Distributed system working condition identification method based on equipment uncertainty

Abstract

The invention provides a distributed system working condition identification method based on equipment uncertainty, and aims to solve working condition identification challenges caused by data heterogeneity. According to the method, the uncertainty of the equipment is quantified, and reliable modeling is effectively carried out on the equipment in the distributed system, so that the accuracy of system working condition identification is improved. By reducing prediction uncertainty in different clients and aggregating reliable clients, the method realizes efficient identification of system working conditions under the condition of data heterogeneity, can significantly improve prediction precision of a global model especially under the condition of large data distribution difference between different devices, and has a good application prospect. And a solid technical basis is provided for reliable state monitoring of a distributed system.

Description

Technical Field

[0001] The present invention relates to the technical field of state monitoring of distributed systems, and in particular to achieving efficient and accurate working condition identification in a distributed environment for devices or systems containing data heterogeneity. This method addresses the data heterogeneity and noise problems existing in different devices, and by quantifying the uncertainty of the devices, reliably models the devices in the distributed system, thereby effectively identifying the working conditions of the system. By reducing the prediction uncertainty in different clients, the present invention can reliably identify the working conditions of the equipment through collaborative modeling. In particular, when there is data heterogeneity between different devices, the present invention can effectively overcome the degradation of model performance caused by label offset and achieve reliable identification of system working conditions. This not only improves the accuracy of system identification, but also provides strong support for the state monitoring of complex equipment networks such as various industrial automation systems, smart grids, and the Internet of Things. Background Art

[0002] In the condition monitoring of distributed systems, especially in scenarios involving multiple devices or systems, the data generated by different devices often have heterogeneity and noise interference. This heterogeneity is usually manifested in differences in the working environment, operation mode, and data collection method of different devices. These factors lead to different distribution characteristics of data, which in turn has a significant negative impact on the prediction accuracy of the working condition identification model based on distributed learning. In practical applications, due to the data differences between different devices, label offset and label noise problems will seriously affect the training process of the model. This phenomenon is particularly prominent in complex device networks such as industrial automation systems, smart grids, and the Internet of Things. As common problems, label offset and label noise seriously restrict the accuracy and reliability of equipment condition monitoring in distributed systems.

[0003] At present, the working condition identification methods of distributed systems usually rely on the data collected independently by each device for modeling. However, existing methods often fail to fully consider the uncertainty of device data heterogeneity and noise, resulting in poor generalization ability of the model when processing data from different devices, and it is difficult to effectively deal with the challenges brought by data heterogeneity. In this case, the accuracy of system working condition identification is often difficult to meet the requirements of industrial applications, which in turn affects the overall stability and security of the distributed system.

[0004] In recent years, with the development of industrial digitalization, the interconnection between various types of equipment and systems has gradually become the norm, which has also brought new challenges and opportunities to the state monitoring in distributed systems. In order to solve the problems of data heterogeneity and noise, some reliable equipment selection strategies have been proposed to improve the reliability of models in complex environments. These methods select equipment by establishing reliability evaluation indicators based on the accuracy of different equipment. However, these methods still have shortcomings when dealing with complex industrial application scenarios, especially when the label features of different equipment are quite different, the reliability of the model is still low. In recent years, the method of quantifying uncertainty can effectively reduce the prediction uncertainty of the model, thereby meeting the requirements of the reliability of the learned model in distributed learning. However, such methods are affected by data heterogeneity in distributed environments and it is difficult to effectively train models of different equipment in a collaborative way. Therefore, how to effectively utilize the data features of each device in a distributed environment and improve the accuracy of working condition identification through collaborative modeling has become an urgent problem to be solved in the field of industrial state monitoring, which has important practical significance.

[0005] The present invention proposes a distributed system operating condition identification method based on device uncertainty, aiming to solve the operating condition identification challenges caused by data heterogeneity. This method effectively reliably models the devices in the distributed system by quantifying the uncertainty of the devices, thereby improving the accuracy of system operating condition identification. By reducing the prediction uncertainty in different clients and aggregating reliable clients, the present invention achieves efficient identification of system operating conditions under data heterogeneity conditions, especially when the data distribution differences between different devices are large, it can significantly improve the prediction accuracy of the global model, and provide a solid technical foundation for reliable state monitoring of distributed systems. Summary of the invention

[0006] The present invention obtains a system operating condition identification method based on equipment uncertainty. The method realizes reliable modeling of system operating conditions of heterogeneous equipment by reducing prediction uncertainty in different clients and aggregating reliable clients, thereby improving the reliable identification of system operating conditions by the model. In industrial automation system equipment, the method can perform reliable system operating condition identification when the data distribution of different equipment is quite different.

[0007] The present invention adopts the following technical solutions and implementation steps:

[0008] (1) Obtaining and preprocessing datasets

[0009] a) Obtaining a working condition data set collected by the equipment, where the data set contains P-type working condition characteristics;

[0010] b) All working condition samples are divided into two groups, as training set and test set respectively;

[0011] The training set owned by each device is represented as in It is represented as a sample pair consisting of the i-th operating condition feature and the operating condition type of the k-th equipment. is the operating characteristic of the i-th sample of the k-th equipment, is the operating condition label of the i-th sample of the k-th equipment, N k is the number of training set samples for the kth device, and the number of test set samples for the kth device is denoted as T k ; The sum of the data sets of all K clients is Z, that is The ratio of the number of samples in the training set to the number of samples in the test set is 4:1, and the working condition categories contained in the training set and the test set are the same;

[0012] c) The working condition features x in the training set and the test set k The dimensions are resized to be the same;

[0013] Normalize the adjusted operating condition characteristics to [0,1], and the normalization formula is:

[0014]

[0015] in is the normalized working condition characteristic, min(·) and Respectively represent taking the minimum and maximum values ​​in the working condition characteristic matrix;

[0016] (2) Initialize global and local models

[0017] a) The server uses a random number in the range [0,1] to initialize the global working condition identification model parameter w G and the [1, K]-dimensional equipment uncertainty list U, where the structure of the global operating condition identification model includes 13 convolutional layers, 5 pooling layers and 3 fully connected layers, and its composition structure is as follows: First, the first two layers of the model are two 3x3 convolutional layers, followed by a 2x2 maximum pooling layer. This combination of convolutional layers and pooling layers is repeatedly connected five times, forming a total of 10 convolutional layers and 5 pooling layers; then, the model is connected to three additional 3x3 convolutional layers; finally, the model is connected to three fully connected layers, where the first two fully connected layers each contain 4096 neurons, and the third fully connected layer contains 1000 neurons, and the output dimension is;

[0018] b) The server communicates globally with local devices and uses the global model parameter vector to initialize the local working condition identification model of each device;

[0019] (3) Client local training

[0020] a) The local device receives the global model parameter vector and uses the global model parameter vector w GUpdate their respective local models;

[0021] b) Train the local model;

[0022] Local model training is divided into two stages: forward propagation and backward propagation;

[0023] In the forward propagation phase, the local device sends the N local working condition data set of the kth client to k The working condition features are randomly divided into multiple feature batches according to the batch sample size M. The t-th feature batch of the k-th client is expressed as Batching features The model is sent to the local working condition identification model in turn to obtain the logical value of the model. The logical value is calculated according to the following formula to get the output of the tth batch of the kth device:

[0024]

[0025] In the back propagation phase, the local device first calculates the terminal uncertainty target loss function and updates the local working condition identification model. The uncertainty target loss function of the kth device in the eth global training cycle is expressed as:

[0026]

[0027] Among them, F k (·) is the loss function of the kth device, is the model parameter of the kth device in the tth training batch under the eth global training cycle, λ is the adjustment factor, which is set to 0.7, is the domain loss function of the kth device, is the calibration loss function of the kth device, The calculation formula is expressed as:

[0028]

[0029] Among them, ln(·) is the logarithmic function, Γ(·) is the gamma function, Ψ(·) is the digamma function, is the target concentration of the tth batch of the kth device, which is a [M, P]-dimensional matrix with each element taking the value of 100. α0 is the target accuracy, which is a [1, P]-dimensional vector with each element taking the value of 100*P. is the output accuracy of the kth device, and its calculation formula is:

[0030]

[0031] in, is the i-th element of the model output in the t-th batch on the k-th device, The calculation formula is:

[0032]

[0033] in, is the global concentration parameter of the tth batch of the kth device, and is the output of the global model for the tth batch sample input; the gradient descent algorithm is used to calculate the gradient of the model parameters for the device uncertainty loss function, and the model parameters of the local operating condition discrimination model are updated. The expression for parameter update is expressed as:

[0034]

[0035] Among them, η t is the gradient descent learning rate for the tth batch, set to 0.01, is the local model parameter of the kth device in the t+1th batch under the eth global training cycle, is the local model parameter of the kth device in the tth batch under the eth global training cycle, F k (·) is the local uncertainty target loss function of the kth device, is the local uncertainty objective loss function parameter The desired gradient;

[0036] c) Upload local uncertainty index and updated working condition identification model;

[0037] The local uncertainty index and the trained working condition identification model are transmitted to the server in the form of a model parameter vector, where the calculation process of the local uncertainty index is:

[0038] First, the samples in the test set are input into the local working condition identification model to obtain the test local concentration of the kth device Then the local uncertainty index of the kth device in the eth global training cycle is calculated as follows:

[0039]

[0040] Where B(·) is the multivariate beta function, is the i-th element of the test local concentration of the k-th device;

[0041] (4) Server Aggregation Global Model

[0042] The server selects the aggregated device. The selection steps are as follows:

[0043] a) Wait for all local devices to complete local training, and collect the model parameter vectors and local uncertainty indexes of all devices in the e-th global training cycle;

[0044] b) Select the aggregation device according to the local uncertainty index. The selection process is as follows:

[0045] First, calculate the uncertainty threshold T of the e-th global training cycle e , and its calculation formula is:

[0046]

[0047] Then, the local uncertainty indexes are sorted and the local uncertainty indexes with a value less than the uncertainty threshold T are selected. e The set of selected devices is represented as S;

[0048] The server aggregates the local model parameter vectors of the devices in the set S to obtain updated global model parameters. The aggregation process is:

[0049] First, calculate the global observation model parameters The calculation formula is:

[0050]

[0051] Where Z represents the total number of training set samples for all K devices, N s is the number of data sets of the sth device in set S, |S| is the number of devices in set S, and w s,e is the model parameter vector of the sth device in the eth global training cycle, is the label observation matrix of the sth device, and its calculation formula is:

[0052]

[0053] in is the observation indicator function, y is the label of the sample, and takes the value of 1 when the k-th device has the i-th type of sample, otherwise it takes the value of 0;

[0054] Next, calculate the global missing model parameters The calculation formula is:

[0055]

[0056] in is the missing observation matrix of the sth device, and its calculation formula is:

[0057]

[0058] in is the missing indicator function, y is the label of the sample, and its value is 0 when the k-th device has the i-th type of sample, otherwise it is 1;

[0059] Finally, the global observation model parameters and global missing model parameters are aggregated, and the calculation formula is:

[0060]

[0061] in is the global model parameter after the model is updated in the e+1th round, ρ is the adjustment factor, and its value is 0.8;

[0062] Send the updated global model parameter vector to all clients;

[0063] (5) Global collaborative iterative training

[0064] The server and different devices perform collaborative training, repeating steps (3)-(4) until the global training cycle e reaches the predetermined number of iterations E, where the value of E is 200;

[0065] (6) Obtaining and using the global operating condition model

[0066] a) The server sends the optimal global model parameter vector to all devices;

[0067] b) The local device uses the received model parameter vector to update the local model to obtain the final working condition identification model;

[0068] c) The equipment uses the final operating condition identification model to identify the collected operating condition data. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The working condition identification accuracy diagram of the distributed system working condition identification method based on equipment uncertainty of the present invention is DETAILED DESCRIPTION

[0070] 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 in conjunction with specific examples.

[0071] The present invention obtains a system operating condition identification method based on equipment uncertainty. The method realizes reliable modeling of system operating conditions of heterogeneous equipment by accounting for prediction uncertainty in different clients and aggregating reliable clients, thereby improving the reliable identification of system operating conditions by the model. In industrial automation system equipment, the method can perform reliable system operating condition identification when the data distribution of different equipment is quite different.

[0072] The present invention adopts the following technical solutions and implementation steps:

[0073] (1) Obtaining and preprocessing datasets

[0074] a) Obtaining a working condition data set collected by the equipment, where the data set contains P-type working condition characteristics;

[0075] b) All working condition samples are divided into two groups, as training set and test set respectively;

[0076] The training set owned by each device is represented as in It is represented as a sample pair consisting of the i-th operating condition feature and the operating condition type of the k-th equipment. is the operating characteristic of the i-th sample of the k-th equipment, is the operating condition label of the i-th sample of the k-th equipment, N k is the number of training set samples for the kth device, and the number of test set samples for the kth device is denoted as T k ; The sum of the data sets of all K clients is Z, that is The ratio of the number of samples in the training set to the number of samples in the test set is 4:1, and the working condition categories contained in the training set and the test set are the same;

[0077] c) The working condition features x in the training set and the test set k The dimensions are resized to be the same;

[0078] Normalize the adjusted operating condition characteristics to [0,1], and the normalization formula is:

[0079]

[0080] in is the normalized working condition characteristic, min(·) and Respectively represent taking the minimum and maximum values ​​in the working condition characteristic matrix;

[0081] (2) Initialize global and local models

[0082] a) The server uses a random number in the range [0,1] to initialize the global working condition identification model parameter w G and the [1, K]-dimensional equipment uncertainty list U, where the structure of the global operating condition identification model includes 13 convolutional layers, 5 pooling layers and 3 fully connected layers, and its composition structure is as follows: First, the first two layers of the model are two 3x3 convolutional layers, followed by a 2x2 maximum pooling layer. This combination of convolutional layers and pooling layers is repeatedly connected five times, forming a total of 10 convolutional layers and 5 pooling layers; then, the model is connected to three additional 3x3 convolutional layers; finally, the model is connected to three fully connected layers, where the first two fully connected layers each contain 4096 neurons, and the third fully connected layer contains 1000 neurons, and the output dimension is;

[0083] b) The server communicates globally with local devices and uses the global model parameter vector to initialize the local working condition identification model of each device;

[0084] (3) Client local training

[0085] a) The local device receives the global model parameter vector and uses the global model parameter vector w G Update their respective local models;

[0086] b) Train the local model;

[0087] Local model training is divided into two stages: forward propagation and backward propagation;

[0088] In the forward propagation phase, the local device sends the N local working condition data set of the kth client to k The working condition features are randomly divided into multiple feature batches according to the batch sample size M. The t-th feature batch of the k-th client is expressed as Batching features The model is sent to the local working condition identification model in turn to obtain the logical value of the model. The logical value is calculated according to the following formula to get the output of the tth batch of the kth device:

[0089]

[0090] In the back propagation phase, the local device first calculates the terminal uncertainty target loss function and updates the local working condition identification model. The uncertainty target loss function of the kth device in the eth global training cycle is expressed as:

[0091]

[0092] Among them, F k (·) is the loss function of the kth device, is the model parameter of the kth device in the tth training batch under the eth global training cycle, λ is the adjustment factor, which is set to 0.7, is the domain loss function of the kth device, is the calibration loss function of the kth device, The calculation formula is expressed as:

[0093]

[0094] Among them, ln(·) is the logarithmic function, Γ(·) is the gamma function, Ψ(·) is the digamma function, is the target concentration of the tth batch of the kth device, which is a [M, P]-dimensional matrix with each element taking the value of 100. α0 is the target accuracy, which is a [1, P]-dimensional vector with each element taking the value of 100*P. is the output accuracy of the kth device, and its calculation formula is:

[0095]

[0096] in, is the i-th element of the model output in the t-th batch on the k-th device, The calculation formula is:

[0097]

[0098] in, is the global concentration parameter of the tth batch of the kth device, and is the output of the global model for the tth batch sample input; the gradient descent algorithm is used to calculate the gradient of the model parameters for the device uncertainty loss function, and the model parameters of the local operating condition discrimination model are updated. The expression for parameter update is expressed as:

[0099]

[0100] Among them, η t is the gradient descent learning rate for the tth batch, set to 0.01, is the local model parameter of the kth device in the t+1th batch under the eth global training cycle, is the local model parameter of the kth device in the tth batch under the eth global training cycle, F k (·) is the local uncertainty target loss function of the kth device, is the local uncertainty objective loss function parameter The desired gradient;

[0101] c) Upload local uncertainty index and updated working condition identification model;

[0102] The local uncertainty index and the trained working condition identification model are transmitted to the server in the form of a model parameter vector, where the calculation process of the local uncertainty index is:

[0103] First, the samples in the test set are input into the local working condition identification model to obtain the test local concentration of the kth device Then the local uncertainty index of the kth device in the eth global training cycle is calculated as follows:

[0104]

[0105] Where B(·) is the multivariate beta function, is the i-th element of the test local concentration of the k-th device;

[0106] (4) Server Aggregation Global Model

[0107] The server selects the aggregated device. The selection steps are as follows:

[0108] a) Wait for all local devices to complete local training, and collect the model parameter vectors and local uncertainty indexes of all devices in the e-th global training cycle;

[0109] b) Select the aggregation device according to the local uncertainty index. The selection process is as follows:

[0110] First, calculate the uncertainty threshold T of the e-th global training cycle e , and its calculation formula is:

[0111]

[0112] Then, the local uncertainty indexes are sorted and the local uncertainty indexes with a value less than the uncertainty threshold T are selected. e The set of selected devices is represented as S;

[0113] The server aggregates the local model parameter vectors of the devices in the set S to obtain updated global model parameters. The aggregation process is:

[0114] First, calculate the global observation model parameters The calculation formula is:

[0115]

[0116] Where Z represents the total number of training set samples for all K devices, N s is the number of data sets of the sth device in set S, |S| is the number of devices in set S, and w s,e is the model parameter vector of the sth device in the eth global training cycle, is the label observation matrix of the sth device, and its calculation formula is:

[0117]

[0118] in is the observation indicator function, y is the label of the sample, and takes the value of 1 when the k-th device has the i-th type of sample, otherwise it takes the value of 0;

[0119] Next, calculate the global missing model parameters The calculation formula is:

[0120]

[0121] in is the missing observation matrix of the sth device, and its calculation formula is:

[0122]

[0123] in is the missing indicator function, y is the label of the sample, and its value is 0 when the k-th device has the i-th type of sample, otherwise it is 1;

[0124] Finally, the global observation model parameters and global missing model parameters are aggregated, and the calculation formula is:

[0125]

[0126] in is the global model parameter after the model is updated in the e+1th round, ρ is the adjustment factor, and its value is 0.8;

[0127] Send the updated global model parameter vector to all clients;

[0128] (5) Global collaborative iterative training

[0129] The server and different devices perform collaborative training, repeating steps (3)-(4) until the global training cycle e reaches the predetermined number of iterations E, where the value of E is 200;

[0130] (6) Obtaining and using the global operating condition model

[0131] a) The server sends the optimal global model parameter vector to all devices;

[0132] b) The local device uses the received model parameter vector to update the local model to obtain the final working condition identification model;

[0133] c) The equipment uses the final operating condition identification model to identify the collected operating condition data.

Claims

1. A distributed system operating condition identification method based on equipment uncertainty, characterized in that: The following steps are involved: (1) Obtaining and preprocessing datasets a) Obtaining a working condition data set collected by the equipment, where the data set contains P-type working condition characteristics; b) All working condition samples are divided into two groups, as training set and test set respectively; The training set owned by each device is represented as in It is represented as a sample pair consisting of the i-th operating condition feature and the operating condition type of the k-th equipment. is the operating characteristic of the i-th sample of the k-th equipment, is the operating condition label of the i-th sample of the k-th equipment, N k is the number of training set samples for the kth device, and the number of test set samples for the kth device is denoted as T k ; The sum of the data sets of all K clients is Z, that is The ratio of the number of samples in the training set to the number of samples in the test set is 4:1, and the working condition categories contained in the training set and the test set are the same; c) The working condition features x in the training set and the test set k The dimensions are resized to be the same; Normalize the adjusted operating condition characteristics to [0,1], and the normalization formula is: in is the normalized working condition characteristic, min(·) and Respectively represent taking the minimum and maximum values ​​in the working condition characteristic matrix; (2) Initialize global and local models a) The server uses a random number in the range [0,1] to initialize the global working condition identification model parameter w G and the [1, K]-dimensional equipment uncertainty list U, where the structure of the global operating condition identification model includes 13 convolutional layers, 5 pooling layers and 3 fully connected layers, and its composition structure is as follows: First, the first two layers of the model are two 3x3 convolutional layers, followed by a 2x2 maximum pooling layer. This combination of convolutional layers and pooling layers is repeatedly connected five times, forming a total of 10 convolutional layers and 5 pooling layers; then, the model is connected to three additional 3x3 convolutional layers; finally, the model is connected to three fully connected layers, where the first two fully connected layers each contain 4096 neurons, and the third fully connected layer contains 1000 neurons, and the output dimension is; b) The server communicates globally with local devices and uses the global model parameter vector to initialize the local working condition identification model of each device; (3) Client local training a) The local device receives the global model parameter vector and uses the global model parameter vector w G Update their respective local models; b) Train the local model; Local model training is divided into two stages: forward propagation and backward propagation; In the forward propagation phase, the local device sends the N local working condition data set of the kth client to k The working condition features are randomly divided into multiple feature batches according to the batch sample size M. The t-th feature batch of the k-th client is expressed as Batching features The model is sent to the local working condition identification model in turn to obtain the logical value of the model. The logical value is calculated according to the following formula to get the output of the tth batch of the kth device: In the back propagation phase, the local device first calculates the terminal uncertainty target loss function and updates the local working condition identification model. The uncertainty target loss function of the kth device in the eth global training cycle is expressed as: Among them, F k (·) is the loss function of the kth device, is the model parameter of the kth device in the tth training batch under the eth global training cycle, λ is the adjustment factor, which is set to 0.7, is the domain loss function of the kth device, is the calibration loss function for the kth device, The calculation formula is expressed as: Among them, ln(·) is the logarithmic function, Γ(·) is the gamma function, Ψ(·) is the digamma function, is the target concentration of the tth batch of the kth device, which is a [M, P]-dimensional matrix with each element taking the value of 100. α0 is the target accuracy, which is a [1, P]-dimensional vector with each element taking the value of 100*P. is the output accuracy of the kth device, and its calculation formula is: in, is the i-th element of the model output in the t-th batch on the k-th device, The calculation formula is: in, is the global concentration parameter of the tth batch of the kth device, and is the output of the global model input for the tth batch of samples; The gradient descent algorithm is used to calculate the gradient of the model parameters for the equipment uncertainty loss function, and the model parameters of the local working condition identification model are updated. The expression for parameter update is expressed as: Among them, η t is the gradient descent learning rate for the tth batch, set to 0.01, is the local model parameter of the kth device in the t+1th batch under the eth global training cycle, is the local model parameter of the kth device in the tth batch under the eth global training cycle, F k (·) is the local uncertainty target loss function of the kth device, is the local uncertainty objective loss function parameter The desired gradient; c) Upload local uncertainty index and updated working condition identification model; The local uncertainty index and the trained working condition identification model are transmitted to the server in the form of a model parameter vector, where the calculation process of the local uncertainty index is: First, the samples in the test set are input into the local working condition identification model to obtain the test local concentration of the kth device Then the local uncertainty index of the kth device in the eth global training cycle is calculated as follows: Where B(·) is the multivariate beta function, is the i-th element of the test local concentration of the k-th device; (4) server aggregation global model The server selects the aggregated device. The selection steps are as follows: a) Wait for all local devices to complete local training, and collect the model parameter vectors and local uncertainty indexes of all devices in the e-th global training cycle; b) Select the aggregation device according to the local uncertainty index. The selection process is as follows: First, calculate the uncertainty threshold T of the e-th global training cycle e , and its calculation formula is: Then, the local uncertainty indexes are sorted and the local uncertainty indexes with a value less than the uncertainty threshold T are selected. e The set of selected devices is represented as S; The server aggregates the local model parameter vectors of the devices in the set S to obtain updated global model parameters. The aggregation process is: First, calculate the global observation model parameters The calculation formula is: Where Z represents the total number of training set samples for all K devices, N s is the number of data sets of the sth device in set S, |S| is the number of devices in set S, and w s,e is the model parameter vector of the sth device in the eth global training cycle, is the label observation matrix of the sth device, and its calculation formula is: in is the observation indicator function, y is the label of the sample, and takes the value of 1 when the k-th device has the i-th type of sample, otherwise it takes the value of 0; Next, calculate the global missing model parameters The calculation formula is: in is the missing observation matrix of the sth device, and its calculation formula is: in is the missing indicator function, y is the label of the sample, and its value is 0 when the k-th device has the i-th type of sample, otherwise it is 1; Finally, the global observation model parameters and global missing model parameters are aggregated, and the calculation formula is: in is the global model parameter after the model is updated in the e+1th round, ρ is the adjustment factor, and its value is 0.8; Send the updated global model parameter vector to all clients; (5) Global collaborative iterative training The server and different devices perform collaborative training, repeating steps (3)-(4) until the global training cycle e reaches the predetermined number of iterations E, where the value of E is 200; (6) Obtaining and using the global operating condition model a) The server sends the optimal global model parameter vector to all devices; b) The local device uses the received model parameter vector to update the local model to obtain the final working condition identification model; c) The equipment uses the final operating condition identification model to identify the collected operating condition data.

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