Width unsupervised domain adaptive two-stage rolling bearing fault diagnosis method and system under class imbalance scene

Abstract

The invention discloses a width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method and system under a class imbalance scene, relates to the field of rolling bearing fault diagnosis, and aims to solve the problem of lack of a method for effectively solving the domain adaptation problem under class imbalance in bearing fault diagnosis in the prior art. Comprising the following steps: step 1, carrying out dimension reduction on data by adopting rolling bearing time domain data; 2, performing feature extraction on the data by utilizing a width learning network model, and performing feature alignment by adopting manifold embedding distribution alignment to obtain a target domain data pseudo tag; 3, performing sample screening based on uncertainty measurement and cosine similarity between samples, and dividing reliable samples and residual samples; introducing a generative adversarial network WGAN-GP containing gradient penalty to perform data enhancement on the screened reliable samples in the target domain to obtain a balanced sample set; and step 4, taking the balanced sample set as a training set, training the width learning network model, and finally inputting residual samples of the target domain for diagnosis.

Description

Technical Field

[0001] The present invention relates to the technical field of rolling bearing fault diagnosis, and in particular to a wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method and system in a category imbalance scenario. Background Art

[0002] As an important component of mechanical equipment, rolling bearings are widely used in important fields such as aerospace, railway transportation, and medical treatment. [1] However, its complex and harsh working environment makes it very easy to have wear, breakage, peeling and other faults. Once a fault occurs, it will affect the accuracy and reliability of the mechanical equipment, causing serious property losses; it will also affect the safety of the mechanical equipment. [2] , resulting in casualties. Therefore, the effective diagnosis of rolling bearing faults has important practical significance.

[0003] In recent years, the emergence of deep learning has opened up a new perspective in the field of fault diagnosis. It overcomes the shortcomings of traditional methods that rely on expert experience in feature extraction, and can effectively capture the deep features of data and achieve end-to-end fault diagnosis. [3-4] When existing deep learning methods train models, they usually assume that all training data and test data come from the same distribution. [5] However, in actual industry, rolling bearings often work under different working conditions as the external environment changes. The model trained with data under a single working condition cannot adapt to all working conditions, resulting in reduced diagnostic accuracy. Transfer learning can effectively share and transfer information between similar fields and tasks, which brings inspiration to solving fault diagnosis problems under different working conditions.

[0004] According to the label information of the target domain data, the transfer learning method can be divided into supervised transfer, semi-supervised transfer and unsupervised transfer. [6]Obviously, semi-supervised transfer and unsupervised transfer are more in line with the actual situation in industrial production, so they have attracted much attention from scholars. Reference [7] uses a small amount of labeled data in the target domain and the knowledge of the source domain data to construct a batch normalized long short-term memory model to generate auxiliary samples. Then, the maximum classifier difference method of transfer is combined with the adversarial strategy to align the probability distribution of the auxiliary samples and the unlabeled data in the target domain, thereby realizing cross-domain diagnosis between different devices. Reference [8] proposes an unsupervised domain adaptation method based on contrastive learning. By designing contrast estimation items to reduce the probability of samples being classified near or on the class boundary, cross-condition bearing fault diagnosis is realized. Reference [9] breaks the fixed pattern of existing methods that most of them are based on the migration from a single source domain to the target domain for fault diagnosis, and proposes a multi-source domain transfer learning method that is more in line with the actual industry, achieving satisfactory results in the problem of unsupervised cross-domain fault diagnosis. Reference

[10] breaks through the closed set domain adaptation category in traditional unsupervised transfer, and proposes a general domain adaptation method with a source domain and target domain weighting mechanism. By using additional outlier identifiers, it can realize automatic identification of unknown fault modes.

[0005] Today's mainstream transfer learning methods are designed in combination with deep learning, and the increasing requirements of diagnostic tasks in actual production have led to increasingly complex models built based on deep learning methods. When faced with massive amounts of data, the training process is extremely time-consuming, making its learning efficiency and speed far lower than actual requirements, and thus becoming an important bottleneck for many applications.

[0006] With the Broad Learning System (BLS) being proposed by Chen et al.

[11] It is proposed that its fast and reliable modeling method provides a new solution to the bottlenecks encountered by the above deep learning methods

[12] . Reference

[13] proposed an adaptive BLS that takes the original vibration signal of rotating machinery as input. An adaptive incremental learning strategy is used to adjust the network structure and avoid retraining, which provides an effective solution for rotating machinery fault diagnosis. Reference

[14] proposed a task incremental BLS method that can sequentially learn different diagnostic tasks without retraining and effectively diagnose faults of key components. In addition, compared with deep learning, wide learning requires fewer hyperparameters to be adjusted, so it is suitable to combine it with a meta-heuristic algorithm to achieve better diagnostic effects by optimizing the number of feature nodes. [15-16] On the other hand, improving the objective function is also a solution to improve the performance of BLS. Reference

[17] added structural information constraint weights to the original objective function, which reduced the intra-class distance and increased the inter-class distance, thus achieving rolling bearing fault diagnosis and location.

[0007] The accuracy of rolling bearing fault diagnosis is not only affected by cross-operating conditions, but also restricted by the problem of data category imbalance. During the service life of rotating machinery, failures are rare, which leads to the fact that the normal state data collected is far more than the fault data. Therefore, when using data to train the model, there will be a problem of category imbalance, which in turn affects the classification performance of the model. The problem of rolling bearing fault diagnosis in actual production is a complex problem that needs to consider both cross-operating conditions and data category imbalance. Therefore, the problem of domain adaptation (Class Imbalanced Domain Adaptation, CIDA) under category imbalance in the field of fault diagnosis is a complex problem that needs to consider cross-operating conditions and data category imbalance at the same time ... be considered at the same time.

[18] This is an issue that deserves further study.

[0008] At present, the mainstream methods for solving the CIDA problem are mostly based on deep learning networks. However, reference

[19] proposed a method that combines width transfer and ensemble learning, which effectively solved the multi-condition fault diagnosis problem in the sewage treatment process. Reference

[20] relied on the classification results of the width learning network to design an active migration sampling strategy to achieve cross-condition diagnosis of mechanical faults. The emergence of these two documents fills the gap in width learning in solving the CIDA problem, but there is also a problem that the impact of the large difference in the sample ratio between the minority class and the majority class on the ensemble learning effect is not considered, resulting in a decrease in the overall model performance. And before obtaining the target domain knowledge, the data distribution difference between the source domain and the target domain is ignored, resulting in the situation where all the minority class samples are misclassified. Summary of the invention

[0009] The technical problems to be solved by the present invention are:

[0010] The existing technology lacks an effective method to solve the domain adaptation problem under class imbalance in bearing fault diagnosis.

[0011] The present invention adopts the following technical solutions to solve the above technical problems:

[0012] The present invention provides a width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in a class imbalance scenario, comprising the following steps:

[0013] Step 1: Use rolling bearing time domain data to reduce the data dimension.

[0014] Step 2: Use the width learning network model to extract features from the data, and use manifold embedding distribution alignment to align features to obtain pseudo labels for target domain data;

[0015] Step 3: Samples are screened based on uncertainty metrics and cosine similarity between samples, and samples in the target domain are divided into reliable samples and remaining samples. Generative adversarial network WGAN-GP with gradient penalty is introduced to perform data enhancement on the screened reliable samples in the target domain to obtain a balanced sample set.

[0016] Step 4: Use the balanced sample set as the training set, initialize the width learning network model and train it, and finally input the remaining samples of the target domain into the trained width learning network model to achieve diagnosis.

[0017] Furthermore, step one includes the following process:

[0018] Using the rolling bearing time domain data, a time domain sample set with a single sample length of L points is constructed by sliding sampling. Each sample is subjected to fast Fourier transform to obtain a frequency domain sample set, and the number of sampling points is set to 8L during the fast Fourier transform. Each frequency domain sample is then divided into several frequency sub-bands, and the RMS of each frequency sub-band is calculated and used as input data to achieve data dimensionality reduction.

[0019] Furthermore, the objective function of the width learning network model in step 2 is:

[0020]

[0021] In the formula, Y is the actual output, λ is the regularization coefficient, W is the connection weight, and the estimated output of the network is By continuously optimizing the estimated output The error between the actual output and the optimal solution of W is expressed as:

[0022] W=(λI+A T A) -1 A T Y=A + Y

[0023] Where I is the unit matrix, A T is the transposed matrix of A, and the pseudo-inverse of A is

[0024] Furthermore, the feature alignment using manifold embedding distribution alignment described in step 2 includes the following process:

[0025] Step 21: Manifold feature transformation, specifically:

[0026] First, PCA is used to obtain the two-domain subspace S s and S t , parameterize the geodesic function φ(t) using the standard Euclidean metric of the Riemannian manifold; let φ(0) = S s ,φ(1)=S t; Then the formula for calculating the shortest distance function between two points is:

[0027] φ(t)=S s U1Γ(t)-R s U2Σ(t)

[0028] In the formula, R s For S s The orthogonal complement of U1, U2, Γ and Σ are given by and After singular value decomposition, we get:

[0029]

[0030] Where Γ and Σ are square matrices whose diagonal elements are S s and S t The sine and cosine functions of the main characters between them;

[0031] Then, integrate all t∈[0,1] on the path so that the geodesic function migrates from φ(0) to φ(1), that is:

[0032]

[0033] In the formula, a i and a j Represents the feature samples of the source domain and the target domain; G is a semi-definite matrix, which is expressed as:

[0034]

[0035]

[0036] Where Λ is a diagonal matrix, Λ 1i ,Λ 2i and Λ 3i are diagonal elements, θ i For S s and S t The protagonist of

[0037] The feature sample set after GFK is expressed as A s and A t The source domain feature sample set and the target domain feature sample set are extracted by the width learning network feature;

[0038] Step 22: Dynamic distribution alignment, including the following process:

[0039] The balance factor μ is used to adaptively adjust the importance of source domain data and target domain data, and adaptively distribute the data. It is expressed as:

[0040]

[0041] Where μ∈[0,1] is the balancing factor, c∈{1,…,C} represents the corresponding category, and D f represents the marginal distribution, represents the conditional distribution;

[0042] Calculate the distribution difference between the two domains, and the adaptive distribution adaptation is expressed as:

[0043]

[0044] In the formula, c∈{1,…,C} represents the corresponding category, H represents the reproducing kernel Hilbert space, and E[·] represents the expected function;

[0045] Measures the distance between different distributions, expressed as:

[0046]

[0047] Where, d M and d c A-distance represents the difference in marginal distribution and the difference in conditional distribution of the cth class respectively;

[0048] Using class conditional distribution approximate To obtain Using source domain data D s The trained BLS is used for the target domain data D t Make predictions and revise the prediction results through iterations;

[0049] Step 2 and 3: Learning the classifier includes the following process:

[0050] Construct a learning classifier f based on structural risk minimization:

[0051]

[0052] Where the first two terms represent the loss of the classifier f on the source domain, is the adaptive distribution adaptation penalty term, R f (·) is the Laplace regularization term, η, τ and ρ are regularization coefficients;

[0053] By iteratively adjusting the target domain data label

[0054] Furthermore, the sample screening described in step 3 is performed based on the uncertainty measurement and the cosine similarity between samples, and the target domain samples are divided into reliable samples and remaining samples, specifically:

[0055] Uncertainty measurement based on edge sampling, measuring the sample confidence R by selecting the difference between the two categories with the largest probability in the model prediction results x ,Right now:

[0056]

[0057] In the formula, Indicates that the sample x belongs to the category The probability of and Indicates the most likely category and the second most likely category;

[0058] Choose to trust R in each minority class x The largest sample is taken as the real label. Then the cosine similarity between all samples in the same category and the feature vector of the sample is calculated.

[0059] Sample x with feature dimension n i and sample x j The cosine similarity is:

[0060]

[0061] Define the minority class sample x i The final score RC is:

[0062]

[0063] In the formula, Represents the sample x i The predicted categories are the same and R x The largest sample;

[0064] Finally, each type of samples is arranged in descending order according to the scores, and a fixed number of samples are selected based on experience. Their pseudo labels are regarded as true labels to obtain reliable samples and remaining samples.

[0065] Furthermore, the objective function of the generative adversarial network WGAN-GP with gradient penalty in step 3 is:

[0066]

[0067] In the formula, E[·] represents the expected function, D(·) and G(·) represent the discriminator function and the generator function respectively; z is the input noise data; ||·||2 represents the 2-norm, γ is the gradient penalty term coefficient, is the gradient operator, Denotes the sample distribution Ψ generated from g (·) and the true sample distribution Ψ r (·) Uniform sampling along the straight line between sampling point pairs, Represents random sampling between real data and generated data.

[0068] The present invention provides a width unsupervised domain adaptation two-stage rolling bearing fault diagnosis system in a category imbalance scenario. The system has a program module corresponding to the steps of the method described in any one of the above technical solutions, and executes the steps in the width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the above category imbalance scenario during operation.

[0069] The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps in the width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in a category imbalance scenario described in any one of the above technical solutions when called by a processor.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] The present invention combines a wide learning network with a non-deep migration method MEDA to quickly obtain target domain prediction results, while achieving the advantage of fast modeling of wide learning; the present invention constructs a composite index based on uncertainty measurement in active learning and cosine similarity between samples, screens out reliable samples from the target domain, and corrects the target domain prediction results in combination with WGAN-GP, which not only makes the model universal, but also still shows high model performance in the case of class imbalance, especially the classification accuracy of minority categories is significantly improved.

[0072] The present invention realizes accurate diagnosis of rolling bearing faults in rotating machinery, and lays a foundation for diagnosis of rolling bearing compound faults and faults of other parts of rotating machinery. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a schematic diagram of the basic structure of a width learning system in an embodiment of the present invention;

[0074] Figure 2 It is a schematic diagram of the function implementation of MEDA in an embodiment of the present invention;

[0075] Figure 3 is a flowchart of a fault diagnosis process in an embodiment of the present invention;

[0076] Figure 4 A schematic diagram of data preprocessing in an embodiment of the present invention;

[0077] Figure 5 is the 0hp inner race fault envelope spectrum in the embodiment of the present invention;

[0078] Figure 6 is a 1hp inner race fault envelope spectrum diagram in an embodiment of the present invention;

[0079] Figure 7 Schematic diagram of the network structure of the generator and the discriminator in the embodiment of the present invention;

[0080] Figure 8 Diagnostic result diagrams of different methods in migration tasks according to embodiments of the present invention;

[0081] Fig. 9 It is a BLS-GFK confusion matrix diagram in an embodiment of the present invention;

[0082] Fig.10 : is a CDAN confusion matrix diagram in an embodiment of the present invention;

[0083] Fig.11 It is a BLS-MEDA confusion matrix diagram in an embodiment of the present invention;

[0084] Fig.12 is the F-Measure under different balancing rates in the embodiment of the present invention;

[0085] Fig.13 This is a diagram showing the impact of different sampling numbers on migration task results in an embodiment of the present invention;

[0086] Fig.14 : is a loss curve diagram of the generator and the discriminator in the embodiment of the present invention;

[0087] Fig.15 Spectrum diagrams of real samples and generated samples in an embodiment of the present invention;

[0088] Fig.16 Diagnostic result diagrams of different methods under class imbalance in an embodiment of the present invention;

[0089] Fig.17 is a confusion matrix diagram in an embodiment of the present invention;

[0090] Fig.18 Graph showing comparative test results of bearings in an embodiment of the present invention. DETAILED DESCRIPTION

[0091] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0092] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0093] In a typical embodiment, Figure 3 As shown, the present invention provides a width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in a category imbalance scenario, comprising the following steps:

[0094] Step 1: Use rolling bearing time domain data to reduce the data dimension.

[0095] Step 2: Use the width learning network model to extract features from the preprocessed data, and use manifold embedding distribution alignment to align features to obtain pseudo labels for target domain data;

[0096] Step 3: Samples are screened based on uncertainty metrics and cosine similarity between samples, and samples in the target domain are divided into reliable samples and remaining samples. Generative adversarial network WGAN-GP with gradient penalty is introduced to perform data enhancement on the screened reliable samples in the target domain to obtain a balanced sample set.

[0097] Step 4: Use the balanced sample set as the training set, initialize the width learning network model and train it, and finally input the remaining samples of the target domain into the trained width learning network model to achieve diagnosis.

[0098] In one embodiment of the present invention, step one comprises the following process: Figure 4 As shown in the figure, a time domain sample set with a single sample length of L points is constructed in the original vibration signal by sliding sampling. Fast Fourier transform is performed on each sample to obtain a frequency domain sample set with richer fault information. It is proposed to set the number of sampling points to 8L when performing fast Fourier transform to reduce the "fence effect". Then, each frequency domain sample is divided into several frequency sub-bands, and the arithmetic root mean square (RMS) that can reflect the signal energy distribution in the frequency domain statistical features is selected, that is, the RMS of each sub-band is calculated, and then it is used as input data to finally achieve data dimensionality reduction.

[0099] The construction process of the width learning network model is:

[0100] BLS has a single hidden layer neural network structure, and its basic structure is as follows Figure 1 As shown in Figure 1, it mainly consists of three parts: a hidden layer A consisting of mapping nodes and enhancement nodes, and an output layer Y. The two layers are connected by weights W.

[0101] First, for the input original data X∈R N×M ,Y∈R N×C, where N is the number of samples, M is the feature dimension, and C is the number of categories. The mapping features are formed through linear transformation, as shown in formula (1):

[0102]

[0103] In the formula, Z i is the characteristic node of the i-th group, there are n groups in total, each group has k neurons, φ i (·) is the linear activation function, and are random weights and biases respectively.

[0104] Secondly, in order to improve the network's ability to approximate arbitrary functions, all feature nodes are connected and enhanced nodes are formed through nonlinear transformation, as shown in formula (2):

[0105]

[0106] In the formula, H j is the jth group of enhanced nodes, with a total of m groups, each with p neurons, ξ j It is a nonlinear activation function that can effectively improve the feature expression ability. and are random weights and biases respectively.

[0107] Next, connect the enhanced node to H m =[H1,H2,…,H m ], and the characteristic node Z n Concatenate to get the input layer A = [Z n |H m ].

[0108] Finally, the estimated output of the network is Where W is the connection weight, and the network training process is the process of solving W. The objective function is established as formula (3):

[0109]

[0110] Where Y is the actual output and λ is the regularization coefficient. The error between the actual output and the optimal solution of W is expressed as formula (4):

[0111] W=(λI+A T A) -1 A T Y=A + Y (4)

[0112] Where I is the unit matrix, A T is the transposed matrix of A; the pseudo-inverse of A is express.

[0113] The entire network only needs to use pseudo-inverse to solve W, and there is no need to repeatedly update weights through gradient descent like deep neural networks, thus improving the training efficiency of the network.

[0114] MEDA is a non-deep transfer learning method with high computational efficiency. This implementation combines it with width learning to overcome the problem of poor real-time performance of traditional deep transfer methods. Figure 2 As shown in Figure 1, we first reduce the data drift between domains through manifold feature transformation, then perform dynamic distribution alignment, and finally learn the classifier f.

[0115] The process of feature alignment using manifold embedding distribution alignment in step 2 is as follows:

[0116] Step 21: Manifold feature transformation. The specific process includes:

[0117] In order to solve the problem of poor migration effect caused by large differences between data domains, MEDA uses the geodesic flow kernel method (GFK) to transform the features in the original space into the manifold space to avoid feature distortion.

[0118] After the width learning network feature extraction, the source domain feature sample set is represented as A s , the target domain feature sample set is A t The process of manifold feature transformation consists of two steps:

[0119] First, PCA is used to obtain the two-domain subspace S s and S t , use the standard Euclidean metric of the Riemannian manifold to parameterize the geodesic function φ(t). Let φ(0) = S s ,φ(1)=S t The shortest distance function between two points is calculated as follows:

[0120] φ(t)=S s U1Γ(t)-R s U2Σ(t) (5)

[0121] In the formula, R s For S s The orthogonal complement of U1, U2, Γ and Σ are given by and After singular value decomposition, we get:

[0122]

[0123] Where Γ and Σ are square matrices. Their diagonal elements are S sand S t The sine and cosine functions of the principal angles between them are used to measure the overlap between subspaces.

[0124] Then, in order to align the features of the source domain data and the target domain data, the geodesic function is migrated from φ(0) to φ(1) by integrating all t∈[0,1] on the path, as shown in Equation (7):

[0125]

[0126] In the formula, a i ,a j represents the feature samples of the source domain and the target domain, G is a semi-definite matrix, which is expressed as formula (8):

[0127]

[0128] Where Λ is a diagonal matrix, Λ 1i ,Λ 2i and Λ 3i are diagonal elements, θ i For S s and S t The protagonist.

[0129] The feature sample set after GFK is expressed as

[0130] Step 22: Dynamic distribution alignment, including the following process:

[0131] Different source domain data and target domain data will have different importance for edge distribution alignment and conditional distribution in domain adaptation tasks due to different feature distributions. If only one of them is considered or both are considered equally important, it is easy to cause network performance degradation. Therefore, the balance factor μ is used to adaptively adjust the importance of the two, and adaptive distribution adaptation It is expressed as formula (9):

[0132]

[0133] Where μ∈[0,1] is the balancing factor, c∈{1,…,C} represents the corresponding category, and D f represents the marginal distribution, Represents conditional distribution

[0134] MMD is used to calculate the distribution difference between the two domains, and the adaptive distribution adaptation is expressed as formula (10):

[0135]

[0136] Where c∈{1,…,C} represents the corresponding category, H represents the reproducing kernel Hilbert space, and E[·] represents the expected function. The first term represents the marginal distribution distance between domains, and the last term represents the conditional distribution distance.

[0137] In order to estimate the balance factor μ, MEDA uses A-distance to measure the distance between different distributions, which is expressed as formula (11):

[0138]

[0139] Where, d M and d c A-distance represents the difference in marginal distribution and the difference in conditional distribution of the cth class respectively.

[0140] Since the target domain data D t There are no labels, so its conditional distribution is It cannot be obtained directly, MEDA uses class conditional distribution approximate To obtain Using source domain data D s The trained BLS is used for the target domain data D t Predictions are made and the prediction results are corrected through iterations. During the whole process, MEDA only uses the soft labels obtained by BLS classification in the first iteration, and subsequent iterations use the results of the previous iteration to automatically correct the target domain labels.

[0141] Finally, the classifier f is learned according to Structural Risk Minimization (SRM), as shown in Equation (12):

[0142]

[0143] Where the first two terms represent the loss of the classifier f on the source domain, is the adaptive distribution adaptation penalty term, R f (·) is the Laplace regularization term, and η, τ, and ρ are regularization coefficients.

[0144] Compared with most existing methods such as CORAL

[23] and JGSA

[24] Different from this, MEDA directly learns cross-domain functions without explicit classifier training. That is, when the soft labels of the target domain obtained by BLS are first fed into After that, it is iterated to directly adjust the target domain data label, and finally obtains

[0145] In step 3, the samples are screened based on uncertainty measurement and cosine similarity between samples, and the target domain samples are divided into reliable samples and remaining samples. Specifically,

[0146] As a common sampling strategy in active learning, the uncertainty measure based on edge sampling measures the sample confidence R by selecting the difference between the two categories with the largest probability in the model prediction results. x , described as formula (13):

[0147]

[0148] In the formula, Indicates that the sample x belongs to the category probability. and Indicates the most likely category and the second most likely category. x The larger it is, the smaller the sample uncertainty is, that is, the higher the label confidence is.

[0149] Since the increase in the class imbalance rate may result in fewer correct samples in the classification results of a minority class, in order to ensure the reliability of the selected samples, only the R in each minority class is selected to be trusted. x The largest sample is considered as the real label. Then the cosine similarity between all samples in the same category and the feature vector of this sample is calculated.

[0150] Sample x with feature dimension n i and sample x j The cosine similarity calculation is as follows:

[0151]

[0152] When the cosine value approaches 1, it indicates that the samples are highly similar, and when it approaches -1, it indicates that they are highly different. Combined with the uncertainty measure based on edge sampling, a composite indicator is constructed. Minority class sample x i The final score of is defined by RC, as shown in formula (15):

[0153]

[0154] In the formula, Represents the sample x i The predicted categories are the same and R x The largest sample. Finally, each class of samples is sorted in descending order according to the score, and a fixed number of samples are selected based on experience, and their pseudo labels are regarded as true labels. In particular, since the majority class samples are far more than the minority class samples, using cosine similarity will cause a large computational overhead. And because of the class imbalance, the pseudo labels of the majority class samples are highly reliable. Therefore, directly using R xArrange them in descending order and select the same number of samples as the minority class after data augmentation for sample annotation.

[0155] In step 3, the generative adversarial network WGAN-GP with gradient penalty is introduced to perform data enhancement on the selected reliable samples in the target domain, which specifically includes the following process:

[0156] WGAN-GP is for GAN

[25] and WGAN

[26] This is an improved method proposed to solve the training instability and gradient vanishing problems in the training. As an effective data enhancement method, WGAN-GP makes up for the adverse effects of sample category imbalance. Its main body consists of two parts: the generator and the discriminator. The working principle is similar to GAN. Both are based on the mutual game between the generator network and the discriminator network. After finally reaching the Nash equilibrium, the ideal generated data is obtained, thereby realizing the data expansion of minority class samples. Its objective function is as follows:

[0157]

[0158] In the formula, E[·] represents the expected function, D(·) and G(·) represent the discriminator function and the generator function respectively. z is the input noise data. ||·||2 represents the 2-norm, γ is the gradient penalty term coefficient, is the gradient operator, Denotes the sample distribution Ψ generated from g (·) and the true sample distribution Ψ r (·) Uniform sampling along the straight line between sampling point pairs, Represents random sampling between real data and generated data.

[0159] WGAN-GP retains the advantage of WGAN in using Wasserstein distance instead of KL and JS divergence to solve the gradient vanishing problem in the original GAN, and uses gradient penalty instead of weight clipping in WGAN to restrict Lipschitz, so that it can stably generate more realistic data.

[0160] The invention discloses a width unsupervised domain adaptive two-stage rolling bearing fault diagnosis method under the category imbalance scenario, such as Figure 3 As shown in the figure, the first stage mainly solves the unsupervised domain adaptation problem through width migration, but the classification accuracy will be adversely affected by the imbalance of categories. Therefore, a new sample screening strategy is proposed in the second stage to select reliable samples in the target domain. Then WGAN-GP is used to enhance the data of reliable samples in the target domain and construct a balanced sample set to solve the problem of imbalanced categories. Finally, the remaining samples in the target domain are sent to the width learning system trained with the balanced sample set to achieve the final diagnosis. The specific process is as follows:

[0161] The width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method (algorithm) in a category imbalance scenario proposed in the present invention is the underlying technical core of the present invention, and various products can be derived based on the algorithm.

[0162] Based on the method proposed in the present invention, a width unsupervised domain adaptation two-stage rolling bearing fault diagnosis system in a category imbalance scenario is developed using a programming language. The system has a program module corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario during operation.

[0163] The computer program of the developed system (software) is stored on a computer-readable storage medium, and the computer program is configured to implement the steps of the above-mentioned wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario when called by a processor. That is, the present invention is materialized on a carrier to become a computer program product.

[0164] Various implementations of the systems and techniques described herein can be realized in digital electronic circuit systems, integrated circuit systems, dedicated ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0165] The computer programs (also referred to as programs, software, software applications, or codes) of the present invention include machine instructions for programmable processors, and these computer programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or device (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0166] The beneficial effects of the present invention will be described below in conjunction with specific embodiments and comparative examples.

[0167] Example 1

[0168] The experimental data of this embodiment comes from the CWRU bearing data set

[27] It is mainly composed of a motor, two bearings with different ports, and a load. The experiment selected a SKF6205 deep groove ball bearing with a sampling frequency of 12kHz at the drive end as the experimental object.

[0169] The experiment uses the electrospark machining method to perform different degrees of pitting on different positions of the rolling bearing to simulate different types of faults. The fault types can be divided into inner ring fault (IR), outer ring fault (OR) and rolling element fault (B) according to the position. And each position has 3 sizes of pitting diameters to simulate different degrees of faults. Finally, add 1 normal state (N), a total of 10 categories. Each category is divided into 4 different working conditions (0hp, 1hp, 2hp, 3hp) according to the different speeds of its load. Among them, hp is British horsepower, 1hp = 0.75kW. To facilitate the subsequent experimental description, the fault data is represented by Table 1.

[0170] Table 1 Experimental data representation method

[0171]

[0172]

[0173] Four sample sets with different balance levels, A, B, C, and D, were designed for subsequent experiments. The specific situation is shown in Table 2.

[0174] Table 2 Sample sets with different imbalance levels

[0175]

[0176] Sample set A represents the balanced sample set, and sample set B simulates the current mainstream unbalanced sample set setting method, with an unbalance rate of 1 / 8. However, in actual industry, for bearings with the same fault position, the deeper the fault, the more difficult it is to obtain samples. Therefore, in order to simulate the actual problem more realistically, sample set C is used to simulate mild unbalance conditions, and sample set D is used to simulate severe unbalance conditions. Sample sets are set according to the same unbalance rate for both source domain data and target domain data.

[0177] Sample set A represents the balanced sample set, and sample set B simulates the current mainstream unbalanced sample set setting method, with an unbalance rate of 1 / 8. However, in actual industry, for bearings with the same fault position, the deeper the fault, the more difficult it is to obtain samples. Therefore, in order to simulate the actual problem more realistically, sample set C is used to simulate mild unbalance conditions, and sample set D is used to simulate severe unbalance conditions. Sample sets are set according to the same unbalance rate for both source domain data and target domain data.

[0178] Taking the vibration signal of the rolling bearing with inner ring failure under 0hp and 1hp conditions as an example, the envelope spectrum analysis is performed on it. The results are as follows: Figure 5 , Figure 6 shown.

[0179] The envelope spectrum can reflect the fault frequency characteristics. From the rolling bearing fault frequency calculation formula, it can be obtained that the theoretical value of the 0hp inner ring fault frequency is 162.5614Hz, and the theoretical value of the 1hp inner ring fault frequency is 160.2998Hz. From the envelope spectrum, it can be obtained that the 0hp inner ring fault frequency is 161.1328Hz, and the 1hp inner ring fault frequency is 158.2031Hz. It is close to the theoretical value. Analysis of the two envelope spectra shows that the fault frequencies of bearings with the same fault type under different working conditions are different but similar, which conforms to the definition of different data distributions in the source domain and the target domain in transfer learning, but there is common knowledge. Therefore, it is feasible to apply transfer learning to solve the problem of rolling bearing fault diagnosis under different working conditions.

[0180] This embodiment selects 1024 points as a single sample length and 150 points as a sliding interval to perform sliding sampling, thereby obtaining a time domain sample set. According to the above scheme, data preprocessing is performed, and the number of frequency subbands is selected as 256, and finally the network input sample set is obtained.

[0181] The richness of fault information contained in data under different working conditions varies, so the migration effects presented by using data under different working conditions as source domains also vary. In order to prove the effectiveness of the method of the present invention, all working conditions are traversed and a total of 12 migration tasks are set. The most challenging sample set D is selected for the experiment, and the specific settings are shown in Table 3.

[0182] Table 3 Composition of the datasets used for each task

[0183]

[0184] This example uses the grid search method, and finally sets the number of feature nodes in the width learning network hyperparameters to 12×14, the number of enhancement nodes to 100, and the regularization coefficient to 2. -31 The number of MEDA iterations is set to 10. Since WGAN-GP is compatible with various network architectures, in order to simplify the architecture of the overall method, a simple 4-layer deep neural network (DNN) is used as the network architecture of the generator and discriminator. Figure 7 shown.

[0185] The hardware environment used in the experiment: CPU model is Intel Xeon W-2123; memory is 32GB; GPU model is NVIDIA GeForce GTX3060.

[0186] Width migration method effectiveness verification experiment:

[0187] In order to verify the effectiveness of the width transfer method BLS-MEDA proposed in the first stage, we used BLS without transfer learning, BLS-GFK with only manifold feature transformation but not dynamic distribution alignment, and a mainstream unsupervised depth transfer method CDAN to conduct comparative experiments on 12 transfer tasks. Each task was repeated 10 times and the average value was taken as the final result. The results are shown in Figure 2. Figure 8 shown.

[0188] from Figure 8 It can be seen that BLS without the use of transfer learning methods is affected by variable working conditions and class imbalance, and the classification accuracy is very low. BLS that has only undergone manifold feature transformation, that is, BLS-GFK, does not consider the different importance of marginal distribution and conditional distribution for specific tasks, resulting in limited improvement in classification accuracy. Although CDAN has a higher overall classification accuracy than BLS-MEDA, it can be seen from Table 5 that its average training time is 259.73s, and the data preprocessing step of converting vibration signals into time-frequency graphs is extremely time-consuming. Compared with BLS-MEDA, which takes an average of 6.84s, the training time cost of CDAN is too high. And affected by class imbalance, the classification accuracy of minority classes is not ideal. In order to further analyze the performance of BLS-MEDA, one of the most challenging tasks 7 is selected, and a confusion matrix is ​​drawn for the classification results of the above method. The experimental results are shown in Figure 9-11 shown.

[0189] observe Figure 9-11 It can be seen that in BLS-GFK, all the minority classes of B021 are misclassified, and the performance cannot be further improved through sample screening. In the classification results of CDAN, the classification effect of samples in normal state is good, but in actual industry, the cost of predicting errors in faulty samples is much higher than the cost of predicting errors in normal samples. The minority class classification accuracy of CDAN and BLS-MEDA is only 93.81% and 88.38%, respectively, which still has a lot of room for improvement. Under this condition, BLS-MEDA can quickly obtain pseudo-labels for target domain data, so it is more suitable for performance improvement in the second stage.

[0190] Comparative experiment of different balance levels:

[0191] In order to explore the impact of imbalance on the diagnosis results, BLS-MEDA was used to conduct experiments on 12 migration tasks on sample sets with four imbalance levels: A, B, C, and D. The experiment was repeated 10 times and the average value was taken as the final result. F-Measure was used as the measurement indicator. Compared with the classification accuracy, it is more sensitive to the classification results of minority classes and can better measure the impact of class imbalance on network performance. The experimental results are shown in Figure 2. Fig.12 shown.

[0192] analyze Fig.12 It can be seen that when performing cross-condition transfer learning under the condition of class imbalance, the classification ability of the minority class will be restricted, resulting in a decline in model performance. Comparing sample set B and sample set C, although the total number of samples in the minority class of sample set C is greater than that of sample set B. However, due to the data imbalance within the minority class in C, which is in line with actual production, its performance is more affected. The imbalance of sample set D is more serious, and its performance decline is also the largest. Therefore, using sample set D for subsequent experiments is more in line with actual working conditions and full of challenges.

[0193] Sample screening strategy effectiveness verification experiment:

[0194] In order to explore the impact of sample screening strategy on the results of the migration task, the samples obtained after being sorted in descending order according to RC were sampled at different levels. x The descending sorting strategy was used as a comparison method. Experiments were conducted on 12 migration tasks and the average values ​​were taken for analysis. Fig.13 shown.

[0195] observe Fig.13 It can be seen that when only one sample is sampled for each minority class, there will be no situation where the pseudo label is different from the real label, so it is feasible to use RC as the screening basis. However, if only one sample is used for each class to enhance the data using WGAN-GP, the fault information provided lacks diversity, so the data enhancement effect is not good. As the number of samples in each class increases, the reliability of the pseudo label will decrease. Once a sample with an incorrect label is selected for data enhancement, the accuracy of the migration result will be greatly affected. Therefore, the final number of samples is selected as 5 for subsequent experiments.

[0196] Data enhancement effectiveness verification experiment:

[0197] In order to explore the authenticity of samples generated by WGAN-GP, the generated samples are compared with real samples from multiple aspects.

[0198] First, set the number of training iterations to 1000 and expand each class to 100 samples. Observe the loss of the generator and the discriminator. The results are as follows: Fig.14shown.

[0199] observe Fig.14 It can be seen that before the 200th iteration, the loss curves of the discriminator and the generator fluctuated greatly, and the two were in conflict with each other. After that, the fluctuations of the two curves became smaller and smaller, and gradually reached a balanced state. The results show that WGAN-GP has achieved good training results.

[0200] Secondly, the loss curve can only show the training effect of the network. In order to better judge the quality of sample generation, the frequency spectrum of the generated sample is compared with that of the real sample to observe the similarity between the two. The results are as follows: Fig.15 As shown in Figure 2, it can be seen that the generated samples are highly similar to the real data under the condition of ignoring certain deviations.

[0201] Finally, the Pearson correlation coefficient (PCC) and cosine value (CV) used in the literature

[28] are used as evaluation indicators to quantify the similarity between the generated samples and the real samples. The range of both indicators is [-1, 1]. The closer the result is to 1, the more similar the two distributions are. According to the results in Table 4, the average values ​​of the indicators of the generated samples and the real samples are both above 0.9, which once again verifies that the generated samples are highly similar to the real samples.

[0202] Table 4 PCC and CV of generated samples

[0203]

[0204] Experimental verification of the proposed method

[0205] After data augmentation, a balanced dataset with 100 samples per class is obtained, which is used to train the initialized BLS, and finally the remaining samples in the target domain are sent to the network for testing to obtain the final target domain classification results.

[0206] In order to verify the effectiveness of the proposed method, the proposed method is compared with three mainstream unsupervised domain adaptation methods and the BLS-MEDA method without data enhancement correction. The training time, minority class classification accuracy, and F-Measure are used to better measure the network performance under class imbalance.

[0207] observe Fig.16As shown in Table 5, among the 12 migration tasks, the method proposed in the present invention has achieved the best performance in 9 of them, and its average classification accuracy of minority classes has reached 98.05%, which is at least 3.68% higher than that of the four comparison methods. BLS-MEDA, as a width migration method proposed in this embodiment for the first stage, is affected by the imbalance of categories and the limited feature extraction ability of the width network itself, and the average classification accuracy of minority classes can only reach 91.30%. After the data enhancement correction in the second stage, although the overall training time increased to 112.02s, the accuracy was increased by 6.75%, and the F-Measure value was also greatly improved. At the same time, it also verified the effectiveness of using data enhancement to correct the diagnosis results in the second stage. The remaining three mainstream unsupervised transfer learning methods are affected by data imbalance, and the F-Measure values ​​are reduced to varying degrees compared with the proposed method. From the perspective of overall training time, since the proposed method is mainly based on a width learning network and a simple 4-layer deep network structure, without considering the extremely time-consuming data preprocessing step of converting the vibration signal into a time-frequency graph, the training time is still less than that of the three deep migration methods.

[0208] Table 5 Performance comparison of different methods (CWRU)

[0209]

[0210] In order to more intuitively observe the effectiveness of the proposed method in the cross-condition fault diagnosis problem under class imbalance, taking the fault diagnosis result in Task 7, which is the same as that in Experiment 1, as an example, a confusion matrix is ​​drawn, as shown in Fig.17 shown.

[0211] Depend on Fig.17 It can be seen that among the 1050 target domain unlabeled data, only three types of faults, B021, IR007, and OR007, are misclassified, with a total of 17 samples. Overall, the diagnostic accuracy of most fault types has reached 100%, and the lowest of the few types of fault types that are misclassified is 92%. Experiments show that compared with the width transfer method without data enhancement correction and the mainstream unsupervised transfer learning method, the two-stage fault diagnosis method based on width unsupervised domain adaptation proposed in this invention can effectively solve the fault diagnosis problem of rolling bearings with unlabeled target domain data and imbalanced categories.

[0212] Other dataset validation experiments:

[0213] In order to further verify the effectiveness of the proposed method, the data of Jiangnan University bearings (JNU) at different speeds were selected as the experimental data set.

[29] , conduct cross-operating condition fault diagnosis experiments on rolling bearings with category imbalance.

[0214] The speed of the bearings of Jiangnan University is different under different working conditions. The corresponding bearing speeds of working conditions 0, 1, and 2 are 600rpm / min, 800rpm / min, and 1000rpm / min, respectively. Among them, the data of each working condition contains 4 types of state vibration data: inner ring fault, outer ring fault, rolling element fault, and normal. The number of normal samples is set to 800, and the number of each fault data is set to 100, and the generalization experiment is carried out with an imbalance rate of 1 / 8. The correspondence between the experimental setting migration task and the working condition is shown in Table 6.

[0215] Table 6 Composition of the bearing experimental data set of Jiangnan University

[0216]

[0217] The experiment was conducted according to the migration tasks set in Table 6. The results are as follows: Fig.18 And as shown in Table 7.

[0218] Table 7 Performance comparison of different methods (JNU)

[0219]

[0220] Depend on Fig.18 It can be seen that in all the migration tasks set, the minority class classification accuracy of the proposed method is higher than that of the other four comparison methods. The average classification accuracy of the minority class is also 96.84%, which is at least 2.87% higher than that of other methods. As can be seen from Table 7, the F-Measure value of the proposed method is higher than that of all the comparison methods, which once again verifies the effectiveness of the proposed method in solving the data imbalance problem. From the perspective of training time, the training time of the proposed method is less than that of the three deep migration methods. The reason is that the time consumption of the proposed method is mainly concentrated in the second-stage data enhancement step, and the number of minority classes determines the time required for this step. When the minority classes are fewer, the speed advantage of the wide network as the main model architecture can be fully utilized. After experimental verification, the method proposed in the present invention can effectively solve the fault diagnosis problem of bearings of Jiangnan University where the target domain is unlabeled and class-imbalanced, further proving the effectiveness of the invented method on different data sets.

[0221] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

[0222] The documents cited in this invention include:

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Claims

1. A wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in a class imbalance scenario, characterized in that: The steps include: Step 1: Use rolling bearing time domain data to reduce the data dimension; Step 2: Use the width learning network model to extract features from the data, and use manifold embedding distribution alignment to align features to obtain pseudo labels for target domain data; Step 3: Samples are screened based on uncertainty metrics and cosine similarity between samples, and samples in the target domain are divided into reliable samples and remaining samples. Generative adversarial network WGAN-GP with gradient penalty is introduced to perform data enhancement on the screened reliable samples in the target domain to obtain a balanced sample set. Step 4: Use the balanced sample set as the training set, initialize the width learning network model and train it, and finally input the remaining samples of the target domain into the trained width learning network model to achieve diagnosis.

2. The wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario according to claim 1 is characterized in that: Step 1 includes the following process: Using the rolling bearing time domain data, a time domain sample set with a single sample length of L points is constructed by sliding sampling. Each sample is subjected to fast Fourier transform to obtain a frequency domain sample set, and the number of sampling points is set to 8L during the fast Fourier transform. Each frequency domain sample is then divided into several frequency sub-bands, and the RMS of each frequency sub-band is calculated and used as input data to achieve data dimensionality reduction.

3. The wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario according to claim 1 is characterized in that: The objective function of the width learning network model in step 2 is: Where Y is the actual output, λ is the regularization coefficient, W is the connection weight, and the estimated output of the network is By continuously optimizing the estimated output The error between the actual output and the optimal solution of W is expressed as: W=(λI+A T A) -1 A T Y=A + Y Where I is the unit matrix, A T is the transposed matrix of A, and the pseudo-inverse of A is 4. The wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario according to claim 3 is characterized in that: The feature alignment using manifold embedding distribution alignment described in step 2 includes the following process: Step 21: Manifold feature transformation, specifically: First, PCA is used to obtain the two-domain subspace S s and S t , parameterize the geodesic function φ(t) using the standard Euclidean metric of the Riemannian manifold; let φ(0) = S s ,φ(1)=S t ; Then the formula for calculating the shortest distance function between two points is: φ(t)=S s U1Γ(t)-R s U2Σ(t) In the formula, R s For S s The orthogonal complement of U1, U2, Γ and Σ are given by and After singular value decomposition, we get: Where Γ and Σ are square matrices whose diagonal elements are S s and S t The sine and cosine functions of the main characters between them; Then, integrate all t∈[0,1] on the path so that the geodesic function migrates from φ(0) to φ(1), that is: In the formula, a i and a j Represents the feature samples of the source domain and the target domain; G is a semi-definite matrix, which is expressed as: Where Λ is a diagonal matrix, Λ 1i ,Λ 2i and Λ 3i are diagonal elements, θ i For S s and S t The protagonist of The feature sample set after GFK is expressed as and A s and A t The source domain feature sample set and the target domain feature sample set are extracted by the width learning network feature; Step 22: Dynamic distribution alignment, including the following process: The balance factor μ is used to adaptively adjust the importance of source domain data and target domain data, and adaptively distribute the data. It is expressed as: Where μ∈[0,1] is the balancing factor, c∈{1,…,C} represents the corresponding category, and D f represents the marginal distribution, represents the conditional distribution; Calculate the distribution difference between the two domains, and the adaptive distribution adaptation is expressed as: In the formula, c∈{1,…,C} represents the corresponding category, H represents the reproducing kernel Hilbert space, and E[·] represents the expected function; Measures the distance between different distributions, expressed as: Where, d M and d c A-distance represents the difference in marginal distribution and the difference in conditional distribution of the cth class respectively; Using class conditional distribution approximate To obtain Using source domain data D s The trained BLS is used for the target domain data D t Make predictions and revise the prediction results through iterations; Step 2 and 3: Learning the classifier includes the following process: Construct a learning classifier f based on structural risk minimization: Where the first two terms represent the loss of the classifier f on the source domain, is the adaptive distribution adaptation penalty term, R f (·) is the Laplace regularization term, η, τ and ρ are regularization coefficients; By iteratively adjusting the target domain data label 5. The wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario according to claim 4 is characterized in that: In step 3, the samples are screened based on uncertainty measurement and cosine similarity between samples, and the target domain samples are divided into reliable samples and remaining samples. Specifically, Uncertainty measurement based on edge sampling, measuring the sample confidence R by selecting the difference between the two categories with the largest probability in the model prediction results x ,Right now: In the formula, Indicates that the sample x belongs to the category The probability of and Indicates the most likely category and the second most likely category; Choose to trust R in each minority class x The largest sample has its pseudo label regarded as the true label; Then calculate the cosine similarity between all samples in the category and the feature vector of the sample; Sample x with feature dimension n i and sample x j The cosine similarity is: Define the minority class sample x i The final score RC is: In the formula, Represents the sample x i The predicted categories are the same and R x The largest sample; Finally, each type of samples is arranged in descending order according to the scores, and a fixed number of samples are selected based on experience. Their pseudo labels are regarded as true labels to obtain reliable samples and remaining samples.

6. The wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the category imbalance scenario according to claim 5 is characterized in that: The objective function of the generative adversarial network WGAN-GP with gradient penalty described in step 3 is: In the formula, E[·] represents the expected function, D(·) and G(·) represent the discriminator function and the generator function respectively; z is the input noise data; ||·||2 represents the 2-norm, γ is the gradient penalty term coefficient, is the gradient operator, Denotes the sample distribution Ψ generated from g (·) and the true sample distribution Ψ r (·) Uniform sampling along the straight line between sampling point pairs, Represents random sampling between real data and generated data.

7. A wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis system in a class imbalance scenario, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 6 above, and executes the steps of the width unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in the above-mentioned category imbalance scenario when running.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps in the wide unsupervised domain adaptation two-stage rolling bearing fault diagnosis method in a category imbalance scenario in any one of claims 1 to 6 when called by a processor.

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