Privacy protection method for industrial data transmission
By adopting technical means such as adaptive timing window strategy, intelligent noise removal and encrypted transmission in industrial data transmission, the problems of data privacy leakage and data quality differences are solved, effective protection of data privacy and improvement of data quality are achieved, and the training efficiency of the global model is optimized.
Patent Information
- Application Number
- CN202510000650.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-02
- Publication Date
- 2025-04-25
- Estimated Expiration
- 2045-01-02
AI Technical Summary
There are problems in existing industrial data transmission with data privacy leakage, data quality differences and efficient aggregation of model parameters, and it is difficult to improve data quality and optimize global model training efficiency while ensuring data privacy.
An industrial data privacy protection method that adopts adaptive timing window strategy, intelligent noise removal, encrypted transmission and privacy protection authentication mechanism. Specific steps include localization processing, local fully connected neural network training, homomorphic encryption and adaptive model aggregation, etc.
Effectively protect the privacy of industrial data, improve data quality and the training effect of global models, and promote industrial intelligence and data-driven optimization applications.
Smart Images

Figure CN119885275A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of data security, and in particular to a privacy protection method for industrial data transmission. Background Art
[0002] With the development of the industrial Internet, the collection and processing of industrial data has gradually become the core link of intelligent manufacturing and industrial optimization. However, industrial data often contains a large amount of sensitive information, including equipment status in the production process, product quality monitoring, personnel behavior data, etc. The privacy protection of this data has become an important challenge in the current industrial digital transformation.
[0003] In the traditional industrial data transmission and processing process, since data needs to be transmitted through public networks and is usually stored in centralized servers, it is prone to security risks such as data leakage, tampering and abuse. Existing privacy protection technologies mainly focus on encrypted transmission and data anonymization, but these technologies still cannot effectively solve the contradiction between data privacy, data quality and model optimization.
[0004] To solve this problem, using federated learning technology for distributed training has become an ideal solution. Federated learning allows each client to train the model locally without uploading the original data to the central server, thereby protecting data privacy. However, the existing federated learning framework still has some problems, such as the risk of privacy leakage during model training, differences in client data quality, and efficient aggregation of model parameters.
[0005] Therefore, how to improve the quality of industrial data and optimize the efficiency of global model training while ensuring data privacy has become a technical problem that needs to be solved urgently. Summary of the invention
[0006] In view of the shortcomings of the prior art, the present invention proposes a privacy protection method for industrial data transmission, which is based on an adaptive timing window strategy, intelligent noise removal, encrypted transmission and privacy protection authentication mechanism. This method can not only ensure the privacy security of industrial data during transmission, but also improve data quality and the training effect of the global model, thereby promoting industrial intelligence and data-driven optimization applications.
[0007] In order to solve the above technical problems, the technical solution of the present invention is:
[0008] A privacy protection method for industrial data transmission, specifically comprising the following steps:
[0009] Step 1: Obtain industrial data and perform local processing. The specific methods include:
[0010] Adaptive time series window strategy: The client dynamically adjusts the size of the data aggregation window based on the volatility and autocorrelation of the data. When the data volatility is large, a smaller window is used to capture instantaneous changes; when the data volatility is small, a larger window is used for data smoothing.
[0011] Specifically, volatility is calculated by calculating the standard deviation σ of the data within the time period t , the autocorrelation is calculated by calculating the autocorrelation coefficient ρ of the data t To measure. The formula for adjusting the window size is:
[0012] ω(t)=α·σ t +β·ρ t
[0013] Among them, α and β are adjustment factors, ω(t) is the dynamically changing window size, and σ t is the standard deviation used to measure volatility, ρ t is the autocorrelation coefficient used to measure autocorrelation.
[0014] Intelligent noise detection and removal: Use a combination of wavelet transform and local statistics to remove noise from data.
[0015] Wavelet transform is used to extract the high-frequency noise component X of the data high , and remove these noises, retaining only the low-frequency valid data X low , the specific formula is:
[0016] X denoised =WT -1 (WT(X)·1 |WT(X)|>θ )
[0017] Among them, X denoised is the data after denoising, WT(X) is the wavelet transform, θ is the retained noise threshold, 1 |WT(X)|>θ is the threshold function;
[0018] Through local statistics, the local mean and local variance of the data points are calculated to further determine the abnormal noise in the data. The specific formula is:
[0019]
[0020] Among them, μ local (x i ) is the local mean, σ local (x i ) is the local variance, and k is the neighbor window size.
[0021] Data cleaning based on quality score: During the data cleaning process, the client calculates the quality score Q(x i), and set the threshold, when the quality score Q(x i ) is less than the threshold, it is judged as low-quality data (Q(x i )<0.7), mark it and remove it. This ensures that the quality score of the data item takes into account the completeness, correctness and consistency of the data. The formula is as follows:
[0022] Q(x i )=ω com ·C(x i )+ω corr ·R(x i )+ω cons ·I(x i )
[0023] Among them, C(x i ) is the data integrity score, R(x i ) is the correctness score of the data, I(x i ) is the consistency score of the data, ω com is the weight of data integrity score, ω corr is the weight of the data correctness score, ω cons The weight of the data consistency score. Low-quality data will be removed to ensure that the data uploaded to the central server can improve the training effect of the global model;
[0024] Step 2: Distribute the localized data to several clients: The localized data is distributed according to the number of clients. Each client will receive part of the data assigned to it and use this data for model training;
[0025] Step 3: Build a local fully connected neural network on the client: Build a local fully connected neural network on each client, use the privacy protection model of multi-layer perceptron (MLP), and train the local network with local data to obtain the optimal model parameters. During the training process, use the mean square error (MSE) as the loss function, update the model parameters based on the back propagation algorithm and optimization algorithm (such as Adam optimizer), and apply the differential privacy mechanism to protect the privacy of client data by adding Laplace noise;
[0026] Step 4: Use homomorphic encryption to encrypt the optimal parameters obtained through training: Each client will homomorphically encrypt the optimal model parameters obtained through training to ensure that the privacy of the model parameters is not leaked during the transmission process. The encrypted data is protected during the transmission process, thereby preventing man-in-the-middle attacks and data leakage;
[0027] Step 5. Each client transmits the encrypted data to the central server: The client uploads the encrypted model parameters to the central server to ensure the security and integrity of the data during transmission;
[0028] Step 6: The central server decrypts the model parameters and applies the adaptive model aggregation strategy for weighted aggregation: After receiving the encrypted data uploaded by all clients, the central server uses the server private key to decrypt it, and then uses the adaptive model aggregation strategy to dynamically weighted aggregate the model parameters uploaded by each client to obtain a global fully connected neural network model. The aggregation strategy is weighted based on the data quality score of each client to ensure that clients with higher quality contribute more to the global model and avoid the adverse effects of low-quality data on the model;
[0029] Step 7: Apply the aggregated global model to make predictions and transfer model parameters for updating: After the global model training is completed, the central server applies the aggregated global fully connected neural network to predict the industrial data and transmits the prediction results to the client. At the same time, the parameters of the global model are transferred to each client for updating and optimizing the local model;
[0030] Step 8: The client applies the model parameters downloaded by the client to adjust the training frequency and dynamically update: The training frequency adjustment mainly controls the frequency of client participation in training through data quality scoring. High-quality data allows the client to participate in more training rounds. The dynamic update strategy mainly controls the client's contribution to the global model through model accuracy differences. Clients with higher accuracy will contribute more to the global model.
[0031] The present invention has the following characteristics and beneficial effects:
[0032] With the above technical solution, data is not directly transmitted, but the model parameters obtained by training the local local fully connected neural network on the local data are transmitted, thereby protecting the privacy of local data and avoiding local data loss. The global fully connected neural network of the central server predicts the local industrial data by applying the model parameters uploaded by the local client. In addition, in order to ensure the accuracy of the global fully connected neural network for the prediction of local industrial data, the low-quality local data is first cleaned on the client, and the central server uses an aggregation strategy to weight the data quality score of each client to ensure that the high-quality client contributes more to the global model and avoids the adverse effects of low-quality data on the model. Finally, according to the training frequency adjustment, the frequency of client participation in training is controlled by the data quality score, and the client participates in more training rounds for high-quality data. And according to the dynamic update strategy, the contribution of the client to the global model is controlled by the difference in model accuracy. The client with higher accuracy will contribute more to the global model, and finally effectively improve the accuracy of the central server predicting industrial data. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative labor.
[0034] Figure 1 This is a flowchart of the industrial data privacy protection method provided in this embodiment.
[0035] Figure 2 This is a flowchart of the local data preprocessing provided in this embodiment.
[0036] Figure 3 A flowchart of the model parameter encryption process provided in this embodiment.
[0037] Figure 4 A flowchart of the adaptive model aggregation provided in this embodiment.
[0038] Figure 5 A flow chart for dynamically updating the model of a local fully connected neural network provided in this embodiment. DETAILED DESCRIPTION
[0039] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.
[0040] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings.
[0041] On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims. Further, in order to make the public have a better understanding of the present invention, some specific details are described in detail in the detailed description of the present invention below. Those skilled in the art can fully understand the present invention without the description of these details.
[0042] In view of the limitations and deficiencies of the existing technology in privacy protection of industrial data transmission, the present invention proposes an innovative solution. The following are specific embodiments:
[0043] This embodiment provides a flowchart of a privacy protection method for industrial data transmission, such as Figure 1 As shown, the method comprises the following steps:
[0044] S1. Obtain industrial data and perform local processing
[0045] Specifically, localized processing methods include: adaptive timing window strategy, intelligent noise detection and removal, and cleaning methods based on data quality scoring, ensuring that the data uploaded by the client improves data quality while protecting privacy. Figure 2 As shown, the sub-steps of step S1 are as follows:
[0046] S1-1, Adaptive timing window strategy
[0047] The client dynamically adjusts the data aggregation window based on the volatility and autocorrelation of industrial data. When the data volatility is large, a smaller window is used to capture instantaneous changes; when the data volatility is small, a larger window is used for data smoothing.
[0048] It should be noted that:
[0049] Small volatility: σ t ∈[0, 1], the data changes steadily, and it is suitable to use a larger window to smooth the data;
[0050] Medium volatility: σ t ∈[1, 2], the data has moderate fluctuations and is suitable for using a medium-sized window;
[0051] Large volatility: σ t ∈[2, 3], the data changes dramatically, and it is suitable to use a smaller window to quickly respond to changes.
[0052] Calculation of volatility and autocorrelation: For each time period data X t , by calculating its standard deviation σt and autocorrelation ρ t To determine the window size:
[0053] First, the data client quantifies volatility by calculating the standard deviation of the data within a time window.
[0054]
[0055] Among them, σ t is the standard deviation of the data in time period t, X t-i represents the data in the time series, μ t is the mean value for this period of time.
[0056] The correlation of the data is then measured by autocorrelation, which is calculated using the following formula:
[0057]
[0058] Among them, ρ t Represents the autocorrelation of the data in time period t.
[0059] The window size is adjusted dynamically according to the data volatility and autocorrelation to ensure that both the smoothness and instantaneous changes of the data can be properly captured. The formula for adjusting the window size is:
[0060] ω(t)=α·σ t +β·ρ t
[0061] Among them, α and β are adjustment factors, ω(t) is the dynamically changing window size, and σ t is the standard deviation used to measure volatility, ρ t is the autocorrelation coefficient used to measure autocorrelation.
[0062] S1-2. Intelligent noise removal method combining wavelet transform and local statistics
[0063] Wavelet transform denoising:
[0064] The data is decomposed by wavelet transform, and the high-frequency noise components are extracted and removed. For each time period signal X, the low-frequency component X is extracted after wavelet transform. low and high frequency noise X high :
[0065] X denoised =WT -1 (WT(X)·1 |WT(X)|>θ )
[0066] Among them, X denoisedis the data after denoising, WT(X) is the wavelet transform, θ is the retained noise threshold, 1 |WT(X)|>θ is the threshold function;
[0067] Local statistics assist judgment:
[0068] By calculating the data point x i The local mean μ in the neighborhood local (x i ) and the local variance σ local (x i ), further judge and remove abnormal noise.
[0069]
[0070] Among them, μ local (x i ) is the local mean, σ local (x i ) is the local variance, and k is the neighbor window size.
[0071] S1-3. Data cleaning method based on quality scoring:
[0072] Calculation of quality score: During the local cleaning process, the client scores the data quality based on the completeness, correctness and consistency of the data. The quality score Q(x i ) is calculated by the following formula:
[0073] Q(x i )=ω com ·C(x i )+ω corr ·R(x i )+ω cons ·I(x i )
[0074] Where: C(x i ) represents the integrity score of the data, R(x i ) represents the correctness score of the data, I(x i ) represents the internal consistency score of the data, ω com is the weight of data integrity score, ω corr is the weight of the data correctness score, ω cons The weight of the data consistency score. The client removes low-quality data based on the quality score. Specifically, by setting a threshold, when the quality score Q(x i ) is less than the threshold, it is judged as low-quality data, marked and removed to ensure that the uploaded data has a high contribution to the global model. In this embodiment, the threshold is set to 0.7. i )<0.7 were evaluated as low-quality data.
[0075] S2. Distribute the localized data to several clients
[0076] In this embodiment, the localized data is evenly distributed according to the number of clients. Each client will receive part of the data allocated to it and use this data for model training;
[0077] S3. Build a local fully connected neural network on the client
[0078] A local fully connected neural network is constructed on each client.
[0079] Specifically, in this embodiment, a privacy protection model based on a multi-layer perceptron (MLP) is used to receive industrial data features through the input layer. The hidden layer uses an activation function (ReLU) to extract deep features, and combines Dropout regularization and L2 regularization to prevent overfitting. The local network is trained with local data to obtain the optimal model parameters. During the training process, the mean square error (MSE) is used as the loss function, and the model parameters are updated based on the back propagation algorithm and the optimization algorithm (such as the Adam optimizer). At the same time, the differential privacy mechanism is applied to protect the client data privacy by adding Laplace noise. The specific formula is as follows:
[0080]
[0081] Among them, g is the original gradient, It means that 0 is the mean value. is the Laplace noise of the scale parameter, Δ is the sensitivity, and ∈ is the privacy budget.
[0082] S4. Use homomorphic encryption to encrypt the optimal parameters obtained through training.
[0083] The client encrypts the trained model parameters using homomorphic encryption technology to ensure that even if the central server receives the encrypted parameters, it cannot decrypt and obtain the original data. The encryption process is set as follows:
[0084] Enc(ω i )=ε hom (ω i )
[0085] where ω i is the model parameter uploaded by the client, ε hom is a homomorphic encryption function.
[0086] S5. Each client transmits the encrypted data to the central server
[0087] The client uploads the encrypted model parameters to the central server to ensure the security and integrity of the data during transmission.
[0088] Specifically, Figure 3 As shown in the figure, the client's local model parameters are uploaded to the central server after being homomorphically encrypted.
[0089] S6. The central server decrypts the model parameters and applies the adaptive model aggregation strategy for weighted aggregation
[0090] After receiving the encrypted data uploaded by all clients, the central server uses the server private key to decrypt it, and then uses the adaptive model aggregation strategy to dynamically weight and aggregate the model parameters uploaded by each client to obtain a global fully connected neural network model. The adaptive aggregation strategy is weighted based on the data quality score of each client to ensure that clients with higher quality contribute more to the global model and avoid adverse effects of low-quality data on the model, such as Figure 4 As shown, the sub-steps of step S6 are as follows:
[0091] S6-1. Decryption of model parameters
[0092] Use the server's private decryption key k dec For Enc(ω i ) to decrypt and restore the model parameters ω i , the specific formula is as follows:
[0093] ω i =D hom (Enc(ω i ), k dec )
[0094] where ω i is the model parameter uploaded by the client, D hom is the homomorphic decryption function.
[0095] S6-2. Weighted aggregation based on data quality
[0096] The quality score is calculated based on the model parameters of each client. The specific formula is as follows:
[0097] Q′(x i )=ω′ com ·C(x i )+ω′ corr ·R(x i )+ω′ cons ·I(x i )
[0098] Among them, Q′(x i ) is the quality score of each client model parameter, C(xi ) is the data integrity score, R(x i ) is the correctness score of the data, I(x i ) is the consistency score of the data, ω′ com is the weight of data integrity score, ω′ corr is the weight of the data correctness score, ω′ cons The weight with which to score the consistency of the data.
[0099] According to the quality score Q′(x i ), assign different weights to the uploaded model parameters, and the model parameter aggregation formula is:
[0100]
[0101] Where N is the number of clients, ω logal is the aggregate weight of the global fully connected neural network, ω i Model parameters uploaded by the client.
[0102] S6-3. Model parameter weight adjustment of local fully connected neural network for low-quality clients
[0103] When the quality score Q′(x i ) is less than the threshold, it is judged as low-quality data and assigned a low weight. In this embodiment, the threshold is set to 0.7. i )<0.7 is considered as low-quality data. The model weight is adjusted through the linear attenuation formula to ensure that the adverse impact of low-quality model parameter data on the global model is minimized. The specific adjustment formula is as follows:
[0104] ω′ i =γ·Q′(x i )·ω i
[0105] Among them, ω i is the model parameter weight uploaded by the original client, ω′ i is the adjusted client model weight, Q′(x i ) is the quality score of the model parameter data, and γ is the weight decay factor, which is used to linearly adjust the weight range of low-quality clients. In this embodiment, γ is set to [0.5, 1.0].
[0106] S7: Apply the aggregated global model to make predictions and transfer model parameters for updating
[0107] After the global model training is completed, the central server uses the aggregated global fully connected neural network to predict the industrial data and transmit the prediction results to the client. At the same time, the parameters of the global model are transmitted to each client for updating and optimizing the local model.
[0108] S8, the client application downloads the model parameters to adjust the training frequency and dynamically update
[0109] like Figure 5 As shown, the sub-steps of step S8 are as follows:
[0110] S8-1. Training frequency adjustment: Dynamically adjust the frequency of each client's participation in model training based on its local data quality score. For example, clients with high data quality will be allowed to participate in model training more frequently. The specific formula is as follows:
[0111] f i =f base ·(1+α·Q′(x i ))
[0112] Among them, f i is the training frequency of client i, f base is the basic training frequency, and α is the adjustment coefficient.
[0113] S8-2, Dynamic update of training strategy: According to the accuracy difference between the local model and the global model during the training process, the training strategy of each client is dynamically adjusted so that the global model can achieve the best performance while ensuring privacy. The specific formula is as follows:
[0114]
[0115] Among them, Δw i (t) is the model parameter update amount of the client at time t, λ is the learning rate adjustment factor, and accuracy i (t)-accuracy global (t) is the accuracy gap between the local model of client i and the global model.
[0116] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.
Claims
1. A privacy protection method for industrial data transmission, characterized in that: The steps include: Step 1: Obtain industrial data and perform local processing; Step 2: Distribute the localized industrial data to several clients; Step 3: Build a local fully connected neural network on the client, and use the allocated industrial data to train the local fully connected neural network to obtain the optimal model parameters; Step 4: Use homomorphic encryption to encrypt the optimal parameters obtained through training; Step 5: Each client transmits the encrypted optimal parameters to the central server; Step 6: The central server receives the encrypted optimal model parameters uploaded by the client, decrypts them, and applies the adaptive model aggregation strategy to dynamically weighted aggregate the decrypted model parameter data to obtain a global fully connected neural network; Step 7: Apply the aggregated global fully connected neural network to predict and obtain industrial data, and transmit the model parameters of the global fully connected neural network to each client; Step 8: The client uses the model parameters downloaded by the application to adjust the training frequency and dynamically update the local fully connected neural network.
2. A privacy protection method for industrial data transmission according to claim 1, characterized in that: In step 1, the localization processing method includes window size adjustment, noise removal and data cleaning.
3. A privacy protection method for industrial data transmission according to claim 2, characterized in that: The window size adjustment method is: The size of the data aggregation window is dynamically adjusted through the adaptive time series window strategy. The window size is determined according to the volatility and autocorrelation of the data. The expression is as follows: ω(t)=α·σ t +b·r t Among them, α and β are adjustment factors, ω(t) is the dynamically changing window size, and σ t is the standard deviation used to measure volatility, ρ t is the autocorrelation coefficient used to measure autocorrelation.
4. The privacy protection method for industrial data transmission according to claim 1 is characterized in that: The noise removal method is: Use wavelet transform to extract the high-frequency noise component X of the data high , and remove these noises, retaining only the low-frequency valid data X low , the specific formula is: X denoised =WT -1 (WT(X)·1 |WT(X)|>θ ) Among them, X denoised is the data after denoising, WT(X) is the wavelet transform, θ is the retained noise threshold, 1 |WT(X)|>θ is the threshold function; Through local statistics, the local mean and local variance of the data points are calculated to further determine the abnormal noise in the data. The specific formula is: Among them, μ local (x i ) is the local mean, σ local (x i ) is the local variance, and k is the neighbor window size.
5. The privacy protection method for industrial data transmission according to claim 1 is characterized in that: The data cleaning method is: By calculating the quality score Q(x i ), and set the threshold, when the quality score Q(x i ) is less than the threshold, it is judged as low-quality data, marked and eliminated. The formula is as follows: Q(x i )=ω com ·C(x i )+ω corr ·R(x i )+ω cons ·I(x i ) Among them, C(x i ) is the data integrity score, R(x i ) is the correctness score of the data, I(x i ) is the consistency score of the data, ω com is the weight of data integrity score, ω corr is the weight of the data correctness score, ω cons The weight with which to score the consistency of the data.
6. The privacy protection method for industrial data transmission according to claim 1 is characterized in that: The local fully connected neural network adopts a privacy protection model of a multi-layer perceptron, and trains the local fully connected neural network through local data to obtain optimal model parameters.
7. The privacy protection method for industrial data transmission according to claim 5 is characterized in that: In step 6, the central server performs quality scoring on the model parameters uploaded by the client, thereby performing weighted aggregation of the model parameters of each client based on data quality.
8. A privacy protection method for industrial data transmission according to claim 7, characterized in that: The method for performing weighted aggregation based on data quality on the model parameters of each client is: The quality score is calculated based on the model parameters of each client. The specific formula is as follows: Q′(x i )=ω′ com ·C(x i )+ω′ corr ·R(x i )+ω′ cons ·I(x i ) Among them, Q′(x i ) is the quality score of each client model parameter, C(x i ) is the data integrity score, R(x i ) is the correctness score of the data, I(x i ) is the consistency score of the data, ω′ com is the weight of data integrity score, ω′ corr is the weight of the data correctness score, ω′ cons The weight for scoring data consistency, According to the quality score Q′(x i ), and set the threshold, when the quality score Q′(x i ) is less than the threshold, it is judged as low-quality data, so different weights are assigned to the uploaded model parameters. The model parameter aggregation formula is: Where N is the number of clients, ω logal is the aggregate weight of the global fully connected neural network, ω i Model parameters uploaded by the client.
9. A privacy protection method for industrial data transmission according to claim 8, characterized in that: The method for adjusting the training frequency is: According to the local data quality score of each client, the frequency of its participation in model training is dynamically adjusted. Clients with higher quality participate in more training. The specific formula is as follows: f i =f base ·(1+α·Q′(x i )) Among them, f i is the training frequency of client i, f base is the basic training frequency, and α is the adjustment coefficient.
10. A privacy protection method for industrial data transmission according to claim 9, characterized in that: The method of dynamically updating the strategy is: The client's training strategy is dynamically adjusted according to the accuracy difference between the local fully connected neural network and the global fully connected neural network, thereby controlling the client's weight in the global model. The specific formula is as follows: Among them, Δw i (t) is the model parameter update amount of the client at time t, λ is the learning rate adjustment factor, and accuracy i (t)-accuracy global (t) is the accuracy gap between the local model of client i and the global model.
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