A power distribution network transient disturbance waveform measurement method based on dictionary learning

Abstract

The application discloses a kind of based on dictionary learning's distribution network transient disturbance waveform measurement method, it is related to power grid signal measurement technical field, constructs the disturbance waveform measurement framework of offline learning with terminal side online decomposition covering main station side;Relative energy acceleration operator is used to determine the start and end time of transient disturbance waveform, realize waveform segmentation;Based on distribution network historical disturbance data set, preliminary learning is carried out using K-SVD algorithm, and initial overcomplete dictionary is generated;After the atom of extracted feature is clustered and redundant atom is pruned using Gaussian mixture model, the dimension of dictionary is reduced, and the decomposition efficiency is improved;Transient signal is sparsely decomposed based on the generated overcomplete dictionary and the decomposition coefficient is uploaded.The application uses the above-mentioned based on dictionary learning's distribution network transient disturbance waveform measurement method, by combining offline training and online decomposition, under the premise of guaranteeing measurement accuracy, effectively reduces redundant information, significantly improves the compression ratio of waveform data and reconstruction efficiency.

Description

Technical Field

[0001] This invention relates to the field of power grid signal measurement technology, and in particular to a method for measuring transient disturbance waveforms in distribution networks based on dictionary learning. Background Technology

[0002] With the large-scale integration of distributed renewable energy, the operating characteristics of new power distribution systems exhibit significant nonlinearity and strong randomness, and their dynamic behavior is becoming increasingly complex, posing a severe challenge to the upgrading of real-time monitoring, control, and protection schemes for power distribution networks. To achieve comprehensive monitoring of transient disturbances in the power distribution network, waveform data with high sampling resolution and high reconstruction accuracy must be acquired. However, the wide geographical distribution, dispersed topology, and numerous monitoring nodes of power distribution networks lead to an explosive growth in the amount of raw waveform data acquired in real time, placing enormous pressure on existing power communication bandwidth. Traditional signal processing methods or matching pursuit algorithms based on fixed analytical dictionaries often cannot adapt to the wide bandwidth and non-stationary characteristics of power distribution network signals, resulting in poor adaptability of dictionary atoms. Typically, extremely high iteration counts are required to achieve satisfactory approximation results, which not only increases the computational burden on edge monitoring terminals but also severely limits the real-time response capability of the monitoring system.

[0003] In the actual operating environment of power distribution networks, signals are often coupled with complex electromagnetic noise, and transient disturbances are characterized by random occurrence and extremely short duration. Existing technologies, without considering noise interference and with incomplete data acquisition, lead to a significant decrease in the robustness of matching pursuit algorithms, resulting in severe overfitting or underfitting during signal reconstruction and reducing the accuracy of signal tracking. Furthermore, due to the lack of a sensitive disturbance start and end time identification mechanism, existing equipment often includes a large amount of steady-state redundant information in waveform recording, further wasting valuable communication and storage resources. Therefore, how to construct a method for measuring transient disturbance waveforms in power distribution networks that can ensure high-fidelity reconstruction accuracy, effectively reduce atomic redundancy, improve the online decomposition speed at the edge side, and possess noise adaptability has become a key technical challenge that urgently needs to be overcome in the field of new power system sensing. Summary of the Invention

[0004] The purpose of this invention is to provide a method for measuring transient disturbance waveforms in power distribution networks based on dictionary learning, which solves the problems of high waveform data transmission pressure, low sensitivity of transient disturbance identification, and insufficient efficiency of sparse decomposition and reconstruction accuracy caused by dictionary redundancy in the process of power distribution network monitoring.

[0005] To achieve the above objectives, this invention provides a method for measuring transient disturbance waveforms in a distribution network based on dictionary learning, comprising the following steps: S1. Construct a disturbance waveform measurement framework that covers offline learning on the master station side and online decomposition on the terminal side; S2. The relative energy acceleration operator REAO is used to monitor the sampling sequence in real time, determine the start and end times of the transient disturbance waveform, and realize the active segmentation of the waveform data accordingly. S3. Based on the historical disturbance dataset, the dictionary atoms and sparse coefficients are updated alternately and iteratively using the regularized K-SVD algorithm to initially construct an overcomplete dictionary that can characterize the typical disturbance features of the distribution network. S4. Extract the time-frequency domain physical features of each atom in the initial overcomplete dictionary, perform cluster analysis in the feature space using Gaussian Mixture Model (GMM), and prune redundant atoms according to the similarity criterion to obtain the final overcomplete dictionary with dimensionality reduction optimization. S5. On the terminal side, the segmented disturbance signal is decomposed by orthogonal matching tracking sparse decomposition using the final complete dictionary to obtain the atomic index and coefficients, and then uploaded to the main station for high-precision waveform reconstruction.

[0006] Preferably, S1 includes: S11. Offline training on the main station side: Collect multi-source historical disturbance waveform data of the distribution network to build a sample library, and periodically execute dictionary learning algorithm to update the atomic sequence; S12. Dictionary distribution and synchronization: The optimized and final complete dictionary is remotely pushed to each monitoring terminal and stored locally for online comparison and retrieval. S13. Terminal-side online decomposition: The monitoring terminal performs rapid matching and tracking of the real-time captured transient disturbance segments based on the final overcomplete dictionary stored locally, realizing the conversion of raw data into representation coefficients; S14. Online reconstruction on the main station side: Receive compressed data frames uploaded by the terminal, retrieve the local dictionary according to the atomic index number in the data frame, and restore the waveform of the entire disturbance process by linear superposition.

[0007] Preferably, S2 includes: S21, Regarding the input signal Define the forward energy acceleration operator FEAO as The backward energy acceleration operator BEAO is The calculation logic is as follows: ; S22, Calculation of the relative energy acceleration operator As shown in the following formula: ; when Greater than the preset trigger threshold When, it is determined to be the start time of the disturbance; when Continuously below the preset end threshold When the time window constraint is met, it is determined to be the end time of the disturbance.

[0008] Preferably, S3 includes: S31. First, the acquired multi-source historical disturbance waveform data of the distribution network is standardized and preprocessed to construct a training dataset. Each column represents a length of The perturbation signal samples; based on the training dataset, a dictionary learning objective function based on the regularized K-SVD algorithm is established. Its expression is as follows: ; In the formula, Let be the overcomplete dictionary matrix to be solved. The coding coefficient matrix, for The row vectors This is a regularization parameter used to balance reconstruction fidelity and atomic sparsity; During the iterative optimization process, the system alternately performs sparse coding and dictionary updates: in the sparse coding phase, the dictionary is fixed. The orthogonal matching pursuit algorithm is used to solve for the condition that satisfies Optimal coefficient matrix under constraints During the dictionary update phase, atoms are updated column by column. and their corresponding nonzero sparsity coefficients The definition does not include the first The residual matrix of contributions from each atom As shown in the following formula: ; S32. To maintain the sparsity pattern, only extract... The middle corresponds to the atom The columns with non-zero positions form the reduced residual matrix. And perform singular value decomposition on it, as shown in the following equation: ; Selecting the left singular matrix The first column vector As the updated atom Select the first singular value With right singular matrix The first column vector The product of these factors serves as the updated non-zero coefficient vector. and perform on the newly generated atoms Norm normalization constraint, satisfying This ensures that the generated initial overcomplete dictionary can accurately characterize the broadband dynamic characteristics of transient disturbance waveforms in the distribution network.

[0009] Preferably, the extraction of time-frequency domain physical features of each atom in the initial overcomplete dictionary in S4 includes: S41. First, for each atom in the initial overcomplete dictionary... Perform multi-dimensional feature extraction, and the extracted features include waveform factors that reflect the wave characteristics of atomic waveforms. And kurtosis characteristics that reflect the concentration of atomic energy distribution ; S42, Extract and Construct as a two-dimensional original feature vector Furthermore, a time index feature is introduced to construct a three-dimensional enhanced feature space, where the Z-axis represents the order index of atom generation; To eliminate the influence of different units on the clustering results, range standardization is performed on the original feature vectors to obtain standardized feature vectors. Its mapping rules are as follows: ; In the formula, and These represent the maximum and minimum values ​​of the corresponding features in the initial overcomplete dictionary set; refined clustering is performed in the feature space based on the waveform geometry and energy distribution of the atoms; S43. The system uses the EM algorithm to iteratively calculate the atom belonging to the first... The posterior probabilities of each feature cluster are used to classify atoms with the highest membership probabilities into the same category. When redundant atom pairs are identified, the atom that contributed more to the reconstruction during training is retained, while the other atom is removed, thus gradually compressing the dictionary size from the initial dimension to the target dimension. This is to improve the computational response speed of terminal devices during online decomposition.

[0010] Preferably, in S41, the waveform factor The calculation formula is as follows: ; In the formula, For atoms in the time window Peak amplitude within, This is the root mean square value of the atom.

[0011] Preferably, in S41, the kurtosis feature The calculation formula is as follows: ; In the formula, The fourth central moment of the atom. The second central moment of the atom, This is the average value of the atoms.

[0012] Preferably, S5 includes: S51, terminal side in the In the next iteration, find the residual signal that is currently... Best matching atomic index Its objective function is: S52. Calculate the reconstructed signal. and residuals ; S53. During the main station reconstruction phase, based on the received sparse vector, the formula is used... The residual energy, including in-band noise, is evaluated, and a robust termination condition is determined based on a weighted evaluation of the difference in deterministic fitness between the last two iterations.

[0013] Preferably, the atomic index in S51 The objective function is shown in the following equation: .

[0014] Preferably, in S53, the robust termination condition is determined by the following formula: ; in, and For weighted parameters, As a measure of fit, This is the termination threshold, used to balance noise interference from global periodicity and local fluctuations.

[0015] Therefore, the present invention employs the above-mentioned dictionary-based method for measuring transient disturbance waveforms in power distribution networks, which has the following beneficial effects: (1) This method uses a cluster-pruned optimized K-SVD (CPK-SVD) overcomplete dictionary design method, and utilizes a Gaussian mixture model (GMM) to perform refined clustering and prune redundant atoms in the atomic feature space, which significantly reduces the dictionary size and atomic coherence. Compared with traditional Fourier or unoptimized dictionaries, the atoms generated by this method can accurately adapt to the non-stationary characteristics of the power distribution network, enabling the matching and tracking process to achieve higher accuracy with fewer iterations, and greatly improving the computational efficiency of the edge side.

[0016] (2) This method adopts a disturbance identification and localization method based on the relative energy acceleration operator (REAO). By calculating the relative difference between forward and backward sliding windows, the interference of signal amplitude on detection sensitivity is effectively eliminated. Compared with traditional methods such as root mean square (RMS) with half-cycle delay, this method can more sensitively capture transient disturbance singularities and achieve accurate segmentation, eliminating steady-state redundant information from the source, significantly improving the data compression ratio and alleviating communication pressure.

[0017] (3) This method constructs a collaborative measurement framework of offline learning at the main station and online decomposition at the terminal. By performing computationally intensive dictionary training at the main station and distributing it to the terminal, the computational pressure is reasonably distributed in the spatiotemporal dimensions. This data-driven closed-loop improvement method enhances the robustness of the algorithm to complex environments. While achieving a high compression ratio, it ensures high reconstruction accuracy and effectively solves the contradiction between massive data monitoring and high reconstruction accuracy requirements.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart of a method for measuring transient disturbance waveforms in a power distribution network based on dictionary learning, according to the present invention. Figure 2 This is a schematic diagram illustrating the construction process of the power distribution network transient waveform measurement framework according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the calculation process of the relative energy acceleration operator in an embodiment of the present invention; Figure 4 This is a diagram showing the clustering results of waveform atoms based on GMM in an embodiment of the present invention; Figure 5 This is a schematic diagram of sparse decomposition on the terminal side according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the measured waveform data in an embodiment of the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Example Please see Figures 1-6This invention provides a method for measuring transient disturbance waveforms in a distribution network based on dictionary learning, comprising the following steps: S1. Construct a disturbance waveform measurement framework that encompasses offline learning on the master station side and online decomposition on the terminal side. For example... Figure 2 As shown, it includes the following steps: S11. Offline training on the main station side: Collect multi-source historical disturbance waveform data of the distribution network to build a sample library, and periodically execute dictionary learning algorithm to update the atomic sequence; S12. Dictionary distribution and synchronization: The optimized and final complete dictionary is remotely pushed to each monitoring terminal and stored locally for online comparison and retrieval. S13. Terminal-side online decomposition: The monitoring terminal performs rapid matching and tracking of the real-time captured transient disturbance segments based on the final overcomplete dictionary stored locally, realizing the conversion of raw data into representation coefficients; S14. Online reconstruction on the main station side: Receive compressed data frames uploaded by the terminal, retrieve the local dictionary according to the atomic index number in the data frame, and restore the waveform of the entire disturbance process by linear superposition.

[0023] S2. The relative energy acceleration operator REAO is used to monitor the sampling sequence in real time, determine the start and end times of transient disturbance waveforms, and thus achieve active segmentation of waveform data. For example... Figure 3 As shown, it includes the following steps: S21, Regarding the input signal Define the forward energy acceleration operator FEAO as The backward energy acceleration operator BEAO is The calculation logic is as follows: ; S22, Calculation of the relative energy acceleration operator As shown in the following formula: ; when Greater than the preset trigger threshold When, it is determined to be the start time of the disturbance; when Continuously below the preset end threshold When the time window constraint is met, it is determined to be the end time of the disturbance.

[0024] S3. Based on historical disturbance datasets, the dictionary atoms and sparse coefficients are iteratively updated alternately using a regularized K-SVD algorithm to initially construct an overcomplete dictionary capable of characterizing typical disturbance features of the distribution network. The detailed mathematical modeling and iterative process for generating the initial overcomplete dictionary includes the following steps: S31. First, the acquired multi-source historical disturbance waveform data of the distribution network is standardized and preprocessed to construct a training dataset. Each column represents a length of The perturbation signal samples; based on the training dataset, a dictionary learning objective function based on the regularized K-SVD algorithm is established. Its expression is as follows: ; In the formula, Let be the overcomplete dictionary matrix to be solved. The coding coefficient matrix, for The row vectors This is a regularization parameter used to balance reconstruction fidelity and atomic sparsity.

[0025] During the iterative optimization process, the system alternately performs sparse coding and dictionary updates: in the sparse coding phase, the dictionary is fixed. The orthogonal matching pursuit algorithm is used to solve for the condition that satisfies Optimal coefficient matrix under constraints During the dictionary update phase, atoms are updated column by column. and their corresponding nonzero sparsity coefficients The definition does not include the first The residual matrix of each atom's contribution As shown in the following formula: ; S32. To maintain the sparsity pattern, only extract... The middle corresponds to the atom The columns with non-zero positions form the reduced residual matrix. And perform singular value decomposition (SVD) on it, as shown in the following equation: ; Selecting the left singular matrix The first column vector As the updated atom Select the first singular value With right singular matrix The first column vector The product of these factors serves as the updated non-zero coefficient vector. and perform on the newly generated atoms Norm normalization constraint, satisfying This ensures that the generated initial overcomplete dictionary can accurately characterize the broadband dynamic characteristics of transient disturbance waveforms in the distribution network.

[0026] S4. Extract the time-frequency domain physical features of each atom in the initial overcomplete dictionary, perform cluster analysis in the feature space using Gaussian Mixture Model (GMM), and prune redundant atoms according to the similarity criterion to obtain the final overcomplete dictionary with dimensionality reduction optimization.

[0027] The time-frequency domain physical feature extraction of Gaussian Mixture Model (GMM) performing clustering pruning includes the following steps: S41. First, for each atom in the initial overcomplete dictionary... Perform multi-dimensional feature extraction, and the extracted features include waveform factors that reflect the wave characteristics of atomic waveforms. And kurtosis characteristics that reflect the concentration of atomic energy distribution ; Waveform factor The calculation formula is as follows: ; In the formula, For atoms in the time window Peak amplitude within, This is the root mean square value of the atom.

[0028] kurtosis features The calculation formula is as follows: ; In the formula, The fourth central moment of the atom. The second central moment of the atom, This is the average value of the atoms.

[0029] S42, Extract and Construct as a two-dimensional original feature vector Furthermore, a time index feature is introduced to construct a three-dimensional enhanced feature space, where the Z-axis represents the order index of atom generation. To eliminate the influence of different dimensions on the clustering effect, range standardization is performed on the original feature vector to obtain a standardized feature vector. Its mapping rules are as follows: ; In the formula, and These represent the maximum and minimum values ​​of the corresponding features in the initial overcomplete dictionary set; refined clustering is performed in the feature space based on the waveform geometry and energy distribution of the atoms; S43. The system uses the EM algorithm to iteratively calculate the atom belonging to the first... The posterior probabilities of each feature cluster are used to group atoms with the highest membership probabilities into the same category. When redundant atom pairs are identified, the atom that contributed more to the reconstruction during training is retained, while the other atom is removed, thus gradually compressing the dictionary size from the initial dimension to the target dimension. This is to improve the computational response speed of terminal devices during online decomposition.

[0030] S5. On the terminal side, the segmented perturbation signal is decomposed using orthogonal matching pursuit sparse decomposition with the final overcomplete dictionary to obtain atomic indices and coefficients, which are then uploaded to the main station for high-precision waveform reconstruction. For example... Figure 5 As shown, it includes the following steps: S51, terminal side in the In the next iteration, find the residual signal that is currently... Best matching atomic index Its objective function is shown in the following equation: .

[0031] S52. Calculate the reconstructed signal. and residuals ; S53. During the main station reconstruction phase, based on the received sparse vector, the formula is used... The residual energy, including in-band noise, is evaluated, and a robust termination condition is determined based on a weighted evaluation of the difference in deterministic fitness between the last two iterations, using the following formula: ; in, and For weighted parameters, As a measure of fit, This is the termination threshold, used to balance noise interference from global periodicity and local fluctuations.

[0032] This embodiment uses measured waveform data from a power distribution network in North China to evaluate the effectiveness of the proposed method for sparse decomposition of waveform data. Figure 6 Taking the waveform data of surge arrester insulation breakdown as an example, the execution process of this method is analyzed. The waveform sampling rate is 3.2kHz, and the duration is 0.32s. For this waveform duration, the proposed method requires 80 atoms to effectively perform sparse decomposition of the signal. These atoms are then uploaded in the form of data frames, with each atom occupying 4 bytes. Compared with directly uploading waveform data (each instantaneous value occupies two bytes), the data volume is reduced by more than 6 times. The average error after reconstruction is 0.1753%, and the maximum error is 0.3126%, which meets the accuracy requirements for distribution network disturbance analysis. This demonstrates the high efficiency of this method for decomposing and reconstructing transient waveform signals in distribution networks.

[0033] Therefore, the present invention adopts the above-mentioned dictionary learning-based distribution network transient disturbance waveform measurement method. By combining offline training with online decomposition, it effectively reduces redundant information and significantly improves the compression ratio and reconstruction efficiency of waveform data while ensuring measurement accuracy. This solves the problem that existing power system measurement devices are unable to capture complex waveform dynamic details due to large data volume and high transmission pressure.

[0034] 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 them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for measuring transient disturbance waveforms in a distribution network based on dictionary learning, characterized in that, Includes the following steps: S1. Construct a disturbance waveform measurement framework that covers offline learning on the main station side and online decomposition on the terminal side; S2. The relative energy acceleration operator REAO is used to monitor the sampling sequence in real time, determine the start and end times of the transient disturbance waveform, and realize the active segmentation of the waveform data accordingly. S3. Based on the historical disturbance dataset, the dictionary atoms and sparse coefficients are updated alternately and iteratively using the regularized K-SVD algorithm to initially construct an overcomplete dictionary that can characterize the typical disturbance features of the distribution network. S4. Extract the time-frequency domain physical features of each atom in the initial overcomplete dictionary, perform cluster analysis in the feature space using Gaussian Mixture Model (GMM), and prune redundant atoms according to the similarity criterion to obtain the final overcomplete dictionary with dimensionality reduction optimization. S5. On the terminal side, the segmented disturbance signal is decomposed by orthogonal matching tracking sparse decomposition using the final complete dictionary to obtain the atomic index and coefficients, and then uploaded to the main station for high-precision waveform reconstruction.

2. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 1, characterized in that, S1 includes: S11. Offline training on the main station side: Collect multi-source historical disturbance waveform data of the distribution network to build a sample library, and periodically execute dictionary learning algorithm to update the atomic sequence; S12. Dictionary distribution and synchronization: The optimized and final complete dictionary is remotely pushed to each monitoring terminal and stored locally for online comparison and retrieval. S13. Terminal-side online decomposition: The monitoring terminal performs rapid matching and tracking of the real-time captured transient disturbance segments based on the final overcomplete dictionary stored locally, realizing the conversion of raw data into representation coefficients; S14. Online reconstruction on the main station side: Receive compressed data frames uploaded by the terminal, retrieve the local dictionary according to the atomic index number in the data frame, and restore the waveform of the entire disturbance process by linear superposition.

3. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 2, characterized in that, S2 includes: S21, Regarding the input signal Define the forward energy acceleration operator FEAO as The backward energy acceleration operator BEAO is The calculation logic is as follows: ； S22, Calculation of the relative energy acceleration operator As shown in the following formula: ； when Greater than the preset trigger threshold When, it is determined to be the start time of the disturbance; when Continuously below the preset end threshold When the time window constraint is met, it is determined to be the end time of the disturbance.

4. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 3, characterized in that, S3 includes: S31. First, the acquired multi-source historical disturbance waveform data of the distribution network is standardized and preprocessed to construct a training dataset. Each column represents a length of The perturbation signal samples; based on the training dataset, a dictionary learning objective function based on the regularized K-SVD algorithm is established. Its expression is as follows: ； In the formula, Let be the overcomplete dictionary matrix to be solved. The coding coefficient matrix, for The row vectors This is a regularization parameter used to balance reconstruction fidelity and atomic sparsity; During the iterative optimization process, the system alternately performs sparse coding and dictionary updates: in the sparse coding phase, the dictionary is fixed. The orthogonal matching pursuit algorithm is used to solve for the condition that satisfies Optimal coefficient matrix under constraints During the dictionary update phase, atoms are updated column by column. and their corresponding nonzero sparsity coefficients The definition does not include the first The residual matrix of each atom's contribution As shown in the following formula: ； S32. To maintain the sparsity pattern, only extract... The middle corresponds to the atom The columns with non-zero positions form the reduced residual matrix. And perform singular value decomposition on it, as shown in the following equation: ； Selecting the left singular matrix The first column vector As the updated atom Select the first singular value With right singular matrix The first column vector The product of these factors serves as the updated non-zero coefficient vector. and perform on the newly generated atoms Norm normalization constraint, satisfying This ensures that the generated initial overcomplete dictionary can accurately characterize the broadband dynamic characteristics of transient disturbance waveforms in the distribution network.

5. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 4, characterized in that, The extraction of time-frequency domain physical features of each atom in the initial overcomplete dictionary in S4 includes: S41. First, for each atom in the initial overcomplete dictionary... Perform multi-dimensional feature extraction, and the extracted features include waveform factors that reflect the wave characteristics of atomic waveforms. And kurtosis characteristics that reflect the concentration of atomic energy distribution ; S42, Extract and Construct as a two-dimensional original feature vector Furthermore, a time index feature is introduced to construct a three-dimensional enhanced feature space, where the Z-axis represents the order index of atom generation; To eliminate the influence of different units on the clustering results, range standardization is performed on the original feature vectors to obtain standardized feature vectors. Its mapping rules are as follows: ； In the formula, and These represent the maximum and minimum values ​​of the corresponding features in the initial overcomplete dictionary set; refined clustering is performed in the feature space based on the waveform geometry and energy distribution of the atoms; S43. The system uses the EM algorithm to iteratively calculate the atom belonging to the first... The posterior probabilities of each feature cluster are used to classify atoms with the highest membership probabilities into the same category. When redundant atom pairs are identified, the atom that contributed more to the reconstruction during training is retained, while the other atom is removed, thus gradually compressing the dictionary size from the initial dimension to the target dimension. This is to improve the computational response speed of terminal devices during online decomposition.

6. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 5, characterized in that, In S41, the waveform factor The calculation formula is as follows: ； In the formula, For atoms in the time window Peak amplitude within, This is the root mean square value of the atom.

7. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 6, characterized in that, In S41, the kurtosis feature The calculation formula is as follows: ； In the formula, The fourth central moment of the atom. The second central moment of the atom. This is the average value of the atoms.

8. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 7, characterized in that, S5 includes: S51, terminal side in the In the next iteration, find the residual signal that is currently... Best matching atomic index Its objective function is: S52. Calculate the reconstructed signal. and residuals ; S53. During the main station reconstruction phase, based on the received sparse vector, the formula is used... The residual energy, including in-band noise, is evaluated, and a robust termination condition is determined based on a weighted evaluation of the difference in deterministic fitness between the last two iterations.

9. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 8, characterized in that, Atomic index in S51 The objective function is shown in the following equation: 。 10. The method for measuring transient disturbance waveforms in a distribution network based on dictionary learning according to claim 9, characterized in that, In S53, the robust termination condition is determined by the following formula: ； in, and For weighted parameters, As a measure of fit, This is the termination threshold, used to balance noise interference from global periodicity and local fluctuations.

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