Double-domain non-convex joint optimization equipment state signal denoising method and system

Abstract

The invention discloses a double-domain non-convex joint optimization equipment state signal denoising method and system, and the method comprises the steps: carrying out the modeling of a partial discharge signal containing aliasing noise, obtaining a one-dimensional observation signal, and converting the one-dimensional observation signal into a two-dimensional observation matrix; based on the two-dimensional observation matrix, obtaining a double-domain collaborative regular model through double-domain decomposition, and optimizing the double-domain collaborative regular model by adopting a non-convex penalty function to obtain a non-convex optimized regular model; and carrying out iterative solution on the non-convex optimization regular model by adopting an improved collaborative alternating direction multiplier algorithm, obtaining an updated two-dimensional observation matrix of the partial discharge signal in combination with an original residual threshold and a dual residual threshold, and carrying out inverse conversion on the two-dimensional observation matrix of the partial discharge signal to obtain a denoised partial discharge signal. Cooperative iteration of double-domain variables is realized based on an improved cooperative alternating direction multiplier algorithm, double-domain residual index dynamic judgment convergence is designed, and redundant iteration is reduced while denoising precision is guaranteed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of partial discharge detection, and particularly relates to a double-domain non-convex joint optimization device state signal denoising method and system. BACKGROUND

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] As the core equipment of the ultra-high voltage power grid, the ultra-high voltage converter transformer has the characteristics of high voltage and large capacity at the grid side, so that the bushing and tap changer are subjected to the combined stress of high temperature, strong electric field and mechanical vibration for a long time, and the internal insulation structure is prone to have weak points and be accompanied by partial discharge. The partial discharge can accelerate the insulation deterioration through electrochemical reaction and thermal aging, and finally may cause insulation breakdown, equipment explosion and even power grid cascading trip, which poses a fundamental threat to the safety of the power system. Therefore, accurately capturing the partial discharge signal in a complex electromagnetic environment is the key to realizing early warning of the insulation state of the equipment.

[0004] The current mainstream partial discharge denoising method still has significant limitations in complex scenarios: although the fast Fourier transform threshold method can realize frequency domain filtering, the effect of suppressing wideband noise is limited, and the deviation of the threshold setting is easy to cause distortion of the pulse characteristics; although the empirical mode decomposition and its improved algorithm can adaptively decompose the signal, it is limited by mode aliasing and end effect, and a large amount of interference is often left in the reconstructed signal; the singular value decomposition method has good filtering effect on periodic narrowband interference, but when the white noise and the partial discharge pulse spectrum overlap, it is difficult to distinguish the two through singular values, so that the signal-to-noise ratio after denoising is limited; the variational mode decomposition method relies on artificial experience trial and error for key parameters, and in the complex electromagnetic environment of the converter transformer, parameter mismatch often leads to incomplete decomposition or excessive noise suppression, which seriously affects the accuracy of subsequent defect diagnosis. The method of "compressed sensing reconstruction + variational mode decomposition" proposed by the prior art can suppress narrowband interference frequency leakage through a window function, and separate the narrowband signal by using the difference in frequency domain sparsity, but it does not break through the limitation of single domain constraint, and the suppression effect on complex aliasing noise still has room for improvement.

[0005] By analyzing the problems of these methods, it can be found that the traditional methods rely on the constraint mechanism of a single domain, and it is difficult to fully characterize the dual characteristics of the partial discharge signal in the time-space distribution and the frequency spectrum. SUMMARY

[0006] In order to overcome the shortcomings of the prior art, the present application provides a double-domain non-convex joint optimization device state signal denoising method and system, which realizes the cooperative iteration of double-domain variables based on an improved ADMM algorithm, and designs a double-domain residual index to dynamically judge the convergence, thereby reducing redundant iterations while ensuring denoising accuracy.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: In a first aspect, the present invention provides a method for denoising device state signals using dual-domain non-convex joint optimization, comprising: Acquire partial discharge signals containing aliasing noise; The partial discharge signal is modeled to obtain a one-dimensional observation signal, which is then converted into a two-dimensional observation matrix. Based on the two-dimensional observation matrix, a two-domain cooperative regularization model is obtained through two-domain decomposition. The two-domain cooperative regularization model is then optimized using a non-convex penalty function to obtain a non-convex optimized regularization model. An improved cooperative alternating direction multiplier algorithm is used to iteratively solve the non-convex optimization regular model. By combining the original residual threshold and the dual residual threshold, the updated two-dimensional observation matrix of the partial discharge signal is obtained. The two-dimensional observation matrix of the partial discharge signal is then inversely transformed to obtain the denoised partial discharge signal.

[0008] In a further technical solution, the partial discharge signal containing aliasing noise includes a partial discharge signal, a periodic narrowband interference signal, and a white noise interference signal.

[0009] A further technical solution involves converting the one-dimensional observation signal into a corresponding two-dimensional observation matrix using the Hankel matrix, and extracting the periodic narrowband interference signal based on the interference basis matrix and sparse representation vector.

[0010] A further technical solution is that the dual-domain collaborative regularization model is expressed as follows:

[0011] in, It is a two-dimensional observation matrix. This is a two-dimensional observation matrix of the partial discharge signal. This is a sparse representation vector of a periodic narrowband interference signal. For the interference basis matrix, It is the Frobenius norm. for Norm, For nuclear norm, For interference regularization coefficients, This is the local discharge regularization coefficient.

[0012] A further technical solution is to replace the convex norm with a minimax nonconvex penalty function, resulting in a nonconvex optimized regularized model, expressed as:

[0013] in, For spectral domain constraints, For spatial constraints, It is a minimum-maximum non-convex penalty function. sparse representation vector The One element, The second observation matrix of the partial discharge signal is the first... A singular value, , Let be the penalty intensity parameter of the minimax nonconvex penalty function. , is the parameter for the degree of nonconvexity of the minimal-maximum nonconvex penalty function.

[0014] A further technical solution yields the updated two-dimensional observation matrix of the partial discharge signal as follows: The non-convex optimization regularization model is decomposed based on the improved cooperative alternating direction multiplier algorithm to obtain the augmented Lagrangian function; Based on the augmented Lagrangian function, the spectral domain variables and spatial domain variables are optimized by thresholding the minimax nonconvex penalty function to obtain the updated spectral domain variables and spatial domain variables. The two-dimensional observation matrix of the partial discharge signal is updated by analytical solution, and the product of the interference basis matrix and the sparse representation vector of the periodic narrowband interference signal is updated by matrix inversion, thereby updating the Lagrange multipliers. Based on the updated two-dimensional observation matrix of the partial discharge signal, spatial variables, the product of the interference basis matrix and the sparse representation vector of the periodic narrowband interference signal, and spectral domain variables, the original residual and dual residual are calculated respectively. Convergence judgment is performed in combination with the corresponding threshold, and finally the updated two-dimensional observation matrix of the partial discharge signal is obtained.

[0015] A further technical solution is that the improved cooperative alternating direction multiplier algorithm introduces the product of the two-dimensional observation matrix of the partial discharge signal, the interference basis matrix, and the sparse representation vector of the periodic narrowband interference signal as an auxiliary variable, decomposing the non-convex optimization regular model into a spatial domain subproblem and a spectral domain subproblem.

[0016] Secondly, the present invention provides a dual-domain non-convex joint optimization system for denoising device state signals, comprising: The signal acquisition module is configured to acquire a partial discharge signal containing aliasing noise; The signal modeling module is configured to: model the partial discharge signal to obtain a one-dimensional observation signal, and convert the one-dimensional observation signal into a two-dimensional observation matrix; based on the two-dimensional observation matrix, obtain a two-domain cooperative regularization model through two-domain decomposition, and optimize the two-domain cooperative regularization model using a non-convex penalty function to obtain a non-convex optimized regularization model; The signal denoising module is configured to: iteratively solve the non-convex optimization regular model using an improved cooperative alternating direction multiplier algorithm; combine the original residual threshold and the dual residual threshold to obtain the updated two-dimensional observation matrix of the partial discharge signal; and perform an inverse transformation on the two-dimensional observation matrix of the partial discharge signal to obtain the denoised partial discharge signal.

[0017] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a dual-domain non-convex joint optimization method for denoising device state signals as described in the first aspect.

[0018] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the device state signal denoising method of dual-domain non-convex joint optimization as described in the first aspect.

[0019] The above one or more technical solutions have the following beneficial effects: This invention focuses on the problem of aliasing of partial discharge signals with noise and interference. It innovatively constructs a non-convex optimization regularization model that coordinates the spatial and spectral domains. By introducing MCP to overcome the theoretical limitations of traditional convex norm constraints, it applies differentiated non-convex constraints to the low-rank characteristics of spatial signals and the sparsity characteristics of spectral signals, thereby effectively stripping away multiple types of interference while accurately preserving the transient characteristics and amplitude information of weak partial discharge pulses. This provides reliable technical support for partial discharge detection in the complex electromagnetic environment of UHV converter transformers.

[0020] This invention combines dual-domain features and non-convex constraints to construct an optimization objective function. In the spatial domain, a low-rank representation of the partial discharge signal is constructed using the Hankel matrix to suppress white noise. In the spectral domain, Fourier transform is used to characterize the spectral sparsity of the periodic narrowband interference signal, constraining the spectral peak characteristics of the signal. At the same time, a non-convex penalty function is used instead of a convex norm to improve the denoising effect.

[0021] This invention employs an improved ADMM algorithm that simultaneously considers the low-rank problem in the spatial domain and the sparsity problem in the spectral domain. It coordinates the iterative updates of the two domains through Lagrange multipliers to ensure the consistency of the dual-domain constraints and avoid local optima caused by single-domain optimization. Furthermore, it designs a dual-domain residual index to dynamically judge convergence, thereby reducing redundant iterations while ensuring denoising accuracy. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0023] Figure 1This is a flowchart illustrating the construction process of the non-convex optimization regularization model according to an embodiment of the present invention; Figure 2 This is a flowchart of the solution process for the non-convex optimization regularization model in an embodiment of the present invention. Detailed Implementation

[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0025] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0026] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0027] Example 1 This embodiment discloses a dual-domain non-convex joint optimization method for denoising device status signals, which includes the following steps: S1: Acquire partial discharge signals containing aliasing noise; S2: The partial discharge signal is modeled to obtain a one-dimensional observation signal, and the one-dimensional observation signal is converted into a two-dimensional observation matrix; based on the two-dimensional observation matrix, a two-domain cooperative regularization model is obtained through two-domain decomposition, and a non-convex penalty function is used to optimize the two-domain cooperative regularization model to obtain a non-convex optimized regularization model. In this embodiment, as Figure 1 As shown, the observed signal of partial discharge (PD) signal. The observed signal often contains periodic narrowband interference signals and Gaussian white noise interference signals. The observed signal is now modeled as follows:

[0028] in, This is a partial discharge signal containing aliasing noise. This is a partial discharge signal. It is a periodic narrowband interference signal. This is a white noise interference signal.

[0029] Based on existing theoretical knowledge and extensive experimental research, partial discharge signals containing aliasing noise mainly include partial discharge signals, periodic narrowband interference signals, and white noise interference signals. The prior knowledge summarized through numerous experiments and theoretical analyses does not directly distinguish between these components, but rather assumes that the observed signal is composed of the superposition of these three types of components with different characteristics, providing a basis for subsequent signal separation using these characteristic differences.

[0030] By selecting a Hankel matrix window length that matches the number of sampling points during the fault cycle of the partial discharge signal, the one-dimensional data of each sub-component of the noisy signal is transformed into a two-dimensional feature matrix (two-dimensional observation matrix) using the Hankel matrix. The one-dimensional observation signal model can then be converted into:

[0031] in, Represents a one-dimensional observation signal The resulting two-dimensional observation matrix This represents the two-dimensional characteristic matrix converted from the partial discharge signal. The column vectors in the matrix have high similarity, forming a low-rank matrix; This represents the two-dimensional characteristic matrix transformed from a periodic interference signal. The column vectors in the matrix do not have similarity, and the matrix is ​​a non-low-rank matrix. This represents the two-dimensional feature matrix transformed from white noise interference signal. The column vectors in the matrix do not have similarity, and it is a non-low-rank matrix.

[0032] For two-dimensional observation matrix Singular value decomposition yields ,in, Represents a left singular matrix. It is a right singular matrix. The matrix is ​​a diagonal matrix representing the energy distribution. The sparsity of partial discharge pulses is reflected in the fact that their singular values ​​are mainly concentrated in the initial stage of the sequence. Therefore, feature information can be enhanced by designing operators to preserve the large initial singular values. Based on the characteristics of different signals, their singular values ​​also have characteristics. The singular values ​​of partial discharge signals have low rank. The step of minimizing the nuclear norm in the later model can effectively extract low-rank information from the observed signal.

[0033] Assumption As the interference basis matrix, to capture periodic harmonic interference, the periodic narrowband signal... After transformation (using the frequency selectivity of the orthogonal Fourier dictionary to convert the time-domain line spectrum signal into frequency-domain sparse coefficients), the interference sparse vector It can be represented as In other words, periodic narrowband interference signals can be extracted based on the interference basis matrix and sparse representation vectors. The two-dimensional observation signal model (two-dimensional observation matrix) can then be expressed as:

[0034] in, This represents the reconstruction operator, which maps coefficients to the observation space.

[0035] In the time domain, the partial discharge signal is represented as a sparsely distributed spike, while the interference is periodic and appears as a continuous waveform. In the frequency domain, the spectrum of the partial discharge signal is concentrated in a specific frequency band, while power frequency interference has strong energy peaks at 50 / 60Hz and its harmonics. Through a dual-domain decomposition of the spatial and spectral domains, the distribution patterns of the partial discharge pulses and interference can be accurately located. Based on the signal model, the low-rank prior of the partial discharge signal in the time domain, and the sparse prior of the periodic narrowband interference, a dual-domain cooperative regularization model (original objective function) can be proposed, expressed as:

[0036] in, It is a two-dimensional observation matrix. This is a two-dimensional observation matrix of the partial discharge signal. This is a sparse representation vector of a periodic narrowband interference signal. For interference base dictionary, It is the Frobenius norm. for Norm, For nuclear norm, For interference regularization coefficients, For local discharge regularization coefficients, For data fidelity items, , This is a regularization term.

[0037] Because when the pulse amplitude is small, the traditional convex norm (such as...) The nuclear norm penalty can over-suppress these signals, leading to the loss of weak signals. Furthermore, the convex norm often sacrifices local details to ensure global optimality. Therefore, the MCP (Mean Cross-Regulation) non-convex penalty function is used to replace the convex norm in the bi-domain collaborative regularization model for optimization. The resulting bi-domain feature objective function based on replacing the convex norm with a non-convex penalty function (i.e., the bi-domain collaborative non-convex optimization model, also known as the non-convex optimization regularization model) is as follows:

[0038] in, For spectral domain constraints, it is used to suppress redundant components in the interference features and retain sparse patterns that match the real interference; Spatial constraints are used to enhance the spectral characteristics of partial discharge pulses and weaken random noise and harmonic interference. It is a minimum-maximum non-convex penalty function; sparse vector The One element; The first of the partial discharge matrix One singular value; , The penalty intensity parameter for MCP, Used to control sparsity; the larger the value, the smaller the retained interfering features. Used to control the degree of singular value shrinkage; , The non-convexity parameter of MCP, Used to adjust the degree of non-convexity, usually taken as... ; Used to adjust the degree of non-convexity, affecting spatial resolution.

[0039] The Minimax Concave Penalty (MCP) function is chosen to constrain the low-rank spatial characteristics of the partial discharge signal and the sparse spectral characteristics of the interference signal. The MCP is chosen over the convex norm primarily because of its unique advantages in sparsity induction, feature selection, and signal preservation, making it suitable for scenarios requiring both interference suppression and key feature preservation. The MCP penalty function is piecewise, imposing a stronger penalty on small-amplitude elements (promoting sparsity) and a more constant penalty on elements exceeding a threshold (avoiding over-suppression of important signals). This characteristic allows for differentiated processing of strong and weak signals, thus more accurately preserving key features. The MCP is defined as follows:

[0040] Its derivative (threshold function) is:

[0041] in, The parameter representing the penalty intensity of MCP, This parameter represents the degree of non-convexity of the MCP. When... When the value is close to 0, the penalty intensity is lower than To reduce the suppression of weak signals, when When the value is large, the penalty approaches 0, preserving the true signal characteristics, through parameters. Control the sparsity to avoid overfitting.

[0042] Furthermore, in the original objective function, The L1 norm regularization term, when replaced by the MCP nonconvex penalty function, becomes... .when When the value is small, the penalty strength of MCP is lower than the L1 norm, reducing excessive suppression of weak interference components and avoiding the loss of components that may contain important information; when When the value is large, the penalty approaches a constant, preserving the true interference characteristics. This is achieved through parameters... Controlling sparsity Adjust the degree of non-convexity to avoid overfitting.

[0043] Furthermore, in the original objective function, The nuclear norm regularization term, when replaced by a non-convex penalty function, becomes... For smaller singular values ​​(which may correspond to noise or interference), the non-convex penalty function imposes a stronger penalty to suppress these interferences; for larger singular values ​​(which correspond to important partial discharge signal characteristics), the penalty strength is reduced, thus preserving these important characteristics. This is achieved through parameters... Controlling the degree of contraction of singular values, Adjusting the degree of non-convexity affects spatial resolution.

[0044] This approach allows for differentiated processing of strong and weak signals, achieving efficient separation of partial discharge signals from interference signals. Furthermore, by introducing multiple parameters, the penalty characteristics of the non-convex penalty function can be flexibly adjusted to adapt to different partial discharge signal scenarios and interference conditions, thereby improving the applicability and flexibility of the model.

[0045] S3: An improved cooperative alternating direction multiplier algorithm is used to iteratively solve the non-convex optimization regular model. Combining the original residual threshold and the dual residual threshold, the updated two-dimensional observation matrix of the partial discharge signal is obtained. The two-dimensional observation matrix of the partial discharge signal is then inversely transformed to obtain the denoised partial discharge signal.

[0046] In this embodiment, as Figure 2 As shown, the traditional Alternating Direction Method of Multipliers (ADMM) algorithm typically uses only a single residual index, which cannot fully reflect the characteristics of dual-domain optimization. This invention designs a dual-domain residual index. This novel convergence judgment mechanism considers both spectral and spatial domain characteristics and innovatively combines the original residual threshold (… ) and dual residual threshold ( This allows for the evaluation of the convergence state of the optimization process from different perspectives.

[0047] When the original residual When the constraint is satisfied, it indicates that the constraint conditions have been fully satisfied, and no further iteration optimization of the constraint-related terms is needed; when the dual residual... When this value is reached, it indicates that the update of the dual variable has become very small, the value of the objective function has stabilized, and the overall mold table of the two-domain optimization is close to the optimal solution. The following is the specific solution process for the two-domain feature objective function: S301: Based on the improved cooperative alternating direction multiplier algorithm, the dual-domain feature objective function (i.e., non-convex optimization regular model) is decomposed to obtain the augmented Lagrangian function.

[0048] This step is fundamental to the entire solution process. By introducing auxiliary variables, the original problem (the dual-domain characteristic objective function) is decomposed into two sub-problems: one in the spatial domain and one in the spectral domain. In other words, the original complex coupled problem is broken down into two relatively simple, alternately solvable sub-problems. The spatial domain sub-problem focuses on optimizing the spatial domain variables. The spectral domain subproblem focuses on optimizing spectral domain variables. This decomposition strategy is an innovative improvement on the traditional ADMM algorithm, suitable for handling partial discharge signals, which have complex dual-domain characteristics. Firstly, this invention introduces... and As an auxiliary variable, the original problem is transformed into a constrained optimization problem:

[0049] Then, we construct the augmented Lagrangian function, which combines the data fitting term, the MCP non-convex penalty term, and the constraint term:

[0050] By introducing Lagrange multipliers and This approach enables the coordinated solution of two subproblems. This decomposition method simplifies the problem's complexity and lays the foundation for subsequent bi-domain collaborative optimization.

[0051] S302: Based on the augmented Lagrangian function, the spatial domain variables and spectral domain variables are optimized by MCP thresholding to obtain the updated spatial domain variables and spectral domain variables.

[0052] (1) Spatial domain optimization (i.e., updating spatial domain variables) Focusing on optimizing the signal frequency components. With other variables fixed, the optimization objective is concentrated on the spatial domain variables. superior:

[0053] This step transforms the complex optimization problem into MCP thresholding of singular values:

[0054] First of all Performing singular value decomposition yields Then, the singular values ​​obtained from singular value decomposition... Applying the MCP threshold rule:

[0055] Since the singular values ​​of the partial discharge pulse are mainly concentrated in the initial stage of the sequence, MCP thresholding of the singular values ​​is performed. According to the MCP thresholding rule, the signal portion with large singular values ​​is retained, while the signal portion with small singular values ​​(mainly including white noise interference) is removed. This processing method can effectively preserve the important frequency components, i.e., the partial discharge signal, while suppressing noise. Finally, the updated two-dimensional observation matrix of the partial discharge signal is obtained through reconstruction. :

[0056] This step fully utilizes the characteristics of the non-convex penalty function of MCP, achieving the effect of "large coefficient, small penalty; small coefficient, large penalty", providing a high-quality spatial foundation for subsequent spectral domain optimization.

[0057] (2) Spectral domain optimization (i.e., updating spectral domain variables) This is another crucial step in the solution process, focusing on optimizing the signal's spectral domain characteristics. Similar to spatial domain optimization, while keeping other variables fixed, the optimization objective is concentrated on the spectral domain variables. superior:

[0058] Applying MCP thresholding to sparse representation vectors:

[0059] First, calculate the auxiliary terms: Then to Applying the MCP threshold rule:

[0060] After investigation Apply MCP thresholding to retain Large signal components, remove For small signal portions, this processing method can effectively extract periodic narrowband signals, preserve the pulse characteristics of partial discharge signals, and suppress spectral noise. Finally, through update operations, we obtain... This step complements spatial domain optimization, together forming the core of dual-domain collaborative optimization.

[0061] S303: Update the auxiliary variable X (the two-dimensional observation matrix of the partial discharge signal) through analytical solution, and update the auxiliary variable through matrix inversion. (The product of the interference basis matrix and the sparse representation vector of the periodic narrowband interference signal), and then the Lagrange multipliers are updated.

[0062] (1) After completing the spatial and spectral domain optimizations, the auxiliary variable X needs to be updated to obtain the updated X. This step updates X using an analytical solution rather than an iterative method, fixing the variable X. ,optimization :

[0063] Taking the derivative with respect to X and setting it to zero, we obtain a closed-form solution: Then, use this closed-form solution to calculate: This analytical solution method avoids complex iterative calculations, ensuring the algorithm's efficiency. Simultaneously, by introducing... The parameters can be flexibly balanced to optimize accuracy and computational efficiency.

[0064] (2) This step uses matrix inversion to handle complex transformation relationships, fixing... Optimize auxiliary variables Received the updated :

[0065] right Taking the derivative and setting it to zero, we obtain a matrix equation: Then, by solving this matrix equation, we obtain: This matrix inversion method can effectively handle complex transformation relationships and ensure the accuracy of the optimization process.

[0066] Updating the Lagrange multipliers ensures coordinated optimization of the two subproblems. and , so that:

[0067] .

[0068] This update method dynamically reflects changes in the optimization process, ensuring the stability and convergence of the algorithm.

[0069] S304: Based on the updated auxiliary variable X, spatial domain variable, and auxiliary variable The original residual and dual residual are calculated for the spectral domain variables respectively. The original residual and dual residual are compared with the corresponding thresholds. When both are less than or equal to the threshold, the algorithm converges and the iterative solution stops.

[0070] Convergence analysis is the final step in the entire solution process and is crucial for ensuring the effectiveness of the algorithm. This step involves designing a two-domain residual index to effectively determine convergence for non-convex optimization problems. Original residuals:

[0071] Dual residuals: .

[0072] By calculating the original residual and dual residuals ,when and The algorithm converges at this point. This dual condition ensures the stability and accuracy of the optimization process. Simultaneously, by introducing an initial residual threshold... and dual residual threshold Two thresholds can strike a balance between optimization accuracy and computational efficiency. Finally, by analyzing the changes in residuals, potential problems during the optimization process can be diagnosed, providing a basis for dynamically adjusting optimization parameters.

[0073] During the iteration process, the improved cooperative alternating direction multiplier algorithm is continuously optimized to suppress noise and retain the partial discharge signal. Finally, the updated auxiliary variable X, i.e. the two-dimensional observation matrix of the partial discharge signal, is subjected to inverse Hankel transformation to convert it back to a one-dimensional signal, thus obtaining the denoised partial discharge signal.

[0074] After obtaining noisy partial discharge (PD) signal data, the observed signal is standardized and input into a dual-domain cooperative ADMM-based MCP non-convex optimization model. Through cooperative iterative optimization in the spectral and spatial domains, the denoised PD signal can be output. The denoising effect is verified by comparing the root mean square error (RMSE) and spectral features, ensuring both effective suppression of noise components and complete preservation of the transient characteristics of the PD pulse (such as rise time and peak value). Finally, the stability and reliability of the denoising results are confirmed through convergence analysis of the dual-domain residual indices (including the original residual threshold and the dual residual threshold), providing a high-quality signal foundation for subsequent PD defect type identification and insulation status assessment.

[0075] In summary, this invention overcomes the limitations of single-dimensional constraints through dual-domain collaboration, preserving pulse morphology in the spatial domain and separating interference in the spectral domain, thus constructing a dual-dimensional closed-loop optimization. It uses a non-convex penalty function instead of a convex norm to overcome the problem of feature loss during convex optimization denoising, accurately preserving weak partial discharge features while suppressing noise. Based on an improved ADMM algorithm, it achieves collaborative iteration of dual-domain variables and designs a dual-domain residual index to dynamically judge convergence, reducing redundant iterations while ensuring denoising accuracy.

[0076] Example 2 This embodiment discloses a dual-domain non-convex joint optimization system for denoising device state signals, including: The signal acquisition module is configured to acquire a partial discharge signal containing aliasing noise; The signal modeling module is configured to: model the partial discharge signal to obtain a one-dimensional observation signal, and convert the one-dimensional observation signal into a two-dimensional observation matrix; based on the two-dimensional observation matrix, obtain a two-domain cooperative regularization model through two-domain decomposition, and optimize the two-domain cooperative regularization model using a non-convex penalty function to obtain a non-convex optimized regularization model; The signal denoising module is configured to: iteratively solve the non-convex optimization regular model using an improved cooperative alternating direction multiplier algorithm; combine the original residual threshold and the dual residual threshold to obtain the updated two-dimensional observation matrix of the partial discharge signal; and perform an inverse transformation on the two-dimensional observation matrix of the partial discharge signal to obtain the denoised partial discharge signal.

[0077] Example 3 The purpose of this embodiment is to provide a computing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method of Embodiment 1.

[0078] Example 4 The purpose of this embodiment is to provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the method of Embodiment 1.

[0079] The steps and methods involved in the apparatuses of Embodiments 3 and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0080] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0082] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for denoising device state signals using dual-domain non-convex joint optimization, characterized in that, include: Acquire partial discharge signals containing aliasing noise; The partial discharge signal is modeled to obtain a one-dimensional observation signal, and then the one-dimensional observation signal is converted into a two-dimensional observation matrix. Based on the two-dimensional observation matrix, a two-domain collaborative regularization model is obtained through two-domain decomposition. The two-domain collaborative regularization model is then optimized using a non-convex penalty function to obtain a non-convex optimized regularization model. An improved cooperative alternating direction multiplier algorithm is used to iteratively solve the non-convex optimization regular model. By combining the original residual threshold and the dual residual threshold, the updated two-dimensional observation matrix of the partial discharge signal is obtained. The two-dimensional observation matrix of the partial discharge signal is then inversely transformed to obtain the denoised partial discharge signal.

2. The device state signal denoising method of dual-domain non-convex joint optimization as described in claim 1, characterized in that, The partial discharge signal containing aliasing noise includes partial discharge signals, periodic narrowband interference signals, and white noise interference signals.

3. The device state signal denoising method of dual-domain non-convex joint optimization as described in claim 2, characterized in that, The one-dimensional observation signal is converted into the corresponding two-dimensional observation matrix using the Hankel matrix, and the periodic narrowband interference signal is extracted based on the interference basis matrix and sparse representation vector.

4. The device state signal denoising method of dual-domain non-convex joint optimization as described in claim 1, characterized in that, The dual-domain collaborative regularization model is expressed as follows: in, It is a two-dimensional observation matrix. This is a two-dimensional observation matrix of the partial discharge signal. This is a sparse representation vector of a periodic narrowband interference signal. For the interference basis matrix, It is the Frobenius norm. for Norm, For nuclear norm, For interference regularization coefficients, This is the local discharge regularization coefficient.

5. The device state signal denoising method of dual-domain non-convex joint optimization as described in claim 4, characterized in that, By replacing the convex norm with a minimax nonconvex penalty function, a nonconvex optimized regularized model is obtained, expressed as: in, For spectral domain constraints, For spatial constraints, It is a minimum-maximum non-convex penalty function. sparse representation vector The One element, The second observation matrix of the partial discharge signal is the first... A singular value, , Let be the penalty intensity parameter of the minimax nonconvex penalty function. , is the parameter for the degree of nonconvexity of the minimal-maximum nonconvex penalty function.

6. The device state signal denoising method of dual-domain non-convex joint optimization as described in claim 1, characterized in that, The updated two-dimensional observation matrix of the partial discharge signal is as follows: The non-convex optimization regularization model is decomposed based on the improved cooperative alternating direction multiplier algorithm to obtain the augmented Lagrangian function; Based on the augmented Lagrangian function, the spectral domain variables and spatial domain variables are optimized by thresholding the minimax nonconvex penalty function to obtain the updated spectral domain variables and spatial domain variables. The two-dimensional observation matrix of the partial discharge signal is updated by analytical solution, and the product of the interference basis matrix and the sparse representation vector of the periodic narrowband interference signal is updated by matrix inversion, thereby updating the Lagrange multipliers. Based on the updated two-dimensional observation matrix of the partial discharge signal, spatial variables, the product of the interference basis matrix and the sparse representation vector of the periodic narrowband interference signal, and spectral domain variables, the original residual and dual residual are calculated respectively. Convergence judgment is performed in combination with the corresponding threshold, and finally the updated two-dimensional observation matrix of the partial discharge signal is obtained.

7. The device state signal denoising method of dual-domain non-convex joint optimization as described in claim 6, characterized in that, The improved cooperative alternating direction multiplier algorithm introduces the product of the two-dimensional observation matrix of the partial discharge signal, the interference basis matrix, and the sparse representation vector of the periodic narrowband interference signal as an auxiliary variable, decomposing the non-convex optimization regular model into a spatial subproblem and a spectral subproblem.

8. A dual-domain non-convex joint optimization system for denoising device state signals, characterized in that, include: The signal acquisition module is configured to acquire a partial discharge signal containing aliasing noise; The signal modeling module is configured to: model the partial discharge signal to obtain a one-dimensional observation signal, and convert the one-dimensional observation signal into a two-dimensional observation matrix; Based on the two-dimensional observation matrix, a two-domain collaborative regularization model is obtained through two-domain decomposition. The two-domain collaborative regularization model is then optimized using a non-convex penalty function to obtain a non-convex optimized regularization model. The signal denoising module is configured to: iteratively solve the non-convex optimization regular model using an improved cooperative alternating direction multiplier algorithm; combine the original residual threshold and the dual residual threshold to obtain the updated two-dimensional observation matrix of the partial discharge signal; and perform an inverse transformation on the two-dimensional observation matrix of the partial discharge signal to obtain the denoised partial discharge signal.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the dual-domain non-convex joint optimization method for denoising device state signals as described in any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the dual-domain non-convex joint optimization device state signal denoising method as described in any one of claims 1-7.

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