CN116952583A - Rolling bearing fault diagnosis method of digital twin driving deep transfer learning model - Google Patents

Abstract

A rolling bearing fault diagnosis method of a digital twin-drive deep transfer learning model relates to the technical field of rolling bearing fault diagnosis and aims to solve the problems that a rolling bearing source domain sample data label is difficult to obtain, the sample size is small and a target domain sample data label is missing under different working conditions. The method comprises the steps of taking a deep groove ball bearing as a research object to establish a three-dimensional model, carrying out dynamic analysis through finite element analysis software and an explicit dynamic algorithm, and carrying out simulation calculation on the model according to an acceleration detection position to obtain rolling bearing fault twin data; secondly, introducing a generation countermeasure network based on Wasserstein distance, and providing an improvement on the generation countermeasure network by using a gradient penalty term, so as to reduce the distribution difference between twin data and real data and realize feature fusion; finally, the concept of transfer learning is utilized, a global attention mechanism is introduced to improve a residual network, domain adaptation processing is carried out on the characteristics extracted by a source domain and a target domain by utilizing the multi-core maximum mean value difference, the transfer learning of unlabeled target domain sample data is realized, and finally a rolling bearing fault diagnosis intelligent model based on digital twin is established. Experiments prove that the method can effectively solve the problem of missing of the bearing labeled sample under different working conditions, and the fault diagnosis accuracy of the rolling bearing is obviously improved.

Description

A digital twin-driven deep transfer learning model for rolling bearing fault diagnosis method

Technical field

The invention relates to a rolling bearing fault diagnosis method using a digital twin-driven deep transfer learning model, and relates to the technical field of rolling bearing fault diagnosis.

Background technique

As one of the most critical components in rotating machinery, rolling bearings are widely used in aerospace, rail transportation and industrial production fields ^[1,2] . The working conditions of rolling bearings are often complex and changeable. Different working conditions lead to changes in bearing vibration characteristics ^[3] , which leads to problems such as difficulty in obtaining labeled data under certain working conditions and missing samples. Therefore, studying rolling bearing fault diagnosis methods under different working conditions is of great significance to ensure the normal operation of rotating machinery ^[4] .

The actual working conditions of bearings are complex and changeable. The traditional fault diagnosis method manually extracts original signal features, which is not conducive to the rapid extraction of fault features and the accurate identification of health status ^[5] . In recent years, deep learning has been continuously used in the field of mechanical intelligent fault diagnosis technology. Because it can overcome the shortcomings of traditional feature extraction methods, its superiority in this field has become increasingly significant. Literature [6] proposes to combine the transitional convolution layer and the global mean pooling layer to replace the traditional fully connected network layer structure, which is applied to fault diagnosis of motor support ball bearings and achieves good diagnostic results. Literature [7] uses attention convolutional neural network to extract key features of rolling bearings to prevent feature loss. At the same time, a domain adaptation layer is added to complete the migration and adaptation of deep features of rolling bearings at different speeds, thereby realizing fault diagnosis of rolling bearings. Literature [8] established a fault response convolution layer based on fault characteristics that do not change with working conditions, used an improved soft threshold function to construct a new fault response network model, and achieved high diagnostic accuracy on four diagnostic cases. Rate. Literature [9] uses improved one-dimensional and two-dimensional convolutional neural networks for two-domain information learning, combines the constructed fault diagnosis model, extracts fault features from the two-domain information of bearing fault samples, and uses padding and dropout techniques to extract fault features from the two-domain information. Features are fully extracted from the original data and overfitting is reduced, significantly improving fault diagnosis accuracy. Literature [10] introduced multi-scale convolution kernels in the first layer of the deep convolutional neural network, and used one-dimensional convolution kernels of different sizes to extract multi-scale features from the original vibration signals of the bearings, achieving intelligent diagnosis of bearing health status.

However, the convolutional neural network used in common deep learning methods is not without drawbacks. As the number of network layers increases, the model performance will degrade. Although the residual network can avoid this phenomenon, it ignores the problem of weight allocation of the network to different channels. In addition, the deep learning framework requires a large number of labeled vibration data samples for model training, which is contrary to the difficulty in obtaining fault samples in real situations, making it impossible to establish a high-precision deep learning fault diagnosis model.

Transfer learning can use known knowledge in a certain field to solve related problems in other fields. It can better solve the problem of large differences in sample distribution and missing labeled samples in the target domain. It has gradually been used by a large number of scholars to research fault diagnosis technology in the field of artificial intelligence. among. Literature [11] introduces a conditional confrontation mechanism and realizes the state identification of bearing feature migration between different specifications through the simultaneous adaptation of source and target domain features and labels. Literature [12] combines long short-term memory network and transfer learning, and uses the original signal data under a single working condition as a training sample to realize end-to-end intelligent monitoring tasks under different working conditions, getting rid of over-reliance on a priori fault data. The above method can effectively deal with the problem of unlabeled sample data in the target domain. However, in actual situations, the source domain data often has a small number of labeled samples under certain working conditions, which is not enough to fully train the model.

With the development of the new generation of information technology, especially the widespread application of artificial intelligence technology in industrial production, Digital Twin (DT) has become a hot topic in industrial informatization research around the world, providing a new solution for the intelligent management of complex equipment. Solution idea ^[13] . Literature [14] proposes to use numerical simulation of rolling bearings to establish a DT model, improve the simulation data through auxiliary classification adversarial neural networks, and conduct verification on public bearing data sets and EMU traction motor bearing data sets, which has a high diagnostic accuracy. Literature [15] introduced DT technology into the support structure of offshore wind turbines, which enabled real-time monitoring, fault diagnosis and operation optimization of the wind turbines, and provided guarantee for the reliability analysis of its support structure. Literature [16] designed an adaptive DT model, using Gaussian process regression, signal modeling through Laguerre filter and fuzzy logic algorithm, combining the proportional integral observer with signal modeling technology, and using Lyapunov Algorithms and adaptive techniques are used for data estimation, and finally support vector machines are used for fault identification. Literature [17] established virtual sensors through the physical information of the nuclear power plant's thermal hydraulic system, and combined real-time factory data to build a performance model for two feedwater heaters to achieve double-blind fault diagnosis and reduce the operation and maintenance costs of the nuclear industry. Literature [18] used Simulink to build a DT model of each component unit of the spacecraft power system, combined with fault mechanism analysis to inject typical faults into the twin model, enriched the type and quantity of fault data, and realized the effectiveness of multiple fault detection models based on twin data. evaluation of.

According to the above-mentioned methods, most of the current research on rolling bearing fault diagnosis technology is based on deep learning and machine learning. The application of DT technology is not yet mature, and the application method is relatively simple. It is imperative to conduct research on the problem of the small number of labeled samples in the source domain and the lack of labeled samples in the target domain under different operating conditions of rolling bearings.

Contents of the invention

The technical problems to be solved by this invention are:

Aiming at the problems of difficulty in obtaining source domain sample data labels of rolling bearings under different working conditions, small sample size, and missing target domain sample data labels, the present invention proposes a rolling bearing fault diagnosis method using a digital twin-driven deep transfer learning model.

The technical solutions adopted by the present invention to solve the above technical problems are:

A rolling bearing fault diagnosis method driven by a digital twin-driven deep transfer learning model. The implementation process of the method is:

1) Establish a rolling bearing DT model

The modeling software ANSYS-Workbench was used to carry out twin modeling and finite element analysis of the rolling bearing. By adding boundary conditions such as different loads and pitting faults of different diameters to simulate actual working conditions, the modeling work of the DT model of the rolling bearing was completed. At the same time, the acceleration probe is set up to perform simulation calculations of vibration signals to obtain twin data;

2) Feature fusion

Introduce the Wasserstein distance-based generative adversarial network (WGAN for short) and input twin data into the generator, input a small amount of real data into the discriminator, and add a gradient penalty term to the objective function of the discriminator, using the gradient penalty term to replace the weight in WGAN Cut to form a new function (an improvement of the generative adversarial network), and perform alternate training to make up for the distribution difference between twin data and real data;

3) Data preprocessing

Synthetic samples are obtained after feature fusion of twin data. Synthetic sample data of known fault types under certain working conditions are selected as the source domain sample set, and real sample data of unknown fault types under other working conditions are selected as the target domain sample set. The target The domain sample set also includes the target domain training sample set and the target domain test sample set; short-time Fourier transform is performed on the vibration signals in the source domain and target domain, and the one-dimensional time domain vibration signal is converted into a two-dimensional time spectrum diagram and used as a subsequent network input;

4) Build a deep transfer learning model

Construct an improved deep residual network and introduce a global attention mechanism to amplify global dimensional interaction features while reducing information dispersion. The activation function under the network framework is changed to FReLU. By extracting edge space features, the model can better distinguish between different class image; the multi-kernel maximum mean difference is used to measure the distribution difference between the source domain and the target domain, calculate the distance between the hidden features in the sample set of the source domain and the target domain, and use it as the objective function together with the classification loss of the improved deep residual network And carry out constraints and optimization to establish a DT-based rolling bearing fault diagnosis model under different working conditions;

5) Trouble diagnosis

Use the target domain test sample set to test the trained fault diagnosis model, compare the diagnosis results of the deep transfer learning model with the real labels of the samples, and obtain the final fault diagnosis results.

Furthermore, the DT model of the rolling bearing takes the SKF6205 deep groove ball bearing as the research object. Considering the impact of radial load and rotation speed on the bearing, ANSYS software is used to establish a three-dimensional model of the rolling bearing and perform finite element analysis. It can reflect the rolling bearing under simulated fault conditions. Twin data of fault characteristics.

Furthermore, according to the explicit dynamics analysis method, DT modeling and finite element analysis are performed on the rolling bearing failure model. The flow is as follows:

1) 3D modeling

Draw a three-dimensional model of the rolling bearing in the normal state (healthy state) based on the physical parameters of the rolling bearing. During the modeling process, the internal and external chamfers of the rolling bearing are not considered;

2) Material settings

Since rolling bearings are not prone to plastic deformation, the bearing components are uniformly set to linear elastic materials with both orthotropic elasticity and isotropic elasticity; in the Workbench processing interface, the stiffness of the bearing components is set to soft body, and the materials are set It is structural steel with a density of 7850kg/m ³ , an elastic modulus of 2.0×e ¹¹ pa, and a Poisson's ratio of 0.3;

3) Contact mode

In the normal operation of a rolling bearing, the contact mode is mainly divided into the contact between the inner ring and the rolling elements, the contact between the outer ring and the rolling elements, and the contact between the rolling elements and the cage. The friction coefficient between the inner and outer ring raceways and the rolling elements is set to 0.1, the friction coefficient between the cage and the rolling elements is set to 0.05, there is generally no contact between the inner and outer rings and the cage, and no setting is required;

4) Meshing

During the operation of the rolling bearing, set the minimum unit size of the geometric grid between the rolling elements and the cage to 1mm, and the minimum unit size of the surface grid to 0.6mm; the minimum unit size of the geometric grid of the inner ring and outer ring is automatically divided, and the minimum unit size of the surface grid is Size is 1.2mm;

5) Apply loads and constraints

Since the six degrees of freedom of the outer ring have been set as fixed, there is no need to add boundary conditions; on the inner ring connection pair, a force of 20000N is set with the X-axis (the axis of the rolling bearing) as the rotation axis, and the Z-axis as the rotation axis. Direction sets the speed required for the current working condition;

In order to simulate different working conditions, it is necessary to add the required rotation speed to the inside of the inner ring of the bearing, and to fix it on the outer surface of the bearing outer ring. It is added by adding a connecting pair (kinematic pair). The inner ring, outer ring, and cage are all Equipped with connecting pair.

Furthermore, the gradient penalty term is used to replace the weight clipping in WGAN to achieve the improvement of the generative adversarial network. In this process,

The gradient penalty term is introduced in the loss function of the discriminator to replace the original weight clipping (truncation). The formula is:

Among them: · represents the p norm; λ represents the regularization coefficient; It is obtained by random interpolation sampling on the connection between the real sample x and the generated sample G(z). The calculation formula is as follows, where μ obeys the uniform distribution on [0,1];

The final objective function of the improved generative adversarial network is:

Furthermore, in the process of building a deep transfer learning model, the feature transfer based on the improved residual network is specifically:

1) Improve the residual network

The residual network is composed of multiple residual blocks stacked. The input of the residual block is z and the output is H(z). The residual refers to the difference between the output value H(z) and the input value identity mapping z. Right now:

f(z)＝H(z)-z (17)

The learning object of the residual network is the residual f(z). During the network training process, it only needs to learn the difference between the input and output of the residual block. During the back propagation process of the model, the input z passes the identity mapping and directly converts the information It is transmitted from the input end of the residual block to the output end to ensure the integrity of the information during the transmission process;

The improvements of the residual network are as follows:

1) Global attention mechanism

The global attention mechanism is introduced to improve the residual network. The improved residual network structure is: convolutional layer plus channel attention, convolutional layer plus spatial attention,

The channel attention sub-module (channel attention) uses a three-dimensional arrangement to retain three-dimensional information, and the spatial attention sub-module (spatial attention) uses two convolutional layers for spatial information fusion;

2) FReLU activation function

Based on the fact that most bearing data distributions are nonlinear, nonlinear activation functions are introduced to strengthen the learning ability of the network and make the network closer to the real situation.

The nonlinear computer vision task activation function FReLU (Funnel ReLU) is used to solve the problem of insensitivity to spatial information. The calculation formula of FReLU is:

FReLU(x)＝max(x,T(x))(19)

Among them: x is the feature input, T(x) is the two-dimensional space condition;

2) Use domain adaptation method for feature migration

1), Maximum mean difference

In transfer learning, given a source domain containing n _s labeled samples and a target domain containing n _t unlabeled samples/> Among them/> is the one-shot label corresponding to the i-th source domain sample x _i ^s ,/> Indicates that the corresponding sample belongs to the mth category of the source domain,/> Represents the jth unlabeled target domain sample. The sample sets of the source domain and the target domain generally obey two similar distributions;

The index that measures the distribution difference between the source domain and the target domain in the domain adaptation problem is the maximum mean difference, which is defined as shown in Equation (20):

Among them, X ^{s and} Represents a feature map that can map original sample data to H,/> Represents the mathematical expectation after the source domain sample X ^s obeying the p distribution is mapped to RKHS;

2) Multi-core maximum mean difference

MK-MMD, a multi-kernel variant using MMD, uses a convex combination of multiple different Gaussian kernel functions {k _u } to form a composite kernel function based on the original MMD feature kernel k(x,x′), which can utilize different kernels. function to enhance distance measurement performance and map the values of the input space to RKHS to obtain the optimal value. Its definition is:

Among them, H _k represents the reproducible Hilbert space with characteristic kernel k;

The kernel defined by multi-core is:

Among them: {β _u } is the coefficient, that is, the weight of multi-core k, and m is the number of cores.

The invention has the following beneficial technical effects:

Zxcv456+ This invention proposes a rolling bearing fault diagnosis method that integrates modeling technology, deep transfer learning and DT technology. It studies the problem of a small number of labeled samples in the source domain and a lack of labeled samples in the target domain under different working conditions of rolling bearings. This method first establishes a three-dimensional model of the rolling bearing and conducts finite element analysis, and obtains twin data of the rolling bearing through fault simulation. Then the gradient penalty term is used to improve the generative adversarial network to achieve feature fusion of twin data and a small amount of real data. Finally, it is proposed to use the improved residual network as the transfer learning model framework, introduce the global attention mechanism and modify the activation function in the framework to the FReLU function, thereby improving the model's learning of insensitive information in deep space, and finally realizing rolling bearings under different working conditions. Troubleshooting.

The method of the present invention uses deep groove ball bearings as the research object to establish a three-dimensional model, conducts dynamic analysis through finite element analysis software and explicit dynamics algorithms, performs simulation calculations on the model according to the acceleration detection position, and obtains rolling bearing fault twin data; secondly, introduces the method based on Wasserstein distance generative adversarial network, and proposed to use gradient penalty term to improve it, reduce the distribution difference between twin data and real data, and achieve feature fusion; finally, using the idea of transfer learning, a global attention mechanism was introduced to residual The difference network is improved, and the multi-core maximum mean difference is used to perform domain adaptation processing on the features extracted from the source domain and the target domain, to achieve transfer learning of unlabeled target domain sample data, and finally establish an intelligent model for rolling bearing fault diagnosis based on digital twins. Experimental verification shows that the proposed method can effectively solve the problem of missing bearing labeled samples under different working conditions, and significantly improves the accuracy of rolling bearing fault diagnosis.

Description of the drawings

Figure 1 is a flow chart of DT modeling and finite element analysis; Figure 2 is a contact diagram. In the figure: (a) the inner ring is in contact with the rolling elements, (b) the outer ring is in contact with the rolling elements, (c) the rolling elements are in contact with the cage Contact; Figure 3 is the mesh division diagram of the rolling bearing SKF6205; Figure 4 is the schematic diagram of the connection pair (screenshot). In the figure: (a) the inner ring connection pair, (b) the outer ring connection pair, (c) the cage connection pair; Figure 5 is a schematic diagram of the original residual block structure; Figure 6 is a schematic diagram of the improved residual network structure; Figure 7 is a schematic diagram of the channel attention sub-module; Figure 8 is a schematic diagram of the spatial attention sub-module; Figure 9 is the FReLU schematic diagram; Figure 10 is a schematic diagram of the digital twin-based The flow chart of rolling bearing fault diagnosis; Figure 11 is a schematic diagram of the bearing test bench; Figure 12 is a comparison experiment diagram before and after twin data feature fusion; Figure 13 is a confusion matrix diagram of improved generative adversarial network classification; Figure 14 is a comparison experiment diagram of different adversarial networks; Figure 15 is a comparative experimental diagram between the method proposed by the present invention and other methods; Figure 16 is a classification confusion matrix diagram of the proposed method; Figure 17 is a comparative experimental diagram between the proposed method and other methods under different specifications.

Detailed ways

In conjunction with Figures 1 to 17, the implementation of a rolling bearing fault diagnosis method based on a digital twin-driven deep transfer learning model is described below:

1 DT model of rolling bearing

This article takes the SKF6205 deep groove ball bearing as the research object. Considering the impact of radial load and rotational speed on the bearing, ANSYS software is used to establish a three-dimensional model of the rolling bearing and perform finite element analysis to simulate twin data that can reflect the failure characteristics of the rolling bearing under fault conditions.

1.1 Explicit dynamics

In the structural simulation of ANSYS-Workbench, finite element analysis methods are mainly divided into two categories: implicit and explicit. The modeling in this article mainly uses the explicit dynamics module for high-speed and impact simulation.

The explicit algorithm uses some difference formats of dynamic equations, such as linear acceleration method, central difference method, etc., and does not require equilibrium iteration or solving for tangent stiffness. The calculation speed has a great advantage compared to the implicit solution. For Nonlinear problems generally do not have convergence problems. Here we mainly explain the central difference method in explicit dynamics, assuming that the displacement x ₀ , velocity v ₀ and acceleration a ₀ at time t=0 are known. Assume that the time solution domain is equally divided into n time intervals Δt, and the solutions at time 0, Δt, 2Δt,..., nΔt have been obtained, and the purpose of calculation is to solve the solution at time t+Δt. The solution equation of the system at time t is:

Ma _t +Cv _t +Kx _t =Q _t (1)

Among them, a _t is the acceleration vector of the system node; v _t is the velocity vector of the system node; x _t is the displacement vector of the system node; M is the mass matrix of the system; C is the damping matrix of the system; K is the stiffness matrix of the system; Q _t is the system node load vector.

Using the Taylor expansion, expand x _t+Δt into a Taylor polynomial at time point t, and take finite terms as the approximation of x _t+Δt , up to the second differential term, to get:

Derivative of equation (2) we get:

v _t+Δt =v _t +a _t Δt (3)

In the [t-Δt,t] interval, the velocity v _t can be approximately expressed by displacement as:

In the [t,t+Δt] interval, the velocity v _t+Δt can be approximately expressed by displacement as:

Substitute Equation (4) and Equation (5) into Equation (3) to obtain the relationship between node acceleration and adjacent displacement:

In the interval [t-Δt,t+Δt], the velocity v _t can be approximated by displacement as:

By substituting Equation (6) and Equation (7) into Equation (1), the recursive formula for the solution at each discrete time point can be obtained:

Equation (8) is the classic central difference format. It can be seen that if t and x _t are known, x _t+Δt can be solved, and then the velocity and acceleration at time t can be obtained.

The stability condition of the central difference algorithm solution is:

In the formula, τ _n is the minimum natural vibration period of the finite element system; Δt _cr is the critical value.

1.2 DT modeling

According to the above dynamic analysis method, DT modeling and finite element analysis are performed on the rolling bearing fault model. The process is shown in Figure 1:

1) 3D modeling

The main physical parameters of rolling bearings are: (1) Bearing pitch diameter D = 39.04mm; (2) Ball diameter d = 7.94mm; (3) Number of balls Z = 9; (4) Contact angle is 0. Use software to draw a three-dimensional model of the rolling bearing under normal conditions. The specific operations will not be described in detail. During the modeling process, the internal and external chamfers of the rolling bearing prevent contact stress and have little impact on the three-dimensional model, so the above factors are not considered.

2) Material settings

In order to solve the problem that rolling bearings are not prone to plastic deformation, the bearing components are uniformly made of linear elastic materials with both orthotropic elasticity and isotropic elasticity. In the Workbench processing interface, set the stiffness of the bearing components to soft body, the material to structural steel, the density to 7850kg/m ³ , the elastic modulus to 2.0×e ¹¹ pa, and the Poisson's ratio to 0.3.

3) Contact mode

In the normal operation of rolling bearings, the contact modes are mainly divided into the contact between the inner ring and the rolling elements, the contact between the outer ring and the rolling elements, and the contact between the rolling elements and the cage. The contact diagram is shown in Figure 2. Set the friction coefficient between the inner and outer ring raceways and the rolling elements to 0.1, and the friction coefficient between the cage and the rolling elements to 0.05. There is generally no contact between the inner and outer rings and the cage, so no settings are required.

4) Meshing

During the operation of the rolling bearing, set the minimum unit size of the geometric grid between the rolling elements and the cage to 1mm, and the minimum unit size of the surface grid to 0.6mm; the minimum unit size of the geometric grid of the inner ring and outer ring is automatically divided, and the minimum unit size of the surface grid is The size is 1.2mm. The overall mesh division of the rolling bearing is shown in Figure 3.

5) Apply loads and constraints

Since the six degrees of freedom of the outer ring have been set as fixed, there is no need to add boundary conditions; set a force of 20000N on the inner ring connecting pair with the X-axis as the rotation axis, and set the current working condition with the Z-axis as the rotation axis. required speed.

In order to simulate different working conditions, it is necessary to add the required rotation speed to the inside of the inner ring of the bearing, and to fix it on the outer surface of the bearing outer ring. Here, the connection pair (kinematic pair) is added, including the inner ring, outer ring, and cage. The connection pair is shown in Figure 4.

2 Feature fusion method based on improved generative adversarial network

Since the established DT model does not take into account the complex working environment of the actual bearing operation, the characteristics contained in the twin data obtained by simulation are relatively single, resulting in low fault diagnosis accuracy. In addition, in actual situations, the sample size of real data is insufficient, so only generation Adversarial networks cannot obtain rich sample data. In response to the above problems, twin data and real data are combined, and through the feature extraction of twin data and real data in the discriminator, it is selected according to the softmax classification result whether to input it into the generator deconvolution layer for reconstruction and fusion, and the two are fused. The resulting synthetic sample data is used for subsequent classification diagnosis.

2.1 Generative Adversarial Network

The structure of the generative adversarial network is relatively simple and mainly consists of a generator and a discriminator. The generator mainly makes the data it generates more realistic by learning the distribution of real sample data, and its input is twin data simulated by the DT model. The discriminator is used to distinguish the authenticity of the received data, and its input includes synthetic samples generated by the generator and real data samples collected from the sensor. Through continuous iterative adversarial training, both the generator and the discriminator are optimized at the same time, and finally reach Nash equilibrium. Its objective function is:

Among them, P _data (x) represents the real sample data, P _y (y) represents the twin sample data, D (·) and G (·) represent the nonlinear functions corresponding to the generator and the discriminator respectively, mainly by making G (·) Minimize and maximize D(·) to train the network.

2.2 Generative adversarial network based on Wasserstein distance

Traditional GAN uses JS/KS divergence to distinguish between the distribution of generated data and the distribution of real data, which may lead to problems such as gradient disappearance and model collapse during the generator training process. In order to solve the gradient dispersion problem in GAN, the Wasserstein distance-based generative adversarial network (Wasserstein GAN, WGAN) uses Wasserstein distance instead of the traditional JS/KS divergence as the optimization objective function of the network. The definition of Wasserstein distance is as shown in Equation (11):

where P _r is the real distribution, P _g is the generated distribution, Π(P _r ,P _g ) represents the set of joint probability distributions γ where P _r and P _g are marginal distributions; W(P _r ,P _g ) represents γ(x ,y) the lower bound of expectation.

Since the lower bound of Equation (11) is difficult to determine, it is difficult to directly calculate the Wasserstein distance between arbitrary distributions. The duality principle of Kantorovich-Rubinstein can be used to measure the distance in functional form, and Equation (11) can be transformed into Equation (12) ):

Among them, K is the supremum bound, f(·) is the distance mapping function, and ‖f‖ _L ≤K represents the K-Lipschitz function.

2.3 Improvements in Generative Adversarial Networks

During the training process, since it is necessary to ensure that the absolute value of the gradient is not greater than a certain fixed constant, that is, to satisfy the K-Lipschitz condition and prevent gradient explosion, the constrained function f is required to be able to obtain _{The upper bound of _ _} K=1, then the objective function is:

When L is as large as possible, L is approximately equal to the Wasserstein distance between the real distribution and the generated distribution. The gradient penalty term is introduced into the loss function of the discriminator to replace the original weight truncation. The formula is:

Among them: · represents the p norm; λ represents the regularization coefficient; It is obtained by random interpolation sampling on the connection between the real sample x and the generated sample G(z). The calculation formula is as follows, where μ obeys the uniform distribution on [0,1].

The final objective function of the improved generative adversarial network is:

3 Feature transfer based on improved residual network

3.1 Residual network and its improvements

3.1.1 Residual network

As the number of CNN layers increases, the performance of the overall network will decrease. The residual network adds identity mapping between the original CNN network layers, so that the original network model's fitting of the target output is transformed into a fitting of the difference. In this way, the network can be deepened without causing any problems. Network performance degradation can effectively solve the above problems. Residual networks are generally stacked by multiple residual blocks. The structure of a single residual block is shown in Figure 5.

The input of the residual block is z, and the output is H(z). The residual refers to the difference between the output value H(z) and the input value identity mapping z, that is:

f(z)＝H(z)-z (17)

The learning object of the residual network is the residual f(z). During the network training process, only the difference between the input and output of the residual block needs to be learned, which is less difficult to learn than CNN. During the back propagation process of the model, the input z directly transfers information from the input end of the residual block to the output end through identity mapping, ensuring the integrity of the information during the transfer process.

3.1.2 Improved residual network

1) Global attention mechanism

Due to the limited receptive field and insufficient correlation in the cross-channel process, the traditional residual network cannot effectively extract data features in actual processing tasks. In response to the above problems, this paper introduces the global attention mechanism to improve the residual network. The improved residual network structure is shown in Figure 6:

The channel attention sub-module uses a three-dimensional arrangement to retain three-dimensional information, and its schematic diagram is shown in Figure 7. The spatial attention submodule uses two convolutional layers for spatial information fusion, and its schematic diagram is shown in Figure 8.

2) FReLU activation function

Since most bearing data distributions are nonlinear, introducing a nonlinear activation function can strengthen the learning ability of the network and make the network closer to the real situation. The commonly used activation function is mainly ReLU (Rectified LinearUnit), and its calculation formula is:

ReLU(x)＝max(0,x) (18)

However, ReLU forcing the output of the x≤0 part to 0 may cause the model to be unable to learn effective features. Therefore, if the learning rate is set too large, it may cause the network to be insensitive to spatial feature information in image processing. To address this problem, literature [19] proposed a new nonlinear computer vision task activation function FReLU (Funnel ReLU) to solve the problem of insensitivity to spatial information. The calculation formula of FReLU is:

FReLU(x)＝max(x,T(x))(19)

Among them: x is the feature input, and T(x) is the two-dimensional space condition.

The schematic diagram of FReLU is shown in Figure 9.

3.2 Domain adaptation method

3.2.1 Maximum mean difference

In transfer learning, given a source domain containing n _s labeled samples and a target domain containing n _t unlabeled samples/> Among them/> is the i-th source domain sample/> The corresponding one-shot tag, /> Indicates that the corresponding sample belongs to the mth category of the source domain,/> Represents the jth unlabeled target domain sample. The sample sets of the source domain and the target domain generally obey two similar distributions.

Domain adaptation is one of the fields of transfer learning research. The traditional domain adaptation method generally performs a global domain transformation on the source domain and the target domain, so that the feature distribution of the transformed source domain and target domain is as similar as possible, and the extracted features are applicable at the same time. Domain-invariant features for multiple domains.

Maximum Mean Discrepancy (MMD) is a common indicator for measuring the distribution difference between the source domain and the target domain in domain adaptation problems. Its definition is as shown in Equation (20):

Among them, X ^s and X ^t represent the source domain and target domain samples respectively; p and q represent the source domain sample distribution and the target domain sample distribution respectively; RKHS); Represents a feature map that can map original sample data to H,/> Represents the mathematical expectation after the source domain sample X ^s obeying the p distribution is mapped to RKHS.

3.2.2 Multi-core maximum mean difference

This paper adopts the multi-kernel variant of MMD (Multi Kernel-maximum Mean-discrepancies, MK-MMD) proposed by Gretton et al. ^[20] . MK-MMD uses multiple The convex combination of different Gaussian kernel functions {k _u } forms a composite kernel function, which can use different kernel functions to enhance distance measurement performance, so that the values of the input space can be mapped to the RKHS more accurately to obtain the optimal value. Its definition formula is converted from formula (20) to formula (21):

Among them, H _k represents the reproducible Hilbert space with characteristic kernel k.

The kernel defined by multi-core is:

Among them: {β _u } is the coefficient, that is, the weight of multi-core k, and m is the number of cores.

4 Rolling bearing fault diagnosis methods and processes

The overall flow diagram of the rolling bearing fault diagnosis system based on DT is shown in Figure 10.

The specific steps are:

1) Establish a rolling bearing DT model

The modeling software ANSYS-Workbench was used to carry out twin modeling and finite element analysis of the rolling bearing. By adding boundary conditions such as different loads and pitting faults of different diameters to simulate actual working conditions, the modeling work of the DT model of the rolling bearing was completed. At the same time, the acceleration probe is set up to perform simulation calculations of vibration signals to obtain twin data.

2) Feature fusion

Introduce WGAN and input twin data into the generator, input a small amount of real data into the discriminator, and add a gradient penalty term to the objective function of the discriminator to replace the original weight clipping, thereby forming a new function and performing alternate training to compensate for the twins. Distribution differences between data and real data.

3) Data preprocessing

Synthetic samples are obtained after feature fusion of twin data. Synthetic sample data of known fault types under certain working conditions are selected as the source domain sample set, and real sample data of unknown fault types under other working conditions are selected as the target domain sample set. The target The domain sample set also includes the target domain training sample set and the target domain test sample set; short-time Fourier transform is performed on the vibration signals in the source domain and target domain, and the one-dimensional time domain vibration signal is converted into a two-dimensional time spectrum diagram and used as a Subsequent network input.

4) Build a deep transfer learning model

Construct an improved deep residual network and introduce a global attention mechanism to amplify global dimensional interaction features while reducing information dispersion. The activation function under the network framework is changed to FReLU. By extracting edge space features, the model can better distinguish between different class image; the multi-kernel maximum mean difference is used to measure the distribution difference between the source domain and the target domain, calculate the distance between the hidden features in the sample set of the source domain and the target domain, and use it as the objective function together with the classification loss of the improved deep residual network And carry out constraints and optimization to establish a fault diagnosis model of rolling bearings under different working conditions based on DT.

5) Trouble diagnosis

Use the target domain test sample set to test the trained fault diagnosis model, compare the diagnosis results of the deep transfer learning model with the real labels of the samples, and obtain the final fault diagnosis results.

5Application and Analysis

5.1 Bearing Data Set

5.1.1 Bearing real data

The data used in the experiment of this article comes from the public data set collected by the bearing test bench of Case Western Reserve University in the United States. The test bench is shown in Figure 11. The test bench includes a motor, torque sensor, power meter and electronic control equipment. For the SKF6205 deep groove ball rolling bearing installed on the drive end of the motor, the running status of the bearing is collected by using an acceleration sensor placed on the motor housing with a magnetic base. vibration signal and set the sampling frequency to 12kHz. In this paper, the bearing vibration data collected under this condition are used for subsequent research and experiments.

Since the initial failure of the bearing manifests as local pitting corrosion, the pitting failure data is obtained by manual processing using an electric discharge machine, including failure data on the inner ring, outer ring, rolling elements and other locations. Among them, three different fault defect diameters are set for each fault location, with sizes of 0.1778mm, 0.3556mm, and 0.5334mm respectively. In addition to the normal working status of the bearing, the collected bearing vibration data is divided into 10 categories. Among them, the vibration data of the bearing without failure is represented by N, and the remaining 9 types of vibration data are simplified for ease of expression, as shown in Table 1.

Table 1 Experimental data representation method

In order to solve the problem of complex working conditions of rolling bearings, the data required for the experiment were collected under different loads (0hp, 1hp, 2hp, 3hp). At the same time, the motor speed also changed according to the different bearing loads. The corresponding relationship between different working conditions of the bearing, the load and the motor speed are shown in Table 2.

Table 2 Correspondence between bearing operating conditions, load, and speed in real data

5.1.2 Bearing twin data

Use ANSYS software to conduct three-dimensional modeling and finite element analysis of the rolling bearing. The analysis time and step control are set to 0.17s and 1 step respectively. The number of sub-steps is 2048. Each sub-step outputs an acceleration vibration data, and the acceleration detection position is The smallest unit of a grid on the outer ring. Combining the above setting conditions and equation (8), the rolling bearing is simulated and the twin data is obtained, as shown in Table 3.

Table 3 Experimental data representation method

In order to correspond to the real data set of rolling bearings, the twin data are marked and represented under different loads and different speeds. The corresponding relationship is shown in Table 4.

Table 4 Correspondence between bearing operating conditions, load, and speed in twin data

A total of 12 migration tasks were set up in this experiment. The composition information of the data sets used in different tasks is shown in Table 5. Among them, each group of tasks uses bearing twin data as the source domain data sample, and uses the bearing real data as the target domain training sample and target domain test sample. There are 300 twin data samples of each category, 30 target domain training samples of each category, and the target domain There are 100 test samples for each category.

Table 5 Composition of data sets used in each task

The total number of iterations epochs during the training process of the generative adversarial model is set to 1000, the learning rate lr is set to 0.0001, and the number of steps in discriminator training is set to 5; the total number of iterations epochs of feature migration is set to 200, and the learning rate lr is set to 0.01. The domain adaptation weight coefficient param is set to 0.3.

The hardware environment used in the experiment: CPU model is Intel Xeon W-2123; memory is 32GB; GPU model is NVIDIA GeForce GTX1080Ti.

5.2 Experiment and analysis

5.2.1 Comparison experiment before and after twin data feature fusion

Since the established DT fault model of the rolling bearing is relatively ideal and ignores the environmental factors and thermal factors that should be affected in the actual situation, in order to ensure the rationality and feasibility of the twin data, a generative adversarial network is used to perform feature fusion (DT+ GAN) to avoid over-idealization of twin data, while improving the accuracy of fault diagnosis, it also ensures the logic of the full-text experiment.

In order to verify the improvement effect of generative adversarial network on twin data, this section adopts the traditional GAN network model. The model structure setting is the same as that in reference [21]. Twin data is used as generator input, real data is used as discriminator input, and loop iteration is set. times and perform short-time Fourier transform on the synthetic samples after adversarial training to obtain the time spectrum diagram. Experiments are compared according to different working conditions. The experimental results are shown in Figure 12.

As can be seen from Figure 12, the highest fault diagnosis accuracy obtained by using original twin data is only 74.4%, which effectively explains that unprocessed twin data is not suitable for establishing a rolling bearing fault diagnosis model; at the same time, only samples generated by the GAN method are used The diagnostic accuracy of the data is not outstanding; however, the diagnostic accuracy of the samples synthesized by combining DT and GAN proposed in this article has been significantly improved, up to 78.1%.

5.2.2 Comparative experiments between improved WGAN and other methods

Since the improved generative adversarial network model used in this article is a variant of WGAN, in order to verify its improvement effect on twin data, it is compared with traditional GAN, classic DCGAN and its parent WGAN method. GAN parameter settings are the same as above, DCGAN The WGAN parameter settings are the same as in this article. In order to more intuitively observe the effectiveness of the method proposed in this article in fault diagnosis problems under different working conditions, a multi-classification confusion matrix is introduced to analyze the diagnosis results. Due to limited space, only the experimental results under 1hp are taken as an example, and the confusion matrix is drawn as shown in Figure 13.

As can be seen from Figure 13, among the 1,000 target domain test samples, taking normal samples as an example, 4 normal samples were misjudged as other fault types, 1 of which was misjudged as an IR14 fault, and 1 was misjudged as an IR14 fault. For B21 faults, and two others were misjudged as OR14 faults, the highest diagnostic accuracy reached 96%, and the diagnostic accuracy for all fault types reached more than 80%.

In order to further verify the performance of the generative adversarial network model used in this article and reflect its strong stability and superiority, the method proposed in this article is applied to bearing data under different working conditions and compared with different generative adversarial network models. Experiment, the results are shown in Figure 14.

It can be clearly seen from Figure 14 that the improved WGAN model used in this article has significant effects. The fault diagnosis accuracy can be improved by up to 11.15% compared with the traditional GAN model, and up to 7.23% compared with the DCGAN model. Compared with the pre-improved WGAN The model can be improved by up to 1.51%, and the average fault diagnosis accuracy can reach 85.24%. Therefore, the improved WGAN model used in this article can better improve the feature expression of twin data, thereby improving the accuracy of bearing fault diagnosis. 5.2.3 Comparative experiments before and after the residual network improvement

In order to verify the ability of the improved residual network to extract deep features used in the feature transfer framework, this section uses the twin data improved by the improved generative adversarial network as the source domain sample, and the bearing real data as the target domain sample. The residual data before and after the improvement are The features extracted by the difference network were used for fault diagnosis respectively, and experiments were conducted on 12 migration tasks. The results are shown in Table 6.

Table 6 Fault diagnosis accuracy before and after the residual network improvement

As can be seen from Table 6, compared with the features extracted using the original residual network structure, the classification effect of the features extracted by the improved residual network is more significant, and the diagnostic accuracy can be increased by 1.8% to 7.1%. This result fully proves that adding the global attention mechanism and changing the activation function under the framework can positively improve the fault diagnosis of rolling bearings under different working conditions, further improving the diagnosis accuracy.

5.2.4 Comparative experiments with other methods

In order to verify the effectiveness and superiority of the method proposed in this article on fault diagnosis problems of rolling bearings under different working conditions, this section compares the proposed method with the Deep Adaptation Network (DAN) using the residual network framework and the Deep Adaptation Network (DAN) using the residual network framework. Comparative experiments were conducted on four methods of DAN of Alexnet framework, literature [22] and literature [23]. During the experiment, the same source domain and target domain data sets and the same migration task were set up. The results are shown in Figure 15.

It can be seen from Figure 15 that the diagnosis accuracy rates of the two different frameworks used by the deep adaptation network are high and low. The average fault diagnosis accuracy rate is around 89%. The methods in [22] and [23] are 93.5% and 93.5% respectively. 92.2%, while the average fault diagnosis accuracy of the method proposed in this article can reach 96.9%.

5.2.5 Extended experiments

Since rolling bearings are in harsh working conditions and there are many specifications of rolling bearings in actual production, the accuracy of traditional fault diagnosis methods under a single specification is low when directly applied to different specifications, and the status information of the rolling bearings under that specification cannot be obtained. In order to further verify that the method proposed in this article has strong generalization and broaden its application scope, it is proposed to diagnose the migration of rolling bearings between different specifications. This section uses bearing data with specification SKF6205 as the source domain sample, and uses bearing data with specification SKF6203 as the target domain sample. The sample number settings are the same as Table 5, and the migration task settings are shown in Table 7.

Table 7Composition of datasets used for eachtask

In order to intuitively highlight the effectiveness of the method proposed in this article when applied to fault diagnosis problems of different specifications, the diagnosis results are analyzed through a multi-classification confusion matrix. Taking the experimental results of migration task 14 as an example, the confusion matrix is drawn as shown in Figure 16. The experimental results are shown in Figure 17.

As can be seen from Figure 16, among the 1000 target domain test samples, the diagnosis accuracy of N, IR14 and OR07 fault types reached 100%, and the average diagnosis accuracy of other fault types reached 96%. It can be seen from the experimental results in Figure 17 that the method proposed in this article achieved better diagnostic results than other comparative experiments in the experiments of 12 different migration tasks, and its average fault diagnosis accuracy increased by at least 3.3%. Therefore, the method proposed in this article not only performs well in migration tasks under different working conditions, but also achieves good universality in migration tasks of different specifications. Combined with the experimental results, it can be concluded that this method has strong Generalizability.

6 Conclusion

1) It is proposed to implement digital twin modeling of rolling bearings through finite element analysis software, establish rolling bearing failure twin models under different working conditions, and simulate them according to the central difference algorithm of explicit dynamics to obtain rich twin data and solve practical problems. The problem is that the sample size of bearing data under certain working conditions is insufficient.

2) The WGAN algorithm is adopted and the gradient penalty term is introduced to improve it, and it is coupled with the objective function of the discriminator. As evidenced by the fault diagnosis accuracy, the performance of the network model is effectively improved. A method combining DT and improved WGAN is proposed to fuse features of twin data with real data, solving the problem that twin data is too ideal and contains single and insufficient features, and further improves the fault diagnosis accuracy.

3) Use the residual network as the feature transfer framework and improve it, introduce the global attention mechanism, amplify the global dimensional interactive features while reducing information dispersion, and change the activation function under this framework to the FReLU function, making the model Capable of deeply extracting spatially insensitive information. The proposed method is applied to rolling bearing fault diagnosis under different working conditions, which solves the problem of scarcity of labeled data for rolling bearings under some working conditions.

4) A digital twin-based fault diagnosis method for rolling bearings under different working conditions is proposed, which can establish an effective fault diagnosis model when the amount of labeled sample data in the source domain is small and the labeled sample data in the target domain is missing. After experimental verification, the highest fault diagnosis accuracy of the method proposed in this article can reach 98.8%, which is at least 1.0% higher than the single diagnosis accuracy of other methods, proving the effectiveness of the proposed method. In addition, this paper extends the proposed method to fault diagnosis between rolling bearings of different specifications, and proves that the method has strong generalization.

The next step will be to conduct experiments on other components of the rotating machinery, which will be the focus of future research.

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Claims (5)

1. A rolling bearing fault diagnosis method of a digital twin driving deep transfer learning model is characterized by comprising the following implementation processes:

1) Building a rolling bearing DT model

Carrying out twin modeling on the rolling bearing by using modeling software ANSYS-Workbench, carrying out finite element analysis, simulating actual working conditions by adding boundary conditions such as pitting faults with different loads and different diameters, and the like, completing modeling work on a DT model of the rolling bearing, and simultaneously carrying out simulation calculation on vibration signals by setting an acceleration probe so as to obtain twin data;

2) Feature fusion

Introducing a generating countermeasure network (WGAN) based on Wasserstein distance, inputting twin data into a generator, inputting a small amount of real data into a discriminator, adding a gradient penalty term into an objective function of the discriminator, and replacing weight clipping in the WGAN with the gradient penalty term so as to form a new function (generating improvement of the countermeasure network), and performing alternate training to make up for distribution difference between the twin data and the real data;

3) Data preprocessing

The method comprises the steps of performing feature fusion on twin data to obtain a synthetic sample, selecting synthetic sample data of known fault types under a certain working condition as a source domain sample set, and selecting real sample data of unknown fault types under other working conditions as a target domain sample set, wherein the target domain sample set further comprises a target domain training sample set and a target domain testing sample set; performing short-time Fourier transform on the vibration signals of the source domain and the target domain, converting the one-dimensional time domain vibration signals into a two-dimensional time-frequency spectrogram, and inputting the two-dimensional time-frequency spectrogram as a subsequent network;

4) Construction of deep migration learning model

An improved depth residual error network is constructed, a global attention mechanism is introduced, global dimensional interaction characteristics are amplified while information dispersion is reduced, an activation function under a network frame is changed into FReLU, and different types of images are better distinguished by the model through extracting edge space characteristics; calculating the distance between implicit features in a source domain and a target domain sample set by adopting the distribution difference between a source domain and a target domain of the multi-core maximum mean value difference measurement, taking the distance and the classification loss of an improved depth residual error network as target functions together, and carrying out constraint and optimization to establish a rolling bearing fault diagnosis model under different working conditions based on DT;

5) Fault diagnosis

And testing the trained fault diagnosis model by using a target domain test sample set, and comparing the diagnosis result of the deep transfer learning model with a sample real label to obtain a final fault diagnosis result.

2. The method for diagnosing the rolling bearing fault of the digital twin driving deep migration learning model is characterized in that a DT model of the rolling bearing takes a SKF6205 deep groove ball bearing as a research object, the influence of radial load and rotating speed on the bearing is considered, a three-dimensional model of the rolling bearing is built by ANSYS software, finite element analysis is carried out, and twin data of the rolling bearing fault characteristics can be reflected under simulated fault conditions.

3. The method for diagnosing a rolling bearing fault of a digital twin driving deep transfer learning model according to claim 2, wherein DT modeling and finite element analysis are performed on the rolling bearing fault model according to an explicit dynamics analysis method, and the flow is as follows:

1) Three-dimensional modeling

Drawing a three-dimensional model of the rolling bearing in a normal state (in a healthy state) according to physical parameters of the rolling bearing, wherein the internal and external chamfers of the rolling bearing are not considered in the process of building the model;

2) Material arrangement

Aiming at the rolling bearing which is not easy to generate plastic deformation, uniformly arranging the bearing parts into a linear elastic material with orthotropic elasticity and isotropic elasticity; at the Workbench treatment interface, the rigidity of the bearing part is set to be soft, the material is set to be structural steel, and the density is 7850kg/m ³ Elastic modulus of 2.0 Xe ¹¹ pa, poisson's ratio of 0.3;

3) Contact mode

In normal operation of the rolling bearing, the contact mode mainly comprises contact of an inner ring and a rolling body, contact of an outer ring and the rolling body and contact of the rolling body and a retainer, wherein the friction coefficient between an inner ring raceway and the rolling body is set to be 0.1, the friction coefficient between the retainer and the rolling body is set to be 0.05, and the inner ring and the outer ring are not contacted generally and are not set;

4) Grid division

In the running process of the rolling bearing, the minimum unit size of the geometric body grid between the rolling body and the retainer is 1mm, and the minimum unit size of the surface grid is 0.6mm; automatically dividing the minimum units of the geometric body grids of the inner ring and the outer ring, wherein the minimum unit size of the surface grid is 1.2mm;

5) Applying load and constraint

Since the six degrees of freedom of the outer ring are all set to be fixed, no boundary condition is required to be added; the inner ring connecting pair is provided with 20000N force in the direction of an X axis (the axis of the rolling bearing) as a rotating shaft and the rotating speed required by the current working condition in the direction of a Z axis as the rotating shaft;

In order to simulate different working conditions, required rotation speed is required to be added to the inner side of the bearing inner ring, fixation is applied to the outer surface of the bearing outer ring, the connection pair (kinematic pair) is added, and the inner ring, the outer ring and the retainer are all provided with the connection pair.

4. A method for diagnosing a rolling bearing failure in a digital twin driving deep transfer learning model according to claim 3, characterized by replacing weight clipping in WGAN with a gradient penalty term, effecting an improvement in generating an countermeasure network, in the process,

introducing a gradient penalty term into a loss function of the discriminator to replace the original weight clipping (truncation), wherein the formula is as follows:

wherein: i represent p-norm; λ represents a regularized term coefficient;is obtained by randomly interpolating samples on a line between a real sample x and a generated sample G (z), the calculation formula is shown below, where μ obeys [0,1 ]]Uniformly distributed on the upper part;

the final improved objective function of generating the antagonism network is:

5. the method for diagnosing a rolling bearing fault of a digital twin driving deep transfer learning model according to claim 4, wherein in the process of constructing the deep transfer learning model, the feature transfer based on an improved residual network is specifically:

First), improvement of residual error network

The residual network is formed by stacking a plurality of residual blocks, the input of the residual blocks is z, the output is H (z), and the residual refers to the difference value of the mapping z between the output value H (z) and the input value identity, namely:

f(z)＝H(z)-z (17)

the learning object of the residual network is residual f (z), only the difference between the input and output of the residual block is needed to be learned in the network training process, and the input z directly transmits information from the input end to the output end of the residual block through identity mapping in the back propagation process of the model, so that the integrity of the information in the transmission process is ensured;

the improvement of the residual network is as follows:

1) Global attention mechanism

Introducing a global attention mechanism to improve a residual network, wherein the improved residual network structure is as follows: the convolution layer adds channel attention, the convolution layer adds spatial attention,

the channel attention sub-module (channel attention) uses three-dimensional arrangement to reserve three-dimensional information, and the space attention sub-module (space attention) uses two convolution layers to perform space information fusion;

2) FReLU activation function

Based on the fact that the bearing data distribution is mostly nonlinear, the nonlinear activation function is introduced to strengthen the learning ability of the network, so that the network is more similar to the real situation,

the problem of insensitivity to spatial information is solved by adopting a nonlinear computer vision task activation function FReLU (Funnel ReLU), and the FReLU calculation formula is as follows:

FReLU(x)＝max(x,T(x))(19)

Wherein: x is the feature input, T (x) is the two-dimensional space condition;

second), adopting domain adaptation method to transfer characteristics

1) Maximum mean difference

In the migration learning, a given one contains n _s Source domain of each tagged sampleAnd one contains n _t Target Domain of individual Label-free samples->Wherein->Is with the ith source domain sample +.>The corresponding one-shot label is used for identifying the one-shot label,indicating that the corresponding sample belongs to the m-th class of the source domain,/->The sample set representing the jth unlabeled target domain sample, the source domain and target domain typically obey two similar distributions;

the index for measuring the distribution difference between the source domain and the target domain in the domain adaptation problem is the maximum mean difference, and the definition is shown in the formula (20):

wherein X is ^s And X ^t Representing source domain and target domain samples, respectively; p and q represent source domain sample distribution and target domain sample distribution, respectively; h is a regenerated hilbert space with a characteristic core;representing a feature map that can map the original sample data to H,/i>Representing a source domain sample X subject to p-distribution ^s Mathematical expectation after mapping to RKHS;

2) Multi-core maximum mean difference

Multi-kernel variants with MMD MK-MMD use multiple different gaussian kernel functions { k over the original MMD characteristic kernel k (x, x') _u The convex combinations of the forms a composite kernel function that may utilize different kernel functions to enhance distance metricsThe values of the input space can be mapped to RKHS to obtain an optimal value, which is defined as:

wherein H is _k Representing a renewable hilbert space with a characteristic kernel k;

kernel defined by the polynuclear is:

wherein: { beta } _u And the number of cores is equal to the number of m, and the number of cores is equal to the number of m.