Partial discharge signal denoising method based on improved variational mode decomposition algorithm

Abstract

The invention belongs to the field of partial discharge detection of high-voltage electrical equipment, and discloses a partial discharge signal denoising method based on an improved variational mode decomposition algorithm, and the method comprises the steps: decomposing an original partial discharge signal into a plurality of intrinsic mode components according to an initial decomposition layer number and an initial penalty factor; determining a target function value; on the basis of a northern eagle optimization algorithm, the number of decomposition layers and penalty factors of an iterative variational mode decomposition algorithm are updated until the number of iterations reaches a preset number of times or the difference of objective function values between two adjacent iterations is smaller than a preset threshold value; screening the target intrinsic mode components based on a kurtosis criterion; and noise in the screened intrinsic mode component is filtered based on a wavelet threshold algorithm, and a denoised partial discharge signal is obtained through signal reconstruction. By combining the variational mode decomposition algorithm, the northern eagle optimization algorithm, the kurtosis criterion and the wavelet threshold algorithm, partial discharge signals can be accurately decomposed, and a good denoising effect is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of partial discharge detection of high-voltage electrical equipment, and particularly relates to a method for denoising partial discharge signals based on an improved variational mode decomposition algorithm. Background Technique

[0002] A partial discharge signal refers to a discharge phenomenon that occurs only in some regions of an insulator under the action of an electric field and does not form a through-discharge channel. This phenomenon usually occurs in high-voltage electrical equipment such as transformers, generators, cables, and switchgear, and is an important diagnostic signal for the insulation aging and faults of power equipment. Therefore, it is crucial to monitor the partial discharge signals of high-voltage electrical equipment.

[0003] However, in a complex interference environment and different monitoring angles, the partial discharge signal will be submerged by noise or signal attenuation will occur, resulting in the collected partial discharge signal being unable to accurately reflect the true partial discharge situation of the high-voltage electrical equipment. Therefore, there is an urgent need to provide a method for denoising partial discharge signals. Summary of the Invention

[0004] The purpose of the present invention is to combine the variational mode decomposition algorithm, the northern goshawk optimization algorithm, the kurtosis criterion, and the wavelet threshold algorithm, so as to accurately decompose the partial discharge signal into multiple target intrinsic mode components, screen out effective intrinsic mode components through the kurtosis criterion, realize the denoising process of the partial discharge signal, and further denoise the partial discharge signal through the wavelet threshold algorithm, achieving a better denoising effect. Furthermore, the denoised partial discharge signal can accurately reflect the true partial discharge situation of the high-voltage electrical equipment.

[0005] In the first aspect, an embodiment of the present invention provides a method for denoising partial discharge signals based on an improved variational mode decomposition algorithm, and the method includes:

[0006] Initialize the decomposition parameters of the variational mode decomposition algorithm to obtain the initial decomposition level and the initial penalty factor;

[0007] Obtain the original partial discharge signal to be denoised, and decompose the partial discharge signal into multiple intrinsic mode components according to the initial decomposition level and the initial penalty factor;

[0008] Take the difference between the sum of the energies of the multiple intrinsic mode components obtained by decomposition and the energy of the original partial discharge signal as the objective function value;

[0009] Based on the northern goshawk optimization algorithm, continuously update and iterate the decomposition level and the penalty factor of the variational mode decomposition algorithm until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determine multiple target intrinsic mode components;

[0010] Screen the multiple target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components;

[0011] Filter the noise in the screened intrinsic mode components based on the wavelet threshold algorithm to obtain the denoised intrinsic mode components, and perform signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal.

[0012] Optionally, continuously update and iterate the decomposition layer number and penalty factor of the variational mode decomposition algorithm based on the northern goshawk optimization algorithm until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determine to obtain multiple target intrinsic mode components, including:

[0013] Update the initial decomposition layer number and initial penalty factor based on the northern goshawk optimization algorithm to obtain the updated decomposition layer number and penalty factor;

[0014] [[ID=ID=14]]Decompose the original partial discharge signal according to the updated decomposition layer number and penalty factor, and calculate the objective function value based on the multiple intrinsic mode components obtained by the decomposition;

[0015] Continuously iteratively update the updated decomposition layer number and penalty factor based on the northern goshawk optimization algorithm, and calculate the objective function value each time the decomposition layer number and penalty factor are updated and iterated until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determine to obtain the target decomposition layer number and target penalty factor;

[0016] Decompose the original partial discharge signal into multiple target intrinsic mode components according to the target initial decomposition layer number and target initial penalty factor.

[0017] Optionally, the screening of the multiple target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components includes:

[0018] Calculate the kurtosis values of the multiple target intrinsic mode components respectively;

[0019] Compare the kurtosis value of each target intrinsic mode component with the kurtosis threshold;

[0020] Use the target intrinsic mode components with kurtosis values greater than the kurtosis threshold as the screened intrinsic mode components.

[0021] Optionally, the filtering of the noise in the screened intrinsic mode components based on the wavelet threshold algorithm to obtain the denoised intrinsic mode components, and the signal reconstruction of the denoised intrinsic mode components to obtain the denoised partial discharge signal includes:

[0022] Transform the filtered intrinsic mode variables into wavelet coefficients in different frequency ranges through the wavelet threshold algorithm;

[0023] Process the detail coefficients in the obtained wavelet coefficients through the preset threshold of the wavelet threshold algorithm to obtain the processed wavelet coefficients;

[0024] Perform inverse transformation on the processed wavelet coefficients to obtain the denoised intrinsic mode components;

[0025] Sum up the denoised intrinsic mode components to obtain the denoised partial discharge signal.

[0026] Optionally, the process of processing the detail coefficients in the obtained wavelet coefficients through the preset threshold of the wavelet threshold algorithm to obtain the processed wavelet coefficients includes:

[0027] Determine the preset threshold of the wavelet threshold algorithm based on the threshold selection rule, where the threshold selection rule is determined based on the standard deviation of the filtered intrinsic mode components and the length of the wavelet coefficients;

[0028] Set the detail coefficients in the obtained wavelet coefficients that are lower than the preset threshold of the wavelet threshold algorithm to 0.

[0029] In a second aspect, an embodiment of the present invention provides a partial discharge signal denoising device based on an improved variational mode decomposition algorithm, and the device includes:

[0030] A decomposition parameter initialization module, configured to initialize the decomposition parameters of the variational mode decomposition algorithm to obtain an initial decomposition layer number and an initial penalty factor;

[0031] A partial discharge signal decomposition module, configured to obtain the original partial discharge signal to be denoised, and decompose the original partial discharge signal into a plurality of intrinsic mode components according to the initial decomposition layer number and the initial penalty factor;

[0032] A target function value determination module, configured to use the difference between the sum of the energies of the decomposed multiple intrinsic mode components and the energy of the original partial discharge signal as the target function value;

[0033] A decomposition parameter update module, configured to continuously update and iterate the decomposition layer number and the penalty factor of the variational mode decomposition algorithm based on the northern goshawk optimization algorithm until the number of iterations reaches a preset number, or the difference between the target function values of two adjacent iterations is less than a preset threshold, and determine a plurality of target intrinsic mode components;

[0034] An intrinsic mode component screening module, configured to screen the plurality of target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components;

[0035] The partial discharge signal denoising module is used to filter out the noise in the selected intrinsic mode components based on the wavelet threshold algorithm, obtain the denoised intrinsic mode components, and perform signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal.

[0036] In a third aspect, an embodiment of the present invention provides an electronic device, including:

[0037] At least one processor;

[0038] A memory for storing executable instructions of the at least one processor;

[0039] Wherein, the at least one processor is configured to execute the instructions to implement the method described in the first aspect.

[0040] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, when the instructions in the computer-readable storage medium are executed by a processor of an electronic device, enabling the electronic device to execute the method described in the first aspect.

[0041] In a fifth aspect, an embodiment of the present invention provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the method described in the first aspect.

[0042] By combining the variational mode decomposition algorithm, the northern goshawk optimization algorithm, the kurtosis criterion, and the wavelet threshold algorithm, the embodiment of the present invention can accurately decompose the original partial discharge signal into multiple target intrinsic mode components, screen out the effective intrinsic mode components through the kurtosis criterion, realize the denoising process of the original partial discharge signal, and further perform denoising processing on the original partial discharge signal through the wavelet threshold algorithm, achieving a better denoising effect. Furthermore, the denoised partial discharge signal can accurately reflect the true partial discharge situation of high-voltage electrical equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 FIG. 1 is a flowchart of a method for denoising partial discharge signals based on an improved variational mode decomposition algorithm provided by an embodiment of the present invention;

[0044] Figure 2 is Figure 1 a flowchart of the specific implementation of S141 in FIG. 1;

[0045] FIG. 3(a) is a time-domain diagram of a pure partial discharge signal, and FIG. 3(b) is a frequency-domain diagram of a pure partial discharge signal;

[0046] Figure 4(a) is the time-domain diagram of the mixed signal obtained by superimposing Gaussian white noise and periodic pulse interference on the pure discharge signal; Figure 4(b) is the time-domain diagram of the mixed signal obtained by superimposing Gaussian white noise and periodic pulse interference on the pure discharge signal;

[0047] Figure 5 It is a schematic diagram of the optimization iteration curve of the NGO algorithm provided by the embodiment of the present invention;

[0048] Figure 6(a) is the time-domain diagram of IMF1 to IMF4 when the optimal parameters [K = 4, α = 510] are obtained by NGO optimization; Figure 6(b) is the frequency-domain diagram of IMF1 to IMF4 when the optimal parameters [K = 4, α = 510] are obtained by NGO optimization;

[0049] Figure 7(a) is a schematic diagram of the reconstructed signal obtained by reconstructing the signal based on IMF1 and IMF3, and Figure 7(b) is a schematic diagram of the reconstructed signal after denoising by the wavelet threshold algorithm;

[0050] Figure 8(a) is a schematic diagram of the denoising result of denoising the partial discharge signal by NGO-VMD-Wavelet; Figure 8(b) is a schematic diagram of the denoising result of denoising the partial discharge signal by PSO-VMD-Wavelet; Figure 8(c) is a schematic diagram of the denoising result of denoising the partial discharge signal by EMD-Wavelet; Figure 8(d) is a schematic diagram of the denoising result of denoising the partial discharge signal by CEEMDAN-Wavelet;

[0051] Figure 9 It is a schematic diagram of the partial discharge signal in the ring main unit collected by the ultrasonic sensor.

[0052] Figure 10 It is a schematic diagram of the iteration number curve of the NGO-VMD algorithm and the PSO-VMD algorithm;

[0053] Figure 11(a) is a schematic diagram of the denoising result of NGO-VMD-Wavelet provided by the embodiment of the present invention; Figure 11(b) is a schematic diagram of the denoising result of EMD-Wavelet; Figure 11(c) is a schematic diagram of the denoising result of CEEMDAN-Wavelet.

[0054] Figure 12 It is a schematic diagram of a partial discharge signal denoising device based on an improved variational mode decomposition algorithm provided by the embodiment of the present invention. Detailed implementation manners

[0055] The present invention will be described in detail below through embodiments.

[0056] Partial discharge signal refers to the discharge phenomenon that occurs only in some regions of an insulator under the action of an electric field and does not form a through-discharge channel. This phenomenon usually occurs in high-voltage electrical equipment such as transformers, generators, cables, and switchgear, and is an important diagnostic signal for the insulation aging and faults of power equipment. Therefore, it is crucial to monitor the partial discharge signals of high-voltage electrical equipment.

[0057] However, in a complex interference environment and under different monitoring angles, partial discharge signals will be submerged by noise or suffer from signal attenuation, etc., resulting in the collected partial discharge signals being unable to accurately reflect the true partial discharge situation of high-voltage electrical equipment. For this reason, there is an urgent need to provide a method for denoising partial discharge signals.

[0058] The embodiment of the present invention provides a method for denoising partial discharge signals based on an improved variational mode decomposition algorithm (Variational Mode Decomposition, VMD). The method for denoising partial discharge signals provided by the embodiment of the present invention can be applicable to many application scenarios. For example, it can denoise the partial discharge signals in a ring main unit to accurately reflect the true partial discharge situation in the ring main unit. In practical applications, the partial discharge signal can be a partial discharge ultrasonic signal, etc., and the embodiment of the present invention does not make specific limitations in this regard.

[0059] Moreover, through simulation data and experimental measured data, combined with three denoising effect evaluation indicators: signal-to-noise ratio, root mean square error, and waveform similarity, the effectiveness of the method for denoising partial discharge signals based on the improved VMD is verified.

[0060] Next, a method for denoising partial discharge signals based on an improved variational mode decomposition algorithm provided by the embodiment of the present invention will be elaborated in detail. As Figure 1 shown, a method for denoising partial discharge signals based on an improved variational mode decomposition algorithm provided by the embodiment of the present invention may include the following steps:

[0061] S110, initialize the decomposition parameters of the variational mode decomposition algorithm to obtain the initial decomposition level and the initial penalty factor.

[0062] Specifically, the VMD algorithm is an adaptive signal decomposition method mainly used to process non-recursive, non-linear, and non-stationary signals. This algorithm constructs a variational problem and continuously iterates to find the optimal solution. Specifically, the core idea of VMD is to represent the original signal (i.e., the partial discharge signal to be denoised) as the sum of K finite-bandwidth intrinsic mode function IMFs, maintain the orthogonality between them, and ensure that the sum of their estimated bandwidths is minimized. It should be noted that those skilled in the art should be able to understand the principle of the VMD algorithm, and it will not be elaborated here.

[0063] When performing local discharge signal decomposition in VMD, each intrinsic mode function has the property of orthogonality. From the perspective of energy, the sum of the energies of each component is equal to the total energy of the original local discharge signal. Therefore, the decomposition process of VMD can maintain the conservation of energy.

[0064] As can be seen from the above description, the VMD algorithm is an adaptive signal decomposition method. Before decomposing the local discharge signal by the VMD algorithm, it is necessary to set the decomposition parameters of the VMD algorithm, which can include the decomposition layer number K and the penalty factor α. Among them, the size of the penalty factor α directly affects the bandwidth of each IMF component. The larger the α value, the smaller the bandwidth of the IMF component; while the smaller the α value, the larger the bandwidth of the IMF component. And the selection of the K value is directly related to the quality of the decomposed intrinsic mode functions. An incorrect K value may lead to over-decomposition or under-decomposition of the local discharge signal.

[0065] When denoising the local discharge signal, first initialize the decomposition parameters of the variational mode decomposition algorithm to obtain the initial decomposition layer number K and the initial penalty factor α. Among them, the initial decomposition layer number K and the initial penalty factor α can be set according to the actual situation, and the embodiments of the present invention do not make specific limitations on this.

[0066] S120, obtain the original local discharge signal to be denoised, and decompose the original local discharge signal into multiple intrinsic mode functions according to the initial decomposition layer number and the initial penalty factor.

[0067] After obtaining the initial decomposition layer number K and the initial penalty factor α, decompose the original local discharge signal to be denoised according to the initial decomposition layer number K and the initial penalty factor α to obtain multiple intrinsic mode functions IMF.

[0068] S130, use the difference between the sum of the energies of the multiple intrinsic mode functions obtained by decomposition and the energy of the original local discharge signal as the objective function value.

[0069] The energy expressions of the local discharge signal to be denoised and each intrinsic mode function component are as follows:

[0070]

[0071] Among them, E is the energy value of the local discharge signal; f(t) is the signal sequence, and n is the number of sampling points.

[0072] When each IMF is orthogonal, the energy E of the original local discharge signal x and the total energy E of each IMF obtained by decomposition sum are equal, and the expression is as follows:

[0073] E x =E1 + E2 + E3 + … + E K =Esum

[0074] When the IMFs are not orthogonal, E x and E sum will have an energy difference E err , and the expression is as follows:

[0075]

[0076] where, E err is used to measure the difference between the total energy of each intrinsic mode component and the total energy of the original partial discharge signal. The larger its value, the more serious the over - decomposition of the partial discharge signal. And the closer its value is to or equal to 0, the more reasonable the decomposition of the partial discharge signal. Therefore, the difference between the total energy of the intrinsic mode components and the total energy of the original partial discharge signal can be used as the objective function value.

[0077] S140. Based on the Northern Goshawk Optimization algorithm, update and iterate the decomposition layer number and penalty factor of the variational mode decomposition algorithm until the number of iterations reaches the preset number, or the difference between the objective function values of two adjacent iterations is less than the preset threshold, to obtain multiple target intrinsic mode components.

[0078] Among them, the preset number and the preset threshold can be determined according to the actual situation. If the number of iterations does not reach the preset number, or the difference between the objective function values of two adjacent iterations is less than the preset threshold, it means that the decomposition parameters of the variational mode decomposition algorithm have not reached the optimal solution and the decomposition of the partial discharge signal is unreasonable. To improve the accuracy and effect of the decomposition of the partial discharge signal, an embodiment of the present invention proposes a method for selecting VMD parameters optimized based on NGO (Northern Goshawk Optimization algorithm) to obtain the best decomposition parameters. This method can more accurately determine the values of K and α, so as to achieve more accurate decomposition of the partial discharge signal.

[0079] As an implementation manner of an embodiment of the present invention, in S140, based on the Northern Goshawk Optimization algorithm, continuously update and iterate the decomposition layer number and penalty factor of the variational mode decomposition algorithm until the number of iterations reaches the preset number, or the difference between the objective function values of two adjacent iterations is less than the preset threshold, to determine and obtain multiple target intrinsic mode components. As Figure 2 shown, it may include the following steps:

[0080] S141. Based on the Northern Goshawk Optimization algorithm, update the initial decomposition layer number and the initial penalty factor to obtain the updated decomposition layer number and penalty factor.

[0081] S142. Decompose the original partial discharge signal according to the updated decomposition layer number and penalty factor, and calculate the objective function value based on the multiple intrinsic mode components obtained by the decomposition.

[0082] S143, Based on the decomposition level and penalty factor after iterative update by the Northern Goshawk Optimization Algorithm, and each time the decomposition level and penalty factor are updated iteratively, the objective function value is calculated until the number of iterations reaches the preset number of times, or the difference between the objective function values of two adjacent iterations is less than the preset threshold, to determine the target decomposition level and target penalty factor.

[0083] S144, Decompose the original partial discharge signal into multiple target intrinsic mode components according to the target initial decomposition level and target initial penalty factor.

[0084] Specifically, in order to find the optimal decomposition level K and penalty factor α, energy tracking is used to recursively solve VMD. The optimization objective is to minimize the difference between the sum of the energies of multiple IMFs and the energy of the original partial discharge signal. The NGO algorithm is used to find the combination with the minimum energy difference. That is to say, the values of K and α are continuously updated through the NGO algorithm until the combination with the minimum energy difference is found. That is, the target decomposition level and target penalty factor are found. After decomposing the partial discharge signal according to the target decomposition level and target penalty factor, at this time, the calculated objective function value is the smallest, and the obtained multiple intrinsic mode components IMF are reasonable, that is, multiple target intrinsic mode components are obtained.

[0085] It should be noted that NGO (Northern Goshawk Optimization) is a swarm intelligence optimization algorithm that simulates the behavior of northern goshawks in identifying and hunting prey. Those skilled in the art should be able to understand the principle of NGO. The NGO algorithm includes core elements such as the position of the goshawk, the number of the goshawk population, and the position of the prey. In the embodiment of the present invention, the position of the goshawk corresponds to the current [K, α]; the number of the goshawk population corresponds to the number of [K, α] generated currently, and the number of the goshawk population can be any natural number N; the position of the prey represents a better [K, α]. At the beginning of the algorithm operation, N [K, α] are randomly generated, that is, [K i (0) ,α i (0) , i = 1... N, that is, N goshawks. If [K i ,α i has been iteratively updated n times currently, then, the position of the goshawk can be recorded as [K i (n) ,α i (n) , at this time, the position of the prey is based on the current [K i (n) ,α i (n), the next target position accurately optimized and adjusted, after the (n + 1)-th iterative optimization calculation, the position of the goshawk changes to [K i (n+1) , α i (n+1) , and then continue to enter the next iteration until the optimization process ends.

[0086] As can be seen from the above description, the embodiment of the present invention optimizes the two parameters K and α in the VMD decomposition based on the NGO algorithm to construct the NGO-VMD method. The following elaborates on the NGO-VMD method in detail.

[0087] First, initialize the positions of the population members, that is, the two-dimensional variable decomposition layer number K and the penalty factor α generated for the first time, in the search space:

[0088]

[0089] Among them, X is the matrix of the northern goshawk population, and X i is the initial solution of the i-th goshawk; x i,j is the value of the i-th goshawk in the j-th dimension. In the embodiment of the present invention, j = 2, x i,,1 = K i， x i,2 = α i .

[0090] The objective function vector is as follows:

[0091]

[0092] Among them, F(X) is the objective function vector, and F(X i ) is the objective function value corresponding to the i-th solution.

[0093] In each iteration of the algorithm, each time a goshawk X i starts to randomly capture prey (that is, explore a position with a smaller objective function), the initial positions of the prey are randomly distributed among the positions of the goshawk population and start to chase. The goshawk moves from the current position to the prey position, which is a process of updating its own parameters to approximate the minimum of the objective function value. Until all goshawks in the goshawk population complete the above process, this iteration is completed.

[0094] After each iteration is completed, the positions of the goshawks and the prey are updated. The positions of the goshawks and the prey are continuously updated through the Northern Goshawk Optimization Algorithm. Each time the positions of the goshawks and the prey are updated and iterated, the objective function values corresponding to all goshawk positions are calculated, and the objective function values corresponding to all goshawk positions are compared to find the minimum value among all the calculated objective function values. The difference is calculated with the minimum objective function value obtained in the previous iteration. If the difference is less than the preset threshold, the iteration stops, or until the number of iterations reaches the preset number, the minimum energy difference combination is obtained. Through the minimum energy difference combination Decompose the original partial discharge signal to obtain multiple target intrinsic mode components.

[0095] S150. Based on the kurtosis criterion, screen multiple target intrinsic mode components to obtain the screened intrinsic mode components.

[0096] Kurtosis (Ku) is a numerical statistic reflecting the distribution characteristics of a random variable and is often used to describe the distribution characteristics of vibration signals. Its mathematical expression is:

[0097]

[0098] Among them, is the mean of the signal x i ; σ is the standard deviation of the signal x i ; N is the signal length.

[0099] The larger the kurtosis value, the more impact components there are in the signal at this time. In the embodiments of the present invention, for reference, the kurtosis value of the normal distribution curve is 3. Since the partial discharge signal appears as a sudden pulse signal in the time domain, its kurtosis value is higher than that of the normal distribution curve. The kurtosis values of white noise and common periodic narrowband interference are relatively small. When the kurtosis value of the measured signal exceeds 3, it can be considered as a partial discharge signal. Among the multiple intrinsic mode variables IMF obtained by decomposition through the VMD algorithm, according to the kurtosis criterion, multiple intrinsic mode variables IMF are screened, that is, the intrinsic mode variables IMF with Ku>3 are retained, so as to screen out the effective intrinsic mode variables IMF among the multiple target intrinsic mode variables IMF, achieving the purpose of removing white noise and common periodic narrowband interference in the partial discharge signal.

[0100] As an implementation manner of the embodiments of the present invention, S150. Based on the kurtosis criterion, screen multiple target intrinsic mode components to obtain the screened intrinsic mode components, which may include the following three steps, namely step a1 to step a3:

[0101] Step a1, calculate the kurtosis values of multiple target intrinsic mode components respectively.

[0102] Step a2: Compare the kurtosis value of each target intrinsic mode component with the kurtosis threshold.

[0103] Step a3: Use the target intrinsic mode components with kurtosis values greater than the kurtosis threshold as the selected intrinsic mode components.

[0104] Specifically, the multiple target intrinsic mode components IMF obtained by decomposition are data sequences. For each data sequence, its kurtosis value can be calculated, that is, the kurtosis value of each target intrinsic mode component can be calculated. It is generally considered that the kurtosis value of the discharge signal is relatively high, that is, the relatively sharp signal is the core signal. By comparing the kurtosis value of each target intrinsic mode component with the kurtosis threshold and using the target intrinsic mode components with kurtosis values greater than the kurtosis threshold as the selected intrinsic mode components, useful intrinsic mode components IMF can be screened out. Among them, the kurtosis threshold can be determined according to the actual situation. For example, if the kurtosis value of the normal distribution curve is 3, the kurtosis threshold can be 3.

[0105] S160: Based on the wavelet threshold algorithm, filter the noise in the selected intrinsic mode components to obtain the denoised intrinsic mode components, and perform signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal.

[0106] After the above steps, the IMF containing the partial discharge signal will still contain background interference such as a certain degree of white noise. Based on the non-stationary and time-correlation characteristics of the discharge signal, the wavelet threshold algorithm (Wavelet) is used to further filter the residual interference signal. The main idea of wavelet threshold denoising is to use the wavelet basis function to transform the non-stationary signal. By changing the scale and position of the basis function, the IMF containing the partial discharge signal (that is, the selected intrinsic mode component IMF) is transformed into wavelet coefficients in different frequency ranges. Generally, it is considered that the detail coefficients in the high-frequency band contain noise, while the approximation coefficients in the low-frequency band contain the main characteristics of the signal. By setting the threshold function to process the detail coefficients and setting the detail coefficients below the threshold to zero, the noise components are removed. Specifically, it is shown as the following formula:

[0107]

[0108] where ω j,k is the wavelet coefficient and λ is the threshold.

[0109] As an implementation manner of the embodiment of the present invention, S160: Based on the wavelet threshold algorithm, filter the noise in the selected intrinsic mode components to obtain the denoised partial discharge signal, which may include the following steps, namely step b1 to step b3:

[0110] Step b1: Use the wavelet threshold algorithm to transform the selected intrinsic mode variables into wavelet coefficients in different frequency ranges.

[0111] Step b2: Process the detail coefficients in the obtained wavelet coefficients through a preset threshold of the wavelet threshold algorithm to obtain processed wavelet coefficients.

[0112] Step b3: Perform inverse transformation on the processed wavelet coefficients to obtain the denoised intrinsic mode component.

[0113] Step b4: Sum up the denoised intrinsic mode components to obtain the denoised partial discharge signal.

[0114] Specifically, after transforming the selected intrinsic mode variables into wavelet coefficients in different frequency ranges through the wavelet threshold algorithm, since the detail coefficients in the wavelet coefficients usually contain noise, the detail coefficients in the wavelet coefficients are processed, that is, the detail coefficients are set to 0 to obtain the processed wavelet coefficients. Then, inverse transformation is performed on the remaining wavelet coefficients to obtain the denoised intrinsic mode components, and then the denoised intrinsic mode components are summed up to reconstruct the effective intrinsic mode components of the partial discharge signal, thereby completing the filtering of the mixed noise in the partial discharge signal.

[0115] As an implementation manner of an embodiment of the present invention, step b2: Process the detail coefficients in the obtained wavelet coefficients through a preset threshold of the wavelet threshold algorithm to obtain processed wavelet coefficients, which may include the following steps, namely step b21 and step b22:

[0116] Step b21: Determine the preset threshold of the wavelet threshold algorithm based on the threshold selection rule.

[0117] Among them, the threshold selection rule is determined based on the standard deviation of the selected intrinsic mode component and the length of the wavelet coefficients, as shown in the following formula:

[0118]

[0119] σ is the standard deviation of the selected intrinsic mode component, N is the length of the wavelet coefficients.

[0120] Step b22: Set the detail coefficients in the obtained wavelet coefficients that are lower than the preset threshold of the wavelet threshold algorithm to 0.

[0121] Since the detail coefficients in the wavelet coefficients usually contain noise, the detail coefficients in the obtained wavelet coefficients that are lower than the preset threshold of the wavelet threshold algorithm are set to 0 to obtain the processed wavelet coefficients.

[0122] The technical solution provided by the embodiment of the present invention first initializes the decomposition parameters of the variational mode decomposition algorithm to obtain the initial decomposition layer number and the initial penalty factor; then obtains the original partial discharge signal to be denoised, and decomposes the original partial discharge signal into multiple intrinsic mode components according to the initial decomposition layer number and the initial penalty factor; takes the difference between the sum of the energies of the multiple intrinsic mode components obtained by the decomposition and the energy of the original partial discharge signal as the objective function value; continuously updates the decomposition layer number and the penalty factor of the variational mode decomposition algorithm based on the northern goshawk optimization algorithm until the number of iterations reaches the preset number, or the difference between the objective function values of two adjacent iterations is less than the preset threshold, indicating that the original partial discharge signal is correctly decomposed, and the obtained multiple target intrinsic mode components are more accurate.

[0123] Then, based on the kurtosis criterion, multiple target intrinsic mode components are screened, and the effective intrinsic mode variables IMF in the multiple target intrinsic mode variables IMF are screened out, achieving the purpose of removing white noise and common periodic narrowband interference in the original partial discharge signal. To improve the denoising effect of the original partial discharge signal, the noise in the screened intrinsic mode components is further filtered by the wavelet threshold algorithm, and the denoised intrinsic mode components are signal-reconstructed to obtain the denoised partial discharge signal. It can be seen that the embodiment of the present invention combines the variational mode decomposition algorithm, the northern goshawk optimization algorithm, the kurtosis criterion, and the wavelet threshold algorithm, which can accurately decompose the original partial discharge signal into multiple target intrinsic mode components, screen out effective intrinsic mode components through the kurtosis criterion, achieve the denoising process of the original partial discharge signal, and further denoise the original partial discharge signal through the wavelet threshold algorithm, achieving a better denoising effect. Furthermore, the denoised partial discharge signal can accurately reflect the true partial discharge situation of high-voltage electrical equipment.

[0124] To verify the effectiveness of the denoising method proposed by the embodiment of the present invention, a noisy signal is constructed based on the waveform characteristics of typical partial discharge signals and typical interference noises for simulation experiments. Generally, it is considered that typical partial discharge signals can be modeled by the following four functions: single exponential decay, double exponential decay, single exponential decay oscillation, and double exponential decay oscillation. The representations of each function model are as follows:

[0125]

[0126] Among them, A is the amplitude of the partial discharge signal; f cis the decaying oscillation frequency; τ is the decay time constant; the sampling frequency is 10 MHz, and the specific simulation parameters are shown in Table 1. The simulated partial discharge signals are constructed using the above 4 mathematical models according to the parameters designed in Table 1. The obtained simulated partial discharge signals are shown in Figs. 3(a) and 3(b). Fig. 3(a) is the time-domain diagram of the pure partial discharge signal, and Fig. 3(b) is the frequency-domain diagram of the pure partial discharge signal.

[0127] Table 1

[0128]

[0129] White noise and periodic narrowband interference are added to the above pure partial discharge signal to simulate the interference situation suffered in actual signal sampling. Among them, the white noise uses Gaussian white noise with N(0, 0.3 2 ) distribution, and the periodic narrowband interference is designed according to the following formula:

[0130]

[0131] where, A i is the amplitude of the interference signal, and f i is the frequency of the interference signal. A i is set to 1 mV, and f i is set to 1 MHz and 4 MHz.

[0132] Fig. 4(a) is the time-domain diagram of the mixed signal obtained by superimposing Gaussian white noise and periodic pulse interference on the pure discharge signal; Fig. 4(b) is the time-domain diagram of the mixed signal obtained by superimposing Gaussian white noise and periodic pulse interference on the pure discharge signal.

[0133] As shown in Fig. 4(a), under the influence of strong noise, the partial discharge signal is submerged, and it is difficult to see the discharge from the time-domain diagram. Using the above noisy signal as a sample, it is processed with the algorithm designed in this paper, and the value ranges of the optimization parameters are set as K ∈ [2, 12] and α ∈ [100, 6000] respectively.

[0134] Set the population size of the NGO algorithm to 40 and the maximum number of iterations to 30. The iteration curve is as Figure 5 shown. It can be observed from Figure 5 that the NGO algorithm reaches the minimum energy difference of 0.0143 at the 23rd iteration, quickly determines the optimal target value of the iteration function, and at the same time maintains a high degree of accuracy. The optimal parameters of the NGO-optimized VMD are [K = 4, α = 510].

[0135] Fig. 6(a) is the time-domain diagram of IMF1 to IMF4 when the NGO optimizes the best parameters [K = 4, α = 510]; Fig. 6(b) is the frequency-domain diagram of IMF1 to IMF4 when the NGO optimizes the best parameters [K = 4, α = 510].

[0136] As can be seen from Figs. 6(a) and 6(b), when the optimal parameter K for NGO optimization is 4, the noise and PD signals are effectively separated in IMF1 and IMF3. Therefore, when the decomposition layer number K is 4, the signal can be completely decomposed.

[0137] By observing the time-domain diagrams of each IMF in Fig. 6(a), it can be found that IMF1 and IMF3 are effective intrinsic mode components. This observation result is further verified in the subsequent kurtosis calculation. The kurtosis values of each intrinsic mode component are calculated as shown in Table 2. As can be seen from Table 2, according to the kurtosis criterion, the kurtosis of IMF2 and IMF4 is less than 3 and should be discarded, while IMF1 and IMF3 are confirmed as effective intrinsic mode components.

[0138] Table 2

[0139]

[0140] Based on IMF1 and IMF3, signal reconstruction is carried out, and the signal shown in Fig. 7(a) is obtained. By comparing Fig. 7(a) with Figs. 4(a) and 4(b), it can be seen that the periodic narrowband interference in the reconstructed signal has disappeared, and the partial discharge characteristics are more prominent, but there are still some residual white noise components.

[0141] Next, wavelet denoising of the reconstructed signal is carried out based on the wavelet threshold algorithm. The decomposition layer number is selected as 4, and the db6 wavelet basis is used. The reconstructed signal after denoising by the wavelet threshold algorithm is shown in Fig. 7(b). As can be seen from Fig. 7(b), the residual white noise can be removed by the wavelet threshold algorithm.

[0142] To further verify the denoising effect of the embodiment of the present invention, the embodiment of the present invention is compared with the existing denoising algorithms.

[0143] To verify the effectiveness of the improved VMD algorithm, EMD-Wavelet (Empirical Mode Decomposition - Wavelet Transform) and CEEMDAN-Wavelet (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise - Wavelet Transform) are introduced for comparison. For the optimization algorithm part, the NGO algorithm is compared with the Particle Swarm Optimization (PSO) algorithm. PSO-VMD-Wavelet is introduced to process the noisy signal, and the denoising effects of the four algorithms are compared. Fig. 8(a) shows the denoising result of using NGO-VMD-Wavelet to denoise the partial discharge signal; Fig. 8(b) shows the denoising result of using PSO-VMD-Wavelet to denoise the partial discharge signal; Fig. 8(c) shows the denoising result of using EMD-Wavelet to denoise the partial discharge signal; Fig. 8(d) shows the denoising result of using CEEMDAN-Wavelet to denoise the partial discharge signal.

[0144] As can be seen from Fig. 8(b), in strong noise, the amplitudes of two typical discharge waveforms become significantly smaller after processing. Due to the improper selection of the decomposition level, a large amount of signal energy loss occurs. As can be seen from Fig. 8(c) and Fig. 8(d), CEEMDAN and EMD denoising cannot extract partial discharge signals well, resulting in signal waveform distortion and aberration.

[0145] To quantitatively analyze the denoising effect of the above methods, three parameters, namely signal-to-noise ratio (SNR), normalized cross-correlation (NCC), and root mean square error (RMSE), are introduced as evaluation criteria, and their calculation formulas are as follows:

[0146]

[0147] Among them, f(i) is the noisy signal; is the denoised signal; the signal-to-noise ratio (SNR) is a ratio that measures the relative intensity between the signal and the noise. The higher the SNR, the more effective signals there are in the partial discharge signal; the waveform similarity coefficient (NCC) is used to compare the similarity between two signals. The closer NCC is to 1, the higher the similarity between the denoised signal and the partial discharge signal; the root mean square error (RMSE) measures the error between the denoised signal and the partial discharge signal. The smaller the RMSE, the more accurate the denoised signal. The specific evaluation results are shown in Table 3.

[0148] As can be seen from Table 3, the denoising method provided by the embodiment of the present invention is superior to the other three algorithms in terms of the three indicators of signal-to-noise ratio, waveform similarity, and root mean square error. Comparing the denoising effect diagrams of the four algorithms, the algorithm of this article can filter out narrowband periodic interference and Gaussian white noise well, and the distortion of the filtered signal is the smallest, and the similarity with the original signal is the highest. This shows that the method of this article has a better suppression effect on noisy partial discharge signals.

[0149] Table 3

[0150]

[0151] Next, in order to test the universality of the embodiment of the present invention for various components in the ring main unit and obtain more experimental data samples. The tip corona discharge defect model in partial discharge defects is used and placed inside the ring main unit. According to the working mode of the partial discharge on-line monitoring system, the ultrasonic signals of partial discharge are continuously collected by the ultrasonic detection method.

[0152] Through the online monitoring system, a large number of partial discharge signals collected by ultrasonic sensors are used as measured signals. The partial discharge signal consists of 5-cycle discharge signals, with a sampling time of 0.1 s and a sampling frequency of 78 KHz for tip discharge ultrasonic data. This discharge data is used to verify the feasibility of the embodiments of the present invention, as Figure 9 shown, is the partial discharge signal collected.

[0153] As Figure 10 shown, are the iteration number curves of the NGO-VMD algorithm and the PSO-VMD algorithm. From Figure 10 it can be seen that the NGO-VMD algorithm reaches the optimal target value at the third iteration and maintains a stable state. However, the PSO-VMD algorithm has two cases where the target value does not change, and reaches the optimal target value stability at the seventh iteration. This shows that the NGO algorithm is superior to the PSO algorithm in terms of convergence accuracy and speed.

[0154] Using the optimal parameter combination obtained by NGO and applying it to VMD decomposition to process the partial discharge signal. The partial discharge signal is processed by the NGO-VMD-Wavelet method provided by the embodiments of the present invention, and at the same time, EMD-Wavelet and CEEMDAN-Wavelet are introduced to compare the advantages and disadvantages of the denoising effects of three different methods.

[0155] Figure 11(a) is the denoising result of the NGO-VMD-Wavelet provided by the embodiments of the present invention; Figure 11(b) is the denoising result of EMD-Wavelet; Figure 11(c) is the denoising result of CEEMDAN-Wavelet. From the waveforms and spectra after denoising in Figure 11(a), Figure 11(b), and Figure 11(c), it can be seen that the NGO-VMD-Wavelet denoising method provided by the embodiments of the present invention can filter out a large amount of noise in the partial discharge signal, and the denoising effect is relatively ideal.

[0156] Further verifies the feasibility and practicality of the technical solution provided by the embodiments of the present invention. Table 4 is a comparison of the denoising effects of three different methods. Since it is difficult to avoid background noise in the experiment, a pure original signal cannot be obtained, and the signal-to-noise ratio or root mean square error cannot be used to evaluate the denoising effect. Therefore, the Noise Rejection Ratio (NRR) before and after signal denoising is introduced to evaluate the signal denoising effect, which characterizes the prominence of the effective signal after denoising. The larger this value is, the more prominent the effective signal after denoising is, and the better the filtering effect. The expression is as follows:

[0157]

[0158] Among them, is the signal variance before denoising, is the signal variance after denoising. The results are shown in Table 4.

[0159] Table 4

[0160]

[0161] As can be seen from Table 4, when denoising the measured partial discharge signal, the denoising method provided by the embodiment of the present invention has a better noise reduction effect, and the burrs in the discharge intervals of each cycle are significantly reduced. Therefore, the denoising method provided by the embodiment of the present invention is selected, which has a great advantage in noise reduction.

[0162] In a second aspect, an embodiment of the present invention provides a partial discharge signal denoising device 120 based on an improved variational mode decomposition algorithm, as Figure 12 shown, the device includes:

[0163] A decomposition parameter initialization module 1210, configured to initialize the decomposition parameters of the variational mode decomposition algorithm to obtain an initial decomposition layer number and an initial penalty factor;

[0164] A partial discharge signal decomposition module 1220, configured to obtain an original partial discharge signal to be denoised, and decompose the original partial discharge signal into a plurality of intrinsic mode components according to the initial decomposition layer number and the initial penalty factor;

[0165] An objective function value determination module 1230, configured to use the difference between the sum of the energies of the decomposed intrinsic mode components and the energy of the original partial discharge signal as the objective function value;

[0166] A decomposition parameter update module 1240, configured to continuously update and iterate the decomposition layer number and the penalty factor of the variational mode decomposition algorithm based on the northern goshawk optimization algorithm until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determine a plurality of target intrinsic mode components;

[0167] An intrinsic mode component screening module 1250, configured to screen the plurality of target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components;

[0168] A partial discharge signal denoising module 1260, configured to filter the noise in the screened intrinsic mode components based on the wavelet threshold algorithm to obtain the denoised intrinsic mode components, and perform signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal.

[0169] In a third aspect, an embodiment of the present invention provides an electronic device, including:

[0170] At least one processor;

[0171] a memory for storing the at least one processor-executable instruction;

[0172] wherein the at least one processor is configured to execute the instructions to implement the method described in the first aspect.

[0173] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium. When the instructions in the computer-readable storage medium are executed by a processor of an electronic device, the electronic device is enabled to execute the method described in the first aspect.

[0174] In a fifth aspect, an embodiment of the present invention provides a computer program product, including a computer program which, when executed by a processor, implements the method described in the first aspect.

[0175] Although the embodiments of the present invention have been shown and described above, the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A local discharge signal denoising method based on an improved variational mode decomposition algorithm, characterized in that, The method includes: Initializing the decomposition parameters of the variational mode decomposition algorithm to obtain the initial decomposition level and the initial penalty factor; Obtaining the original partial discharge signal to be denoised, and decomposing the original partial discharge signal into multiple intrinsic mode components according to the initial decomposition level and the initial penalty factor; Taking the difference between the sum of the energies of the multiple intrinsic mode components obtained by decomposition and the energy of the original partial discharge signal as the objective function value; Updating and iterating the decomposition level and the penalty factor of the variational mode decomposition algorithm based on the northern goshawk optimization algorithm until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determining multiple target intrinsic mode components; Screening the multiple target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components; Filtering the noise in the screened intrinsic mode components based on the wavelet threshold algorithm to obtain the denoised intrinsic mode components, and performing signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal.

2. The method according to claim 1, wherein The continuously updating and iterating the decomposition level and the penalty factor of the variational mode decomposition algorithm based on the northern goshawk optimization algorithm until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determining multiple target intrinsic mode components includes: Updating the initial decomposition level and the initial penalty factor based on the northern goshawk optimization algorithm to obtain the updated decomposition level and the penalty factor; Decomposing the original partial discharge signal according to the updated decomposition level and the penalty factor, and calculating the objective function value based on the multiple intrinsic mode components obtained by decomposition; Iteratively updating the updated decomposition level and the penalty factor based on the northern goshawk optimization algorithm, and calculating the objective function value each time the decomposition level and the penalty factor are updated and iterated until the number of iterations reaches a preset number, or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determining the target decomposition level and the target penalty factor; Decomposing the original partial discharge signal into multiple target intrinsic mode components according to the target initial decomposition level and the target initial penalty factor.

3. The method according to claim 1, characterized in that The screening the multiple target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components includes: Calculating the kurtosis values of the multiple target intrinsic mode components respectively; Comparing the kurtosis value of each target intrinsic mode component with the kurtosis threshold; Taking the target intrinsic mode components with kurtosis values greater than the kurtosis threshold as the screened intrinsic mode components.

4. The method according to any one of claims 1 to 3, characterized in that, The filtering the noise in the screened intrinsic mode components based on the wavelet threshold algorithm to obtain the denoised intrinsic mode components, and performing signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal includes: Transforming the screened intrinsic mode variables into wavelet coefficients in different frequency ranges through the wavelet threshold algorithm; Processing the detail coefficients in the obtained wavelet coefficients through a preset threshold of the wavelet threshold algorithm to obtain the processed wavelet coefficients; Performing inverse transformation on the processed wavelet coefficients to obtain the denoised intrinsic mode components; Sum the denoised intrinsic mode components to obtain the denoised partial discharge signal.

5. The method according to claim 4, wherein Processing the detail coefficients in the obtained wavelet coefficients through a preset threshold of the wavelet threshold algorithm to obtain the processed wavelet coefficients includes: Determining the preset threshold of the wavelet threshold algorithm based on a threshold selection rule, where the threshold selection rule is determined based on the standard deviation of the screened intrinsic mode components and the length of the wavelet coefficients; Setting the detail coefficients in the obtained wavelet coefficients that are lower than the preset threshold of the wavelet threshold algorithm to 0.

6. A partial discharge signal denoising device based on an improved variational mode decomposition algorithm, characterized in that, The device includes: A decomposition parameter initialization module for initializing the decomposition parameters of the variational mode decomposition algorithm to obtain the initial decomposition level and the initial penalty factor; A partial discharge signal decomposition module for obtaining the original partial discharge signal to be denoised and decomposing the original partial discharge signal into multiple intrinsic mode components according to the initial decomposition level and the initial penalty factor; An objective function value determination module for taking the difference between the sum of the energies of the multiple decomposed intrinsic mode components and the energy of the original partial discharge signal as the objective function value; A decomposition parameter update module for continuously updating and iterating the decomposition level and the penalty factor of the variational mode decomposition algorithm based on the Northern Goshawk optimization algorithm until the number of iterations reaches a preset number or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determining multiple target intrinsic mode components; An intrinsic mode component screening module for screening the multiple target intrinsic mode components based on the kurtosis criterion to obtain the screened intrinsic mode components; A partial discharge signal denoising module for filtering the noise in the screened intrinsic mode components based on the wavelet threshold algorithm to obtain the denoised intrinsic mode components, and performing signal reconstruction on the denoised intrinsic mode components to obtain the denoised partial discharge signal.

7. The device according to claim 6, characterized in that, The decomposition parameter update module is specifically configured to: Update the initial decomposition level and the initial penalty factor based on the Northern Goshawk optimization algorithm to obtain the updated decomposition level and the penalty factor; Decompose the original partial discharge signal according to the updated decomposition level and the penalty factor, and calculate the objective function value based on the multiple decomposed intrinsic mode components; Continuously iteratively update the updated decomposition level and the penalty factor based on the Northern Goshawk optimization algorithm, and calculate the objective function value each time the decomposition level and the penalty factor are updated and iterated until the number of iterations reaches a preset number or the difference between the objective function values of two adjacent iterations is less than a preset threshold, and determining the target decomposition level and the target penalty factor; Decompose the original partial discharge signal into multiple target intrinsic mode components according to the target initial decomposition level and the target initial penalty factor.

8. An electronic device, characterized in that, Includes: At least one processor; A memory for storing instructions executable by the at least one processor; Wherein, the at least one processor is configured to execute the instructions to implement the method according to any one of claims 1-5.

9. A computer-readable storage medium, characterized in that, When the instructions in the computer-readable storage medium are executed by the processor of the electronic device, the electronic device can execute the method according to any one of claims 1-5.

10. A computer program product, characterized in that, Comprising a computer program which, when executed by a processor, implements the method according to any one of claims 1 to 5.

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