A single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis, and related electronic devices and storage media.

Abstract

This invention discloses a single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis, along with an electronic device and storage medium. The central server calculates the independent local covariance matrix for each fault category and the pooled covariance matrix shared by all categories based on global statistics for each data category. These are then weighted and smoothly fused to generate a regularized covariance matrix. A global regularized discriminant analysis classifier is constructed based on the regularized covariance matrix and the category means extracted from the global statistics. When the central server receives new transformer data to be tested, it uses the backpropagation-free global regularized discriminant analysis classifier to calculate the posterior discriminant score belonging to each fault category and classifies it to the category with the highest score for transformer fault diagnosis. This invention aims to solve the performance-efficiency trade-off problem inherent in existing federated learning methods when processing transformer fault datasets with heterogeneous labels.

Description

Technical Field

[0001] This invention belongs to the field of distributed machine learning and fault diagnosis, specifically relating to a federated learning fault diagnosis method for efficiently and collaboratively training machine learning models while protecting data privacy, and in particular a method that can build a high-performance global classification model on heterogeneous data with only a single round of communication. Background Technology

[0002] Power transformers are the core hub of the power grid system, and their stable operation is directly related to the safety and reliability of the power system. Traditional transformer fault diagnosis (such as DGA combined with graphing methods) relies on expert experience and is limited by communication efficiency and fault complexity, making it difficult to achieve high-precision automated diagnosis. With the development of smart grids, data-driven models based on deep learning have shown great potential in achieving accurate fault classification by integrating multi-source sensor information such as DGA, partial discharge, and vibration. However, this monitoring data is usually scattered across different substations or power dispatch centers. Centralized methods for processing data not only incur high transmission and storage costs but also pose serious data privacy and sovereignty security risks, hindering data sharing between different entities. Federated learning provides an ideal distributed solution for this. It allows participating parties (such as substations) to train models locally, uploading only intermediate parameters (such as gradients or weights), without sharing raw data, thereby collaboratively building a high-performance global diagnostic model while protecting privacy. However, existing federated learning methods (such as the classic FedAvg) mostly use multi-round iterative communication to optimize deep network weights, which results in high communication overhead and significant latency in edge computing environments with poor network conditions. For tasks with strong statistical classification characteristics, such as fault diagnosis, directly constructing a statistical classifier may be more efficient. This invention proposes a single-round federated learning method based on Regularized Discriminant Analysis (RDA). This method utilizes a pre-trained deep model to extract features locally at each substation, and then calculates sufficient statistics for the features (such as the mean, count, and covariance components for fault category classification). The server only needs to aggregate these statistics once to directly construct a global RDA discriminant model, eliminating the need for multiple iterations. In summary, the method of this invention can efficiently and quickly construct a high-precision global diagnostic model, greatly reducing the dependence on communication bandwidth and effectively overcoming the communication bottleneck of traditional federated learning, thus showing broad application prospects in the field of transformer fault diagnosis. Summary of the Invention

[0003] To address the challenges of federated learning posed by communication pressures and distributional differences in transformer fault diagnosis, this invention aims to resolve the performance-efficiency trade-offs inherent in existing federated learning methods when processing heterogeneous transformer fault datasets. It provides a single-round federated learning method based on Regularized Discriminant Analysis (RDA) for transformer fault diagnosis, along with associated electronic devices and storage media.

[0004] A single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis includes the following steps:

[0005] Step 1: Each client connects to a transformer, and each client obtains the one-dimensional transformer fault data of its own transformer and converts it into two-dimensional RGB image fault data;

[0006] Step 2: Each client uses a feature extractor to map the two-dimensional RGB image fault data into feature vectors. After calculating sufficient statistics for each fault category according to the single round of communication requirements, the client uploads the data to the central server.

[0007] Step 3: The central server receives and aggregates all the sufficient statistics for each fault category uploaded by all clients at once, and calculates and reconstructs the global statistics for each data category;

[0008] Step 4: Based on the global statistics of each data category, the central server calculates the independent local covariance matrix for each fault category and the pooled covariance matrix shared by all categories. The local covariance matrix for each fault category and the pooled covariance matrix shared by all categories are weighted and smoothed by a preset regularization hyperparameter to generate a regularized covariance matrix.

[0009] Step 5: The central server constructs a global regularized discriminant analysis classifier based on the regularized covariance matrix and the class mean extracted from the global statistics. When the central server receives new transformer data to be tested, it uses the global regularized discriminant analysis classifier trained without backpropagation to calculate the posterior discriminant score belonging to each fault category and classifies it into the category with the highest score for transformer fault diagnosis.

[0010] In step 1, the one-dimensional transformer fault data includes data on five gases: CH4, H2, C2H6, C2H2, and C2H4. To fully explore the multidimensional physical meaning of the dissolved gas analysis (DGA) data in transformer oil and overcome the problems of large ranges in the absolute values ​​of different gas concentrations and single feature dimensions, the client first converts the original one-dimensional transformer fault data into a multi-channel feature tensor before inputting the data into the pre-trained feature extractor. The specific data preprocessing process is as follows:

[0011] First, obtain the concentration vectors of five characteristic gases for a single transformer monitoring sample: These correspond to hydrogen, methane, ethane, ethylene, and acetylene, respectively. Therefore, a feature tensor is constructed, which contains three feature channels:

[0012] (1) First channel (R channel) – Relative proportion feature matrix:

[0013] Physical meaning: Used to detect which of two characteristic gases is dominant. This design aligns with the core idea of ​​the IEC three-ratio method in transformer fault diagnosis. Mapping formula:

[0014] Using this formula, if the characteristic gas If the concentrations are equal, the matrix element values ​​approach 1; if the concentrations are equal, the values ​​approach 0.5. This relative proportion characteristic matrix is ​​a variant of a symmetric matrix, satisfying... Furthermore, each element is naturally normalized to the range [0, 1], where, For a preset very small positive number (e.g., 10), -7 This is used to prevent the denominator from being zero and to ensure the numerical stability of the relative proportion feature matrix calculation.

[0015] (2) Second channel (G channel) – Log-absolute difference matrix:

[0016] Physical meaning: Used to measure the absolute range between different gas concentrations. When a transformer fault occurs, certain trace gases (such as...) It may be only a few microliters per liter, while the main characteristic gases (such as...) The range can be as high as several thousand microliters per liter. Direct subtraction would obscure the crucial changes in trace gases; therefore, this method employs the natural logarithm for smoothing, preserving minute fluctuations while overcoming extremely large ranges. Mapping formula:

[0017]

[0018] After calculating the entire initial difference matrix Then, use the maximum value in the matrix. Perform a global normalization operation to map it to the interval [0, 1], and obtain the final result. Channel matrix:

[0019]

[0020] (3) Third channel (B channel) - Associated coexistence feature matrix:

[0021] Physical meaning: Used to measure the "co-occurrence surge intensity" of any two gases. For example, in transformer overheating faults, it is usually accompanied by... and Simultaneously, it surged. Mapping formula:

[0022]

[0023] Among them, the denominator term This represents the maximum concentration of these five gases in the current sample. Using the square of the maximum value as a penalty benchmark, the coexistence feature matrix is ​​naturally normalized globally to the range [0, 1]. Finally, the relative proportion feature matrix calculated above is... Log-absolute difference matrix and the associated coexistence feature matrix The features are stitched together according to spatial dimensions to generate the final multi-channel three-dimensional feature tensor.

[0024] The two-dimensional RGB image fault data includes: data of the log-absolute difference matrix, data of the log-absolute difference matrix, and data of the coexistence feature matrix.

[0025] In step 2, there are several clients, each with the same neural network model structure. The model is a ResNet18 pre-trained on ImageNet, which is used as a feature extractor to extract the feature vectors before entering the final fully connected layer. Then, the number of samples in each category of the local dataset, the sum of the category features, and the sum of the outer products of the category features are calculated and uploaded. The specific calculation process of the client includes:

[0026] (1) Number of local samples :

[0027]

[0028] (2) Sum of category features

[0029]

[0030] (3) Sum of cross-products

[0031]

[0032] in, Indicates the first Among the clients belonging to the first The local sample dataset of the class (the number of samples corresponding to it is denoted as ). )

[0033] In step 2, after receiving the statistics from each client, the server aggregates the statistics from each client into a global statistic. The server-side calculation process specifically includes:

[0034] (1) Global sample size :

[0035]

[0036] in Indicates the first Client Data volume of class samples

[0037] (2) Sum of global category features :

[0038]

[0039] in This represents the sum of the feature vectors obtained by the feature extractor for all samples belonging to category j in the i-th client.

[0040] (3) Sum of global outer products :

[0041]

[0042] In step 3, sufficient statistics for each fault category include the number of samples, the first moment of the features, and the sum of the outer products of the features.

[0043] After aggregating global statistics, the central server calculates an independent covariance matrix for each data category and a pooled covariance matrix shared by all data categories. It then uses preset regularization hyperparameters to weight and fuse these independent and pooled covariance matrices, generating a final regularized covariance matrix for each data category.

[0044] For the The mean of the class features of each class is calculated by dividing the sum of its class features by the total number of samples. The formula for calculating the prototype of a class is:

[0045]

[0046] in For the first The sum of the categorical features of each class. For the first The total number of samples in each class.

[0047] The formula for calculating the covariance matrix is:

[0048]

[0049] in For the first The sum of the global outer products of all classes.

[0050] The formula for calculating the pooling covariance matrix is:

[0051]

[0052] in, This represents the total number of global samples across all fault categories. ,and This represents the total number of transformer fault categories.

[0053] In step 4, the central server calculates the independent local covariance matrix for each fault category based on the global statistics for each data category, specifically including:

[0054] Calculate the product of the first-order moment vector of the characteristic features and the transpose of the first-order moment vector of the characteristic features in the sufficient statistics of each fault category to generate the mean outer product matrix.

[0055] The sample size in the sufficient statistics for each fault category is multiplied by the mean outer product matrix to generate the mean offset matrix.

[0056] Calculate the difference matrix between the sum of the feature outer products and the mean offset matrix;

[0057] Multiplying the difference matrix by a scaling factor yields a local covariance matrix independent of each fault category.

[0058] The central server calculates a pooled covariance matrix shared by all categories based on global statistics for each data category, specifically including:

[0059] Based on the global statistics for each data category, obtain the total number of global samples and the total number of fault categories for all fault categories;

[0060] For each fault category, the number of samples is reduced by one to obtain the local degrees of freedom for that fault category;

[0061] Multiply the local covariance matrix that is independent of the fault category by the local degrees of freedom to generate the weighted local covariance matrix of the fault category;

[0062] The weighted local covariance matrices of all fault categories are summed to generate an aggregated covariance matrix;

[0063] Calculate the difference between the total number of global samples and the total number of fault categories to obtain the global degrees of freedom, and take the reciprocal of the global degrees of freedom as the global scaling factor;

[0064] Multiplying the aggregated covariance matrix by the global scaling factor yields a pooled covariance matrix shared by all data categories.

[0065] The generated regularized covariance matrix is ​​utilized on the server side, specifically including:

[0066] (a) Based on the set hyperparameters, the server performs a certain operation for each category. Construct the final RDA covariance matrix

[0067]

[0068] in It is a preset regularization hyperparameter that takes values ​​in the range [0,1].

[0069] (b) Classification discriminant function

[0070] For a given new sample x, the RDA classifier will classify each class... Calculate a discriminant function; this score corresponds to the category to which the sample belongs. The posterior probability is proportional to the logarithm of the probability. The formula for its calculation is:

[0071] (c) Final classification criteria

[0072] The classifier assigns new samples to the discriminant function. In the largest category

[0073]

[0074] In step 5, the central server constructs a global regularized discriminant analysis classifier based on the regularized covariance matrix and the class means extracted from the global statistics. Specifically, this includes:

[0075] Calculate the inverse of the regularized covariance matrix and the logarithm of its determinant;

[0076] The inverse matrix of the regularized covariance matrix, the logarithm of the determinant, and the class mean extracted from the global statistics are solidified into classifier parameters in analytical form, and a global regularized discriminant analysis classifier is constructed.

[0077] An electronic device includes a processor and a memory, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis.

[0078] A computer-readable storage medium having a computer program stored thereon, characterized in that, when the program is executed by a processor, it implements the single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis.

[0079] Compared with the prior art, the present invention has the following advantages:

[0080] The single-round federated learning method based on regularized discriminant analysis of this invention demonstrates excellent robustness and flexibility in scenarios with high communication pressure and non-independent identically distributed (IID) data. It requires only one client-to-server communication to complete the global model construction, significantly reducing communication overhead and training time, making it suitable for large-scale, network-constrained scenarios. By aggregating global statistical information, this method naturally eliminates the impact of uneven client data distribution (non-IID), and the constructed global model is insensitive to data heterogeneity, exhibiting higher classification accuracy and generalization ability compared to similar methods. Furthermore, by introducing RDA and hyperparameters… This method finds a better balance between model bias and variance. Compared to LDA, which makes overly strong assumptions, and QDA, which is prone to overfitting, this invention achieves higher classification accuracy on a wider range of datasets (especially complex datasets with many categories). Furthermore, this method uses a training-free server-side architecture, rather than the time-consuming gradient descent methods of traditional approaches, which reduces the computational burden on the server. In terms of privacy protection, the entire process only exchanges feature statistics without individual raw information; there is no communication between clients, effectively protecting the privacy of each client's raw data. Attached Figure Description

[0081] Figure 1 This is a mechanism framework for single-round federated learning based on regularized discriminant analysis.

[0082] Figure 2 This is a diagram of the original fault sample data of the transformer.

[0083] Figure 3 This illustrates the relationship between the accuracy of this algorithm and the heterogeneity of the sample data.

[0084] Figure 4 The feature map of client sample category distribution (Dirichlet distribution parameter β=1.0).

[0085] Figure 5 The feature map of the client sample category distribution (Dirichlet distribution parameter β=2.0).

[0086] Figure 6 The feature map of the client sample category distribution (Dirichlet distribution parameter β=3.0).

[0087] Figure 7 The feature map of the client sample category distribution (Dirichlet distribution parameter β=4.0). Detailed Implementation

[0088] To make the objectives, design concepts, and technical solutions of the embodiments of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings.

[0089] like Figure 1 As shown, a single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis is presented. The method includes the following steps:

[0090] Step 1: Each client obtains the one-dimensional transformer fault data of its respective node and converts it into two-dimensional RGB image fault data through a multi-channel mapping based on physical meaning;

[0091] Step 2: Each client uses a feature extractor to map the two-dimensional RGB image fault data into feature vectors. After calculating sufficient statistics for each fault category according to the single round of communication requirements, the client uploads the data to the central server.

[0092] Step 3: The central server receives and aggregates all the sufficient statistics for each fault category uploaded by all clients at once, and calculates and reconstructs the global statistics for each data category;

[0093] Step 4: Based on the global statistics of each data category, the central server calculates the independent local covariance matrix for each fault category and the pooled covariance matrix shared by all categories. The local covariance matrix for each fault category and the pooled covariance matrix shared by all categories are weighted and smoothed by a preset regularization hyperparameter to generate a regularized covariance matrix.

[0094] Step 5: The central server constructs a global regularized discriminant analysis classifier that does not require backpropagation training based on the regularized covariance matrix and the class mean extracted from the global statistics. When the central server receives new transformer data to be tested, it uses the global regularized discriminant analysis classifier that does not require backpropagation training to calculate the posterior discriminant score belonging to each fault category and classifies it into the category with the highest score for transformer fault diagnosis.

[0095] In step 1, within the federated learning framework, there are *m* clients, each possessing its own private dataset. These datasets are non-independent and identically distributed, potentially exhibiting issues such as small data volume, high noise levels, and diverse attributes. These local datasets are sampled from M different distributions and have varying sizes. The goal of federated learning is to train a global model *w*, which optimizes the following loss function across all clients:

[0096]

[0097] in It is based on the local dataset of the i-th client. Calculated empirical risk target, It is an empirical risk target calculated based on a local dataset. Indicates from The sample, The model parameters are: At that time, for a single data sample The calculated loss value (e.g., the value obtained from the cross-entropy loss function). In contrast, the goal of personalized federated learning (pFL) is to personalize the global model using labeled data from each client to better adapt to local data distributions:

[0098]

[0099] In step 1, to fully explore the multidimensional physical meaning of dissolved gas analysis (DGA) data in transformer oil and overcome the problems of large ranges in the absolute values ​​of different gas concentrations and single feature dimensions, the client first transforms the original one-dimensional transformer fault data into a multi-channel three-dimensional feature tensor before inputting the data into the pre-trained feature extractor. The specific data preprocessing process is as follows:

[0100] First, obtain the concentration vectors of five characteristic gases for a single transformer monitoring sample: These correspond to hydrogen, methane, ethane, ethylene, and acetylene, respectively. From this, a tensor is constructed containing three characteristic channels:

[0101] (1) First Channel (R Channel) – Relative Proportional Feature Matrix: Used to capture which of two characteristic gases is dominant, aligning with the core idea of ​​the IEC three-ratio method in transformer fault diagnosis. The mapping formula is:

[0102]

[0103] Using this formula, if the characteristic gas If the concentrations are equal, the matrix element values ​​approach 1; if the concentrations are equal, the values ​​approach 0.5. This relative proportion characteristic matrix is ​​a variant of a symmetric matrix, satisfying... Furthermore, each element is naturally normalized to the range [0, 1].

[0104] (2) Second channel (G channel) – Log-absolute difference matrix: used to measure the absolute span between different gas concentrations. Due to certain trace gases (such as...) The range might be only a few microliters per liter, while the main characteristic gas could be as high as several thousand microliters per liter. This method uses the natural logarithm for smoothing, which overcomes the large range while preserving the small fluctuation characteristics. The initial mapping formula is:

[0105]

[0106] After calculating the entire initial difference matrix Then, use the maximum value in the matrix. Perform a global normalization operation to map it to the interval [0, 1], resulting in the final G-channel matrix:

[0107]

[0108] (3) Third Channel (B Channel) – Co-occurrence Feature Matrix: Used to measure the “co-occurrence surge intensity” of any two gases. The mapping formula is:

[0109]

[0110] Among them, the denominator term This represents the maximum concentration of the five gases in the current sample. Using the square of the maximum value as a penalty benchmark, the coexistence feature matrix is ​​naturally normalized globally to the range [0,1]. The relative proportion feature matrix R, the log-absolute difference matrix G, and the coexistence feature matrix B obtained above are concatenated according to their spatial dimensions to generate the final multi-channel three-dimensional feature tensor.

[0111] In step 2, the neural network model structure is identical for all clients in this method. The model is a ResNet18 pre-trained on ImageNet, which is used as a feature extractor to extract the feature vectors before entering the final fully connected layer. Then, the number of samples in each category of the local dataset, the sum of category features, and the sum of the outer products of category features are calculated and uploaded. Specifically, this includes:

[0112] (1) Number of local samples :

[0113]

[0114] Let be the number of samples of class i in the j-th client.

[0115] (2) Sum of category features :

[0116]

[0117] (3) Sum of cross-products :

[0118]

[0119] i represents the i-th client out of M clients, and j represents the j-th category in a total of k clients. This represents the number of samples of class j in the i-th client. The meaning is the feature vector extracted after inputting the data sample x into the pre-trained ResNet18 feature extractor.

[0120] In step 3, after receiving the statistics from the client, the server calculates the global statistics, which include the global sample count for each category, the sum of global category features, and the sum of global outer products. Specifically, this includes:

[0121] (1) Global sample size:

[0122]

[0123] in This represents the amount of data for the i-th client sample of class j.

[0124] (2) Sum of global category features:

[0125]

[0126] In fact, it represents the sum of the feature vectors obtained by the feature extractor for all samples belonging to category j in the i-th client.

[0127] (3) Sum of global outer products:

[0128]

[0129] In step 4, after aggregating the global statistics, the central server calculates an independent covariance matrix for each data category and a pooled covariance matrix shared by all data categories. It then uses preset regularization hyperparameters to weight and fuse the independent and pooled covariance matrices, generating a final regularized covariance matrix for each data category.

[0130] For the The prototype is the mean of the categorical features of each class, calculated by dividing the sum of its categorical features by the total number of samples. The formula for calculating the prototype of a class is:

[0131]

[0132] in The sum of the category features of the j-th class. Let be the total number of samples in the j-th class.

[0133] The formula for calculating the covariance matrix is:

[0134]

[0135] in It represents the sum of the global outer products of the j-th class.

[0136] The formula for calculating the pooling covariance matrix is ​​as follows:

[0137]

[0138] In step 5, after calculating the pooling covariance matrix and the covariance matrix of each class, the server will construct the RDA covariance matrix and finally use the constructed classifier for classification.

[0139] (1) Based on the set hyperparameters, the server constructs the final RDA covariance matrix for each category j.

[0140]

[0141] in This is a preset regularization hyperparameter with values ​​in the range [0,1]. It should be lowered when the amount of data for certain categories after federated aggregation is small. To increase stability; when the amount of data for all categories is very sufficient, the value can be increased. In pursuit of higher precision.

[0142] Classification discriminant function:

[0143] In step 5, for a given new sample x, the RDA classifier will classify each class... Calculate a discriminant function; this score corresponds to the category to which the sample belongs. The posterior probability is proportional to the logarithm of the probability. The formula for its calculation is:

[0144]

[0145] The first part of the discriminant function To use the covariance matrix specific to class j To measure the sample To category mean Statistical distance, Part 2 It is a shape penalty term that penalizes overly dispersed categories by using the determinant of the covariance matrix. (Part Three) Prior probabilities provide a base score bonus for the more common categories in the dataset. When classifying the test set data, the model calculates a prior probability for each category. Score. The final classifier will categorize new samples into the discriminant function. In the largest category.

[0146]

[0147] This invention employs a regularized discriminant analysis federated learning method based on statistical information, illustrating its effectiveness in transformer fault diagnosis through examples. Experiments demonstrate the performance of this method. The original transformer fault data sample is shown below. Figure 2 As shown, the dataset contains 740 "normal" sample points and 1581 "fault" sample points (including 309 "high-energy discharge" sample points, 305 "low-energy discharge" sample points, 158 "partial discharge" sample points, 118 "low-temperature overheating" sample points, 133 "medium-temperature overheating" sample points, and 558 "high-temperature overheating" sample points). With increasing data heterogeneity (such as...), Figure 3 As shown in the figure, the accuracy of this algorithm remains consistently good. It is worth noting that this algorithm, due to the superiority of constructing a classifier based on statistical information, exhibits excellent performance in scenarios with heterogeneous data.

[0148] In the experimental simulation verification stage of this invention, in order to realistically simulate the "non-independent identically distributed (Non-IID)" characteristic of transformer edge monitoring equipment in the actual power grid environment, that is, the transformer fault types and quantities collected from different substations vary greatly (data heterogeneity), this method uses the Dirichlet Distribution to partition the above-mentioned dissolved gas dataset of oil-immersed transformers into client-side segments (e.g., ...). Figure 4 (As shown in Figures 5, 6, and 7). The Dirichlet distribution is a set of continuous multivariate probability distributions, often used as the conjugate prior of a multivariate distribution in probability and statistics. In the data partitioning strategy of federated learning, it is assumed that the global dataset has K data categories and there are M clients participating in the computation. For any client i, the distribution vector of the proportion of each category of data in its assigned local dataset is... Obtain the parameter as The sampling formula for the Dirichlet distribution is expressed as: in, This represents the prior probability distribution of the global category. Concentration parameters are used to control the degree of data heterogeneity. In a federated collaborative scenario for transformer fault diagnosis, the concentration parameter... The physical meaning of this data and its specific impact on data partitioning are as follows: Strong data heterogeneity (Non-IID): When the... When the value of (e.g., approaching 0) is high, the sampling results of the distribution vector will become extremely sparse. This means that specific transformer fault data (such as "high-energy discharge") will be concentrated and distributed to a very small number of clients, while most clients may only have 1 or 2 status data locally (e.g., only "normal" and "low temperature overheating"). This highly replicates the "long-tail distribution" island phenomenon in real power grids where some substations operate well year-round and rarely experience specific serious faults. Data Identical Distribution (IID): When the value of is increased... When the value of is taken to be close to infinity, the proportion of different fault data allocated to each client will tend to be uniform, that is, the data label distribution of each client will be infinitely close to the global real data distribution.

[0149] By introducing and adjusting the concentration parameter of the Dirichlet distribution This method can quantitatively control and reproduce the degree of data heterogeneity among federated learning clients. Combined with... Figure 3 Simulation results show that when the Dirichlet distribution parameter decreases, i.e., when data heterogeneity increases, existing conventional federated methods often lead to global model collapse due to local model divergence. However, this invention, relying on a regularized discriminator built based on statistical information, maintains extremely high accuracy even in highly heterogeneous scenarios, fully demonstrating the algorithm's superior robustness and effectiveness in dealing with heterogeneous transformer tag data.

[0150] like Figure 3 As shown, the horizontal axis represents the Dirichlet distribution parameter β, and the vertical axis represents the accuracy. When the Dirichlet parameter β decreases, indicating increasing data heterogeneity, the robustness of the algorithm is fully demonstrated. Particularly when β = 1, exhibiting strong heterogeneity, the algorithm's accuracy remains high. This result indicates that the regularized discriminator constructed based on statistical information helps the model combat data heterogeneity. Furthermore, the federated learning method based on a regularized discriminator constructed from statistical information proposed in this invention can effectively address the communication efficiency requirements and data heterogeneity issues in transformer fault diagnosis scenarios, exhibiting significant advantages in both model accuracy and communication efficiency. Experimental verification on a dissolved gas fault dataset of oil-immersed transformers demonstrates the method's excellent performance in diverse data environments, validating its broad application potential and high efficiency.

Claims

1. A single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis, characterized in that, Includes the following steps: Step 1: Each client connects to a transformer, and each client obtains the one-dimensional transformer fault data of its own transformer and converts it into two-dimensional RGB image fault data; Step 2: Each client uses a feature extractor to map the two-dimensional RGB image fault data into feature vectors. After calculating sufficient statistics for each fault category according to the single round of communication requirements, the client uploads the data to the central server. Step 3: The central server receives and aggregates all the sufficient statistics for each fault category uploaded by all clients at once, and calculates and reconstructs the global statistics for each data category; Step 4: Based on the global statistics of each data category, the central server calculates the independent local covariance matrix for each fault category and the pooled covariance matrix shared by all categories. The local covariance matrix for each fault category and the pooled covariance matrix shared by all categories are weighted and smoothed by a preset regularization hyperparameter to generate a regularized covariance matrix. Step 5: The central server constructs a global regularized discriminant analysis classifier based on the regularized covariance matrix and the class mean extracted from the global statistics. When the central server receives new transformer data to be tested, it uses the global regularized discriminant analysis classifier trained without backpropagation to calculate the posterior discriminant score belonging to each fault category and classifies it into the category with the highest score for transformer fault diagnosis.

2. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that: In step 1, the fault data is converted into two-dimensional RGB image data. Specifically, this includes: capturing the relative proportion feature matrix, log-absolute difference matrix, and coexistence feature matrix of each pair of gases in the one-dimensional transformer fault data and converting them into two-dimensional RGB image fault data.

3. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that: In step 1, the one-dimensional transformer fault data includes data on five gases: CH4, H2, C2H6, C2H2, and C2H4.

4. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that, In step 2, the feature extractor uses a residual neural network.

5. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that, In step 3, sufficient statistics for each fault category include the number of samples, the first moment of the features, and the sum of the outer products of the features.

6. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that, In step 4, the central server calculates the independent local covariance matrix for each fault category based on the global statistics for each data category, specifically including: Calculate the product of the first-order moment vector of the characteristic features and the transpose of the first-order moment vector of the characteristic features in the sufficient statistics of each fault category to generate the mean outer product matrix. The sample size in the sufficient statistics for each fault category is multiplied by the mean outer product matrix to generate the mean offset matrix. Calculate the difference matrix between the sum of the feature outer products and the mean offset matrix; Multiplying the difference matrix by a scaling factor yields a local covariance matrix independent of each fault category.

7. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that, In step 4, the central server calculates the pooled covariance matrix shared by all categories based on the global statistics for each data category, specifically including: Based on the global statistics for each data category, obtain the total number of global samples and the total number of fault categories for all fault categories; For each fault category, the number of samples is reduced by one to obtain the local degrees of freedom for that fault category; Multiply the local covariance matrix that is independent of the fault category by the local degrees of freedom to generate the weighted local covariance matrix of the fault category; The weighted local covariance matrices of all fault categories are summed to generate an aggregated covariance matrix; Calculate the difference between the total number of global samples and the total number of fault categories to obtain the global degrees of freedom, and take the reciprocal of the global degrees of freedom as the global scaling factor; Multiplying the aggregated covariance matrix by the global scaling factor yields a pooled covariance matrix shared by all classes.

8. The single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis according to claim 1, characterized in that, In step 5, the central server constructs a global regularized discriminant analysis classifier based on the regularized covariance matrix and the class means extracted from the global statistics. Specifically, this includes: Calculate the inverse of the regularized covariance matrix and the logarithm of its determinant; The inverse matrix of the regularized covariance matrix, the logarithm of the determinant, and the class mean extracted from the global statistics are solidified into classifier parameters in analytical form, and a global regularized discriminant analysis classifier is constructed.

9. An electronic device comprising a processor and a memory, characterized in that, The memory stores a computer program, and when the processor executes the computer program, it implements the single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the single-round federated learning method based on regularized discriminant analysis for transformer fault diagnosis as described in any one of claims 1 to 8.

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