Helium Leak Detection Method and System for Switchgear

Abstract

The present invention discloses a helium leak detection method and system for switchgear, comprising the following steps: performing adaptive multi-resolution decomposition, anomaly detection, and non-linear manifold alignment on original data to extract dynamic features; applying adaptive tensor decomposition and multi-scale causal network analysis to construct a fused multi-modal representation; performing non-linear dynamics system reconstruction and persistent homology analysis to extract spatio-temporal features; constructing a multi-layer graph structure and applying a dynamic graph embedding algorithm to generate a graph topology anomaly detection result; constructing a multi-objective optimization framework and a dynamic parameter adjustment strategy to generate an optimized anomaly detection result. Through multi-scale analysis, non-linear modeling, and dynamic optimization, the present method realizes high-precision, high-efficiency, and adaptive detection of helium leak detection for switchgear, improving the accuracy and reliability of detection.

Description

Technical Field

[0001] The present invention relates to detection technologies, in particular to a helium leak detection method and system for switchgear cabinets. Background Art

[0002] As a key device in the power system, the sealing performance of switchgear cabinets directly affects the safety and reliability of the entire system. Due to its high sensitivity and non-destructive detection characteristics, helium leak detection technology is playing an increasingly important role in the sealing detection of switchgear cabinets. With the continuous expansion of the power grid scale and the improvement of the intelligent level, switchgear cabinets are facing a more complex operating environment and higher reliability requirements. An accurate and efficient helium leak detection method can not only timely detect potential sealing problems, prevent the occurrence of serious accidents, but also optimize maintenance strategies, extend the equipment life, and reduce operating costs. In addition, in the context of the transformation of the power system to clean energy, reducing the leakage of greenhouse gases such as SF6 has also become an important issue.

[0003] Currently, certain progress has been made in the helium leak detection technology for switchgear cabinets. The traditional helium mass spectrometry leak detection method determines the leakage situation by measuring the concentration of helium gas, which has high sensitivity. However, this method often requires complex equipment and professional operation, making it difficult to achieve large-scale on-site applications. In recent years, detection methods based on pressure changes have been widely applied, inferring the leakage situation by monitoring the pressure changes in the sealed chamber. This method is simple to operate but lacks sensitivity in detecting micro-leaks. At the same time, some researchers have attempted to apply acoustic detection technology to helium leak detection, locating the leak point by analyzing the acoustic wave characteristics generated by the leak. This method has a certain positioning ability but is easily interfered in a complex electromagnetic environment. In addition, some researchers have started to attempt to introduce machine learning technology into helium leak detection analysis to improve the accuracy and efficiency of detection by establishing a data model.

[0004] However, the existing helium leak detection technology for switchgear cabinets still faces some challenges. In terms of multi-sensor data fusion, existing methods often adopt simple linear combinations or weighted averages, making it difficult to effectively handle the non-linear relationship and time-varying characteristics between different types of sensor data. Additionally, in terms of leak mode recognition, most methods only focus on static features, ignoring the dynamic evolution characteristics of the leak process, resulting in insufficient recognition ability for complex leak scenarios (such as multi-point micro-leaks or intermittent leaks). Existing anomaly detection algorithms are usually based on preset thresholds, lacking adaptability and being difficult to cope with the dynamic changes in the operating environment of switchgear cabinets.

[0005] In particular, when dealing with large-scale switchgear cabinet systems, the computational efficiency and scalability of existing methods also face challenges, making it difficult to achieve real-time monitoring and rapid response. The existence of these problems limits the application effect of helium leak detection technology in the sealing detection of switchgear cabinets. Summary of the Invention

[0006] Objective of the invention: To provide a helium leak detection method and system for switchgear, aiming to solve the above problems existing in the prior art.

[0007] Technical solution: A helium leak detection method for switchgear includes the following steps:

[0008] Step S1: Obtain raw data from sensors in real time, organize the raw data into an N-dimensional raw data tensor, apply an adaptive multi-resolution decomposition algorithm to the raw data tensor to obtain a decomposed data tensor; construct a persistence diagram based on the decomposed data tensor and calculate persistent homology for anomaly detection and repair to generate a cleaned data tensor; perform non-linear manifold alignment on the cleaned data tensor to obtain an aligned six-dimensional data tensor, and extract dynamic features from the aligned data tensor to generate a dynamic feature matrix;

[0009] Step S2: Obtain the aligned data tensor and apply an adaptive tensor decomposition algorithm to it to obtain a low-dimensional representation; construct a multi-scale causal network based on the low-dimensional representation to generate a multi-scale causal adjacency matrix; construct a time-varying information flow network using the multi-scale causal adjacency matrix and the dynamic feature matrix; construct a fused multi-modal representation based on the low-dimensional representation, the multi-scale causal adjacency matrix, and the time-varying information flow network;

[0010] Step S3: Read the fused multi-modal representation, perform non-linear dynamics system reconstruction on the low-dimensional representation in the multi-modal representation to obtain a phase space trajectory; calculate persistent homology based on the phase space trajectory to generate a persistence diagram; extract dynamic patterns from the phase space trajectory and the persistence diagram to obtain a pattern matrix; combine the phase space trajectory, the persistence diagram, and the pattern matrix into a spatio-temporal feature representation;

[0011] Step S4: Read and construct a multi-layer graph structure based on the fused multi-modal representation and the spatio-temporal feature representation, apply a dynamic graph spectrum embedding algorithm to the multi-layer graph structure to obtain a node low-dimensional representation, calculate local and global topological features based on the node low-dimensional representation to construct an anomaly detection index; combine the multi-layer graph structure, the node low-dimensional representation, and the anomaly detection index into a graph topology anomaly detection result;

[0012] Step S5: Read the graph topology anomaly detection result and construct a set of key parameters and a multi-objective optimization framework to obtain a non-dominated solution set, construct a dynamic parameter adjustment strategy based on the non-dominated solution set to generate a time-varying optimal parameter set; combine the graph topology anomaly detection result and the time-varying optimal parameter set into an optimized anomaly detection result.

[0013] According to another aspect of the present application, there is also provided a helium leak detection system for switchgear, including:

[0014] At least one processor; and,

[0015] A memory communicatively connected to at least one of the processors; wherein,

[0016] The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the helium leak detection method for switchgear cabinets described in any one of the above technical solutions.

[0017] Advantageous effects: It improves the high precision, high efficiency and adaptive detection of helium leak detection in large-scale switchgear cabinet systems, and improves the accuracy and reliability of detection. Description of the Drawings

[0018] Figure 1 is a flowchart of the present invention.

[0019] Figure 2 is a flowchart of step S1 of the present invention.

[0020] Figure 3 is a flowchart of step S2 of the present invention.

[0021] Figure 4 is a flowchart of step S3 of the present invention.

[0022] Figure 5 is a flowchart of step S4 of the present invention.

[0023] Figure 6 is a flowchart of step S5 of the present invention. Detailed Embodiments

[0024] As Figure 1 shown, the helium leak detection method for switchgear cabinets includes the following steps:

[0025] Step S1: Real-time obtain raw data from sensors, organize the raw data into an N-dimensional raw data tensor, apply an adaptive multi-resolution decomposition algorithm to the raw data tensor to obtain a decomposed data tensor; construct a persistence diagram based on the decomposed data tensor and calculate persistent homology, perform anomaly detection and repair to generate a cleaned data tensor; perform non-linear manifold alignment on the cleaned data tensor to obtain an aligned six-dimensional data tensor, and extract dynamic features from the aligned data tensor to generate a dynamic feature matrix;

[0026] Step S2: Obtain the aligned data tensor and apply an adaptive tensor decomposition algorithm to it to obtain a low-dimensional representation; construct a multi-scale causal network based on the low-dimensional representation to generate a multi-scale causal adjacency matrix; use the multi-scale causal adjacency matrix and the dynamic feature matrix to construct a time-varying information flow network; construct a fused multi-modal representation based on the low-dimensional representation, the multi-scale causal adjacency matrix and the time-varying information flow network;

[0027] Step S3: Read the fused multi-modal representation, perform non-linear dynamical system reconstruction on the low-dimensional representation in the multi-modal representation to obtain the phase space trajectory; calculate the persistent homology based on the phase space trajectory to generate the persistence diagram; extract the dynamic patterns from the phase space trajectory and the persistence diagram to obtain the pattern matrix; combine the phase space trajectory, the persistence diagram, and the pattern matrix into a spatio-temporal feature representation;

[0028] Step S4: Read and construct a multi-layer graph structure based on the fused multi-modal representation and the spatio-temporal feature representation, apply the dynamic graph spectral embedding algorithm to the multi-layer graph structure to obtain the low-dimensional representation of the nodes, calculate the local and global topological features based on the low-dimensional representation of the nodes, and construct an anomaly detection index; combine the multi-layer graph structure, the low-dimensional representation of the nodes, and the anomaly detection index into the graph topology anomaly detection result;

[0029] Step S5: Read the graph topology anomaly detection result and construct a set of key parameters and a multi-objective optimization framework to obtain the non-dominated solution set, construct a dynamic parameter adjustment strategy based on the non-dominated solution set to generate a time-varying optimal parameter set; combine the graph topology anomaly detection result and the time-varying optimal parameter set into the optimized anomaly detection result.

[0030] In this embodiment, from data preprocessing, multi-modal fusion, dynamic pattern extraction, anomaly detection to parameter optimization, a closed-loop intelligent detection framework is formed. This solution can effectively handle high-dimensional data, non-linear relationships, and time-varying characteristics in the helium leak detection process of switchgear, improving the accuracy, sensitivity, and reliability of detection. Especially in the face of complex industrial environments and changing operating conditions, this solution shows excellent robustness and adaptability. Through multi-scale analysis and graph structure representation, this solution can handle both small leaks and large-scale leaks simultaneously and accurately locate the leak source. The dynamic optimization mechanism enables the system to continuously improve and adapt to equipment aging and environmental changes. In addition, the modular design of this solution makes it have good scalability and versatility, and it is not only applicable to switchgear but also can be extended to the detection of other sealed devices. Generally speaking, this solution provides strong technical support for the preventive maintenance, fault diagnosis, and reliability improvement of switchgear, and is expected to significantly reduce maintenance costs, improve equipment life, and operation safety.

[0031] According to one aspect of the present application, step S1 is specifically:

[0032] Step S11: Real-time obtain partial raw data from at least two sensors; calculate the change rate of each sensor signal according to the partial raw data to determine the adaptive sampling frequency; resample all sensor data using the adaptive sampling frequency; and organize the resampled data into a raw data tensor;

[0033] Step S12: Read the original data tensor, apply the adaptive multi-resolution decomposition algorithm to each sensor signal in the tensor, and perform multi-scale decomposition on the signal using wavelet transform to obtain the initial decomposition set; apply empirical mode decomposition to the initial decomposition set to obtain the multi-scale component set; calculate the information entropy and computational complexity of each decomposition level; construct and optimize the objective function, and select the optimal decomposition level; based on the optimal level, select the corresponding components from the multi-scale component set; combine the processed signals to generate the decomposed data tensor.

[0034] Step S13: Read the decomposed data tensor, construct the time-delay embedding vector for each decomposition level of each sensor signal in the decomposed data tensor; construct a complex based on the embedding vector, calculate the persistence data to obtain the persistence diagram; calculate the anomaly metric, compare the anomaly metric with the preset threshold, and mark the anomaly data points; use the local linear regression method to repair the anomaly data points; reorganize the repaired data to generate the cleaned data tensor.

[0035] Step S14: Read the cleaned data tensor and use the dimensionality reduction algorithm to embed each sensor signal at each decomposition level into a high-dimensional manifold; calculate the geodesic distance between the high-dimensional manifolds; set the sensor importance weights, construct the objective function, and use the optimization algorithm to minimize the objective function to obtain the optimal alignment parameters; based on the optimal alignment parameters, transform the data to obtain the aligned data tensor.

[0036] Step S15: Read the aligned data tensor, apply the time-frequency analysis method to each sensor signal at each decomposition level in the data tensor; calculate the statistical moments of the time-frequency representation; extract the geometric features; form the feature set; calculate the information entropy of each feature and the mutual information between features; and construct the feature importance score, sort and select the features based on the importance score; organize the selected features into a dynamic feature matrix.

[0037] In this embodiment, high-quality preprocessing and feature extraction of helium leak detection data for switchgear are achieved. First, the adaptive multi-resolution decomposition algorithm is used to decompose the original data, effectively separating signal components of different scales and improving the accuracy of subsequent analysis. The introduction of persistent homology makes anomaly detection and repair more robust, capable of capturing complex topological structure changes. The non-linear manifold alignment technology solves the non-linear deviation between multi-sensor data, enabling data from different sources to be analyzed in a unified feature space. Dynamic feature extraction further enhances the method's ability to characterize time-varying patterns. The synergistic effect of these technologies enables the method to extract high-quality, multi-scale, and time-varying feature representations from the original data of switchgear helium leak detection, laying a solid foundation for subsequent anomaly detection and analysis. Especially in the complex electromagnetic environment of switchgear, this method can effectively suppress noise interference, extract the characteristics of real helium leakage signals, and improve the sensitivity and reliability of detection.

[0038] According to one aspect of the present application, step S2 is specifically as follows:

[0039] Step S21: Read the aligned data tensor and the dynamic feature matrix; initialize the decomposition rank parameter; apply Tucker decomposition to the data tensor to obtain the core tensor and factor matrices; calculate the Tucker reconstruction error; apply CP decomposition to the data tensor to obtain factor matrices; calculate the CP reconstruction error, compare the errors of the two decomposition methods, and select the method with the smaller error; reconstruct the data based on the selected decomposition method to obtain a low-dimensional representation; reshape the low-dimensional representation into a low-dimensional data tensor;

[0040] Step S22: Read the low-dimensional data tensor; construct a set of time scales; calculate the multi-scale Granger causality for each pair of sensor signals in the low-dimensional data tensor at each time scale; perform wavelet transform on the low-dimensional data tensor at each scale to obtain wavelet coefficients; construct a vector autoregressive model; calculate the F statistic; calculate the multi-scale causal strength; organize all the multi-scale causal strengths into a multi-scale causal adjacency matrix;

[0041] Step S23: Read the multi-scale causal adjacency matrix and the dynamic feature matrix; calculate the conditional entropy for each pair of sensor signals in the dynamic feature matrix at each time point; estimate the probability from the dynamic feature matrix using the kernel density estimation method; calculate the information flow; construct a time-varying information flow network with sensors as nodes and information flow as edge weights; apply a community detection algorithm to the time-varying information flow network to identify the dynamic community structure; calculate the centrality index of each node in the time-varying information flow network; represent the time-varying information flow network as a combination of an adjacency matrix and a node attribute matrix; combine the low-dimensional data tensor, the multi-scale causal adjacency matrix, and the time-varying information flow network into a fused multi-modal representation.

[0042] In this embodiment, a multi-modal and multi-scale representation of the helium leak detection data of the switchgear is achieved. The adaptive tensor decomposition algorithm can effectively reduce the data dimension while retaining key information. The construction of the multi-scale causal network reveals the causal relationship between helium leak signals at different scales, which helps to understand the leakage mechanism. The introduction of the time-varying information flow network captures the dynamic changes during the leakage process. The combination of these technologies enables this method to comprehensively characterize the complex dynamic behavior in the helium leak detection process of the switchgear. Especially when dealing with large-scale and high-dimensional detection data, this method exhibits excellent computational efficiency and scalability. Through the fusion of multi-modal representations, this method can simultaneously utilize data from multiple sensors (such as pressure, temperature, electromagnetic field, etc.) to comprehensively evaluate the sealing performance of the switchgear, improving the accuracy and reliability of the detection. In addition, multi-scale analysis enables this method to capture both minor leaks and large-scale leaks simultaneously, meeting different degrees of sealing requirements.

[0043] According to one aspect of the present application, step S3 is specifically as follows:

[0044] Step S31: Read the low-dimensional data tensor in the fused multi-modal representation; calculate the mutual information function for each sensor component in the low-dimensional data tensor; select the time delay at which the mutual information function first reaches the local minimum as the optimal time delay; estimate the optimal embedding dimension using the false nearest neighbor method; construct candidate embedding vectors; for each candidate embedding dimension, predict future values using the k-nearest neighbor method and calculate the prediction error; when the prediction error no longer decreases significantly, take this dimension as the optimal embedding dimension; construct the phase space trajectory using the optimal time delay and the optimal embedding dimension; repeat this process for all sensor components in the low-dimensional data tensor to obtain the complete phase space trajectory;

[0045] Step S32: Read the complete phase space trajectory; apply a sliding window to the phase space trajectory to obtain a set of time series; construct a Vietoris-Rips complex for each time series in the set of time series; calculate the multi-dimensional persistent homology of the complex to obtain a persistence diagram; combine the persistence diagrams of all windows into a time-varying persistence diagram; calculate the statistical features of the time-varying persistence diagram, including persistent entropy and Betti number curves; define a topological complexity metric; combine the time-varying persistence diagram and the topological complexity metric into a topological feature representation;

[0046] Step S33: Read the complete phase space trajectory and topological feature representation; apply continuous wavelet transform to the phase space trajectory; calculate the wavelet energy spectrum; identify significant peaks in the wavelet energy spectrum to obtain a candidate pattern set; for each candidate pattern in the candidate pattern set, calculate its duration and energy; define a pattern importance index; sort the candidate patterns according to the pattern importance index and select the main dynamic patterns; for each selected main dynamic pattern, extract its time-frequency features and shape features; combine the extracted features with the topological features of the corresponding time period to form a pattern descriptor; organize all pattern descriptors into a pattern matrix; combine the phase space trajectory, time-varying persistence diagram and pattern matrix into a spatio-temporal feature representation.

[0047] In this embodiment, through nonlinear dynamics reconstruction and persistent homology analysis, the complex dynamic patterns in the helium leak detection data of switchgear are deeply explored. The phase space reconstruction technique can recover the intrinsic dynamics of the system from time series data and effectively capture the nonlinear and non-stationary characteristics during the helium leakage process. The calculation of persistent homology provides in-depth insights into the topological structure of the data and can identify stable leakage patterns and transient anomalies. The dynamic pattern extraction further enhances the method's ability to characterize time-varying behavior. The comprehensive application of these techniques enables the method to extract rich spatio-temporal feature representations from the helium leak detection data of switchgear. Especially when dealing with complex leakage situations, such as multi-point micro-leakage or intermittent leakage, the method shows excellent recognition ability. By analyzing the phase space trajectory and persistence diagram, the leakage source can be accurately located, the leakage rate can be estimated, and even the development trend of the leakage can be predicted. This provides strong support for the preventive maintenance and fault diagnosis of switchgear.

[0048] According to one aspect of the present application, step S4 is specifically as follows:

[0049] Step S41: Read the fused multi-modal representation and spatio-temporal feature representation; define a set of layers, each layer representing a different type of interaction or scale; for each layer in the set of layers, construct a set of nodes, including sensor nodes and virtual nodes generated from the dynamic patterns in the spatio-temporal feature representation; construct an edge set based on the similarity in the low-dimensional data tensor, the causal relationship in the multi-scale causal adjacency matrix, and the information flow in the time-varying information flow network; define a set of node attributes, including the features in the low-dimensional data tensor, the dynamic features in the phase space trajectory, and the topological features in the time-varying persistence diagram; calculate the inter-layer coupling strength; construct an inter-layer edge set to connect nodes representing the same entity or highly correlated nodes in different layers; integrate the information of all layers to form a multi-layer graph structure.

[0050] Step S42: Read the multi-layer graph structure; Initialize the node embedding matrix; Define the intra-layer loss function based on the adjacency matrix of each layer; Define the inter-layer loss function based on the inter-layer coupling strength; Define the attribute preservation loss function based on the node attribute set; Construct the overall objective function by combining the intra-layer loss, inter-layer loss, and attribute preservation loss; Use the stochastic gradient descent method to optimize the overall objective function; Update the node embedding matrix until the objective function converges or reaches the maximum number of iterations; Output the final node embedding.

[0051] Step S43: Read the node embedding and multi-layer graph structure; For each node in the multi-layer graph structure, calculate the local topological features; Extract the k-hop neighborhood of the node; Calculate the local clustering coefficient; Calculate the local disassortativity coefficient; Calculate the local PageRank; Combine these features to obtain the local topological features; Calculate the global topological features; Apply the spectral clustering algorithm to the node embedding to obtain the community membership of the nodes; Calculate the centrality metrics of the nodes, including eigenvector centrality and betweenness centrality; Calculate the structural roles of the nodes; Combine these features to obtain the global topological features; Define the anomaly score by combining the local and global topological features; Combine the multi-layer graph structure, node embedding, and anomaly score into the graph topology anomaly detection result.

[0052] By constructing a multi-layer graph structure and applying a dynamic graph embedding algorithm, efficient anomaly detection of switchgear helium leak detection data is achieved. The multi-layer graph structure can represent relationships of different types and scales simultaneously, such as the spatial relationships between sensors, the similarity of measurement values, etc. The dynamic graph embedding algorithm maps the complex graph structure into a low-dimensional space, improving the computational efficiency. The calculation of local and global topological features makes the anomaly detection more comprehensive and robust. The combination of these technologies enables this method to quickly and accurately identify the anomaly patterns in the switchgear helium leak detection process. Especially when dealing with large-scale switchgear systems, this method shows excellent scalability. By analyzing the low-dimensional representation and topological features of the nodes, abnormal sensors or abnormal areas can be quickly located, shortening the fault diagnosis time. In addition, the use of the graph structure also enables this method to consider the complex structural relationships inside the switchgear, such as the connectivity between different compartments, thus providing more accurate leak location results.

[0053] According to one aspect of the present application, step S5 is specifically as follows:

[0054] Step S51: Read the graph topology anomaly detection results and the set of key parameters used in all previous steps; Define the detection accuracy objective function, which is the area under the receiver operating characteristic curve based on the anomaly scores; Define the computational efficiency objective function, which is based on the total computational time and the maximum allowed computational time; Construct a set of constraints, including the parameter value ranges and resource limitations; Initialize the population, where each individual represents a set of parameter configurations; For each individual in the population, calculate the objective function values; Use non-dominated sorting to stratify the population and obtain the non-dominated ranks; Calculate the crowding distance; Perform selection, crossover, and mutation operations based on the non-dominated ranks and crowding distances to generate a new population; Repeat the steps from initializing the population to generating a new population until the maximum number of iterations is reached or convergence occurs; Output the final non-dominated solution set.

[0055] Step S52: Read the non-dominated solution set and the graph topology anomaly detection results; Define the performance metrics, combining precision, recall, and false positive rate; Initialize the Q function, where the state represents the current parameter configuration and the action represents the parameter adjustment strategy; Define the state transition function, which represents the probability of transitioning from one state to another after performing an action; Define the reward function, which is based on the change in the performance metrics; Use the Q-learning algorithm to update the Q function; At each time step, select an action with an ε-greedy strategy; Execute the selected action, update the parameter configuration, and obtain a new state; Observe the reward and update the Q function; Based on the updated Q function, generate a time-varying optimal parameter set; Combine the graph topology anomaly detection results and the time-varying optimal parameter set into an optimized anomaly detection result.

[0056] Through multi-objective optimization and dynamic parameter adjustment, the adaptive optimization of the switchgear helium leak detection method is achieved. The multi-objective optimization framework can simultaneously consider multiple objectives such as detection accuracy and computational efficiency to find the best balance point. The generation of the non-dominated solution set provides a series of Pareto optimal solutions, offering flexibility for decision-making. The dynamic parameter adjustment strategy enables the method to adapt to changes in the switchgear operating state and always maintain the best performance. The synergistic effect of these technologies enables the method to always maintain high-efficiency and accurate detection capabilities under different working conditions. Especially in long-term monitoring tasks, the method demonstrates excellent stability and adaptability. By continuously optimizing the parameter settings, the method can adapt to the impacts brought by factors such as switchgear aging and environmental changes and maintain the consistency of detection performance. In addition, the generation of the time-varying optimal parameter set also provides an important reference for the intelligent operation and maintenance of switchgear, which can guide the dynamic adjustment of key parameters such as detection frequency and sensitivity to maximize the detection effect while minimizing resource consumption.

[0057] According to one aspect of the present application, in the step S12, specifically:

[0058] Step S121: Read the original data tensor; apply the sliding window technique to each sensor signal in the data tensor; within each window, estimate the local fractal dimension using the improved box-counting method; calculate the fractal spectrum of the signal to obtain the variation of the fractal dimension over time; store the fractal dimension time series as a fractal feature matrix;

[0059] Step S122: Read the fractal feature matrix; use the dynamic programming algorithm to find the optimal segmentation points on the fractal dimension time series; each segmentation corresponds to a characteristic scale; calculate the average fractal dimension of each segmentation; adaptively select the decomposition basis function family according to the average fractal dimension; store the selected basis function family and the corresponding scale information as a scale selection matrix;

[0060] Step S123: Read the original data tensor and the scale selection matrix; for each sensor signal in the data tensor, perform decomposition at each adaptively selected scale; use the basis function family corresponding to that scale for signal decomposition; calculate the decomposition coefficients at each scale; combine the decomposition coefficients of all scales into a multi-scale decomposition tensor;

[0061] Step S124: Read the multi-scale decomposition tensor; apply kernel principal component analysis to extract non-linear features for the coefficients of each scale in the decomposition tensor; perform non-linear mapping using the radial basis function kernel; select the principal components that can explain 90% of the variance; store the extracted non-linear features as a feature tensor;

[0062] Step S125: Read the feature tensor and the original data tensor; use the particle swarm optimization algorithm to find the optimal reconstruction weights; the objective function is the weighted sum of the reconstruction error and the information entropy; for each time point, based on the current optimal weights, reconstruct the features in the feature tensor into a signal; combine the reconstructed signals into a reconstructed data tensor;

[0063] Step S126: Read the reconstructed data tensor and the original data tensor; calculate the residual between the reconstructed data tensor and the original data tensor; process the residual using an adaptive Kalman filter; the parameters of the filter are dynamically adjusted according to the statistical characteristics of the residual; add the filtered residual to the reconstructed data tensor to obtain a fine-reconstructed data tensor;

[0064] Step S127: Read the fine-reconstructed data tensor and the original data tensor; calculate multiple evaluation metrics, including the root mean square error, the structural similarity index, and the information retention rate; use the fuzzy comprehensive evaluation method to synthesize multiple metrics into a single quality score; if the quality score is lower than the preset threshold, return to Step S122 for parameter adjustment and re-decomposition;

[0065] Step S128, read the finely reconstructed data tensor, the multi-scale decomposition tensor and the feature tensor; align the size and structure of the finely reconstructed data tensor with the original data tensor; combine the multi-scale decomposition tensor and the feature tensor to generate an enhanced feature tensor; merge the finely reconstructed data tensor and the enhanced feature tensor to form the final decomposition data tensor.

[0066] Through signal processing technology, high-quality decomposition and enhancement of the raw data of switchgear helium leak detection are achieved. The adaptive multi-resolution decomposition algorithm can automatically select the optimal decomposition scale according to the local characteristics of the signal and effectively separate different frequency components. The introduction of fractal analysis and kernel principal component analysis further improves the nonlinear ability of feature extraction. The application of adaptive Kalman filter effectively suppresses noise interference. The synergy of these technologies enables this method to extract high-quality, multi-scale feature representations from complex switchgear helium leak detection signals. In particular, this method shows excellent performance when processing non-stationary, multi-scale leakage signals. Through adaptive decomposition, both fast-changing transient leakage and slowly evolving long-term leakage trends can be captured simultaneously. The introduction of fractal analysis enables the method to identify self-similar structures in the signal, which is particularly effective for detecting tiny periodic leaks. Kernel principal component analysis enhances the method's ability to extract nonlinear features and can capture complex leakage patterns. In addition, the quality assessment and parameter adaptive adjustment mechanism ensure the reliability and consistency of the decomposition results, providing a high-quality data foundation for subsequent analysis.

[0067] According to one aspect of the present application, step S14 is specifically:

[0068] Step S141, read the cleaned data tensor; apply the t-SNE algorithm to perform initial dimensionality reduction on each decomposition level of each sensor signal in the data tensor; use cosine similarity as a distance metric; generate an initial low-dimensional embedding matrix;

[0069] Step S142, read the initial low-dimensional embedding matrix; use the dynamic time warping algorithm to calculate the similarity between time series; construct an adaptive Gaussian kernel function based on the DTW distance; calculate the kernel matrix; store the kernel matrix as a similarity matrix;

[0070] Step S143, read the similarity matrix and the initial low-dimensional embedding matrix; construct the graph Laplacian matrix; define the manifold consistency objective function, combining local preservation and global alignment; optimize the objective function using the alternating direction multiplier method; update the low-dimensional embedding matrix; store the optimized low-dimensional embedding matrix as the aligned embedding matrix;

[0071] Step S144: Read the alignment embedding matrix; Use a recurrent neural network (RNN) to learn the time-varying mapping function; The input of the RNN is the embedding vectors at adjacent time steps, and the output is the predicted embedding at the next time step; Minimize the prediction error and the manifold consistency loss; Store the learned RNN model parameters as the time-varying mapping model;

[0072] Step S145: Read the time-varying mapping model and the alignment embedding matrix; For the missing or future time point data, use the learned RNN model for interpolation or extrapolation; Generate the complete time series embedding; Combine the interpolation and extrapolation results with the original alignment embedding matrix to form the extended embedding matrix;

[0073] Step S146: Read the extended embedding matrix; Use wavelet transform to perform multi-scale decomposition on the embedding; Apply the local linear embedding algorithm at each scale; Combine the embedding results at different scales through weighted summation; The weights are dynamically adjusted using an adaptive fuzzy inference system; Generate the fused multi-scale embedding matrix;

[0074] Step S147: Read the fused multi-scale embedding matrix; Construct the persistent homology features; Use the persistent homology information to guide the manifold deformation; Minimize the Wasserstein distance to preserve the topological structure; Apply the discrete exterior differential operator for smoothing; Generate the topology-preserving embedding matrix;

[0075] Step S148: Read the topology-preserving embedding matrix and the original data tensor; Calculate the geodesic distance preservation rate before and after manifold alignment; Evaluate the preservation degree of the local neighborhood structure; Use the mutual information criterion to quantify the alignment degree between different sensor signals; Synthesize multiple indicators to generate the alignment quality score;

[0076] Step S149: Read the topology-preserving embedding matrix, the alignment quality score, and the original data tensor; Based on the alignment quality score, adaptively adjust the embedding weights; Map the weighted embedding back to the original data space; Fuse it with the original data tensor to generate the final aligned data tensor.

[0077] In this embodiment, the non-linear alignment of multi-sensor data in the switchgear is achieved. The combination of the t-SNE algorithm and dynamic time warping effectively solves the dual challenges of high-dimensional data dimensionality reduction and time series alignment. The introduction of the graph Laplacian matrix takes into account the local structure of the data and enhances the alignment accuracy. The application of the recurrent neural network realizes the learning of the time-varying mapping function, enabling the method to adapt to the dynamically changing alignment relationship. The comprehensive application of these technologies enables the method to eliminate the non-linear deviation between multi-sensors while maintaining the essential characteristics of the data. Especially when dealing with the complex electromagnetic environment and temperature distribution inside the switchgear, this method exhibits excellent performance. Through precise data alignment, the systematic errors caused by factors such as position and sensitivity between different sensors can be eliminated, improving the accuracy of subsequent analysis. The multi-scale alignment and topology preservation mechanism ensure that the key structural information will not be lost during the alignment process, which is crucial for identifying complex leakage patterns. In addition, the adaptive weight adjustment mechanism enables the method to dynamically balance the contributions of different sensors and maximize the information utilization efficiency.

[0078] According to one aspect of the present application, step S21 is specifically as follows:

[0079] Step S211: Read the aligned data tensor and the dynamic feature matrix; perform normalization processing on the data tensor; calculate the modal correlation matrix of the tensor; use the spectral clustering algorithm to group the modes; generate the modal grouping information matrix;

[0080] Step S212: Read the modal grouping information matrix; for each modal group, call a predetermined kernel function; automatically select the kernel function hyperparameters using Gaussian process regression; generate the kernel function parameter matrix; apply the kernel function to the original data tensor to generate the kernelized data tensor;

[0081] Step S213: Read the kernelized data tensor; use the sliding window technique to apply tensor singular value decomposition to each time window; calculate the singular value decay curve; estimate the optimal rank of each window using the Bayesian information criterion; predict the rank of the future time window using a long short-term memory network; generate the dynamic rank estimation sequence;

[0082] Step S214: Read the kernelized data tensor and the dynamic rank estimation sequence; for each modal group, apply different tensor decomposition methods: for the dense modal group, use Tucker decomposition; for the sparse modal group, use CP decomposition; for the mixed modal group, use the tensor train selection algorithm; combine the dynamic rank information and perform the decomposition operation; generate the set of decomposition factor matrices and the core tensor;

[0083] Step S215: Read the set of decomposed factor matrices; apply structured sparse regularization to each factor matrix; use the proximal gradient descent algorithm to optimize the regularized objective function; introduce temporal smoothing constraints to ensure the temporal continuity of the factors; generate the set of regularized factor matrices;

[0084] Step S216: Read the set of regularized factor matrices and the core tensor; call the adaptive fusion network based on the attention mechanism; use reinforcement learning to train the fusion strategy, and the reward function combines the reconstruction error and the information retention rate; generate the optimal fusion weight matrix;

[0085] Step S217: Read the fusion weight matrix and the newly incoming real-time data; adopt the incremental update rule based on the stochastic approximation algorithm; perform online updates on the factor matrices and the core tensor; use exponential moving average to maintain long-term statistical information; generate the updated decomposition result;

[0086] Step S218: Read the updated decomposition result and the original data tensor; calculate the reconstruction error tensor; perform principal component analysis on the error tensor to extract the main error patterns; call the pre-built error predictor based on the wavelet neural network; generate the error compensation model;

[0087] Step S219: Read the updated decomposition result, the error compensation model and the original data tensor; reconstruct the data tensor based on the decomposition result to obtain the low-dimensional representation.

[0088] In this embodiment, the efficient dimensionality reduction and feature extraction of the helium leak detection data of the switchgear are realized. The introduction of the kernel function enhances the modeling ability of the method for nonlinear relationships. The dynamic rank estimation technology can adaptively select the optimal decomposition rank, avoiding information loss and overfitting. The structured sparse regularization promotes the interpretability and stability of the factors. The synergistic effect of these technologies enables the method to extract low-dimensional but information-rich representations from the high-dimensional switchgear detection data. Especially when dealing with the fusion of data from multiple sensors (such as pressure, temperature, acoustics, etc.), the method shows excellent performance. Through kernelization, the complex nonlinear relationships between different types of data can be effectively captured, such as the influence of temperature on the sensitivity of the pressure sensor. The dynamic rank estimation enables the method to adapt to the changes in the operating state of the switchgear, such as the transition from normal operation to the fault state. The sparse regularization helps to identify the most critical feature combinations, improving the interpretability and noise resistance of the method. In addition, the incremental update and error compensation mechanisms enable the method to process real-time data streams, providing the possibility for the online monitoring of the switchgear.

[0089] According to another aspect of the present application, there is also provided a helium leak detection system for a switchgear, including:

[0090] At least one processor; and,

[0091] A memory communicatively connected to at least one of the processors; wherein,

[0092] The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the helium leak detection method for switchgear described in any one of the above technical solutions.

[0093] According to one aspect of the present application, step S23 is specifically as follows:

[0094] Step S231: Read the multi-scale causal adjacency matrix and the dynamic feature matrix. Apply empirical mode decomposition (EMD) to each time series in the dynamic feature matrix. Generate multiple intrinsic mode functions (IMFs). Calculate the Hilbert transform for each IMF to obtain the instantaneous frequency and amplitude. Store the decomposition result as a multi-scale time series tensor.

[0095] Step S232: Read the multi-scale time series tensor. For each scale, calculate the traditional Shannon entropy. Introduce Renyi entropy and Tsallis entropy as supplementary information metrics. Use the particle swarm optimization algorithm to adaptively select the optimal α parameter. Construct a comprehensive information metric index. Store the result as an adaptive information metric matrix.

[0096] Step S233: Read the adaptive information metric matrix and the multi-scale causal adjacency matrix. Use time-varying Granger causality test to infer causal relationships within each time window. Introduce transfer entropy as a supplementary measure of non-linear causality. Use the adaptive LASSO method for sparsification processing. Generate a dynamic causal network sequence.

[0097] Step S234: Read the dynamic causal network sequence. Apply the maximum flow algorithm to identify the main information flow paths. Introduce the concept of marginal information gain to quantify the information contribution of each path. Use the PageRank algorithm to evaluate the importance of nodes in information propagation. Generate an information flow path importance matrix.

[0098] Step S235: Read the dynamic causal network sequence. Calculate the time-varying network degree distribution, clustering coefficient, and betweenness centrality. Introduce the spectral clustering method to identify the dynamic community structure. Use the Infomap algorithm to analyze the diffusion pattern of information flow in the network. Generate a network topology feature vector sequence.

[0099] Step S236: Read the information flow path importance matrix and the network topology feature vector sequence. Design a hierarchical attention mechanism to adaptively integrate information flows at different scales. Use a graph neural network to capture the high-order dependencies between nodes. Apply the dynamic time warping (DTW) algorithm to align information flows at different scales. Generate a multi-level information flow representation.

[0100] Step S237: Read the multi-level information flow representation. Construct a time-varying adjacency matrix using an adaptive threshold method. Introduce the concept of Forman-Ricci curvature to quantify the information flow resistance in the network. Apply spectral methods for network structure optimization. Generate an optimized time-varying information flow network.

[0101] Step S238: Read the optimized time-varying information flow network. Apply a multi-scale skeleton network extraction algorithm to identify the core structure of the network. Use the Louvain method for dynamic community detection. Introduce a metric based on information theory to evaluate community stability. Analyze community splitting, merging, and evolution patterns. Generate a dynamic community structure sequence.

[0102] Step S239: Read the dynamic community structure sequence and the time-varying information flow network. Design a temporal prediction model based on the Graph Attention Network (GAT). Introduce an adaptive sampling strategy to balance short-term and long-term dependencies. Use adversarial training to improve the generalization ability of the model. Generate an information flow prediction model.

[0103] Step S2310: Read the information flow prediction model, the time-varying information flow network, and the dynamic community structure sequence. Calculate multiple evaluation metrics, including prediction accuracy, network stability, and information flow efficiency. Use the fuzzy comprehensive evaluation method to generate an overall score. Combine the time-varying information flow network, the dynamic community structure, and the prediction model into the final dynamic information flow analysis result. Output this combined result as the output of the multi-scale adaptive dynamic information flow analysis.

[0104] In this embodiment, a high-precision characterization of the complex dynamic information flow in the helium leak detection data of switchgear is achieved. The combination of empirical mode decomposition and adaptive information metrics provides the ability to deeply analyze multi-scale non-stationary signals. The introduction of time-varying Granger causality and transfer entropy enhances the method's ability to identify non-linear causal relationships. The construction of dynamic community detection and information flow prediction models provides insights into the long-term evolution of system behavior. The comprehensive application of these technologies enables the method to comprehensively and accurately describe the complex information propagation and interaction processes inside the switchgear. Especially when analyzing large switchgear systems or complex multi-point leakage scenarios, this method exhibits excellent performance. Through multi-scale information flow analysis, rapid local leakage events and slowly evolving global seal performance degradation can be captured simultaneously. The construction of a dynamic causal network helps to understand the mutual influence between different components, such as how a leak in one area affects the pressure distribution in other areas. Community structure analysis can identify key subsystems or weak links in the system, providing guidance for targeted maintenance. In addition, the introduction of the information flow prediction model endows the method with the ability of predictive maintenance, enabling potential leakage risks to be identified in advance. The application of adaptive sampling and adversarial training further improves the generalization ability and robustness of the model, enabling it to cope with the dynamic changes in the switchgear operating environment. Generally speaking, this step not only provides an in-depth understanding of the helium leak detection process of switchgear, but also provides strong data support for fault diagnosis, risk assessment and maintenance decision-making, and is expected to significantly improve the operating reliability and maintenance efficiency of switchgear.

[0105] According to one aspect of the present application, step S31 is specifically as follows:

[0106] Step S311: Read the low-dimensional data tensor in the fused multi-modal representation. Apply the wavelet threshold denoising method and use the adaptive threshold selection algorithm. Calculate the signal-to-noise ratio and the denoising effect. Generate the denoised data tensor.

[0107] Step S312: Read the denoised data tensor. Calculate the sample entropy, fuzzy entropy, and permutation entropy. Use the sliding window technique to obtain the change of entropy over time. Apply principal component analysis to reduce the dimension of the entropy features. Generate the multi-scale entropy feature matrix.

[0108] Step S313: Read the denoised data tensor and the multi-scale entropy feature matrix. Calculate the self-mutual information function. Use the adaptive kernel density estimation method. Find the first local minimum of the self-mutual information function. Introduce an entropy-based correction factor. Generate the initial time delay estimate.

[0109] Step S314: Read the initial time delay estimate and the denoised data tensor. Apply the false nearest neighbor algorithm. Use the recurrence plot analysis method. Calculate the correlation dimension. Combine the results of these methods to generate a candidate set of embedding dimensions.

[0110] Step S315: Read the candidate set of embedding dimensions, the initial time delay estimate, and the denoised data tensor. For each candidate embedding dimension, reconstruct the phase space. Calculate the maximum Lyapunov exponent. Use the Wolf algorithm and the Rosenstein algorithm, and take the weighted average of the two. Generate the Lyapunov exponent matrix.

[0111] Step S316: Read the Lyapunov exponent matrix, the candidate set of embedding dimensions, and the initial time delay estimate. Calculate the deterministic test statistic. Evaluate the fractal dimension of the reconstructed attractor. Use the mutual information rate criterion. Combine these metrics to construct the reconstruction quality score. Generate the reconstruction quality score matrix.

[0112] Step S317: Read the reconstruction quality score matrix, the Lyapunov exponent matrix, and the multi-scale entropy feature matrix. Construct a multi-objective optimization problem with the objectives of maximizing the reconstruction quality, maximizing the Lyapunov exponent, and minimizing the computational complexity. Solve it using the improved NSGA-III algorithm to generate the Pareto optimal solution set.

[0113] Step S318: Read the Pareto optimal solution set. Adopt a decision-making system based on fuzzy logic. Consider the dynamic characteristics of the system and the computational resource constraints. Adaptively select the optimal combination of time delay and embedding dimension. Generate the optimal reconstruction parameter set.

[0114] Step S319: Read the optimal reconstruction parameter set and the denoised data tensor. Reconstruct the phase space using the selected time delay and embedding dimension. Apply kernel principal component analysis for manifold learning. Introduce the diffusion map method to capture the nonlinear structure. Generate the reconstructed phase space trajectory.

[0115] Step S3110: Read the reconstructed phase space trajectory. Calculate the recurrence plot and the cross recurrence plot of the trajectory. Analyze the periodicity and intermittency of the system. Use the high-order spectral analysis method to detect weak chaos. Construct a prediction model based on the Echo State Network. Generate the system stability report and the short-term prediction results.

[0116] Step S3111: Read the system stability report, the short-term prediction results, and the reconstructed phase space trajectory. Calculate the reconstruction fidelity metric. Evaluate the performance of the prediction model. Generate the comprehensive evaluation report. Combine the reconstructed phase space trajectory, the optimal reconstruction parameter set, the prediction model, and the evaluation report into the final nonlinear dynamics reconstruction result. Output this comprehensive result as the output of the adaptive multi-criteria nonlinear dynamics reconstruction.

[0117] In this embodiment, an accurate characterization of the complex dynamic behavior in the helium leak detection data of switchgear is achieved. The combination of adaptive denoising and multi-scale entropy analysis provides a high-quality and information-rich data basis for subsequent analysis. The adaptive selection of the optimal time delay and embedding dimension ensures the accuracy of phase space reconstruction. The calculation of Lyapunov exponents and deterministic tests provides in-depth insights into the dynamic characteristics of the system. The synergistic effect of these techniques enables this method to recover the inherent dynamic structure of the system from the time series data of helium leak detection in switchgear. Especially when dealing with complex non-linear and non-stationary leakage processes, this method exhibits excellent performance. Through phase space reconstruction, a seemingly random time series can be transformed into a structured trajectory, thereby revealing potential leakage patterns. The calculation of the maximum Lyapunov exponent helps to evaluate the stability and predictability of the system, which is crucial for distinguishing normal fluctuations from abnormal leaks. The introduction of multi-objective optimization ensures the global optimality of the reconstruction parameters, balancing the reconstruction quality, computational efficiency, and model complexity. In addition, the application of kernel principal component analysis and diffusion map methods further enhances the method's ability to extract non-linear features and helps to identify subtle leakage precursors. The construction of the prediction model not only provides short-term prediction capabilities but also provides an important basis for the health state assessment of switchgear.

[0118] According to one aspect of the present application, step S33 is specifically as follows:

[0119] Step S331: Read the complete phase space trajectory and topological feature representation. Apply continuous wavelet transform, using adaptive wavelet basis functions. Calculate the time-frequency energy spectrum. Introduce the Wigner-Ville distribution to enhance the time-frequency resolution. Generate a multi-resolution time-frequency representation matrix.

[0120] Step S332: Read the multi-resolution time-frequency representation matrix. Apply an adaptive threshold segmentation algorithm. Use morphological operations to optimize the segmentation result. Calculate the shape descriptors of the segmented regions. Generate an initial pattern candidate set.

[0121] Step S333: Read the initial pattern candidate set and the multi-resolution time-frequency representation matrix. Extract time-domain features (mean, variance, skewness, kurtosis). Calculate frequency-domain features (power spectral density, spectral entropy). Extract time-frequency joint features (instantaneous frequency, group delay). Use an adaptive feature selection algorithm based on the maximum correlation minimum redundancy (mRMR) criterion. Generate a set of dynamic feature vectors.

[0122] Step S334: Read the set of dynamic feature vectors and the topological feature representation. Calculate persistent homology features (Betti number curves, persistence diagrams). Extract algebraic topological features (Euler characteristic curves). Design a feature fusion network based on the attention mechanism. Learn the optimal feature combination strategy. Generate a fused feature matrix.

[0123] Step S335: Read the fused feature matrix. Apply the adaptive spectral clustering algorithm to automatically determine the optimal number of clusters. Introduce a multi-view learning framework to integrate clustering results at different scales. Use a consensus matrix to evaluate clustering stability. Generate multi-scale pattern clustering results.

[0124] Step S336: Read the multi-scale pattern clustering results. Apply a sequential pattern mining algorithm (such as PrefixSpan). Introduce time constraints and consider the periodicity and intermittency of patterns. Use a Markov decision process to model pattern transitions. Calculate the pattern transition probability matrix. Generate a temporal pattern library.

[0125] Step S337: Read the temporal pattern library and the fused feature matrix. Design an outlier detector based on the Isolation Forest. Introduce the Dynamic Time Warping (DTW) to measure pattern similarity. Calculate the outlier scores of patterns. Use extreme value theory to determine the adaptive threshold. Generate an outlier pattern report.

[0126] Step S338: Read the temporal pattern library and the outlier pattern report. Construct a pattern evolution graph. Analyze the processes of pattern splitting, merging, and transformation. Use complex network theory to quantify the importance of patterns. Apply information flow theory to analyze the causal relationships between patterns. Generate a pattern evolution analysis report.

[0127] Step S339: Read the pattern evolution analysis report and the fused feature matrix. Adopt a deep temporal model (such as TCN or Transformer). Introduce an attention mechanism to capture long-term dependencies. Use Bayesian optimization to automatically adjust the model hyperparameters. Apply ensemble learning to improve prediction stability. Generate a pattern prediction model.

[0128] Step S3310: Read the pattern prediction model and the pattern evolution analysis report. Design a semantic mapping system based on a knowledge graph. Convert numerical features into interpretable semantic descriptions. Apply causal reasoning to explain the relationships between patterns. Generate a pattern semantic interpretation report.

[0129] Step S3311: Read the pattern semantic interpretation report, the pattern prediction model, and the outlier pattern report. Calculate the integrity, consistency, and novelty metrics of pattern extraction. Evaluate the performance of the prediction model (accuracy, recall, F1-score). Design an interactive visualization interface to display the dynamic evolution process of patterns. Generate a comprehensive evaluation report and visualization results.

[0130] Step S3312: Read the comprehensive evaluation report, the visualization results, the pattern prediction model, and the pattern semantic interpretation report. Integrate all analysis results to generate a final dynamic pattern extraction report. Combine the phase space trajectory, the time-varying persistence diagram, and the pattern matrix into an enhanced spatio-temporal feature representation.

[0131] In this embodiment, an efficient extraction and interpretation of complex dynamic patterns in the helium leak detection data of switchgear is achieved. The application of adaptive wavelet transform and Wigner-Ville distribution provides a multi-angle analysis of the time-frequency characteristics of signals. The introduction of persistent homology and algebraic topology features enhances the sensitivity of the method to changes in data structure. The combination of sequential pattern mining and anomaly detection enables an accurate distinction between normal and abnormal patterns. The comprehensive application of these technologies enables the method to extract rich and multi-scale dynamic patterns from the spatio-temporal data of helium leak detection in switchgear. Especially when dealing with complex multi-point leakage or intermittent leakage scenarios, the method demonstrates excellent recognition ability. Through multi-resolution time-frequency analysis, rapid transient leaks and slowly evolving seal performance degradation can be captured simultaneously. The calculation of topological features helps identify stable structures in the data, which is particularly important for distinguishing persistent leaks from temporary disturbances. Pattern evolution analysis can not only track the development process of leaks but also predict their future trends. The introduction of deep time series models further enhances the prediction ability of the method, providing strong support for preventive maintenance. In addition, the application of knowledge graph and natural language generation technologies improves the interpretability of model outputs, enabling maintenance personnel to intuitively understand and apply complex data analysis results.

[0132] According to one aspect of the present application, step S42 is specifically as follows:

[0133] Step S421: Read the multi-layer graph structure. Perform spectral decomposition on the graph for each time step. Calculate the eigenvalue distribution of the Laplacian matrix. Smooth the time series graph structure using an adaptive kernel function. Generate a preprocessed time-varying graph sequence.

[0134] Step S422: Read the preprocessed time-varying graph sequence and the node attribute set. Design a multi-modal attention mechanism to adaptively fuse different types of node features. Use a cross-modal autoencoder to learn the correlation between features. Apply contrastive learning to improve the discriminability of feature representations. Generate a fused feature matrix.

[0135] Step S423: Read the fused feature matrix. Perform an initial low-dimensional mapping using the t-SNE algorithm. Apply UMAP to preserve the global structure of the data. Combine local linear embedding (LLE) to capture local features. Use an integration strategy to merge multiple initialization results. Generate an initial dynamic embedding matrix.

[0136] Step S424: Read the initial dynamic embedding matrix and the preprocessed time-varying graph sequence. Design a temporal smoothing term based on the Wasserstein distance. Introduce dynamic time warping (DTW) to measure the similarity of embedding sequences. Construct a temporal regularization term to balance static structure preservation and dynamic evolution capture. Generate a temporal consistency constraint function.

[0137] Step S425: Read the fused feature matrix and the preprocessed time-varying graph sequence. Construct a multi-scale graph convolutional network to capture structural information in different ranges. Design an adaptive pooling layer to dynamically adjust the receptive field size. Introduce skip connections to fuse features at different scales. Generate a multi-scale structural representation.

[0138] Step S426: Read the preprocessed time-varying graph sequence. Design an importance sampling method based on node centrality. Introduce a time-series aware negative sample generation strategy. Use reinforcement learning to optimize the sampling strategy to maximize the discriminability of the embeddings. Generate a dynamic negative sample set.

[0139] Step S427: Read the time-series consistency constraint function, the multi-scale structural representation, and the dynamic negative sample set. Design an adaptive weight mechanism to dynamically balance different objective terms. Introduce a curriculum learning strategy to gradually increase the task difficulty. Construct a comprehensive optimization objective function including a structure preservation term, a time-series consistency term, and a contrastive learning term. Generate an optimization objective function.

[0140] Step S428: Read the optimization objective function and the initial dynamic embedding matrix. Design an adaptive learning rate adjustment strategy based on Nesterov momentum. Introduce gradient accumulation technology to handle large-scale graph data. Use gradient clipping to prevent gradient explosion. Apply a second-order optimization method (such as L-BFGS) to accelerate convergence. Generate an optimized dynamic embedding matrix.

[0141] Step S429: Read the optimized dynamic embedding matrix. Use Procrustes analysis to align the embedding spaces at different time steps. Apply an equivariant graph attention network to enhance the rotational invariance of the embeddings. Introduce manifold alignment technology to maintain time-series consistency. Generate a calibrated dynamic embedding matrix.

[0142] Step S4210: Read the calibrated dynamic embedding matrix and the newly incoming real-time graph data. Design a sliding-window-based incremental update strategy. Use spectral sparse regularization to maintain the sparsity of the embeddings. Apply an online learning algorithm, such as online stochastic gradient descent, to update the embeddings in real time. Generate an updated dynamic embedding matrix.

[0143] Step S4211: Read the updated dynamic embedding matrix and the preprocessed time-varying graph sequence. Calculate the link prediction accuracy, node classification performance, and clustering effect. Evaluate the stability and time-series consistency of the embeddings. Use persistent homology to analyze the topological properties of the embeddings. Generate an embedding quality assessment report.

[0144] Step S4212: Read the embedding quality assessment report and the updated dynamic embedding matrix. Based on the evaluation results, adaptively adjust the weights of the optimization objective. Use Bayesian optimization to automatically adjust the hyperparameters. Apply a meta-learning strategy to improve the model's adaptability to new tasks. Generate a fine-tuned dynamic embedding matrix.

[0145] Step S4213: Read the fine-tuned dynamic embedding matrix, the embedding quality assessment report, and the multi-layer graph structure. Integrate all the analysis results to generate the final dynamic graph embedding report. Associate the dynamic embedding matrix with the original graph structure information to form an enhanced graph representation.

[0146] In this embodiment, the efficient dynamic graph embedding of switchgear helium leak detection data is achieved. The introduction of graph wave decomposition and multi-scale structure representation provides a basis for capturing topological structures at different scales. The application of the adaptive attention mechanism and contrastive learning enhances the discriminative and expressive capabilities of the embedding. The design of the temporal consistency constraint and incremental update strategy ensures the continuity and real-time nature of the embedding in the time dimension. The synergistic effect of these technologies enables this method to transform complex switchgear helium leak detection data into low-dimensional and information-rich embedding representations. Especially when dealing with large-scale and multi-sensor detection systems, this method exhibits excellent computational efficiency and scalability. Through multi-scale graph representation, local micro-leaks and global system state changes can be captured simultaneously. The introduction of the attention mechanism enables the model to automatically focus on the most relevant features and relationships, improving the accuracy of anomaly detection. The combination of contrastive learning and temporal consistency constraint not only enhances the discriminative ability of the embedding but also ensures the coherence of temporal analysis. The application of temporal analysis and equivariant graph attention network solves the problem of rotational invariance in the embedding space, making the embedding results at different time points comparable. In addition, the design of the incremental update and online learning strategy enables this method to adapt to the dynamic changes in the operating state of the switchgear, providing the possibility for real-time monitoring and early warning. The introduction of the comprehensive performance evaluation and adaptive adjustment mechanism further ensures the stability and effectiveness of the method in long-term applications, laying a solid data foundation for the intelligent operation and maintenance of switchgear.

[0147] According to one aspect of the present application, step S43 is specifically as follows:

[0148] Step S431: Read the node embedding and the multi-layer graph structure. Apply graph wave decomposition to obtain subgraphs at multiple scales. Use the Spectral Coarsening algorithm for graph coarsening. Construct a graph pyramid structure. Generate a multi-scale graph representation set.

[0149] Step S432: Read the multi-scale graph representation set. For each scale of the graph: Calculate the Forman-Ricci curvature of the k-order neighborhood. Estimate the Betti number of the local homology group. Calculate the persistent heat kernel signature of the node. Extract local graph kernel features. Integrate the multi-scale features to generate a local topological feature matrix.

[0150] Step S433: Read the multi-scale graph representation set. For each scale of the graph: Calculate the spectral entropy and Von Neumann entropy. Extract the global persistent homology features. Calculate the Ollivier-Ricci curvature of the graph. Estimate the distortion and asymptotic dimension of the graph. Fuse the multi-scale features to generate a global topological feature vector.

[0151] Step S434: Read the local topological feature matrix and the global topological feature vector. Design a recursive Bayesian filter to track the temporal evolution of the features. Use particle filtering to handle non-Gaussian noise. Construct a dynamic topological feature state space model. Generate a time-varying topological feature sequence.

[0152] Step S435: Read the time-varying topological feature sequence and the node embeddings. Design a self-attention mechanism to capture the long-range dependencies between the features. Use cross-modal Transformer to fuse different types of features. Apply contrastive learning to enhance the discriminability of the features. Generate a fused feature tensor.

[0153] Step S436: Read the fused feature tensor. Use extreme value theory to model the tail of the feature distribution. Apply adaptive kernel density estimation to fit the multi-dimensional feature distribution. Design an online expectation maximization algorithm to dynamically update the distribution parameters. Generate an adaptive anomaly threshold function.

[0154] Step S437: Read the fused feature tensor and the adaptive anomaly threshold function. For each node: Calculate the local anomaly score using the Isolation Forest algorithm. Apply the Local Outlier Factor (LOF) method. Construct a local One-Class SVM model. Use the reconstruction error of the autoencoder as an anomaly metric. Integrate the results of multiple models to generate a local anomaly scoring matrix.

[0155] Step S438: Read the fused feature tensor and the adaptive anomaly threshold function. At the full-graph scale: Apply a graph neural network to detect abnormal subgraph structures. Use spectral clustering to identify abnormal communities. Calculate the global graph shape statistics to detect overall topological changes. Apply a dynamic graph convolutional network to capture temporal anomaly patterns. Integrate the results of multiple scales to generate a global anomaly pattern report.

[0156] Step S439: Read the local anomaly scoring matrix and the global anomaly pattern report. Construct a graph causal model to infer the propagation path of the anomalies. Use counterfactual reasoning to evaluate the scope of influence of the anomalies. Apply intervention theory to identify the key anomaly sources. Generate an anomaly causal relationship graph.

[0157] Step S4310: Read the anomaly causal relationship graph and the time-varying topological feature sequence. Apply a spatio-temporal LSTM network to model the spatio-temporal dependencies of the anomalies. Use a graph attention mechanism to capture the long-range correlations between the anomalies. Construct an anomaly co-occurrence network to analyze the synergistic effects of the anomaly patterns. Generate a spatio-temporal anomaly correlation report.

[0158] Step S4311: Read the spatio-temporal anomaly correlation report and the anomaly causality diagram. Design an explanation generation system based on a knowledge graph. Use SHAP values to quantify the contribution of features to the anomaly. Apply a natural language generation model to create a human - understandable anomaly description. Generate an anomaly explanation report.

[0159] Step S4312: Read the anomaly explanation report and the fused feature tensor. Design a reinforcement learning framework to optimize the anomaly detection strategy. Use an active learning method to select the most informative samples for manual annotation. Apply transfer learning to improve the generalization ability of the model in new scenarios. Update the detection model parameters to generate an optimized anomaly detection model.

[0160] Step S4313: Read the optimized anomaly detection model, the anomaly explanation report, and the spatio - temporal anomaly correlation report. Calculate multiple evaluation metrics, including precision, recall, F1 - score, and AUC. Evaluate the stability and computational efficiency of the model. Generate a comprehensive performance evaluation report. Integrate the multi - layer graph structure, the anomaly detection results, and the evaluation report to form the final topological anomaly detection result. Output this comprehensive result as the final output of the multi - scale adaptive topological anomaly detection.

[0161] In this embodiment, multi-scale adaptive topological anomaly detection of helium leak detection data for switchgear is achieved. The calculation of Forman-Ricci curvature and persistent homology provides in-depth insights into the topological structure of the data. The application of self-attention mechanism and cross-modal Transformer enhances the effect of feature fusion. The combination of extreme value theory and adaptive kernel density estimation provides a theoretical basis for the dynamic adjustment of anomaly thresholds. The comprehensive application of these technologies enables this method to accurately identify various types and scales of anomalies from complex helium leak detection data of switchgear. Especially when dealing with large switchgear systems or complex multi-point leakage scenarios, this method exhibits excellent detection performance and interpretability. Through multi-scale topological feature analysis, both local tiny leaks and global system anomalies can be captured simultaneously. The introduction of graph neural network enables the method to make full use of the structural information inside the switchgear, improving the accuracy of anomaly localization. The application of causal model and counterfactual reasoning can not only identify anomalies, but also infer the propagation path and influence range of anomalies, providing an important basis for fault diagnosis and risk assessment. The combination of spatio-temporal LSTM and graph attention mechanism enhances the method's ability to detect long-term and complex anomaly patterns. In addition, the introduction of knowledge graph and natural language generation technologies improves the interpretability of anomaly detection results, enabling complex data analysis results to be intuitively understood and applied by maintenance personnel. The application of reinforcement learning and active learning strategies enables the system to continuously optimize and self-improve, adapting to the dynamic changes in the operating environment of the switchgear. The design of comprehensive performance evaluation and model update mechanism further ensures the effectiveness and reliability of the method in long-term applications, providing strong technical support for the preventive maintenance and intelligent operation of switchgear.

[0162] According to one aspect of the present application, step S51 is specifically as follows:

[0163] Step S511: Read the graph topological anomaly detection results and the set of key parameters used in all previous steps. Construct an objective function set, including detection accuracy, computational efficiency, and model complexity. Define the decision variable space and constraint conditions. Generate an initial population using Latin hypercube sampling. Calculate the objective function values of the initial population. Generate an initial population matrix and an objective value matrix.

[0164] Step S512: Read the initial population matrix. Dynamically adjust the crossover probability based on population diversity. Design a hybrid strategy of simulated binary crossover (SBX) and differential evolution (DE). Introduce an adaptive crossover distribution index and automatically adjust it according to the convergence degree. Construct an adaptive selection probability distribution for the crossover operation. Generate an adaptive crossover operator.

[0165] Step S513: Read the target value matrix. Design an intelligent mutation operator based on the Gaussian process. Construct an adaptive adjustment mechanism for the mutation intensity, which is dynamically adjusted according to the position of the individual on the non-dominated front. Introduce Cauchy distribution mutation to enhance the ability to jump out of local optima. Design a mutation direction guiding strategy using the target gradient information. Generate the intelligent mutation operator.

[0166] Step S514: Read the target value matrix of the current population. Implement a fast non-dominated sorting algorithm based on bitmaps. Use parallel computing technology to accelerate the sorting process. Introduce an approximate non-dominated sorting strategy to handle large-scale populations. Calculate the domination number and the dominated set of each solution. Generate the non-dominated rank matrix and the front set.

[0167] Step S515: Read the non-dominated rank matrix and the front set. Use the K-means++ algorithm to generate initial reference points in the objective space. Design a dynamic reference point adjustment strategy, which is adaptively updated according to the current front distribution. Introduce local density estimation to optimize the distribution of reference points in sparse regions. Construct an adaptive reference point update mechanism. Generate the adaptive reference point set.

[0168] Step S516: Read the front set and the adaptive reference point set. Design a method for calculating the local crowding degree based on reference points. Introduce the L∞-norm to replace the Euclidean distance to improve the calculation efficiency. Use a k-d tree to accelerate the nearest neighbor search. Consider different scales in the objective space and introduce an adaptive normalization strategy. Generate the improved crowding degree matrix.

[0169] Step S517: Read the non-dominated rank matrix, the improved crowding degree matrix and the current population. Implement the ε-dominance strategy to balance convergence and diversity. Design an elite individual selection mechanism based on reference points. Construct an adaptive pressure adjustment strategy for environmental selection to dynamically balance exploration and exploitation. Generate the new generation population matrix.

[0170] Step S518: Read the new generation population matrix and the historical optimal solution sets. Calculate the hypervolume index and the generational distance. Design a convergence evaluation criterion based on entropy. Construct a multi-criterion termination judgment mechanism, comprehensively considering the number of iterations, the calculation time and the convergence quality. Generate the termination condition evaluation result.

[0171] Step S519: Read the termination condition evaluation result and the new generation population matrix. Dynamically adjust the calculation resource allocation based on the convergence speed of each objective. Design a target switching strategy to focus on different objectives at different iteration stages. Construct a resource allocation strategy based on reinforcement learning to maximize the overall optimization efficiency. Generate the resource allocation plan.

[0172] Step S5110: Read the new generation population matrix and the resource allocation plan. Perform local search on the selected elite individuals. Use a hybrid strategy of Pattern Search and Nelder-Mead simplex method. Design an adaptive step size adjustment mechanism. Repair the solutions that violate the constraints and use the Lagrange multiplier method to handle the constraints. Generate the optimized population matrix.

[0173] Step S5111: Read the optimized population matrix. Divide the total population into multiple subpopulations. Design a parallel evolution strategy based on the island model. Construct the migration topology and migration strategy between subpopulations. Introduce a diversity evaluation mechanism to maintain the diversity of subpopulations. Design a dynamic population size adjustment strategy. Generate the co-evolved multi-population matrix.

[0174] Step S5112: Read the co-evolved multi-population matrix. Reconstruct the Pareto front using SPEA2 (Improved Strength Pareto Evolutionary Algorithm 2). Apply Gaussian process regression to smooth and interpolate the discrete Pareto front. Construct a parametric representation of the front for subsequent decision-making. Generate the reconstructed and smoothed Pareto front.

[0175] Step S5113: Read the reconstructed and smoothed Pareto front. Implement an interactive multi-criteria decision support system. Use the TOPSIS method to rank the solutions. Introduce a fuzzy preference relation to handle the uncertain preferences of decision-makers. Construct a solution selection strategy based on regret theory. Generate the final non-dominated solution set and the decision recommendation report.

[0176] Step S5114: Read the final non-dominated solution set and the decision recommendation report. Calculate the performance metrics of multi-objective optimization, including convergence, diversity, and stability metrics. Evaluate the computational efficiency and scalability of the algorithm. Generate a comprehensive performance evaluation report. Integrate the non-dominated solution set, decision recommendations, and performance evaluation to form the final multi-objective optimization result. Output this comprehensive result as the final output of the adaptive multi-objective co-optimization framework.

[0177] In this embodiment, an adaptive multi-objective collaborative optimization of the switchgear helium leak detection method is achieved. The introduction of Latin hypercube sampling and intelligent mutation operators enhances the diversity and search efficiency of the initial population. The application of dynamic reference point adjustment and ε-dominance strategy ensures the convergence and diversity of the optimization process. The combination of parallel evolution and Gaussian process regression further improves the computational efficiency and prediction ability of the algorithm. The synergistic effect of these technologies enables the method to find the best balance among multiple objectives such as detection accuracy, computational efficiency, and model complexity. Especially when dealing with large-scale and multi-variable switchgear detection systems, this method exhibits excellent optimization performance and adaptability. Through multi-objective optimization, multiple key indicators such as detection sensitivity, false positive rate, and calculation time can be considered simultaneously, providing customized solutions for different application scenarios. The design of adaptive crossover and mutation strategies enables the algorithm to adjust the search direction and intensity according to the real-time feedback of the optimization process, effectively avoiding local optima. The dynamic adjustment of reference points and the improvement of crowding degree calculation ensure the uniform distribution of solutions in the objective space, providing a rich set of alternative solutions. The introduction of parallel computing and resource allocation optimization improves the efficiency of the algorithm when dealing with large-scale problems. In addition, the design of an interactive multi-criteria decision support system provides a tool for decision-makers to flexibly select the final solution and make trade-offs according to actual needs. The smoothing and interpolation of the Pareto front by Gaussian process regression provide a theoretical basis for continuous decision-making. The generation of comprehensive performance evaluation and decision-making recommendation reports further enhances the usability and credibility of the method, providing comprehensive and scientific decision-making support for the parameter optimization and performance tuning of the switchgear helium leak detection system.

[0178] In another embodiment of the present application, the specific implementation process is as follows:

[0179] Step S11: Obtain data from at least two sensors (different switchgears may belong to different manufacturers and are equipped with different sensors). Obtain helium concentration data a(t) from a helium mass spectrometer. Obtain pressure distribution data b(t) from a pressure sensor array. Obtain temperature distribution data c(t) from a temperature sensor network. Obtain acoustic signal data d(t) from an acoustic sensor array. Obtain electromagnetic field intensity data e(t) from an electromagnetic field sensor. Calculate the change rate of each sensor signal v_i(t)=|d_i(t) / dt|, where i represents the sensor type. Based on the change rate v_i(t), calculate the adaptive sampling frequency f(t)=max(f_min, min(f_max, k*max(v_i(t)))), where f_min and f_max are the minimum and maximum sampling frequencies respectively, and k is a proportionality coefficient. Resample all sensor data using the calculated f(t). Organize the resampled data into the original data tensor R(t, f(t), [a, b, c, d, e]).

[0180] Step S12: Read the original data tensor R(t, f(t), [a, b, c, d, e]) obtained in step S11. For each sensor signal i in R, apply the adaptive multi-resolution decomposition algorithm. First, perform multi-scale decomposition of the signal using wavelet transform to obtain the initial decomposition set {W_i}_j, where j represents the decomposition level. Then, apply empirical mode decomposition to each {W_i}_j to obtain the multi-scale component set {IMF_i}_j. Calculate the information entropy H_j and computational complexity C_j for each decomposition level j. Define the objective function O_j = w1*H_j - w2*C_j, where w1 and w2 are weight coefficients. Select the level j_opt that maximizes O_j as the optimal decomposition level. Based on j_opt, select the corresponding multi-scale components from {IMF_i}_j. Combine all the processed signals to generate a six-dimensional decomposed data tensor D(t, f(t), [a, b, c, d, e], j).

[0181] Step S13: Read the decomposed data tensor D(t, f(t), [a, b, c, d, e], j) obtained in step S12. For each decomposition level j of each sensor signal i in D, construct the time-delay embedding vector V_ij(t) = [x_ij(t), x_ij(t+τ),..., x_ij(t+(m-1)τ)], where τ is the time delay and m is the embedding dimension. Construct the Vietoris-Rips complex based on V_ij(t) and calculate the 0-dimensional and 1-dimensional persistent homology. Obtain the persistence diagram PD_ij, which contains the birth time α_k and death time β_k. Calculate the anomaly metric AD_ij = Σ_k(β_k - α_k) / (t_max - t_min). Compare AD_ij with the pre-set adaptive threshold τ_ij. If AD_ij > τ_ij, mark this data point as an anomaly. For the data points marked as anomalies, use the local linear regression method for repair. Re-organize the repaired data to generate the cleaned six-dimensional data tensor C(t, f(t), [a, b, c, d, e], j).

[0182] Step S14: Read the cleaned data tensor C(t, f(t), [a, b, c, d, e], j) obtained in step S13. For each decomposition level j of each sensor signal i in the cleaned data tensor C, use the Isomap algorithm to embed it into a high-dimensional manifold to obtain the manifold M_ij. Calculate the geodesic distance between manifolds d_g(M_ij, M_kl) = min(Σ_pd_E(x_p, x_{p+1})), where d_E is the Euclidean distance and x_p is a point on the geodesic. Set the sensor importance weight w_ij and construct the objective function E = Σ_i,j,kw_ij * w_kl * d_g(M_ij, M_kl). Use the gradient descent method to minimize the objective function E to obtain the optimal alignment parameter θ*. Based on θ*, transform the data in the cleaned data tensor C to obtain the aligned six-dimensional data tensor A(t, f(t), [a, b, c, d, e], j).

[0183] Step S15: Read the aligned data tensor A(t, f(t), [a, b, c, d, e], j) obtained in step S14. For each decomposition level j of each sensor signal i in A, apply the short-time Fourier transform to obtain the time-frequency representation S_ij(t, ω). Calculate the statistical moments of S_ij(t, ω), including the mean μ_ij(t), variance σ²_ij(t), skewness γ_ij(t), and kurtosis κ_ij(t). Extract geometric features, including the fractal dimension D_ij(t) and Lyapunov exponent λ_ij(t). Combine all features to form the feature set F_ij(t) = [μ_ij(t), σ²_ij(t), γ_ij(t), κ_ij(t), D_ij(t), λ_ij(t)]. Calculate the Shannon entropy H(F_k) and the mutual information between features I(F_k;F_l) for each feature. Define the feature importance score S(F_k) = H(F_k) - Σ_l≠kI(F_k;F_l). Sort the features based on S(F_k) and select the n features with the highest scores. Organize the selected features into a dynamic feature matrix F(t, [f_1(t),..., f_n(t)]).

[0184] Step S21: Read the aligned data tensor A(t, f(t), [a, b, c, d, e], j) output by Step S1. Initialize the Tucker ranks (R1, R2, R3, R4, R5, R6) and the CP rank R. Apply Tucker decomposition to A to obtain the core tensor G and the factor matrices U_i. Calculate the Tucker reconstruction error E_T = ||A - G×1U_1×2U_2×3U_3×4U_4×5U_5×6U_6||_F / ||A||_F. Apply CP decomposition to A to obtain the factor matrices V_i. Calculate the CP reconstruction error E_C. Compare E_T and E_C and select the decomposition method with the smaller error. If Tucker decomposition is selected, then L = G×1U_1×2U_2×3U_3×4U_4×5U_5×6U_6; if CP decomposition is selected, then L = Σ_r=1 R v_1 r ○v_2 r ○v_3 r ○v_4 r ○v_5 r ○v_6 r , where ○ represents the outer product and r represents the index variable. Reshape L into a low-dimensional representation L(t, r, [a, b, c, d, e]).

[0185] Step S22: Read the low-dimensional representation L(t, r, [a, b, c, d, e]) obtained in Step S21. Define the set of time scales S = {s_1, s_2,..., s_K}. For each time scale s_k and each pair of sensors (i, j), calculate the multi-scale Granger causality. First, perform wavelet transform on L at scale s_k to obtain the wavelet coefficients W_i(s_k, t) and W_j(s_k, t). Construct a VAR model: W_i(s_k, t) = Σ_p=1 P a_pW_i(s_k, t - p) + Σ_p=1 P b_pW_j(s_k, t - p) + ε(t). Calculate the F statistic F_ij(s_k) = (RSS_R - RSS_U) / RSS_U * (T - 2P - 1) / P, where RSS_R and RSS_U are the residual sum of squares of the restricted and unrestricted models respectively, T is the number of samples, and P is the lag order. Calculate the multi-scale causal intensity MCI(i, j, s_k) = Σ_tw(s_k, t) * F_ij(s_k, t), where w(s_k, t) is the time-varying weight function. Organize all MCI(i, j, s_k) into a multi-scale causal adjacency matrix C(s, t, [a, b, c, d, e]).

[0186] Step S23: Read the multi-scale causal adjacency matrix C(s, t, [a, b, c, d, e]) obtained in step S22 and the dynamic feature matrix F(t, [f_1(t),..., f_n(t)]) output in step S1. For each pair of sensors (i, j) and each time point t, calculate the conditional entropy H(X_i(t)|X_j(t)) = -Σ_x_i,x_j p(x_i, x_j) log(p(x_i|x_j)), where the probabilities are estimated from F using the kernel density estimation method. Calculate the information flow IF(i, j, t) = Σ_s MCI(i, j, s, t) * H(X_i(t)|X_j(t)). Construct the time-varying information flow network G(t), where the nodes represent sensors and the edge weights are IF(i, j, t). Apply a community detection algorithm, such as the Louvain method, to G(t) to identify the dynamic community structure. Calculate the centrality metrics of each node, such as degree centrality and eigenvector centrality. Represent G(t) as a combination of an adjacency matrix and a node attribute matrix G(t, [a, b, c, d, e]). Finally, combine the low-dimensional representation L, the multi-scale causal adjacency matrix C, and the time-varying information flow network G into a fused multi-modal representation M(t, [L, C, G]).

[0187] Step S31: Read the low-dimensional representation L(t, r, [a, b, c, d, e]) in the fused multi-modal representation M(t, [L, C, G]) output in step S2. For each sensor component in L, calculate the mutual information function MI(τ) = Σ p(x(t), x(t + τ)) log(p(x(t), x(t + τ)) / (p(x(t)) p(x(t + τ)))), where the probabilities are calculated using the kernel density estimation method. Select the τ that makes MI(τ) reach the local minimum for the first time as the optimal time delay τ_opt. Estimate the optimal embedding dimension m_opt using the false prediction method. Construct the candidate embedding vector Y_m(t) = [x(t), x(t + τ_opt),..., x(t + (m - 1)τ_opt)], with m increasing from 1. For each m, use the k-nearest neighbor method to predict x(t + T) and calculate the prediction error E(m). When E(m) no longer decreases significantly, take this m value as m_opt. Use τ_opt and m_opt to construct the phase space trajectory X(t, τ_opt, m_opt) = [x(t), x(t + τ_opt),..., x(t + (m_opt - 1)τ_opt)]. Repeat this process for all sensor components to obtain the complete phase space trajectory X(t, τ, m).

[0188] Step S32: Read the phase space trajectory X(t, τ, m) obtained in step S31. Apply a sliding window to X with window size w and step size s to obtain a time series {X_i}, where i represents the window index. Construct a Vietoris-Rips complex VR_i(ε) for each X_i, with ε being the distance threshold. Calculate the k-dimensional persistent homology (k = 0, 1, 2) of VR_i(ε) to obtain the persistence diagram PD_k,i. Combine the persistence diagrams of all windows into a time-varying persistence diagram PD_k(t). Calculate the statistical features of PD_k(t), including the persistence entropy PE_k(t)=-Σ(l_j / Σl_j)log(l_j / Σl_j), where l_j is the length of the j-th persistence interval, and the Betti number curve β_k(t, ε). Define the topological complexity metric TC(t)=Σ_kw_k*(PE_k(t)+Σ_εβ_k(t, ε) / max(β_k(t, ε))), where w_k is the weight coefficient. Combine PD_k(t) and TC(t) into a topological feature representation TF(t, [PD, TC]).

[0189] Step S33: Read the phase space trajectory X(t, τ, m) obtained in step S31 and the topological feature representation TF(t, [PD, TC]) obtained in step S32. Apply the continuous wavelet transform CWT(t, s)=∫X(t')ψ*((t'-t) / s)dt' to X, where ψ is the wavelet function and s is the scale parameter. Calculate the wavelet energy spectrum WE(t, s)=|CWT(t, s)| 2 . Identify the significant peaks in WE(t, s) to obtain a set of candidate patterns {C_i(t, s)}. For each C_i(t, s), calculate its duration D_i and energy E_i. Define the pattern importance index PI_i=E_i*D_i / Σ_j(E_j*D_j). Sort the candidate patterns according to PI_i and select the top p patterns as the main dynamic patterns. For each selected pattern, extract its time-frequency feature TF_i and shape feature SF_i. Combine TF_i and SF_i with the topological feature TF of the corresponding time period to form a pattern descriptor PD_i=[TF_i, SF_i, TF]. Organize all PD_i into a pattern matrix P(t, p). Finally, combine the phase space trajectory X, the persistence diagram PD_k, and the pattern matrix P into a spatio-temporal feature representation TS(t, [X, PD, P]).

[0190] Step S41: Read the fused multi-modal representation M(t, [L, C, G]) output by step S2 and the spatio-temporal feature representation TS(t, [X, PD, P]) output by step S3. Define a set of layers Λ = {λ_1, λ_2,..., λ_K}, where each layer represents a different type of interaction or scale. For each layer λ_k, construct a node set V_k, including sensor nodes and virtual nodes generated from the dynamic patterns in TS. Construct an edge set E_k based on the similarity in L, the causality in C, and the information flow in G. Define a node attribute set A_k, including the features in L, the dynamic features in X, and the topological features in PD. Calculate the inter-layer coupling strength IC(λ_i, λ_j) = Σ_v, wE(v_i, w_j) / (|V_i| * |V_j|), where E(v_i, w_j) is the weight of the cross-layer edge. Construct an inter-layer edge set E_ij to connect nodes representing the same entity or highly related nodes in different layers. Integrate the information of all layers to form a multi-layer graph structure ML-G(t, [V, E, A]), where V = ∪V_k, E = (∪E_k) ∪ (∪E_ij), and A = ∪A_k.

[0191] Step S42: Read the multi-layer graph structure ML-G(t, [V, E, A]) constructed in step S41. Initialize the node embedding matrix Z(0) ∈ R (|V|×d) , where d is the embedding dimension. Define the intra-layer loss function L_intra = Σ_kΣ_(i, j∈V_k)||Z_i - Z_j|| 2 *A_k(i, j), where A_k is the adjacency matrix of the k-th layer. Define the inter-layer loss function L_inter = Σ_(i, j∈V, l(i)≠l(j))||Z_i - Z_j|| 2 *IC(l(i), l(j)), where l(i) represents the layer to which node i belongs. Define the attribute preservation loss function L_attr = Σ_i||Z_i - f(A_i)|| 2 , where f is the attribute transformation function. Construct the overall objective function L = α * L_intra + β * L_inter + γ * L_attr, where α, β, and γ are trade-off coefficients. Use the stochastic gradient descent method to optimize L, and the update rule is Z(t + 1) = Z(t) - η▽L, where η is the learning rate and ▽ represents the gradient. Stop the optimization when L converges or reaches the maximum number of iterations. Output the final node embedding Z(t, d).

[0192] Step S43: Read the node embedding Z(t, d) obtained in step S42 and the multi-layer graph structure ML-G(t, [V, E, A]) constructed in step S41. For each node v, calculate the local topological feature LTF(v, t). First, extract the k-hop neighborhood N_k(v) of v. Calculate the local clustering coefficient LCC(v) = 2|E(N_k(v))| / (|N_k(v)|*(|N_k(v)| - 1)). Calculate the local assortativity coefficient LAC(v) = Σ_(u∈N_k(v))|deg(v) - deg(u)| / (|N_k(v)|*deg(v)). Calculate the local page rank LPR(v), which is iteratively calculated using the PersonalRank algorithm on N_k(v). Combine these features to get LTF(v, t) = [LCC(v), LAC(v), LPR(v)]. Calculate the global topological feature GTF(v, t). Apply the spectral clustering algorithm to cluster Z(t, d) to obtain the community membership C(v) of the nodes. Calculate the centrality metrics of node v, including the eigenvector centrality EVC(v) and the betweenness centrality BC(v). Calculate the structural role SR(v) of node v, which is extracted based on the local and global features of the node using the RolX algorithm. Combine these features to get GTF(v, t) = [C(v), EVC(v), BC(v), SR(v)]. Define the anomaly score AS(v, t) = w_1*D_L(LTF(v, t), μ_L) + w_2*D_G(GTF(v, t), μ_G), where D_L and D_G are the distance functions for local and global features respectively, μ_L and μ_G are the corresponding reference distributions, and w_1 and w_2 are the weight coefficients. Combine ML-G, Z, and AS into the graph topology anomaly detection result GT(t, [ML-G, Z, AS]).

[0193] Step S51: Read the graph topology anomaly detection result GT(t, [ML-G, Z, AS]) output by step S4 and the set of key parameters P = {p_1, p_2,..., p_n} used in all previous steps. Define the detection accuracy objective function f_1(P) = 1 - AUC(ROC(AS)), where ROC is the Receiver Operating Characteristic curve and AUC is the Area Under the Curve. Define the computational efficiency objective function f_2(P) = T_compute(P) / T_max, where T_compute is the total computation time and T_max is the maximum allowed computation time. Construct the constraint set C = {c_1(P) ≤ 0, c_2(P) ≤ 0,..., c_m(P) ≤ 0}, including parameter value ranges and resource limitations. Initialize the population X = {x_1, x_2,..., x_N}, where each individual x_i represents a set of parameter configurations. For each x_i, calculate the objective function values f_1(x_i) and f_2(x_i). Use non-dominated sorting to stratify the population and obtain the non-dominated rank R(x_i). Calculate the crowding distance D(x_i) = Σ_k(f_k(x_i + 1) - f_k(x_i - 1)) / (f_k_max - f_k_min). Perform selection, crossover, and mutation operations based on R(x_i) and D(x_i) to generate a new population. Repeat the steps from initializing the population to generating a new population until the maximum number of iterations is reached or convergence occurs. Output the final non-dominated solution set NS(P_opt).

[0194] Step S52: Read the non-dominated solution set NS(P_opt) obtained in step S51 and the graph topology anomaly detection result GT(t, [ML-G, Z, AS]) output in step S4. Define the performance index PI(t) = w_1*Precision(t) + w_2*Recall(t) - w_3*FPR(t), where Precision, Recall, and FPR are the precision rate, recall rate, and false positive rate respectively, and w_1, w_2, and w_3 are weight coefficients. Initialize the Q function Q(s, a) = 0, where s is the state representing the current parameter configuration, and a is the action representing the parameter adjustment strategy. Define the state transition function T(s, a, s') = P(s'|s, a), which represents the probability of transitioning from state s to state s' after executing action a. Define the reward function R(s, a) = ΔPI(t), that is, the change in the performance index. Use the Q-learning algorithm to update the Q function: Q(s, a) ← Q(s, a) + α[R(s, a) + γmax_a'Q(s', a') - Q(s, a)], where α is the learning rate and γ is the discount factor. At each time step t, select the action a_t with an ε-greedy policy, with probability 1 - ε select max_aQ(s_t, a), and with probability ε select randomly. Execute the selected action a_t, update the parameter configuration, and obtain the new state s_t+1. Observe the reward R(s_t, a_t) and update the Q function. Based on the updated Q function, generate the time-varying optimal parameter set P_opt(t). Combine GT and P_opt(t) into the optimized anomaly detection result OD(t, [GT, P_opt]).

[0195] It should be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without conflict. To avoid unnecessary repetition, the present invention will not describe various possible combination methods separately.

Claims

1. Helium leak detection method for switchgear, characterized in that, It includes the following steps: Step S1: Obtain raw data from sensors in real time, organize the raw data into an N-dimensional raw data tensor, apply an adaptive multi-resolution decomposition algorithm to the raw data tensor to obtain a decomposed data tensor; Construct a persistence diagram based on the decomposed data tensor and calculate persistent homology, perform anomaly detection and repair to generate a cleaned data tensor; Perform non-linear manifold alignment on the cleaned data tensor to obtain an aligned data tensor, extract dynamic features from the aligned data tensor to generate a dynamic feature matrix; N is a natural number greater than 1; Step S2: Obtain the aligned data tensor and apply an adaptive tensor decomposition algorithm to it to obtain a low-dimensional representation; Construct a multi-scale causal network based on the low-dimensional representation to generate a multi-scale causal adjacency matrix; construct a time-varying information flow network using the multi-scale causal adjacency matrix and the dynamic feature matrix; construct a fused multi-modal representation based on the low-dimensional representation, the multi-scale causal adjacency matrix, and the time-varying information flow network; Step S3: Read the fused multi-modal representation, perform non-linear dynamical system reconstruction on the low-dimensional representation in the multi-modal representation to obtain a phase space trajectory; Calculate persistent homology based on the phase space trajectory to generate a persistence diagram; extract dynamic patterns from the phase space trajectory and the persistence diagram to obtain a pattern matrix; Combine the phase space trajectory, the persistence diagram, and the pattern matrix into a spatio-temporal feature representation; Step S4: Read and construct a multi-layer graph structure based on the fused multi-modal representation and the spatio-temporal feature representation, apply a dynamic graph spectral embedding algorithm to the multi-layer graph structure to obtain a low-dimensional node representation, calculate local and global topological features based on the low-dimensional node representation to construct an anomaly detection metric; combine the multi-layer graph structure, the low-dimensional node representation, and the anomaly detection metric into a graph topology anomaly detection result; Step S5: Read the graph topology anomaly detection result and construct a set of key parameters and a multi-objective optimization framework to obtain a non-dominated solution set, construct a dynamic parameter adjustment strategy based on the non-dominated solution set to generate a time-varying optimal parameter set; combine the graph topology anomaly detection result and the time-varying optimal parameter set into an optimized anomaly detection result; Step S2 specifically is: Step S21: Read the aligned data tensor and the dynamic feature matrix; initialize the decomposition rank parameter; apply Tucker decomposition to the data tensor to obtain a core tensor and factor matrices; calculate the Tucker reconstruction error; apply CP decomposition to the data tensor to obtain factor matrices; Calculate the CP reconstruction error, compare the errors of the two decomposition methods, select the method with the smaller error; reconstruct the data based on the selected decomposition method to obtain a low-dimensional representation; reshape the low-dimensional representation into a low-dimensional data tensor; Step S22: Read the low-dimensional data tensor; construct a set of time scales; calculate multi-scale Granger causality for each pair of sensor signals in the low-dimensional data tensor at each time scale; perform wavelet transform on the low-dimensional data tensor at each scale to obtain wavelet coefficients; construct a vector autoregressive model; calculate the F statistic; calculate the multi-scale causal strength; organize all the multi-scale causal strengths into a multi-scale causal adjacency matrix; Step S23: Read the multi-scale causal adjacency matrix and the dynamic feature matrix; For each pair of sensor signals in the dynamic feature matrix, calculate the conditional entropy at each time point; use the kernel density estimation method to estimate probabilities from the dynamic feature matrix; calculate the information flow; construct a time-varying information flow network with sensors as nodes and information flow as edge weights; Apply a community detection algorithm to the time-varying information flow network to identify the dynamic community structure; calculate the centrality index of each node in the time-varying information flow network; represent the time-varying information flow network as a combination of an adjacency matrix and a node attribute matrix; combine the low-dimensional data tensor, the multi-scale causal adjacency matrix, and the time-varying information flow network into a fused multi-modal representation; Step S3 is specifically as follows: Step S31: Read the low-dimensional data tensor in the fused multi-modal representation; calculate the mutual information function for each sensor component in the low-dimensional data tensor; select the time delay at which the mutual information function first reaches a local minimum as the optimal time delay; Estimate the optimal embedding dimension using the false prediction method; Construct candidate embedding vectors; for each candidate embedding dimension, use the k-nearest neighbor method to predict future values and calculate the prediction error; when the prediction error no longer decreases significantly, take this dimension as the optimal embedding dimension; Construct a phase space trajectory using the optimal time delay and the optimal embedding dimension; repeat this process for all sensor components in the low-dimensional data tensor to obtain a complete phase space trajectory; Step S32: Read the complete phase space trajectory; apply a sliding window to the phase space trajectory to obtain a set of time series; construct a Vietoris-Rips complex for each time series in the set of time series; calculate the multi-dimensional persistent homology of the complex to obtain a persistence diagram; combine the persistence diagrams of all windows into a time-varying persistence diagram; calculate the statistical features of the time-varying persistence diagram, including persistent entropy and Betti number curves; define a topological complexity metric; combine the time-varying persistence diagram and the topological complexity metric into a topological feature representation; Step S33: Read the complete phase space trajectory and the topological feature representation; Apply continuous wavelet transform to the phase space trajectory; calculate the wavelet energy spectrum; identify significant peaks in the wavelet energy spectrum to obtain a set of candidate patterns; For each candidate pattern in the set of candidate patterns, calculate its duration and energy; define a pattern importance index; rank the candidate patterns according to the pattern importance index and select the main dynamic patterns; For each selected main dynamic pattern, extract its time-frequency features and shape features; Combine the extracted features with the topological features of the corresponding time period to form a pattern descriptor; organize all pattern descriptors into a pattern matrix; combine the phase space trajectory, the time-varying persistence diagram, and the pattern matrix into a spatio-temporal feature representation; Step S4 is specifically as follows: Step S41: Read the fused multi-modal representation and spatio-temporal feature representation; Define a set of layers, where each layer represents a different interaction type or scale; For each layer in the set of layers, construct a set of nodes, including sensor nodes and virtual nodes generated from the dynamic patterns in the spatio-temporal feature representation; Construct an edge set based on the similarity in the low-dimensional data tensor, the causal relationships in the multi-scale causal adjacency matrix, and the information flow in the time-varying information flow network; Define a set of node attributes, including the features in the low-dimensional data tensor, the dynamic features in the phase space trajectory, and the topological features in the time-varying persistence diagram; Calculate the inter-layer coupling strength; Construct an inter-layer edge set to connect nodes representing the same entity or highly correlated nodes in different layers; Integrate the information of all layers to form a multi-layer graph structure; Step S42: Read the multi-layer graph structure; Initialize the node embedding matrix; Define an intra-layer loss function based on the adjacency matrix of each layer; Define an inter-layer loss function based on the inter-layer coupling strength; Define an attribute preservation loss function based on the set of node attributes; Construct an overall objective function by combining the intra-layer loss, the inter-layer loss, and the attribute preservation loss; Use the stochastic gradient descent method to optimize the overall objective function; Update the node embedding matrix until the objective function converges or reaches the maximum number of iterations; Output the final node embedding; Step S43: Read the node embedding and the multi-layer graph structure; For each node in the multi-layer graph structure, calculate the local topological features; Extract the k-hop neighborhood of the node; Calculate the local clustering coefficient; Calculate the local disassortativity coefficient; Calculate the local PageRank; Combine these features to obtain the local topological features; Calculate the global topological features; Apply the spectral clustering algorithm to the node embedding to obtain the community membership of the nodes; Calculate the centrality metrics of the nodes, including the eigenvector centrality and the betweenness centrality; Calculate the structural roles of the nodes; Combine these features to obtain the global topological features; Define an anomaly score by combining the local and global topological features; Combine the multi-layer graph structure, the node embedding, and the anomaly score into the graph topological anomaly detection result.

2. The helium leak detection method for switchgear according to claim 1, characterized in that, Step S1 is specifically as follows: Step S11: Real-time obtain partial raw data from at least two sensors; Calculate the change rate of each sensor signal based on the partial raw data to determine the adaptive sampling frequency; Resample all sensor data using the adaptive sampling frequency; And organize the resampled data into a raw data tensor; Step S12: Read the raw data tensor, apply the adaptive multi-resolution decomposition algorithm to each sensor signal in the tensor, and perform multi-scale decomposition on the signal using wavelet transform to obtain an initial decomposition set; Apply empirical mode decomposition to the initial decomposition set to obtain a multi-scale component set; Calculate the information entropy and computational complexity of each decomposition level; Construct and optimize the objective function to select the optimal decomposition level; Based on the optimal level, select the corresponding components from the multi-scale component set; Combine the processed signals to generate a decomposed data tensor; Step S13: Read the decomposed data tensor, construct time-delay embedding vectors for each decomposition level of each sensor signal in the decomposed data tensor; construct a complex based on the embedding vectors, calculate the persistence data, and obtain the persistence diagram; calculate the anomaly metric, compare the anomaly metric with a preset threshold, and mark the anomaly data points; Repair the anomaly data points using the local linear regression method; reorganize the repaired data to generate the cleaned data tensor; Step S14: Read the cleaned data tensor and embed each decomposition level of each sensor signal into a high-dimensional manifold using a dimensionality reduction algorithm; Calculate the geodesic distance between the high-dimensional manifolds; set the sensor importance weights, construct the objective function, and use an optimization algorithm to minimize the objective function to obtain the optimal alignment parameters; based on the optimal alignment parameters, transform the data to obtain the aligned data tensor; Step S15: Read the aligned data tensor and apply the time-frequency analysis method to each decomposition level of each sensor signal in the data tensor; Calculate the statistical moments of the time-frequency representation; extract the geometric features; Form the feature set; calculate the information entropy of each feature and the mutual information between features; and construct the feature importance scores, sort and select the features based on the importance scores; organize the selected features into a dynamic feature matrix.

3. The helium leak detection method for switchgear according to claim 2, characterized in that, Step S5 specifically is: Step S51: Read the graph topology anomaly detection results and the set of key parameters used in all previous steps; define the detection accuracy objective function, the area under the receiver operating characteristic curve based on the anomaly scores; define the computational efficiency objective function, based on the total computational time and the maximum allowed computational time; construct a set of constraints, including the parameter value ranges and resource limitations; initialize the population, where each individual represents a set of parameter configurations; for each individual in the population, calculate the objective function values; use non-dominated sorting to stratify the population to obtain the non-dominated ranks; calculate the crowding distance; perform selection, crossover, and mutation operations based on the non-dominated ranks and the crowding distance to generate a new population; Until the maximum number of iterations is reached or convergence occurs; output the final non-dominated solution set; Step S52: Read the non-dominated solution set and the graph topology anomaly detection results; define the performance metrics, combining precision, recall, and false positive rate; initialize the Q function, where the state represents the current parameter configuration and the action represents the parameter adjustment strategy; Define the state transition function, representing the probability of transitioning from one state to another after performing an action; define the reward function, based on the change in the performance metrics; Use the Q-learning algorithm to update the Q function; at each time step, select an action with an ε-greedy strategy; execute the selected action, update the parameter configuration, and obtain a new state; Observe the reward and update the Q function; based on the updated Q function, generate a time-varying optimal parameter set; combine the graph topology anomaly detection results and the time-varying optimal parameter set into the optimized anomaly detection results.

4. The helium leak detection method for switchgear according to claim 3, characterized in that In the said step S12, specifically: Step S121: Read the original data tensor; for each sensor signal in the data tensor, apply the sliding window technique; within each window, use the improved box-counting method to estimate the local fractal dimension; calculate the fractal spectrum of the signal to obtain the variation of the fractal dimension over time; store the fractal dimension time series as a fractal feature matrix; Step S122: Read the fractal feature matrix; Use the dynamic programming algorithm to find the optimal segmentation points on the fractal dimension time series; each segmentation corresponds to a characteristic scale; Calculate the average fractal dimension of each segment; adaptively select the decomposition basis function family according to the average fractal dimension; store the selected basis function family and the corresponding scale information as a scale selection matrix; Step S123: Read the original data tensor and the scale selection matrix; for each sensor signal in the data tensor, decompose it at each adaptively selected scale; use the basis function family corresponding to this scale for signal decomposition; calculate the decomposition coefficients at each scale; combine the decomposition coefficients of all scales into a multi-scale decomposition tensor; Step S124: Read the multi-scale decomposition tensor; for the coefficients of each scale in the decomposition tensor, apply kernel principal component analysis to extract non-linear features; Use the radial basis function kernel for non-linear mapping; select the principal components that can explain 90% of the variance; store the extracted non-linear features as a feature tensor; Step S125: Read the feature tensor and the original data tensor; use the particle swarm optimization algorithm to find the optimal reconstruction weights; the objective function is the weighted sum of the reconstruction error and the information entropy; for each time point, based on the current optimal weights, reconstruct the features in the feature tensor into a signal; combine the reconstructed signals into a reconstructed data tensor; Step S126: Read the reconstructed data tensor and the original data tensor; calculate the residual between the reconstructed data tensor and the original data tensor; Use an adaptive Kalman filter to process the residual; The parameters of the filter are dynamically adjusted according to the statistical characteristics of the residual; Add the filtered residual to the reconstructed data tensor to obtain a refined reconstructed data tensor; Step S127: Read the refined reconstructed data tensor and the original data tensor; Calculate multiple evaluation metrics, including the root mean square error, the structural similarity index, and the information retention rate; Use the fuzzy comprehensive evaluation method to synthesize multiple metrics into a single quality score; if the quality score is lower than the preset threshold, return to Step S122 for parameter adjustment and re-decomposition; Step S128: Read the refined reconstructed data tensor, the multi-scale decomposition tensor, and the feature tensor; Align the size and structure of the refined reconstructed data tensor with those of the original data tensor; Combine the multi-scale decomposition tensor and the feature tensor to generate an enhanced feature tensor; Merge the refined reconstructed data tensor and the enhanced feature tensor to form the final decomposition data tensor.

5. The helium leak detection method for switchgear as described in claim 3, characterized in that, Step S14 specifically is: Step S141: Read the cleaned data tensor; for each decomposition level of each sensor signal in the data tensor, apply the t-SNE algorithm for initial dimensionality reduction; use the cosine similarity as the distance metric; Generate an initial low-dimensional embedding matrix; Step S142: Read the initial low-dimensional embedding matrix; Use the dynamic time warping algorithm to calculate the similarity between time series; Construct an adaptive Gaussian kernel function based on the DTW distance; Calculate the kernel matrix; Store the kernel matrix as a similarity matrix; Step S143: Read the similarity matrix and the initial low-dimensional embedding matrix; Construct a graph Laplacian matrix; Define a manifold consistency objective function, combining local preservation and global alignment; Use the alternating direction multiplier method to optimize the objective function; Update the low-dimensional embedding matrix; Store the optimized low-dimensional embedding matrix as an aligned embedding matrix; Step S144: Read the aligned embedding matrix; Use a recurrent neural network (RNN) to learn a time-varying mapping function; The input of the RNN is the embedding vectors at adjacent time steps, and the output is the predicted embedding at the next time step; Minimize the prediction error and the manifold consistency loss; Store the learned RNN model parameters as a time-varying mapping model; Step S145: Read the time-varying mapping model and the aligned embedding matrix; For missing or future time point data, use the learned RNN model for interpolation or extrapolation; Generate a complete time series embedding; Combine the interpolation and extrapolation results with the original aligned embedding matrix to form an extended embedding matrix; Step S146: Read the extended embedding matrix; Perform multi-scale decomposition of the embedding using wavelet transform; Apply the local linear embedding algorithm at each scale; Combine the embedding results at different scales through weighted summation; The weights are dynamically adjusted using an adaptive fuzzy inference system; Generate a fused multi-scale embedding matrix; Step S147: Read the fused multi-scale embedding matrix; Construct persistent homology features; Use persistent homology information to guide manifold deformation; Minimize the Wasserstein distance to preserve the topological structure; Apply the discrete exterior differential operator for smoothing; Generate a topology-preserving embedding matrix; Step S148: Read the topology-preserving embedding matrix and the original data tensor; Calculate the geodesic distance preservation rate before and after manifold alignment; Evaluate the preservation degree of the local neighborhood structure; Use the mutual information criterion to quantify the alignment degree between different sensor signals; Combine multiple indicators to generate an alignment quality score; Step S149: Read the topology-preserving embedding matrix, the alignment quality score, and the original data tensor; Adaptive adjust the embedding weights based on the alignment quality score; Map the weighted embedding back to the original data space; Fuse it with the original data tensor to generate the final aligned data tensor.

6. The helium leak detection method for switchgear according to claim 3, characterized in that, Step S21 is specifically as follows: Step S211: Read the aligned data tensor and the dynamic feature matrix; Normalize the data tensor; Calculate the modal correlation matrix of the tensor; Use the spectral clustering algorithm to group the modes; Generate a modal grouping information matrix; Step S212: Read the modal grouping information matrix; For each modal group, call a predetermined kernel function; Automatically select the kernel function hyperparameters using Gaussian process regression; Generate a kernel function parameter matrix; Apply the kernel function to the original data tensor to generate a kernelized data tensor; Step S213: Read the kernelized data tensor; Use the sliding window technique to apply tensor singular value decomposition to each time window; Calculate the singular value decay curve; Use the Bayesian information criterion to estimate the optimal rank of each window; Use a long short-term memory network to predict the rank of future time windows; Generate a dynamic rank estimation sequence; Step S214: Read the kernelized data tensor and the dynamic rank estimation sequence; for each modality group, apply different tensor decomposition methods: for the dense modality group, use Tucker decomposition; for the sparse modality group, use CP decomposition; for the mixed modality group, use the tensor train selection algorithm; combine the dynamic rank information and perform the decomposition operation; Generate a set of decomposed factor matrices and a core tensor; Step S215: Read the set of decomposed factor matrices; apply structured sparse regularization to each factor matrix; use the proximal gradient descent algorithm to optimize the regularization objective function; introduce a temporal smoothing constraint to ensure the temporal continuity of the factors; generate a set of regularized factor matrices; Step S216: Read the set of regularized factor matrices and the core tensor; call the attention mechanism-based adaptive fusion network; Use reinforcement learning to train the fusion strategy, and the reward function combines the reconstruction error and the information retention rate; generate an optimal fusion weight matrix; Step S217: Read the fusion weight matrix and the newly incoming real-time data; Adopt an incremental update rule based on the stochastic approximation algorithm; perform online updates on the factor matrices and the core tensor; use exponential moving average to maintain long-term statistical information; Generate an updated decomposition result; Step S218: Read the updated decomposition result and the original data tensor; calculate the reconstruction error tensor; Perform principal component analysis on the error tensor to extract the main error patterns; Call the pre-built error predictor based on the wavelet neural network; Generate an error compensation model; Step S219: Read the updated decomposition result, the error compensation model and the original data tensor; Reconstruct the data tensor based on the decomposition result to obtain a low-dimensional representation.

7. A helium leak detection system for a switchgear cabinet, characterized in that, Including: At least one processor; And, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the helium leak detection method for switchgear according to any one of claims 1 to 6.

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