Partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition

Abstract

This invention discloses a partial discharge (PD) signal denoising method based on image information entropy and multivariate variational mode decomposition (MMD). The method involves converting the noisy signal into a grayscale image, calculating the image information entropy, and optimizing the number of modes K in the MMD by combining Pearson correlation coefficient and execution efficiency to determine the optimal value. The noisy PD signal is then decomposed. The kurtosis value of each intrinsic mode component is calculated, and the nature of the mode component is determined based on a threshold, classifying it as either a dominant PD component or a noise component. A mathematical statistical method using the 3σ criterion is employed to filter out normally distributed white noise. The reconstructed signal is then denoised using an improved wavelet thresholding method to obtain the denoised PD signal. This denoising method accurately reduces noise in noisy PD signals, achieving good noise suppression and restoring the waveform characteristics of the PD signal while maintaining high execution efficiency.

Description

Technical Field

[0001] This invention belongs to the field of power system engineering signal processing and high-voltage insulation monitoring technology, specifically involving a partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition. Background Technology

[0002] Insulation defects in electrical equipment are always accompanied by partial discharge. The continuous development of partial discharge leads to further deterioration of the insulation, ultimately causing equipment failure. Therefore, partial discharge (PD) testing helps to detect and eliminate potential defects before equipment failure occurs. Partial discharge is an effective method for evaluating the insulation condition of cables and is crucial for assessing the health status of power equipment. PD testing is a commonly used method, but due to the complex and harsh electromagnetic environment in the field, there may be white noise interference or periodic narrowband interference. These interferences can cause severe distortion of the PD signal waveform, affecting the accuracy of the test results, or even burying them in background noise, thus affecting subsequent defect diagnosis and condition assessment. Summary of the Invention

[0003] The purpose of this invention is to provide a partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition, which solves the problems of white noise, periodic narrowband interference, and weak adaptability in the denoising process when detecting partial discharge in cable terminals.

[0004] The technical solution adopted in this invention is a partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition, which is implemented according to the following steps:

[0005] Step 1: Decompose the noisy partial discharge signal to determine the number of modes in the multivariate variational mode decomposition algorithm;

[0006] Step 2: Determine whether the modal characteristics belong to the dominant component of partial discharge or the noise component;

[0007] Step 3: Filter the noise components;

[0008] Step 4: The filtered noise component is superimposed with the dominant partial discharge component to obtain the reconstructed partial discharge signal. The reconstructed partial discharge signal Z is then subjected to improved wavelet threshold denoising to obtain the denoised partial discharge signal.

[0009] The invention is further characterized by:

[0010] Step 1 is as follows:

[0011] Step 1.1: Decompose the noisy partial discharge signal X using a multivariate variational mode decomposition algorithm to obtain the intrinsic mode components (IMFs). nn = 1, 2, ..., K, where n is the mode number and K is the number of modes. The initial conditions are defined as: K = 1, and the maximum number of iterations is 2000.

[0012] Step 1.2: By superimposing intrinsic mode components (IMFs) n The reconstructed partial discharge signal Y after the first noise filtering is obtained and converted into a two-dimensional image in JPG format;

[0013] Step 1.3: Obtain a grayscale image from the two-dimensional image through grayscale processing, and calculate the one-dimensional information entropy H of the grayscale image;

[0014] Step 1.4: Calculate the Pearson correlation coefficient ρ between the noisy partial discharge signal X and the reconstructed partial discharge signal Y, and the execution efficiency η of the multivariate variational mode decomposition algorithm;

[0015] Step 1.5: Determine if ρ > 0.95. If not, then K = K + 1 and return to step 1.1. Otherwise, determine if the information entropy H is minimum. If it is minimum, output the modality number K as the modality number of the multivariate variational mode decomposition algorithm. Otherwise, return to step 1.1.

[0016] The formula for obtaining a grayscale image from a two-dimensional image through grayscale processing in step 1.3 is:

[0017] Gray=0.2126R+0.7152G+0.0772B

[0018] Where R, G, and B represent the pixels of the red, green, and blue primary color components in the image, respectively.

[0019] The formula for calculating the one-dimensional information entropy H of the grayscale image in step 1.3 is:

[0020]

[0021] Where, p i This represents the probability of a pixel with a grayscale value of i appearing.

[0022] The formula for calculating the Pearson correlation coefficient ρ between the noisy partial discharge signal X and the reconstituted partial discharge signal Y in step 1.3 is as follows:

[0023] Where X and Y are the noisy partial discharge signal and the reconstituted partial discharge signal, respectively; cov(X,Y) is the covariance of the noisy partial discharge signal and the reconstituted partial discharge signal; σ X σ Y E(X) and E(Y) are the standard deviations of the noisy partial discharge signal and the reconstructed partial discharge signal, respectively; E(X) and E(Y) are the expected values ​​of the noisy partial discharge signal and the reconstructed partial discharge signal, respectively.

[0024] The formula for calculating the execution efficiency η of the multivariate variational mode decomposition algorithm is:

[0025]

[0026] Where ρ is the Pearson correlation coefficient and t is the running time of the multivariate variational mode decomposition algorithm, in seconds.

[0027] Step 2 is as follows:

[0028] Step 2.1: Based on the determined number of modes, the partial discharge signal is decomposed using a multivariate variational mode decomposition algorithm to obtain each mode component;

[0029] Step 2.2: Calculate the kurtosis value of each modal component;

[0030] Step 2.3: Calculate the kurtosis values ​​of a standard sine wave y1 with an amplitude of 1mV and a frequency of 1Hz and a double exponential decaying signal y2 under Gaussian white noise with a signal-to-noise ratio of 0dB. and because Therefore, a larger value of 3.20 is used as the threshold ε to distinguish the characteristic properties of each modal component: when the kurtosis value of a modal component is greater than 3.20, the modal component is determined to be the dominant component of partial discharge; otherwise, the modal component is a noise component.

[0031] Step 3 involves applying a 3σ criterion filter to the noise components. The calculation formula for the 3σ criterion filter is as follows:

[0032]

[0033] in, It is the standard deviation of each modal component. This represents the mean value of each modal component;

[0034] The Gaussian white noise with a normal distribution is filtered out to obtain the filtered noise component, which is the second noise filtering step.

[0035] In step 4, the wavelet threshold for reconstructing the partial discharge signal Z is improved as follows:

[0036] The improved threshold expression is as follows:

[0037]

[0038] Where λ is the general threshold, λ′ is the improved wavelet threshold; σ is the standard deviation of the reconstructed partial discharge signal; and N is the number of sampling points.

[0039] The improved threshold function expression is as follows:

[0040]

[0041] Where ω represents the unprocessed wavelet coefficients, and ω′ represents the wavelet coefficients after thresholding.

[0042] Wavelet thresholding denoising was performed on the reconstructed partial discharge signal Z by improving the threshold function and threshold pair.

[0043] Step 4 involves superimposing the filtered noise component with the dominant partial discharge component to obtain the reconstructed partial discharge signal. The calculation formula is as follows:

[0044] Z = a1IMF1 + a2IMF2 + ... + a n IMF n +b1IMF1+b2IMF2+…b n IMF n

[0045] a n =Logical{k(IMF n )>3.20}

[0046]

[0047] Where Logical{·} is the logical judgment function, returning 1 if {·} is satisfied, and 0 if {·} is not satisfied; k(·) is used to calculate the kurtosis value; IMF n Let n be the modal component, n be the modal number, and n = 1, 2, ..., K, where K is the number of modes; It is the standard deviation of each modal component. This represents the mean of each modal component.

[0048] The beneficial effects of this invention are:

[0049] 1) Optimizing the MVMD algorithm parameters by considering multiple factors: By converting the PD signal into a grayscale image or an RGB two-dimensional image through grayscale processing, the image information entropy is calculated and can be used as one of the criteria for judging image quality. The value of R=G=B is called the grayscale value. Converting to a grayscale image preserves its gradient information, greatly improves calculation speed and data transmission rate, and also increases visual contrast, highlighting the target area. Under different modal parameters, the determinism of the reconstructed PD signal grayscale image varies, as does the amount of information it contains. A smaller image information entropy value indicates a more even distribution of grayscale values, meaning the reconstructed PD signal contains more average information. This indicates a high degree of matching between the modal decomposition and the waveform characteristics of the PD signal, suggesting the highest determinism of the PD pulse under this decomposition method and relatively weaker noise. Based on this, the optimal number of modes K is comprehensively considered by combining the Pearson correlation coefficient and the algorithm execution efficiency η, enabling the PD signal to be decomposed efficiently and reasonably without distortion, thereby minimizing modal aliasing or signal distortion.

[0050] 2) The threshold for determining modal characteristics has physical significance: Utilizing the sensitivity of kurtosis to noise, Gaussian white noise with different signal-to-noise ratios was added to a standard sinusoidal signal and a double exponential decay function signal for simulation. When the signal-to-noise ratio is greater than 0dB, some characteristics of these two signals can be basically distinguished. Therefore, the kurtosis value at a signal-to-noise ratio of 0dB is taken as the threshold ε to distinguish the dominant PD component from the noise component. Due to the random nature of environmental noise distribution, in practical applications, the kurtosis values ​​of signals y1 and y2 at a signal-to-noise ratio of 0dB should be tested 30 times and averaged. The maximum value of the two should be taken as the representative threshold ε for determining modal characteristics, which has physical significance.

[0051] 3) Novel Improved Wavelet Threshold Function and Threshold: The improved wavelet threshold function of this invention is matched with the PD signal waveform, and its exponentially decaying coefficient can better fit the characteristics of the PD signal. The improvement of the wavelet threshold is based on the general threshold and is related to the number of decomposition levels, so that it can better track the detailed features of each decomposition level of the PD signal and further improve the denoising effect. Attached Figure Description

[0052] Figure 1 This is a flowchart of the partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition of the present invention.

[0053] Figure 2 This is a flowchart illustrating the optimization process of modal parameter K in this invention.

[0054] Figure 3 The waveform diagram of the simulated PD signal of this invention includes a clean PD signal, periodic narrowband interference, and a noisy PD signal;

[0055] Figure 4 This is a multivariate variational mode decomposition diagram of the parameter improvement of the noisy PD signal in this invention;

[0056] Figure 5 This is a schematic diagram showing the simulation results of two signals, a standard sinusoidal signal y1 and a double exponential decay signal y2, under different signal-to-noise ratios in this invention.

[0057] Figure 6 The denoising waveform of the denoising method of the present invention is shown in the embodiment of the present invention, taking a simulated PD signal as the object;

[0058] Figure 7 The diagram shows the measured PD signal and the measured PD signal with added noise in an embodiment of the present invention.

[0059] Figure 8 The denoising waveform diagram of the denoising method of the present invention is shown in the embodiment of the present invention, using the measured PD signal as the object. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0061] This invention relates to a partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition, such as... Figure 1 As shown, please follow these steps:

[0062] Step 1: Decompose the noisy partial discharge signal to determine the number of modes in the multivariate variational mode decomposition algorithm; for example... Figure 2 As shown, the specific process is as follows:

[0063] Step 1.1: Decompose the noisy partial discharge signal X using a multivariate variational mode decomposition algorithm to obtain the intrinsic mode components (IMFs). n n = 1, 2, ..., K, where n is the mode number and K is the number of modes. The initial conditions are defined as: K = 1, and the maximum number of iterations is 2000.

[0064] Step 1.2: By superimposing intrinsic mode components (IMFs) n The reconstructed partial discharge signal Y after the first noise filtering is obtained and converted into a two-dimensional image in JPG format;

[0065] The formula for calculating Y is as follows:

[0066] Y = IMF1 + IMF2 + ... + IMF n

[0067] Among them, IMF n Let n be the modal component, n be the modal number, n = 1, 2, ..., K, and K be the number of modes.

[0068] Step 1.3: Obtain a grayscale image from the two-dimensional image through grayscale processing, and calculate the one-dimensional information entropy H of the grayscale image;

[0069] The formula for obtaining a grayscale image from a two-dimensional image through grayscale processing is:

[0070] Gray=0.2126R+0.7152G+0.0772B

[0071] Where R, G, and B represent the pixels of the red, green, and blue primary color components in the image, respectively.

[0072] The formula for calculating the one-dimensional information entropy H of the grayscale image in step 1.3 is:

[0073]

[0074] Where, p i This represents the probability of a pixel with a grayscale value of i appearing.

[0075] The formula for calculating the Pearson correlation coefficient ρ between the noisy partial discharge signal X and the reconstituted partial discharge signal Y is as follows:

[0076]

[0077] Where X and Y are the noisy partial discharge signal and the reconstituted partial discharge signal, respectively; cov(X,Y) is the covariance of the noisy partial discharge signal and the reconstituted partial discharge signal; σ X σ Y E(X) and E(Y) are the standard deviations of the noisy partial discharge signal and the reconstructed partial discharge signal, respectively; E(X) and E(Y) are the expected values ​​of the noisy partial discharge signal and the reconstructed partial discharge signal, respectively.

[0078] Step 1.4: Calculate the Pearson correlation coefficient ρ between the noisy partial discharge signal X and the reconstructed partial discharge signal Y, and the execution efficiency η of the multivariate variational mode decomposition algorithm;

[0079] The formula for calculating the execution efficiency η of the multivariate variational mode decomposition algorithm is:

[0080]

[0081] Where ρ is the Pearson correlation coefficient and t is the running time of the multivariate variational mode decomposition algorithm, in seconds.

[0082] Step 1.5: Determine if ρ > 0.95. If not, then K = K + 1 and return to step 1.1. Otherwise, determine if the information entropy H is minimum. If it is minimum, output the modality number K as the modality number of the multivariate variational mode decomposition algorithm. Otherwise, return to step 1.1.

[0083] Correlation coefficient ρ: such as Figure 2 As shown, when the correlation coefficient ρ between the noisy PD signal X and the reconstructed PD signal Y is greater than 0.95, it indicates that the original PD signal has been completely decomposed.

[0084] Image information entropy H: The degree of determinism of the grayscale image of the reconstructed PD signal varies under different modal parameters K, and the amount of information it contains also varies. Among them, when the image information entropy value is the smallest, it indicates that the degree of determinism of the partial discharge signal is the largest under this decomposition method, and its noise content is also relatively small.

[0085] Algorithm execution efficiency η: As the modal parameter K increases, the reconstructed PD signal will more closely approximate the original PD signal, and the energy loss caused by modal decomposition will decrease accordingly. Therefore, the Pearson correlation coefficient will increase with the increase of K. The execution efficiency η of the MVMD algorithm is defined as the ratio of the Pearson correlation coefficient to the execution time required by the MVMD algorithm, as shown in the following formula. The higher the execution efficiency of the algorithm, the higher the timeliness of denoising. When K is too large, the growth rate of the K-η relationship curve decreases significantly. Therefore, the execution efficiency of the MVMD algorithm will decrease significantly when K is too large, affecting the timeliness of the denoising results.

[0086]

[0087] In the formula, ρ is the Pearson correlation coefficient, and t is the time required for the MVMD algorithm to run, in seconds.

[0088] Step 2: Determine whether the modal characteristics belong to the dominant component of partial discharge or the noise component; the specific process is as follows:

[0089] Step 2.1: Based on the determined number of modes, the partial discharge signal is decomposed using a multivariate variational mode decomposition algorithm to obtain each mode component;

[0090] Step 2.2: Calculate the kurtosis value of each modal component;

[0091] Step 2.3: Calculate the kurtosis values ​​of a standard sine wave y1 with an amplitude of 1mV and a frequency of 1Hz and a double exponential decaying signal y2 under Gaussian white noise with a signal-to-noise ratio of 0dB. and because Therefore, a larger value of 3.20 is used as the threshold ε to distinguish the characteristic properties of each modal component: when the kurtosis value of a modal component is greater than 3.20, the modal component is determined to be the dominant component of partial discharge; otherwise, the modal component is a noise component.

[0092] When the signal-to-noise ratio (SNR) of a standard sinusoidal signal y1 and a double-exponentially decaying signal y2 is higher than 0 dB, some characteristics of these two signals can be basically distinguished. Therefore, the kurtosis value at an SNR of 0 dB plays a role in distinguishing between the dominant component of partial discharge and the noise component. The process for determining the threshold ε is as follows:

[0093] The expression for a standard sine wave y1 with an amplitude of 1mV and a frequency of 1Hz is as follows:

[0094] y = sin(2πt)

[0095] The expression for the double exponentially decaying signal y2 is as follows:

[0096]

[0097] Where A is the amplitude of the double exponential decay function, which is 3mV; τ is the decay coefficient, set to 0.5μs; t x The signal generation time is 0μs, 5μs, 10μs, 15μs, 20μs, 25μs, 30μs, and 35μs, respectively.

[0098] The threshold ε is calculated as follows:

[0099]

[0100] in, Let y1 be the kurtosis value of a standard sinusoidal signal y1 under Gaussian white noise with a signal-to-noise ratio of 0 dB. y2 represents the kurtosis value of the double exponentially decaying signal y2 under Gaussian white noise with a signal-to-noise ratio of 0dB. The mean of the standard sinusoidal signal y1 is... The mean of the double exponentially decaying signal y2; The standard deviation of the standard sine signal y1. Let y1 be the standard deviation of the double exponentially decaying signal y2, and N be the number of sampling points. Due to the random nature of environmental noise distribution, in practical applications, the kurtosis values ​​of both signals y1 and y2 should be tested 30 times each at a signal-to-noise ratio of 0 dB, and the mean kurtosis values ​​of both signals y1 and y2 should be calculated for each. Then, the maximum value among the mean kurtosis values ​​is taken as the threshold ε.

[0101] Step 3: Filter the noise components; specifically, apply the 3σ criterion to the noise components. White noise follows a normal distribution, while partial discharge signals do not. Therefore, when a portion of the data of a certain mode component falls within... When the noise level is within the specified range, the modal component can be treated as white noise interference and filtered out. The calculation formula for the 3σ criterion filtering is as follows:

[0102]

[0103] in, It is the standard deviation of each modal component. This represents the mean value of each modal component;

[0104] The Gaussian white noise with a normal distribution is filtered out to obtain the filtered noise component, which is the second noise filtering step.

[0105] Step 4: The filtered noise component is superimposed with the dominant partial discharge component to obtain the reconstructed partial discharge signal. The reconstructed partial discharge signal Z is then subjected to improved wavelet threshold denoising to obtain the denoised partial discharge signal.

[0106] The wavelet threshold is improved by applying the following method to the reconstructed partial discharge signal Z:

[0107] The improved threshold expression is as follows:

[0108]

[0109] Where λ is the general threshold, λ′ is the improved wavelet threshold; σ is the standard deviation of the reconstructed partial discharge signal; and N is the number of sampling points.

[0110] The improved threshold function expression is as follows:

[0111]

[0112] Where ω represents the unprocessed wavelet coefficients, and ω′ represents the wavelet coefficients after thresholding.

[0113] Wavelet thresholding denoising was performed on the reconstructed partial discharge signal Z by improving the threshold function and threshold pair.

[0114] The formula for reconstructing the partial discharge signal is obtained by superimposing the filtered noise component with the dominant partial discharge component:

[0115] Z = a1IMF1 + a2IMF2 + ... + a n IMF n +b1IMF1+b2IMF2+…b n IMF n

[0116] a n =Logical{k(IMF n )>3.20}

[0117]

[0118] Where Logical{·} is the logical judgment function, returning 1 if {·} is satisfied, and 0 if {·} is not satisfied; k(·) is used to calculate the kurtosis value; IMFn Let n be the modal component, n be the modal number, and n = 1, 2, ..., K, where K is the number of modes; It is the standard deviation of each modal component. This represents the mean of each modal component.

[0119] The working principle of the partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition in this invention is as follows:

[0120] 1. Image information entropy

[0121] Entropy measures the expected value of a random variable, while information entropy measures the degree of disorder in the distribution of a sample set. Suppose a discrete random variable has n possible outcomes with probabilities p1, p2, ..., p... n Then, its Shannon information entropy (denoted by the symbol H) is expressed as follows:

[0122]

[0123] In the formula, the base of the logarithmic operator is not specified and can be chosen arbitrarily. The base determines the unit of the resulting information entropy. When the base is 2, the unit of information entropy is bit, which is also the most commonly used unit of information entropy. The more dispersed or more uniform the distribution of the random variable, the greater the information entropy value.

[0124] For an image, this random variable refers to the pixel values ​​appearing at different locations within the image. The amount of information contained in the grayscale features distributed at different locations in the image is the one-dimensional information entropy of the image. If p i Let H represent the probability of a pixel with gray value i appearing. Then, the image information entropy H is defined as follows:

[0125]

[0126] 2. Multivariable variational mode decomposition

[0127] A novel variational variational mode decomposition (VMD) multivariate extension is proposed, suitable for processing multivariate measurement data, and incorporates the Frobenius norm (F-norm). As a generalized extension of the original VMD algorithm to multivariate data in multidimensional space, it is key to converting single-channel to multi-channel processing. Its main objective is to extract K predefined multivariate modulated oscillations u from input data x(t) containing C data channels. k (t), that is, x(t)=[x1(t), x2(t),…x C [t], its expression is:

[0128]

[0129] Among them, u k(t)=[u1(t), u2(t), …u C The goal is to extract a set of multivariate modulated oscillations from the input data. The multivariate oscillation modes {u} extracted from the input data x(t) k (t)} must satisfy the following two conditions: (1) the total bandwidth of the extraction modes is minimized; (2) the sum of the extraction modes can accurately recover the original signal u. k (t).

[0130] To achieve the conditions, use Indicate u k The vector analysis of (t) is expressed as follows:

[0131]

[0132] u k The bandwidth of (t) can be increased by using harmonic shifting. The L2 norm of the gradient function is used to estimate the multivariate variational mode decomposition cost function f. Then, the relevant constraint variational optimization problem changes, and its expression becomes:

[0133]

[0134] In the corresponding VMD optimization problem, the multivariate extension of the cost function is given by the following equation:

[0135]

[0136] in This indicates that it corresponds to u k The analytic signal of (t); symbol Represents the partial derivative operation with respect to time; {u k} and {ω k} represent the sets of all K modes and their center frequencies, respectively.

[0137] Another key point to emphasize in equation (4) is the single frequency component ω. k For the entire vector Harmonic mixing. Searching for a single common-frequency component ω in multiple channels. k To obtain multi-element oscillations, it is necessary to estimate the bandwidth of the modulated multi-element oscillation signal. The single-sided spectrum of each channel is based on the center frequency ω. k The signal is shifted and converted from a single channel to a multi-channel signal using the Frobenius norm.

[0138] The introduction of the Frobenius norm allows for topological adjustments to the space, defining the Frobenius norm of matrix W as the norm of each element ω of matrix W. ijThe square root of the sum of the squares of the absolute values ​​of is expressed as:

[0139]

[0140] This makes the representation of f more convenient; its expression is:

[0141]

[0142] in This represents the analytical modulated signal corresponding to the number of channels c and the number of modes k. Unlike the vector signal in equation (4), It is a complex-valued signal with a single component in equation (5). A multivariate variational mode decomposition variational constraint model is constructed, and its expression is:

[0143]

[0144] In the model of equation (5) above, there are multiple linear equality constraints corresponding to the total number of channels. Therefore, the corresponding augmented Lagrangian function changes, and its expression is:

[0145]

[0146] The unconstrained optimization problem described above is solved using the ADMM method. Solving the problem using ADMM transforms the complex optimization problem into a series of iterative sub-optimization problems. These sub-problems are easier to handle because they seek to iteratively minimize the cost function for a single function, rather than simultaneously optimizing the cost function for all optimization variables.

[0147] u is updated iteratively using the alternating direction multiplier method. k ω k Given the Lagrange operator λ, consider the following sub-optimization problem in the nth iteration, whose expression is:

[0148]

[0149] The optimal solution of the variational model, i.e., all estimated frequency domain modes, can be obtained, and its expression is:

[0150]

[0151] In the formula: α is the penalty factor; and x c (ω), λ n (ω), and The Fourier transform of ; n is the number of iterations.

[0152] In the next stage, in order to obtain the center frequency ω kThe update iteratively solves the following sub-optimization problems:

[0153]

[0154] The estimated modal center frequencies are:

[0155]

[0156] It estimates the new frequency as the centroid of the power spectrum of the relevant mode. The update relationship between the mode and the center frequency in the spectral domain is given in Equations (11) and (12), respectively, forming the key to the multivariate variational mode decomposition algorithm.

[0157] The basic steps of the multivariate variational mode decomposition algorithm are as follows:

[0158] (1) Initialization and n;

[0159] (2) Update u according to equations (11) and (12). k and ω k ;

[0160] (3) Update λ:

[0161] (4) For a given discrimination precision e > 0, if If the iteration stops, then return to step 2; otherwise, return to step 2.

[0162] From the final algorithm perspective, the multivariate variational mode decomposition algorithm is relatively simple. First, each mode is continuously updated directly in the frequency domain and finally transformed to the time domain through inverse Fourier transform. Second, the center frequency, which serves as the centroid of the power spectrum of each mode, is re-estimated and updated cyclically in this manner.

[0163] 3. Wavelet decomposition and its improved algorithm

[0164] This invention uses wavelet thresholding to reduce noise components. The approach to noise reduction using wavelet transform is as follows:

[0165] First, after determining the wavelet basis functions and decomposition levels, wavelet decomposition calculations are performed on the signal. Second, the thresholds for high-frequency coefficients at different decomposition scales need to be quantized. Finally, one-dimensional wavelet reconstruction is performed. Among these three steps, the determination of the wavelet threshold and the selection of the threshold function are particularly critical, directly affecting the quality of the denoised PD signal. Specifically, the threshold selection must not only ensure effective noise elimination but also avoid removing the partial discharge signal and, as far as possible, maintain the amplitude of the PD signal.

[0166] The expression for the threshold function is as follows:

[0167]

[0168] Where ω represents the unprocessed wavelet coefficients, and ω′ represents the wavelet coefficients after thresholding.

[0169] The threshold is set using the following expression:

[0170]

[0171] Where λ is the general threshold, λ′ is the improved wavelet threshold of this invention, and this invention tracks the wavelet decomposition layer i based on the general threshold; σ is the standard deviation of the reconstructed PD signal; and N is the number of sampling points.

[0172] Example

[0173] (1) Noise reduction of simulated signals:

[0174] The pure PD waveform is simulated using a double exponential decay function f1 and a double exponential oscillatory decay function f2, respectively, and is achieved by the following equations:

[0175]

[0176]

[0177] In the formula, A1 and A2 are the signal amplitudes of the double exponential decay function f1(t) and the double exponential oscillatory decay function f2(t), respectively, and the two mathematical models are taken as 3mV and 5mV, respectively; τ1 and τ2 are the attenuation coefficients, taken as 0.5μs and 0.6μs, respectively; f c The oscillation frequency is set to 3MHz.

[0178] The sampling frequency was set to 50MHz and the time was 40μs, resulting in a clean PD signal as follows: Figure 3 As shown in (a), Gaussian white noise with an SNR of -1dB was added, along with periodic narrowband interference with specific parameter settings as shown in Table 1. A series of sinusoidal signals of different amplitudes and frequencies generate periodic narrowband interference, achieved by the following formula, with the waveform shown below. Figure 3 As shown in (b). The PD signal after adding noise is shown in [image]. Figure 3 As shown in (c), the original PD signal is no longer recognizable, and its feature information has been completely submerged in noise.

[0179]

[0180] In the formula, A i Here, fi is the amplitude, and fi is the frequency. This is the initial phase angle.

[0181] Table 1

[0182]

[0183] First, the noisy signal X is subjected to multivariate variational mode decomposition after modal parameter optimization (K=6 is obtained according to the optimization process of K). The waveforms of each IMF after decomposition are as follows: Figure 4 As shown in Table 2, kurtosis was calculated for IMF1 to IMF6 respectively, and the kurtosis values ​​for each IMF are shown in Table 2.

[0184] Table 2

[0185] Modal Components (IMF) <![CDATA[Kurtosis value k n > IMF1 34.7300 IMF2 37.8184 IMF3 3.4475 IMF4 2.7999 IMF5 3.1453 IMF6 2.5677

[0186] Simulation results for the standard sinusoidal signal y1 and the double exponentially decaying signal y2 at different signal-to-noise ratios are as follows: Figure 5 As shown, the kurtosis value at a signal-to-noise ratio of 0dB can distinguish between the dominant partial discharge (PD) components and noise components. The kurtosis values ​​of IMF1, IMF2, and IMF3 are all greater than 3.20, while the kurtosis values ​​of IMF4, IMF5, and IMF6 are less than the threshold of 3.20. Therefore, IMF1 to IMF3 are classified as PD dominant components, and the remaining modal components are considered noise components. Noise is filtered out using the 3σ criterion. The filtered signal is then superimposed with the PD dominant components for reconstruction. Finally, an improved wavelet threshold denoising method is used for noise reduction, resulting in a denoised signal with a relatively small error compared to the original signal. The result is shown in the figure. Figure 6 As shown.

[0187] (2) Noise reduction of the measured signal:

[0188] On-site detection revealed partial discharge at a mid-joint of a 529m long XLPE cable connecting the ring main unit to the distribution room. The defect signal was as follows: Figure 7 (a) At this time, the sampling frequency of the field device is 369Hz, and the noise content of the measured signal is relatively small. Therefore, a certain degree of Gaussian white noise is added to mask it, resulting in the following: Figure 7 (b) shows the noisy measured PD signal. The denoised PD signal is obtained by denoising using the denoising method proposed in this invention, as shown below. Figure 8 As shown, the waveform of the denoised PD signal is smooth and has little residual noise, indicating that it can effectively suppress white noise.

[0189] This invention addresses the problems of white noise, periodic narrowband interference, and weak adaptability in the denoising process during partial discharge detection of cable terminals. It proposes a novel adaptive multivariate variational mode decomposition (MMD) denoising method based on image information entropy. The aim is to accurately denoise noisy PD signals, achieving good noise suppression and restoring the waveform characteristics of the PD signal while maximizing algorithm efficiency. First, the noisy signal is converted into a grayscale image, and the image information entropy is calculated. Then, the number of modes K in the multivariate variational mode decomposition is optimized by combining the Pearson correlation coefficient and execution efficiency to determine the optimal value before decomposing the noisy PD signal. Second, the kurtosis value of each intrinsic mode component is calculated, and the nature of the mode component is determined based on a threshold, classifying it as either a dominant PD component or a noise component. Then, a mathematical statistical method using the 3σ criterion is employed to filter out normally distributed white noise. Finally, the reconstructed signal is denoised using an improved wavelet thresholding method to obtain the denoised PD signal.

Claims

1. A method for denoising partial discharge signals based on image information entropy and multivariate variational mode decomposition, characterized in that, The specific steps are as follows: Step 1: Decompose the noisy partial discharge signal to determine the number of modes in the multivariate variational mode decomposition algorithm; Step 2: Determine whether the modal characteristics belong to the dominant component of partial discharge or the noise component; Step 3: Filter the noise components; Step 4: The filtered noise component is superimposed with the dominant partial discharge component to obtain the reconstructed partial discharge signal. The reconstructed partial discharge signal Z is then subjected to improved wavelet threshold denoising to obtain the denoised partial discharge signal. The improvement of the wavelet threshold on the reconstructed partial discharge signal Z in step 4 specifically involves: The improved threshold expression is as follows: Where λ is the general threshold, λ′ is the improved wavelet threshold; σ is the standard deviation of the reconstructed partial discharge signal; and N is the number of sampling points. The improved threshold function expression is as follows: Where ω represents the unprocessed wavelet coefficients, and ω′ represents the wavelet coefficients after thresholding. Wavelet thresholding denoising was performed on the reconstructed partial discharge signal Z by improving the threshold function and threshold pair.

2. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: Decompose the noisy partial discharge signal X using a multivariate variational mode decomposition algorithm to obtain the intrinsic mode components (IMFs). n n = 1, 2, ..., K, where n is the mode number and K is the number of modes. The initial conditions are defined as: K = 1, and the maximum number of iterations is 2000. Step 1.2: By superimposing intrinsic mode components (IMFs) n The reconstructed partial discharge signal Y after the first noise filtering is obtained and converted into a two-dimensional image in JPG format; Step 1.3: Obtain a grayscale image from the two-dimensional image through grayscale processing, and calculate the one-dimensional information entropy H of the grayscale image; Step 1.4: Calculate the Pearson correlation coefficient ρ between the noisy partial discharge signal X and the reconstructed partial discharge signal Y, and the execution efficiency η of the multivariate variational mode decomposition algorithm; Step 1.5: Determine if ρ > 0.

95. If not, then K = K + 1 and return to step 1.

1. Otherwise, determine if the information entropy H is minimum. If it is minimum, output the modality number K as the modality number of the multivariate variational mode decomposition algorithm. Otherwise, return to step 1.

1.

3. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 2, characterized in that, The formula for obtaining a grayscale image from a two-dimensional image through grayscale processing, as described in step 1.3, is: Gray=0.2126R+0.7152G+0.0772B Where R, G, and B represent the pixels of the red, green, and blue primary color components in the image, respectively.

4. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 2, characterized in that, The formula for calculating the one-dimensional information entropy H of the grayscale image in step 1.3 is: Where, p i This represents the probability of a pixel with a grayscale value of i appearing.

5. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 2, characterized in that, The formula for calculating the Pearson correlation coefficient ρ between the noisy partial discharge signal X and the reconstituted partial discharge signal Y in step 1.3 is as follows: Where X and Y are the noisy partial discharge signal and the reconstituted partial discharge signal, respectively; cov(X,Y) is the covariance of the noisy partial discharge signal and the reconstituted partial discharge signal; σ X σ Y E(X) and E(Y) are the standard deviations of the noisy partial discharge signal and the reconstructed partial discharge signal, respectively; E(X) and E(Y) are the expected values ​​of the noisy partial discharge signal and the reconstructed partial discharge signal, respectively.

6. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 2, characterized in that, The formula for calculating the execution efficiency η of the multivariate variational mode decomposition algorithm is as follows: Where ρ is the Pearson correlation coefficient and t is the running time of the multivariate variational mode decomposition algorithm, in seconds.

7. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 1, characterized in that, Step 2 is as follows: Step 2.1: Based on the determined number of modes, the partial discharge signal is decomposed using a multivariate variational mode decomposition algorithm to obtain each mode component; Step 2.2: Calculate the kurtosis value of each modal component; Step 2.3: Calculate the kurtosis values ​​of a standard sine wave y1 with an amplitude of 1mV and a frequency of 1Hz and a double exponential decaying signal y2 under Gaussian white noise with a signal-to-noise ratio of 0dB. and because Therefore, a larger value of 3.20 is used as the threshold ε to distinguish the characteristic properties of each modal component: when the kurtosis value of a modal component is greater than 3.20, the modal component is determined to be the dominant component of partial discharge; otherwise, the modal component is a noise component.

8. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 1, characterized in that, Step 3 involves applying a 3σ criterion filter to the noise components. The calculation formula for the 3σ criterion filter is as follows: in, It is the standard deviation of each modal component. This represents the mean value of each modal component; The Gaussian white noise with a normal distribution is filtered out to obtain the filtered noise component, which is the second noise filtering step.

9. The partial discharge signal denoising method based on image information entropy and multivariate variational mode decomposition according to claim 1, characterized in that, Step 4 involves superimposing the filtered noise component with the dominant partial discharge component to obtain the reconstructed partial discharge signal. The calculation formula is as follows: Z=a1IMF1+a2IMF2+…a n MFI n +b1IMF1+b2IMF2+…b n MFI n Where Logical{·} is the logical judgment function, returning 1 if {·} is satisfied, and 0 if {·} is not satisfied; k(·) is used to calculate the kurtosis value; IMF n Let n be the modal component, n be the modal number, and n = 1, 2, ..., K, where K is the number of modes; It is the standard deviation of each modal component. This represents the mean of each modal component.

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