Partial discharge signal adaptive denoising method based on optimized continuous variational mode decomposition and improved wavelet threshold

Abstract

The invention relates to a partial discharge signal adaptive denoising method based on optimized continuous variational mode decomposition and improved wavelet threshold, which comprises the following steps: constructing an optimization framework of signal decomposition and reconstruction, performing adaptive decomposition and mode screening of signals under the background of strong noise, comparing each obtained mode component with a preset kurtosis threshold, and performing denoising on the partial discharge signals. A noise dominant mode and a signal dominant mode are effectively distinguished; in modal screening, the impact characteristic of the partial discharge signal and the statistical distribution difference of noise are fully considered, so that the integrity of signal component retention is improved; after modal screening is completed, a screened signal dominant modal is taken as a processing object, an improved wavelet threshold function is combined with an intelligent optimization algorithm to carry out adaptive threshold denoising processing, and an optimal denoising effect is determined by optimizing threshold function shape parameters and wavelet basis selection. And the integrity, fidelity and signal-to-noise ratio of partial discharge signal denoising are improved.

Description

Technical Field

[0001] This invention belongs to the field of power equipment condition monitoring and fault diagnosis technology, specifically relating to an adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet threshold. Background Technology

[0002] Partial discharge (PD) detection is a key technology for assessing the insulation condition of power equipment. However, in actual monitoring, the acquired PD signals are often overwhelmed by strong background noise, mainly including white noise and periodic narrowband interference, which seriously affects the feature extraction and fault diagnosis accuracy of PD signals. Therefore, effectively suppressing noise and extracting clean PD signals is one of the core challenges in the field of online monitoring of power equipment.

[0003] In the field of signal denoising, wavelet thresholding is a widely used technique. Its core idea is to decompose the signal into different scales using wavelet transform, utilize the difference in coefficient distribution between the effective signal and noise in the wavelet domain, process the coefficients by setting a threshold, and finally reconstruct the signal. However, one of the core bottlenecks of this method lies in the selection of the threshold function. Traditional threshold functions are mainly divided into two categories: 1. Hard thresholding function: This function retains all wavelet coefficients whose absolute value is greater than the threshold, while setting coefficients smaller than the threshold to zero. Although this can better preserve the local features of the signal (such as impact edges), the function is discontinuous at the threshold point, which can easily cause oscillations at the discontinuities during signal reconstruction, resulting in false impacts or spikes in the denoised signal.

[0004] 2. Soft Thresholding Function: This function continuously shrinks wavelet coefficients with absolute values ​​greater than a threshold towards zero, while setting coefficients with values ​​less than the threshold to zero. Although this function is continuous and avoids oscillations, this constant shrinkage can lead to excessive smoothing of the signal, causing amplitude attenuation and blurred edges. For non-stationary signals like partial discharge signals, which contain rich impulsive characteristics, soft thresholding can severely weaken or even distort the amplitude and shape of the discharge pulse, resulting in the loss of crucial diagnostic information.

[0005] Although some improved threshold functions have emerged to attempt to alter the characteristics of hard and soft thresholds, these improvements often introduce new, fixed-form functions and lack a mechanism for adaptive adjustment based on signal characteristics. Furthermore, the effectiveness of wavelet denoising heavily depends on the selection of multiple parameters, such as the threshold, wavelet basis, and number of decomposition levels. The optimal combination of these parameters typically varies depending on the signal, making adaptive selection difficult with traditional methods.

[0006] In non-stationary signal processing, Variational Mode Decomposition (VMD), as a non-recursive signal decomposition technique, has attracted widespread attention due to its ability to effectively suppress mode aliasing. However, VMD methods suffer from a significant application bottleneck: their decomposition performance is highly dependent on the artificial presets of two key parameters: the number of modes K and the penalty factor α. These parameters are typically set based on user experience or extensive trial and error, lacking adaptability.

[0007] To overcome the difficulty of setting VMD parameters, researchers proposed Successive Variational Mode Decomposition (SVMD). SVMD employs a continuous, stepwise selection strategy. Its core advantage lies in the fact that it does not require pre-setting the total number of modes K, thus fundamentally avoiding the problems of over-decomposition or under-decomposition of modes caused by improper K values. However, the performance of SVMD still depends on the setting of the penalty factor α, and currently, there is still a lack of an adaptive, optimization mechanism for selecting α based on specific signal characteristics.

[0008] In summary, existing technologies face a dual challenge: on the one hand, the key parameters of SVMD need to be optimized to achieve the best decomposition; on the other hand, even if effective modal components are obtained, traditional wavelet thresholding denoising methods, due to their inherent functional defects and non-adaptive parameter selection, are still unable to achieve high-fidelity denoising of PD signals.

[0009] Combining modal decomposition with improved, adaptive threshold denoising techniques and automating key parameters throughout the process is an effective way to improve the denoising performance of partial discharge signals. Summary of the Invention

[0010] The purpose of this invention is to address the shortcomings and deficiencies of existing technologies by providing an adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet threshold. This method adaptively determines the optimal penalty factor for SVMD and the optimal parameters for improved wavelet threshold through a two-level optimization mechanism, achieving adaptive processing throughout the entire process from decomposition and screening to denoising.

[0011] The technical problem solved by this invention is achieved through the following technical solution: An adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet thresholding, the method comprising the following steps: S1. Continuous variational mode decomposition of parameters based on the Fox Optimization Algorithm (FOX); S2. Modal component selection based on kurtosis criterion; calculate the kurtosis value of each IMF component obtained in S1; set a kurtosis threshold, determine the IMF components with kurtosis values ​​greater than the threshold as "partial discharge signal dominant mode" and retain them; determine the IMF components with kurtosis values ​​less than or equal to the threshold as "noise dominant mode" and discard them directly; S3. Denoising processing based on the improved wavelet threshold optimization algorithm (SSA); S4. Signal reconstruction: Linearly superimpose all the IMF components of the "partial discharge signal dominant mode" after processing in S3 to reconstruct the denoised partial discharge signal y(t).

[0012] Furthermore, S1 specifically involves: inputting a noisy partial discharge signal x(t), setting the parameters of the Fox Optimization Algorithm (FOX), including population size, maximum number of iterations, and the search range of the SVMD penalty factor α; using the maximization of the overall envelope spectrum peak factor of all IMF components obtained after SVMD decomposition as the objective function; FOX iteratively searches within the search space of the penalty factor α, and for each candidate α value, performs SVMD to continuously decompose the partial discharge signal x(t) to obtain a set of IMF components, and calculates the overall envelope spectrum peak factor of all IMF components, ultimately finding the optimal penalty factor α_opt that maximizes the overall envelope spectrum peak factor; using the obtained optimal penalty factor α_opt, performing SVMD decomposition on the original partial discharge signal x(t) to obtain IMF components from high frequency to low frequency, namely IMF1, IMF2, ..., IMF M M is automatically determined by the algorithm.

[0013] Moreover, S3 specifically refers to: An improved wavelet thresholding function is adopted, which achieves a smooth transition between hard and soft thresholding functions by introducing adjustable parameters. Wavelet thresholding denoising is performed on each IMF component of the "partial discharge signal dominant mode" selected by S2. The Sparrow Optimization Algorithm (SSA) is used to adaptively select the optimal wavelet basis, threshold λ, and parameters a and b in the improved thresholding function for each IMF component. The optimization objective function is to maximize the signal-to-noise ratio (SNR) of the denoised IMF component. Finally, the optimal parameter combination that maximizes the SNR is found, and this combination is used to perform the final denoising processing on the IMF component.

[0014] Furthermore, the mathematical expression for the improved threshold function of S3 is as follows: ; in: These are the original wavelet coefficients; These are the wavelet coefficients after thresholding. For the threshold; and To introduce adjustable shape parameters, via parameters and Achieve flexible control over processing characteristics: the function at the threshold point Continuous, when rigidity greater than When it provides appropriate contraction to eliminate noise; when Much larger When the shrinkage rate decreases, it can be adjusted... (range [0, 1]) and (Range [0.1, 5.0]), achieving a smooth transition between hard and soft thresholds, finding the optimal compromise point for signals with different characteristics.

[0015] Furthermore, the mathematical expression of the denoised partial discharge signal y(t) obtained by signal reconstruction in S4 is as follows: ; in: It is the denoised partial discharge signal obtained from the final reconstruction; It is the total number of dominant modes of partial discharge signals retained after screening; It is the first The pure mode components are obtained after the dominant mode of the partial discharge signal is processed by the improved wavelet threshold denoising based on SSA optimization. This indicates a linear superposition of all preserved and denoised modal components.

[0016] The advantages and beneficial effects of this invention are as follows: 1. The noise reduction effect of the present invention is further improved, and it is superior to the prior art in terms of NCC, SNR and MSE. It effectively removes noise while retaining the characteristics of the partial discharge signal.

[0017] 2. This invention adaptively determines the optimal penalty factor for SVMD and the optimal parameters for improving the wavelet threshold through a two-level optimization mechanism, realizing adaptive processing throughout the entire process from decomposition and screening to denoising. Attached Figure Description

[0018] Figure 1 This is the time-domain diagram of the original partial discharge signal of the present invention; Figure 2 This is the original partial discharge signal frequency domain diagram of the present invention; Figure 3 This is a time-domain diagram of the noisy partial discharge signal of the present invention; Figure 4 This is the frequency domain diagram of the noisy partial discharge signal of the present invention; Figure 5 These are time-domain diagrams of the modal components of this invention; Figure 6The frequency domain diagrams of each modal component of this invention are shown. Figure 7 The image shows the denoising result of db4 wavelet thresholding. Figure 8 The image shows the denoising results of CEEMDAN combined with wavelet thresholding. Figure 9 This is a diagram showing the denoising results of the present invention. Detailed Implementation

[0019] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0020] Partial discharge (PD) is a phenomenon of localized electrical breakdown in insulation systems, often occurring at defects in the insulating material or in areas of concentrated electric field between dielectrics. This discharge does not form a complete breakdown path throughout the insulation material but is confined to a specific area. PD typically occurs in locations with high electric field strength, such as defects, bubbles, or inclusions in the insulating material. This phenomenon generates high-frequency electromagnetic and acoustic signals, which can be captured and analyzed using specialized equipment. Accurate PD signal extraction helps in-depth assessment of the extent of insulation damage, providing crucial information for developing effective equipment maintenance strategies. By monitoring and analyzing PD signals, the aging of the insulating material and the severity of defects can be understood in a timely manner, thereby predicting potential insulation breakdown risks. This key information helps prevent equipment failures and ensures the safety and efficiency of the power system. Therefore, the accurate extraction and analysis of PD signals plays a vital role in the daily maintenance and equipment safety assurance of power systems.

[0021] Traditional PD signal processing methods mainly include a series of signal processing techniques such as time-domain thresholding, wavelet transform, empirical mode decomposition (EMD), and its improved algorithms. The core idea of ​​these methods is to separate noise from useful PD signals by directly processing the acquired raw signals. However, due to the complex electromagnetic interference, white noise, and periodic noise present in substations, and the non-stationary and transient characteristics of PD signals, these traditional methods face severe challenges when processing actual PD signals: Although wavelet transform has good time-frequency localization characteristics, its denoising effect heavily depends on the manual selection of wavelet basis functions, decomposition levels, and threshold rules. At the same time, the discontinuity of traditional hard thresholding functions leads to oscillations in the reconstructed signal, while soft thresholding functions cause PD pulse amplitude attenuation due to constant contraction. Although empirical mode decomposition methods are adaptive, they suffer from obvious mode mixing and endpoint effects, and their performance degrades sharply under low signal-to-noise ratio conditions. More fundamentally, the key parameters in existing methods (such as the number of modes and penalty factor in variational mode decomposition) usually rely on user experience or are determined through a large number of trial and error, lacking an adaptive optimization mechanism for specific signals. Combining advanced signal decomposition algorithms with threshold denoising techniques is indeed an effective solution. However, in most existing denoising method studies, in order to simplify the calculation process and reduce implementation complexity, the adaptive selection of algorithm parameters and the optimized design of threshold functions are generally ignored. An adaptive correlation mechanism between parameter settings and signal characteristics has not been established, and the combined effects of the non-stationary characteristics of PD signals and the time-varying characteristics of field noise on the denoising effect have not been fully considered. As a result, the robustness and adaptability of these methods in practical engineering applications are severely limited.

[0022] Combining advanced signal decomposition algorithms with threshold denoising techniques is indeed an effective solution. However, in most existing denoising method studies, in order to simplify the computation process and reduce implementation complexity, the adaptive selection of algorithm parameters and the optimized design of the threshold function are generally neglected. Specifically, this manifests in the following ways: the adaptive correlation mechanism between parameter settings and signal characteristics is not established, and the combined effects of the non-stationary characteristics of PD signals and the time-varying characteristics of field noise on the denoising effect are not fully considered. As a result, the robustness and adaptability of these methods in practical engineering applications are severely limited.

[0023] In view of the above problems, embodiments of the present invention provide an adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet thresholding. Its innovation lies in the following: the method includes constructing an optimized framework for signal decomposition and reconstruction, performing adaptive decomposition and mode selection of the signal under strong noise background, comparing each obtained mode component with a preset kurtosis threshold, and effectively distinguishing between noise-dominant and signal-dominant modes. During mode selection, the impact characteristics of the partial discharge signal and the statistical distribution differences of noise are fully considered, thereby improving the integrity of signal component retention. After completing mode selection, the selected signal-dominant modes are used as processing objects, and adaptive thresholding denoising is performed using an improved wavelet thresholding function combined with an intelligent optimization algorithm. The optimal denoising effect is determined by optimizing the thresholding function shape parameters and wavelet basis selection, thereby improving the integrity, fidelity, and signal-to-noise ratio of partial discharge signal denoising.

[0024] First, the principle of Variational Mode Decomposition (VMD) is introduced. VMD decomposes a signal into multiple eigenmode functions with finite bandwidths and different center frequencies. A variational model is constructed first, and then each mode is obtained by solving this model. The variational problem is described as finding k modes that minimize the sum of their bandwidths. The constrained variational problem can be expressed as: (1) In the formula: The number of modes, For the first A BLIMF, For the first The center frequency of each BLIMF Let be the Dirac distribution function. This is the input signal.

[0025] By introducing a quadratic penalty factor and Lagrange multipliers to make the problem unconstrained, the augmented Lagrange multiplier is as follows: (2) In the formula: As a secondary penalty factor, Let be the Lagrange multipliers. Using the alternating direction method of multipliers (ADMM) iterative solution, we can obtain... , The optimal value.

[0026] In the application of Variational Mode Decomposition (VMD) algorithms, the preset number of mode functions K is a critical and sensitive parameter setting issue. When K is set too high, it may lead to overlap and interference of frequency components between different modes, causing mode aliasing. Conversely, if K is set too low, different feature components that should be separated in the signal may be forcibly merged into the same mode, resulting in redundant and repetitive modes. This parameter sensitivity severely restricts the effectiveness of VMD in practical engineering applications. In contrast, Continuous Variational Mode Decomposition (SVMD) fundamentally avoids the need to preset the number of mode functions K through an improved decomposition mechanism. This method employs a sequential extraction strategy, which can adaptively determine the appropriate number of modes, and has lower computational complexity than the VMD algorithm, making it more suitable for practical engineering applications. The basic principles of the SVMD method will be explained in detail below.

[0027] Assuming the input signal Decomposed into two parts: the first First-order modal signal and residual signal .

[0028] (3) In the formula, the residual signal It consists of two parts: the sum of previously obtained modes. and the unprocessed part of the signal .

[0029] (4) The SVMD method is based on the following four criteria, each of which is explained in terms of its principle.

[0030] (1) Each mode function should be compact around its center frequency. Therefore, the first... The first mode minimizes the following criterion: (5) In the formula, yes The center frequency of the first-order modal function, This represents the convolution operation.

[0031] (2) In Residual signal at frequencies with effective components Energy should be minimized

[14] As shown in the VME method

[19] This constraint is achieved by using a filter with the following frequency response: (6) In order to and To minimize the spectral overlap between them, we should make Filtered Energy minimization. Therefore, we consider the following criteria to minimize the residual signal and the first... Spectral overlap of first-order modal signals: (7) In the formula, It is the impulse response of the filter described by equation (4).

[0032] (3) Through the minimization criterion and To extract the first In the case of a first-order mode, the mode may differ from previously obtained modes. A certain mode in the first-order mode repeats. To avoid this problem, note that the first-order mode repeats... First mode The phenomenon that the extracted modes should have lower energies near their center frequencies is helpful. This constraint can be addressed by combining it with the construction criteria. A similar approach can be used, namely, employing a filter with a specific frequency response, the form of which is as follows: (8) The additional criteria are as follows: (9) in, It is the impulse response of the filter in equation (6).

[0033] (4) The last constraint is to ensure that from The first-order mode function and the unprocessed portion of the signal can be completely reconstructed. : (10) Therefore, when it is known When the first mode is in operation, extract the first mode. The problem of the first-order modal function can be expressed as a constraint minimization problem, where , and The combination guarantees minimization under the constraints of equation (10): (11) in It is balance , and The parameters can be solved using the Lagrange multiplier method.

[0034] The above explains the specific principles of the SVMD method. Although the SVMD method effectively avoids the problem of pre-setting the number of modes K through its continuous decomposition mechanism, its decomposition accuracy still significantly depends on the value of the penalty factor. This parameter directly affects the bandwidth setting and center frequency extraction of the modal components—a penalty factor value that is too small will result in an excessively wide modal bandwidth, which may introduce noise interference; a penalty factor value that is too large will result in an excessively narrow bandwidth, which may lose useful signal components. Traditional methods often rely on expert experience or grid search for parameter selection, a process that is not only time-consuming and laborious, but also difficult to guarantee that the optimal solution can be obtained under different noise environments. To solve this problem of adaptive parameter optimization, this invention introduces the Fox Optimization Algorithm (FOX).

[0035] The Fox Optimization Algorithm simulates the hunting behavior of a fox lurking in snow: when snow covers the ground, it obstructs the prey's vision, forcing the fox to randomly search for prey. By estimating the time difference between sending and receiving sound waves, the fox determines the distance between itself and the prey. After determining the distance, the fox estimates the jump distance required to catch the prey, and then randomly walks based on the shortest time and optimal position, ultimately finding the prey's location. The Fox Optimization Algorithm mainly consists of a development phase and a search phase. The development phase primarily involves jumping to approach the optimal position to hunt prey, while the search phase uses random walks to approach the best hunting position.

[0036] During the development phase, to determine a new location, it is necessary to calculate the sound propagation distance. The sound propagation distance... The calculation formula is as follows: (12) in, It is the number of iterations. It is the time it takes for sound waves to travel over snow. It's the speed of sound in the snow.

[0037] Formula (13) is used to calculate It needs to be based on the current optimal position. To determine the speed of sound propagation.

[0038] (13) Distance between the fox and its prey It is half the distance the sound travels, calculated using the following formula: (14) Once the fox has determined its distance from its prey, it must leap to the optimal position to catch it. To do this, it must find the appropriate leap height, calculated using the following formula: (15) in, It is gravitational acceleration. It is the average time for sound to travel, equal to the propagation time. Half of that, because the time required for jumping up and down is equal. The calculation is as follows: (16) in Calculate the total time for each sequence. It is the dimension of the fox's position.

[0039] if The fox will leap in the northeast direction. and Multiply by This increases the likelihood of reaching a new location and getting closer to the optimal solution. Otherwise, the fox will jump in the opposite direction. and Multiply by Therefore, the new position is calculated as follows: (17) in , .

[0040] During the exploration phase, the fox searches for prey by randomly wandering around based on the best location discovered so far. To ensure that the fox's random movements lead it to the optimal location, a minimum time variable is used. and Adjust the search: (18) (19) in It is the maximum number of iterations.

[0041] The fox's location update strategy is as follows: (20) This algorithm simulates the hunting intelligence of fox packs, efficiently searching the parameter space through a balance mechanism of global exploration and local exploitation. When applied to SVMD parameter optimization, it aims to maximize the peak factor of the overall envelope spectrum of the decomposed modal components, automatically finding the optimal penalty factor. This enables adaptive decomposition of partial discharge signals with different characteristics, laying a solid foundation for subsequent denoising processing.

[0042] Crest factor of envelope spectrum The envelope factor (EFF) is a dimensionless index used to measure the intensity of periodic impulse components in a signal. By analyzing the morphology of the signal's envelope spectrum, it effectively distinguishes impulse oscillation signals generated by partial discharge from stable background noise. Its calculation is based on the following principle: partial discharge signals are generated by a series of repetitive electrical pulses, each pulse exciting a high-frequency decaying oscillation. The amplitude envelope of these oscillations (i.e., the profile of the signal amplitude changing over time) contains information about the pulse repetition frequency. Spectral analysis of the envelope (i.e., obtaining its envelope spectrum) allows observation of discrete spectral lines at the repetition frequency and its harmonics in the frequency domain. The envelope peak factor works by quantifying the prominence of these discrete spectral lines.

[0043] Its mathematical definition is: for a sequence of envelope spectrum amplitudes Its envelope spectrum peak factor The calculation formula is: ;(twenty one) in, This represents the maximum amplitude in the envelope spectrum, corresponding to the strongest spectral line of the impact component in the frequency domain; The root mean square value represents the entire envelope spectrum, reflecting the overall energy level or average amplitude of the envelope spectrum.

[0044] therefore, The physical meaning is: the degree of prominence of the amplitude of the largest spectral line in the envelope spectrum relative to the average level of the entire spectrum. The larger the value, the more obvious and pure the periodic impulse characteristics in the signal. The envelope spectrum peak factor differs significantly between modes rich in periodic impulse characteristics and noise-dominated modes. Therefore, using it as the fitness function of the fox optimization algorithm can effectively guide the optimization process, enabling SVMD decomposition to extract the set of modes with the most significant impulse characteristics. This lays a solid foundation for subsequent accurate denoising and fully demonstrates the scientific nature and superiority of the technical solution of this invention.

[0045] After achieving adaptive decomposition of the signal using the FOX-SVMD model, this invention employs the kurtosis criterion to intelligently filter the decomposed modal components, so as to accurately distinguish between "partial discharge signal-dominant mode" and "noise-dominant mode".

[0046] Kurtosis is a fourth-order statistic used in signal processing to measure the steepness of a probability density distribution. For a signal sequence with zero mean... ;(twenty two) in, This represents the expected value. For Gaussian white noise and periodic narrowband interference, the distribution is relatively flat, with kurtosis values ​​close to or less than 3. For partial discharge signals, due to their generation mechanism being transient, rapidly changing current pulses, even if they appear as oscillating decaying waves, the "impact" of their origin leads to a much larger-than-average amplitude sample in the signal. This results in a "heavy" characteristic in the probability density distribution at both ends, the so-called "heavy-tailed" distribution, thus causing its kurtosis value to be significantly greater than 3.

[0047] Based on the above principles, the present invention is implemented as follows: For each IMF component obtained from FOX-SVMD decomposition Calculate its kurtosis value The threshold for discrimination will be determined. Setting it to 3 will satisfy the requirement. The IMF components were identified as "partial discharge signal dominant modes." These modes contain oscillatory components dominated by partial discharge impulse characteristics and are retained for the next processing stage; those that meet the requirements... The IMF components were identified as "noise-dominated modes". These modes are mainly composed of Gaussian noise or stationary disturbances and are therefore discarded.

[0048] The ingenuity of this invention lies in the effective functional complementarity between the kurtosis criterion and the aforementioned envelope spectrum peak factor: the envelope spectrum peak factor serves as an optimization target in the decomposition stage, guiding SVMD to find the decomposition method that best highlights the periodic impact characteristics, with the advantage of distinguishing between periodic impacts and stationary interference; the kurtosis criterion serves as a criterion in the screening stage, directly screening based on the impact intensity of the signal, with the advantage of high sensitivity to transient pulses. The two work together to construct a complete technical chain from "optimized decomposition" to "precise screening," ensuring that the true partial discharge signal components can be extracted with high fidelity from complex background noise, providing a reliable data foundation for subsequent fault diagnosis.

[0049] After successfully identifying the dominant mode of the partial discharge signal, this invention proposes an improved wavelet threshold function to address the inherent defects of traditional wavelet threshold denoising. Furthermore, it innovatively employs the Sparrow Optimization Algorithm (SSA) to adaptively optimize the parameters of this function, thereby achieving high-fidelity denoising of the partial discharge signal.

[0050] Traditional hard thresholding functions are discontinuous at the threshold point, making the reconstructed signal prone to oscillations. Soft thresholding functions, while continuous, constantly shrink wavelet coefficients above the threshold, leading to excessive signal smoothing and amplitude attenuation. Both of these are serious drawbacks for partial discharge signals that require precise preservation of the impact amplitude.

[0051] To address the above problems, this invention designs a continuous and differentiable improved threshold function, the mathematical expression of which is as follows: ;(twenty three) in: These are the original wavelet coefficients; These are the wavelet coefficients after thresholding. For the threshold; and The adjustable shape parameters introduced in this invention.

[0052] This function takes parameters and It enables flexible adjustment of processing characteristics: the function at the threshold point It is continuous at this point, avoiding the oscillations caused by the hard threshold function. This function does not undergo constant contraction; when... rigidity greater than When it provides appropriate contraction to eliminate noise; when Much larger At this time, the contraction rate decreases, thus preserving the large coefficient representing the strong partial discharge pulse to the maximum extent. This is achieved by adjusting... (range [0, 1]) and (Range [0.1, 5.0]), which can achieve a smooth transition between hard and soft thresholds and find the optimal compromise point for signals with different characteristics.

[0053] Although the improved threshold function performs well, its effectiveness depends on a set of optimal parameters, including the wavelet basis functions. Threshold scaling factor and shape parameters and Therefore, this invention introduces the Sparrow Optimization Algorithm (SSA) to solve this complex multi-parameter joint optimization problem. The basic principles of the Sparrow Optimization Algorithm will be introduced below.

[0054] The sparrow optimization algorithm uses an n-dimensional linear solution space to represent the position of each sparrow, as shown below: ;(twenty four) in: Indicates the number of dimensions of the variable; This indicates the population size of sparrows.

[0055] The sparrow's fitness value is: (25) in: This represents the fitness value.

[0056] Sparrow populations include three roles: discoverers, followers, and watchdogs. The allocation of roles is dynamic. In each search cycle, individuals with good fitness will be promoted to discoverers, ensuring that each individual has the opportunity to lead the population's search behavior.

[0057] Discoverers are the most fit within the population, and their numbers remain stable between 10% and 20%. Discoverers possess dynamic decision-making capabilities, autonomously choosing to deepen their search at their current location or initiate a migration mechanism to search for new areas based on a safety assessment of their surroundings. The discoveryer location update formula is shown below: (26) in, Indicates the first In the next iteration, the... Only sparrows in the first The position in the dimension; yes Random numbers; This is a warning value, and its range is: ; It is a safe value, and its range is [value range missing]. ; It is a random number that follows a standard normal distribution; Represents a set of all elements Su Duwei of Matrix. When At that time, sparrow populations can move freely within a safe area; when At times, sparrow populations need to move to safe areas to search for food.

[0058] Followers consist of non-discoverer individuals, initially distributed in resource-poor areas. To improve efficiency, they will cluster towards discoverers with high fitness and engage in localized development around them. The system simulates competition through dynamic resource allocation: when the follower density in a certain area becomes saturated, some individuals will migrate due to resource shortages and explore new areas. The follower position update formula is shown below: (27) in, and These represent the current globally optimal and worst positions, respectively. for A matrix, where each element is randomly assigned the value 1 or -1. .when At that time, the first A less fit follower flies to another area.

[0059] The watchdogs are responsible for threat perception. Once they detect environmental danger, they immediately sound an alarm, guiding the population to take evasive action. The position update formula for the watchdogs is as follows: (28) in, This is the current globally optimal position; It is a random number that follows a standard normal distribution, and it is the step size control parameter; yes Random numbers. , and These represent the fitness values ​​of the current individual sparrow, the globally optimal value, and the worst value, respectively. It is a very small constant used to avoid division by zero error. When When this occurs, it means the sparrow population is on the periphery and vulnerable to predators; when At this time, it means that the sparrow has realized the danger signal and moved to another location.

[0060] The parameters to be optimized are encoded as position vectors of individual sparrows. ,in: From the dictionary Discrete selection; The threshold scaling factor is used in the continuous interval. Internal search; exist Internal search; exist Internal search.

[0061] When executing the sparrow optimization algorithm, the fitness function of this invention is defined as the signal-to-noise ratio (SNR) of the denoised modal component, and its maximization is sought: (29) The formula for calculating the signal-to-noise ratio is: (30) in, This is the IMF component that needs to be denoised. These are the components after wavelet thresholding. Maximizing SNR directly guarantees the optimization of the final denoising effect.

[0062] After obtaining the optimal denoising parameters for each dominant mode of partial discharge signal using the sparrow optimization algorithm and completing wavelet threshold denoising, this invention enters the final signal reconstruction stage. The purpose of this stage is to reintegrate the refined signal modes to generate a complete denoised partial discharge signal.

[0063] The signal reconstruction process is concise yet crucial, and its mathematical expression is as follows: (31) in, It is the denoised partial discharge signal obtained from the final reconstruction; It is the total number of dominant modes of partial discharge signals retained after screening; It is the first The pure mode components are obtained after the dominant mode of the partial discharge signal is processed by the improved wavelet threshold denoising based on SSA optimization. This indicates a linear superposition of all preserved and denoised modal components.

[0064] The following examples demonstrate the denoising results in detail. Partial discharge signals can be simulated using the following four mathematical models.

[0065] Single exponential decay model: (32) Double exponential decay model: (33) Single exponential decay oscillation model: (34) Double exponential decay oscillation model: (35) In the formula, The signal amplitude, , Let be the signal attenuation constant. Let be the oscillation frequency of the signal. This paper simulates the signal using one single exponentially decaying oscillation model and two double exponential oscillation models, with parameter settings shown in Table 1. The sampling frequency is 10 GHz, and the number of sampling points is 1000.

[0066] Table 1 Partial Discharge Signal Parameters Periodic narrowband interference The frequencies were set to 0.8 GHz and 2 GHz, with a signal amplitude of 0.5 mV for both; white noise. It is Gaussian white noise with a mean of 0 and a variance of 0.01, following a normal distribution. (Partial discharge noisy signal) Represented as: (36) The original partial discharge signal time-domain plot is shown below. Figure 1 Frequency domain diagram (see) Figure 2 The time-domain plot of the noisy partial discharge signal is shown below. Figure 3 Frequency domain diagram (see) Figure 4 .

[0067] For the aforementioned noisy partial discharge signal, the FOX algorithm is used to optimize the SVMD parameters with the objective function of maximizing the envelope spectrum peak factor, and the penalty factor is set to a range of [value missing]. After optimization using the FOX algorithm, the optimal penalty factor for the aforementioned noisy partial discharge signal was determined to be 1524. Using this parameter, SVMD decomposition yielded five modal components. The time-domain plots of the decomposed modes are shown below. Figure 5 The corresponding frequency domain diagram is shown below. Figure 6 .

[0068] The kurtosis values ​​of each mode component were calculated, as shown in Table 2 below. From Table 2, it can be seen that the kurtosis values ​​of modes 1, 3, and 5 are much greater than 3, indicating that they are the dominant components of the partial discharge signal. The kurtosis values ​​of modes 2 and 4 are less than 3, indicating that they are the dominant components of noise. Therefore, modes 2 and 4 are discarded.

[0069] Table 2 Kurtosis values ​​of each modal component The wavelet threshold parameters of the preserved partial discharge signal are processed using the sparrow optimization algorithm. The optimized wavelet threshold parameters for mode 1 are as follows: The optimized wavelet threshold parameters for mode 3 are: The optimized wavelet threshold parameters for mode 5 are: The optimized wavelet threshold parameters are used to perform wavelet thresholding on each mode, and then the denoised signal can be obtained by reconstruction.

[0070] To verify the denoising effect of the method of the present invention, it was compared with two other methods: db4 wavelet thresholding and CEEMDAN combined with wavelet thresholding. The denoising results of db4 wavelet thresholding are as follows: Figure 7 As shown, the denoising results of CEEMDAN combined with wavelet thresholding are as follows: Figure 8 As shown, the denoising results of the present invention are as follows: Figure 9 As shown.

[0071] This invention selects three evaluation indicators—normalized correlation coefficient (NCC), signal-to-noise ratio (SNR), and mean square error (MSE)—to quantitatively evaluate the denoising effect. The expressions for these evaluation indicators are shown below.

[0072] (37) (38) (39) in, This is the original PD signal; The above metrics are calculated and compared with the original PD signal after denoising using the three methods. The evaluation metrics are shown in Table 3.

[0073] Table 3 Evaluation Indicators for Noise Reduction Effect Depend on Figure 7 , 8 As shown in Tables 9 and 3, the CEEMDAN combined with wavelet threshold denoising method is superior to the db4 wavelet threshold denoising method. The denoising effect of this invention is further improved, and it is superior to the other two methods in terms of NCC, SNR and MSE. It effectively removes noise while preserving the characteristics of the partial discharge signal.

[0074] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. An adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet thresholding, characterized in that: The steps of the method are as follows: S1. Continuous variational mode decomposition of parameters based on the Fox Optimization Algorithm (FOX); S2. Modal component selection based on kurtosis criterion; calculate the kurtosis value of each IMF component obtained in S1; Set a kurtosis threshold. IMF components with kurtosis values ​​greater than the threshold are identified as "partial discharge signal dominant modes" and retained. IMF components with kurtosis values ​​less than or equal to the threshold are identified as "noise dominant modes" and discarded. S3. Denoising processing based on the improved wavelet threshold optimization algorithm (SSA); S4. Signal reconstruction: Linearly superimpose all the IMF components of the "partial discharge signal dominant mode" after processing in S3 to reconstruct the denoised partial discharge signal y(t).

2. The adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet thresholding as described in claim 1, characterized in that: S1 specifically involves: inputting a noisy partial discharge signal x(t), setting the parameters of the Fox Optimization Algorithm (FOX), including population size, maximum number of iterations, and the search range of the SVMD penalty factor α; using the maximization of the overall envelope spectrum peak factor of all IMF components obtained after SVMD decomposition as the objective function; FOX iteratively searches within the search space of the penalty factor α, and for each candidate α value, performs SVMD to continuously decompose the partial discharge signal x(t) to obtain a set of IMF components, and calculates the overall envelope spectrum peak factor of all IMF components, ultimately finding the optimal penalty factor α_opt that maximizes the overall envelope spectrum peak factor; using the obtained optimal penalty factor α_opt, performing SVMD decomposition on the original partial discharge signal x(t) to obtain IMF components from high frequency to low frequency, i.e., IMF1, IMF2, ..., IMF... M M is automatically determined by the algorithm.

3. The adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet threshold as described in claim 1, characterized in that: Specifically, S3 is: An improved wavelet thresholding function is adopted, which achieves a smooth transition between hard and soft thresholding functions by introducing adjustable parameters. Wavelet thresholding denoising is performed on each "partial discharge signal dominant mode" IMF component selected by S2. The Sparrow Optimization Algorithm (SSA) is used to adaptively select the optimal wavelet basis, threshold λ, and parameters a and b in the improved thresholding function for each IMF component. The optimization objective function is to maximize the signal-to-noise ratio (SNR) of the denoised IMF component. Finally, the optimal parameter combination that maximizes the SNR is found, and this combination is used to perform the final denoising processing on the IMF component.

4. The adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet threshold as described in claim 3, characterized in that: The mathematical expression for the improved threshold function of S3 is as follows: ； in: These are the original wavelet coefficients; These are the wavelet coefficients after thresholding. For the threshold; and To introduce adjustable shape parameters, via parameters and Achieve flexible control over processing characteristics: the function at the threshold point Continuous, when rigidity greater than When it provides appropriate contraction to eliminate noise; when Much larger When the shrinkage rate decreases, it can be adjusted... (range [0,1]) and (Range [0.1, 5.0]), achieving a smooth transition between hard and soft thresholds, finding the optimal compromise point for signals with different characteristics.

5. The adaptive denoising method for partial discharge signals based on optimized continuous variational mode decomposition and improved wavelet threshold as described in claim 1, characterized in that: The mathematical expression of the denoised partial discharge signal y(t) obtained by signal reconstruction in S4 is as follows: ； in: It is the denoised partial discharge signal obtained from the final reconstruction; It is the total number of dominant modes of partial discharge signals retained after screening; It is the first The pure mode components are obtained after the dominant mode of the partial discharge signal is processed by the improved wavelet threshold denoising based on SSA optimization. This indicates a linear superposition of all preserved and denoised modal components.

Images