Physical guidance multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal equipment

Through a physical-guided multi-level federated learning method for heterogeneous terminal devices, the problems of data heterogeneity and lack of physical mechanisms in the battery degradation process are solved, and accurate prediction of the battery health status of electric vehicles, drones, robots and other equipment is achieved, thereby improving the safety and monitoring effect of terminal devices.

CN120632453APending Publication Date: 2025-09-12UNIV FOR SCI & TECH ZHENGZHOU
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Patent Information

Application Number
CN202510740374.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-05-28
Publication Date
2025-09-12

AI Technical Summary

Technical Problem

Existing technologies find it difficult to effectively deal with the data heterogeneity and lack of physical mechanisms in the battery degradation process, resulting in insufficient accuracy in battery health status prediction. In particular, the existing federated learning framework lacks generalization on heterogeneous terminal devices such as electric vehicles, drones, and robots.

Method used

A physical-guided multi-level federated learning method is adopted for heterogeneous terminal devices. By establishing a three-layer federated learning framework, the physical mechanism of battery aging is embedded in the neural network model. A pattern dynamic recognition module, an environmental perception attention mechanism and a physical constraint module are designed. Model screening and error-aware weighting strategies are designed between each layer to realize the training of the global model.

Benefits of technology

It improves the accuracy and generalization of battery health status prediction, enhances the physical consistency and safety of the battery degradation process, and improves the energy storage unit monitoring effect of terminal equipment.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention provides a physical guidance multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal equipment, and mainly relates to the field of artificial intelligence and energy storage health estimation. The method mainly comprises the following steps: taking power battery data of various devices such as an electric vehicle, an unmanned aerial vehicle and a robot as local data of a client, and performing data preprocessing; establishing a lightweight model for each client, and embedding a battery aging physical mechanism into a neural network model; a multi-layer federated learning framework is established, the first layer is a client formed by all devices, the second layer is local servers of multiple types of devices (electric vehicles, unmanned aerial vehicles and robots), and the third layer is a central server; designing a model screening strategy and an error perception weighted aggregation strategy between the client and the local server, and designing a model compression strategy between the local server and the central server; and obtaining a global model through multiple rounds of training, and estimating the health state of the power battery of the target equipment. In order to solve the problem that generalization of power battery health estimation in multiple heterogeneous devices is weak, a multi-level federated learning framework is designed, meanwhile, physical mechanisms and data modeling are combined, the limitation that the accuracy of battery health state estimation is insufficient is overcome, model estimation errors are remarkably reduced, and therefore the safety of an energy storage system is improved.
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Description

Technical Field

[0001] The present invention relates to battery health state prediction and deep learning, and in particular to a physical-guided multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal devices. Background Art

[0002] The development of new energy technologies has effectively alleviated the global energy crisis and environmental pollution. Batteries, as a key energy storage unit, offer advantages such as high energy density and long lifespan, and are widely used in electric vehicles, drones, robots, and other fields. However, as batteries degrade over time, their safety becomes particularly important. Battery degradation not only leads to reduced performance but also poses potential safety risks. Therefore, accurately assessing the battery's state of health (SOH) is crucial to ensuring its safe operation. However, because the battery's SOH cannot be directly measured, accurately predicting its degradation process remains a major challenge.

[0003] Data-driven methods estimate SOH directly from historical data. Degradation path-based methods estimate the remaining useful life (RUL) through weighted transformation, conversion, and compensation variables to approximate the true degradation trajectory of health indicators. However, such approximations may introduce errors, thereby reducing prediction accuracy. The extreme learning machine (ELM) method based on particle swarm optimization (PSO) is used to improve the SOH estimation effect. However, the global optimization nature of PSO may cause oscillations near the local optimum, hindering convergence to the global optimum. These methods have difficulty capturing the nonlinear relationships and high-dimensional characteristics inherent in the complex battery degradation process.

[0004] Deep learning technology has shown significant advantages in time series modeling due to its powerful nonlinear representation capabilities. A variational autoencoder (VAE) based on decomposition of time channel structure and feature fusion is applied to RUL prediction. However, its dependence on multi-layer perceptron (MLP) limits its ability to capture dynamic time patterns. A long short-term memory (LSTM) network is used to capture the dynamic evolution of battery health and enhance degradation trend estimation. In addition, a gated recurrent unit-attention structure is introduced to extract key health indicators and improve dynamic health status perception. For long sequence modeling, the Informer model utilizes sequence decomposition and adaptive error correction to improve SOH prediction accuracy. However, these methods ignore the physical knowledge of the battery degradation process, which may lead to a lack of physical consistency in the prediction.

[0005] In addition, since battery cells are typically deployed on distributed terminal devices, federated learning provides a privacy-preserving framework for collaborative modeling across multiple data sources and has been successfully applied to SOH estimation. However, the operating scenarios of various types of terminal devices, such as electric vehicles, drones, and robots, vary greatly, and the same type of devices have multiple energy storage systems. For example, electric vehicles are divided into cars, trucks, bicycles, etc., showing strong heterogeneity in data distribution. This makes the traditional two-layer federated learning framework based on the client-server structure still face challenges in terms of versatility and adaptability. Therefore, it is necessary to design an effective multi-layer federated learning framework to address the strong heterogeneity of data, while embedding the physical mechanism of battery degradation to achieve accurate prediction of the health status of the energy storage unit of the target terminal device. Summary of the Invention

[0006] In order to address the shortcomings and deficiencies in the prior art, the present invention proposes a physical-guided multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal devices.

[0007] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0008] S1. Use the power battery data of various devices such as electric vehicles, drones, and robots as client local data and perform data preprocessing;

[0009] S2. Build a lightweight model for each client and embed the physical mechanism of battery aging into the neural network model:

[0010] S3. Establish a multi-layered federated learning framework, where the first layer is the client formed by each device, the second layer is the local server of multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server;

[0011] S4. Design a model screening strategy and error-aware weighted aggregation strategy between the client and the local server, and design a model compression strategy between the local server and the central server;

[0012] S5. After multiple rounds of training, a global model is obtained to estimate the health status of the target device's power battery.

[0013] In the above step S1, the power battery data of electric vehicles, drones, and robots is imported and pre-processed, and each battery data is treated as client private data;

[0014] In step S2 above, the physically guided pattern-aware timing network, as the client model structure, captures the battery degradation characteristics, specifically including:

[0015] S21. Design a pattern dynamic recognition module to capture the temporal decay evolution pattern and potential environmental disturbance patterns (such as temperature changes) during battery degradation. Use moving average to smooth the time series curve and extract the low-frequency trend as the main component TE(x) reflecting the temporal evolution information. Inspired by signal decomposition, the residual between the original series and its smoothed version is regarded as the high-frequency component dominated by environmental disturbances, representing the potential environmental information LC(x).

[0016] S22. Design an environment-aware attention mechanism. Environmental factors affect battery degradation, and their impact varies dynamically over time. Understanding the interaction between the two can effectively improve the prediction of battery state of health (SOH). Therefore, the potential environmental information is mapped into a query vector Q, and the temporal decay evolution information is mapped into a key vector K and a value vector V. The interaction between environmental information and temporal decay evolution is learned through the environment-aware attention mechanism.

[0017] S23. Design a time series network, feed the captured interaction features into the network model, and calculate the regression loss with the help of MSE Complete the structural design of the lightweight model. The regression loss formula is as follows:

[0018]

[0019] S24. Design physical constraint module. The capacity increment (IC) curve describes the relationship between the capacity increment and the voltage change during constant current charge and discharge. The IC curve is obtained by calculating the relationship between the voltage increment ΔV and the corresponding capacity increment ΔQ. By analyzing the changes in the IC curve, the degree of battery aging can be effectively evaluated, especially the curve peak IC (P) has a monotonic relationship with the battery SOH. Therefore, the design of physical loss To constrain the prediction results of the neural network, the formula is as follows:

[0020]

[0021] S25. Design prediction loss with regression loss and physical loss The training process of the neural network model is jointly constrained by dynamic weighting. The formula is as follows:

[0022]

[0023] In step S3 above, a multi-layer federated learning framework is established, where the first layer is the client formed by each device, the second layer is the local server of multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server. Specifically:

[0024] S31. Establish a client layer (the first layer), which includes multiple types of clients such as electric vehicles, drones, and robots. For example, electric vehicle clients include electric cars, electric trucks, and electric bicycles. Drones and robots are also divided into different brands and devices that work in different scenarios. Each client uses local data to train its own client model and then uploads it to the local server layer.

[0025] S32. Establish a local server layer (second layer), which mainly includes electric vehicle local servers, drone local servers, and robot local servers. Each local server aggregates the models uploaded by various clients to generate a local server model, which is then uploaded to the central server layer.

[0026] S33. Establish a central server layer (the third layer), aggregate various local server models, generate a global model, and then send the parameters to the local servers, which in turn send them to each client to complete a round of training.

[0027] In step S4 above, a model screening strategy and an error-aware weighted aggregation strategy are designed between the client and the local server, and a model compression strategy is designed between the local server and the central server, specifically including:

[0028] S41. When the client model is uploaded to the server, a model screening strategy and an error-aware weighted aggregation strategy are designed between the client and the local server:

[0029] S42. When the local server model is uploaded to the central server, a model compression strategy is designed between the local server and the central server.

[0030] In the above step S5, a global model is obtained after multiple rounds of training to estimate the health status of the target device's power battery;

[0031] The beneficial effects of the present invention are: a physical-guided multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal devices. In view of the significant heterogeneity in battery monitoring data of various devices such as electric vehicles, drones, robots, etc., which leads to the problem of insufficient generalization of existing SOH prediction models based on federated learning. At the same time, the existing methods ignore the physical mechanism of battery degradation. Therefore, the present invention designs a three-layer federated learning framework and proposes a method for embedding battery physical mechanisms into a deep learning model, thereby realizing the health prediction of the power battery of the target device, which has significant application value in improving the safety of terminal devices equipped with energy storage units. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0033] Figure 1 This is a flow chart of the physical-guided multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal devices of the present invention.

[0034] Figure 2 This is a schematic diagram of the physical-guided pattern-aware timing network structure of the present invention.

[0035] Figure 3 Schematic diagram of the multi-level federated learning framework of the present invention. DETAILED DESCRIPTION

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0037] Batteries are the most common energy storage units and are widely used in the energy supply of various devices such as electric vehicles, drones, and robots. However, the existing federated learning framework generally consists of a two-layer client-server structure, which makes it difficult to overcome the heterogeneous problem of battery data from different devices. At the same time, it ignores the physical mechanism of the battery, making it difficult to effectively predict the SOH of the battery. To address the problem of limited accuracy in SOH estimation of target devices, the present invention proposes a physical-guided multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal devices. The main steps include: taking the power battery data of various devices such as electric vehicles, drones, and robots as client local data for data preprocessing; establishing a lightweight model for each client and embedding the physical mechanism of battery aging into a neural network model; establishing a multi-level federated learning framework, in which the first layer is the client formed by each device, the second layer is the local server for multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server; designing a model screening strategy and an error-aware weighted aggregation strategy between the client and the local server, and designing a model compression strategy between the local server and the central server; obtaining a global model after multiple rounds of training to estimate the health status of the power battery of the target device;

[0038] A physical guided multi-level federated learning method for energy storage unit degradation estimation for heterogeneous terminal devices. The specific process is as follows Figure 1As shown, the implementation steps are as follows:

[0039] S1. Use the power battery data of various devices such as electric vehicles, drones, and robots as client local data and perform data preprocessing;

[0040] S2. Build a lightweight model for each client and embed the physical mechanism of battery aging into the neural network model;

[0041] S3. Establish a multi-layered federated learning framework, where the first layer is the client formed by each device, the second layer is the local server of multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server;

[0042] S4. Design a model screening strategy and error-aware weighted aggregation strategy between the client and the local server, and design a model compression strategy between the local server and the central server;

[0043] S5. After multiple rounds of training, a global model is obtained to estimate the health status of the target device's power battery.

[0044] In the above step S1, the power battery data of electric vehicles, drones, and robots is imported and pre-processed. Each battery data is treated as client private data, specifically including:

[0045] S11, uniformly process the data formats and sampling frequencies of different devices, and mark SOH, and at the same time, monitor the voltage, current, temperature and other data x=[x1,x2,...,x t ] to normalize the data to reduce the dimensionality difference and improve the convergence of the model;

[0046] S12. Extract six key statistical features from each battery sequence of each device: variance, skewness, maximum, minimum, average, and peak. These features characterize the dynamic trends under different health states and serve as input to the client model.

[0047] In the above step S2, the physically guided pattern-aware timing network, as the client model structure, captures the battery degradation characteristics, such as Figure 2 As shown, specifically including:

[0048] S21. Design a pattern dynamic recognition module to capture the temporal decay evolution pattern and potential environmental disturbance pattern (such as temperature change) during battery degradation. Use moving average to smooth the time series curve and extract the low-frequency trend as the main component TE(x) reflecting the time evolution information. Inspired by signal decomposition, the residual between the original series and its smoothed version is regarded as the high-frequency component dominated by environmental disturbances, representing the potential environmental information LC(x). The formula is as follows:

[0049] TE(x)=AvgPool(Padding(x))

[0050] LC(x)=(x-TE(x))

[0051] S22. Design an environment-aware attention mechanism. Environmental factors affect battery degradation, and the degree of their impact changes dynamically over time. Understanding the interaction between the two can effectively improve the prediction of battery SOH. Therefore, the potential environmental information is mapped into a query vector Q, and the temporal decay evolution information is mapped into a key vector K and a value vector V. The interaction between environmental information and temporal decay evolution is learned through the environment-aware attention mechanism. The attention weight calculation formula is as follows:

[0052]

[0053] Among them, a i Represents the attention weight of the i-th key. The softmax function in the traditional self-attention mechanism is replaced by the ReLU activation function, and then a square operation is performed. This nonlinear transformation helps capture more complex patterns. In order to eliminate the influence of sample length, a normalization factor is introduced. Where l is the length of the input sequence. The value vector is weighted by the attention weight to obtain the final attention output matrix Z;

[0054] S23. Design a time series network, feed the captured interaction feature Z into the network model, and calculate the true value y with the help of MSE i and predicted values The difference between the two represents the regression loss Complete the structural design of the lightweight model. The regression loss formula is as follows:

[0055]

[0056] S24. Design the physical constraint module. The capacity increment (IC) curve describes the relationship between the capacity increment and the voltage change during constant current charge and discharge. The IC curve is obtained by calculating the relationship between the voltage increment ΔV and the corresponding capacity increment ΔQ. The formula is as follows:

[0057]

[0058] Analyzing the changes in the IC curve can effectively evaluate the degree of battery aging, especially the curve peak IC (P) has a monotonic relationship with the battery SOH. Design physical loss To constrain the prediction results of the neural network, the formula is as follows:

[0059]

[0060] S25. Design prediction loss with regression loss and physical loss The training process of the neural network model is jointly constrained by dynamic weighting. The formula is as follows:

[0061]

[0062] In the above step S3, a multi-level federated learning framework is established, in which the first layer is the client formed by each device, the second layer is the local server of multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server. Figure 3 As shown, specifically:

[0063] S31. Establish a client layer (the first layer), which includes multiple types of clients such as electric vehicles, drones, and robots. For example, electric vehicle clients include electric cars, electric trucks, and electric bicycles. Drones and robots are also divided into different brands and devices that work in different scenarios. Each client uses local data to train its own client model and then uploads it to the local server layer.

[0064] S32. Establish a local server layer (second layer), which mainly includes electric vehicle local servers, drone local servers, and robot local servers. Each local server aggregates the models uploaded by various clients to generate a local server model, which is then uploaded to the central server layer.

[0065] S33. Establish a central server layer (the third layer), aggregate various local server models, generate a global model, and then send the parameters to the local servers, which in turn send them to each client to complete a round of training.

[0066] In the above step S4, a model screening strategy and an error-aware weighted aggregation strategy are designed between the client and the local server, and a model compression strategy is designed between the local server and the central server, such as Figure 3 As shown, specifically including:

[0067] S41. When the client model is uploaded to the server, a model screening strategy and an error-aware weighted aggregation strategy are designed between the client and the local server. Specifically:

[0068] S411, design a client screening strategy based on time. In the process of communicating with the local server, all client models are uploaded in the first round. Starting from the second round of upload, the client data volume D c A time threshold is set based on the time of the last round of model upload. Only clients within the time requirement are stored in the model upload sequence. The time threshold calculation formula is as follows:

[0069]

[0070] is the ratio of the data volume of client c to the average data volume of all clients, is the upload time of client c in round r-1, and α is the weight parameter;

[0071] S412. Design a client screening strategy based on model quality. For client models in the model upload sequence, only when the prediction error of the client model is less than the number of the previous training rounds, that is, when the current model effect is better than the previous round, will the client be uploaded to the local server. Otherwise, this round of communication will be skipped.

[0072] S413. Design an error-aware weighted aggregation strategy. For client models uploaded to the local server, since the larger the prediction error, the worse the model effect, and the smaller the proportion in the aggregation process, the inverse of the prediction error of each client model is used as the model weight, and weighted aggregation is performed to generate a client aggregate model.

[0073] S42. When the local server model is uploaded to the central server, a model compression strategy is designed between the local server and the central server. Specifically:

[0074] S421. Design gradient sparsification to retain only the elements that have the greatest impact on model updates, such as the first s elements with the largest absolute values, thereby compressing the amount of transmitted data and forming coefficient updates. Set all non-retained elements to 0 and record their indices.

[0075] S422. Design an error compensation mechanism. During the sparsification process, a large number of low-amplitude but potentially long-term important updates are discarded. Therefore, a residual buffer is introduced to cache the residuals in a local server and add them to the new gradient differentials in the next round of training. In this way, in the form of "continuous error tracking", low-frequency important updates are accumulated into a high-quality upload.

[0076] S423: Update the global model, perform sparse reconstruction on the data packets uploaded by all local servers, and update the global model through weighted aggregation.

[0077] In the above step S5, a global model is obtained after multiple rounds of training to estimate the health status of the target device's power battery;

[0078] The present invention addresses the problem that the battery monitoring data of various devices such as electric vehicles, drones, and robots have significant heterogeneity, resulting in insufficient generalization of existing SOH prediction models based on federated learning. At the same time, existing methods ignore the physical mechanism of battery degradation. Therefore, the present invention designs a three-layer federated learning framework and proposes a method of embedding battery physical mechanisms into a deep learning model, thereby realizing health prediction of the power battery of the target device, which has significant application value in improving the safety of terminal devices equipped with energy storage units.

[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A physical-guided multi-level federated learning energy storage unit degradation estimation method for heterogeneous terminal devices, characterized by: The specific steps are as follows: S1. Use the power battery data of various devices such as electric vehicles, drones, and robots as client local data and perform data preprocessing; S2. Build a lightweight model for each client and embed the physical mechanism of battery aging into the neural network model; S3. Establish a multi-layered federated learning framework, where the first layer is the client formed by each device, the second layer is the local server of multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server; S4. Design a model screening strategy and error-aware weighted aggregation strategy between the client and the local server, and design a model compression strategy between the local server and the central server; S5. After multiple rounds of training, a global model is obtained to estimate the health status of the target device's power battery.

2. The method for estimating energy storage unit degradation based on physical guidance and multi-level federated learning for heterogeneous terminal devices according to claim 1 is characterized in that: Step S2 establishes a lightweight model for each client and embeds the physical mechanism of battery aging into the neural network model, including the following steps: S21. Design a pattern dynamic recognition module to capture the temporal decay evolution pattern and potential environmental disturbance patterns (such as temperature changes) during battery degradation. S22. Design an environment-aware attention mechanism. Environmental factors affect battery degradation, and their impact varies dynamically over time. Understanding the interaction between the two can effectively improve the prediction of battery state of health (SOH). Therefore, the potential environmental information is mapped into a query vector Q, and the temporal decay evolution information is mapped into a key vector K and a value vector V. The interaction between environmental information and temporal decay evolution is learned through the environment-aware attention mechanism. S23. Design a time series network, feed the captured interaction features into the network model, and calculate the regression loss with the help of MSE Complete the structural design of the lightweight model; S24. Design physical constraint module. The capacity increment (IC) curve describes the relationship between the capacity increment and the voltage change during constant current charge and discharge. The IC curve is obtained by calculating the relationship between the voltage increment ΔV and the corresponding capacity increment ΔQ. By analyzing the changes in the IC curve, the degree of battery aging can be effectively evaluated, especially the curve peak IC (P) has a monotonic relationship with the battery SOH. Therefore, the design of physical loss To constrain the prediction results of the neural network, the formula is as follows: S25. Design prediction loss with regression loss and physical loss The training process of the neural network model is jointly constrained by dynamic weighting. The formula is as follows:

3. The lithium battery health status perception method based on contribution perception federated learning according to claim 1 is characterized in that: Step S3 establishes a multi-layer federated learning framework, where the first layer is the client formed by each device, the second layer is the local server of multiple types of devices (electric vehicles, drones, robots), and the third layer is the central server, including the following steps: S31. Establish a client layer (the first layer), which includes multiple types of clients such as electric vehicles, drones, and robots. For example, electric vehicle clients include electric cars, electric trucks, and electric bicycles. Drones and robots are also divided into different brands and devices that work in different scenarios. Each client uses local data to train its own client model and then uploads it to the local server layer. S32. Establish a local server layer (second layer), which mainly includes electric vehicle local servers, drone local servers, and robot local servers. Each local server aggregates the models uploaded by various clients to generate a local server model, which is then uploaded to the central server layer. S33. Establish a central server layer (the third layer), aggregate various local server models, generate a global model, and then send the parameters to the local servers, which in turn send them to each client to complete a round of training.

4. The method according to claim 1, wherein The design of the model screening strategy and the error-aware weighted aggregation strategy between the client and the local server in step S4 includes the following steps: S41. Design a client screening strategy based on time. In the process of communicating with the local server, all client models are uploaded in the first round. Starting from the second round, the client data volume D c Design a time threshold so that only clients within the time requirement are stored in the model upload sequence. The time threshold calculation formula is as follows: is the ratio of the data volume of client c to the average data volume of all clients, is the upload time of client c in round r-1, and α is the weight parameter; S42. Design a client screening strategy based on model quality. For client models in the model upload sequence, only when the prediction error of the client model is less than the number of the previous training rounds, that is, when the current model effect is better than the previous round, the client will be uploaded to the local server. Otherwise, the current round of communication will be skipped. S43. Design an error-aware weighted aggregation strategy. For the client models uploaded to the local server, use the inverse of the prediction error of each client model as the model weight, perform weighted aggregation, and generate a client aggregation model.

5. The method according to claim 1, characterized in that Designing a model compression strategy between the local server and the central server in step S4 includes the following steps: S51. Design gradient sparsification to retain only the elements that have the greatest impact on model updates, such as the first s elements with the largest absolute values, thereby compressing the amount of transmitted data and forming coefficient updates. Set all non-retained elements to 0 and record their indices. S52. Design an error compensation mechanism. During the sparsification process, a large number of low-amplitude but potentially long-term important updates are discarded. Therefore, a residual buffer is introduced to cache the residuals in a local server and add them to the new gradient differentials in the next round of training. In this way, in the form of "continuous error tracking", low-frequency important updates are accumulated into a high-quality upload. S53: Update the global model, perform sparse reconstruction on the data packets uploaded by all local servers, and update the global model through weighted aggregation.

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