A harmonic reducer fault diagnosis method and system based on personalized federated jump aggregation strategy

Abstract

The present invention discloses a harmonic reducer fault diagnosis method and system with a personalized federal jump aggregation strategy, which relates to the technical field of reducer fault diagnosis, and solves the problem of low fault diagnosis accuracy caused by data distribution differences between different harmonic reducer users under data islands. The technical points of the present invention include: proposing a model construction method based on secondary aggregation for deploying personalized local models, which is user-centric, and deploys a personalized initialization model suitable for the local data set for each user through secondary aggregation, while using L2 regularization to avoid overfitting and solve the problem of decreased global model accuracy; proposing a federal aggregation strategy based on cyclic weights to accelerate global model convergence; in the stage of global model parameter issuance, a model parameter jump aggregation strategy is proposed to overcome the disadvantage of slow convergence of the FedAvg algorithm without increasing additional computing overhead. The present invention is suitable for multi-user harmonic reducer collaborative fault diagnosis that ensures data privacy.

Description

Technical Field

[0001] The present invention relates to the technical field of speed reducer fault diagnosis, and in particular to a harmonic speed reducer fault diagnosis method and system with a personalized federal jump aggregation strategy. Background Art

[0002] Industrial robots are widely used in defense industry, equipment manufacturing industry, aerospace industry, electronic and electrical industry and other fields due to their high operating precision and low operating cost. [1] As a key component of industrial robots, harmonic reducers can accurately adjust the rotation angle of industrial robots. [2] However, due to the complex and changeable working conditions of industrial robots in actual applications, harmonic reducers are prone to failures such as flexible bearing wear and rigid wheel tooth breakage. [3] These faults not only lead to the performance degradation of the harmonic reducer itself, but also directly affect the production efficiency of the entire equipment and even cause safety accidents. [4] Therefore, accurate fault diagnosis for harmonic reducers has important practical significance for improving the reliability and safety of industrial robots.

[0003] In recent years, with the rapid development of artificial intelligence, intelligent fault diagnosis methods based on deep learning have been successfully applied to the field of harmonic reducer diagnosis. [5] . Chen et al. [6] The convolutional neural network is used to perform deep feature learning on the time-frequency graph of the industrial robot motor voltage signal to achieve effective identification of the health status of the harmonic reducer. Zhou et al. [7] proposed a deep learning fault diagnosis method based on one-dimensional convolutional neural network, which uses continuous time-domain vibration signals as data sets to train the fault diagnosis model of harmonic reducers. [8] According to the time series characteristics of the vibration signal of the harmonic reducer, a fault diagnosis method of the harmonic reducer combining the convolutional neural network and the long short-term memory network is proposed. He et al. [9] The multi-scale hybrid convolutional neural network is used for fault diagnosis of industrial robot harmonic reducers, and the accuracy rate on 4 data sets is over 90%.

[0004] The above-mentioned deep learning-based fault diagnosis methods require a large amount of labeled data for model training. However, in industrial scenarios, it is often difficult to obtain data with accurate labels and sufficient quantity. Therefore, it is usually difficult for a single user to build a fault diagnosis model alone.

[10] .

[0005] In reality, multiple companies or factories may have similar industrial robots, and each user collects harmonic reducer status data independently. Therefore, building a fault diagnosis model with centralized local data from multiple users can solve the problem of scarce data from individual users.

[11] However, in engineering scenarios, data centralization is difficult to achieve. First, as a new production factor, data is becoming increasingly important. Due to issues such as corporate competition, privacy, and production safety, data cannot be shared between companies.

[12] Secondly, fast data transmission requires a large bandwidth of the industrial Internet, which leads to high costs for data concentration and data analysis. Therefore, it is not feasible to directly concentrate multi-user local data for centralized fault diagnosis model training.

[0006] To solve the above problems, federated learning came into being

[13] Federated learning is a distributed model training method that can implicitly centralize multi-user distributed data information, ensuring that each user's data privacy is not leaked.

[14] In industrial scenarios, mechanical fault diagnosis methods based on federated learning have attracted the attention of many scholars. [15,16] . Jiang et al.

[17] proposed the DeepFedWT federated deep learning framework, and used the federated average algorithm to solve the problem of multi-wind turbine collaborative fault diagnosis under data silos. Qin et al.

[18] A federated learning method based on wavelet packet decomposition is proposed for train bogie fault diagnosis, which realizes diagnostic knowledge sharing under privacy protection.

[0007] The above literature can provide theoretical support for the fault diagnosis of multi-user harmonic reducers under island privacy, but it is still necessary to assume that the characteristic distribution of multi-user harmonic reducer data is the same.

[19] However, in actual projects, the private data of different users often come from different working conditions, resulting in distribution differences between user data, that is, user data heterogeneity.

[20] If the classic federated average algorithm is still used, the diagnostic performance of the global model will be reduced, the convergence speed will be slow, and even the global model will not converge.

[21] .

[0008] To address the above problems, two solutions have been proposed. The first solution is to improve the model aggregation effect, thereby enhancing the global model diagnosis performance. Chen et al.

[22] Aiming at the difference distribution of data among users, a weighted federated average algorithm based on difference degree is proposed, which can dynamically adjust the weights of different clients in model aggregation. The experimental results on the bearing dataset prove the effectiveness of the method. Wang et al.

[23] The federated minimax algorithm is used to aggregate the model parameters of each user, and the coordinated fault diagnosis of multi-user gas-insulated switches under different working conditions is realized. Geng et al.

[24] A weighted model aggregation strategy based on F1 score is proposed to reduce the impact of distribution differences. The improved aggregation strategy has a significant improvement in the fault classification accuracy of bearing datasets. Ma et al.

[25] The weight of each user model is redistributed according to the contribution of each category, and two class-weighted aggregation strategies are proposed to solve the problem of different user data distribution.

[26] et al. used the Hessian matrix as the scale matrix to capture the parameter changes of the user model, thereby calculating the aggregation weight for each user model. The above literature effectively solves the distribution difference problem between different user data, but the improved model parameter aggregation algorithm adds additional computational overhead.

[0009] Personalized federated learning is another solution that is user-centric and is committed to training a "dedicated model" for each user, thereby addressing the problem of decreased global model accuracy caused by differences in data distribution between users.

[27] This method aims to ensure that each user can get the optimal model by reducing the impact of distribution differences. Fallah et al.

[28] Combining the model agnostic meta-learning (MAML) framework with federated learning, the Per-FedAvg algorithm is proposed to solve the problem of data heterogeneity. Oh et al.

[29] The FedBABU algorithm is proposed, which uses user private data to fine-tune the classifier of the global model to achieve user personalized model training. However, in the above personalized federated learning method, when users perform local model training, they directly use the global model sent by the server as the initialization model, which will lead to a sharp decline in model diagnostic performance, hindering the next iterative optimization training. Summary of the invention

[0010] In view of the distribution differences among multi-user private data, the diagnostic performance degradation caused by user model initialization in the personalized federated learning method, and the additional overhead caused by the improved aggregation algorithm, the present invention proposes a harmonic reducer fault diagnosis method and system with a personalized federated jump aggregation strategy.

[0011] According to one aspect of the present invention, a harmonic reducer fault diagnosis method with a personalized federated jump aggregation strategy is proposed, the method comprising:

[0012] S1. Each local harmonic reducer user builds a personalized local model using a secondary aggregation method; the secondary aggregation method is: the aggregation of multiple user models performed on the server is the first aggregation, and the personalized local initial model training performed by the local user is the secondary aggregation;

[0013] S2, each local harmonic reducer user uploads personalized local model parameters to the server;

[0014] S3. The server updates the global model using a cyclic weight strategy and adopts a jump aggregation strategy to send the global model parameters to each local harmonic reducer user; the jump aggregation strategy is: the server periodically skips the global federation aggregation step and directly randomly distributes the received user personalized local model to all users;

[0015] S4, repeat the above steps until the maximum number of federation iterations is reached, and obtain the final federation global model;

[0016] S5. Utilize the federal global model to perform local harmonic reducer fault diagnosis.

[0017] Furthermore, the specific steps of S1 include: each local harmonic reducer user obtains a personalized local initialization model using secondary aggregation, which is expressed as:

[0018]

[0019] in, represents the initial model parameters of the i-th user in the t-th round; Θ t-1 is the global model parameter sent by the server in round t-1, is the local model parameter of the i-th user in the t-1th round; ⊙ is the Hadamard operation; W i is the personalized aggregation weight; is updated information;

[0020] In the process of training the personalized initialization model using the local dataset, a penalty term based on L2 regularization is added, which is expressed as:

[0021]

[0022] Among them, the first term on the right side of the equation is the cross entropy loss function, the second term on the right side of the equation is the regularization term; n is the number of samples, m is the number of categories, and y ij is the probability that the true label of the i-th sample is in the j-th class, is the probability that the i-th sample is predicted to be the j-th class; λ is used to control the size of the regularization term.

[0023] Furthermore, the cyclic weight strategy described in S3 is: the weight sum δ of the federated average aggregation algorithm is changed from 1 to a cyclic change similar to an inverted sawtooth wave, and the change rule formula is expressed as:

[0024] δ(t cur )=A(1-t cur / T * )+q adj

[0025] Among them, t cur(0≤t≤T * ) is the ordinal number in the current cycle, A is the amplitude of the weight, T * is the number of traversals in a cycle, q adj is the lower limit of weight.

[0026] Furthermore, the mathematical expression of the jump aggregation strategy in S3 is:

[0027]

[0028] Among them, I periodic ={t|t∈R + &&1<t<T&&t modΔ=0},R + is the set of all positive integers, Δ is the given integer of jump aggregation, and t mod Δ = 0 is the judgment condition; is the model of the kth user, and is An element in Yes A randomly shuffled collection; is the cycle weight δ(t cur ) set; δ i is the weight of each user; N is the number of users.

[0029] Furthermore, the local data set includes various state data of the harmonic reducer under various working conditions, and the state data includes a normal state and different types of fault states.

[0030] According to another aspect of the present invention, a harmonic reducer fault diagnosis system with a personalized federated jump aggregation strategy is proposed, the system comprising:

[0031] A global model training module includes a local model building module submodule and a global model updating submodule; wherein the local model building submodule is configured so that each local harmonic reducer user builds a personalized local model using a secondary aggregation method; the secondary aggregation method is: the aggregation of multiple user models performed on the server is the first aggregation, and the personalized local initial model training performed on the local user is the secondary aggregation; each local harmonic reducer user uploads personalized local model parameters to the server; the global model updating submodule is configured so that the server updates the global model using a cyclic weight strategy, and adopts a jump aggregation strategy to send the global model parameters to each local harmonic reducer user; the jump aggregation strategy is: the server periodically skips the global federation aggregation step, and directly randomly distributes the received user personalized local models to all users; repeats the construction steps of the local model building module submodule and the update steps of the global model updating submodule until the maximum number of federation iterations is reached, and the final federation global model is obtained;

[0032] A fault diagnosis module is configured to perform local harmonic reducer fault diagnosis using the federated global model.

[0033] Furthermore, in the local model building submodule, the specific step of each local harmonic reducer user building a personalized local model by using a secondary aggregation method includes: each local harmonic reducer user uses secondary aggregation to obtain a personalized local initialization model, which is expressed as:

[0034]

[0035] in, represents the initial model parameters of the i-th user in the t-th round; Θ t-1 is the global model parameter sent by the server in round t-1, is the local model parameter of the i-th user in the t-1th round; ⊙ is the Hadamard operation; W i is the personalized aggregation weight; is updated information;

[0036] In the process of training the personalized initialization model using the local dataset, a penalty term based on L2 regularization is added, which is expressed as:

[0037]

[0038] Among them, the first term on the right side of the equation is the cross entropy loss function, the second term on the right side of the equation is the regularization term; n is the number of samples, m is the number of categories, and y ij is the probability that the true label of the i-th sample is in the j-th class, is the probability that the i-th sample is predicted to be the j-th class; λ is used to control the size of the regularization term.

[0039] Furthermore, the cyclic weight strategy in the global model update submodule is: the weight sum δ of the federated average aggregation algorithm is changed from 1 to a cyclic change similar to an inverted sawtooth wave, and the change rule formula is expressed as:

[0040] δ(t cur )=A(1-t cur / T * )+q adj

[0041] Among them, t cur (0≤t≤T * ) is the ordinal number in the current cycle, A is the amplitude of the weight, T * is the number of traversals in a cycle, q adj is the lower limit of weight.

[0042] Furthermore, the mathematical expression of the jump aggregation strategy in the global model update submodule is:

[0043]

[0044] Among them, I periodic ={t|t∈R + &&1<t<T&&t modΔ=0},R + is the set of all positive integers, Δ is the given integer of jump aggregation, and t mod Δ = 0 is the judgment condition; is the model of the kth user, and is An element in Yes A randomly shuffled collection; is the cycle weight δ(t cur ) set; δ i is the weight of each user; N is the number of users.

[0045] Furthermore, the local data set in the local model building submodule includes various state data of the harmonic reducer under various working conditions, and the state data includes a normal state and different types of fault states.

[0046] The beneficial technical effects of the present invention are:

[0047] This paper aims at multi-user harmonic reducer collaborative fault diagnosis and proposes a fault diagnosis framework (PFL-HR) and method based on personalized federated learning. The main contributions and innovations of this paper are as follows:

[0048] 1) A personalized federated aggregation strategy of skip cycle weights is proposed, and a harmonic reducer fault diagnosis framework (PFL-HR) and model based on personalized federated learning are constructed, which is suitable for multi-user harmonic reducer collaborative fault diagnosis with guaranteed data privacy.

[0049] 2) A personalized local model construction method based on secondary aggregation is proposed. This method is user-centric and deploys a personalized initialization model suitable for the local dataset for each user through secondary aggregation. At the same time, L2 regularization is used to avoid overfitting, thereby solving the problem of decreased global model accuracy caused by differences in data distribution between users.

[0050] 3) A federated aggregation strategy based on jump cycle weights is proposed. This strategy overcomes the slow convergence of the FedAvg algorithm without adding additional computational overhead, and allows the user model to acquire knowledge from more data, further improving the accuracy of the diagnostic model.

[0051] The experimental results of the harmonic reducer dataset of the self-built test bench verified that the proposed PFL-HR framework can construct an effective fault diagnosis model under multi-user harmonic reducer data island privacy distribution and different working conditions. The method proposed in this invention achieves performance very close to that of the centralized learning scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0053] Figure 1 It is a flowchart of a harmonic reducer fault diagnosis method of a personalized federal jump aggregation strategy described in the present invention.

[0054] Figure 2 It is a schematic diagram of constructing a local model based on secondary aggregation in an embodiment of the present invention.

[0055] Figure 3 Schematic diagram of cyclic weights in an embodiment of the present invention.

[0056] Figure 4 It is a vibration signal acquisition test platform for the harmonic reducer in the embodiment of the present invention.

[0057] Figure 5 It is a structural diagram of the measurement and control system in an embodiment of the present invention.

[0058] Figure 6 1 is a diagram of sensor positions in an embodiment of the present invention.

[0059] Figure 7 The following are the appearances of some faults of the harmonic reducer in the embodiment of the present invention; wherein, (a) indicates pitting fault of the rolling element (15 times); (b) indicates pitting fault of the inner ring (5 times); (c) indicates missing teeth of the flex spline; and (d) indicates missing teeth of the rigid spline.

[0060] Figure 8 It is the influence of the parameters of the loop weights in different diagnostic tasks on the global accuracy in the embodiment of the present invention; among them, (a) corresponds to T-C2; (b) corresponds to T-B2; (c) corresponds to T-C2.

[0061] Fig. 9 3 is a comparison result diagram of the global model accuracy before and after the improvement of each part in PFL-HR in an embodiment of the present invention.

[0062] Fig.10 3 is a comparison result diagram of the change curve of the global model accuracy in the embodiment of the present invention; among them, (a) corresponds to T-A2; (b) corresponds to T-B2; (c) corresponds to T-C2.

[0063] Fig.11 2 is a comparison result diagram of the Loss change curve in the embodiment of the present invention; wherein, (a) corresponds to T-A2; (b) corresponds to T-B2; (c) corresponds to T-C2.

[0064] Fig.12 3 is a comparison result diagram of the global accuracy under different tasks in the embodiment of the present invention.

[0065] Fig.13 It is the global accuracy of different federated learning algorithms in different diagnostic tasks in the embodiments of the present invention.

[0066] Fig.14 is the confusion matrix (%) between the method of the present invention and FedAvg at T-C2; wherein, (a) corresponds to FedAvg; (b) corresponds to the method of the present invention.

[0067] Fig.15 It is the visualization result of the features learned by the method of the present invention and FedAvg in T-C2; among them, (a) corresponds to FedAvg (sorted from left to right: user 1-user 5); (b) corresponds to the method of the present invention (sorted from left to right: user 1-user 5). DETAILED DESCRIPTION

[0068] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0069] The embodiment of the present invention proposes a harmonic reducer fault diagnosis method with a personalized federated jump aggregation strategy, the method comprising:

[0070] S1. Each local harmonic reducer user builds a personalized local model using a secondary aggregation method; the secondary aggregation method is: the aggregation of multiple user models performed on the server is the first aggregation, and the personalized local initial model training performed by the local user is the secondary aggregation;

[0071] S2, each local harmonic reducer user uploads personalized local model parameters to the server;

[0072] S3. The server updates the global model using a cyclic weight strategy and adopts a jump aggregation strategy to send the global model parameters to each local harmonic reducer user; the jump aggregation strategy is: the server periodically skips the global federation aggregation step and directly randomly distributes the received user personalized local model to all users;

[0073] S4, repeat the above steps until the maximum number of federation iterations is reached, and obtain the final federation global model;

[0074] S5. Utilize the federal global model to perform local harmonic reducer fault diagnosis.

[0075] According to an embodiment of the present invention, the present invention conducts a detailed study of the PFL-HR framework and method based on the following assumptions:

[0076] 1. In the federated learning framework, there is one server and multiple users. Each user has less labeled training data and cannot independently complete the establishment of the fault diagnosis model.

[0077] 2. All local private data cannot leave the user's local area. Users can only transmit model parameters, and the model parameters will not be accessed, leaked or hijacked during the transmission process, thus ensuring data privacy.

[0078] 3. Since each user’s harmonic reducer is in a different working condition, the distribution of user data is different.

[0079] Assume that there are N users in the federated learning framework. Represents the private dataset of the i-th user. is the jth data, Represents a label. i Represents the number of industrial user data of the i-th industry. The research goal of the present invention is to use the annotated private harmonic reducer data for collaborative training by each user without sharing data, and to construct N personalized local fault diagnosis models y=f suitable for each user. i (x) and an optimal global diagnostic model y = f global (x).

[0080] The PFL-HR framework consists of a server, multiple local harmonic reducer users, and a personalized federation aggregation strategy. The personalized federation aggregation strategy includes a personalized local model construction method based on secondary aggregation and a federation aggregation strategy based on jump cycle weights. Figure 1As shown in the figure. First, each user builds a personalized local model using the secondary aggregation method; second, the user uploads the model parameters to the server, and the server updates the global model using the cyclic weight strategy; finally, the server adopts the jump aggregation strategy to send the model parameters to the user; the above steps are repeated until the maximum number of federation iterations is reached, and the final federated global model is obtained.

[0081] 1) Personalized local model construction based on secondary aggregation

[0082] When there are differences in the distribution of data between users, the global model aggregated based on the federated average algorithm is often not suitable for every user.

[30] . Therefore, each user needs to build his own personalized local model according to his own data distribution. Therefore, the present invention proposes a personalized local model construction method (PLMC) based on secondary aggregation. In this method, the aggregation of multiple user models performed on the server is the first aggregation, and the personalized local initial model training performed by local users is the secondary aggregation. The method is divided into two steps: the user uses secondary aggregation to obtain a personalized local initialization model to alleviate the regression phenomenon; in the process of training the personalized initialization model using the local data set, a penalty term based on L2 regularization is added to prevent model overfitting. The local data set includes multiple state data of the harmonic reducer under various working conditions, and the state data includes a normal state and different types of fault states.

[0083] Each user re-aggregates the model sent by the server and the local model to obtain a personalized initialization model:

[0084]

[0085] Among them, Θ t-1 is the global model parameter sent by the server in round t-1, is the local model parameter of the i-th user in round t-1. The initial model parameters of the i-th user in the t-th round, ⊙ is the Hadamard operation, W i is the personalized aggregation weight, is the update information. User i trains W through a gradient-based learning method i :

[0086]

[0087] Among them, η * Learning rate for training the aggregate weights.

[0088] Note that in the first round of federated communication, the user does not have a local model. Therefore, no secondary aggregation is performed when training the user's local model.

[0089] After the local model is initialized, user i performs local model training. Since the amount of data for each user is small, to prevent the model from overfitting, an L2 regularization term is added to the loss function.

[31] This method uses the cross entropy loss function with an L2 regularization term for local model training, and its mathematical expression is:

[0090]

[0091] Among them, the first term is the cross entropy loss function, the second term is the regularization term, y ij is the probability that the true label of the i-th sample is in the j-th class, is the probability that the i-th sample is predicted to be the j-th class, n is the number of samples, m is the number of categories, and λ is used to control the size of the regularization term. The larger the λ, the greater the constraint on the complexity of the model. Figure 2 It is a schematic diagram of the personalized local model construction method based on secondary aggregation.

[0092] 2) Federation aggregation strategy based on jump cycle weight

[0093] The federated average algorithm is a classic parameter aggregation algorithm, and its mathematical expression is:

[0094]

[0095] in, δ i =n i / n global is the weight of each user, n global Represents the total data volume of all industrial users. When the data distribution of each user is inconsistent, when the global model is updated using the federated average algorithm, there is a problem that the model converges slowly or even does not converge. To this end, the present invention proposes a federated aggregation strategy based on cyclic weight (CW) to accelerate the convergence of the global model.

[0096] Li et al.

[32] We re-examined the weighted aggregation process and gained new insights into federation training: when the sum of weights δ is less than 1, it will cause a global weight contraction effect, thereby accelerating model convergence. Inspired by this, combined with the idea of ​​the cosine annealing algorithm, the weight sum δ of the federation average aggregation algorithm is changed from 1 to a cyclic change similar to an inverted sawtooth wave. Only the sum of the aggregate weights in each communication round needs to be changed, and no additional computational cost is added. Change rule formula:

[0097] δ(t cur )=A(1-t cur / T * )+q adj (5)

[0098] Among them, t cur (0≤t≤T * ) is the ordinal number in the current cycle, A is the amplitude of the weight, T * is the number of epochs in a cycle, q adj is the weight lower limit. For example, let the federation global epoch = 100, T * =20, A=0.4, q adj = 0.8, then the global model aggregation weight changes as follows Figure 3 shown.

[0099] In the training process of federated learning, if a user's local model can be trained on as many other users' private data sets as possible, it can absorb more comprehensive knowledge. In view of this, the server adopts the jump aggregation strategy (SA) to expand the training paradigm and improve the effectiveness of model training. Specifically: the server periodically skips the global federation aggregation step and directly randomly distributes the received user model to all users. The comparison diagram of aggregation and dispersion is shown in Figure 1 Shown in the upper pink dashed line.

[0100] Therefore, at the beginning of the tth round, the kth user participating in the training will obtain the model parameters sent by the server according to the judgment conditions. The mathematical expression of jump aggregation is:

[0101]

[0102] Among them, I periodic ={t|t∈R + &&1<t<T&&t modΔ=0},R + is the set of all positive integers, Δ is a given integer for jump aggregation, and t mod Δ = 0 is the judgment condition. is the model of the kth user, and is An element in . Yes After random shuffle, the set. periodic , the server randomly distributes the user’s model to other users and performs jump aggregation. periodic Therefore, the user obtains the model parameters and cannot distinguish whether the received model is a global model or a model of a certain user, thus ensuring privacy.

[0103] The federation aggregation strategy based on cyclic weights and the model parameter jump aggregation strategy are combined, and T * =Δ, the formula of the federation aggregation strategy (CW+SA) based on jump cycle weight is expressed as:

[0104]

[0105] in, is the cycle weight δ(t cur )gather.

[0106] The pseudo code process of PFL-HR is as follows: Algorithm 1.

[0107]

[0108]

[0109] The technical effect of the present invention is further verified through experiments.

[0110] The experimental data are all from the harmonic reducer vibration signal acquisition test bench built in the laboratory. Figure 4 As shown in the figure, it mainly includes a drive motor, a load motor, a vibration sensor, a coupling, a torque and speed sensor and a test piece. The structure diagram of the measurement and control system is shown in Figure 5 As shown. Figure 6 As shown, the vibration sensor is arranged at the 12 o'clock direction of the input end of the test piece, and the wave generator is used as the input end. The harmonic reducer vibration signal acquisition test platform collects vibration signals of the harmonic reducer to be tested under different working conditions at a sampling frequency of 100kHz. The model of the harmonic reducer to be tested is the green LCSG-32-50-I. The experimental data used in the experiment were collected under 4 working conditions, and each working condition corresponds to a different constant speed, which are 1000r / min, 1200r / min, 1400r / min, and 1600r / min. The data set under each working condition includes 10 state data of the harmonic reducer, and the state details are shown in Table 1. The inner ring fault, outer ring fault, and rolling element fault are made by laser pitting. The numbers represent the number of laser pitting, and the output energy is 2.6 joules; the manufacturing process of the faulty parts with missing teeth on the rigid wheel and the flexible wheel is wire cutting process. The appearance of some faults is as follows Figure 7 shown.

[0111] Table 1 Experimental data representation

[0112]

[0113] To ensure that the sample contains complete fault information, during the data preprocessing process, the sample dimension intercepted is proportional to the speed at the input end of the harmonic reducer, and its expression is:

[0114] n=60 / V h ×10 5 ×3 (8)

[0115] Where V his the input speed in r / min; then the intercepted original vibration signal is converted into a time-frequency diagram through wavelet transform, and the dimension is 3×32×32.

[0116] In order to verify the effectiveness of the proposed personalized federated learning fault diagnosis method (PFL-HR) in the distributed fault diagnosis of harmonic reducers, six diagnostic tasks were designed, namely T-A1, T-A2, T-B1, T-B2, T-C1, and T-C2. Each task contains five users, and the settings of the diagnostic tasks are shown in Table 2. The detailed information on the data category and quantity of each user is shown in Table 3. Among them, the training set data and test set data of each user are divided into 1:1.

[0117] Table 2 Working conditions of different user data in fault diagnosis tasks (r / min)

[0118]

[0119]

[0120] Table 3 Data categories and quantities used in different tasks

[0121]

[0122] The experiment was completed on a computer with NVIDIA RTX 3080Ti and 64GB memory, and its software environment was Pytorch1.13.1 and Python3.8. The experiment used the stacking of convolutional layers, pooling layers, and fully connected layers to build a CNN-based harmonic reducer fault diagnosis model as a user local model. The feature extraction layer consists of 2 convolutional layers and 2 maximum pooling layers, and the classifier consists of a fully connected layer. The specific structure is shown in Table 4. The local model training is updated using the SGD optimizer, and the learning rate is set to 0.001. The global training epoch is set to 100, and the local training epoch is 10.

[0123] Table 4 Convolutional neural network structure

[0124]

[0125] In order to demonstrate the effectiveness of the federated collaborative modeling method proposed in the present invention, the following methods are selected for comparison.

[0126] (1) Centralized: This method follows the traditional centralized machine learning scheme and integrates all the data of different users into a large training dataset for training the fault diagnosis model.

[0127] (2) FedAvg

[14] :The federated average algorithm is a widely used method in the field of federated learning. Its main process is: users synchronously train local models, and after training, the local model parameters are uploaded to the server; the server performs average aggregation to form a global model, and the aggregated global model is distributed to each user. After multiple iterations, the optimal global model is finally obtained.

[0128] (3)Per-FedAvg

[28] :This method uses model-agnostic meta-learning to solve the personalized federated learning problem. Its goal is to find an initialization model and use this initial model to perform a few rounds of training on the data of each user to obtain a better local model.

[0129] (4) FedBABU

[29] :This method decouples the user model into a feature extractor related to generality and a classifier related to personalization. Only the feature extractor of the model is updated during aggregation, and the classifier is fine-tuned during local training to achieve personalization.

[0130] Experimental results and analysis: To reduce the randomness of the experimental results, all experimental results are the average results of 5 experiments. To verify the effectiveness of the proposed method PFL-HR, it is necessary to first determine the parameters in formula (5). There are 3 parameters in formula (5), namely, T * , A, q adj . Multiple groups of experiments were conducted through network search methods to find suitable parameters, and the search range was: 5≤T * ≤20, 0.8≤q adj ≤1,0≤A≤0.4. Due to limited space, only four groups of parameter comparison tests are shown. The four groups of parameters are: R(1)={T * =100,A=0.4,q adj =0.8}, R(2)={T * =5,A=0.19,q adj =0.91}, R(3)={T * =10,A=0.27,q adj =0.88}, R(4)={T * =20,A=0.4,q adj =0.8}, where R(1) is not within the search range, representing an extreme case, i.e., T = T * , there is only one cycle in the aggregation weight, and it has been on a downward trend. The global accuracy comparison results in different fault diagnosis tasks are as follows Figure 8 As shown. Figure 8 It can be seen that the fourth group of parameters has the best effect, so the parameters of the remaining experiments are also selected as R(4).

[0131] A. Comparative experiments before and after the improvement of each part of the proposed method: In order to verify the impact of each part of the proposed method on the model accuracy, FedAvg, PLMC, CW+SA and PFL-HR were used for comparative experiments. The results are shown in the figure. Fig. 9 As shown in the figure, PLMC represents the proposed personalized local model building method, CW represents the proposed cyclic weight-based federation aggregation strategy, and SA represents the proposed model parameter jump aggregation strategy.

[0132] By analyzing Fig. 9 It can be seen that the model accuracy of the PLMC method alone is better than that of the FedAvg method, which is at least 3.1% higher. When the proposed method removes PLMC, that is, only the CW+SA method is used, the experimental results are better than those of the FedAvg method, but the accuracy of PFL-HR is also lower than that of the proposed method, which proves the effectiveness of PLMC and CW+SA from two aspects. In the six diagnostic tasks, the average fault diagnosis accuracy of PFL-HR is 97.7%.

[0133] B. Experiment on the effectiveness of CW strategy

[0134] The jump cycle weight federation aggregation strategy (CW+SA) is decomposed into CW and SA for further experimental verification. In order to verify that the proposed CW method can improve the model convergence speed, the accuracy change curve and loss function change curve of the global model are plotted. Due to limited space, only tasks T-A2, T-B2, and T-C2 are taken as examples. Fig.10 and Fig.11 The comparison results of FedAvg (green line), CW (blue line), PLMC+SA (yellow line), and PFL-HR (red line) algorithms are shown respectively.

[0135] Depend on Fig.10 and 11 It can be seen that, affected by the CW algorithm, the accuracy curve and loss curve of the proposed method PFL-HR and the one using only the CW algorithm fluctuate, but the curves of the proposed method converge faster. Fig.10 In the , compared with the other three methods, the proposed method can improve the accuracy to more than 90% faster, and finally achieve the highest accuracy diagnosis result; Fig.11 In the figure, the loss curve of the proposed method shows the lowest position and decreases most rapidly during the training process, reaching the lowest loss value at the end of training.

[0136] C. Experiment on the effectiveness of SA strategy

[0137] To verify the effectiveness of the proposed jump aggregation strategy (SA), SA is used to conduct comparative experiments with FedAvg, PLMC+CW, and PFL-HR. The accuracy results of the global model on different diagnostic tasks are shown in the following table. Fig.12 shown.

[0138] according to Fig.12 The experimental results shown in the figure show that the accuracy of the model optimized by the SA method is at least 2.2% higher than that of the FedAvg algorithm. On the other hand, the experimental results using the PLMC+CW method show that its accuracy is lower than that of the proposed PFL-HR, which proves the effectiveness of SA from two aspects.

[0139] D. Comparative Experiments on Different Federated Learning Algorithms

[0140] Fig.13 The accuracy of the proposed method PFL-HR and various comparison methods in different diagnostic tasks is demonstrated. The FedAvg method cannot solve the problem caused by the difference in data distribution between users, so the accuracy is still not high, with an average accuracy of about 53.7%. FedBABU and Per-FedAvg consider the problem of data distribution differences between users and use personalized federated learning methods to obtain a global model, so their accuracy is higher than that of FedAvg. The proposed method uses personalized local modeling and an aggregation strategy based on jump cycle weights to make its performance comparable to that of the centralized method. Compared with FedAvg, the average accuracy of the global model is improved by 44%.

[0141] In order to more intuitively explain the classification results of each class in different tasks, a multi-classification confusion matrix is ​​introduced to analyze the diagnosis results. Due to space limitations, only the fault diagnosis results in T-C2 are taken as an example to draw the confusion matrix as shown in Fig.14 shown.

[0142] Depend on Fig.14 It can be seen that since the FedAvg method cannot effectively solve the problem of data distribution differences among users, its fault diagnosis accuracy is low, and most fault categories are misclassified; the PFL-HR proposed in the present invention can effectively solve the fault diagnosis of harmonic reducers under different working conditions, so the fault diagnosis accuracy of the method proposed in the present invention is high.

[0143] Next, the features learned by FedAvg and PFL-HR are visualized.

[33] Reduce the dimension of the features learned for each user. Fig.15 This is the result of feature visualization under T-C2. Compared with FedAvg, the PFL-HR proposed in this invention has achieved better visualization results in different tasks, and the classification boundaries are clearer. For example, Fig.15Better intra-class compactness and inter-class separability are observed for user 2 and user 5, which further verifies the superiority of the proposed method.

[0144] To compare other performance indicators of different algorithms, Table 4 shows the time results of different methods training 100 epochs. As shown in Table 5, the training time of the proposed method PFL-HR is 9.3% longer than that of FedAvg on average. However, according to the above experimental results, since the proposed method converges faster, the global accuracy can reach more than 90% in 20 epochs, which is more efficient.

[0145] Table 5 Running time of different methods under different diagnostic tasks (s)

[0146]

[0147] Aiming at the problem of multi-user harmonic reducer collaborative fault diagnosis under isolated privacy data, this paper proposes a harmonic reducer fault diagnosis method (PFL-HR) with a personalized federated jump aggregation strategy to ensure data privacy, and realizes multi-user collaborative fault diagnosis under different working conditions. Through multiple groups of experimental verification, the following conclusions are obtained:

[0148] (1) In view of the data distribution differences between multiple users, a personalized local model construction method based on secondary aggregation is proposed. This method perceives the local data distribution by element aggregation of the global model and the local model to construct a personalized local model. At the same time, L2 regularization is used in the local model training process to avoid overfitting and reduce the impact of distribution differences. Experimental results show that compared with using FedAvg, the global accuracy of the personalized local model construction method is improved by 3.1%.

[0149] (2) In view of the additional overhead brought by the improved aggregation algorithm, a federated aggregation strategy based on skip cycle weights is proposed. This strategy accelerates the convergence of the global model by flexibly adjusting the aggregation weights of each communication round without increasing the computational overhead, and uses dynamic gradient updates to traverse local minima and saddle points. It also extends the training paradigm by periodically skipping the global model aggregation, thereby improving the effectiveness of model training. Experimental results show that after one cycle (20 epochs), this strategy improves the global model accuracy to about 90%, and the average accuracy can reach 83.8%.

[0150] (3) A harmonic reducer fault diagnosis method with personalized federated jump aggregation strategy (PFL-HR) is proposed. Under the privacy distribution of multi-user harmonic reducer data islands, this framework and strategy can solve the problem of data distribution differences between users caused by different working conditions and effectively establish a global fault diagnosis model with an average accuracy of 97.7%.

[0151] Another embodiment of the present invention provides a harmonic reducer fault diagnosis system with a personalized federated jump aggregation strategy, the system comprising:

[0152] A global model training module includes a local model building module submodule and a global model updating submodule; wherein the local model building submodule is configured so that each local harmonic reducer user builds a personalized local model using a secondary aggregation method; the secondary aggregation method is: the aggregation of multiple user models performed on the server is the first aggregation, and the personalized local initial model training performed on the local user is the secondary aggregation; each local harmonic reducer user uploads personalized local model parameters to the server; the global model updating submodule is configured so that the server updates the global model using a cyclic weight strategy, and adopts a jump aggregation strategy to send the global model parameters to each local harmonic reducer user; the jump aggregation strategy is: the server periodically skips the global federation aggregation step, and directly randomly distributes the received user personalized local models to all users; repeats the construction steps of the local model building module submodule and the update steps of the global model updating submodule until the maximum number of federation iterations is reached, and the final federation global model is obtained;

[0153] A fault diagnosis module is configured to perform local harmonic reducer fault diagnosis using the federated global model.

[0154] In this embodiment, optionally, the specific step of each local harmonic reducer user in the local model construction submodule constructing a personalized local model using a secondary aggregation method includes: each local harmonic reducer user obtains a personalized local initialization model using secondary aggregation, which is expressed as:

[0155]

[0156] in, represents the initial model parameters of the i-th user in the t-th round; Θ t-1 is the global model parameter sent by the server in round t-1, is the local model parameter of the i-th user in the t-1th round; ⊙ is the Hadamard operation; W i is the personalized aggregation weight; is updated information;

[0157] In the process of training the personalized initialization model using the local dataset, a penalty term based on L2 regularization is added, which is expressed as:

[0158]

[0159] Among them, the first term on the right side of the equation is the cross entropy loss function, the second term on the right side of the equation is the regularization term; n is the number of samples, m is the number of categories, and y ijis the probability that the true label of the i-th sample is in the j-th class, is the probability that the i-th sample is predicted to be the j-th class; λ is used to control the size of the regularization term.

[0160] In this embodiment, optionally, the cyclic weight strategy in the global model update submodule is: the weight sum δ of the federated average aggregation algorithm is changed from 1 to a cyclic change similar to an inverted sawtooth wave, and the change rule formula is expressed as:

[0161] δ(t cur )=A(1-t cur / T * )+q adj

[0162] Among them, t cur (0≤t≤T * ) is the ordinal number in the current cycle, A is the amplitude of the weight, T * is the number of traversals in a cycle, q adj is the lower limit of weight.

[0163] In this embodiment, optionally, the mathematical expression of the jump aggregation strategy in the global model updating submodule is:

[0164]

[0165] Among them, I periodic ={t|t∈R + &&1<t<T&&t modΔ=0},R + is the set of all positive integers, Δ is the given integer of jump aggregation, and t mod Δ = 0 is the judgment condition; is the model of the kth user, and is An element in Yes A randomly shuffled collection; is the cycle weight δ(t cur ) set; δ i is the weight of each user; N is the number of users.

[0166] In this embodiment, optionally, the local data set in the local model building submodule includes various state data of the harmonic reducer under various working conditions, and the state data includes a normal state and different types of fault states.

[0167] The function of the harmonic reducer fault diagnosis system with a personalized federal jump aggregation strategy described in this embodiment can be described by the harmonic reducer fault diagnosis method with the aforementioned personalized federal jump aggregation strategy. Therefore, for the parts not described in detail in this embodiment, please refer to the above method embodiments and will not be repeated here.

[0168] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.

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Claims

1. A harmonic reducer fault diagnosis method with personalized federated jump aggregation strategy, characterized in that: include: S1, each local harmonic reducer user builds a personalized local model using the secondary aggregation method; The secondary aggregation method is as follows: the aggregation of multiple user models on the server is the first aggregation, and the personalized local initial model training performed by the local user is the secondary aggregation; each local harmonic reducer user obtains a personalized local initialization model by using the secondary aggregation, which is expressed as: in, represents the initial model parameters of the i-th user in the t-th round; Θ t-1 is the global model parameter sent by the server in round t-1, is the local model parameter of the i-th user in the t-1th round; ⊙ is the Hadamard operation; W i is the personalized aggregation weight; is updated information; In the process of training the personalized initialization model using the local dataset, a penalty term based on L2 regularization is added, which is expressed as: Among them, the first term on the right side of the equation is the cross entropy loss function, the second term on the right side of the equation is the regularization term; n is the number of samples, m is the number of categories, and y ij is the probability that the true label of the i-th sample is in the j-th class, is the probability that the i-th sample is predicted to be the j-th class; λ is used to control the size of the regularization term; S2, each local harmonic reducer user uploads personalized local model parameters to the server; S3. The server updates the global model using the cyclic weight strategy and adopts the jump aggregation strategy to send the global model parameters to each local harmonic reducer user. The jump aggregation strategy is: the server periodically skips the global federation aggregation step and directly distributes the received user personalized local model to all users randomly. The cyclic weight strategy is: the weight and δ of the federation average aggregation algorithm are changed from 1 to a cyclic change similar to an inverted sawtooth wave. The change rule formula is expressed as: δ(t cur )=A(1-t cur / T * )+q adj Among them, t cur (0≤t≤T * ) is the ordinal number in the current cycle, A is the amplitude of the weight, T * is the number of traversals in a cycle, q adj is the lower limit of weight; The mathematical expression of the jump aggregation strategy is: Among them, I periodic ={t|t∈R + &&1<t<T&&t modΔ=0},R + is the set of all positive integers, Δ is the given integer of jump aggregation, and t mod Δ = 0 is the judgment condition; is the model of the kth user, and is An element in Yes A randomly shuffled collection; is the cycle weight δ(t cur ) set; δ i is the weight of each user; N represents the number of users; S4, repeat the above steps until the maximum number of federation iterations is reached, and obtain the final federation global model; S5. Utilize the federal global model to perform local harmonic reducer fault diagnosis.

2. The method for fault diagnosis of harmonic reducer with personalized federated jump aggregation strategy according to claim 1 is characterized in that: The local data set includes various state data of the harmonic reducer under various working conditions, and the state data includes a normal state and different types of fault states.

3. A harmonic reducer fault diagnosis system with personalized federated jump aggregation strategy, characterized in that: include: The global model training module includes a local model building module submodule and a global model updating submodule; wherein the local model building submodule is configured so that each local harmonic reducer user builds a personalized local model using a secondary aggregation method; the secondary aggregation method is: the aggregation of multiple user models performed on the server is the first aggregation, and the personalized local initial model training performed by the local user is the secondary aggregation; each local harmonic reducer user uploads the personalized local model parameters to the server; the specific steps of each local harmonic reducer user building a personalized local model using the secondary aggregation method include: each local harmonic reducer user uses the secondary aggregation to obtain a personalized local initialization model, which is expressed as: in, represents the initial model parameters of the i-th user in the t-th round; Θ t-1 is the global model parameter sent by the server in round t-1, is the local model parameter of the i-th user in the t-1th round; ⊙ is the Hadamard operation; W i is the personalized aggregation weight; is updated information; In the process of training the personalized initialization model using the local dataset, a penalty term based on L2 regularization is added, which is expressed as: Among them, the first term on the right side of the equation is the cross entropy loss function, the second term on the right side of the equation is the regularization term; n is the number of samples, m is the number of categories, and y ij is the probability that the true label of the i-th sample is in the j-th class, is the probability that the i-th sample is predicted to be the j-th class; λ is used to control the size of the regularization term; The global model update submodule is configured such that the server updates the global model using a cyclic weight strategy, and adopts a jump aggregation strategy to send the global model parameters to each local harmonic reducer user; the jump aggregation strategy is: the server periodically skips the global federation aggregation step, and directly randomly distributes the received user personalized local model to all users; repeats the construction steps of the local model construction module submodule and the update steps of the global model update submodule until the maximum number of federation iterations is reached, and the final federated global model is obtained; the cyclic weight strategy is: the weight sum δ of the federation average aggregation algorithm is changed from 1 to a cyclic change similar to an inverted sawtooth wave, and the change law formula is expressed as: δ(t cur )=A(1-t cur / T * )+q adj Among them, t cur (0≤t≤T * ) is the ordinal number in the current cycle, A is the amplitude of the weight, T * is the number of traversals in a cycle, q adj is the weight lower limit; the mathematical expression of the jump aggregation strategy is: Among them, I periodic ={t|t∈R + &&1<t<T&&t modΔ=0},R + is the set of all positive integers, Δ is the given integer of jump aggregation, and t mod Δ = 0 is the judgment condition; is the model of the kth user, and is An element in Yes A randomly shuffled collection; is the cycle weight δ(t cur ) set; δ i is the weight of each user; N represents the number of users; A fault diagnosis module is configured to perform local harmonic reducer fault diagnosis using the federated global model.

4. A harmonic reducer fault diagnosis system with a personalized federated jump aggregation strategy according to claim 3, characterized in that: The local data set in the local model building submodule includes various state data of the harmonic reducer under various working conditions, and the state data includes a normal state and different types of fault states.

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