Rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission

Abstract

The application discloses a kind of based on multi-source optimal transmission rolling bearing cross-machine domain adaptation fault diagnosis method, comprising the following steps: obtaining the data of each machine bearing each working condition, establish multi-source domain-target domain database;Establish feature extraction deep variational auto-encoding network model, extract the data characteristics of each machine;Establish deep domain adaptation model based on optimal transmission, the data of source domain machine and the data of target machine are jointly migrated to common subspace, and deep training is carried out;Establish label classification model, obtain bearing fault diagnosis result.The application establishes the fault diagnosis model that can be well applied to target machine, realizes end-to-end fault diagnosis;Through variational auto-encoding network, good features of interpretation can be automatically extracted, reduce the operation complexity of classification algorithm, improve the accuracy of classification algorithm, both can make up the defect of single working condition fault data scarcity, and can solve the domain drift problem of same machine multi-working condition data fusion.

Description

Technical Field

[0001] This invention relates to a method for cross-machine domain adaptive fault diagnosis of rolling bearings based on multi-source optimal transmission. Background Technology

[0002] Bearings, as supporting rotating mechanical parts in rotating machinery, are affected by various external environmental factors, such as changes in operating conditions, load, and noise. These factors often lead to domain drift in the data distribution on the same machine. This domain drift will cause classifiers applied to data in the source domain to fail to achieve the same results in the target domain.

[0003] In practice, fault data available under single-condition operation is scarce; moreover, we often cannot obtain a large amount of usable labeled data for the target machine, especially fault information, making it difficult to diagnose the future state of the machine using its labeled data. Furthermore, many new machines not yet in use lack existing state information, yet condition monitoring is still necessary for industrial safety. However, different machines have different sampling frequencies, mechanical structures, and resonance characteristics, resulting in significant differences in data distribution. The inter-domain difference in data from the same machine is far less than the inter-domain difference in data from different machines. Due to the greater domain drift between different machines, many well-labeled classifiers applied under the same machine condition will misclassify more samples. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission, which has high diagnostic accuracy and wide applicability.

[0005] The technical solution of this invention to solve the above problems is: a rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission, comprising the following steps:

[0006] 1) Obtain data on the bearings of each machine under various operating conditions and establish a multi-source domain-target domain database;

[0007] 2) Establish a feature extraction deep variational autoencoder network model to extract data features from each machine in the multi-source domain-target domain database;

[0008] 3) Establish a deep domain adaptation model based on optimal transmission, transfer the data of the source domain machine and the target machine to a common subspace, and perform deep training to reduce domain drift across machines;

[0009] 4) Establish a label classification model to obtain bearing fault diagnosis results.

[0010] The above-mentioned rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission, in step 1), acquires data of four state categories of bearings from each machine: normal, inner ring fault, ball fault, and outer ring fault; the acceleration data of a certain bearing with different working conditions and loads and the corresponding labels are denoted as the source domain, abbreviated as SD; the unlabeled single-working-condition data of another bearing is taken as the target domain, abbreviated as TD; all data are normalized, and then the time domain information is converted into frequency domain information through Fourier transform; the t-SNE visualization features are used, and there are 4 categories in both domains, represented by four different notations.

[0011] In the above-mentioned cross-machine domain adaptive fault diagnosis method for rolling bearings based on multi-source optimal transmission, in step 2), the feature extraction deep variational autoencoder network model is constructed based on VAE. VAE is a type of autoencoder network that combines neural networks and Bayesian formulas, possessing basic encoding and decoding structures. The variational autoencoder network includes an input layer, a hidden layer, a random sampling layer, and an output layer connected in sequence. The input layer is responsible for acquiring the feature representation of the input data; the hidden layer is responsible for reducing the dimensionality of the features of the input data and generating latent variables; the random sampling layer assigns a specific probability distribution to the latent variables, making them interpretable, and samples new features according to the probability distribution; the output layer reconstructs the input data from the sampled features; the hidden layer fits the distribution of the input data to a Gaussian distribution, and then samples on this Gaussian distribution to reconstruct the original input data; therefore, VAE assumes the probability distribution of the latent variables, making them interpretable.

[0012] Let the sample set be {X1, X2, ..., X...} m}, its whole is represented by X; for a certain real sample X k Let k = 1, 2, ..., m. Assume there exists a unique element belonging to X. k The posterior distribution P(Z|X) k ), using P(Z|X k Describe a given X k Generate a model with latent variable Z, and assume P(Z|X) k ) = N(0,1);

[0013] P(Z)=P(ZX k )P(X k (1)

[0014] P(Z) represents the probability distribution of the latent variable Z; P(X) k ) represents sample X k The probability distribution; according to Bayes' formula (1), through P(Z|X k Exclusively for X k The assumption is that the distribution P(Z|X) kThe sampled Z can be restored to X. k In, and for the sample set {X1,X2,...,X...} m There are m independent, multivariate Gaussian distributions; to find the distribution specific to X k Gaussian distribution P(Z|X) k The mean and variance of ) are calculated by constructing two neural networks, as shown in equation (2):

[0015]

[0016] Get exclusive to X k mean μ k and variance This can describe the corresponding Gaussian distribution P(Z|X). k In this way, a Z can be sampled from the distribution. k and through a generator and reconstruction loss function Restore it to X k To make all P(Z|X) k To align with N(0,I), the KL divergence is used to measure the distance between the Gaussian distribution and the standard normal distribution, i.e., KL(N(μ,σ)) = KL(N(μ,σ)). 2 )||N(0,I)), as shown in equation (3):

[0017]

[0018] Where d is the dimension of the sampled latent variable Z, and μ i and These represent the mean and the i-th component of the variance vector of the Gaussian distribution, respectively.

[0019] Because the sampling operation cannot compute gradients, while the sampling result does have a gradient, the reparameter recalculation technique is introduced—from N(μ,σ)... 2 Sampling a Z in the model is equivalent to randomly selecting a point from the standard normal distribution, denoted as ε, and letting Z = μ + ε*σ. In this way, the sampling operation does not need to participate in gradient descent, but instead the sampling result participates, making the entire model trainable.

[0020] To reduce computation, the original data is dimensionality-reduced. In the basic VAE structure, two hidden layers, z1 and z2, are added. The mathematical relationships between z1, z2, and the input / output layers are as follows:

[0021]

[0022] In this context, ω and b are the weight matrix and bias vector, respectively. The combination of the weight variable ω and the bias variable b is called f;w The activation function is defined by subscripts 1 and 2, which correspond to hidden layers z1 and z2, respectively. Similar to autoencoders, the loss function is reconstructed. as follows:

[0023]

[0024] Combining equation (3), the loss function of the feature extractor built based on VAE is:

[0025] In the above-mentioned rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission, in step 3), the data of the source domain machine includes multi-condition data features and their labels, and joint migration of features and labels is performed; the data of the target machine includes single-condition data features.

[0026] The optimal transmission distance, also known as the Wasserstein distance or Earth-Mover distance, is defined as the distance between non-overlapping probability distributions. Given a loss function of c, consider how to distribute a set of distributions with shape μ... s Sand transported to a shape of μ t The cost is minimized in the pit; the Kantorovich problem defines a relaxed solution to the optimal transport problem. There exists a transport plan γ∈Γ(μ) s ,μ t ), Γ(μ s ,μ t ) represents all variables with marginal distribution μ s and μ t The probabilistically coupled set, μ s and μ t The p-order Wasserstein distance W between them p (μ s ,μ t The definition is as shown in equation (6):

[0027]

[0028] inf denotes the infimum. For a function y = f(x), among all constants M that make f(x) greater than or equal to M, the maximum value of M, max(M), (that is, the minimum value of the function y = f(x)) is called the infimum of the function y = f(x). γ Represent a solution; Γ Represents the marginal distribution μ s and μ t Probabilistic coupling;

[0029] For the cross-machine domain adaptation problem, the optimal transmission distance needs to be discretized; let the marginal distributions of the source and target domain samples be μ. S and μT Then the optimal transmission γ * The following is given:

[0030]

[0031]

[0032]

[0033]

[0034] The i-th sample in the source domain The probability distribution; The i-th sample in the target domain The probability distribution; n, m, d refer to the number of samples, which are the total number of samples in each sample set, and the number of samples is not the same between sets; an m*n dimension positive real number measure space, 1 n 1 m These are n-dimensional and m-dimensional vectors, respectively, where all elements are 1. and The i-th sample in the source domain and the i-th sample in the target domain The corresponding Dirac function, <.,.> F Let Frobenius distance be . The cost matrix is ​​represented by T; T written upright indicates the transpose, and T written slanted indicates the target domain.

[0035] When using OT distance to reduce cross-machine domain drift, both feature and label differences are considered. For the feature space, Euclidean distance is used as the metric; for the label space, cross-entropy loss is used as the metric. Therefore, the loss function is as shown in equation (11):

[0036]

[0037] in, Let be the label of the i-th sample in the source domain. d represents the j-th sample in the target domain. Euc (.,.) refers to the Euclidean distance, L(.,.) refers to the cross-entropy function, and z=f(X) refers to the dimensionality reduction feature; therefore, the optimization function (10) can be rewritten as:

[0038]

[0039] in, This represents a pseudo-tag in the target domain.

[0040] In the above-mentioned rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission, in step 4), the label classification model is a Softmax classifier. The input of this classifier is the data features of the common subspace, and the output is the probability of each fault of the bearing.

[0041] The Softmax function is used to calculate the probability that a sample belongs to a certain class Y∈{1,2,...,K}, as shown in equation (13):

[0042]

[0043] K represents the number of label categories; for The transpose of ; a regular T represents the transpose, and a slashed T represents the target domain;

[0044] For multi-class classification problems, the Softmax function is used as the label classifier, and the cross-entropy between the probability distribution of the predicted label f ​​and the probability distribution of the true label is used as the loss function, as shown in equation (14):

[0045]

[0046] Let P(y) be the classification loss function. pre P(y) represents the probability distribution of the predicted label; auc ) represents the probability distribution of the true labels.

[0047] In the above-mentioned rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission, step 3) involves deep training to solve for the parameters of the feature extractor, label predictor g, and OT planning γ, which is achieved by minimizing the objective function of equation (15):

[0048]

[0049] Equation (15) can fix γ i,j We use the values ​​of f and g to solve for the values ​​of f and g, i.e., equation (16):

[0050]

[0051] γ i,j Corresponding to The transportation plan is an element of the overall transportation planning matrix γ;

[0052] Solving for γ by fixing the values ​​of f and g i,j That is, equation (17):

[0053]

[0054] The beneficial effects of this invention are as follows:

[0055] 1) This invention utilizes fault information from machines similar to the target machine to establish a fault diagnosis model that can be effectively applied to the target machine, achieving end-to-end fault diagnosis. This solves the problem in practical engineering where the target machine cannot obtain a large amount of usable tag data, especially fault information.

[0056] 2) This invention can automatically extract interpretable features through variational autoencoder networks, reduce the computational complexity of classification algorithms, and improve the accuracy of classification algorithms. It can not only make up for the lack of single-condition fault data, but also solve the domain drift problem of multi-condition data fusion of the same machine.

[0057] 3) This invention processes the features extracted by variational autoencoder networks with optimal transmission distance, enabling joint transfer learning of features and labels in the source domain and features in the target domain, thereby improving the similarity of features between the source and target domains and achieving fault diagnosis of systems across machine levels.

[0058] 4) This invention has the advantages of high accuracy and wide application range. It can not only be used for fault diagnosis of rolling bearings in wind power systems, but also widely applied to a series of complex systems such as automobiles, aviation, and high-speed railways. Attached Figure Description

[0059] Figure 1 This is a flowchart of the present invention.

[0060] Figure 2 This is a distribution map of fault data characteristics.

[0061] Figure 3 This is a diagram of the variational autoencoder network structure.

[0062] Figure 4 This is a structural diagram of the hidden layer.

[0063] Figure 5 This is a schematic diagram of the optimal transmission method.

[0064] Figure 6 This is a diagram showing the results of cross-machine diagnostics. Detailed Implementation

[0065] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0066] like Figure 1 As shown, a cross-machine domain adaptive fault diagnosis method for rolling bearings based on multi-source optimal transmission includes the following steps:

[0067] 1) Obtain data on the bearings of each machine under various operating conditions and establish a multi-source domain-target domain database.

[0068] Acceleration data for a bearing under different operating conditions and loads, along with corresponding labels, are denoted as the Source Domain (SD). Unlabeled, single-condition data for another bearing is designated as the Target Domain (TD). All data are normalized, and then Fourier transform is used to convert the time-domain information to the frequency-domain information. The differences in features are visualized using t-SNE. Figure 2 As shown, both domains have four categories, represented by four different notations. Figure 2 All data in the source domain are represented by hollow patterns, and all data in the target domain are represented by solid patterns. (Comparison) Figure 2 The fault data feature distribution map shows that the distribution differences of the same category of fault features across different machines are still smaller than the distribution differences of different categories of fault features within the same machine. This is also a prerequisite for cross-machine diagnostics.

[0069] 2) Establish a feature extraction deep variational autoencoder network model to extract data features from each machine in the multi-source domain-target domain database.

[0070] Good feature extraction is a prerequisite for accurate classification. Feature extractors built on VAEs can obtain effective features in multi-source domain data scenarios under different operating conditions on the same machine. The feature extraction deep variational autoencoder network model is built on a VAE. A VAE is a type of autoencoder network that combines neural networks and Bayesian formulas, possessing basic encoding and decoding structures, specifically as follows... Figure 3 As shown, the variational autoencoder network consists of an input layer, a hidden layer, a random sampling layer, and an output layer connected in sequence. The input layer is responsible for acquiring the feature representation of the input data; the hidden layer is responsible for reducing the dimensionality of the features of the input data and generating latent variables; the random sampling layer assigns a specific probability distribution to the latent variables to make them interpretable and samples new features according to the probability distribution; the output layer reconstructs the input data from the sampled features; the hidden layer fits the distribution of the input data to a Gaussian distribution and then samples from this Gaussian distribution to reconstruct the original input data.

[0071] The unique feature of VAEs is their additional hidden layer. This hidden layer fits the distribution of the input data to a Gaussian distribution, and then samples from this Gaussian distribution to reconstruct the original input data. Therefore, VAEs assume the probability distribution of the latent variables, making them interpretable.

[0072] Let the sample set be {X1, X2, ..., X...} m}, its whole is represented by X; for a certain real sample X k Let k = 1, 2, ..., m. Assume there exists a unique element belonging to X. k The posterior distribution P(Z|X) k ), using P(Z|X k Describe a given Xk Generate a model with latent variable Z, and assume P(Z|X) k ) = N(0,1);

[0073] P(Z)=P(ZX k )P(X k (1)

[0074] P(Z) represents the probability distribution of the latent variable Z; P(X) k ) represents sample X k The probability distribution; according to Bayes' formula (1), through P(Z|X k Exclusively for X k Based on the assumption, there is reason to believe that from the distribution P(Z|X) k The sampled Z can be restored to X. k In, and for the sample set {X1,X2,...,X...} m There are m independent, multivariate Gaussian distributions; to find the distribution specific to X k Gaussian distribution P(Z|X) k The mean and variance of ) are calculated by constructing two neural networks, as shown in equation (2):

[0075]

[0076] Get exclusive to X k mean μ k and variance This can describe the corresponding Gaussian distribution P(Z|X). k In this way, a Z can be sampled from the distribution. k and through a generator and reconstruction loss function Restore it to X k To make all P(Z|X) k To align with N(0,1), the KL divergence is used to measure the distance between the Gaussian distribution and the standard normal distribution, i.e., KL(N(μ,σ)) = KL(N(μ,σ)). 2 )||N(0,I)), as shown in equation (3):

[0077]

[0078] Where d is the dimension of the sampled latent variable Z, and μ i and These represent the mean and the i-th component of the variance vector of the Gaussian distribution, respectively.

[0079] Because the sampling operation cannot compute gradients, while the sampling result does have a gradient, the reparameter recalculation technique is introduced—from N(μ,σ)... 2Sampling a Z in the model is equivalent to randomly selecting a point from the standard normal distribution, denoted as ε, and letting Z = μ + ε*σ. In this way, the sampling operation does not need to participate in gradient descent, but instead the sampling result participates, making the entire model trainable.

[0080] To reduce computation, the original data is dimensionality-reduced; in the basic VAE structure, features such as... Figure 4 The mathematical relationships between the two hidden layers z1 and z2 shown and the input / output layers are as follows:

[0081]

[0082] In this context, ω and b are the weight matrix and bias vector, respectively. This is the name given to the combination of the weight variable ω and the bias variable b; The activation function is defined by subscripts 1 and 2, which correspond to hidden layers z1 and z2, respectively. Similar to autoencoders, the loss function is reconstructed. as follows:

[0083]

[0084] Combining equation (3), the loss function of the feature extractor built based on VAE is:

[0085] 3) Establish a deep domain adaptation model based on optimal transmission, transfer the data of the source domain machine and the target machine to a common subspace, and perform deep training to reduce domain drift between machines.

[0086] The source machine's data includes multi-condition data features and their labels, and joint feature and label transfer is performed; the target machine's data includes single-condition data features.

[0087] The optimal transmission distance, also known as the Wasserstein distance or Earth-Mover distance, is defined as the distance between non-overlapping probability distributions. Given a loss function of c, consider how to distribute a set of distributions with shape μ... s Sand transported to a shape of μ t The lowest cost is found in the pit, such as Figure 5 μ s and μ t The p-order Wasserstein distance W between them p (μ s ,μ t The definition is as shown in equation (6):

[0088]

[0089] inf denotes the infimum. For a function y = f(x), among all constants M that make f(x) greater than or equal to M, the maximum value of M, max(M), (that is, the minimum value of the function y = f(x)) is called the infimum of the function y = f(x). γ Γ represents a solution; μ represents the marginal distribution. s and μ t Probabilistic coupling.

[0090] For the cross-machine domain adaptation problem, the optimal transmission distance needs to be discretized; let the marginal distributions of the source and target domain samples be μ. S and μ T Then the optimal transmission γ * The following is given:

[0091]

[0092]

[0093]

[0094]

[0095] The i-th sample in the source domain The probability distribution; The i-th sample in the target domain The probability distribution; n, m, d refer to the number of samples, which are the total number of samples in each sample set, and the number of samples is not the same between sets; an m*n dimension positive real number measure space, 1 n 1 m These are n-dimensional and m-dimensional vectors, respectively, where all elements are 1. and The i-th sample in the source domain and the i-th sample in the target domain The corresponding Dirac function, <.,.> F Let Frobenius distance be . T represents the cost matrix; T written upright represents the transpose, and T written slanted represents the target domain.

[0096] When using OT distance to reduce cross-machine domain drift, both feature and label differences are considered. For the feature space, Euclidean distance is used as the metric; for the label space, cross-entropy loss is used as the metric. Therefore, the loss function is as shown in equation (11):

[0097]

[0098] in, Let be the label of the i-th sample in the source domain. d represents the j-th sample in the target domain. Euc (.,.) refers to the Euclidean distance, L(.,.) refers to the cross-entropy function, and z=f(X) refers to the dimensionality reduction feature; therefore, the optimization function (10) can be rewritten as:

[0099]

[0100] in, This represents a pseudo-tag in the target domain.

[0101] Applying the proposed method to cross-machine bearing fault category diagnosis requires solving for the parameters of the feature extractor, label predictor g, and OT planning γ, which is achieved by minimizing the objective function of equation (15):

[0102]

[0103] Equation (15) can fix γ i,j We use the values ​​of f and g to solve for the values ​​of f and g, i.e., equation (16):

[0104]

[0105] γ i,j Corresponding to The transportation plan is an element of the overall transportation planning matrix γ;

[0106] Solving for γ by fixing the values ​​of f and g i,j That is, equation (17):

[0107]

[0108] 4) Establish a label classification model to obtain bearing fault diagnosis results.

[0109] The label classification model is a Softmax classifier. The input of the classifier is the data features of the common subspace, and the output is the probability of each bearing fault.

[0110] The Softmax function is used to calculate the probability that a sample belongs to a certain class, as shown in equation (13):

[0111]

[0112] K represents the number of label categories; for The transpose of ; a regular T represents the transpose, and a slashed T represents the target domain;

[0113] For multi-class classification problems, the Softmax function is used as the label classifier, and the cross-entropy between the probability distribution of the predicted label f ​​and the probability distribution of the true label is used as the loss function, as shown in equation (14):

[0114]

[0115] Let P(y) be the classification loss function. pre P(y) represents the probability distribution of the predicted label; auc ) represents the probability distribution of the true labels.

[0116] Figure 6 After using the method of this invention, the data features represented by t-SNE visualization are shown, with hollow and solid areas representing all data in the source and target domains, respectively. As can be seen from the figure, the multi-source domain deep variational autoencoder cross-machine diagnostic method of this invention, based on optimal transmission, can utilize data from the source machine domain to solve fault diagnosis problems in the target machine domain, achieving good results.

[0117] The significant data distribution differences across machines render many previous AI-based fault diagnosis techniques ineffective. This invention combines deep learning technology, using variational autoencoders (VACs) to extract interpretable feature representations and more evenly distribute features of different categories in the latent space. Furthermore, it optimizes the transmission distance for processing the features extracted by the VACs, reducing domain drift across machines. Compared to existing technologies that often take tens of minutes, the end-to-end diagnostic process of this invention takes less than 1 minute, significantly improving usability in industrial scenarios while maintaining accuracy. In addition, this invention has excellent generalization capabilities and can be widely applied to complex, high-noise, dynamic, and variable-condition transmission systems in industries such as automotive and aviation.

Claims

1. A method for cross-machine domain adaptive fault diagnosis of rolling bearings based on multi-source optimal transmission, characterized in that, Includes the following steps: 1) Obtain data on the bearings of each machine under various operating conditions and establish a multi-source domain-target domain database; 2) Establish a feature extraction deep variational autoencoder network model to extract data features from each machine in the multi-source domain-target domain database; 3) Establish a deep domain adaptation model based on optimal transmission, transfer the data of the source domain machine and the target machine to a common subspace, and perform deep training to reduce domain drift across machines; In step 3), the data of the source machine includes multi-condition data features and their labels, and joint migration of features and labels is performed; the data of the target machine includes single-condition data features. The optimal transmission distance, also known as the Wasserstein distance or Earth-Mover distance, is defined as the distance between non-overlapping probability distributions. Given a loss function of c, consider how to distribute a set of data with the following shape... The sand was transported to a shape that was The cost is minimized in the pit; the Kantorovich problem defines a relaxed solution to the optimal transport problem; there exists a transport plan. , For all those with marginal distributions and A set of probabilistic couplings. and p-order Wasserstein distance between Defined as in equation (6): (6)； inf denotes the infimum. For a function y=f(x), among all constants M that make f(x) greater than or equal to M, the maximum value of M, max(M), (that is, the minimum value of the function y=f(x)) is called the infimum of the function y=f(x). Represent a solution; Represents marginal distribution and Probabilistic coupling; For the cross-machine domain adaptation problem, the optimal transmission distance needs to be discretized; let the marginal distributions of the source and target domain samples be respectively... and Then the optimal transmission The following is given: (7)； (8)； (9)； (10)； The i-th sample in the source domain The probability distribution; The i-th sample in the target domain The probability distribution; n, m, d refer to the number of samples, which are the total number of samples in each sample set, and the number of samples is not the same between sets; m*n dimension positive real number measure space. , These are n-dimensional and m-dimensional vectors, respectively, where all elements are 1. and The i-th sample in the source domain and the i-th sample in the target domain The corresponding Dirac function, Let Frobenius distance be . The cost matrix is ​​represented by T; T written upright indicates the transpose, and T written slanted indicates the target domain. When using OT distance to reduce cross-machine domain drift, both feature and label differences are considered. For the feature space, Euclidean distance is used as the metric; for the label space, cross-entropy loss is used as the metric. Therefore, the loss function is as shown in equation (11): (11)； in, Let be the label of the i-th sample in the source domain. The j-th sample in the target domain; Refers to Euclidean distance. Refers to the cross-entropy function. The characteristic of dimensionality reduction is referred to; therefore, the optimization function (10) can be rewritten as: (12)； in, Represents pseudo-tags in the target domain; 4) Establish a label classification model to obtain bearing fault diagnosis results.

2. The rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission according to claim 1, characterized in that, In step 1), data on the four status categories of bearings of each machine are acquired: normal, inner ring fault, ball fault, and outer ring fault. Acceleration data and corresponding labels of a bearing with different working conditions and loads are denoted as the source domain, abbreviated as SD. Data of a single working condition without labels of another bearing is denoted as the target domain, abbreviated as TD. All data are normalized and then converted from time domain information to frequency domain information through Fourier transform. The features are visualized using t-SNE. There are four categories in both domains, represented by four different notations.

3. The rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission according to claim 1, characterized in that, In step 2), the feature extraction deep variational autoencoder network model is built based on VAE. VAE is a type of autoencoder network that combines neural networks and Bayesian formulas, possessing basic encoding and decoding structures. The variational autoencoder network contains an input layer, a hidden layer, a random sampling layer, and an output layer connected in sequence. The input layer is responsible for acquiring the feature representation of the input data; the hidden layer is responsible for reducing the dimensionality of the input data features and generating latent variables; the random sampling layer assigns a probability distribution to the latent variables, making them interpretable, and samples new features according to the probability distribution; the output layer reconstructs the input data from the sampled features; the hidden layer fits the distribution of the input data to a Gaussian distribution, and then samples on this Gaussian distribution to reconstruct the original input data. Therefore, VAE assumes the probability distribution of the latent variables, making them interpretable. Sample set The whole is represented by X; for a certain real sample X k Let k = 1, 2, ..., m. Assume there exists a unique element belonging to X. k The posterior distribution P(Z|X) k ), using P(Z|X k Describe a given X k Generate a model with latent variable Z, and assume P(Z|X) k )=N(0,1); (1)； This represents the probability distribution of the latent variable Z; Indicates sample X k The probability distribution; according to Bayes' formula (1), through P(Z|X k Exclusively for X k The assumption is that the distribution P(Z|X) k The sampled Z can be restored to X. k In, and for the sample set There are m independent, multivariate Gaussian distributions; to find the distribution specific to X k Gaussian distribution P(Z|X) k The mean and variance of ) are calculated by constructing two neural networks, as shown in equation (2): (2)； Get exclusive to X k mean and variance This can describe the corresponding Gaussian distribution P(Z|X). k In this way, a Z can be sampled from the distribution. k and through a generator and reconstruction loss function To restore it to X k To make all P(Z|X) k To align with N(0,1), the KL divergence is used to measure the distance between the Gaussian distribution and the standard normal distribution, i.e. As shown in equation (3): (3)； Where d is the dimension of the sampled latent variable Z. and These represent the mean and the i-th component of the variance vector of the Gaussian distribution, respectively. Because the sampling operation cannot calculate the gradient, while the sampling result does have a gradient, the reparameter recalculation technique is introduced—from... Sampling a Z from the middle is equivalent to randomly selecting a point from the standard normal distribution; this point is denoted as Z. and order In this way, the sampling operation no longer needs to participate in gradient descent; instead, the sampling result participates, making the entire model trainable. To reduce computation, the original data was dimensionality reduced; two hidden layers were added to the basic VAE structure. and , , The mathematical relationship with the input / output layers is as follows: (4)； middle b and b are the weight matrix and bias vector, respectively. Weight variables The combined term for the bias variable b; The function is called the activation function, and the subscripts 1 and 2 correspond to the hidden layers, respectively. and Similar to autoencoders, the loss function is reconstructed. as follows: (5)； Combining equation (3), the loss function of the feature extractor built based on VAE is: .

4. The rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission according to claim 3, characterized in that, In step 4), the label classification model is a Softmax classifier. The input of this classifier is the data features of the common subspace, and the output is the probability of each bearing fault. The Softmax function is used to calculate which class a sample belongs to. The probability of is shown in equation (13): (13)； K represents the number of label categories; for The transpose of ; a regular T represents the transpose, and a slashed T represents the target domain; For multi-class classification problems, the Softmax function is used as the label classifier, and the cross-entropy between the probability distribution of the predicted label f ​​and the probability distribution of the true label is used as the loss function, as shown in equation (14): (14)； The classification loss function; To predict the probability distribution of the labels; This represents the probability distribution of the true labels.

5. The rolling bearing cross-machine domain adaptive fault diagnosis method based on multi-source optimal transmission according to claim 4, characterized in that, In step 3), deep training is performed to solve for the feature extractor, label predictor g, and OT programming. The parameters are obtained by minimizing the objective function of equation (15): (15)； Formula (15) can be fixed We use the values ​​of f and g to solve for the values ​​of f and g, i.e., equation (16): (16)； Corresponding to Transportation planning, forming an overall transportation planning matrix One of the elements; Solving by fixing the values ​​of f and g That is, equation (17): (17)。

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