Federal learning fault diagnosis method and system for harmonic reducer multi-source unbalanced data

Abstract

The invention discloses a federated learning fault diagnosis method and a federated learning fault diagnosis system for multi-source unbalanced data of a harmonic reducer, relates to a harmonic reducer fault diagnosis technology, and aims to solve the problem of low diagnosis accuracy caused by unbalanced sample numbers of different fault categories of the harmonic reducer of an industrial robot and limited single-source signal acquisition information. The method is technically characterized by comprising the following steps of: performing wavelet transform on multi-source signals of different users to construct a time-frequency graph data set; carrying out equalization processing on the unbalanced data set by utilizing an improved data enhancement method; an effective channel attention mechanism is introduced, and the output of a residual branch is weighted through a learnable weight, so that the adaptability of the model to different residual information and the extraction capability of the model to data key features are enhanced; the method comprises the following steps: mining complementary information among multi-source signals through an improved multi-mode variational auto-encoder to perform feature fusion, and constructing a multi-user personalized local model; and the server aggregates local model parameters and updates the model, and guarantees user island privacy data through federal learning, thereby performing fault diagnosis on the harmonic reducer under the multi-source unbalanced data. A harmonic reducer signal acquisition experiment platform is established for verification, the characteristics of multi-source unbalanced data can be effectively extracted by the method, information fusion is realized, the average fault diagnosis accuracy is 98.8%, and the performance is superior to that of the compared method.

Description

TECHNICAL FIELD

[0001] The present application relates to harmonic reducer fault diagnosis technology, and in particular to a federated learning fault diagnosis method and system for multi-source unbalanced data of a harmonic reducer. BACKGROUND

[0002] Harmonic reducers are initially widely used in the driving parts of aerospace equipment, and with the development of technology, their application fields have gradually expanded to robots, optical equipment and medical devices, etc., among which, the application of harmonic reducers in industrial robot joints is the most common [1] As the core component of industrial robots, harmonic reducers have the advantages of high reduction ratio, large transmission ratio and high transmission precision [2] The fault risk of harmonic reducers is higher than that of conventional reducers, and if an abnormality occurs, it may lead to a decrease in production efficiency and unexpected downtime, and even the life safety of production line workers will be seriously threatened [3] Because the harmonic reducer is in normal working condition for a long time, there is little fault data, resulting in unbalanced data of different fault types, while users hope to keep private data from being shared, resulting in data islands, and the information obtained by a single sensor is often limited, which makes the fault diagnosis of the harmonic reducer more difficult. Therefore, it is of great practical significance to diagnose the multi-source unbalanced data of the harmonic reducer under the premise of protecting data privacy.

[0003] With the rapid development of artificial intelligence, deep learning has been widely practiced in the fault diagnosis of rotating machinery such as harmonic reducers due to its excellent feature extraction capability [4] Document [5] proposes an adaptive model combining one-dimensional convolutional neural network and matrix kernel to adjust the convolution kernel scale and improve the feature extraction capability of the harmonic reducer time domain signal. Document [6] proposes a fault diagnosis method based on a multi-scale hybrid convolutional neural network to extract more comprehensive fault features from the multi-channel signals of the harmonic reducer. Document [7] uses the cross-correlation method to determine the starting position of the whole cycle data of the vibration signal, and determines the data length through the phase difference spectrum correction to achieve good results in the actual diagnosis process. Document [8] proposes a fault feature extraction method combining continuous Morlet wavelet transform and Hilbert spectrum analysis to realize the fault diagnosis of the harmonic reducer flexible bearing. Document [9] proposes a fault diagnosis method based on a double-path convolutional neural network combined with a multi-channel hybrid attention mechanism and a bidirectional gated recurrent unit to realize effective diagnosis of the harmonic reducer under different working conditions.

[0004] The above method is set to balance the data of each category when constructing the dataset. However, in actual situations, the data of each category is often unbalanced, and the number of normal samples is much larger than that of fault samples, which affects the construction of fault diagnosis model

[10] . Therefore, it is necessary to solve the problem of low fault diagnosis accuracy of minority class samples caused by unbalanced data. Literature

[11] proposes a two-step clustering algorithm to enhance the oversampling technology algorithm for unbalanced data, which realizes the fault diagnosis of rolling bearings. Literature

[12] proposes an improved generative adversarial network to generate data to solve the problem of data imbalance, which can better diagnose the gearbox fault. Literature

[13] proposes a new fault diagnosis method based on spectral alignment and deep transmission convolutional neural network, which extracts features from unbalanced bearing data using a data augmentation module. The experimental results show that the diagnosis results are more excellent than other methods. Literature

[14] constructs a Gaussian mixture model to obtain the distribution representation of samples, extracts samples with similar distribution from the majority class to the original sample set, and establishes a balanced labeled sample set. The proposed method can effectively improve the fault diagnosis rate. The above research considers the problem of fault diagnosis under data imbalance from the perspective of single source data.

[0005] However, when in the real industrial situation, due to the restriction of physical characteristics and precision of the sensor itself, the information collected by a single sensor is limited, and it is often difficult to cover all the characteristics in the equipment running process

[15] . Moreover, the sensor used in the detection link of the harmonic reducer may cause the data obtained by a single sensor to lack comprehensiveness and stability due to the coordinated movement with the joint of the industrial robot

[16] . In view of the limitations of single sensor in collecting equipment running information, which may easily lead to false diagnosis, the use of multi-sensor collaborative operation can more comprehensively collect equipment running state data. Therefore, using multi-source data to carry out fault diagnosis can effectively reduce the misdiagnosis rate in theory

[17] . In recent years, many scholars at home and abroad have actively researched multi-sensor information fusion technology in the field of mechanical equipment fault diagnosis, aiming to improve the diagnosis accuracy

[18] . Literature

[19] proposes a harmonic reducer fault diagnosis method based on multi-sensor data fusion and gravitational search algorithm, which significantly improves the fault diagnosis accuracy. Literature

[20] proposes to use an autoregressive model to extract the features of the vibration signal, and then complete the data fusion through a cascade neural network. The experimental results show that the diagnosis results of multi-sensor data fusion are more excellent in accuracy compared with single-sensor diagnosis. Literature

[21] fuses the vibration signals of the harmonic reducer multi-sensor, and realizes fault diagnosis under different working conditions through the sub-domain adaptation method. Literature

[22] proposes a coupled convolution residual network to realize the fusion of rolling bearing vibration signal and acoustic emission signal information flow, and obtains better diagnosis accuracy.

[0006] When supported by sufficient training data, deep learning methods can achieve good accuracy in fault diagnosis. However, due to economic cost constraints and related legal regulations, etc., it is generally difficult for industrial users to obtain sufficient high-quality data in actual situations. At the same time, for the sake of data security, industrial users tend to keep data locally, which leads to the phenomenon of data islands and data privacy protection problems

[23] . For the above problems, the intelligent diagnosis technology based on deep learning has certain limitations. Federated learning is a distributed training framework that can effectively solve the problems of data islands and data privacy protection that deep learning is difficult to deal with

[24] . Literature

[25] uses an improved lightweight network SqueezeNet as a federated framework user-end feature extraction network to reduce model training time and improve reciprocating machine fault diagnosis accuracy. Literature

[26] proposes a federated framework for multi-user hybrid fault diagnosis, which divides the user-end network into multiple parallel networks to better achieve rotating machine fault diagnosis. The above researches use federated learning methods to protect the data privacy of different user ends, and improve the fault diagnosis by improving the feature extraction network of the local user end, but do not consider the problem of individualization of different clients.

[0007] In view of the fact that the normal state samples of the harmonic reducer are more, the fault category samples are less, and the single source signal is difficult to provide comprehensive fault information, resulting in unsatisfactory fault diagnosis results, it is imperative to propose a federated learning fault diagnosis method for multi-source unbalanced data of harmonic reducer. SUMMARY

[0008] The technical problem to be solved by the present application is:

[0009] The present application provides a federated learning fault diagnosis method and system for multi-source unbalanced data of harmonic reducer to solve the problem of unbalanced sample quantity of different fault categories of industrial robot harmonic reducer and the problem of limited information obtained from single source signal, which leads to low diagnosis accuracy.

[0010] The technical scheme adopted by the present application to solve the above technical problem is:

[0011] A federated learning fault diagnosis method for multi-source unbalanced data of harmonic reducer, the method comprising:

[0012] Step one, signal acquisition: build a signal acquisition experiment platform, install harmonic reducers of different fault categories, and collect vibration signal and acoustic emission signal data, control the driving motor and load motor through the host computer software, adjust the different speeds and loads of the harmonic reducer, simulate different working conditions, and realize signal acquisition of the harmonic reducer under different working conditions;

[0013] Step two, data preprocessing: wavelet transform is used on the collected one-dimensional signal to obtain a two-dimensional image that can more comprehensively and intuitively present the time-frequency information of the sample, which is used to construct an unbalanced data set;

[0014] Step three, model construction: data augmentation is performed on the unbalanced data through a data augmentation method, the residual network is improved by introducing an effective channel attention mechanism and weighting the output of the residual branch through a learnable weight, the improved residual network is used to extract the features of the vibration signal and the acoustic emission signal, the complementary information of the multi-source signals is mined through a multi-modal variational autoencoder, and the obtained classification loss and the loss of the multi-modal variational autoencoder are used as the model training loss;

[0015] Through iterative training, the loss function value of model training is obtained, the gradient of network weight is calculated according to the loss function by using the back propagation algorithm, the model parameters are iteratively updated in the direction of minimizing the loss function by using the gradient descent method, and the model is continuously optimized;

[0016] Under the framework of federated learning, the user-end models are trained, the local model parameters obtained after the training of each user are uploaded to the server, the MMVAE encoder part parameters are uploaded, the other parts are used as the personalized layers of the user-end, the parameter aggregation is performed on the parameters by using the federated averaging algorithm, the global model is obtained, and the fault diagnosis model of the harmonic reducer under multi-source unbalanced data is established through iterative training;

[0017] Step four, fault diagnosis: the test set is input into the trained fault diagnosis model to obtain the fault diagnosis result of the harmonic reducer.

[0018] Further, the data augmentation is: relying on the composition of new synthetic samples by convex combination of existing training samples and their corresponding labels, which is used to reduce overfitting in deep neural networks; if (x i , y i ), (x j , y j ) is a training example composed of data x i , x j and its related labels y i , y j , Mixup creates synthetic data and labels as shown in formula (1) and formula (2):

[0019]

[0020] Where λ ~ beta (theta, theta) is a beta distribution, and theta > 0; And are the generated new data and labels;

[0021] The data sampling strategy is shown in equation (3):

[0022]

[0023] where q i represents the probability of sampling from the i-th class, n k represents the number of samples of the k-th class, and K is the number of sample classes; in this case, selecting l = 1 is equivalent to selecting samples whose probability is equal to the frequency of its class in the training set, while selecting l = 0 leads to the sampling probability of each class being q i = 1 / K, (x i , y i ) and (x j , y j ) are selected from the two probability spaces l = 1 and l = 0, respectively; in the new round of training process, the weights of different types of samples in the new round are recalculated according to the data enhancement results obtained by the model in the last round of training, and in this way, the generated sample space is more balanced;

[0024] The focal loss function is used to replace the original cross-entropy loss function as the model classification loss function to improve the fault diagnosis ability of the model in the case of data imbalance, as shown in equation (4):

[0025]

[0026] where α is the balance factor, γ is the focal factor, and p i represents the probability of predicting the i-th class.

[0027] Further, the process of the improved residual network is as follows:

[0028] The residual block is the basic architecture of the residual network ResNet, which adds the identity mapping of the input x and the features F(x) extracted by the convolution layer to obtain the output H(x) of the residual block;

[0029] The channel attention module ECA is introduced to effectively increase the expression ability of the convolutional neural network, and the ECA module is a very lightweight plug-and-play module, as shown in the schematic diagram of Figure 2 .

[0030] The output of the residual block of ResNet is shown in equation (5):

[0031] H(x)=F(x)+x (5)

[0032] The output of the residual block is the addition of the feature F(x) extracted by the convolution layer and the original input x, which helps to alleviate problems such as gradient disappearance, thereby more effectively training a deep model; in order to control the influence of each component, a learnable weight is introduced between the input and the feature extracted by the convolution layer, as shown in formula (6):

[0033] H(x) = F(x) + μx (6)

[0034] Where μ is the weight that adjusts the influence of the input data.

[0035] Further, the federated learning is specifically:

[0036] The federated learning framework adopts a federated averaging algorithm as the parameter aggregation method, and its expression is as shown in formula (7):

[0037]

[0038] Where, is the local model parameter of the tth user in the jth round of federation; G j+1 is the global model parameter in the j+1th round;

[0039] Multi-sensor information fusion is combined with federated learning to learn information from different sensors and protect the privacy of data. The multi-modal variational autoencoder MMVAE method is used to process data from multiple sensors at the same time, capture the mutual relationship between different sensor data through a shared latent space, and effectively fuse the information of different sensors.

[0040] The multi-modal variational autoencoder uses an improved ResNet neural network as an encoder to extract features and map the features of different sensors to a latent variable space, ensuring that the model extracts complementary information from different signals. The mean and standard deviation obtained from the encoder output are used to describe the distribution of the latent variable in the latent space. The self-attention mechanism layer SA adaptively weights the generated latent variables, which can better capture the correlation between features. The data is reconstructed through the decoder, and the self-attention mechanism calculation formula is as shown in formula (8):

[0041]

[0042] Where Q is the query matrix, K is the key matrix, V is the key vector, d is the dimension of the key, and Softmax is the activation function.

[0043] The latent variables in the MMVAE latent space contain feature information of the original input data. By improving the model structure of MMVAE and fully mining the feature information in the latent variables, harmonic reducer fault diagnosis is realized.

[0044] According to the optimized model structure, the loss function is improved: first, the loss function is combined by the MSE and the KL divergence, as shown in formula (9) and formula (10):

[0045]

[0046] Wherein, x i represents the original data, represents the reconstructed data, μ i represents the mean of the hidden variable, σ i represents the variance of the hidden variable, the MSE is used to evaluate the difference between the reconstructed data and the original data, and the KL divergence is used to measure the similarity between the hidden variable and the standard normal distribution, so as to better guide the training process of the model, and the loss function of the MMVAE is obtained, as shown in formula (11):

[0047] L MMVAE =L MSE +L KL (11)

[0048] Finally, the loss of the multi-modal variational autoencoder is weighted and summed with the model classification loss as shown in formula (4) as the overall loss function of the model, as shown in formula (12):

[0049] L=L class +ωL MMVAE (12)

[0050] Wherein, ω is a hyperparameter, and the multi-modal variational autoencoder and the fault classification branch are jointly trained; in this way, the generation process of the reconstructed data can inversely affect the generation of the hidden variable, so that the hidden variable better represents the feature information of the original data, thereby improving the accuracy of fault diagnosis.

[0051] Further, in the federated learning system, the server sends the global model parameters to the client, the client uses the data owned by itself to train the model, and the network layer is reserved as a local individualized layer when the parameters are uploaded, and then the other model parameters are sent back to the server, and these model parameters are aggregated on the server to generate a new global model.

[0052] A federated learning fault diagnosis system for multi-source unbalanced data of harmonic reducer, the system has program modules corresponding to the steps of the technical solution, and runs to execute the steps in the method.

[0053] A computer-readable storage medium stores a computer program configured to implement the steps of the federated learning fault diagnosis method for harmonic reducer multi-source unbalanced data when called by a processor.

[0054] The present application has the following beneficial technical effects:

[0055] The method of the present application processes different user multi-source unbalanced data through data enhancement technology to reduce the unbalance of the data; uses an effective channel attention mechanism and dynamically weights the different branches of the residual network to strengthen the network's feature extraction capability for multi-source data; and further improves the accuracy of fault diagnosis by fusing the features of multi-source data through a multi-modal variational autoencoder, and uses federated learning to protect the privacy of isolated data and perform personalized processing on the client to build a fault diagnosis model, thereby effectively realizing the fault diagnosis of harmonic reducer multi-source unbalanced data.

[0056] The present application effectively solves the problem of imbalance in the number of samples of different fault categories of industrial robot harmonic reducers, as well as the problem of limited information obtained from single-source signals, which leads to low diagnostic accuracy. The method of the present application performs wavelet transform on multi-source signals from different users to construct a time-frequency graph dataset; uses an improved data enhancement method to balance the unbalanced dataset; introduces an effective channel attention mechanism and weights the output of the residual branch through a learnable weight to enhance the model's adaptability to different residual information and its ability to extract key features from data; uses an improved multi-modal variational autoencoder to mine complementary information between multi-source signals for feature fusion and construct a personalized local model for multiple users; the server aggregates local model parameters and updates the model, and through federated learning, protects the privacy of user isolated data, thereby performing fault diagnosis on harmonic reducers under multi-source unbalanced data. Through the construction of a harmonic reducer signal acquisition experimental platform, the method can effectively extract features from multi-source unbalanced data and achieve information fusion, with an average fault diagnosis accuracy of 98.8%, outperforming the compared methods. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 is a residual block structure diagram, Figure 2 is an ECA module schematic diagram; Figure 3 is a federated learning framework diagram; Figure 4 is a multi-modal variational autoencoder block diagram; Figure 5 is an improved multi-modal variational autoencoder block diagram; Figure 6 is a fault diagnosis flowchart; Figure 7 is a photo of a harmonic reducer signal acquisition experimental platform; Figure 8 is a measurement and control system block diagram; Figure 9The time-frequency diagram of the inner ring of the flexible bearing in the different signal working condition A moderate fault is shown in the figure, wherein (a) is a vibration signal, and (b) is an acoustic emission signal; Figure 10 The diagnostic result comparison chart before and after the improvement of the data enhancement method is shown in the figure; Figure 11 The diagnostic result comparison chart of different training sets is shown in the figure, wherein (a) is an accuracy comparison, (b) is a G-mean comparison, and (c) is a F-measure comparison; Figure 12 The feature visualization chart of the original residual network is shown in the figure, Figure 13 The feature visualization chart of the improved residual network is shown in the figure; Figure 14 The confusion matrix chart of the original residual network is shown in the figure, Figure 15 The confusion matrix chart of the improved residual network is shown in the figure; Figure 16 The fault diagnosis result comparison chart of the multi-source signal and the single-source signal is shown in the figure; Figure 17 The radar chart comparison before and after the improvement of the multi-source information fusion method is shown in the figure; Figure 18 The comparison result chart of the method and other multi-source information fusion methods is shown in the figure. DETAILED DESCRIPTION

[0058] Combining the drawings Figures 1-18 The implementation process of the federated learning fault diagnosis method for the harmonic reducer multi-source unbalance data is described as follows:

[0059] 1 Data enhancement algorithm

[0060] 1.1 Mixup data enhancement algorithm

[0061] Mixup is a data enhancement algorithm

[27] , which is originally proposed to improve the performance of deep learning by reducing overfitting. It relies on reducing overfitting in deep neural networks by combining existing training samples and their corresponding labels to form new synthetic samples. If (x i , y i ), (x j , y j ) are training examples composed of data x i , x j and its related labels y i , y j , Mixup creates synthetic data and labels as shown in formula (1) and formula (2):

[0062]

[0063] Where λ ~ β (θ, θ) is a beta distribution, and θ > 0. And are the generated new data and labels.

[0064] 1.2 Improvement of Mixup data enhancement algorithm

[0065] When faced with data imbalance, most intelligent fault diagnosis models tend to focus more on majority class samples while ignoring the important information contained in minority class samples. This significantly affects the model's ability to judge different faults. In a long-tail distribution, directly using Mixup may increase the imbalance of the dataset. An improved sampling strategy can be used to mitigate this effect. The data sampling strategy is shown in formula (3):

[0066]

[0067] Among them, q i represents the probability of sampling from the i-th class, n k In this case, choosing l = 1 is equivalent to selecting samples with a probability equal to the frequency of their class in the training set, while choosing l = 0 results in a sampling probability of q for each class. i =1 / K,(x i ,y i ) and (x j ,y j ) are selected from the two probability spaces of l = 1 and l = 0. During the new round of training, the weights of different types of samples in the new round are recalculated based on the data augmentation results obtained in the previous round of model training. In this way, the generated sample space is made more balanced.

[0068] In order to further improve the model's fault diagnosis ability under data imbalance, the focus loss function is used instead of the original cross entropy loss function as the model classification loss function, as shown in formula (4):

[0069]

[0070] Where α is the balance factor, γ is the focus factor, and p i represents the probability of predicting the i-th class. The focus loss function makes the model pay more attention to samples with high misclassification frequency, thereby improving the classification accuracy of the model and further solving the problem of data imbalance.

[0071] 2 Improved Residual Network

[0072] 2.1 Residual Network

[0073] With the development of deep learning technology, the network becomes deeper, and problems such as gradient vanishing and network degradation occur. Residual Network (ResNet) can alleviate these problems to a certain extent. The residual block is the basic architecture of ResNet. The residual block output H(x) is obtained by adding the identity mapping of the input x to the feature F(x) extracted by the convolution layer, as shown in Figure 1 shown.

[0074] 2.2 Improvement of residual network

[0075] In order to improve the performance of the residual network, an efficient channel attention module (ECA) is introduced, which can effectively increase the expression ability of the convolutional neural network, avoid dimension reduction, and reduce the amount of calculation and the number of parameters, but can bring obvious performance gain. The ECA module is a very lightweight plug-and-play module, which has the advantages of high computational efficiency and strong universality in comparison with many attention mechanisms, and its schematic diagram is shown as Figure 2 .

[0076] The output of the residual block of ResNet is shown as formula (5):

[0077] H(x)=F(x)+x (5)

[0078] The output of the residual block is to add the features F(x) extracted by the convolutional layer and the original input x, which helps to alleviate problems such as gradient disappearance, so as to more effectively train a deep model. However, the influence of the features extracted by the convolutional layer and the original input on the model training may not be equal. In order to control the influence of each component, a learnable weight is introduced between the input and the features extracted by the convolutional layer. As shown in formula (6):

[0079] H(x)=F(x)+μx (6)

[0080] Where μ is the weight that adjusts the influence of the input data.

[0081] 3 Federated learning

[0082] 3.1 Federated learning framework

[0083] Federated learning (FL) is an alternative system paradigm to centralized machine learning. In the federated learning system, the server sends the global model parameters to the client, the client trains the model using the data owned by itself, and the parameters are uploaded while part of the network layer is reserved as a local personalized layer, and then the other model parameters are sent back to the server, and these model parameters are aggregated on the server to generate a new global model. The federated framework adopts federated averaging algorithm as the parameter aggregation method, and its expression is shown as formula (7):

[0084]

[0085] Where, is the local model parameter of the tth user in the jth round of federation; G j+1 is the global model parameter in the j+1th round.

[0086] The system performs repeated iterations until the global model converges in performance on a given task. In the face of the "data island" problem, federated learning can help multiple users build a shared high-performance model, and because the data is not shared with other users, the privacy of customer data is protected. The federated learning framework is as shown in Figure 3

[0087] 3.2 Multi-source information fusion

[0088] Multi-source information fusion is also called multi-sensor information fusion, which uses multiple sensors to collect information. The multi-source information fusion method can collect more comprehensive and accurate information than a single sensor

[28] . With the rapid development of various sensor technologies, multiple sensor data can be obtained. Using multi-source data information for modeling, different sensor data can provide complementary information to improve the representation ability of the model. Combined with federated learning, information can be learned from different sensors, and the privacy of the data can be protected. In order to better learn the information of different sensor data, the Multimodal Variational Autoencoder (MMVAE) method

[29] is used. This method can simultaneously process data from multiple sensors and capture the relationship between different sensor data through a shared latent space. In this way, the information of different sensors can be effectively fused, thereby improving the model's ability to analyze multi-source data. The model structure is as shown in Figure 4

[0089] The Multimodal Variational Autoencoder uses an improved ResNet neural network as the encoder to extract features, which can effectively improve the feature extraction ability of the model. The features of different sensors are mapped to the latent variable space. This joint modeling method ensures that the model can extract complementary information from different signals. The mean and standard deviation obtained from the encoder output are used to describe the distribution of the latent variable in the latent space. The self-attention mechanism layer (SA) adaptively weights the generated latent variables to better capture the correlation between features. The data is reconstructed through the decoder, and the self-attention mechanism calculation formula is as shown in equation (8):

[0090]

[0091] where Q is the query matrix, K is the key matrix, V is the key vector, d is the dimension of the key, and Softmax is the activation function.

[0092] ​​The latent variables of the MMVAE potential space contain the feature information of the original input data. In this paper, the model structure of MMVAE is improved, and the feature information in the latent variables is fully mined to realize the fault diagnosis of harmonic reducer, as shown in Figure 5 .

[0093] According to the model structure optimized in this paper, the loss function is improved. First, the loss function combining MSE and KL divergence is used, as shown in equations (9) and (10):

[0094]

[0095] Where x i represents the original data, represents the reconstructed data, μ i represents the mean of the latent variable, σ i represents the variance of the latent variable, MSE is used to evaluate the difference between the reconstructed data and the original data, and KL divergence is used to measure the similarity between the latent variable and the standard normal distribution, so as to better guide the training process of the model, and obtain the loss function of MMVAE, as shown in equation (11):

[0096] L MMVAE = L MSE + L KL (11)

[0097] Finally, the loss of the multi-modal variational autoencoder is weighted and summed with the model classification loss as shown in equation (4) to obtain the overall loss function of the model, as shown in equation (12):

[0098] L = L class + ωL MMVAE (12)

[0099] Where ω is a hyperparameter, and the multi-modal variational autoencoder and the fault classification branch are jointly trained. In this way, the generation process of the reconstructed data can inversely affect the generation of the latent variable, so that the latent variable can better represent the feature information of the original data, thereby improving the accuracy of fault diagnosis.

[0100] 4 Fault diagnosis method for multi-source unbalanced data of harmonic reducer

[0101] The flow chart of the federated learning fault diagnosis method for multi-source unbalanced data of harmonic reducer is shown in Figure 6 . The specific steps are as follows:

[0102] (1) Signal acquisition: A signal acquisition experiment platform was built. By installing harmonic reducers of different fault categories, vibration signal and acoustic emission signal data acquisition was carried out. The host computer software was used to control the driving motor and load motor, and the different speeds and loads of the harmonic reducer were adjusted to simulate different working conditions and achieve signal acquisition of the harmonic reducer under different working conditions.

[0103] (2) Data preprocessing: The one-dimensional signal collected was processed using wavelet transform to obtain a two-dimensional image that can more comprehensively and intuitively present the time-frequency information of the sample, which was used to construct an unbalanced data set.

[0104] (3) Model construction: The unbalanced data was enhanced by data enhancement method. The network was improved by introducing effective channel attention mechanism and weighting the output of residual branch through learnable weight. The improved residual network was used to extract the features of vibration signal and acoustic emission signal, and the complementary information of multi-source signal was mined through multi-modal variational autoencoder. The obtained classification loss and the loss of multi-modal variational autoencoder were used as the model training loss. Through iterative training, the loss function value of model training was obtained. Using the back propagation algorithm, the gradient of network weight was calculated according to the loss function. The model parameters were iteratively updated in the direction of minimizing the loss function by gradient descent method to ensure continuous optimization of the model. Under the framework of federated learning, the user-end models were trained, and the local model parameters obtained after training were uploaded to the server. The MMVAE encoder parameters were uploaded, and the other parts were used as the personalized layer of the user-end. The parameter aggregation was performed using federated averaging algorithm to obtain the global model. Through iterative training, the fault diagnosis model of harmonic reducer under multi-source unbalanced data was established.

[0105] (4) Fault diagnosis: The test set was input into the trained fault diagnosis model to obtain the fault diagnosis result of the harmonic reducer.

[0106] 5 Application and analysis

[0107] 5.1 Building signal acquisition experiment platform

[0108] The experimental data used in this paper were obtained through the harmonic reducer signal acquisition experiment platform built in the laboratory, and the experimental platform is shown in Figure 7 .

[0109] The measurement and control system of the harmonic reducer signal acquisition experiment platform is composed of a data acquisition instrument, an acceleration sensor, an acoustic emission sensor, a harmonic reducer to be tested, a torque speed sensor, a coupling, a driving motor, a load motor, a motor controller and other parts. The structure diagram is shown in Figure 8 . The motor controller is used to control the load motor and the driving motor, the speed and load of the harmonic reducer are set, and the signals of the harmonic reducer under different working conditions are collected by the acceleration sensor and the acoustic emission sensor.

[0110] 5.2 Introduction of experimental data set

[0111] The research object of the experiment is the green harmonic wave LCSG-32-50-C-I type harmonic reducer. According to its structure and actual failure, different fault types of harmonic reducer are realized. The experimental data includes normal state, rolling body gravity fault, rigid wheel tooth fault, flexible bearing outer ring light, medium and heavy fault and flexible bearing inner ring light, medium and heavy fault, a total of 10 types of state. Among them, the light fault of flexible bearing is laser ablation 1 time, the medium fault is laser ablation 5 times, and the heavy fault is laser ablation 10 times. In order to express the 10 kinds of harmonic reducer data more conveniently, the expression method is shown in Table 1. For example, IR10 represents the heavy fault of the inner ring of the flexible bearing of the harmonic reducer.

[0112] Table 1 Expression method of different categories of data

[0113]

[0114] In order to simulate the actual scene, the number of normal state samples is large, and the number of fault samples is small. The data sets with the normal sample to fault sample ratio of 2:1, 10:1, 20:1 and 50:1 are constructed. The detailed data set division is shown in Table 2.

[0115] Table 2 Unbalanced data set division

[0116]

[0117]

[0118] The harmonic reducer data set used in the experiment includes 8 working conditions. The specific description of different working condition data is shown in Table 3.

[0119] Table 3 Description of data of different working conditions

[0120]

[0121] The collected signal is preprocessed, and the one-dimensional signal collected is converted into a time-frequency graph by using wavelet transform. Taking the medium fault of the inner ring of the flexible bearing in working condition A as an example, Figure 9 (a) and Figure 9 (b) are the time-frequency graphs of vibration signal and acoustic emission signal respectively.

[0122] A total of 8 tasks are set in the experiment. The working conditions corresponding to different users in federated learning in each task are shown in Table 4.

[0123] Table 4 User data set setting under different tasks

[0124]

[0125]

[0126] The number of training iterations in the method herein is set to 100, the learning rate is set to 0.01, and the activation function is selected as the ReLU function. Comparative experiments before and after the improvement of the data enhancement method

[0127] To verify the reliability of the proposed data enhancement method in fault diagnosis under imbalanced data, methods 1 and 2 are compared. Method 1 does not use data enhancement methods and uses a cross-entropy loss function as the loss function. Method 2 uses the improved Mixup method and uses a cross-entropy loss function as the loss function. In tasks 1 to 4, under the federated learning framework, the vibration signal and acoustic emission signal training set 2 are input into the model, and the original residual network is used to extract features from the input data. The specific experimental results are shown in Figure 10 .

[0128] According to Figure 10 , in the comparative experiment of harmonic reducer fault diagnosis under imbalanced data, the improvement of the data enhancement method and the selection of the loss function are beneficial to improve the fault diagnosis ability of the model. The proposed method improves the average accuracy by about 7.6% and 4.1% compared with the previous two methods.

[0129] When dealing with imbalanced data sets, it is often difficult to comprehensively and accurately reflect the model performance by only using classification accuracy as a single evaluation indicator. Therefore, this experiment introduces G-mean and F-Measure as supplementary evaluation indicators, which are more sensitive to the classification performance of minority class samples, thus more accurately measuring network performance. Taking task 1 as an example, under the federated learning framework, the vibration signal and acoustic emission signal training set with four imbalanced proportions are input into the model, and the original residual network is used to extract features from the input data. The specific experimental results are shown in Figure 11 .

[0130] According to Figure 11 , in the comparative experiment using four imbalanced training sets and measuring three classification performance indicators, the proposed method improves the three evaluation indicators compared with the other two methods, and at least improves by 7.1%, 4.5% and 7.6% compared with method 1. In summary, the combination of the improved Mixup data enhancement method and the focal loss function can improve the classification performance of the model under imbalanced data.

[0131] 5.4 Comparative experiments before and after the improvement of the residual network

[0132] To explore the effectiveness of introducing ECA attention mechanism and weighting the output of residual branch by learnable weight, the data features are extracted by the improved and unimproved residual network respectively, and the features are visualized by t-SNE algorithm. Taking task 5 as an example, the vibration signal and acoustic emission signal training set 2 are input into the model under the federated learning framework, and the feature visualization diagram is as shown in Figure 12 、 Figure 13 .

[0133] As can be seen from Figure 12 and Figure 13 , in the feature visualization diagram before the improvement of the residual network, the intra-class distance is large at the L1 and L2 markers, there is misclassification at the L3 and L4 markers, and the inter-class distance is small at the L5 marker. These two classes belong to the fault of the outer ring of the flexible bearing, and the deep features have certain similarity. In the feature visualization diagram after the improvement of the residual network, although there are misclassified data at the L6 and L7 markers, the deep features extracted by the improved residual network have clearer class boundaries and more compact clusters. Therefore, it can be preliminarily determined that the method of introducing ECA attention mechanism and weighting the output of residual branch by learnable weight can more effectively extract the features of the harmonic reducer, which helps to enhance the fault diagnosis performance of the model.

[0134] To further verify that the improved residual network can effectively extract the deep features of the data in the fault diagnosis of the harmonic reducer under unbalanced data, taking task 5 as an example, the vibration signal and acoustic emission signal training set 2 are input, and the diagnosis results are plotted into a confusion matrix as shown in Figure 14 and Figure 15 .

[0135] As can be seen from Figure 14 and Figure 15 , when the data features are extracted by the unimproved residual network for fault diagnosis, there are a large number of misclassified data for B10, CMT and OR1, and there are also a small number of misclassified data for the remaining classes. Although the improved residual network still has misclassified data, the number of misclassified data is reduced, and the classification accuracy of OR1 and CMT is greatly improved. Therefore, the improved residual network can enhance the extraction of key features of the data, and thus better realize the fault diagnosis of the harmonic reducer under unbalanced data.

[0136] 5.5 Multi-source signal and single-source signal comparison experiment

[0137] To verify the superiority of multi-source signals in the fault diagnosis of harmonic reducer unbalanced data, take task 5 to task 8 as an example, input the training set 2 of multi-source signals and single-source signals into the model, the multi-source signals are vibration signals and acoustic emission signals, and the single-source signals are vibration signals or acoustic emission signals. Under the framework of federated learning, use the improved residual network combined with data enhancement method for comparative experiment, and the specific experimental results are shown in Figure 16 The improved residual network is used to extract data features, and the comparative experiment of fault diagnosis under unbalanced data is carried out. In task 5, task 6 and task 7, the accuracy of fault diagnosis of acoustic emission signal in single-source signal is the highest, and in task 8, the performance of vibration signal in single-source signal is the best, but they are lower than the fault diagnosis accuracy after multi-source information fusion. In this experiment, the average accuracy of multi-source signals as input is about 1.2% and 0.9% higher than that of single-source signals.

[0138] In summary, the method based on multi-source information fusion can make full use of the information of different signals for fault diagnosis of harmonic reducer unbalanced data, and can avoid the problem of insufficient description of harmonic reducer running information by single-source signal.

[0139] 5.6 Comparison experiment before and after improvement of multi-source information fusion method

[0140] To verify the superiority of the multi-source information fusion method used in this topic in the fault diagnosis of harmonic reducer multi-source unbalanced data, under the federated framework, the vibration signal and acoustic emission signal training set 2 are input into the improved feature extraction network, and different methods are used for feature fusion, and comprehensive experiment is carried out in 8 fault diagnosis tasks, and the experimental results are shown in the form of radar chart, as shown in Figure 17

[0141] It can be seen from Figure 17 that the accuracy of the improved MMVAE method for feature fusion is improved compared with the direct feature splicing method in the 8 fault diagnosis tasks before and after the improvement of the residual network. Among them, the accuracy is improved by an average of 6% when using the original residual network to extract features for comparison, and the fault diagnosis accuracy is improved by an average of 4.3% when using the improved residual network to extract features for comparison. The average accuracy of the improved residual network combined with MMVAE for fault diagnosis is improved by 8.7% compared with the method of directly splicing and fusing features of the original residual network in the 8 fault diagnosis tasks, especially in task 7, the accuracy is improved by 12.3%.

[0142] ​From the analysis of the above experimental results, it can be seen that the improved residual network can improve the feature extraction ability of the model and dynamically adjust the attention degree to different features, but for multi-source signals, directly using the feature splicing method cannot fully tap the potential correlation between different signals. MMVAE enables the model to tap the complementary information between different signals in the latent variable space and further process the features of different signals through the self-attention mechanism to enhance the feature representation, thereby enhancing the processing ability of the model for multi-source signals and further improving the ability of the model for fault diagnosis of harmonic reducer multi-source unbalanced data.

[0143] 5.7 Comparison of the method proposed with other multi-source information fusion methods

[0144] To further verify the effectiveness of the proposed method for fault diagnosis of harmonic reducer multi-source unbalanced data, the proposed method is compared with four multi-source information fusion methods, namely, Hybrid Multi-Scale Convolutional Neural Network (HMS-MACNN), Group Normalization Parallel Convolutional Neural Networks (GPCNN), Self-Attention-Dynamic Adaptive Convolutional Neural Network (SA-DACNN), and Deep Residual Neural Network (DRNN). The training set of the vibration signal and the acoustic emission signal is input into the model, and the test is performed in eight fault diagnosis tasks, and the results are shown in Figure 18

[0145] From the experimental results of Figure 18 It can be seen that in the eight fault diagnosis tasks, the diagnostic accuracy of the proposed method is improved compared to other multi-source information fusion methods, with an average accuracy of 98.8%, and compared to HMS-MACNN, GPCNN, SA-DACNN, and DRNN multi-source information fusion methods, the average accuracy is improved by 6.9%, 11.4%, 3.4%, and 7.4%, respectively. From the above experiments, it can be seen that the proposed method is effective for fault diagnosis of harmonic reducer multi-source unbalanced data.

[0146] 6 Conclusion

[0147] ​To solve the problem of low diagnostic accuracy caused by the fact that the number of normal state samples of industrial robot harmonic reducer is more than that of fault samples and single source signal cannot fully characterize the operation characteristics of harmonic reducer, and the privacy data of different users is not shared, a federated learning fault diagnosis method for multi-source unbalanced data of harmonic reducer is proposed. The conclusion is as follows through the verification of the harmonic reducer signal collection experiment platform:

[0148] (1) An improved Mixup combined with a focal loss function is proposed to solve the data imbalance problem. According to the number of samples of different categories, the sampling strategy of the data is dynamically adjusted, and the focal loss function is combined to make the model pay more attention to the categories with more misclassifications in training. The average accuracy of the proposed method is improved by 7.6% and 4.1% respectively compared with other methods in different tasks. The effectiveness of the three index evaluation methods verifies that the proposed method improves the classification ability of the model under data imbalance.

[0149] (2) An effective channel attention mechanism is introduced into the residual network, and a feature extraction network method is proposed to weight the output of the residual branch with learnable weights, which adjusts the attention of the model to different features and better extracts deep features of data. Through feature visualization and confusion matrix method, it is verified that the improved residual network can improve the extraction ability of harmonic reducer fault features.

[0150] (3) A federated learning fault diagnosis method for multi-source unbalanced data of harmonic reducer is proposed. This method ensures the privacy of different user data under the personalized federated learning framework, extracts the complementary information between different signals by improving the multi-modal variational autoencoder, and uses the self-attention mechanism to adaptively adjust the feature information. Under the condition of multi-source unbalanced data, an effective harmonic reducer fault diagnosis model is established. Through 8 fault diagnosis tasks, the average accuracy of the proposed method reaches 98.8%, and the fault diagnosis accuracy is at least 3.4% higher than that of the other comparative methods.

[0151] The experimental data has been used to fully verify the harmonic reducer fault diagnosis method in the experiment. In the next step, the harmonic reducer composite fault data and other rotating mechanical component data will be used for experimental research.

[0152] The reference cited in the invention is as follows:

[0153] [1] Zhang X, Wang P, Zhang C, et al. Precision degradation failure and related competitive failure reliability evaluation of harmonic reducer [J]. Vibration and shock, 2024, 43(15): 277-287.

[0154] Zhang X, Wang P, Zhang CH M, et al. Research on the reliability evaluation of precision degradation failure and related competing failures of harmonic reducer[J]. Journal of Vibration and Shock, 2024, 43(15): 277-287.

[0155] [2] Pan BS, Xue SH, Xie SJ, et al. Remaining useful life prediction method of harmonic reducer based on the crack propagation of the flex-spline[J]. Computer Integrated Manufacturing Systems, 2024, 30(11): 4030-4041.

[0156] PAN B S, XUE SH CH, XIE SH J, et al. Remaining useful life prediction method of harmonic reducer based on the crack propagation of the flex-spline[J]. Computer Integrated Manufacturing Systems, 2024, 30(11): 4030-4041.

[0157] [3] JIA Y, LI Y, XU M, et al. A fault diagnosis scheme for harmonic reducer under practical operating conditions[J]. Measurement, 2024, 227: 114234.

[0158] [4] Kang Shouqiang, Xiao Yang, Wang Yuqing, et al. Fault diagnosis method for different specifications of rolling bearings based on federal model migration[J]. Vibration and Shock, 2023, 42(22): 184-192.

[0159] KANG SH Q, XIAO Y, WANG Y J, et al. Fault diagnosis method for different specification rolling bearings based on the method of federated model transfer learning[J]. Journal of Vibration and Shock, 2023, 42(22): 184-192.

[0160] [5] ZHOU X, ZHOU H C, HE Y M, et al. Harmonic reducer in-situ fault diagnosis for industrial robots based on deep learning[J]. Science China Technological Sciences, 2022, 65(9): 2116-2126.

[0161] [6] HE Y, CHEN J, ZHOU X, et al. In-situ fault diagnosis for the harmonic reducer of industrial robots via multi-scale mixed convolutional neural networks[J]. Journal of Manufacturing Systems, 2023, 66: 233-247.

[0162] [7] CHEN R X, ZHANG Y, YANG L X, et al. Health condition assessment of harmonic reducer based on integer-period data and convolutional neural network[J]. Chinese Journal of Scientific Instrument, 2020, 41(02): 245-252.

[0163] CHEN R X, ZHANG Y, YANG L X, et al. Health condition assessment of harmonic reducer based on integer-period data and convolutional neural network[J]. Chinese Journal of Scientific Instrument, 2020, 41(02): 245-252.

[0164] [8]Guo YY,Zhao XZ,Shangguan WB,et al.Fault frequency analysis of flexible elliptical bearings and feature extraction using CMWT-FH[J].Journal of Mechanical Engineering,2019,55(23):154-161.

[0165] Guo YY,Zhao XZ,Shangguan WB,et al.Fault frequency analysis of flexible elliptical bearings and feature extraction using CMWT-FH[J].Journal of Mechanical Engineering,2019,55(23):154-161.

[0166] [9]Li K,Yang R,Wei T,et al.Fault diagnosis of the harmonic reducer based on dual-path convolutional network with multi-channel hybrid attention mechanism[J].Measurement Science and Technology,2024,36(1):016130.

[0167]

[10] Meng Z,Guan Y,Pan ZZ,et al.Research on fault diagnosis of rolling bearings based on secondary data augmentation and deep convolution[J].Journal of Mechanical Engineering,2021,57(23):106-115.

[0168] Meng Z,Guan Y,Pan ZZ,et al.Research on fault diagnosis of rolling bearings based on secondary data augmentation and deep convolution[J].Journal of Mechanical Engineering,2021,57(23):106-115.

[0169]

[11] HANG Q, YANG J, XING L. Diagnosis of rolling bearing based on classification for high dimensional unbalanced data[J]. IEEE Access, 2019, 7: 79159-79172.

[0170]

[12] SU Y, MENG L, KONG X, et al. Generative adversarial networks for gearbox of wind turbine with unbalanced data sets in fault diagnosis[J]. IEEE Sensors Journal, 2022, 22(13): 13285-13298.

[0171]

[13] LU F, TONG Q, FENG Z, et al. Unbalanced bearing fault diagnosis under various speeds based on spectrum alignment and deep transfer convolution neural network[J]. IEEE Transactions on Industrial Informatics, 2022, 19(7): 8295-8306.

[0172]

[14] LU J, WU W, HUANG X, et al. A modified active learning intelligent fault diagnosis method for rolling bearings with unbalanced samples[J]. Advanced Engineering Informatics, 2024, 60: 102397.

[0173]

[15] ZHANG H, YU QY, QIN CQ, et al. Bearing fault diagnosis based on information fusion and dual connection attention residual network[J]. Vibration and Shock, 2023, 42(20): 114-123.

[0174] ZHANG H L, YU Q Y, QIN CH Q, et al. Bearing fault diagnosis based on double-connected attention residual network and information fusion[J]. Journal of Vibration and Shock, 2023, 42(20): 114-123.

[0175]

[16] WU J, JIANG L, LI J, et al. Discovering new prognostic features for the harmonic reducer in remaining useful life prediction[J]. Shock and Vibration, 2023, 4(05): 2381638.

[0176]

[17] SHAO H, LIN J, ZHANG L, et al. A novel approach of multisensory fusion to collaborative fault diagnosis in maintenance[J]. Information Fusion, 2021, 74: 65-76.

[0177]

[18] ZHAO X, JIA M, DING P, et al. Intelligent fault diagnosis of multichannel motor–rotor system based on multimanifold deep extreme learning machine[J]. IEEE / ASME Transactions on Mechatronics, 2020, 25(5): 2177-2187.

[0178]

[19] HSIEH N K, YU T Y. Fault detection in harmonic drive using multi-sensor data fusion and gravitational search algorithm[J]. Machines, 2024, 12(12): 831.

[0179]

[20] LIU Q,WANG H P.A case study on multisensor data fusion for imbalance diagnosis of rotating machinery[J].Ai Edam,2001,15(3):203-210.

[0180]

[21] KANG SH Q,ZHANG W D,WANG Y J,et al.Fault diagnosis method of harmonic reducer under different working conditions based on information fusion subdomain adaptation[J].Chinese Journal of Scientific Instrument.

[0181] KANG SH Q,ZHANG W D,WANG Y J,et al.Fault diagnosis method of harmonic reducer under different working conditions based on information fusion subdomain adaptation[J].Chinese Journal of Scientific Instrument.

[0182]

[22] ZHANG Y,YU K,LEI Z,et al.Integrated intelligent fault diagnosis approach of offshore wind turbine bearing based on information stream fusion and semi-supervised learning[J].Expert Systems with Applications,2023,232:120854.

[0183]

[23] KANG SH Q,YANG J W,WANG Y J,et al.Fault diagnosis method of rolling bearing under different working conditions based on federal multi-representation domain adaptation[J].Chinese Journal of Scientific Instrument.

[0184] KANG SH Q, YANG J W, WANG Y J, et al. Fault diagnosis method of rolling bearings under different working conditions based on federated multi-representation domain adaptation[J]. Chinese Journal of Scientific Instrument, 2023, 44(06): 165-176.

[0185]

[24] LI Z, LI Z, LI Y, et al. An intelligent diagnosis method for machine fault based on federated learning[J]. Applied Sciences, 2021, 11(24): 12117.

[0186]

[25] ZHANG J, DUAN L, LI K, et al. Improved lightweight federated learning network for fault feature extraction of reciprocating machinery[J]. Measurement Science and Technology, 2024, 35(4): 045115.

[0187]

[26] MEHTA M, CHEN S, TANG H, et al. A federated learning approach to mixed fault diagnosis in rotating machinery[J]. Journal of Manufacturing Systems, 2023, 68: 687-694.

[0188]

[27] ZHANG H, CISSE M, DAUPHIN Y N, et al. mixup: Beyond empirical risk minimization[C] / / International Conference on Learning Representations, 2018, 1-13.

[0189]

[28] XIAO L F. Research on fault diagnosis methods of rolling bearings of rotating machinery based on multi-source information fusion[D]. Yanshan University, 2023.

[0190]

[29] SHI Y, PAIGE B, TORR P. Variational mixture-of-experts autoencoders for multi-modal deep generative models[J]. Advances in neural information processing systems, 2019, 32.

Claims

1. A federated learning fault diagnosis method for multi-source imbalance data of harmonic reducers, characterized by: The method comprises: Step 1: Signal acquisition: Build a signal acquisition experimental platform. Install harmonic reducers with different fault types to collect vibration and acoustic emission signal data. Use the host computer software to control the drive motor and load motor, adjust the speed and load of the harmonic reducer, simulate different working conditions, and realize the signal acquisition of the harmonic reducer under different working conditions. Step 2: Data preprocessing: Use wavelet transform on the collected one-dimensional signal to obtain a two-dimensional image that can more comprehensively and intuitively present the sample time-frequency information, which is used to construct an unbalanced data set; Step 3: Model Construction: Data augmentation methods are used to enhance the imbalanced data. The residual network is improved by introducing an effective channel attention mechanism and weighting the output of the residual branch with learnable weights. The improved residual network is used to extract the features of vibration and acoustic emission signals. The complementary information of multi-source signals is mined through a multimodal variational autoencoder. The obtained classification loss and the loss of the multimodal variational autoencoder are used as the model training loss. Through iterative training, the loss function value of the model training is obtained. The back propagation algorithm is used to calculate the gradient of the network weight according to the loss function. The model parameters are iteratively updated in the direction of minimizing the loss function through the gradient descent method to ensure continuous optimization of the model. Within the framework of federated learning, each user-side model is trained, and the local model parameters obtained after training are uploaded to the server. Some parameters of the MMVAE encoder are uploaded, and the remaining parameters serve as the user-side personalization layer. The federated averaging algorithm is used to aggregate the parameters to obtain a global model. Through iterative training, a fault diagnosis model for harmonic reducers under multi-source unbalanced data is established. Step 4: Fault diagnosis: Input the test set into the trained fault diagnosis model to obtain the harmonic reducer fault diagnosis results.

2. The method for federated learning fault diagnosis of multi-source imbalance data of harmonic reducer according to claim 1, characterized in that: The data enhancement is to rely on forming new synthetic samples by convexly combining existing training samples and their corresponding labels to reduce overfitting in deep neural networks; if (x i ,y i ), (x j ,y j ) is derived from the data x i , x j and its related tags y i ,y j The training examples composed of , then Mixup creates synthetic data and labels as shown in formula (1) and formula (2): Among them, the β distribution of λ ~ β (θ, θ), and θ>0; and is the new data and labels generated; The data sampling strategy is shown in formula (3): Among them, q i represents the probability of sampling from the i-th class, n k represents the number of samples of the kth class, K is the number of sample classes; in this case, choosing l = 1 is equivalent to selecting samples with a probability equal to the frequency of their class in the training set, while choosing l = 0 results in a sampling probability of q for each class i =1 / K,(x i ,y i ) and (x j ,y j ) are selected from the two probability spaces of l = 1 and l = 0 respectively; in the new round of training, the weights of different types of samples in the new round are recalculated according to the data augmentation results obtained in the previous round of model training, so that the generated sample space is more balanced; Using the focus loss function instead of the original cross entropy loss function as the model classification loss function improves the model's fault diagnosis ability under data imbalance conditions, as shown in formula (4): Where α is the balance factor, γ is the focus factor, and p i Represents the probability of predicting the i-th category.

3. A federated learning fault diagnosis method for multi-source imbalance data of harmonic reducers according to claim 1 or 2, characterized in that: The process of the improved residual network is: The residual block is the basic architecture of the residual network ResNet. The residual block output H(x) is obtained by adding the identity mapping of the input x to the feature F(x) extracted by the convolutional layer. The channel attention module ECA is introduced to effectively increase the expressive power of convolutional neural networks. The ECA module is a very lightweight plug-and-play module. The residual block output of ResNet is shown in formula (5): H(x)=F(x)+x (5) The output of the residual block is the sum of the features F(x) extracted by the convolutional layer and the original input x, which helps alleviate problems such as gradient disappearance and thus trains deep models more efficiently. In order to control the influence of each component, a learnable weight is introduced between the input and the features extracted by the convolutional layer, as shown in formula (6): H(x)=F(x)+μx (6) Where μ is the weight that adjusts the influence of input data.

4. A federated learning fault diagnosis method for multi-source imbalance data of harmonic reducers according to claim 1 or 2, characterized in that: The federated learning is specifically as follows: The federated learning framework uses the federated averaging algorithm as the parameter aggregation method, and its expression is shown in formula (7): in, is the local model parameter of the tth user in the jth round of federation; G j+1 is the global model parameter of the j+1th round; Multi-sensor information fusion is combined with federated learning to learn information from different sensors while protecting data privacy. The multimodal variational autoencoder (MMVAE) method is used to simultaneously process data from multiple sensors. The relationship between different sensor data is captured through a shared latent space, effectively fusing information from different sensors. The multimodal variational autoencoder uses the improved ResNet neural network as an encoder to extract features, maps the features of different sensors to the latent variable space, ensures that the model extracts complementary information from different signals, uses the mean and standard deviation obtained from the encoder output to describe the distribution of latent variables in the latent space, introduces the latent variables generated by the self-attention mechanism layer SA adaptive weighting, can better capture the correlation between features, and reconstructs data through the decoder. The calculation formula of the self-attention mechanism is shown in formula (8): Among them, Q is the query matrix, K is the key matrix, V is the key vector, d is the dimension of the key, and Softmax is the activation function. The latent variables in the MMVAE latent space contain the characteristic information of the original input data. By improving the model structure of MMVAE and fully mining the characteristic information in the latent variables, the fault diagnosis of harmonic reducer can be realized. The loss function is improved according to the optimized model structure: First, by combining the loss functions of MSE and KL divergence, the expressions are shown in formulas (9) and (10): Among them, x i Represents the original data, Represents the reconstructed data, μ i represents the mean of the latent variable, σ i represents the variance of the latent variable, MSE is used to evaluate the difference between the reconstructed data and the original data, and KL divergence is used to measure the similarity between the latent variable and the standard normal distribution, so as to better guide the training process of the model and obtain the loss function of MMVAE, as shown in formula (11): L MMVAE =L MSE +L KL (11) Finally, the loss of the multimodal variational autoencoder and the model classification loss are weighted and summed as shown in formula (4) to serve as the overall loss function of the model, as shown in formula (12): L=L class +ωL MMVAE (12) Here, ω is a hyperparameter, and the multimodal variational autoencoder and the fault classification branch are jointly trained. In this way, the generation process of reconstructed data can reversely affect the generation of latent variables, so that the latent variables can better represent the characteristic information of the original data, thereby improving the accuracy of fault diagnosis.

5. The method for federated learning fault diagnosis of multi-source imbalance data of harmonic reducer according to claim 4 is characterized in that: In a federated learning system, the server sends global model parameters to the client, which uses its own data to train the model. When uploading parameters, it retains some network layers as local personalized layers, and then sends other model parameters back to the server, where they are aggregated to generate a new global model.

6. A federated learning fault diagnosis system for multi-source imbalance data of harmonic reducers, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 5, and executes the steps of the federated learning fault diagnosis method for multi-source imbalance data of harmonic reducers during operation.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a federated learning fault diagnosis method for multi-source imbalance data of a harmonic reducer according to any one of claims 1 to 5 when called by a processor.

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