the normalized cross-correlation coefficients of detail coefficients at adjacent scales to generate the initial edge probability distribution; Receive the processed coefficient energy distribution from the feedback of the single continuous threshold function, and calculate the actual processed edge preservation index; The scale-related confidence distribution is adjusted based on the difference between the edge preservation index and the initial edge probability distribution. Determine whether the iterative change of the confidence distribution is lower than a preset threshold, and output the converged scale-correlated confidence distribution.

[0009] Furthermore, the generation of the continuous threshold field distribution includes: Estimate the noise level of detail coefficients at each scale and generate an initial threshold distribution; Construct a threshold field energy functional that includes a data fidelity term, a spatial smoothing term, and a marginal constraint term, wherein the marginal constraint term is weighted by the scale-related confidence distribution; By solving the Euler-Lagrange equations of the energy functional, a continuous threshold field distribution that minimizes the energy functional is obtained.

[0010] Furthermore, the single continuous threshold function achieves continuous soft thresholding of wavelet coefficients through confidence-adaptive modulation and progressive shrinkage control. The specific formula of the function is as follows: ; in, For the k-th wavelet coefficient of the j-th layer, The processed wavelet coefficients, Let (j, k) be the local threshold of the continuous threshold field. Let (j, k) be the local confidence level of the scale correlation. The confidence modulation function is... It is an asymptotically shrinking function.

[0011] Furthermore, the confidence modulation function adaptively adjusts the threshold contraction intensity based on the deviation between the local confidence and the reference confidence through an S-shaped nonlinear mapping. The specific implementation formula is as follows: ; in, The modulation coefficient is used to control the steepness of the S-curve. This is a preset confidence level reference value; When local confidence Higher than the reference value When the modulation function output approaches zero, threshold shrinkage is suppressed to preserve signal edge characteristics; when the local confidence level... Below the reference value When the modulation function output approaches 1, the threshold shrinkage is enhanced to strengthen noise suppression.

[0012] Furthermore, the iterative optimization closed loop includes: Calculate the energy concentration of the detail coefficients processed by the single continuous threshold function described in S600 within a preset edge window; Adjust the confidence values ​​at the corresponding positions in the scale-related confidence distribution based on the comparison results.

[0013] Furthermore, the calculation of the spectral entropy distribution includes: The digitized signal is subjected to a windowed Fourier transform to obtain the spectrum. The spectrum is divided into several sub-bands and the energy ratio of each sub-band is calculated as a probability measure. The Shannon entropy distribution is obtained by calculating the probability measure of each sub-band, the location of local minimum values ​​of the spectral entropy is identified, and the frequency range of narrowband interference concentration is adaptively determined as the constraint target for constructing the spectral constraint matrix.

[0014] Furthermore, the calculation of the normalized cross-correlation coefficient includes: The detail coefficients of adjacent scales are length normalized, and the ratio of the centered covariance to the geometric mean of their respective variances is calculated to obtain the normalized cross-correlation coefficient. A scale correlation matrix is ​​constructed based on the normalized cross-correlation coefficients. The correlation threshold is adaptively determined based on the noise level and truncated. After normalization, an initial scale correlation confidence distribution is generated, which serves as the initial value for the iterative correction.

[0015] A partial discharge signal denoising system based on an improved wavelet thresholding algorithm, used to implement any of the partial discharge signal denoising methods described above, comprising: The signal acquisition module is used to acquire the raw partial discharge signals of power equipment; A preprocessing module, connected to the signal acquisition module, is used for conditioning and digitizing the raw signal; A spectrum-constrained singular value decomposition module, connected to the preprocessing module, is used to construct the digitized signal into a Hankel matrix, perform spectrum-constrained singular value decomposition on the Hankel matrix, the spectrum constraint is determined according to the spectrum entropy distribution of the digitized signal, such that the singular vectors obtained by decomposition are orthogonal to the narrowband interference frequency range indicated by the spectrum entropy in the frequency domain, and the signal is reconstructed after setting the singular values ​​that satisfy the orthogonality condition to zero, thereby obtaining a narrowband interference suppression signal; A multi-scale wavelet decomposition module, connected to the spectrum-constrained singular value decomposition module, is used to perform multi-scale wavelet decomposition on the narrowband interference suppression signal to obtain approximation coefficients and detail coefficients at each scale. The scale correlation dynamic estimation module is connected to the multi-scale wavelet decomposition module. It is used to establish an initial scale correlation estimate based on the normalized cross-correlation coefficient of detail coefficients between adjacent scales, and to iteratively correct the initial scale correlation estimate according to the processed coefficient energy distribution fed back by the continuous modulation threshold processing module, so as to generate a converged scale correlation confidence distribution. The threshold field evolution generation module is connected to the scale-related dynamic estimation module and the multi-scale wavelet decomposition module. It is used to determine the initial threshold distribution based on the noise statistical characteristics of the detail coefficients at each scale, and to generate a continuous threshold field distribution by solving the extremum problem of the threshold field energy functional using the scale-related confidence distribution as the boundary constraint condition. A continuous modulation threshold processing module, connected to the threshold field evolution generation module, is used to process detail coefficients using a single continuous threshold function. The shrinkage characteristics of the threshold function are continuously modulated by the local thresholds of the continuous threshold field distribution and the local confidence of the scale-related confidence distribution. The wavelet reconstruction module is connected to the continuous modulation threshold processing module and is used to perform inverse wavelet transform based on the processed detail coefficients and approximation coefficients to obtain the denoised partial discharge signal. The scale-related dynamic estimation module establishes a feedback connection with the continuous modulation threshold processing module to transmit the energy concentration information of the processed coefficients back to the scale-related dynamic estimation module for iterative correction.

[0016] The technical solution provided by this invention has the following advantages compared with the known prior art: This invention accurately eliminates narrowband interference through singular value decomposition with spectral constraints, while adaptively suppressing white noise using continuous threshold field distribution. Compared with traditional cascaded processing methods, it achieves synergistic suppression of narrowband interference and white noise, significantly improving the detection sensitivity of partial discharge signals and providing reliable technical support for the early detection of insulation defects in equipment.

[0017] This invention establishes a scale-related confidence distribution based on the correlation of detail coefficients at adjacent scales, and dynamically optimizes it through an iterative mechanism to establish an iterative optimization closed loop. This effectively solves the contradiction between signal edge preservation and noise suppression. The closed-loop structure enables the threshold processing to be adaptively adjusted according to the actual edge preservation effect, which significantly improves the accuracy of fault mode recognition and can adapt to different equipment and operating conditions without manual parameter adjustment. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0019] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] The present invention will be further described below with reference to embodiments.

[0022] Example: Reference Figure 1 This embodiment provides a method for denoising partial discharge signals based on an improved wavelet thresholding algorithm, the specific steps of which include: S100: Collect the original partial discharge signal of the power equipment, preprocess the original signal to obtain a digital signal; In one specific embodiment, a high-frequency current sensor or an ultra-high-frequency sensor is used to couple a partial discharge signal from the grounding wire or observation window of the power equipment. The sensor has a frequency response range of 1MHz to 100MHz and a sensitivity better than 5pC.

[0023] Preprocessing includes signal conditioning and digitization. The signal conditioning circuitry includes a bandpass filter (passband range 1MHz-50MHz, used to filter out power frequency and harmonic interference) and a programmable gain amplifier (gain range 0-60dB, automatically adjusted according to signal strength). The high-speed data acquisition card is set to a sampling rate of 100MS / s, a resolution of 12 bits, an acquisition time of 10ms, and each frame of data contains 1×10⁻⁶ bytes. 6 One sampling point.

[0024] After digitizing the acquired raw signal, a digitized signal x(n) is obtained, n=1,2,...,N, where N=1×10⁻⁶. 6 .

[0025] S200. Perform spectral-constrained singular value decomposition on the digitized signal. The spectral constraints are determined based on the spectral entropy distribution of the digitized signal, so that the singular vectors obtained by decomposition are orthogonal to the narrowband interference frequency range indicated by the spectral entropy in the frequency domain. After setting the singular values ​​that satisfy the orthogonality condition to zero, the signal is reconstructed to obtain the narrowband interference suppression signal. Specifically, this step is used to suppress narrowband interference, such as mobile communication signals and broadcast signals.

[0026] First, the digitized signal x(n) is constructed as a Hankel matrix H. Specifically, with an embedding dimension L=500, the dimension of the Hankel matrix is ​​L×(N-L+1), which is 500×999501. The matrix is ​​constructed as follows: ; Secondly, the spectral entropy distribution of the digitized signal is calculated. Specific steps include: (1) Perform windowed Fourier transform on signal x(n), using Hanning window as the window function, with a window length of 1024 points, an overlap rate of 50%, and 2048 FFT points; (2) Divide the spectrum into K=256 subbands, each subband having a width of ,in =100MHz is the sampling rate; (3) Calculate the energy percentage of each subband as a probability measure: ; in, Let K be the energy of the k-th subband, where k = 1, 2, ..., K; (4) Calculate the spectral entropy distribution: ; Identify the narrowband frequency range corresponding to the local minimum of spectral entropy. In one specific embodiment, a threshold is set. ,when If three consecutive subbands meet this condition, it is determined to be a narrowband interference frequency range.

[0027] Construct a spectral constraint matrix C such that its column space is orthogonal to the frequency domain subspace corresponding to the narrowband interference frequency range. Solve for the generalized singular value decomposition with orthogonal constraints: ; in, Let L be a left singular vector matrix of dimension L×L, and let its column vectors be the singular vectors. Given an L×(N-L+1) dimensional diagonal singular value matrix, the diagonal elements... For the corresponding singular values; It is the transpose of a (N-L+1)×(N-L+1) dimensional right singular vector matrix.

[0028] After reconstructing the signal by setting the singular values ​​corresponding to the non-orthogonal singular vectors to zero, the narrowband interference suppression signal is obtained. .

[0029] S300. Perform multi-scale wavelet decomposition on the narrowband interference suppression signal to obtain the approximation coefficients and detail coefficients at each scale. Narrowband interference suppression signal Multi-scale wavelet decomposition is performed. In a specific embodiment, the db8 wavelet is selected as the mother wavelet, and the number of decomposition levels J=5.

[0030] The decomposition process uses the Mallat algorithm, and the specific formula is as follows: ; in, The approximate coefficients for the J-th layer are... Let be the detail coefficient of the j-th layer.

[0031] S400. Establish scale correlation confidence distribution based on normalized cross-correlation coefficients of detail coefficients between adjacent scales; Traditional wavelet thresholding denoising uses a uniform threshold for each layer and position, ignoring the correlation characteristics of signals at different scales and positions. Partial discharge pulses have strong correlations between adjacent scales, while noise has weak correlations. In a specific embodiment, a scale correlation confidence distribution is established based on the normalized cross-correlation coefficient to quantify the probability of signal edges.

[0032] First, the detail coefficients at adjacent scales are normalized in length. Taking the j-th and (j+1)-th layers as an example, due to their different lengths, it is necessary to downsample the longer coefficients or upsample the shorter coefficients to make their lengths consistent. Downsampling is used to extract the detail coefficients of the j-th layer by a factor of 2.

[0033] The formula for calculating the normalized cross-correlation coefficient is as follows: ; in, and These are the values ​​of the detail coefficients of the j-th and (j+1)-th layers after centralization at position k.

[0034] Construct a scaled correlation matrix P based on the normalized cross-correlation coefficients, whose elements are: , representing the scale correlation confidence at the k-th position in the j-th layer. The correlation threshold is adaptively determined based on the noise level. ,when season Otherwise, keep the original value. After normalization, an initial scale-related confidence distribution is generated.

[0035] S500. Determine the initial threshold distribution based on the noise statistical characteristics of the detail coefficients at each scale, use the scale-related confidence distribution as the boundary constraint, and generate a continuous threshold field distribution by solving the extremum problem of the threshold field energy functional. In a specific embodiment, the noise levels of detail coefficients at different scales are typically different, and the signal-to-noise ratio also varies at different locations within the same scale. Traditional methods use a hierarchical uniform threshold, resulting in insufficient denoising in areas with low noise levels and excessive denoising in signal edge regions. This invention generates a spatially continuous threshold field, achieving an adaptive spatial distribution of the threshold.

[0036] First, noise levels at various scales are estimated. A robust median estimation method is employed, leveraging the robustness of wavelet coefficient medians to standard deviation; even with large signal margins, the median accurately reflects the noise level. The initial threshold distribution uses a general threshold form, incorporating noise level estimates and a correction factor based on signal length.

[0037] A threshold field energy functional is constructed, which includes three constraints: a data fidelity term to ensure that the deviation between the coefficients after threshold processing and the original coefficients is controllable; a spatial smoothing term to ensure that the threshold changes continuously in space and avoids the pseudo-Gibbs phenomenon caused by threshold jumps at adjacent positions; and an edge constraint term weighted by a scale-correlated confidence distribution, which forces the threshold to be close to the initial value in high-confidence edge regions to protect the signal, and allows the threshold to be adaptively adjusted in low-confidence regions to enhance denoising.

[0038] By solving the Euler-Lagrange equations of the energy functional and using the finite difference method for numerical iteration, the continuous threshold field distribution is obtained.

[0039] S600: A single continuous threshold function is used to process the detail coefficients. The shrinkage characteristics of the threshold function are continuously modulated by the local threshold of the continuous threshold field distribution and the local confidence of the scale-related confidence distribution. Specifically, a single continuous threshold function achieves continuous soft thresholding of wavelet coefficients through confidence-adaptive modulation and progressive shrinkage control. The specific formula for the function is as follows: ; in, For the k-th wavelet coefficient of the j-th layer, The processed wavelet coefficients, Let (j, k) be the local threshold of the continuous threshold field. Let (j, k) be the local confidence level of the scale correlation. The confidence modulation function is... It is an asymptotically shrinking function.

[0040] The confidence modulation function adaptively adjusts the threshold contraction intensity based on the deviation between the local confidence and the reference confidence through an S-shaped nonlinear mapping. The specific formula is as follows: ; in, The modulation coefficient is used to control the steepness of the S-curve. This is a preset confidence level reference value; When local confidence Higher than the reference value When the modulation function output approaches zero, threshold shrinkage is suppressed to preserve signal edge characteristics; when the local confidence level... Below the reference value When the modulation function output approaches 1, the threshold shrinkage is enhanced to strengthen noise suppression.

[0041] S700: Based on the processed detail coefficients and approximation coefficients, perform inverse wavelet transform to obtain the denoised partial discharge signal; Specifically, based on the processed detail coefficients and approximation coefficients, inverse wavelet transform is performed, and the Mallat reconstruction algorithm is used to synthesize the denoised partial discharge signal.

[0042] The iterative optimization closed loop feeds back the energy concentration of the processed coefficients to the scale-correlated confidence distribution for correction. An energy concentration index within the edge window is calculated; this index reflects the degree of energy distribution concentration, with a higher value indicating better edge preservation. The confidence distribution is adjusted based on the edge preservation index: if edge preservation is better than expected, the confidence at that location is increased; if it is worse than expected, the confidence is decreased. Convergence is determined when the iterative change in the confidence distribution is below a preset threshold; typically, a stable state is reached in 3-5 iterations.

[0043] Reference Figure 2 This embodiment provides a partial discharge signal denoising system based on an improved wavelet thresholding algorithm. The system includes the following modules: The signal acquisition module is used to acquire the raw partial discharge signals of power equipment; The preprocessing module, connected to the signal acquisition module, is used for conditioning and digitizing the raw signal; The spectrum-constrained singular value decomposition module, connected to the preprocessing module, is used to construct a Hankel matrix from the digitized signal and perform spectrum-constrained singular value decomposition on the Hankel matrix. The spectrum constraint is determined according to the spectrum entropy distribution of the digitized signal, so that the singular vectors obtained by decomposition are orthogonal to the narrowband interference frequency range indicated by the spectrum entropy in the frequency domain. After setting the singular values ​​that meet the orthogonality condition to zero, the signal is reconstructed to obtain the narrowband interference suppression signal. The multi-scale wavelet decomposition module, connected to the spectrum-constrained singular value decomposition module, is used to perform multi-scale wavelet decomposition on narrowband interference-suppressed signals to obtain approximation coefficients and detail coefficients at each scale. The scale correlation dynamic estimation module, connected to the multi-scale wavelet decomposition module, is used to establish an initial scale correlation estimate based on the normalized cross-correlation coefficients of detail coefficients between adjacent scales, and to iteratively correct the initial scale correlation estimate based on the processed coefficient energy distribution fed back by the continuous modulation threshold processing module, thereby generating a converged scale correlation confidence distribution. The threshold field evolution generation module is connected to the scale-related dynamic estimation module and the multi-scale wavelet decomposition module. It is used to determine the initial threshold distribution based on the noise statistical characteristics of the detail coefficients at each scale, and to generate a continuous threshold field distribution by solving the extremum problem of the threshold field energy functional using the scale-related confidence distribution as the boundary constraint. The continuous modulation threshold processing module, connected to the threshold field evolution generation module, is used to process the detail coefficients using a single continuous threshold function. The shrinkage characteristics of the threshold function are continuously modulated by the local threshold of the continuous threshold field distribution and the local confidence of the scale-related confidence distribution. The wavelet reconstruction module, connected to the continuous modulation threshold processing module, is used to perform inverse wavelet transform based on the processed detail coefficients and approximation coefficients to obtain the denoised partial discharge signal.

[0044] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for denoising partial discharge signals based on an improved wavelet thresholding algorithm, characterized in that, The specific steps include: S100: Acquire the original partial discharge signal of the power equipment, preprocess the original signal to obtain a digital signal; S200. Perform spectral-constrained singular value decomposition on the digitized signal. The spectral constraints are determined based on the spectral entropy distribution of the digitized signal, so that the singular vectors obtained by decomposition are orthogonal to the narrowband interference frequency range indicated by the spectral entropy in the frequency domain. After setting the singular values ​​that satisfy the orthogonality condition to zero, the signal is reconstructed to obtain the narrowband interference suppression signal. S300. Perform multi-scale wavelet decomposition on the narrowband interference suppression signal to obtain the approximation coefficients and detail coefficients at each scale. S400. Establish scale correlation confidence distribution based on normalized cross-correlation coefficients of detail coefficients between adjacent scales; S500. Determine the initial threshold distribution based on the noise statistical characteristics of the detail coefficients at each scale, and use the scale-related confidence distribution as the boundary constraint condition. Generate a continuous threshold field distribution by solving the extremum problem of the threshold field energy functional. S600. A single continuous threshold function is used to process the detail coefficients. The shrinkage characteristics of the threshold function are continuously modulated by the local threshold of the continuous threshold field distribution and the local confidence of the scale-related confidence distribution to obtain the processed detail coefficients and the energy distribution of the processed detail coefficients. S700: Based on the processed detail coefficients and approximation coefficients, perform inverse wavelet transform to obtain the denoised partial discharge signal; The scale-related confidence distribution is iteratively corrected based on the coefficient energy distribution processed by the single continuous threshold function in S600, forming an iterative optimization closed loop.

2. The method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The spectral-constrained singular value decomposition includes: The digitized signal is constructed into a Hankel matrix; Calculate the spectral entropy distribution of the digitized signal and identify the narrowband frequency range corresponding to the local minimum of the spectral entropy; Construct a spectral constraint matrix, wherein the column space of the spectral constraint matrix is ​​orthogonal to the frequency domain subspace corresponding to the narrowband frequency range; Solve the generalized singular value decomposition problem with orthogonality constraints to obtain singular vectors orthogonal to the frequency domain of narrowband interference under the spectral constraints; Set the singular values ​​corresponding to non-orthogonal singular vectors to zero, and retain the singular values ​​corresponding to orthogonal singular vectors for signal reconstruction.

3. The method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The generation of the scale-related confidence distribution includes: Calculate the normalized cross-correlation coefficients of detail coefficients at adjacent scales to generate the initial edge probability distribution; Receive the processed coefficient energy distribution from the feedback of the single continuous threshold function, and calculate the actual processed edge preservation index; The scale-related confidence distribution is adjusted based on the difference between the edge preservation index and the initial edge probability distribution. Determine whether the iterative change of the confidence distribution is lower than a preset threshold, and output the converged scale-correlated confidence distribution.

4. The method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The generation of the continuous threshold field distribution includes: Estimate the noise level of detail coefficients at each scale and generate an initial threshold distribution; Construct a threshold field energy functional that includes a data fidelity term, a spatial smoothing term, and a marginal constraint term, wherein the marginal constraint term is weighted by the scale-related confidence distribution; By solving the Euler-Lagrange equations of the energy functional, a continuous threshold field distribution that minimizes the energy functional is obtained.

5. A method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The single continuous threshold function achieves continuous soft thresholding of wavelet coefficients through confidence-adaptive modulation and progressive shrinkage control. The specific formula of the function is as follows: ； in, For the k-th wavelet coefficient of the j-th layer, The processed wavelet coefficients, Let (j, k) be the local threshold of the continuous threshold field. Let (j, k) be the local confidence level of the scale correlation. The confidence modulation function is... It is an asymptotically shrinking function.

6. A method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 5, characterized in that, The confidence modulation function adaptively adjusts the threshold contraction intensity based on the deviation between the local confidence and the reference confidence through an S-shaped nonlinear mapping. The specific implementation formula is as follows: ； in, The modulation coefficient is used to control the steepness of the S-curve. This is a preset confidence level reference value; When local confidence Higher than the reference value When the modulation function output approaches zero, threshold shrinkage is suppressed to preserve signal edge characteristics; when the local confidence level... Below the reference value When the modulation function output approaches 1, the threshold shrinkage is enhanced to strengthen noise suppression.

7. A method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The iterative optimization closed loop includes: Calculate the energy concentration of the detail coefficients after processing by the single continuous threshold function described in S600 within a preset edge window; Adjust the confidence values ​​at the corresponding positions in the scale-related confidence distribution based on the comparison results.

8. A method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The calculation of the spectral entropy distribution includes: The spectrum is obtained by performing a windowed Fourier transform on the digitized signal, and the spectrum is divided into several sub-bands and the energy ratio of each sub-band is calculated as a probability measure. The Shannon entropy distribution is obtained by calculating the probability measure of each sub-band, the location of local minimum values ​​of the spectral entropy is identified, and the frequency range of narrowband interference concentration is adaptively determined as the constraint target for constructing the spectral constraint matrix.

9. A method for denoising partial discharge signals based on an improved wavelet thresholding algorithm according to claim 1, characterized in that, The calculation of the normalized cross-correlation coefficient includes: The detail coefficients of adjacent scales are length normalized, and the ratio of the centered covariance to the geometric mean of their respective variances is calculated to obtain the normalized cross-correlation coefficient. A scale correlation matrix is ​​constructed based on the normalized cross-correlation coefficients. The correlation threshold is adaptively determined based on the noise level and truncated. After normalization, an initial scale correlation confidence distribution is generated, which serves as the initial value for the iterative correction.

10. A partial discharge signal denoising system based on an improved wavelet thresholding algorithm, used to implement the partial discharge signal denoising method according to any one of claims 1 to 9, characterized in that, include: The signal acquisition module is used to acquire the raw partial discharge signals of power equipment; A preprocessing module, connected to the signal acquisition module, is used for conditioning and digitizing the raw signal; A spectrum-constrained singular value decomposition module, connected to the preprocessing module, is used to construct the digitized signal into a Hankel matrix, perform spectrum-constrained singular value decomposition on the Hankel matrix, the spectrum constraint is determined according to the spectrum entropy distribution of the digitized signal, such that the singular vectors obtained by decomposition are orthogonal to the narrowband interference frequency range indicated by the spectrum entropy in the frequency domain, and the signal is reconstructed after setting the singular values ​​that satisfy the orthogonality condition to zero, thereby obtaining a narrowband interference suppression signal; A multi-scale wavelet decomposition module, connected to the spectrum-constrained singular value decomposition module, is used to perform multi-scale wavelet decomposition on the narrowband interference suppression signal to obtain approximation coefficients and detail coefficients at each scale. The scale correlation dynamic estimation module is connected to the multi-scale wavelet decomposition module. It is used to establish an initial scale correlation estimate based on the normalized cross-correlation coefficient of detail coefficients between adjacent scales, and to iteratively correct the initial scale correlation estimate according to the processed coefficient energy distribution fed back by the continuous modulation threshold processing module, so as to generate a converged scale correlation confidence distribution. The threshold field evolution generation module is connected to the scale-related dynamic estimation module and the multi-scale wavelet decomposition module. It is used to determine the initial threshold distribution based on the noise statistical characteristics of the detail coefficients at each scale, and to generate a continuous threshold field distribution by solving the extremum problem of the threshold field energy functional using the scale-related confidence distribution as the boundary constraint condition. A continuous modulation threshold processing module, connected to the threshold field evolution generation module, is used to process detail coefficients using a single continuous threshold function. The shrinkage characteristics of the threshold function are continuously modulated by the local thresholds of the continuous threshold field distribution and the local confidence of the scale-related confidence distribution. The wavelet reconstruction module is connected to the continuous modulation threshold processing module and is used to perform inverse wavelet transform based on the processed detail coefficients and approximation coefficients to obtain the denoised partial discharge signal. The scale-related dynamic estimation module establishes a feedback connection with the continuous modulation threshold processing module to transmit the energy concentration information of the processed coefficients back to the scale-related dynamic estimation module for iterative correction.

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