An Ultrasonic Denoising Method and System Based on SGF-ASO Optimization Algorithm

Abstract

This invention provides an ultrasonic denoising method and system based on the SGF-ASO optimization algorithm, belonging to the field of electrical equipment condition monitoring and fault diagnosis technology. The method includes: acquiring ultrasonic echo signals from transformer windings and preprocessing them; performing SGF analysis on the preprocessed ultrasonic echo signals to generate multi-scale spectra and extracting spatial gradient features, generating a fused spectral gradient map through cross-scale fusion; constructing an oil temperature-adaptive ASO constraint model to perform adaptive sparse optimization on the multi-scale spectra; performing inverse short-time Fourier transform on each scale of the optimized multi-scale spectrum to obtain a multi-scale time-domain signal set, and fusing the time-domain signal set to output the denoised ultrasonic echo signal. This invention enhances the structural preservation capability of ultrasonic signals in high-temperature and complex environments, achieving high-fidelity noise reduction and oil temperature-adaptive processing through a multi-scale gradient-guided sparse optimization mechanism.

Description

Technical Field

[0001] This invention belongs to the field of electrical equipment condition monitoring and fault diagnosis technology, and more specifically, relates to an ultrasonic denoising method and system based on the SGF-ASO optimization algorithm. Background Technology

[0002] During the operation of a power system, the transformer, as a core energy conversion device, directly affects the stability and safety of the entire system due to the condition of its windings. With the increasing load on power equipment and the influence of non-ideal factors such as rising ambient temperatures, especially in high-temperature oil-immersed transformers, windings are prone to mechanical deformation, loosening, or insulation aging, posing potential risks. To achieve early and accurate diagnosis, non-contact ultrasonic testing methods have gained widespread attention. Compared to traditional electrical testing methods, ultrasonic signals have advantages such as strong penetration, sensitivity to insulation damage, and non-destructive nature, making them particularly suitable for detecting internal winding defects or weak anomalies such as partial discharge.

[0003] However, ultrasonic signals are highly susceptible to contamination from complex backgrounds such as surrounding oil medium disturbances, electromagnetic interference, and thermal noise during propagation, resulting in typical challenges such as non-stationarity, low signal-to-noise ratio, and high transient feature obscuring of the original signal. Especially in transformer environments operating under high loads, traditional filtering or single-scale Fourier denoising algorithms often struggle to balance signal integrity with noise suppression. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides an ultrasonic denoising method and system based on the SGF-ASO optimization algorithm. The aim is to achieve high-fidelity and structure-preserving noise reduction processing of ultrasonic signals under strong non-stationary interference, which is particularly suitable for power equipment health assessment scenarios such as high-temperature transformer winding condition monitoring.

[0005] The present invention adopts the following technical solution.

[0006] The first aspect of this invention provides an ultrasonic denoising method based on the SGF-ASO optimization algorithm, comprising the following steps:

[0007] Acquire ultrasonic echo signals from transformer windings and perform preprocessing;

[0008] SGF analysis was performed on the preprocessed ultrasonic echo signal to generate multi-scale spectra and extract spatial gradient features. A fused spectral gradient map was generated by cross-scale fusion.

[0009] Using the fused spectral gradient map as a structural guide, an oil temperature-adaptive ASO constraint model is constructed to perform adaptive sparse optimization on the multi-scale spectrum;

[0010] Inverse short-time Fourier transform is performed on each scale spectrum in the optimized multi-scale spectrum to obtain a multi-scale time-domain signal set. The time-domain signal set is then fused to output a denoised ultrasonic echo signal.

[0011] Optionally, the preprocessing includes:

[0012] The ultrasonic echo signal is subjected to mean elimination to remove the DC component of the signal;

[0013] The passband range of the bandpass filter is set according to the frequency band of mechanical vibration of the transformer winding, and the bandpass filtering operation is performed.

[0014] The maximum absolute value normalization process is used to normalize the amplitude of the bandpass filtered signal to a preset dynamic range.

[0015] Optionally, performing SGF analysis on the preprocessed ultrasonic echo signal includes:

[0016] Based on the preprocessed ultrasonic echo signal, multi-scale spectra are obtained using STFTs with different window lengths.

[0017] Calculate the gradient magnitude of the spectrum at each scale along the time and frequency axes to form a multi-scale gradient map;

[0018] The gradient threshold weighting factor is determined based on the transformer winding structure type, and the adaptive enhancement threshold of the gradient map at each scale is calculated using the gradient threshold weighting factor.

[0019] Based on the adaptive enhancement threshold, the gradient map at each scale is binarized to generate a mask for structurally significant regions.

[0020] The original spectra at each scale are weighted and fused using the mask to generate a fused spectral gradient map.

[0021] Optionally, the step of determining the gradient threshold weighting factor based on the transformer winding structure type includes:

[0022] The transformer winding structure type is determined based on preset classification rules, and the structure type includes composite insulation structure and homogeneous symmetrical structure;

[0023] For transformer windings with composite insulation structure, the gradient threshold weighting factor is set to the first preset range.

[0024] For transformer windings with homogeneous and symmetrical structures, the gradient threshold weighting factor is set to a second preset range.

[0025] Wherein, the lower limit of the first preset range is greater than the upper limit of the second preset range.

[0026] Optionally, the step of calculating the adaptive enhancement threshold of the gradient map at each scale using the gradient threshold weighting factor includes:

[0027] The adaptive enhancement threshold of the gradient map at each scale is obtained by calculating the median of the gradient magnitude and then multiplying it by the gradient threshold weighting factor.

[0028] Optionally, the acquisition of multi-scale spectra using STFTs with different window lengths includes:

[0029] The high-frequency transient characteristics of the winding are captured by a set short-window STFT, and the low-frequency steady-state characteristics of the winding are extracted by a set long-window STFT.

[0030] Optionally, the construction of the oil temperature adaptive ASO constraint model includes:

[0031] Establish a sparse optimization objective function that includes a spectrum reconstruction error term and a structure-guided sparse penalty term, wherein the spectrum reconstruction error term is the squared L2 distance between the optimized spectrum and the noisy spectrum, and the structure-guided sparse penalty term is the L1 constraint of the spectral coefficients weighted by the fused spectrum gradient map.

[0032] The weight parameters of the structure-guided sparse penalty term are dynamically correlated with the transformer operating oil temperature.

[0033] The sparse optimization objective function is solved using FISTA, and the optimized multi-scale spectrum is output.

[0034] Optionally, the calculation of the weight parameters of the structure-guided sparse penalty term includes:

[0035] Set the ambient temperature reference weight, room temperature reference temperature, transformer maximum operating temperature, and adjustment coefficient;

[0036] The difference between the real-time oil temperature and the room temperature reference temperature is calculated and divided by the difference between the transformer's maximum operating temperature and the room temperature reference temperature to obtain the normalized proportional coefficient.

[0037] Multiply the proportional coefficient by the adjustment coefficient, add 1, and then multiply by the room temperature reference weight to output the final weight parameter value.

[0038] Optionally, solving the sparse optimization objective function using FISTA includes:

[0039] Initialize the iteration variables and step size parameters;

[0040] In each iteration, the gradient direction of the objective function is calculated;

[0041] Update the spectrum estimate based on the current iteration step size and gradient direction;

[0042] A soft thresholding operation is performed on the updated spectrum estimate. The threshold for the soft thresholding operation is determined by the weighting parameter of the structure-guided sparse penalty term and the fused spectrum gradient map.

[0043] Update acceleration parameters;

[0044] Repeat the iterations until the preset convergence condition is met or the maximum number of iterations is reached.

[0045] The second aspect of this invention provides an ultrasonic denoising system based on the SGF-ASO optimization algorithm, and an ultrasonic denoising method based on the SGF-ASO optimization algorithm described in the first aspect of this invention, comprising:

[0046] The signal acquisition module, preprocessing module, spectral gradient analysis module, sparse optimization module, and signal reconstruction module include:

[0047] The signal acquisition module is used to acquire ultrasonic echo signals from the transformer windings via an ultrasonic transducer.

[0048] The preprocessing module is used to perform mean elimination, bandpass filtering, and maximum absolute value normalization on the signal.

[0049] The spectral gradient analysis module is used to perform multi-window long STFT to generate multi-scale spectra, extract each spectral gradient, and fuse them to generate a structure guidance map.

[0050] The sparse optimization module is used to constrain the sparse optimization process with a structure-guided graph, dynamically adjust the penalty weights according to the oil temperature, and solve the optimization spectrum using the FISTA algorithm.

[0051] The signal reconstruction module is used to perform inverse STFT on the optimized spectrum and fuse it to output a denoised signal.

[0052] Compared with the prior art, the beneficial effects of the present invention include at least the following:

[0053] (1) This invention provides an ultrasonic signal processing method based on multi-resolution spectral gradient analysis. Its core innovation lies in: employing short-time Fourier transform to perform layered modeling of the ultrasonic signal, with different window lengths corresponding to different time-frequency resolutions, thereby simultaneously capturing transient high-frequency pulses and low-frequency background patterns within a unified spectral framework. Based on this, a spectral gradient map is introduced for edge-aware modeling, generating a frequency structure mask. This mask can selectively preserve significant structural regions in the spectral domain while softly suppressing unstructured noise. This method significantly improves the local contrast and structural clarity of the ultrasonic signal spectrum under non-stationary noise backgrounds, providing higher-quality data support for subsequent fault detection or feature extraction.

[0054] (2) This invention further proposes a spectrum denoising method that integrates an adaptive sparse optimization (ASO) mechanism. Based on sparse representation theory, this method constructs an optimization model with structural prior constraints: by assigning weighted regularization terms to structural regions in the multi-scale spectrum, it suppresses low-sparseness, approximately uniformly distributed background interference components while preserving anomalous structural information. Furthermore, the algorithm introduces signal scene perception parameters to adaptively adjust the regularization coefficient and gradient threshold, achieving adaptive optimization for the application object and environmental noise characteristics. To improve solution efficiency, the method integrates a fast iterative threshold shrinkage algorithm, significantly reducing computational complexity while ensuring the physical consistency and accuracy of the sparse solution, and introduces a temperature-related regularization weight function. This enhances the robustness of the algorithm under high oil temperature conditions in transformers. Overall, the proposed method demonstrates higher robustness, sensitivity, and noise reduction performance in scenarios such as high-temperature oil-immersed transformer windings, and possesses broad engineering practical value. Attached Figure Description

[0055] Figure 1 This is a flowchart of the SGF-ASO optimization algorithm provided according to an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the simulated original ultrasonic signal and the noise-tainted ultrasonic signal provided in accordance with the embodiments of the present invention;

[0057] Figure 3 This is a schematic diagram of STFT decomposition results corresponding to different window lengths provided in accordance with embodiments of the present invention;

[0058] Figure 4 These are the original spectrum and the denoised spectrum provided according to embodiments of the present invention;

[0059] Figure 5 This is a schematic diagram of the ultrasonic signal after denoising using the SGF-ASO optimization algorithm provided in accordance with an embodiment of the present invention;

[0060] Figure 6 This is a flowchart of a method provided according to an embodiment of the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0062] In Example 1, this invention provides an ultrasonic denoising method based on the SGF-ASO optimization algorithm, such as... Figure 6 As shown, it includes the following steps:

[0063] Step S1: Acquire the ultrasonic echo signal of the transformer winding and perform preprocessing.

[0064] Preferably, in this example, the acquisition and noise reduction preprocessing of ultrasonic signals from transformer windings includes the following steps:

[0065] Step S11: Select an ultrasonic transducer suitable for testing the transformer windings based on the actual appearance data and internal structure of the transformer windings.

[0066] Step S12: The transmitter emits an ultrasonic signal, and the receiver receives the ultrasonic signal after it has propagated through the inside of the transformer windings.

[0067] Step S13: Preprocess the received ultrasonic echo signal for subsequent operations.

[0068] Preferably, the ultrasonic echo signal received during docking is preprocessed, including the following steps:

[0069] Step S131: Remove the DC component from the ultrasonic echo signal to eliminate the constant offset in the signal and prevent the spectrum from being dominated by low-frequency peaks.

[0070] DC component removal is a fundamental operation in signal cleaning, and its main purpose is to eliminate constant offsets in the signal that may be introduced by the bias of the acquisition equipment or power supply drift. This operation is usually achieved by subtracting the mean of the entire signal, thereby avoiding the low-frequency spikes caused by the DC component in the frequency domain, which would otherwise mask the true physical characteristics with spectral distortion.

[0071] Step S132, Band-pass filtering, using an FIR / IIR filter to filter out high-frequency noise and low-frequency drift;

[0072] Implementing bandpass filtering is equally crucial. The passband range should be appropriately set based on the transformer winding structure and transducer frequency response characteristics, typically ranging from 20kHz to 300kHz. FIR filters with good phase response can be used to ensure signal shape preservation, or IIR filters can be used in applications with higher real-time requirements to reduce computational load. When designing filters, excessive passband ripple or the introduction of insufficient out-of-band attenuation side peaks should be avoided. Furthermore, in practical applications, it is recommended to visualize and verify the filtering effect using frequency response analysis tools.

[0073] Step S133, Max-abs normalization, the specific formula is as follows:

[0074]

[0075] To standardize the amplitude range between different samples, prevent sparse optimization from being affected by extreme values.

[0076] Max-abs normalization is a crucial step in improving the convergence and robustness of the algorithm. By dividing all sampled points of the signal by its maximum absolute value, it ensures that the processed signal's numerical range is uniformly within [−1, 1], helping to avoid numerical instability issues in subsequent spectral processing or sparse modeling. In implementation, it should be ensured that the normalization operation is performed only on the filtered signal to prevent high-amplitude noise points from interfering with the normalization result. Through this series of preprocessing steps, invalid interference components in the original echo signal are significantly suppressed, while the signal's structure and characteristics are preserved, thus laying a solid foundation for subsequent multi-resolution spectral analysis and denoising optimization.

[0077] Preferably, the ultrasonic echo signal received during docking is preprocessed and can also undergo window weighting to reduce boundary leakage. This step has a particularly large impact on short signal segments or edge parts.

[0078] Step S2: Perform multi-resolution spectral gradient analysis on the preprocessed ultrasonic signal to generate a multi-scale spectrum. Extract spatial gradient features based on the multi-scale spectrum and generate a fused spectral gradient map through cross-scale fusion.

[0079] Preferably, step S2 includes:

[0080] like Figure 1As shown, SGF (Spectral Gradient Fusion) for ultrasonic signals refers to extracting gradient features from the spectrum at different time-frequency resolution scales by performing Short-Time Fourier Transform (STFT) on the ultrasonic signal. This extracts key information such as structural edges, transient changes, and local discontinuities in the signal. Based on this, information fusion mechanisms at different scales, such as weighted averaging, maximum response fusion, or structure-guided fusion strategies, are used to synthesize the response intensity and spatial consistency of the spectral gradients at each resolution, ultimately forming a fused spectral image with stronger contrast and higher structural sensitivity. The greatest advantage of this method is that, on the one hand, it fully utilizes the heterogeneous expressive power of spectral gradients at different scales for noise and structural responses, enhancing weak structures and detailed regions at certain scales; on the other hand, the fusion operation effectively suppresses the spread of unstructured random noise in the spectral gradient, improving the robustness and localization accuracy of structural edges. Compared to single-scale spectral analysis, SGF not only improves adaptability to non-steady-state, broadband signals (such as ultrasonic echoes), but also significantly enhances the sparse expressiveness of the signal while preserving structural details, providing high-quality structural priors for subsequent sparse optimization and denoising. This method is particularly suitable for handling ultrasonic detection tasks with low signal-to-noise ratios and complex structural features, such as the high-resolution identification and early diagnosis of transformer winding defects in this invention.

[0081] In this embodiment, the SGF (Spectral Gradient Fusion) analysis of the ultrasonic signal includes the following steps:

[0082] Step S21: Perform a Short-Time Fourier Transform (STFT) on the input signal, and perform time-frequency analysis on the signal with different window lengths to obtain complete complex spectrum information at multiple time-frequency resolutions. Long windows are used for low frequencies, and short windows are used for high frequencies. The STFT is defined as follows:

[0083]

[0084] In the formula, and Represents the time factor. Represents frequency, and These represent the original ultrasonic signal and the window function, respectively. The window function can be either a Hanning window or a Hamming window. The Hanning window is suitable for tasks more sensitive to time-domain edges, such as transient signal detection, impact response extraction, and non-stationary event analysis; the Hamming window is suitable for applications emphasizing the dominant frequency and sensitivity to low-frequency interference, such as speech, harmonics, periodic signals, and steady-state signal processing. In this invention, the ultrasonic signal used to detect the transformer winding state has instantaneous high frequencies, weak structural signals, and strong background noise. Therefore, a Hanning window is chosen to reduce interference from boundary artifacts and spectral leakage. Three window lengths are selected: 128, 256, and 512. Smaller windows extract high-frequency details, while larger windows are used for low-frequency trends.

[0085] The Hanning window is a cosine square function, and its time-domain form can be expressed as:

[0086]

[0087] Where k is the kth sample point of the current window function, and N is the total length of the window function, that is, the width of the window, which is also the sample point of the window function used in each frame of STFT;

[0088] The Hamming window function is an improved raised cosine function, defined as:

[0089]

[0090] For example, the present invention can obtain noise-free signals and noisy signals through simulation on the MATLAB platform, such as... Figure 2 As shown, the STFT results for different window lengths are obtained simultaneously. Figure 3 As shown.

[0091] The resulting spectra are then stacked into a spectral volume map to enhance the perception of noise and signal structure at different time scales.

[0092] Step S22: Extract the amplitude spectrum from the spectrum at each scale and calculate its gradient information on the frequency axis and time axis to obtain the multi-scale spectral gradient map. The spatial gradient formula for the STFT amplitude spectrum is as follows:

[0093]

[0094] These gradients reflect the edges, textures, or abrupt changes in the energy distribution of the signal spectrum, and can be regarded as a multidimensional characterization of the signal structure saliency.

[0095] Since the edges of high-frequency defects exhibit high-amplitude gradient changes in the frequency spectrum, an adaptive gradient enhancement strategy is used to obtain the gradient threshold, i.e.:

[0096]

[0097] This is the gradient threshold weighting factor, with a value range of [2,5], used to control the enhancement degree of structural response in multi-scale spectral gradient fusion. Specifically, for complex large transformer windings with complex metal inserts or heterogeneous composite structures, Preferably 4 to 5; for simple transformer windings with uniform structure and strong axial symmetry, Preferably, the threshold is 2 to 3. After calculating the adaptive enhancement threshold, a threshold-based structure mask can be optionally extracted from the spectral gradient map to select gradient values ​​higher than the threshold value. Regions identified as structurally significant are considered structurally significant, while regions below a threshold are treated as noise-dominated areas. This approach helps introduce spatial guidance information in subsequent sparse optimization, enabling differentiated treatment of structural and unstructured regions. The adaptive gradient-enhanced threshold is not only used for identifying structurally significant regions but is also the core basis for constructing structure-aware weights in sparse optimization. Its introduction greatly enhances the robustness and adaptability of the method, making it particularly suitable for detecting subtle defects in complex electrical equipment structures.

[0098] Step S23: Spectral Gradient Fusion is used to weighted integrate gradient maps at different scales, as shown in the following formula:

[0099]

[0100] in, Represents the weights corresponding to each spatial gradient. The weighting strategy, based on prior information such as entropy, local contrast, and frequency band energy distribution, ensures that the fusion result reflects high-resolution details while maintaining robustness at low resolution. This fused gradient map not only accurately locates the structural regions of the signal but also mitigates inconsistent noise perturbations across the cross-scale spectrum.

[0101] Step S3: Using the fused spectral gradient map as a structural guide, a sparse optimization model is constructed to perform adaptive sparse optimization on the multi-scale spectrum, resulting in the optimized multi-scale spectrum.

[0102] This paper utilizes an Adaptive Sparse Optimization (ASO) constraint model to optimize the spectrum, aiming to dynamically balance the relationship between signal sparsity and structure preservation during denoising, thereby improving the reconstruction quality and structural expressiveness of the spectrum. ASO constructs a sparse optimization model with structural priors, incorporating structural information from multi-scale spectral gradients as guidance, ensuring higher weighting for edge features, transient changes, and weak structural responses during sparse recovery. Simultaneously, the adaptive mechanism allows the model to dynamically adjust regularization parameters or sparse constraint strength based on the local structural strength and sparsity at each time-frequency point, thus suppressing unstructured noise while avoiding over-smoothing of important features. Compared to traditional fixed-parameter sparse reconstruction methods, ASO not only improves the fidelity and detail preservation of the reconstructed signal but also significantly enhances the robustness of the algorithm in non-steady-state, low signal-to-noise ratio environments, making it particularly suitable for refined denoising of complex and rapidly changing ultrasonic detection signals.

[0103] In this embodiment, an ASO constraint model is constructed to optimize the spectrum obtained in step S2 while preserving the sensitive region of the spectral structure. This includes the following steps:

[0104] Step S31: Set a sparse representation objective. While preserving the spectral structure in sensitive regions, apply a sparse penalty term to the spectral coefficients in non-significant regions, thus making the optimization problem expressible as:

[0105]

[0106] This model directly performs sparse construction on the spectrum in the STFT domain. Among other things, The spectrum contains noise. The estimated spectrum at the k-th scale is obtained by solving an optimization algorithm, i.e., from noisy observations. The clean spectrum recovered from it For frequency resolution, its value directly depends on the length N of the window function and the sampling frequency. , The calculation formula is: , For point-by-point multiplication, As a weighted parameter dependent on oil temperature, it not only balances the relationship between sparsity and fidelity but also suppresses the amplitude of thermal disturbance noise at high temperatures, making the optimization model more robust and sensitive to high-temperature conditions. The expression is as follows:

[0107]

[0108] in, The default regularization weights are set at room temperature. The reference temperature, i.e. the standard benchmark at room temperature, is 25℃. The maximum expected temperature is set to 110℃; This is the adjustment coefficient, with a value range of [0.3, 0.5].

[0109] Step S32, use FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) for each scale. The FISTA iterative form is as follows: Efficiently solve sparse optimization models with structural priors.

[0110] initialization:

[0111] Step k:

[0112]

[0113]

[0114] Iteration stopped: or .

[0115] in: As the initial value of the momentum factor, in this invention, we set... =1, For auxiliary variables used for initialization, the value is generally taken as... Used to construct the acceleration gradient direction. For the initial estimation of sparse solutions, this invention uses an all-zero matrix. The original ultrasound signal. Indicates STFT; This is the inverse STFT transform; The threshold for the stopping criterion; This represents the maximum number of iterations. For regularization parameters; This is the iteration step size; As a weighting operator, the weighting operator in this invention plays a selective penalty role in sparse optimization, that is, it applies stronger sparsity compression to unstructured regions. Therefore, it is set... ;

[0116] Rewritten in a form applicable to the solution of this invention, the k-th step can be expressed as:

[0117]

[0118] This is the Lipschitz constant. Describe the objective function right gradient, Calculate according to the following formula:

[0119]

[0120] Obtain the denoised spectrum Output optimized multi-scale spectrum ,like Figure 4 As shown.

[0121] This invention presents an ultrasonic denoising method based on multi-resolution spectral gradient analysis and optimized sparse optimization theory. The ultrasonic signal is divided into multiple short-time windows using STFT (Short-Time Frame Transform). Fourier transform is performed on the signal within each window, and the resulting multi-scale spectra are stacked to form a spectral volumetric map. Gradient amplitude is used as an edge-preserving denoising guide. A sparse representation model is then introduced onto the spectrogram. Finally, the sparsely reconstructed spectrogram undergoes an inverse transform to obtain the denoised time-domain signal. The feasibility of ultrasonic signal denoising based on the SGF-ASO optimization algorithm is verified through software simulation using MATLAB.

[0122] Step S4: Perform inverse short-time Fourier transform on the optimized spectrum at each scale to reconstruct the multi-scale time-domain signal, fuse the multi-scale time-domain signal, and output the final denoising result.

[0123] Preferably, step S4 includes:

[0124] Step S41: The optimized multi-scale spectrum obtained in step S3 is reconstructed using inverse STFT to obtain denoised signals at multiple scales. The inverse STFT expression is shown below:

[0125]

[0126] in, The optimized spectrum at the k-th scale is the original spectrum. The results after spectral gradient analysis and sparsity optimization This represents the time-domain signal reconstructed at the k-th scale;

[0127] It should be noted that the inverse STFT must use the same window length and overlap ratio as the original STFT.

[0128] Step S42: The reconstructed signals at all scales are weighted and fused to obtain the final output, as shown in the figure. Figure 5 As shown, the formula is as follows:

[0129]

[0130] Similarly, This fusion process further improves the overall fidelity and perceptual consistency of the signal, especially in the presence of complex background noise, it can effectively preserve the key details in the original signal.

[0131] Reconstructing the optimized spectrum using inverse STFT and generating the final signal through a weighted fusion strategy is a crucial step in multi-resolution denoising methods. Its core lies in extracting information from optimized spectra across multiple scales and effectively unifying structural consistency and signal integrity. Specifically, after multi-resolution spectral analysis and sparse optimization, each scale corresponds to an independent denoised spectrum. These spectra each possess advantages in time and frequency resolution, capable of capturing rapidly changing signal characteristics and stable, slowly changing structures, respectively. To avoid information loss or artifact introduction caused by single-scale reconstruction, the algorithm performs inverse STFT (iSTFT) operations on the optimized spectrum at each scale, restoring it to a time-domain signal. Based on criteria such as signal-to-noise ratio, adaptive structural strength, and spectral energy distribution, different fusion weights are assigned to each scale. Weighted fusion strategies typically employ structure-guided weighting, energy-driven fusion, or learning-based fusion, superimposing time-domain signals from different scales according to weights to form the final reconstructed signal, thereby achieving complementary advantages. The significant advantages of this method are: on the one hand, the fusion of multi-scale spectra can effectively enhance the expression of weak structural information and suppress residual local noise at different scales; on the other hand, the inverse STFT ensures the physical consistency and phase continuity of the signal reconstruction, so that the final output has higher structural fidelity and auditory (or physical) usability, which is particularly suitable for processing non-stationary signals such as ultrasonic signals that are structurally sensitive and have a large amplitude dynamic range.

[0132] An ultrasonic denoising method based on multi-resolution spectral gradient analysis and sparse optimization theory demonstrates significant advantages in addressing complex noise interference in non-stationary high-temperature environments of transformers. This method first constructs a complete spectral representation of the signal at different time-frequency resolutions using multi-scale short-time Fourier transform (STFT), capturing instantaneous structural features caused by weak defects such as winding vibration and partial discharge, thus avoiding the masking of low-energy signals by single-scale analysis under high-temperature disturbances. Simultaneously, a spectral gradient fusion mechanism is introduced to accurately extract edge changes and structural jumps in the frequency domain, enhancing the separability of signal and noise and effectively addressing non-stationary thermal disturbances and background noise induced by high oil temperatures. Furthermore, a structure-aware sparse optimization model is used, fusing gradient information as prior knowledge, and adaptively adjusting the signal restoration process through weighted sparse constraints. This results in the suppression of noise components while preserving the true physical structure, exhibiting significant recovery capabilities, particularly for low-amplitude, non-periodic signals.

[0133] Overall, the ultrasonic denoising method based on multi-resolution spectral gradient analysis and optimized sparse optimization theory algorithm of the present invention significantly improves the robustness and accuracy of ultrasonic detection under high-temperature operating conditions while maintaining signal details and structural continuity. It provides a more reliable and engineering-feasible signal basis for early fault location of transformers, plays an important practical role in improving the interference of high load oil temperature on ultrasonic signal quality, and has significant practical value and promotion potential for improving the stability of high-voltage power systems.

[0134] In Embodiment 2, this invention provides an ultrasonic denoising system based on the SGF-ASO optimization algorithm, which is based on the ultrasonic denoising method based on the SGF-ASO optimization algorithm described in Embodiment 1, and includes:

[0135] The signal acquisition module is used to acquire ultrasonic echo signals from the transformer windings via an ultrasonic transducer.

[0136] The preprocessing module is used to perform mean elimination, bandpass filtering, and maximum absolute value normalization on the signal.

[0137] The spectral gradient analysis module is used to perform multi-window long STFT to generate multi-scale spectra, extract each spectral gradient, and fuse them to generate a structure guidance map.

[0138] The sparse optimization module is used to constrain the sparse optimization process with a structure-guided graph, dynamically adjust the penalty weights according to the oil temperature, and solve the optimization spectrum using the FISTA algorithm.

[0139] The signal reconstruction module is used to perform inverse STFT on the optimized spectrum and fuse it to output a denoised signal.

[0140] To address this technical bottleneck, this invention introduces an ultrasonic denoising method combining multi-resolution spectral gradient analysis and adaptive sparse optimization. This method fully utilizes the transient nature and strong local structural abruptness of ultrasonic signals. First, it extracts the spectral information of the signal under different time windows through multi-scale short-time Fourier transform, and then calculates the time and frequency gradients of each spectrum to characterize local abrupt changes and structural edges of the signal. Subsequently, a cross-scale fusion strategy is used to integrate the spectral gradient maps, resulting in a fused spectrum with enhanced structural response and stronger noise suppression capabilities. Next, guided by the fused spectrum, a sparse optimization model with structural priors is constructed by introducing a temperature-related regularized weight function. This enhances the robustness of the algorithm under high oil temperature conditions in transformers. The model utilizes the FISTA algorithm for efficient solution, outputting an optimized multi-scale spectrum. Finally, the time-domain signal is reconstructed and fused through inverse STFT to obtain the final denoising result, achieving fine-grained signal stripping and reconstruction.

[0141] Under complex operating conditions, such as high-temperature oil immersion environment and non-steady-state load fluctuation, the method of this invention exhibits stronger robustness, higher transient retention capability and effective noise suppression effect, providing a highly sensitive and high-precision signal preprocessing means for monitoring the structural state of transformer windings, which has important practical value and research significance.

[0142] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. An ultrasonic denoising method based on an SGF-ASO optimization algorithm, characterized in that, The method comprises the following steps: Collecting an ultrasonic echo signal of a transformer winding and performing preprocessing; Performing SGF analysis on the preprocessed ultrasonic echo signal to generate a multi-scale spectrum and extract spatial gradient features, and generating a fused spectrum gradient atlas through cross-scale fusion; The SGF analysis on the preprocessed ultrasonic echo signal comprises: Based on the preprocessed ultrasonic echo signal, different window lengths of STFT are used to obtain a multi-scale spectrum; The gradient amplitudes of each scale spectrum on the time axis and the frequency axis are calculated to form a multi-scale gradient atlas; A gradient threshold weight factor is determined based on the structure type of the transformer winding, and the adaptive enhancement threshold of each scale gradient atlas is calculated using the gradient threshold weight factor; Based on the adaptive enhancement threshold, each scale gradient atlas is binarized and segmented to generate a mask of a structure salient region; The mask is used to weight and fuse each scale original spectrum to generate a fused spectrum gradient atlas; The adaptive enhancement threshold of each scale gradient atlas is calculated using the gradient threshold weight factor, which comprises: The adaptive enhancement threshold of each scale gradient atlas is calculated by multiplying the median of the gradient amplitude of each scale gradient atlas by the gradient threshold weight factor; An oil temperature adaptive ASO constraint model is constructed based on the fused spectrum gradient atlas as a structure guide to perform adaptive sparse optimization on the multi-scale spectrum; The construction of the oil temperature adaptive ASO constraint model comprises: A sparse optimization objective function is established, which includes a spectrum reconstruction error term and a structure-guided sparse penalty term, wherein the spectrum reconstruction error term is the squared two-norm distance between the optimized spectrum and the noisy spectrum, and the structure-guided sparse penalty term is a spectrum coefficient one-norm constraint weighted by the fused spectrum gradient atlas; The weight parameter of the structure-guided sparse penalty term is dynamically associated with the operating oil temperature of the transformer; The sparse optimization objective function is solved by FISTA to output the optimized multi-scale spectrum; The calculation of the weight parameter of the structure-guided sparse penalty term comprises: A normal temperature reference weight, a room temperature reference temperature, a maximum operating temperature of the transformer, and an adjustment coefficient are set; The difference between the real-time oil temperature and the room temperature reference temperature is divided by the difference between the maximum operating temperature of the transformer and the room temperature reference temperature to obtain a normalized proportion coefficient; The proportion coefficient is multiplied by the adjustment coefficient and then added to 1, and then multiplied by the normal temperature reference weight to output the final weight parameter value; Inverse short-time Fourier transforms are performed on each scale spectrum in the optimized multi-scale spectrum to obtain a multi-scale time domain signal set, and the time domain signal set is fused to output the denoised ultrasonic echo signal.

2. The ultrasonic wave denoising method based on the SGF-ASO optimization algorithm according to claim 1, wherein: The preprocessing comprises: Performing mean elimination operation on the ultrasonic echo signal to remove the direct current component of the signal; Setting the passband range of a band-pass filter according to the mechanical vibration frequency band of the transformer winding, and performing band-pass filtering operation; The band-pass filtered signal is processed by maximum absolute value normalization to unify its amplitude to a preset dynamic range.

3. The ultrasonic wave denoising method based on the SGF-ASO optimization algorithm according to claim 1, wherein: The multi-scale spectrum obtained by the STFT with different window lengths comprises: The STFT with a set short window length is used to capture the high-frequency transient characteristics of the winding, and the STFT with a set long window length is used to extract the low-frequency steady-state characteristics of the winding.

4. The ultrasonic denoising method based on the SGF-ASO optimization algorithm according to claim 1, characterized in that: The FISTA is used to solve the sparse optimization objective function, comprising: Initializing an iteration variable and a step size parameter; In each iteration, the gradient direction of the objective function is calculated; The spectrum estimation value is updated according to the current iteration step size and the gradient direction; The updated spectrum estimation value is subjected to a soft threshold shrinkage operation, and the threshold of the soft threshold shrinkage operation is determined by the weight parameter of the structure-guided sparse penalty term and the fusion spectrum gradient atlas; The acceleration parameter is updated; Repeat the iteration until the preset convergence condition is met or the maximum iteration number is reached.

5. An ultrasonic denoising system based on SGF-ASO optimization algorithm, the ultrasonic denoising method based on any one of claims 1-4, characterized in that, Comprise: The signal acquisition module, the preprocessing module, the spectrum gradient analysis module, the sparse optimization module and the signal reconstruction module, wherein: The signal acquisition module is used to collect the ultrasonic echo signal of the transformer winding through the ultrasonic transducer; The preprocessing module is used to perform mean elimination, band pass filtering and maximum absolute value normalization processing on the signal; The spectrum gradient analysis module is used to perform multi-window length STFT to generate multi-scale spectrum, extract each spectrum gradient and fuse to generate a structure-guided atlas; The sparse optimization module is used to constrain the sparse optimization process with the structure-guided atlas, dynamically adjust the penalty weight according to the oil temperature, and solve the optimization spectrum by the FISTA algorithm; The signal reconstruction module is used to perform inverse STFT on the optimization spectrum and fuse to output the denoised signal.

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