Power transient recording waveform identification method and system based on time-frequency analysis

Abstract

The application provides a power transient recording waveform recognition method and system based on time-frequency analysis, relates to the power waveform recognition technical field, and comprises the following steps: acquiring waveform data collected by a transient recording device to perform multi-scale wavelet decomposition, extracting an instantaneous amplitude envelope and an instantaneous frequency trajectory through Hilbert transformation, and obtaining a transient characteristic tensor through correlation mapping; calculating a mutual information matrix based on the transient characteristic tensor, constructing a bidirectional time-frequency dependence graph to obtain a time-frequency joint representation vector through message transmission; determining a category boundary surface according to a Riemann geometric measure to calculate a local curvature distribution of a characteristic manifold, extracting a gradient field along a normal vector and calculating a divergence and a curl, combining the time-frequency joint representation vector to obtain a manifold enhanced feature vector, and calculating a cluster inter-geodesic distance matrix after clustering to perform category division and map a recognition result.

Description

Technical Field

[0001] This invention relates to the field of power waveform recognition technology, and in particular to a method and system for identifying power transient waveforms based on time-frequency analysis. Background Technology

[0002] Transient waveform recording equipment plays a crucial data acquisition role in distribution network fault location and type identification, directly recording the complete dynamic changes of voltage and current during the fault instant and the recovery process. Existing technologies typically employ a two-stage process of signal analysis plus pattern classification, using Fourier transform, short-time Fourier transform, or wavelet transform as the core tools for time-frequency feature extraction. After obtaining the spectral energy distribution or time-frequency spectrum, category mapping is completed. This approach can achieve good accuracy under laboratory sample conditions, thus becoming the most widely used baseline scheme in this field.

[0003] In existing technologies, feature representation capabilities are limited by fixed resolution or preset basis. Once the window length of the short-time Fourier transform is determined, the time-domain accuracy and frequency-domain accuracy become mutually restrictive. It is difficult to simultaneously capture the start time of abrupt changes and subtle frequency shifts in the numerous non-stationary and non-uniform modulation components present in the transient state of distribution network faults. Although wavelet transform introduces the idea of ​​multi-resolution, the number of decomposition layers and the selection of basis functions still rely on human experience. Faced with waveform morphology drift under different feeder topologies and different transition resistance conditions, the stability of the features is obviously insufficient, which can easily lead to misjudgment between similar fault types.

[0004] Furthermore, existing technologies heavily rely on the scale and quality of labeled samples. Deep recognition models based on convolutional neural networks require a large number of class-balanced transient waveform samples for training. However, in actual engineering projects, field waveform data often contains a large amount of abnormal noise, missing channels, and unlabeled events, making the effective samples available for supervised learning very limited. This often leads to severe performance degradation when the model is transferred across sites and scenarios. While manually designed features combined with shallow classifiers have lower sample requirements, they are limited to explicit morphological differences that can be described by expert experience. They are insufficient for recognizing fault scenarios with weak waveform features but rich physical connotations, such as complex high-resistance grounding and intermittent arcing. This results in high maintenance costs in field applications, and the recognition accuracy is insufficient to meet the reliability requirements of fault assessment. Summary of the Invention

[0005] This invention provides a method and system for identifying transient waveforms in power systems based on time-frequency analysis, which can at least solve some of the problems existing in the prior art.

[0006] A first aspect of the present invention provides a method for identifying power transient waveforms based on time-frequency analysis, comprising: Waveform data acquired by transient recording equipment is decomposed into decomposition coefficients for different frequency bands using multi-scale wavelet decomposition. Hilbert transform is then applied to the decomposition coefficients to extract the instantaneous amplitude envelope and instantaneous frequency trajectory. The time-frequency evolution path of the instantaneous frequency trajectory is determined and correlated with the instantaneous amplitude envelope to obtain the transient feature tensor. The mutual information matrix of time and frequency dimensions is calculated based on the transient feature tensor. A bidirectional time-frequency dependency graph is constructed based on the mutual information matrix and message passing is performed. The time-frequency joint representation vector is obtained based on the neighborhood messages received by each node. The Riemannian geometric metric of the feature manifold space is calculated based on the time-frequency joint representation vector. The local curvature distribution of the feature manifold is calculated and the category boundary is determined according to the Riemannian geometric metric. The gradient field is extracted along the normal vector direction of the category boundary and the divergence distribution and curl distribution are calculated. The boundary sensitive features are determined based on the divergence distribution and curl distribution and the manifold enhancement feature vector is obtained by combining the time-frequency joint representation vector. The manifold enhancement feature vector is clustered to obtain multiple feature clusters. The geodesic distance of different feature clusters in the manifold space is calculated and the inter-cluster geodesic distance matrix is ​​constructed. The category is divided based on the inter-cluster geodesic distance matrix and mapped to the preset type label space to obtain the recognition result.

[0007] In one alternative implementation, Waveform data acquired by a transient recording device is decomposed using multi-scale wavelet decomposition to obtain decomposition coefficients for different frequency bands. Hilbert transform is then applied to these decomposition coefficients to extract instantaneous amplitude envelopes and instantaneous frequency trajectories. The time-frequency evolution path of the instantaneous frequency trajectory is determined and correlated with the instantaneous amplitude envelope to obtain a transient feature tensor, including: The waveform data collected by the transient recording device is acquired and the sliding window is used to divide the time-domain frames into multiple time-domain frames. Multi-scale wavelet decomposition is performed on the time-domain frames to obtain wavelet coefficients at different scale levels, and the frames are divided into multiple frequency bands according to the frequency response range to obtain the corresponding decomposition coefficients. The decomposed coefficients are subjected to Hilbert transform to obtain an analytical signal. The real and imaginary parts are extracted from the analytical signal and the square root of the amplitude is calculated to obtain the instantaneous amplitude envelope. The phase angle of the analytical signal is calculated and time derivative is performed to obtain the instantaneous frequency. The instantaneous frequency is sampled on the time axis and frequency change points are marked. The instantaneous frequency trajectory is constructed based on the time position and frequency value of the frequency change points. The time-frequency evolution path is obtained by determining the two-dimensional coordinate sequence of the instantaneous frequency trajectory in the time-frequency plane. The Euclidean distance between adjacent coordinate points in the time-frequency evolution path is calculated and accumulated to obtain the trajectory length. Based on the trajectory length, the arc length parameterization of the time-frequency evolution path is performed to obtain a normalized trajectory representation. The time coordinates in the normalized trajectory representation are aligned and matched with the time index of the instantaneous amplitude envelope. Based on the aligned time nodes, the tensor outer product operation is performed on the normalized trajectory representation and the instantaneous amplitude envelope to obtain the transient feature tensor.

[0008] In one alternative implementation, Based on the transient feature tensor, the mutual information matrix in the time and frequency dimensions is calculated. A bidirectional time-frequency dependency graph is constructed based on the mutual information matrix, and message passing is performed. The joint time-frequency representation vector is obtained based on the neighborhood messages received by each node, including: The transient feature tensor is sliced ​​along the time dimension and frequency dimension to obtain time slice features and frequency slice features respectively. The joint probability distribution and marginal probability distribution between the time slice features and the frequency slice features are calculated. Based on the joint probability distribution and the marginal probability distribution, the mutual information value is calculated to construct a mutual information matrix. The mutual information matrix is ​​subjected to threshold filtering to retain elements that exceed a preset threshold. The row index of the retained elements is used as the time node, the column index is used as the frequency node, and the mutual information value of the retained elements is used as the edge weight to establish connection edges to obtain a bidirectional time-frequency dependency graph. Extract the corresponding features of each node from the transient feature tensor as the initial node features, find the neighboring nodes corresponding to each node in the bidirectional time-frequency dependency graph and obtain the neighboring node features, concatenate the neighboring node features along the neighborhood dimension and perform gated fusion with the current node features to obtain the updated node features, repeat the iteration to obtain the final node features, and arrange them in the time dimension and frequency dimension to obtain the time feature sequence and the frequency feature sequence, and construct the time-frequency joint representation vector based on the time feature sequence and the frequency feature sequence.

[0009] In one alternative implementation, The Riemannian geometric metric of the feature manifold space is calculated based on the time-frequency joint characterization vector. The local curvature distribution of the feature manifold is calculated based on the Riemannian geometric metric, and the class boundary is determined. The gradient field is extracted along the normal vector direction of the class boundary, and the divergence and curl distributions are calculated, including: The time-frequency joint representation vector is expanded into a grid according to the time dimension and the frequency dimension to obtain multiple time-frequency feature points. The time-frequency feature points are mapped to a high-dimensional feature manifold space and the local neighborhood relationship between different time-frequency feature points is calculated. A tangent space basis is constructed based on the local neighborhood relationship. The Riemann distance between time-frequency feature points is calculated under the tangent space basis and a Riemann geometric metric tensor is constructed. Based on the Riemannian geometric metric tensor, the cross-sectional curvature of each time-frequency feature point on the feature manifold is calculated. The cross-sectional curvature is spatially integrated to obtain the local curvature distribution. Regions in the local curvature distribution whose curvature gradient exceeds a preset gradient threshold are identified as candidate boundary regions. Curvature maxima in the candidate boundary regions are extracted to determine the category boundary. The tangent plane of the category interface is calculated in the feature manifold space, the orthogonal complement space of the tangent plane is solved to obtain the normal vector direction, the directional derivative of the time-frequency joint characterization vector is calculated along the normal vector direction to obtain the gradient field, the divergence operator is performed on the gradient field to obtain the divergence distribution, and the curl operator is performed on the gradient field to obtain the curl distribution.

[0010] In one alternative implementation, Spatial integration of the cross-sectional curvature yields a local curvature distribution. Regions within this local curvature distribution whose curvature gradient exceeds a preset gradient threshold are identified as candidate boundary regions. Curvature maxima within these candidate boundary regions are extracted to determine the category boundary, including: A neighborhood of the Earth centered on a time-frequency feature point is constructed, and the curvature of the cross section is integrated within the Earth to obtain the Gaussian curvature integral. Based on the Gaussian curvature integral, the curvature density is calculated to obtain the local curvature distribution. Covariant differentiation is performed on the local curvature distribution to obtain the curvature gradient field. Persistent homology analysis is performed on the curvature gradient field to extract the birth and death pairs of the zero-dimensional persistence graph. Based on the persistence length of the birth and death pairs, stable curvature change points are screened and aggregated to obtain candidate boundary regions. In the tangent space of the candidate boundary region, a Hessian matrix is ​​constructed and eigenvalues ​​are calculated. The saddle point positions where the eigenvalue signs change are identified, and local maxima points are extracted along the principal curvature direction. The geodesic coordinates of the local maxima points in the manifold space are calculated, and a minimum spanning tree is constructed based on the geodesic distance between adjacent point pairs. Geodesic tracing is performed on the minimum spanning tree to obtain the connection path. The connection path is smoothed, and the smoothed curve is extended by normal cluster in the manifold space to obtain the category boundary.

[0011] In one alternative implementation, Based on the divergence and curl distributions, boundary-sensitive features are determined, and the manifold enhancement feature vector is obtained by combining the time-frequency joint representation vector. The manifold enhancement feature vector is then clustered to obtain multiple feature clusters, including: Gaussian smoothing is applied to the divergence distribution to obtain a smoothed divergence field, and the spatial gradient corresponding to the smoothed divergence field is calculated to obtain a divergence rate of change field. Singular value decomposition is performed on the curl distribution to obtain a curl principal direction field, which is then concatenated with the divergence rate of change field to obtain a boundary sensitive feature vector. The cross-correlation coefficient between the boundary sensitive feature vector and the time-frequency joint representation vector is calculated and used as a correlation weight. The boundary sensitive feature vector is weighted based on the correlation weight to obtain a weighted boundary feature vector, which is then fused with the time-frequency joint representation vector to obtain a manifold enhancement feature vector. Principal component analysis is performed on the manifold enhancement feature vector to reduce its dimensionality, resulting in a dimensionality-reduced feature vector. A similarity graph is constructed based on the dimensionality-reduced feature vector, and the graph Laplacian matrix is ​​calculated. Eigenvalue decomposition is performed on the graph Laplacian matrix to obtain a spectral embedding space. Density peak detection is used to identify representative cluster points in the spectral embedding space, and nearest neighbor assignment is performed to obtain the category classification. Based on the category classification, the manifold enhancement feature vector is divided into multiple feature clusters.

[0012] In one alternative implementation, Calculate the geodesic distances of different feature clusters in the manifold space and construct an inter-cluster geodesic distance matrix. Based on the inter-cluster geodesic distance matrix, perform category classification and map it to a preset type label space to obtain the recognition results, including: Extract the centroid feature vector corresponding to each feature cluster from the multiple feature clusters and determine the centroid position. Construct an initial connection path between different centroid positions and sample intermediate points along the initial connection path. Project the intermediate points onto a preset manifold surface to obtain surface correction points. Connect adjacent surface correction points to construct segmented paths and calculate the arc length of each segment. Accumulate the segmented arc lengths and perform local curvature compensation to obtain the corrected geodesic distance. Calculate the corrected geodesic distance between different feature clusters and organize them in matrix form to obtain the inter-cluster geodesic distance matrix. The inter-cluster geodesic distance matrix is ​​decomposed into eigenvalues ​​to obtain a distance feature value sequence. The distance feature value sequence is then subjected to a difference operation, and the difference peak is identified to determine the feature value gap. Based on the feature value gap, the number of categories is determined and the corresponding distance feature vectors are extracted. The distance feature vectors are then normalized to obtain category division coordinates. The category division coordinates are then symbolically encoded to obtain the cluster category label index. The category label index is mapped to a preset type label space and labeled according to the feature clusters corresponding to the manifold enhancement feature vector to obtain the recognition result.

[0013] A second aspect of the present invention provides a power transient waveform recognition system based on time-frequency analysis, comprising: The feature extraction unit is used to acquire waveform data collected by the transient recording device, perform multi-scale wavelet decomposition to obtain decomposition coefficients of different frequency bands, perform Hilbert transform on the decomposition coefficients to extract instantaneous amplitude envelope and instantaneous frequency trajectory, determine the time-frequency evolution path of the instantaneous frequency trajectory and associate it with the instantaneous amplitude envelope to obtain transient feature tensor; The time-frequency representation unit is used to calculate the mutual information matrix of the time dimension and the frequency dimension based on the transient feature tensor, construct a bidirectional time-frequency dependency graph based on the mutual information matrix and perform message passing, and obtain the time-frequency joint representation vector based on the neighborhood messages received by each node. The manifold classification unit is used to calculate the Riemannian geometric metric of the feature manifold space based on the time-frequency joint representation vector, calculate the local curvature distribution of the feature manifold and determine the category boundary according to the Riemannian geometric metric, extract the gradient field along the normal vector direction of the category boundary and calculate the divergence distribution and curl distribution, determine the boundary sensitive features based on the divergence distribution and curl distribution and solve for the manifold enhancement feature vector by combining the time-frequency joint representation vector, cluster the manifold enhancement feature vector to obtain multiple feature clusters, calculate the geodesic distance of different feature clusters in the manifold space and construct the inter-cluster geodesic distance matrix, classify the categories based on the inter-cluster geodesic distance matrix and map to the preset type label space to obtain the recognition result.

[0014] A third aspect of the present invention provides an electronic device, comprising: A processor and a memory for storing processor-executable instructions, wherein the processor is configured to invoke instructions stored in the memory to perform the aforementioned method.

[0015] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0016] In this invention, multi-scale wavelet decomposition is used to divide transient waveforms into different frequency bands. Combined with Hilbert transform, instantaneous amplitude envelopes and instantaneous frequency trajectories are extracted, accurately depicting the non-stationary evolution of transient signals in the time-frequency domain. Mapping the instantaneous frequency trajectory and amplitude envelope to a transient feature tensor effectively preserves weak abrupt changes and local fluctuations in the signal, significantly improving the completeness and noise resistance of feature description. Calculating the mutual information matrix of the time and frequency dimensions based on the transient feature tensor captures nonlinear dependencies, thereby constructing a bidirectional time-frequency dependency graph and transmitting neighborhood messages, enabling the joint time-frequency representation vector to possess both temporal continuity and frequency selectivity. The message passing mechanism enhances the contextual awareness of features in the time-frequency space, avoiding recognition bias caused by local anomalies. Riemannian geometric metrics are used to characterize the intrinsic structure of the feature manifold. The class boundaries are determined through local curvature distribution, and the gradient field is extracted along the normal direction, with divergence and curl calculated. This strengthens the geometrically sensitive features at the boundaries, amplifies the separation trend of different classes in the feature space, and reduces misjudgments caused by overlapping areas between classes. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the power transient waveform identification method based on time-frequency analysis according to an embodiment of the present invention. Figure 2 This is a bidirectional time-frequency dependence graph of the power transient waveform identification method based on time-frequency analysis according to an embodiment of the present invention; Figure 3 This is a flowchart illustrating the feature cluster classification and identification process of the power transient waveform recognition method based on time-frequency analysis, as described in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0020] Figure 1 This is a flowchart illustrating the power transient waveform identification method based on time-frequency analysis according to an embodiment of the present invention. Figure 1 As shown, the method includes: Waveform data acquired by transient recording equipment is decomposed into decomposition coefficients for different frequency bands using multi-scale wavelet decomposition. Hilbert transform is then applied to the decomposition coefficients to extract the instantaneous amplitude envelope and instantaneous frequency trajectory. The time-frequency evolution path of the instantaneous frequency trajectory is determined and correlated with the instantaneous amplitude envelope to obtain the transient feature tensor. The mutual information matrix of time and frequency dimensions is calculated based on the transient feature tensor. A bidirectional time-frequency dependency graph is constructed based on the mutual information matrix and message passing is performed. The time-frequency joint representation vector is obtained based on the neighborhood messages received by each node. The Riemannian geometric metric of the feature manifold space is calculated based on the time-frequency joint representation vector. The local curvature distribution of the feature manifold is calculated and the category boundary is determined according to the Riemannian geometric metric. The gradient field is extracted along the normal vector direction of the category boundary and the divergence distribution and curl distribution are calculated. The boundary sensitive features are determined based on the divergence distribution and curl distribution and the manifold enhancement feature vector is obtained by combining the time-frequency joint representation vector. The manifold enhancement feature vector is clustered to obtain multiple feature clusters. The geodesic distance of different feature clusters in the manifold space is calculated and the inter-cluster geodesic distance matrix is ​​constructed. The category is divided based on the inter-cluster geodesic distance matrix and mapped to the preset type label space to obtain the recognition result.

[0021] In one alternative implementation, Waveform data acquired by a transient recording device is decomposed using multi-scale wavelet decomposition to obtain decomposition coefficients for different frequency bands. Hilbert transform is then applied to these decomposition coefficients to extract instantaneous amplitude envelopes and instantaneous frequency trajectories. The time-frequency evolution path of the instantaneous frequency trajectory is determined and correlated with the instantaneous amplitude envelope to obtain a transient feature tensor, including: The waveform data collected by the transient recording device is acquired and the sliding window is used to divide the time-domain frames into multiple time-domain frames. Multi-scale wavelet decomposition is performed on the time-domain frames to obtain wavelet coefficients at different scale levels, and the frames are divided into multiple frequency bands according to the frequency response range to obtain the corresponding decomposition coefficients. The decomposed coefficients are subjected to Hilbert transform to obtain an analytical signal. The real and imaginary parts are extracted from the analytical signal and the square root of the amplitude is calculated to obtain the instantaneous amplitude envelope. The phase angle of the analytical signal is calculated and time derivative is performed to obtain the instantaneous frequency. The instantaneous frequency is sampled on the time axis and frequency change points are marked. The instantaneous frequency trajectory is constructed based on the time position and frequency value of the frequency change points. The time-frequency evolution path is obtained by determining the two-dimensional coordinate sequence of the instantaneous frequency trajectory in the time-frequency plane. The Euclidean distance between adjacent coordinate points in the time-frequency evolution path is calculated and accumulated to obtain the trajectory length. Based on the trajectory length, the arc length parameterization of the time-frequency evolution path is performed to obtain a normalized trajectory representation. The time coordinates in the normalized trajectory representation are aligned and matched with the time index of the instantaneous amplitude envelope. Based on the aligned time nodes, the tensor outer product operation is performed on the normalized trajectory representation and the instantaneous amplitude envelope to obtain the transient feature tensor.

[0022] After acquiring the raw waveform data output by the transient waveform recording equipment, preprocessing is required to meet the requirements of subsequent multi-scale analysis. A sliding window framing operation is applied to the raw waveform signal. The window length and step size are determined based on the typical duration of the transient event. Typically, the window length covers several power frequency cycles, and the step size is half the window length to ensure sufficient overlap between adjacent frames, thereby avoiding the loss of transient features at frame boundaries. Each time-domain frame independently preserves the complete waveform morphology within that time period, providing a localized time-domain segment for subsequent decomposition.

[0023] Multi-scale wavelet decomposition is performed on each time-domain frame. Wavelet basis functions with good time-frequency localization properties are selected. The number of decomposition levels is determined jointly based on the signal sampling rate and the frequency band of interest. The sampling rate is used as an example. The number of decomposition layers is For example, the first layer( The corresponding frequency response range is ,in Sampling rate, This represents the total number of decomposition levels. This serves as the index for the current decomposition layer. The detail coefficients and final approximation coefficients generated by each layer are assigned to their corresponding frequency bands according to their frequency response range, forming a set of decomposition coefficients for multiple frequency bands. The decomposition coefficients of the high-frequency bands mainly reflect transient impulses and rapid oscillation components, while the decomposition coefficients of the low-frequency bands retain the fundamental power frequency and the gradual variation trend. The decomposition coefficients of different frequency bands together constitute a multi-resolution description of the original waveform.

[0024] Applying a Hilbert transform to the decomposed coefficient sequences of each frequency band converts the real-valued coefficient sequences into analytic signals. The real part of the analytic signal is the original decomposed coefficient sequence itself, and the imaginary part is its Hilbert transform result; together, they constitute a complex-valued analytic signal. The real part is then extracted from the analytic signal. With the imaginary part Instantaneous amplitude envelope It is obtained by calculating the sum of the squares of the real and imaginary parts and then taking the square root, that is... ,in To analyze the real part of the signal, To analyze the imaginary part of the signal, The variable is time. Instantaneous amplitude envelope. This reflects the trend of signal energy change over time, with significant amplitude abrupt changes occurring at the moment of transient events.

[0025] Instantaneous phase It is obtained by calculating the phase angle of the analytic signal, i.e. ,in The instantaneous phase is given. The instantaneous frequency is obtained by differentiating the instantaneous phase sequence over time. ,Right now ,in The instantaneous frequency is represented by the time derivative. In the discrete implementation, the time derivative is approximated by dividing the phase difference between adjacent sampling points by the sampling interval, and the phase winding is unwound to ensure the continuity of the instantaneous frequency. The instantaneous frequency sequence is uniformly sampled along the time axis, and frequency abrupt changes are marked by detecting positions where the instantaneous frequency difference between adjacent sampling points exceeds a preset threshold. The time position of the frequency abrupt change records the occurrence time of the transient event on the time axis, and the corresponding instantaneous frequency value reflects the dominant oscillation frequency at the current moment. An ordered sequence of time positions and corresponding frequency values ​​of all frequency abrupt changes is formed, constructing an instantaneous frequency trajectory. This trajectory describes the jump pattern of the signal frequency components over time in the form of a discrete point set.

[0026] Determine the two-dimensional coordinate sequence of the instantaneous frequency trajectory on the time-frequency plane. Each coordinate point is composed of a time coordinate and the corresponding instantaneous frequency value, forming a time-frequency evolution path. Calculate the Euclidean distance between adjacent coordinate points in the time-frequency evolution path, and let the i-th... The coordinate points are Then the distance between adjacent points is ,in For the first Time coordinates of each coordinate point The coordinates are indexed. The total length of the trajectory is obtained by accumulating the distances between all adjacent points. ,Right now ,in This represents the total number of coordinate points. The total trajectory length is used. Based on the total trajectory length, the time-frequency evolution path is parameterized by arc length, mapping each coordinate point to... Normalized arc length parameter within the interval ,Right now ,in For the first Normalized arc length parameter for each coordinate point For the summation index, The range of values ​​is , Indicating the first time-frequency evolution path From point 1 to point 2 The distance between points. After arc length parameterization, the time-frequency evolution path is represented by a normalized trajectory with equal arc length intervals, eliminating the problem of incomparable path lengths caused by differences in duration between different transient events.

[0027] The time coordinates in the normalized trajectory representation are aligned with the time indices of the instantaneous amplitude envelope. Since their sampling densities may differ, a linear interpolation method is used to resample the normalized trajectory representation to the same temporal resolution as the instantaneous amplitude envelope, ensuring that both the normalized trajectory coordinates and the corresponding instantaneous amplitude envelope values ​​exist at each aligned time node. After alignment, a tensor outer product operation is performed on the normalized trajectory representation vector and the instantaneous amplitude envelope scalar at each time node. Let the normalized trajectory representation at a certain aligned time node be a column vector. (Including normalized time and normalized frequency coordinates), the corresponding instantaneous amplitude envelope value is a scalar. Then the outer product of this node is a matrix. ,in For the normalized trajectory coordinate vector, This represents the instantaneous amplitude envelope. The outer product results of all time points are stacked along the time axis, and the results corresponding to multiple frequency bands are spliced ​​along the frequency band dimension to finally obtain a three-dimensional transient feature tensor. Its three dimensions correspond to time, frequency band, and trajectory-amplitude joint features, respectively, which fully preserves the structured information of the transient signal in the three dimensions of time, frequency, and amplitude.

[0028] In one alternative implementation, Based on the transient feature tensor, the mutual information matrix in the time and frequency dimensions is calculated. A bidirectional time-frequency dependency graph is constructed based on the mutual information matrix, and message passing is performed. The joint time-frequency representation vector is obtained based on the neighborhood messages received by each node, including: The transient feature tensor is sliced ​​along the time dimension and frequency dimension to obtain time slice features and frequency slice features respectively. The joint probability distribution and marginal probability distribution between the time slice features and the frequency slice features are calculated. Based on the joint probability distribution and the marginal probability distribution, the mutual information value is calculated to construct a mutual information matrix. The mutual information matrix is ​​subjected to threshold filtering to retain elements that exceed a preset threshold. The row index of the retained elements is used as the time node, the column index is used as the frequency node, and the mutual information value of the retained elements is used as the edge weight to establish connection edges to obtain a bidirectional time-frequency dependency graph. Extract the corresponding features of each node from the transient feature tensor as the initial node features, find the neighboring nodes corresponding to each node in the bidirectional time-frequency dependency graph and obtain the neighboring node features, concatenate the neighboring node features along the neighborhood dimension and perform gated fusion with the current node features to obtain the updated node features, repeat the iteration to obtain the final node features, and arrange them in the time dimension and frequency dimension to obtain the time feature sequence and the frequency feature sequence, and construct the time-frequency joint representation vector based on the time feature sequence and the frequency feature sequence.

[0029] Transient feature tensors possess different physical meanings in the time and frequency dimensions, making it difficult to capture the intrinsic relationship between these two dimensions through direct statistical modeling of the overall tensor. Therefore, the transient feature tensor is sliced ​​along the time dimension, with each time step corresponding to a time-slice feature vector containing the feature values ​​across all frequency channels at that moment. Slicing along the frequency dimension yields frequency-slice feature vectors, with each frequency channel corresponding to a vector containing the feature values ​​from all time steps. The time-slice and frequency-slice features characterize the local distribution of the signal in the time and frequency domains, respectively, providing structured statistical samples for subsequent mutual information calculations.

[0030] When calculating the joint probability distribution between time slice features and frequency slice features, the value spaces of the two types of slice features are discretized into several intervals. The frequency of each interval combination is counted and normalized to obtain the joint probability distribution matrix. The marginal probability distributions are obtained by summing the joint probability distribution matrix along the time and frequency dimensions, respectively. Based on the joint probability distribution... With marginal probability distribution , Calculate each pair of time nodes according to the definition of mutual information. With frequency node Mutual information values ​​between The formula is: For each combination of time and frequency nodes, calculate the mutual information value and fill it into the mutual information matrix. The row index corresponds to the time node, the column index corresponds to the frequency node, and the matrix elements... That is, a node With nodes The mutual information value between the time and frequency dimensions. The mutual information matrix fully characterizes the statistical dependence strength between the time and frequency dimensions, providing a quantitative basis for subsequent graph structure construction.

[0031] Mutual information matrix Perform threshold filtering, and set the preset threshold as follows: , retain satisfaction The elements with the highest frequency are set to zero, while the rest are set to zero. The row index of each element is retained as the time node number, the column index as the frequency node number, and the mutual information value of the elements is retained. This serves as the weight of the corresponding connecting edge. Since the dependency between time nodes and frequency nodes is bidirectional, i.e., time nodes... For frequency nodes Yes, it has an impact on frequency nodes. Time nodes This also has an impact, therefore, for each preserved edge in the graph, a connection is simultaneously established from... arrive and from arrive Directed edges, with edge weights all taking Thus, a bidirectional time-frequency dependency graph is constructed. Threshold The choice of threshold directly affects the sparsity of the graph: too low a threshold will introduce a large number of weakly dependent edges, increasing the noise of message passing; too high a threshold may lose effective time-frequency correlations. It is usually adaptively determined based on the statistical distribution of the mutual information matrix (such as the mean plus one standard deviation).

[0032] Extract the feature vectors corresponding to each node from the transient feature tensor as the initial node features. For time nodes... Its initial feature is the transient feature tensor at time step The slice vector at the frequency node; Its initial feature is the transient feature tensor in the frequency channel. The slice vector at that location. In the bidirectional time-frequency dependence graph. In this process, the set of neighboring nodes for each node is found, and the current feature vector of each neighboring node is obtained. The features of all neighboring nodes are then concatenated along the neighborhood dimension to obtain the aggregated neighborhood feature. The aggregated neighborhood feature is then gated and fused with the current node's own features: a gate vector is introduced. The gate vector is calculated by concatenating the current node's features with the aggregated features of its neighborhood, followed by a linear transformation and a sigmoid activation function. Each component takes a value between 0 and 1, used to control the fusion ratio of neighborhood information and its own information. Updated node features Calculated by the following formula: ,in For the current node's characteristics, This is a neighborhood aggregation feature. This represents element-wise multiplication. The gated fusion mechanism enables nodes to adaptively adjust the update magnitude of their features based on the relevance of neighborhood information, avoiding excessive smoothing that leads to feature convergence among nodes.

[0033] The message passing and gating fusion process involves multiple iterations. In each iteration, all nodes synchronously update their features. The number of iterations is determined based on the graph diameter and task complexity, typically ranging from 2 to 4 iterations. After multiple iterations, the features of each node have fully integrated the time-frequency dependency information within its multi-hop neighborhood, resulting in the final node features. The final features of all time nodes are arranged in time step order to obtain the time feature sequence; the final features of all frequency nodes are arranged in frequency channel order to obtain the frequency feature sequence. The time feature sequence captures the dynamic evolution of the signal in the time domain, while the frequency feature sequence reflects the energy distribution and variation trend of each frequency component throughout the entire time span.

[0034] The time-frequency feature sequence is concatenated or weighted and fused with the frequency feature sequence to obtain a joint time-frequency representation vector. Concatenation directly links the feature vectors of the two sequences along the feature dimension, preserving complete information in both the time and frequency domains. Weighted fusion, on the other hand, balances the contributions of the two sequences using learnable weight parameters, making it suitable for scenarios where the importance of time-domain and frequency-domain features differs significantly. The joint time-frequency representation vector integrates the structured dependencies of transient signals in both the time and frequency dimensions, providing high-quality feature input for subsequent geometric analysis and category recognition in the manifold space.

[0035] Figure 2 This is a bidirectional time-frequency dependency graph of the power transient waveform identification method based on time-frequency analysis in an embodiment of the present invention, showing the bidirectional connection relationship between the time nodes and frequency nodes retained after threshold filtering by the mutual information matrix. Figure 2 The top represents time nodes (T0 to T57, represented by solid circles), and the bottom represents frequency nodes (F1 to F7, represented by hollow circles). The bidirectional connection between nodes indicates that the mutual information value between the corresponding time-frequency node pairs exceeds the preset threshold of 0.30. The thickness and grayscale of the connection reflect the magnitude of the mutual information value.

[0036] from Figure 2 It can be observed that the connection between time node T12 and frequency node F4 is relatively thick, corresponding to a mutual information value of 0.72; the connection between time node T18 and frequency node F6 is the thickest, with a mutual information value of 0.79, the highest among all retained edges, indicating that the statistical dependency between this time-frequency node pair is the strongest, and the corresponding time-frequency region contains the most critical joint change information in the transient waveform; the connection between time node T24 and frequency node F3 is the second thickest, with a mutual information value of 0.65; the connection between time node T57 and frequency node F4 is also relatively thick, with a mutual information value of 0.68. The time-frequency region covered by the aforementioned four high mutual information connection edges corresponds precisely to the core period in the transient event where amplitude envelope mutation and instantaneous frequency drift occur simultaneously, and is a key hub for information flow in the subsequent message transmission process.

[0037] Furthermore, the connections between time node T7 and frequency node F1 (mutual information value 0.56), between time node T3 and frequency node F5 (mutual information value 0.34), and between time nodes T0 and F2, T40 and F2, and T52 and F1 (mutual information values ​​all below 0.20) are thin and light in gray, indicating that the dependencies between these time-frequency combinations are weak and their contribution to the joint time-frequency representation is limited. After threshold screening, a total of 9 pairs of time-frequency nodes were retained and bidirectional connecting edges were established. This ensured that the constructed time-frequency dependency graph maintained the integrity of key time-frequency associations while effectively controlling the sparsity of the graph structure, providing a reliable graph topology foundation for subsequent gating fusion and message iteration.

[0038] In one alternative implementation, The Riemannian geometric metric of the feature manifold space is calculated based on the time-frequency joint characterization vector. The local curvature distribution of the feature manifold is calculated based on the Riemannian geometric metric, and the class boundary is determined. The gradient field is extracted along the normal vector direction of the class boundary, and the divergence and curl distributions are calculated, including: The time-frequency joint representation vector is expanded into a grid according to the time dimension and the frequency dimension to obtain multiple time-frequency feature points. The time-frequency feature points are mapped to a high-dimensional feature manifold space and the local neighborhood relationship between different time-frequency feature points is calculated. A tangent space basis is constructed based on the local neighborhood relationship. The Riemann distance between time-frequency feature points is calculated under the tangent space basis and a Riemann geometric metric tensor is constructed. Based on the Riemannian geometric metric tensor, the cross-sectional curvature of each time-frequency feature point on the feature manifold is calculated. The cross-sectional curvature is spatially integrated to obtain the local curvature distribution. Regions in the local curvature distribution whose curvature gradient exceeds a preset gradient threshold are identified as candidate boundary regions. Curvature maxima in the candidate boundary regions are extracted to determine the category boundary. The tangent plane of the category interface is calculated in the feature manifold space, the orthogonal complement space of the tangent plane is solved to obtain the normal vector direction, the directional derivative of the time-frequency joint characterization vector is calculated along the normal vector direction to obtain the gradient field, the divergence operator is performed on the gradient field to obtain the divergence distribution, and the curl operator is performed on the gradient field to obtain the curl distribution.

[0039] The time-frequency joint representation vector is unfolded into a grid along both the time and frequency dimensions, making the implicit time and frequency axis information in the original vector explicit. This forms a set of time-frequency feature points under a two-dimensional coordinate index. The time dimension is evenly divided into several time grid points according to the sampling interval, and the frequency dimension is divided into corresponding frequency grid points according to the frequency band covered by wavelet decomposition. The grid points of the two dimensions intersect to form a regular grid, and each grid node corresponds to a time-frequency feature point. The feature point carries the local feature components extracted from the time-frequency joint representation vector. The purpose of the grid unfolding is to transform the feature information, which was originally stored in a sequential form, into a point cloud structure with spatial topological significance, providing a geometric basis for subsequent manifold mapping.

[0040] Time-frequency feature points are mapped to a high-dimensional feature manifold space, and a nonlinear embedding method is used to ensure that the continuity of local neighborhood relationships between adjacent feature points in the original time-frequency domain is maintained in the high-dimensional space. For each time-frequency feature point, Euclidean distance is used as the initial metric to search for its corresponding feature manifold in the high-dimensional space. The nearest neighbor points form the local neighborhood set of each time-frequency feature point. Establishing local neighborhood relationships requires balancing the continuity of the time dimension with the correlation of the frequency dimension to avoid incorrectly including distant points across frequency bands in the neighborhood. Based on the local neighborhood set, principal component analysis is performed on the neighborhood point set of each time-frequency feature point to extract the principal direction of the neighborhood point set. This principal direction spans the basis of the tangent space at that point. The dimension of the tangent space basis is determined by the intrinsic dimension of the neighborhood point set, and is usually determined by retaining components whose singular values ​​are significantly greater than the noise level after singular value decomposition. After the tangent space basis is constructed, in the corresponding basis coordinate system, the displacement vector between adjacent time-frequency feature points can be decomposed into components in the tangent space and components in the normal space. The components in the tangent space reflect the locally flat structure of the manifold, while the components in the normal space are related to the curvature of the manifold.

[0041] When calculating the Riemann distance between time-frequency feature points on a tangent space basis, it is necessary to define a Riemann metric tensor at each point. . The inner product matrix of the basis vectors of the tangent space is given by its elements. Indicates the first The and the first The inner product value between tangent vectors. Two adjacent time-frequency feature points. and Riemann distance between It is obtained by integrating the Riemannian metric tensor along the geodesic connecting the two points, under the local linear approximation. It can be represented as: , This is the Riemann metric tensor for this local region. The Riemann distances of all adjacent point pairs are summed to form a Riemann geometric metric tensor field covering the entire characteristic manifold, providing a basis for subsequent curvature calculations.

[0042] When calculating the cross-sectional curvature of each time-frequency feature point on a characteristic manifold based on the Riemannian geometric metric tensor, the Riemann curvature tensor is used. The projection value along a given two-dimensional cross-section. For time-frequency feature points. Choose two linearly independent tangent vectors in the tangent space. and Cross-sectional curvature Defined as: ,in Let be the component value of the Riemann curvature tensor along this cross-sectional direction, with the denominator being the square of the cross-sectional area, used for normalization. After calculating the cross-sectional curvature for all time-frequency feature points, a weighted integral is performed on the cross-sectional curvature values ​​within a spatial neighborhood. The integration weight is inversely proportional to the Riemann distance from the neighborhood point to the center point, yielding the local curvature distribution value at each time-frequency feature point. The local curvature distribution forms a continuous scalar field across the entire feature manifold. High curvature regions correspond to transition zones between different categories in the feature space, while low curvature regions correspond to flat regions within a category.

[0043] Identify curvature gradients exceeding a preset gradient threshold in local curvature distributions. When calculating the spatial gradient of a scalar field with local curvature distribution in a region, the gradient magnitude is... Exceed The connected regions are labeled as candidate boundary regions. Within these candidate boundary regions, curvature maxima are further extracted, i.e., points whose local curvature values ​​are higher than those of all their neighbors. These curvature maxima are then fitted to a smooth hypersurface, which serves as the category boundary, its geometry reflecting the natural boundaries of different transient types in the feature manifold space.

[0044] In the feature manifold space, the tangent plane of the class boundary is computed by spanning the set of tangent vectors at each point on the boundary. The dimension of the tangent plane is one less than that of the feature manifold, and its orthogonal complement space is a one-dimensional subspace. The unit vector of this subspace is the normal vector. The direction of the normal vector is uniquely determined by the local geometry of the interface, pointing in the direction of the fastest increase in curvature. When calculating the directional derivative of the joint time-frequency characterization vector along the normal vector direction, the eigenvalue function on the characteristic manifold... along By taking the directional derivative, we obtain the gradient field vector. The gradient field describes the rate of change distribution of eigenvalues ​​in the direction perpendicular to the interface.

[0045] Perform divergence operator operations on the gradient field to calculate the sum of the partial derivatives of the gradient field vector in each coordinate direction, and the divergence distribution. This reflects the source-sink characteristics of the gradient field. Positive divergence regions correspond to areas where eigenvalues ​​diffuse outwards, while negative divergence regions correspond to areas where eigenvalues ​​converge inwards. These two types of regions correspond to different category core regions and category edge regions, respectively, in transient type identification. When performing curl operator operations on the gradient field, the difference in cross-partial derivatives between the components of the gradient field vector is calculated, and the curl distribution is determined. Reflecting the circulation characteristics of the gradient field, regions with large curl amplitudes typically correspond to complex regions on the feature manifold where topological singularities or class intersections exist. Identifying these regions helps in the accurate localization of subsequent boundary-sensitive features. The divergence distribution and curl distribution together constitute a complete description of the gradient field's geometry, providing sufficient local geometric information for the extraction of boundary-sensitive features.

[0046] In one alternative implementation, Spatial integration of the cross-sectional curvature yields a local curvature distribution. Regions within this local curvature distribution whose curvature gradient exceeds a preset gradient threshold are identified as candidate boundary regions. Curvature maxima within these candidate boundary regions are extracted to determine the category boundary, including: A neighborhood of the Earth centered on a time-frequency feature point is constructed, and the curvature of the cross section is integrated within the Earth to obtain the Gaussian curvature integral. Based on the Gaussian curvature integral, the curvature density is calculated to obtain the local curvature distribution. Covariant differentiation is performed on the local curvature distribution to obtain the curvature gradient field. Persistent homology analysis is performed on the curvature gradient field to extract the birth and death pairs of the zero-dimensional persistence graph. Based on the persistence length of the birth and death pairs, stable curvature change points are screened and aggregated to obtain candidate boundary regions. In the tangent space of the candidate boundary region, a Hessian matrix is ​​constructed and eigenvalues ​​are calculated. The saddle point positions where the eigenvalue signs change are identified, and local maxima points are extracted along the principal curvature direction. The geodesic coordinates of the local maxima points in the manifold space are calculated, and a minimum spanning tree is constructed based on the geodesic distance between adjacent point pairs. Geodesic tracing is performed on the minimum spanning tree to obtain the connection path. The connection path is smoothed, and the smoothed curve is extended by normal cluster in the manifold space to obtain the category boundary.

[0047] In determining the category boundary, spatial integration of the cross-sectional curvature is required to obtain a statistically significant local curvature distribution. A geodesic neighborhood is constructed on the characteristic manifold, centered on the time-frequency feature point. The radius of the geodesic is adaptively determined by the local geometry of the manifold, typically using the median of the geodesic distances between adjacent feature points within the neighborhood as a reference value. Inside the geodesic, a Riemann integral is performed on the cross-sectional curvature, with the integration process proceeding along the natural measure of the manifold. The result is a Gaussian curvature integral, which comprehensively reflects the overall curvature distribution within the geodesic neighborhood, eliminating the instabilities introduced by local noise in single-point curvature estimation. Dividing the Gaussian curvature integral by the Riemann volume of the geodesic yields the curvature density value, which is used as the local curvature distribution value at that feature point. This results in a continuous local curvature distribution field across the entire characteristic manifold.

[0048] Performing covariant differentiation on the local curvature distribution field yields the curvature gradient field. The covariant differentiation is performed within the connection structure of the manifold, ensuring that the gradient calculation is independent of the chosen coordinate system. The resulting curvature gradient field exhibits tensor covariance on the tangent bundle of the manifold. Each component of the curvature gradient field describes the rate of change of the local curvature distribution along the corresponding tangential direction. Regions with larger gradient magnitudes correspond to locations where curvature changes drastically; these locations often geometrically correspond to transition zones between different categories of feature points.

[0049] Continuous cohomology analysis is performed on the curvature gradient field to extract topologically stable curvature variation structures. The analysis uses the curvature gradient magnitude as a filtering function; as the filtering threshold increases, a sequence of upper level sets of the curvature gradient field is gradually constructed, and the birth and death processes of each topological feature (connected component) are tracked. In the zero-dimensional continuous graph, each birth and death pair... The moment corresponding to the birth of a connected component With the moment of extinction Its duration is defined as This reflects the topological stability of the connected component during the filtering process. Birth-death pairs with longer durations correspond to real structural changes in the curvature gradient field, while birth-death pairs with shorter durations typically originate from noise or localized small perturbations. A duration threshold is set. Filter to meet The stable curvature change points are then spatially aggregated in the manifold space, merging those with geodesic distances smaller than the aggregation radius. The adjacent stable points are used to obtain several candidate boundary regions.

[0050] Within each candidate boundary region, the geometric location of the category boundary is further precisely determined. At each feature point within the candidate boundary region, a Hessian matrix is ​​constructed in its tangent space. The elements of the Hessian matrix are the second-order covariant derivatives of the local curvature distribution values ​​with respect to the tangent space coordinates. Perform eigenvalue decomposition to obtain the eigenvalue set. and the corresponding set of feature vectors At a saddle point, the eigenvalues ​​of the Hessian matrix contain both positive and negative values, meaning the sign of the eigenvalues ​​changes. This sign change characteristic is used to identify the location of the saddle point. At the identified saddle point, a local maximum is searched along the principal curvature directions (i.e., the directions of the eigenvectors corresponding to the largest positive and largest negative eigenvalues). The local maximum satisfies the condition that the first derivative along all tangent directions is zero and the Hessian matrix is ​​negative definite.

[0051] Calculate the geodesic coordinates of each local maxima in the manifold space, and construct a minimum spanning tree based on the geodesic distances between adjacent pairs of maxima. The minimum spanning tree is constructed using either Prim's algorithm or Kruskal's algorithm, with geodesic distance as the edge weight, ensuring that the total path length connecting all maxima is minimized. Perform geodesic tracing on the minimum spanning tree, solving the geodesic equations along each edge of the tree on the manifold to obtain the geodesic paths connecting adjacent maxima, and then concatenate all geodesic paths to form a network of connected paths.

[0052] The connecting paths are smoothed to eliminate the bends and jitter introduced by discrete geodesic tracing. The smoothing process is performed within the intrinsic geometry of the manifold, using spline interpolation on the manifold to minimize the curve's bending energy while keeping the curve endpoints fixed. The bending energy is defined as the integral of the square of the curve's geodesic curvature along the arc length. The smoothed curves possess a continuous tangent vector field on the manifold, and are geometrically closer to the true class boundary.

[0053] In a manifold space, a smoothed curve is extended using a normal bundle, expanding the one-dimensional curve into a hypersurface in the higher-dimensional manifold, i.e., a class boundary. The process of normal bundle extension is as follows: at each point of the smoothed curve, the normal vector subspace orthogonal to the tangent vector of the curve is calculated in the tangent space of that point. Then, the extension is performed along each direction of the normal vector subspace with a preset extension step size. Extending outwards, a tubular neighborhood surface with the original curve as its ridge is generated. During the extension process, the compatibility of the generated surface with the local geometry of the manifold is continuously checked; if the extension point deviates from the manifold beyond the tolerance... Then, project it back to the nearest point on the manifold. After extension by the normal bundle, we obtain a class boundary that is continuously distributed on the characteristic manifold. This boundary divides the manifold into several regions, each corresponding to a characteristic distribution of a class of transient waveforms.

[0054] In one alternative implementation, Based on the divergence and curl distributions, boundary-sensitive features are determined, and the manifold enhancement feature vector is obtained by combining the time-frequency joint representation vector. The manifold enhancement feature vector is then clustered to obtain multiple feature clusters, including: Gaussian smoothing is applied to the divergence distribution to obtain a smoothed divergence field, and the spatial gradient corresponding to the smoothed divergence field is calculated to obtain a divergence rate of change field. Singular value decomposition is performed on the curl distribution to obtain a curl principal direction field, which is then concatenated with the divergence rate of change field to obtain a boundary sensitive feature vector. The cross-correlation coefficient between the boundary sensitive feature vector and the time-frequency joint representation vector is calculated and used as a correlation weight. The boundary sensitive feature vector is weighted based on the correlation weight to obtain a weighted boundary feature vector, which is then fused with the time-frequency joint representation vector to obtain a manifold enhancement feature vector. Principal component analysis is performed on the manifold enhancement feature vector to reduce its dimensionality, resulting in a dimensionality-reduced feature vector. A similarity graph is constructed based on the dimensionality-reduced feature vector, and the graph Laplacian matrix is ​​calculated. Eigenvalue decomposition is performed on the graph Laplacian matrix to obtain a spectral embedding space. Density peak detection is used to identify representative cluster points in the spectral embedding space, and nearest neighbor assignment is performed to obtain the category classification. Based on the category classification, the manifold enhancement feature vector is divided into multiple feature clusters.

[0055] After obtaining the divergence distribution, Gaussian smoothing is applied to eliminate the interference of local noise on boundary judgment. The kernel size and standard deviation of Gaussian smoothing are adaptively determined based on the local density of the feature manifold: the kernel size is appropriately reduced in densely distributed feature points to preserve details, while the kernel size is increased in sparse regions to enhance the smoothing effect. The smoothed divergence field is then obtained. Partial derivatives of the smoothed divergence field are calculated in each dimension of the feature space, and these partial derivatives are concatenated into a vector to form the divergence rate of change field. The divergence rate of change field reflects the trend of divergence variation in space; regions with larger amplitudes correspond to locations where divergence changes abruptly, and these locations usually coincide highly with geometrical abrupt changes in class boundaries.

[0056] Singular value decomposition (SVD) is performed on the curl distribution, decomposing the curl field into several orthogonal principal direction components. The left singular vectors corresponding to the first few singular values ​​are taken as the principal curl directions. These principal curl directions capture the rotational patterns with the most concentrated energy in the curl field, representing the dominant directions of local rotational structures on the feature manifold. After aligning the principal curl direction field with the divergence rate of change field in dimension, vector concatenation is performed along the directions of each component of the feature vector, merging the two into a unified boundary-sensitive feature vector. This boundary-sensitive feature vector simultaneously encodes the spatial variation trend of divergence and the dominant rotational direction of curl, characterizing the local structure near the class boundary from two complementary geometric perspectives.

[0057] The cross-correlation coefficient between the boundary-sensitive feature vector and the time-frequency joint representation vector is calculated to measure their linear correlation in the feature space. The cross-correlation coefficient is calculated point-by-point within a sliding window, with the window size and step size determined based on the dimension of the feature vectors. For each feature point, its boundary-sensitive feature vector and time-frequency joint representation vector are both zero-mean normalized, and the inner product of the normalized vectors is calculated to obtain the cross-correlation coefficient at that point, which is used as the correlation weight. A higher correlation weight indicates stronger consistency between the boundary-sensitive feature and the time-frequency joint representation at that point, and the corresponding boundary-sensitive feature should be given a larger contribution proportion during fusion.

[0058] The boundary-sensitive feature vector is weighted element-wise based on relevance weights to obtain a weighted boundary feature vector. This weighting operation strengthens boundary information highly correlated with the time-frequency joint representation, while relatively suppressing noise components with lower correlation. The weighted boundary feature vector is then fused with the time-frequency joint representation vector using a concatenation followed by linear transformation for dimensionality reduction: the two vectors are first directly concatenated along their feature dimensions, and then a learnable linear projection matrix maps the concatenated high-dimensional vector back to the same dimensional space as the time-frequency joint representation vector. This preserves complementary information from both classes of features while controlling the growth of the feature dimension. The resulting manifold-enhanced feature vector incorporates geometrically sensitive information from the manifold boundary, building upon the time-frequency joint representation and exhibiting stronger class discrimination capabilities.

[0059] Principal component analysis (PCA) is performed on the enhanced feature vectors of the manifold to reduce dimensionality. The covariance matrix of all feature points is calculated, and eigenvalue decomposition is performed on the covariance matrix. The eigenvalues ​​are then sorted from largest to smallest, and the top principal component directions corresponding to the cumulative variance contribution rate reaching a preset proportion (e.g., 95%) are selected. All feature points are projected onto these principal component directions to obtain the reduced feature vectors. Dimensionality reduction removes redundant information while preserving the main directions of feature variation, which contributes to the stability of subsequent similarity calculations.

[0060] A similarity graph is constructed based on dimensionality-reduced feature vectors. Each feature point is treated as a node, and the cosine similarity between any two nodes' dimensionality-reduced feature vectors is calculated. Node pairs with similarity exceeding a preset threshold are connected by edges, with the edge weights taken from the corresponding cosine similarity values. The graph Laplacian matrix is ​​calculated for the similarity graph: first, a degree matrix (a diagonal matrix, where diagonal elements represent the weighted degrees of each node) is constructed; then, the adjacency weight matrix is ​​subtracted from the degree matrix to obtain the graph Laplacian matrix, which is then symmetrically normalized to eliminate the influence of differences in node degree. Eigenvalue decomposition is performed on the normalized graph Laplacian matrix, and the eigenvectors corresponding to the smallest non-zero eigenvalues ​​are selected. The coordinates of each node on these eigenvectors are combined to form its spectral embedding coordinates, thus mapping all feature points into a low-dimensional spectral embedding space. In the spectral embedding space, points with similar structures in the original feature space are close to each other on the embedding coordinates, which is beneficial for clearly defining cluster boundaries.

[0061] Density peak detection is performed in the spectral embedding space. The local density of each point (measured by the number of points in a fixed-radius neighborhood) and the distance from that point to the nearest point among all points with higher density (i.e., the relative distance) are calculated. The product of local density and relative distance is used as a scoring metric for representative points of clusters. Points with significantly higher scores than their surrounding points are identified as representative points, representing the density peak centers of each feature cluster. Nearest neighbor assignment is performed on non-representative points: each non-representative point is processed sequentially in descending order of local density, and assigned to the category of the nearest assigned point with its spectral embedding coordinates, until all points have been assigned a category. Based on the category assignment, the manifold-enhanced feature vectors are divided into multiple feature clusters. Each feature cluster corresponds to a density peak region in the spectral embedding space, and the feature points within a cluster exhibit high consistency in manifold structure and time-frequency characteristics.

[0062] Figure 3 This is a flowchart illustrating the feature cluster classification and identification process of the power transient waveform recognition method based on time-frequency analysis, as described in an embodiment of the present invention.

[0063] In one alternative implementation, Calculate the geodesic distances of different feature clusters in the manifold space and construct an inter-cluster geodesic distance matrix. Based on the inter-cluster geodesic distance matrix, perform category classification and map it to a preset type label space to obtain the recognition results, including: Extract the centroid feature vector corresponding to each feature cluster from the multiple feature clusters and determine the centroid position. Construct an initial connection path between different centroid positions and sample intermediate points along the initial connection path. Project the intermediate points onto a preset manifold surface to obtain surface correction points. Connect adjacent surface correction points to construct segmented paths and calculate the arc length of each segment. Accumulate the segmented arc lengths and perform local curvature compensation to obtain the corrected geodesic distance. Calculate the corrected geodesic distance between different feature clusters and organize them in matrix form to obtain the inter-cluster geodesic distance matrix. The inter-cluster geodesic distance matrix is ​​decomposed into eigenvalues ​​to obtain a distance feature value sequence. The distance feature value sequence is then subjected to a difference operation, and the difference peak is identified to determine the feature value gap. Based on the feature value gap, the number of categories is determined and the corresponding distance feature vectors are extracted. The distance feature vectors are then normalized to obtain category division coordinates. The category division coordinates are then symbolically encoded to obtain the cluster category label index. The category label index is mapped to a preset type label space and labeled according to the feature clusters corresponding to the manifold enhancement feature vector to obtain the recognition result.

[0064] The centroid eigenvectors corresponding to each of the multiple feature clusters are extracted. The mean of all member eigenvectors within each cluster is used as the estimated value of the centroid, thereby determining the centroid position of each cluster in the manifold space. Since the feature manifold itself has a non-Euclidean curved structure, the straight-line connection between two centroids does not necessarily lie on the manifold surface; therefore, the Euclidean straight-line distance cannot be directly used to replace the actual geodesic distance. To address this, an initial connection path is constructed between different centroid positions. Specifically, the straight-line segment between two centroids is divided at equal intervals, and several intermediate points are uniformly sampled along this segment. The sampling density is adaptively determined based on the product of the Euclidean distance between the centroids and the local curvature of the manifold; regions with greater curvature are sampled more densely to ensure the accuracy of subsequent projection steps.

[0065] The aforementioned intermediate points are projected one by one onto a preset manifold surface using nearest neighbor tangent space projection. For each intermediate point, the nearest reference point on the manifold is searched within its corresponding neighborhood, and the tangent space at the nearest reference point is constructed. Then, the intermediate point is mapped along the normal vector direction to the intersection of the tangent space and the manifold, obtaining the surface correction point. The set of surface correction points forms a polygonal path approximately along the manifold's orientation. Adjacent surface correction points are connected to form a segmented path, and the arc length of each segment, i.e., the Euclidean distance between adjacent correction points, is calculated. The arc lengths of all segments are summed to obtain an initial estimate of the total path length along the manifold surface.

[0066] Relying solely on the sum of segmented arc lengths for the path length still results in a systematic underestimation in regions with high manifold curvature, because the polygonal path introduces a "cutting" error in curved areas. Therefore, a local curvature compensation mechanism is introduced: for each surface correction point traversed by the path, the calculated local curvature distribution value at that point is read. According to the correction amount of curvature to arc length Compensation is performed, and the correction amount is related to the arc length of that segment. The relationship between curvature value and The compensation amounts for each segment are summed and then superimposed onto the total path length to obtain the corrected geodesic distance. This process is repeated pairwise for all feature clusters. The calculated corrected geodesic distances are then organized in matrix form, with rows and columns corresponding to the indices of different feature clusters, thus constructing an inter-cluster geodesic distance matrix. This matrix is ​​symmetric, with zero diagonal elements and off-diagonal elements reflecting the true topological spacing of different clusters in the manifold space.

[0067] inter-cluster geodesic distance matrix Eigenvalue decomposition is performed to obtain a distance eigenvalue sequence, which is then arranged in ascending order. The eigenvalue sequence itself encodes the main variation patterns of the inter-cluster distance structure: smaller eigenvalues ​​correspond to a tight structure within clusters, while larger eigenvalues ​​correspond to a degree of separation between clusters. First-order differencing is performed on this eigenvalue sequence to calculate the difference between adjacent eigenvalues, forming a difference sequence. The location of the maximum difference peak is identified in the difference sequence; this location corresponds to an eigenvalue gap, i.e., the turning point where eigenvalues ​​abruptly change from a dense distribution to a sparse distribution. The physical meaning of the eigenvalue gap is that eigenvalues ​​before the gap correspond to continuous changes within the manifold, while eigenvalues ​​after the gap correspond to abrupt separation between different categories. Therefore, the gap location directly indicates the number of naturally occurring categories in the data. .

[0068] Based on the determined number of categories Extract the corresponding first eigenvalues ​​from the eigenvalue decomposition results. There are several distance feature vectors, which span a low-dimensional class region subspace. The extracted distance feature vectors are normalized so that the magnitude of each feature vector is uniformly 1. The normalized coordinates are the class-separating coordinates. In the low-dimensional subspace, the class-separating coordinates map the centroids of different clusters to distinguishable points, and the geodesic distance relationships between clusters are preserved in this coordinate system.

[0069] The coordinates for classifying categories are symbolically encoded. Each coordinate component is divided into intervals according to its numerical range, mapping the coordinate values ​​to a discrete sequence of symbols, forming a class label index for each feature cluster. The interval division for symbolic encoding is determined based on the statistical distribution characteristics of the classifying coordinates, avoiding instability in the encoding results due to small perturbations in the coordinate values. After encoding, each feature cluster corresponds to a unique class label index, and the indices of different categories are distinguishable from each other in the symbol space.

[0070] The category label index is mapped to a pre-defined type label space, which stores the semantic category names of various transient waveforms, such as voltage sag, current inrush, and harmonic distortion. The mapping process is completed through a lookup table, mapping the symbol encoding index one-to-one with the entries in the type label space. For manifold-enhanced feature vectors, the corresponding semantic label is searched in the type label space based on the category label index of its feature cluster, and the annotation is completed. Finally, the recognition result for each transient waveform is output, presented in the form of a semantic category name, for use in subsequent power system fault analysis and processing.

[0071] A second aspect of the present invention provides a power transient waveform recognition system based on time-frequency analysis, comprising: The feature extraction unit is used to acquire waveform data collected by the transient recording device, perform multi-scale wavelet decomposition to obtain decomposition coefficients of different frequency bands, perform Hilbert transform on the decomposition coefficients to extract instantaneous amplitude envelope and instantaneous frequency trajectory, determine the time-frequency evolution path of the instantaneous frequency trajectory and associate it with the instantaneous amplitude envelope to obtain transient feature tensor; The time-frequency representation unit is used to calculate the mutual information matrix of the time dimension and the frequency dimension based on the transient feature tensor, construct a bidirectional time-frequency dependency graph based on the mutual information matrix and perform message passing, and obtain the time-frequency joint representation vector based on the neighborhood messages received by each node. The manifold classification unit is used to calculate the Riemannian geometric metric of the feature manifold space based on the time-frequency joint representation vector, calculate the local curvature distribution of the feature manifold and determine the category boundary according to the Riemannian geometric metric, extract the gradient field along the normal vector direction of the category boundary and calculate the divergence distribution and curl distribution, determine the boundary sensitive features based on the divergence distribution and curl distribution and solve for the manifold enhancement feature vector by combining the time-frequency joint representation vector, cluster the manifold enhancement feature vector to obtain multiple feature clusters, calculate the geodesic distance of different feature clusters in the manifold space and construct the inter-cluster geodesic distance matrix, classify the categories based on the inter-cluster geodesic distance matrix and map to the preset type label space to obtain the recognition result.

[0072] A third aspect of the present invention provides an electronic device, comprising: A processor and a memory for storing processor-executable instructions, wherein the processor is configured to invoke instructions stored in the memory to perform the aforementioned method.

[0073] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0074] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0075] 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 the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying transient waveforms in power systems based on time-frequency analysis, characterized in that, include: Waveform data acquired by transient recording equipment is decomposed into decomposition coefficients for different frequency bands using multi-scale wavelet decomposition. Hilbert transform is then applied to the decomposition coefficients to extract the instantaneous amplitude envelope and instantaneous frequency trajectory. The time-frequency evolution path of the instantaneous frequency trajectory is determined and correlated with the instantaneous amplitude envelope to obtain the transient feature tensor. The mutual information matrix of time and frequency dimensions is calculated based on the transient feature tensor. A bidirectional time-frequency dependency graph is constructed based on the mutual information matrix and message passing is performed. The time-frequency joint representation vector is obtained based on the neighborhood messages received by each node. The Riemannian geometric metric of the feature manifold space is calculated based on the time-frequency joint representation vector. The local curvature distribution of the feature manifold is calculated and the category boundary is determined according to the Riemannian geometric metric. The gradient field is extracted along the normal vector direction of the category boundary and the divergence distribution and curl distribution are calculated. The boundary sensitive features are determined based on the divergence distribution and curl distribution and the manifold enhancement feature vector is obtained by combining the time-frequency joint representation vector. The manifold enhancement feature vector is clustered to obtain multiple feature clusters. The geodesic distance of different feature clusters in the manifold space is calculated and the inter-cluster geodesic distance matrix is ​​constructed. The category is divided based on the inter-cluster geodesic distance matrix and mapped to the preset type label space to obtain the recognition result.

2. The method according to claim 1, characterized in that, Waveform data acquired by a transient recording device is decomposed using multi-scale wavelet decomposition to obtain decomposition coefficients for different frequency bands. Hilbert transform is then applied to these decomposition coefficients to extract instantaneous amplitude envelopes and instantaneous frequency trajectories. The time-frequency evolution path of the instantaneous frequency trajectory is determined and correlated with the instantaneous amplitude envelope to obtain a transient feature tensor, including: The waveform data collected by the transient recording device is acquired and the sliding window is used to divide the time-domain frames into multiple time-domain frames. Multi-scale wavelet decomposition is performed on the time-domain frames to obtain wavelet coefficients at different scale levels, and the frames are divided into multiple frequency bands according to the frequency response range to obtain the corresponding decomposition coefficients. The decomposed coefficients are subjected to Hilbert transform to obtain an analytical signal. The real and imaginary parts are extracted from the analytical signal and the square root of the amplitude is calculated to obtain the instantaneous amplitude envelope. The phase angle of the analytical signal is calculated and time derivative is performed to obtain the instantaneous frequency. The instantaneous frequency is sampled on the time axis and frequency change points are marked. The instantaneous frequency trajectory is constructed based on the time position and frequency value of the frequency change points. The time-frequency evolution path is obtained by determining the two-dimensional coordinate sequence of the instantaneous frequency trajectory in the time-frequency plane. The Euclidean distance between adjacent coordinate points in the time-frequency evolution path is calculated and accumulated to obtain the trajectory length. Based on the trajectory length, the arc length parameterization of the time-frequency evolution path is performed to obtain a normalized trajectory representation. The time coordinates in the normalized trajectory representation are aligned and matched with the time index of the instantaneous amplitude envelope. Based on the aligned time nodes, the tensor outer product operation is performed on the normalized trajectory representation and the instantaneous amplitude envelope to obtain the transient feature tensor.

3. The method according to claim 1, characterized in that, Based on the transient feature tensor, the mutual information matrix in the time and frequency dimensions is calculated. A bidirectional time-frequency dependency graph is constructed based on the mutual information matrix, and message passing is performed. The joint time-frequency representation vector is obtained based on the neighborhood messages received by each node, including: The transient feature tensor is sliced ​​along the time dimension and frequency dimension to obtain time slice features and frequency slice features respectively. The joint probability distribution and marginal probability distribution between the time slice features and the frequency slice features are calculated. Based on the joint probability distribution and the marginal probability distribution, the mutual information value is calculated to construct a mutual information matrix. The mutual information matrix is ​​subjected to threshold filtering to retain elements that exceed a preset threshold. The row index of the retained elements is used as the time node, the column index is used as the frequency node, and the mutual information value of the retained elements is used as the edge weight to establish connection edges to obtain a bidirectional time-frequency dependency graph. Extract the corresponding features of each node from the transient feature tensor as the initial node features, find the neighboring nodes corresponding to each node in the bidirectional time-frequency dependency graph and obtain the neighboring node features, concatenate the neighboring node features along the neighborhood dimension and perform gated fusion with the current node features to obtain the updated node features, repeat the iteration to obtain the final node features, and arrange them in the time dimension and frequency dimension to obtain the time feature sequence and the frequency feature sequence, and construct the time-frequency joint representation vector based on the time feature sequence and the frequency feature sequence.

4. The method according to claim 1, characterized in that, The Riemannian geometric metric of the feature manifold space is calculated based on the time-frequency joint characterization vector. The local curvature distribution of the feature manifold is calculated based on the Riemannian geometric metric, and the class boundary is determined. The gradient field is extracted along the normal vector direction of the class boundary, and the divergence and curl distributions are calculated, including: The time-frequency joint representation vector is expanded into a grid according to the time dimension and the frequency dimension to obtain multiple time-frequency feature points. The time-frequency feature points are mapped to a high-dimensional feature manifold space and the local neighborhood relationship between different time-frequency feature points is calculated. A tangent space basis is constructed based on the local neighborhood relationship. The Riemann distance between time-frequency feature points is calculated under the tangent space basis and a Riemann geometric metric tensor is constructed. Based on the Riemannian geometric metric tensor, the cross-sectional curvature of each time-frequency feature point on the feature manifold is calculated. The cross-sectional curvature is spatially integrated to obtain the local curvature distribution. Regions in the local curvature distribution whose curvature gradient exceeds a preset gradient threshold are identified as candidate boundary regions. Curvature maxima in the candidate boundary regions are extracted to determine the category boundary. The tangent plane of the category interface is calculated in the feature manifold space, the orthogonal complement space of the tangent plane is solved to obtain the normal vector direction, the directional derivative of the time-frequency joint characterization vector is calculated along the normal vector direction to obtain the gradient field, the divergence operator is performed on the gradient field to obtain the divergence distribution, and the curl operator is performed on the gradient field to obtain the curl distribution.

5. The method according to claim 4, characterized in that, Spatial integration of the cross-sectional curvature yields a local curvature distribution. Regions within this local curvature distribution whose curvature gradient exceeds a preset gradient threshold are identified as candidate boundary regions. Curvature maxima within these candidate boundary regions are extracted to determine the category boundary, including: A neighborhood of the Earth centered on a time-frequency feature point is constructed, and the curvature of the cross section is integrated within the Earth to obtain the Gaussian curvature integral. Based on the Gaussian curvature integral, the curvature density is calculated to obtain the local curvature distribution. Covariant differentiation is performed on the local curvature distribution to obtain the curvature gradient field. Persistent homology analysis is performed on the curvature gradient field to extract the birth and death pairs of the zero-dimensional persistence graph. Based on the persistence length of the birth and death pairs, stable curvature change points are screened and aggregated to obtain candidate boundary regions. In the tangent space of the candidate boundary region, a Hessian matrix is ​​constructed and eigenvalues ​​are calculated. The saddle point positions where the eigenvalue signs change are identified, and local maxima points are extracted along the principal curvature direction. The geodesic coordinates of the local maxima points in the manifold space are calculated, and a minimum spanning tree is constructed based on the geodesic distance between adjacent point pairs. Geodesic tracing is performed on the minimum spanning tree to obtain the connection path. The connection path is smoothed, and the smoothed curve is extended by normal cluster in the manifold space to obtain the category boundary.

6. The method according to claim 1, characterized in that, Based on the divergence and curl distributions, boundary-sensitive features are determined, and the manifold enhancement feature vector is obtained by combining the time-frequency joint representation vector. The manifold enhancement feature vector is then clustered to obtain multiple feature clusters, including: Gaussian smoothing is applied to the divergence distribution to obtain a smoothed divergence field, and the spatial gradient corresponding to the smoothed divergence field is calculated to obtain a divergence rate of change field. Singular value decomposition is performed on the curl distribution to obtain a curl principal direction field, which is then concatenated with the divergence rate of change field to obtain a boundary sensitive feature vector. The cross-correlation coefficient between the boundary sensitive feature vector and the time-frequency joint representation vector is calculated and used as a correlation weight. The boundary sensitive feature vector is weighted based on the correlation weight to obtain a weighted boundary feature vector, which is then fused with the time-frequency joint representation vector to obtain a manifold enhancement feature vector. Principal component analysis is performed on the manifold enhancement feature vector to reduce its dimensionality, resulting in a dimensionality-reduced feature vector. A similarity graph is constructed based on the dimensionality-reduced feature vector, and the graph Laplacian matrix is ​​calculated. Eigenvalue decomposition is performed on the graph Laplacian matrix to obtain a spectral embedding space. Density peak detection is used to identify representative cluster points in the spectral embedding space, and nearest neighbor assignment is performed to obtain the category classification. Based on the category classification, the manifold enhancement feature vector is divided into multiple feature clusters.

7. The method according to claim 1, characterized in that, Calculate the geodesic distances of different feature clusters in the manifold space and construct an inter-cluster geodesic distance matrix. Based on the inter-cluster geodesic distance matrix, perform category classification and map it to a preset type label space to obtain the recognition results, including: Extract the centroid feature vector corresponding to each feature cluster from the multiple feature clusters and determine the centroid position. Construct an initial connection path between different centroid positions and sample intermediate points along the initial connection path. Project the intermediate points onto a preset manifold surface to obtain surface correction points. Connect adjacent surface correction points to construct segmented paths and calculate the arc length of each segment. Accumulate the segmented arc lengths and perform local curvature compensation to obtain the corrected geodesic distance. Calculate the corrected geodesic distance between different feature clusters and organize them in matrix form to obtain the inter-cluster geodesic distance matrix. The inter-cluster geodesic distance matrix is ​​decomposed into eigenvalues ​​to obtain a distance feature value sequence. The distance feature value sequence is then subjected to a difference operation, and the difference peak is identified to determine the feature value gap. Based on the feature value gap, the number of categories is determined and the corresponding distance feature vectors are extracted. The distance feature vectors are then normalized to obtain category division coordinates. The category division coordinates are then symbolically encoded to obtain the cluster category label index. The category label index is mapped to a preset type label space and labeled according to the feature clusters corresponding to the manifold enhancement feature vector to obtain the recognition result.

8. A power transient waveform recognition system based on time-frequency analysis, used to implement the method of any one of claims 1-7, characterized in that, include: The feature extraction unit is used to acquire waveform data collected by the transient recording device, perform multi-scale wavelet decomposition to obtain decomposition coefficients of different frequency bands, perform Hilbert transform on the decomposition coefficients to extract instantaneous amplitude envelope and instantaneous frequency trajectory, determine the time-frequency evolution path of the instantaneous frequency trajectory and associate it with the instantaneous amplitude envelope to obtain transient feature tensor; The time-frequency representation unit is used to calculate the mutual information matrix of the time dimension and the frequency dimension based on the transient feature tensor, construct a bidirectional time-frequency dependency graph based on the mutual information matrix and perform message passing, and obtain the time-frequency joint representation vector based on the neighborhood messages received by each node. The manifold classification unit is used to calculate the Riemannian geometric metric of the feature manifold space based on the time-frequency joint representation vector, calculate the local curvature distribution of the feature manifold and determine the category boundary according to the Riemannian geometric metric, extract the gradient field along the normal vector direction of the category boundary and calculate the divergence distribution and curl distribution, determine the boundary sensitive features based on the divergence distribution and curl distribution and solve for the manifold enhancement feature vector by combining the time-frequency joint representation vector, cluster the manifold enhancement feature vector to obtain multiple feature clusters, calculate the geodesic distance of different feature clusters in the manifold space and construct the inter-cluster geodesic distance matrix, classify the categories based on the inter-cluster geodesic distance matrix and map to the preset type label space to obtain the recognition result.

9. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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