Ultrasonic signal joint denoising method based on AMFD-PEO algorithm

Abstract

The invention relates to the technical field of electrical equipment nondestructive testing, and provides an AMFD-PEO algorithm-based ultrasonic signal joint denoising method, which comprises the following steps of: scanning a target detection area of a transformer winding through an ultrasonic detector, and collecting an original echo signal; constructing an ultrasonic echo signal parameterization model, taking characteristic parameters in the parameterization model as optimization variables, constructing a target function taking fitting errors between the parameterization model and the original echo signals as measurement, and performing iterative optimization on the characteristic parameters to obtain an optimal characteristic parameter solution; and substituting the optimal characteristic parameter solution into the parameterized model to output a de-noised pure signal, and considering the global search capability and the local convergence speed to effectively solve the problems of insufficient signal fidelity and low de-noising efficiency in a strong noise background. A parameterized echo model is constructed, an efficient search optimization mechanism of a nonlinear and multi-peak objective function is introduced to carry out feature parameter global optimization, and noise components in an original echo signal are effectively suppressed.

Description

Technical Field

[0001] This invention relates to the field of non-destructive testing technology for power equipment, and in particular to a method for joint denoising of ultrasonic signals based on the AMFD-PEO algorithm. Background Technology

[0002] Transformers, as pivotal equipment in power systems, are used in voltage transformation, power transmission, and power distribution, playing a crucial role in connecting power generation, transmission, and distribution systems. Therefore, even minor transformer faults can pose a serious threat to the normal operation of the power system. For example, a transformer burning out or shutting down, if not addressed promptly, could potentially lead to large-scale power outages and enormous economic losses. Deformation faults in transformer windings have become a significant factor threatening the normal operation of power systems. Furthermore, traditional power equipment testing methods cannot obtain transformer winding parameters in real time, essentially placing the surrounding lines of substations in a high-risk state. Therefore, efficient and accurate non-destructive testing technologies are needed to detect and monitor winding deformation to prevent potential risks.

[0003] In recent years, ultrasonic testing technology has been widely used in the field of non-destructive testing of power equipment due to its characteristics of being radiation-free, penetrating, and highly sensitive. Especially in the detection of transformer winding deformation, ultrasonic waves can reflect changes in the internal structure of materials and have the ability to identify minute deformations or cracks. However, in actual testing processes, ultrasonic signals are easily affected by external environmental noise, electromagnetic interference from equipment, and background noise, resulting in a large amount of noise components mixed into the acquired signal. This reduces the signal-to-noise ratio and affects the accuracy and reliability of deformation identification. Therefore, how to effectively denoise the ultrasonic signals acquired during the testing process has become one of the key technologies for improving testing quality.

[0004] Currently, research on denoising ultrasonic signals from transformer windings is still in its early stages. Existing methods, such as wavelet transform, empirical mode decomposition, adaptive filters, and deep neural networks, while improving signal quality to some extent, struggle to balance noise suppression and signal feature preservation in high-noise environments. A significant trade-off exists between denoising accuracy, fidelity, and computational efficiency, hindering their practical application in high-reliability power system scenarios. Therefore, a novel denoising method with strong noise immunity, signal feature preservation, and optimized convergence efficiency is urgently needed to improve the application effectiveness and stability of ultrasonic testing in transformer winding monitoring. Summary of the Invention

[0005] To address the aforementioned problems of severe noise interference in ultrasonic signals and the difficulty of balancing signal fidelity and computational efficiency in traditional denoising methods, this invention proposes a joint ultrasonic signal denoising method based on the AMFD-PEO algorithm for high-precision denoising of ultrasonic echo signals from transformer windings. This method constructs a parameterized echo signal model and designs an optimization function with the goal of minimizing the fitting error, using feature parameters as optimization variables. It combines the global search capability of the peak-exploration dual optimization algorithm in a complex search space to achieve efficient suppression of noise components and accurate reconstruction of key signal features. To achieve the above objectives, the present invention utilizes the following techniques: This invention provides a joint denoising method for ultrasonic signals based on the AMFD-PEO algorithm, comprising: Step S1: Scan the target detection area of ​​the transformer winding with an ultrasonic detector and collect the original echo signal to obtain the acoustic response characteristics of the internal structural state of the transformer winding. Step S2: Based on the acquired original echo signal, an adaptive multi-scale waveform fusion decomposition algorithm is used to construct a parameterized model of the ultrasonic echo signal containing multiple characteristic parameters, which is used to characterize the variation law of the original echo signal in amplitude, attenuation factor, frequency, phase and Gaussian white noise. Step S3: The obtained parameterized model is decomposed into at least one sub-waveform by an adaptive multi-scale waveform fusion decomposition algorithm. The feature parameters are used as optimization variables. The objective function is constructed with the fitting error between the parameterized decomposition model and the original echo signal as the metric. The peak exploration dual optimization algorithm is used to iteratively optimize the feature parameters to obtain the optimal feature parameter solution. Step S4: Substitute the optimal feature parameter solution into the parameterized model and output the denoised clean signal for transformer winding status assessment or structural anomaly judgment.

[0006] Furthermore, the mathematical expression of the parameterized decomposition model using the adaptive multi-scale waveform fusion decomposition algorithm is as follows: in, For the amplitude of each wavelet, Let be the attenuation factor of each wavelet. For the frequencies of each wavelet, For the phase of each wavelet, The decomposed Gaussian white noise; The subscript index variable indicates the index of the first index. There are 10 echo signal components, where n is the number of decomposition layers. This is the original echo signal.

[0007] Furthermore, the original echo signal is decomposed into at least one sub-waveform, the steps of which include: Step S31: Assume the parameter space dimension D=4 corresponds to Define the parameter search grid as follows: ; For amplitude layer, As an attenuation layer, For frequency layer, Phase layer, The i-th amplitude; Let j be the attenuation factor; For the kth frequency, For the m-th phase, The total number of grid points for the decomposed Gaussian white noise is . ,in This represents the total number of sampling points for the ultrasonic echo signal; where, These are the minimum and maximum values ​​of the amplitude, respectively. These are the minimum and maximum values ​​of the attenuation factor, respectively. These are the minimum and maximum values ​​of the frequency, respectively. , , , These represent the number of sampling points for the amplitude layer, attenuation layer, frequency layer, and phase layer, respectively. Step S32: For each grid point Calculate the matching degree: ; Where, the basis functions are ; The original echo signal With parameterized basis functions similarity matching degree The amplitude is the i-th amplitude; Let j be the attenuation factor; For the kth frequency, For the m-th phase, Let represent a set of candidate parameter vectors composed of the i-th amplitude, j-th attenuation factor, k-th frequency, and m-th phase in the search space; t is the time variable. , which is the basis function and the reference waveform used for fitting the original echo signal; Step S33: Perform frequency-attenuation joint clustering to construct the feature matrix F: The frequency parameter corresponding to the i-th candidate solution. Let be the decay factor parameter of the i-th candidate solution. Let be the similarity matching degree of the i-th candidate solution; i is the index of the candidate solution, and N is the total number of candidate solutions; Identifying principal component centers using density clustering: ,in ≤n; For each cluster center Solve the following: ; And the analytical solution is obtained as follows: , ; in: ; These represent the optimal amplitude and optimal phase of the p-th component obtained through optimization. , Let T be the amplitude and phase to be solved, and T be the sampling time length. , Here, dt represents the decay factor and frequency corresponding to the cluster center, respectively; p represents the index of the cluster center. , These are the cosine correlation integral and the sine correlation integral, respectively; Step S34: Extract the decomposed components through hierarchical clustering. The four parameter values ​​yield the waveform reconstruction expression after each decomposition as follows: ; The noise signal separation expression can be derived from the waveform reconstruction expression obtained after each decomposition: ; This separates the noise from the ultrasonic signal, resulting in the final ultrasonic signal reconstruction expression obtained through the adaptive multi-scale waveform fusion decomposition algorithm: ; The decomposed Gaussian white noise, The original echo signal, For the denoised signal after parameter estimation and reconstruction, These represent the optimal amplitude and optimal phase of the p-th component obtained through optimization. These are the frequencies corresponding to the cluster centers. For amplitude, As the attenuation factor, For frequency, For phase.

[0008] Furthermore, using the feature parameters as optimization variables, the objective function is constructed to measure the fitting error between the parameterized decomposition model and the original echo signal. The steps include: As optimization variables, the following objective function is constructed to measure the fitting error: ; in, It is the noisy, unresolved raw echo signal. This is the reconstructed signal from the parametric model, where T is the total number of signal sampling points. Indicates the sampling index. Indicates the index of the decomposed signal. This indicates the number of decomposition layers of the decomposed signal.

[0009] Furthermore, a peak-exploration dual optimization algorithm is used to iteratively optimize the feature parameters to obtain the optimal feature parameter solution. The steps include: Step S35: Peak region exploration stage, simulating multiple explorers randomly distributed in local space, using a probability-guided mechanism to search for potential peak regions, local search mechanism to achieve multi-region parallel search and information sharing, and locally adaptively changing the ultrasonic echo signal data set to obtain the local optimal solution; Step S36: Peak Climbing Stage. After determining the candidate peak region, the explorer performs local optimization along the gradient direction or the empirical climbing path to approximate the optimal solution, and finds the global optimal solution of the ultrasonic echo signal data set in the iterative loop. Step S37: Simulate the explorer's emergency danger avoidance method. When the local search stagnates or deviates from the global optimum, abandon the original peak exploration path and choose a completely different exploration path.

[0010] Further, step S35 includes: Step S351: The explorer In iteration The data for the optimization variables at the next time step are ;in, Let be the position of the i-th solution vector in the t-th iteration. These represent the amplitude, attenuation factor, frequency, and phase of the t-th iteration, respectively. Step S352: Set the parameter boundaries to the maximum and minimum values ​​of the sampled values ​​for each optimization variable: , , ;in, The k-th parameter The maximum and minimum values ​​of the samples; Step S353: Add local perturbations to the data of the optimization variables. ;in, Let be the local perturbation solutions of the i-th solution vector after the t-th iteration update. To adaptively control the search range, the step size dynamically decreases with iteration, and its mathematical expression is as follows: , The initial step size is set to 0.2. The attenuation intensity coefficient is set to 5; D is the dimension scaling matrix, expressed as follows: : ; The normalization constant is usually set to 10 to ensure that the disturbance amplitude is proportional to the range of variables. and The k-th parameter The maximum and minimum values ​​of the samples, Let be a four-dimensional standard Gaussian random vector, its expression is: .

[0011] Furthermore, in step S36, the globally optimal solution for the ultrasonic echo signal data set found in the iterative loop is expressed as follows: ; in, The learning rate for the gradient of the adaptive global optimal solution is expressed as: This indicates a decay from 0.78 to 0.08. For random perturbation vectors, To obtain the global partial derivative with respect to the optimization vector, Given a four-dimensional diagonal matrix where the diagonal elements are random numbers in the range [0.8, 1.2], scale each dimension independently and randomly. The current global optimal solution is equal to the solution at the current time. Local perturbation solutions generated by local search for optimal solutions .

[0012] Furthermore, after the optimization steps S35 and S36 are completed, boundary constraint processing is performed. After perturbation, the solution needs to be projected onto the feasible region, as shown in the formula. ; in, It is a tiny random offset.

[0013] Further, in step S37, the simulated explorer's emergency danger avoidance method is to calculate the fitness function value of the decomposed ultrasonic signal of T sampling points. The fitness function is measured by the difference between the optimized signal and the original signal. The fitness function values ​​are sorted, the minimum value is discarded, and random reconstruction is performed.

[0014] The fitness function formula for simulating an explorer's emergency danger avoidance methods is: ; ; The fitness function formula for calculating the emergency danger avoidance method of the decomposed ultrasonic signal with T sampling points. That is, optimize the difference function between the signal and the original signal, sort them according to the fitness function value, discard the one with the smallest value that is least different from the original signal, and then perform random reconstruction.

[0015] Furthermore, step S3 also includes determining whether a preset termination condition is met; if the maximum number of iterations is reached... If the error convergence change of the optimal solution in multiple consecutive rounds is less than a set threshold, the optimization process is terminated, and the currently obtained optimal feature parameter solution is output, including... In each iteration, the fitness function value corresponding to the optimization variable for each sampling point is calculated. Based on the sorting results of the fitness function values ​​from smallest to largest, and since the fitness function value represents the difference between the optimized ultrasonic signal amplitude and the original ultrasonic signal amplitude, it is known that the smaller the difference, the worse the optimization effect. Therefore, the solution vectors with lower fitness function values ​​are removed according to the preset elimination ratio. Furthermore, in each iteration, the objective function for all sampling points is calculated. If the preset maximum number of iterations or the rate of change of the fitness function value of the optimal solution vector in several consecutive rounds is reached, then... If the objective function no longer changes and the optimization result has reached the set threshold, the iteration terminates and the currently obtained optimal feature parameter solution is output.

[0016] Compared with the prior art, the present invention has at least one of the following beneficial effects: This invention effectively addresses the problems of insufficient signal fidelity and low denoising efficiency in strong noise environments by balancing global search capability with local convergence speed. It constructs a parameterized echo model and introduces an efficient search and optimization mechanism for nonlinear, multi-peak objective functions to globally optimize feature parameters, effectively suppressing noise components in the original echo signal.

[0017] Secondly, this invention can significantly improve the signal-to-noise ratio without damaging key signal characteristics. Experimental results show that the method of this invention can reduce noise components in ultrasonic echo signals by more than 80%, which is more significant than traditional methods. Simultaneously, in suppressing high-frequency noise, this invention achieves more precise noise control through frequency domain feature analysis, effectively avoiding signal distortion. Furthermore, thanks to the improved signal quality after optimization, this invention further enhances the three-dimensional imaging accuracy of the internal structure of transformer windings. Test results show that the spatial resolution and structural fidelity of the reconstructed image after processing with this invention are improved by approximately 20%, which is more beneficial for subsequent key tasks such as deformation detection, structural anomaly identification, and fault location. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the steps of the ultrasonic signal joint denoising method based on the AMFD-PEO algorithm of this invention. Figure 2 This is a waveform diagram of the original noisy ultrasonic signal in an embodiment of the present invention; Figure 3 The image shows the simulated signal waveform after processing by the AMFD-PEO algorithm in this embodiment of the invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0021] First Embodiment To more clearly illustrate the ultrasonic signal joint denoising method based on the AMFD-PEO algorithm proposed in this invention, the following detailed description is provided with reference to specific embodiments. This embodiment aims to demonstrate how the technical solution of this invention can be applied to the non-destructive testing of transformer windings. By modeling and optimizing the ultrasonic detection signal, noise components in the signal are effectively removed, thereby improving signal quality and subsequent detection accuracy.

[0022] In ultrasonic non-destructive testing of transformer windings, signal quality directly affects the accuracy and reliability of fault identification. To improve the quality of ultrasonic echo signals, various signal denoising methods have been proposed in existing technologies, mainly including wavelet transform, empirical mode decomposition (EMD), adaptive filtering, and deep learning.

[0023] Among these methods, wavelet transform, through multi-scale decomposition and threshold denoising strategies, improves the preservation of local signal features to some extent. However, its denoising performance depends on the selection of wavelet basis and threshold function, resulting in signal detail loss and complex parameter adjustment. Empirical mode decomposition (EMD) can adaptively decompose signals into several modal components, but it is prone to modal aliasing, endpoint effects, and long computation time. Adaptive filtering methods have certain advantages in processing non-stationary signals, but they are highly dependent on the statistical characteristics of the input signal and are difficult to adapt to the dynamic parameter adjustment problem under complex noise backgrounds. In recent years, deep learning methods have been gradually applied to ultrasonic denoising scenarios, possessing strong nonlinear modeling capabilities. However, their dependence on large-scale labeled data and high model training resource consumption limit their deployment in practical industrial environments.

[0024] In summary, while existing methods have some effect on ultrasonic signal denoising, they generally suffer from limited noise resistance, strong parameter dependence, insufficient feature preservation, or high computational resource requirements, making it difficult to balance multiple performance indicators such as detection accuracy, signal fidelity, and system real-time performance.

[0025] To address the shortcomings of existing technologies, the inventors, through in-depth analysis of the coupling characteristics between ultrasonic signals and noise in the time and frequency domains, and combining the global search capability of swarm intelligence optimization algorithms in high-dimensional nonlinear optimization problems, proposed a novel approach to ultrasonic signal denoising: The ultrasonic echo signal is modeled as a parameterized model containing key physical parameters (such as amplitude, frequency, phase, and attenuation factor). A fitting error between the original signal and the model-reconstructed signal is constructed as the objective function, and a peak-exploration dual optimization algorithm is used to perform high-precision inversion and optimization of the model parameters, thereby achieving effective separation of signal and noise. The denoising method provided by this invention exhibits excellent performance in the field of transformer winding detection, and is particularly suitable for signal enhancement and detail preservation in complex background noise scenarios in power systems. It can achieve the following technical effects: (1) Through the global search and local disturbance coordination mechanism of the peak exploration dual optimization algorithm, the noise component of the ultrasonic signal is significantly reduced, and the noise reduction rate exceeds 80% in typical simulation scenarios; (2) By using the optimized high-fidelity ultrasonic signal, the three-dimensional imaging accuracy of the winding structure is improved, and the reconstruction error is reduced by about 20%, which helps to improve the accuracy of anomaly identification and structure discrimination; (3) At the frequency domain level, combined with the objective function guidance strategy of the peak exploration dual optimization algorithm, high-frequency noise can be accurately identified and suppressed, while maintaining the key components in the original signal, avoiding the problem of spectrum loss in traditional methods. The specific implementation method is as follows: This invention provides a joint denoising method for ultrasonic signals based on the AMFD-PEO algorithm, comprising: Step S1: Scan the target detection area of ​​the transformer winding with an ultrasonic detector and collect the original echo signal to obtain the acoustic response characteristics of the internal structural state of the transformer winding. Step S2: Based on the acquired raw echo signal, construct a parameterized model of the ultrasonic echo signal containing multiple feature parameters using an adaptive multi-scale waveform fusion decomposition algorithm. , Among them, the characteristic parameters include amplitude. Attenuation factor ,frequency With phase and Gaussian white noise ; used to characterize the variation of the original echo signal in amplitude, attenuation factor, frequency, phase, and Gaussian white noise; Step S3: The obtained parameterized model is decomposed into at least one sub-waveform by the Adaptive Multiscale Waveform Fusion Decomposition (AMFD) algorithm. The feature parameters are used as optimization variables. The objective function is constructed to measure the fitting error between the parameterized decomposition model and the original echo signal. The feature parameters are iteratively optimized by the Peak Exploration Optimization (PEO) algorithm to obtain the optimal feature parameter solution. Step S4: Substitute the optimal feature parameter solution into the parameterized model and output the denoised clean signal for transformer winding status assessment or structural anomaly judgment.

[0026] Furthermore, the mathematical expression of the parameterized decomposition model using the adaptive multi-scale waveform fusion decomposition algorithm is as follows: in, For the amplitude of each wavelet, Let be the attenuation factor of each wavelet. For the frequencies of each wavelet, For the phase of each wavelet, The decomposed Gaussian white noise, The subscript index variable indicates the index of the first index. There are 10 echo signal components, where n is the number of decomposition layers. This is the original echo signal.

[0027] Further, the original echo signal is decomposed into at least one sub-waveform, the steps of which include: Step S31: Assume the parameter space dimension D=4 corresponds to Define the parameter search grid as follows: ; For amplitude layer, As an attenuation layer, For frequency layer, Phase layer, The amplitude is the i-th amplitude; Let j be the attenuation factor; For the kth frequency, For the m-th phase, The total number of grid points for the decomposed Gaussian white noise is . ,in This represents the total number of sampling points for the ultrasonic echo signal; where, These are the minimum and maximum values ​​of the amplitude, respectively. These are the minimum and maximum values ​​of the attenuation factor, respectively. These are the minimum and maximum values ​​of the frequency, respectively. , , , These represent the number of sampling points for the amplitude layer, attenuation layer, frequency layer, and phase layer, respectively. Step S32: For each grid point Calculate the matching degree: ; Where, the basis functions are ; The original echo signal With parameterized basis functions similarity matching degree The amplitude is the i-th amplitude; Let j be the attenuation factor; For the kth frequency, For the m-th phase, Let represent a set of candidate parameter vectors composed of the i-th amplitude, j-th attenuation factor, k-th frequency, and m-th phase in the search space; t is the time variable. , which is the basis function and the reference waveform used for fitting the original echo signal; Step S33: Perform frequency-attenuation joint clustering to construct the feature matrix F: ; The frequency parameter corresponding to the i-th candidate solution. Let be the decay factor parameter of the i-th candidate solution. Let be the similarity matching degree of the i-th candidate solution; i is the index of the candidate solution, and N is the total number of candidate solutions; Identifying principal component centers using density clustering: ,in ≤n; For each cluster center Solve the following: ; And the analytical solution is obtained as follows: , ; in: ; These represent the optimal amplitude and optimal phase of the p-th component obtained through optimization. , Let T be the amplitude and phase to be solved, and T be the sampling time length. , Here, dt represents the decay factor and frequency corresponding to the cluster center, respectively; p represents the index of the cluster center. , These are the cosine correlation integral and the sine correlation integral, respectively; Step S34: Extract the decomposed components through hierarchical clustering. The four parameter values ​​yield the waveform reconstruction expression after each decomposition as follows: ; The noise signal separation expression can be derived from the waveform reconstruction expression obtained after each decomposition: ; This separates the noise from the ultrasonic signal, resulting in the final ultrasonic signal reconstruction expression obtained through the adaptive multi-scale waveform fusion decomposition algorithm: ; The decomposed Gaussian white noise, The original echo signal, For the denoised signal after parameter estimation and reconstruction, These represent the optimal amplitude and optimal phase of the p-th component obtained through optimization. These are the frequencies corresponding to the cluster centers. For amplitude, As the attenuation factor, For frequency, For phase.

[0028] Furthermore, using the feature parameters as optimization variables, the objective function is constructed to measure the fitting error between the parameterized decomposition model and the original echo signal. The steps include: As optimization variables, the following objective function is constructed to measure the fitting error: ; in, It is the noisy, unresolved raw echo signal. This is the reconstructed signal from the parametric model, where T is the total number of signal sampling points. Indicates the sampling index. Indicates the index of the decomposed signal. This indicates the number of decomposition layers of the decomposed signal.

[0029] Furthermore, a peak-exploration dual optimization algorithm is used to iteratively optimize the feature parameters to obtain the optimal feature parameter solution. The steps include: Step S35: Peak region exploration stage, simulating multiple explorers randomly distributed in local space, using a probability-guided mechanism to search for potential peak regions, local search mechanism to achieve multi-region parallel search and information sharing, and locally adaptively changing the ultrasonic echo signal data set to obtain the local optimal solution; Step S36: Peak Climbing Stage. After determining the candidate peak region, the explorer performs local optimization along the gradient direction or the empirical climbing path to approximate the optimal solution, and finds the global optimal solution of the ultrasonic echo signal data set in the iterative loop. Step S37: Simulate the explorer's emergency danger avoidance methods. When the local search stagnates or deviates from the global optimum, abandon the original peak exploration path and choose a completely different exploration path.

[0030] Further, step S35 includes: Step S351: Explorer In iteration The data for the optimization variables at the next time step are ;in, Let be the position of the i-th solution vector in the t-th iteration. These represent the amplitude, attenuation factor, frequency, and phase of the t-th iteration, respectively. Step S352: Set the parameter boundaries to the maximum and minimum values ​​of the sampled values ​​for each optimization variable: , , ;in, , The k-th parameter The maximum and minimum values ​​of the samples; Step S353: Add local perturbations to the data of the optimization variables. ;in, Let be the local perturbation solutions of the i-th solution vector after the t-th iteration update. To adaptively control the search range, the step size dynamically decreases with iteration, and its mathematical expression is as follows: , The initial step size is set to 0.2. The attenuation intensity coefficient is set to 5; D is the dimension scaling matrix, expressed as follows: : ; and The k-th parameter The maximum and minimum values ​​of the samples, Let be a four-dimensional standard Gaussian random vector, its expression is: .

[0032] Furthermore, in step S36, the globally optimal solution for the ultrasonic echo signal data set found in the iterative loop is expressed as follows: ; in, The learning rate for the gradient of the adaptive global optimal solution is expressed as: This indicates a decay from 0.78 to 0.08. For random perturbation vectors, To obtain the global partial derivative with respect to the optimization vector, Given a four-dimensional diagonal matrix where the diagonal elements are random numbers in the range [0.8, 1.2], scale each dimension independently and randomly. The current global optimal solution is equal to the solution at the current time. Local search for optimal solution generation .

[0033] Furthermore, after the optimization steps S35 and S36 are completed, boundary constraint processing is performed. After perturbation, the solution needs to be projected onto the feasible region, as shown in the formula. ; in, It is a tiny random offset.

[0034] Furthermore, in step S37, the fitness function formula for simulating the explorer's emergency danger avoidance method is: ; ; Calculate the decomposed ultrasonic signal at T sampling points The fitness function for emergency danger avoidance is the difference function between the optimized signal and the original signal. The signals are sorted according to their fitness function values, and the signals with the smallest difference from the original signal are discarded and then randomly reconstructed.

[0035] Furthermore, step S3 also includes determining whether a preset termination condition is met; if the maximum number of iterations is reached... If the error convergence change of the optimal solution in multiple consecutive rounds is less than a set threshold, the optimization process is terminated, and the currently obtained optimal feature parameter solution is output, including... In each iteration, the fitness function value corresponding to the optimization variable for each sampling point is calculated. Based on the sorting results of the fitness function values ​​from smallest to largest, and since the fitness function value represents the difference between the optimized ultrasonic signal amplitude and the original ultrasonic signal amplitude, it is known that the smaller the difference, the worse the optimization effect. Therefore, the solution vectors with lower fitness function values ​​are removed according to the preset elimination ratio. Furthermore, in each iteration, the global fitness function value, i.e., the objective function, is calculated for all sampling points. If the preset maximum number of iterations or the rate of change of the fitness function value of the optimal solution vector in several consecutive rounds is reached, then... If the global fitness function value, i.e. the objective function, no longer changes, and the optimization result has reached the set threshold, the iteration terminates, and the currently obtained optimal feature parameter solution is output.

[0036] To verify the effectiveness of the denoising method based on the AMFD-PEO algorithm proposed in this invention in the ultrasonic signal processing of transformer windings, a simulation experiment was conducted on the noisy simulated ultrasonic waveform. Figure 2 The image shows the original noisy ultrasonic signal waveform obtained in a simulated environment. The proposed peak-exploration dual optimization algorithm is used to denoise this noisy simulation signal, and the result is as follows. Figure 3 As shown, noise interference in the signal is significantly reduced, and the principal components of the signal are effectively preserved.

[0037] After simulation, comparisons with traditional methods such as low-pass filtering and wavelet denoising in terms of signal-to-noise ratio improvement (SNR), reconstruction error (MSE), and signal fidelity further confirmed the feasibility of the denoising optimization algorithm proposed in this invention. method SNR MSE Fidelity low-pass filter 10.2 0.015 85.6% Wavelet denoising 12.8 0.012 89.2% The method in this embodiment 15.6 0.008 93.4% Table 1 As can be seen from the data in the table, the proposed ultrasonic signal denoising method based on the peak exploration dual optimization algorithm outperforms traditional methods in multiple performance indicators, especially in terms of signal-to-noise ratio improvement and signal fidelity, which verifies its robustness and practicality in high-noise environments.

[0038] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A joint denoising method for ultrasonic signals based on the AMFD-PEO algorithm, characterized in that, include: Step S1: Scan the target detection area of ​​the transformer winding with an ultrasonic detector and collect the original echo signal to obtain the acoustic response characteristics of the internal structural state of the transformer winding. Step S2: Based on the acquired original echo signal, an adaptive multi-scale waveform fusion decomposition algorithm is used to construct a parameterized model of the ultrasonic echo signal containing multiple feature parameters, which is used to characterize the variation law of the original echo signal in amplitude, attenuation factor, frequency, phase and Gaussian white noise. Step S3: The obtained parameterized model is used to decompose the original echo signal into at least one sub-waveform by the adaptive multi-scale waveform fusion decomposition algorithm. The feature parameters are used as optimization variables to construct an objective function that measures the fitting error between the parameterized decomposition model and the original echo signal. The peak exploration dual optimization algorithm is used to iteratively optimize the feature parameters to obtain the optimal feature parameter solution. Step S4: Substitute the optimal feature parameter solution into the parameterized model and output the denoised clean signal for the transformer winding status assessment or structural anomaly judgment.

2. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 1, characterized in that, The mathematical expression of the parameterized decomposition model using the adaptive multi-scale waveform fusion decomposition algorithm is as follows: in, Let the amplitude of each wavelet be denoted as . The attenuation factor for each of the wavelets, The frequency of each of the wavelets, The phase of each of the wavelets, The decomposed Gaussian white noise, The subscript index variable indicates the index of the first index. There are 10 echo signal components, where n is the number of decomposition layers. The original echo signal.

3. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 2, characterized in that, The original echo signal is decomposed into at least one sub-waveform, the steps of which include: Step S31: Assume the parameter space dimension D=4 corresponds to Define the parameter search grid as follows: ； For amplitude layer, As an attenuation layer, For frequency layer, Phase layer, The amplitude is the i-th amplitude; Let j be the attenuation factor; For the kth frequency, For the m-th phase, The total number of grid points for the decomposed Gaussian white noise is . ,in This represents the total number of sampling points for the ultrasonic echo signal; where, These are the minimum and maximum values ​​of the amplitude, respectively. These are the minimum and maximum values ​​of the attenuation factor, respectively. These are the minimum and maximum values ​​of the frequency, respectively. , , , These represent the number of sampling points for the amplitude layer, attenuation layer, frequency layer, and phase layer, respectively. Step S32: For each grid point Calculate the matching degree: ； Where, the basis functions are ; The original echo signal With parameterized basis functions The similarity matching degree, the The i-th amplitude; The j-th attenuation factor; For the kth frequency, the For the m-th phase, Let represent a set of candidate parameter vectors composed of the i-th amplitude, the j-th attenuation factor, the k-th frequency, and the m-th phase in the search space; t is a time variable. The basis function is a reference waveform used to fit the original echo signal; Step S33: Perform frequency-attenuation joint clustering to construct the feature matrix F: Let be the frequency parameter corresponding to the i-th candidate solution. Let be the decay factor parameter of the i-th candidate solution. Let be the similarity matching degree of the i-th candidate solution; i is the index of the candidate solution, and N is the total number of candidate solutions; Identifying principal component centers using density clustering: ,in ≤n; For each cluster center Solve the following: ; And the analytical solution is obtained as follows: , ； in: ; These represent the optimal amplitude and optimal phase of the p-th component obtained through optimization. , Let T be the amplitude and phase to be solved, and T be the sampling time length. , Here, dt represents the attenuation factor and the frequency corresponding to the cluster center, respectively; p represents the index of the cluster center. , These are the cosine correlation integral and the sine correlation integral, respectively; Step S34: Extract the decomposed components through hierarchical clustering. The four parameter values ​​yield the waveform reconstruction expression after each decomposition as follows: ； The noise signal separation expression can be derived from the waveform reconstruction expression obtained after each decomposition: ; The ultrasonic signal reconstruction expression obtained through the adaptive multi-scale waveform fusion decomposition algorithm is as follows: ; The decomposed Gaussian white noise, The original echo signal, For the denoised signal after parameter estimation and reconstruction, These are the optimal amplitude and optimal phase of the p-th component obtained through optimization, respectively. These are the frequencies corresponding to the cluster centers. The amplitude, The attenuation factor is... For the frequency, The phase is described.

4. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 3, characterized in that, Using the feature parameters as optimization variables, the objective function is to measure the fitting error between the parameterized decomposition model and the original echo signal. The steps include: As the optimization variable, the following objective function is constructed to measure the fitting error: ; Among them, the It is the noisy, unresolved original echo signal. It is the reconstructed signal of the parameterized model, where T is the total number of signal sampling points. Indicates the sampling index. Indicates the index of the decomposed signal. This indicates the number of decomposition layers in the decomposed signal.

5. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 4, characterized in that, The peak exploration dual optimization algorithm is used to iteratively optimize the feature parameters to obtain the optimal feature parameter solution. The steps include: Step S35: Peak region exploration stage, simulating multiple explorers randomly distributed in local space, using a probability-guided mechanism to search for potential peak regions, local search mechanism to achieve multi-region parallel search and information sharing, and locally adaptively changing the ultrasonic echo signal data set to obtain the local optimal solution; Step S36: Peak Climbing Stage. After determining the candidate peak region, the explorer performs local optimization along the gradient direction or the empirical climbing path to approximate the optimal solution, and finds the global optimal solution of the ultrasonic echo signal data set in the iterative loop. Step S37: Simulate the explorer's emergency danger avoidance methods. When the local search stagnates or deviates from the global optimum, abandon the original peak exploration path and choose a completely different exploration path.

6. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 5, characterized in that, Step S35 includes: Step S351: The explorer In iteration The data of the optimization variables at the next time step are ;in, Let be the position of the i-th solution vector in the t-th iteration. These are the amplitude, the attenuation factor, the frequency, and the phase in the t-th iteration, respectively. Step S352: Set the parameter boundaries to the maximum and minimum values ​​of the sampled values ​​for each optimization variable: , , ;in, , The k-th parameter The maximum and minimum values ​​of the samples; Step S353: Add local perturbations to the data of the optimization variables. ;in, These are the local perturbation solutions of the i-th solution vector after the t-th iteration update. To adaptively control the search range, the step size dynamically decreases with iteration, and its mathematical expression is as follows: , The initial step size is set to 0.

2. The attenuation intensity coefficient is set to 5; D is the dimension scaling matrix, expressed as follows: : ; The normalization constant is usually set to 10 to ensure that the disturbance amplitude is proportional to the range of variables. and The k-th parameter The maximum and minimum values ​​of the samples, Let be a four-dimensional standard Gaussian random vector, its expression is: .

7. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 6, characterized in that, In step S36, the globally optimal solution for the ultrasonic echo signal data set found in the iterative loop is expressed in the following form: ； in, To adapt the learning rate of the global optimal solution gradient, Let be a random perturbation vector, and be a four-dimensional diagonal matrix where the diagonal elements are random numbers in the range [0.8, 1.2]. The currently stated global optimal solution is equal to the solution at the current time. The local perturbation solution generated by the local search for the optimal solution.

8. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 5, characterized in that, After the optimization steps in steps S35 and S36 are completed, boundary constraint processing is performed. After the perturbation, the solution needs to be projected onto the feasible region.

9. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 6, characterized in that, In step S37, the simulated emergency danger avoidance method of the explorer is to calculate the fitness function value of the decomposed ultrasonic signal of T sampling points. The fitness function is measured by the difference between the optimized signal and the original signal. The fitness function values ​​are sorted, the minimum value is discarded, and random reconstruction is performed.

10. The ultrasonic signal joint denoising method based on the AMFD-PEO algorithm according to claim 9, characterized in that, Step S3 also includes determining whether a preset termination condition is met; if the maximum number of iterations is reached... If the error convergence change of the optimal solution in multiple consecutive rounds is less than a set threshold, the optimization process is terminated, and the currently obtained optimal feature parameter solution is output. include, In each iteration, the fitness function value corresponding to the optimization variable of each sampling point is calculated, and the fitness function value is sorted from smallest to largest. Since the fitness function value represents the difference between the optimized ultrasonic signal amplitude and the original ultrasonic signal amplitude, it is known that the smaller the difference, the worse the optimization effect. Therefore, the solution vectors with lower fitness function values ​​are removed according to the preset elimination ratio. Furthermore, in each iteration, the objective function for all sampling points is calculated. If the preset maximum number of iterations or the change in the fitness function value of the solution vector in a series of consecutive rounds is reached... If the objective function no longer changes and the optimization result has reached the set threshold, the iteration terminates and the currently obtained optimal feature parameter solution is output.

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