A bearing fault diagnosis method integrating neighborhood relations and maintaining alignment with manifold embedding distribution

Abstract

The present invention discloses a bearing fault diagnosis method that integrates neighborhood relationship preservation and manifold embedding distribution alignment, which includes four steps: (1) signal processing and time-frequency statistical feature extraction; (2) domain adaptation feature selection, and a domain adaptation feature evaluation method based on naive Bayes classification accuracy and domain difference; (3) domain adaptation based on neighborhood relationship preservation and manifold embedding distribution alignment, after mapping the source domain and target domain feature data to the Grassmann manifold, the adaptive dynamic distribution alignment is performed, taking into account the category label information and neighborhood relationship preservation, thereby reducing the distribution difference between the training data and the unknown data while improving the separability of the feature data; (4) training and testing the bearing cross-domain fault diagnosis model. The cross-domain fault diagnosis performance of the model constructed by the present invention is significantly better than that of other models. The domain adaptation feature evaluation method combined with naive Bayes classification accuracy and domain difference can significantly improve the accuracy of cross-domain fault diagnosis.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault diagnosis, and in particular to a bearing fault diagnosis method that fuses neighborhood relations and maintains alignment with manifold embedding distribution. Background Art

[0002] In recent years, with the rapid development of artificial intelligence technologies such as data mining, deep learning and transfer learning, more and more researchers at home and abroad have conducted research on bearing fault diagnosis based on artificial intelligence and achieved rich results.

[0003] To address the problem that traditional machine learning methods are unable to adaptively extract fault feature information of bearings under complex and variable working conditions, Zhao Xiaoqiang et al. designed a dual-path parallel multi-scale residual neural network based on residual neural networks that integrates an attention mechanism. This improved the network's ability to adaptively extract fault features and achieved higher fault diagnosis accuracy.

[0004] In response to the difficulties in obtaining real fault data under actual working conditions and the large differences between target and source domain signals, Wen Jiangtao and others faced challenges in cross-working-condition migration recognition of deep models, such as difficulty in feature extraction and classification, and weak model generalization. They introduced unsupervised learning and proposed an improved method based on self-supervised learning combined with adversarial migration. This method creates auxiliary tasks based on the characteristics of the signal itself, learns from a large amount of unlabeled data, and establishes the intrinsic connection between the source and target domain fault categories. The source domain knowledge is then transferred to the target domain through adversarial domain adaptation and joint maximum mean difference. The difference between the two domains is optimized by combining auxiliary tasks, ultimately achieving accurate fault classification in the target domain.

[0005] Pan Xiaobo et al. proposed a cross-domain fault diagnosis method for bearings based on feature transfer learning. By performing feature transfer selection on high-dimensional deep feature sets, a feature subset that is more beneficial for cross-domain fault diagnosis is obtained. Then, balanced distribution adaptation is used to reduce the distribution difference between source domain and target domain samples, thereby improving the cross-domain fault diagnosis performance of the fault diagnosis model.

[0006] In response to the problems of poor generalization ability and low diagnostic accuracy of traditional deep learning models under variable working conditions, Pan Xuejiao et al. proposed a rolling bearing fault diagnosis method based on SK-ResNet and transfer learning. This method integrates the selective kernel network (SKNet) into the residual network (ResNet) to improve the feature extraction ability, and then uses the improved difference alignment loss (DDM) based on multi-kernel maximum mean difference (MK-MMD) and correlation alignment (CORAL) to narrow the feature distribution differences of rolling bearing fault data under variable working conditions, thereby improving the rolling bearing fault diagnosis accuracy and model generalization ability under variable working conditions.

[0007] Hu et al. proposed a new balanced adaptive regularization method by comprehensively considering the relationship between conditional probability distribution and marginal probability distribution. It more effectively reduced the distribution difference while improving the adaptability of the model, thereby improving the accuracy of cross-domain fault diagnosis.

[0008] Although abundant research results in recent years have effectively improved the fault diagnosis performance of bearings under variable operating conditions, the above-mentioned methods and similar fault diagnosis methods still face important challenges when applied to bearing fault diagnosis in actual industrial scenarios: (1) Deep learning-based models often require a large number of training samples with complete fault categories to achieve ideal variable operating condition fault diagnosis performance, but it is difficult to obtain sufficient and complete fault samples of equipment in actual industrial scenarios; (2) The differences in sample distribution caused by variable operating conditions of equipment make it difficult for fault diagnosis models trained with limited samples to achieve ideal fault diagnosis accuracy; (3) The training cost of fault diagnosis models based on deep learning is high and they are easily restricted by scenarios with limited computing resources.

[0009] The main content and steps of the article "Rolling Bearing Fault Diagnosis Based on SK-ResNet and Transfer Learning" published in the journal "Combined Machine Tools and Automated Machining Technology" in October 2024 are as follows:

[0010] Aiming at the problems of poor generalization ability and low diagnostic accuracy of traditional deep learning models under variable working conditions, a rolling bearing fault diagnosis method based on SK-ResNet and transfer learning is proposed.

[0011] First, the collected time domain signal is subjected to fast Fourier transform (FFT) to obtain the frequency domain signal, and then weighted fusion is performed to obtain a new time-frequency domain data set;

[0012] Secondly: Integrate the Selective Kernel Network (SKNet) into the Residual Network (ResNet) to improve feature extraction capabilities;

[0013] Then: the difference alignment loss (DDM) improved by multi-kernel maximum mean difference (MK-MMD) and correlation alignment (CORAL) is used to reduce the distribution difference of rolling bearing fault data features under variable working conditions, and it is applied to multiple modules of the model to further reduce the distribution distance between features.

[0014] Finally: Use the trained model to perform rolling bearing fault diagnosis on the target domain test data, obtain the classification results, and output the fault diagnosis accuracy.

[0015] The technical solution mainly has the following problems:

[0016] (1) Only the Fourier transform is used to process the original bearing vibration signal to obtain the frequency domain signal, and then the time domain signal and the frequency domain signal are weighted and fused to form a new time-frequency domain signal with time domain characteristics and frequency domain characteristics. This processing method of extracting only time domain and frequency domain signals is difficult to extract fault information from the nonlinear and strongly non-stationary bearing vibration signal, which in turn affects the effect of fault feature extraction.

[0017] (2) The improved difference alignment loss (DDM) based on multi-kernel maximum mean difference (MK-MMD) and correlation alignment (CORAL) is used to reduce the difference in the distribution of rolling bearing fault data under variable working conditions. This method does not effectively analyze the extracted features themselves, but only constrains the feature data from the perspective of minimizing the two differences. It ignores the consideration of feature classification performance and easily leads to poor diagnostic results of the fault diagnosis model. Summary of the Invention

[0018] The purpose of the present invention is to overcome the defects and shortcomings of the existing technology, and to provide a bearing fault diagnosis method that integrates neighborhood relationships and maintains alignment with manifold embedding distribution, so as to solve the problems faced in the process of bearing fault diagnosis under variable working conditions, such as insufficient adaptive extraction capabilities of bearing fault features with high separability and domain adaptation; the distribution differences between data caused by variable working conditions still seriously affect the accuracy of fault diagnosis; in the fault diagnosis model combined with transfer learning, it is easy to ignore the improvement of feature classification performance while considering the distribution difference measurement between the source domain and the target domain.

[0019] To achieve the above object, the present invention provides the following technical solutions:

[0020] A bearing fault diagnosis method that integrates neighborhood relations and maintains alignment with manifold embedding distribution includes the following four steps:

[0021] (1) Signal processing and time-frequency statistical feature extraction

[0022] The vibration signals of bearings with known working conditions and bearing vibration signals with unknown working conditions are obtained. Based on the bearing vibration signals with known working conditions, a variety of time-frequency domain statistical feature data are extracted as a labeled source domain feature set. Based on the bearing vibration signals with unknown working conditions, a variety of time-frequency domain statistical feature data are extracted as an unlabeled target domain feature set. The vibration signals of bearings with known working conditions and bearing vibration signals with unknown working conditions are processed using empirical mode decomposition (EMD) to extract intrinsic mode components, calculate time-frequency domain statistical features, and construct an original feature set.

[0023] (2) Domain Adaptation Feature Selection

[0024] Based on the original feature set obtained in step (1), the naive Bayes classification algorithm is used to process each feature data in the source domain to obtain the classification accuracy CA of the feature. The classification accuracy CA is also used as the classification accuracy CA of the corresponding class statistical feature data in the target domain feature set. The classification accuracy CA represents the discriminative ability of each statistical feature data in the source domain feature set and the target domain feature set;

[0025] Then, based on the feature data in the source and target domains under normal conditions, the maximum mean difference and KL divergence of the marginal probability of the features between different domains are calculated to characterize the cross-domain stability of the features.

[0026] Finally, the domain adaptation feature selection index RCD is constructed based on the fault classification accuracy, the maximum mean difference of marginal probability and KL divergence;

[0027] (3) Domain adaptation based on neighborhood relationships to maintain alignment with the manifold embedding distribution

[0028] For the domain adaptation feature selection index obtained in step (2), features are selected from the source domain and the target domain to construct a subset and perform domain adaptation processing; Grassmann manifold subspace learning is performed on the source domain and target domain feature subsets. In the learned manifold subspace, the adaptive dynamic distribution alignment process is performed, taking into account the category label information and the neighborhood relationship between samples, so as to reduce the distribution difference between the source domain and the target domain while improving the separability of the feature data;

[0029] (4) Training and testing of bearing cross-domain fault diagnosis model

[0030] After the adaptive dynamic distribution alignment in step (3), the source domain and target domain feature sets are used for training and testing the cross-domain fault diagnosis model respectively; based on the labeled source domain feature data, the fault pattern recognition classifier is trained under the principle of structural risk minimization to obtain the cross-domain fault diagnosis model of the bearing; then, the unlabeled target domain feature data is input into the trained classifier to predict the category label and obtain the cross-domain fault diagnosis result.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) The model trained by the fault diagnosis framework of the bearing fault diagnosis method proposed in the present invention, which integrates neighborhood relationships and maintains alignment with the manifold embedding distribution, can achieve ideal variable working condition fault diagnosis performance. Based on the actual bearing fault data set, the maximum accuracy of all cross-domain fault diagnosis tasks is not less than 98%, and can reach up to 100%; based on the own bearing fault data, the cross-domain fault diagnosis accuracy can reach up to 95.17%, which is significantly better than other fault diagnosis models constructed based on classic feature transfer learning methods. Therefore, it has the potential to be applied to the identification of bearing fault states of rotating mechanical equipment in industrial scenarios.

[0033] (2) Compared with the fault diagnosis model based on deep learning, the fault diagnosis method proposed in the present invention does not require high computing resources, has low training costs, and is more suitable for actual industrial scene equipment with limited computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flowchart of the present invention. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0036] A bearing fault diagnosis method that integrates neighborhood relations and maintains alignment with manifold embedding distribution includes the following four steps:

[0037] (1) Signal processing and time-frequency statistical feature extraction

[0038] The vibration signals of bearings with known working conditions and bearing vibration signals with unknown working conditions are obtained. Based on the bearing vibration signals with known working conditions, a variety of time-frequency domain statistical feature data are extracted as a labeled source domain feature set. Based on the bearing vibration signals with unknown working conditions, a variety of time-frequency domain statistical feature data are extracted as an unlabeled target domain feature set. The vibration signals of bearings with known working conditions and bearing vibration signals with unknown working conditions are processed using empirical mode decomposition (EMD) to extract intrinsic mode components, calculate time-frequency domain statistical features, and construct an original feature set.

[0039] (2) Domain Adaptation Feature Selection

[0040] Based on the original feature set obtained in step (1), the naive Bayes classification algorithm is used to process each feature data in the source domain to obtain the classification accuracy CA of the feature. The classification accuracy CA is also used as the classification accuracy CA of the corresponding class statistical feature data in the target domain feature set. The classification accuracy CA represents the discriminative ability of each statistical feature data in the source domain feature set and the target domain feature set;

[0041] Then, based on the feature data in the source and target domains under normal conditions, the maximum mean difference and KL divergence of the marginal probability of the features between different domains are calculated to characterize the cross-domain stability of the features.

[0042] Finally, the domain adaptation feature selection index RCD is constructed based on the fault classification accuracy, the maximum mean difference of marginal probability and KL divergence;

[0043] (3) Domain adaptation based on neighborhood relationships to maintain alignment with the manifold embedding distribution

[0044] For the domain adaptation feature selection index obtained in step (2), features are selected from the source domain and the target domain to construct a subset and perform domain adaptation processing; Grassmann manifold subspace learning is performed on the source domain and target domain feature subsets. In the learned manifold subspace, the adaptive dynamic distribution alignment process is performed, taking into account the category label information and the neighborhood relationship between samples, so as to reduce the distribution difference between the source domain and the target domain while improving the separability of the feature data;

[0045] (4) Training and testing of bearing cross-domain fault diagnosis model

[0046] After the adaptive dynamic distribution alignment in step (3), the source domain and target domain feature sets are used for training and testing the cross-domain fault diagnosis model respectively; based on the labeled source domain feature data, the fault pattern recognition classifier is trained under the principle of structural risk minimization to obtain the cross-domain fault diagnosis model of the bearing; then, the unlabeled target domain feature data is input into the trained classifier to predict the category label and obtain the cross-domain fault diagnosis result.

[0047] Furthermore, in step (1), EMD, as a classic time-frequency analysis method, can decompose the signal according to its own time scale characteristics, decomposing the complex original signal into the sum of several complete, almost orthogonal intrinsic mode function components and residual components. Each IMF component corresponds to a vibration mode of a specific signal at a discrete frequency. The decomposed IMF components must meet the following two conditions:

[0048] 1) In the entire IMF data segment, the number of extreme points and the number of zero-crossing points must be equal or differ by no more than one;

[0049] 2) At any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper and lower envelopes are locally symmetrical with respect to the time axis.

[0050] The decomposition steps of the EMD algorithm are as follows:

[0051] Step S11. Find the maximum and minimum points of the original signal x(t), and draw the upper envelope x according to the obtained extreme points. α (t) and the lower envelope x β (t), and find the average value of the upper and lower envelopes to obtain the mean envelope M1(t):

[0052]

[0053] Step S12: Subtract M1(t) from the original signal x(t) to obtain the intermediate signal H1(t).

[0054] H1(t)=x(t)-M1(t) (2)

[0055] Step S13. Determine whether the intermediate signal satisfies the two constraints of the IMF. If so, output it as IMF1. If not, use the intermediate signal H1(t) as the new input signal and repeat steps S11 and S12 until the output intermediate signal H1(t) satisfies the two constraints of the IMF. When H1(t) satisfies the two constraints, H1(t) is output as the first IMF component, denoted as c1(t).

[0056] Step S14. After obtaining c1(t) through step S13, use the original signal x(t) minus c1(t) as the new original signal x1(t), and repeat steps S11-S13 until the residual x is obtained. n (t) is a monotonic function or a constant; thus, the original signal x(t) is decomposed into n IMF components c by the EMD algorithm. i (t) and a residual r(t), we can get the following expression:

[0057]

[0058] Among them, each IMF component c i (t) represents each frequency component in the original signal, and is arranged in order from high frequency to low frequency, reflecting the local characteristics of the original signal; the residual component r(t) represents the average trend of the signal; the intrinsic mode function component c containing each resonance frequency band is obtained based on EMD decomposition i (t), envelope detection can be achieved by Hilbert transform;

[0059]

[0060] Where: dτ is the differential of τ, c i (τ) is the value of the i-th IMF component of the signal x(t) at time τ;

[0061] Envelope signal HE[c i (t)] filters out the frequency components of high-frequency attenuated vibrations and retains the low-frequency components containing fault characteristic information. Therefore, the envelope signal can be spectrally analyzed to extract characteristic information reflecting rolling bearing faults from the IMF component and its envelope spectrum.

[0062] Time-frequency domain statistical feature extraction:

[0063] Each vibration signal sample is decomposed using EMD to obtain different IMF components. For example, the first four IMF components obtained by EMD processing are used for statistical feature extraction. The four Hilbert Envelope Spectra (HES) and one Hilbert Marginal Spectrum (HMS) corresponding to these fourth-order IMF components are calculated. Based on these four IMF components, four HESs, and one HMS, the 18 statistical parameters shown in Table 1 are calculated, resulting in a total of 162 statistical features, which constitute the original time-frequency statistical feature set for subsequent processing.

[0064] Table 1-18 statistical parameters

[0065] Serial number name Serial number name 1 Extremely poor 10 Form Factor 2 mean 11 Skewness 3 Standard deviation 12 Power spectral entropy 4 Kurtosis 13 Singular spectral entropy 5 energy 14 Approximate entropy 6 Energy entropy 15 Sample entropy 7 Kurtosis 16 Fuzzy entropy 8 Crest Factor 17 Permutation Entropy 9 Pulse Factor 18 Envelope entropy

[0066] Furthermore, in step (2) of domain adaptation feature selection, although the time-frequency analysis method can extract fault feature information from non-stationary and nonlinear fault vibration signals, it is also easy to introduce a large amount of redundant and interfering information. Therefore, in order to improve the effect of distribution adaptation between feature data in different domains and the accuracy of fault pattern recognition, this application proposes a new domain adaptation feature evaluation method based on naive Bayes classification accuracy and inter-domain differences, and selects features with good feature discrimination ability and domain invariance for domain adaptation processing.

[0067] This new domain adaptation feature evaluation method DFERD based on naive Bayes classification accuracy and inter-domain difference mainly includes two aspects: discriminant performance evaluation based on feature classification accuracy and inter-domain difference evaluation based on multiple distance indicators.

[0068] (1) Evaluation of discriminant performance based on feature classification accuracy

[0069] The Naive Bayes (NB) classification algorithm is a classification method based on the Bayesian theorem. Based on training samples, it applies the Bayesian formula to predict the category of the test data. Its main idea is to link the prior and posterior probabilities of an event and use the prior information to predict the posterior probability. This paper uses the Naive Bayes classification algorithm to classify the feature data in the source domain, and uses the classification accuracy to characterize the discriminative performance of each feature.

[0070] In the DFERD method, the naive Bayesian classification algorithm is first used to process the feature data in the source domain to obtain the classification accuracy (CA) of the feature. Given a source domain feature set containing D feature samples, Among them, the dth feature The expression is as follows:

[0071]

[0072] Where, is the nth feature sample of the kth fault category, K is the number of fault categories in the source domain feature data, and N is the total number of feature samples; the naive Bayesian classification algorithm is used to obtain the CA of D features in the source domain, forming a feature importance score sequence S IS as follows:

[0073] S IS ={CA(1),CA(2),…,CA(D)} (6)

[0074] When the CA value of a feature is larger, the discriminant performance of the feature is better and the feature is more suitable for fault classification.

[0075] (2) Inter-domain difference evaluation based on multiple distance indicators

[0076] To effectively quantify the distribution differences between features in different domains, this paper uses the maximum mean difference and Kullback-Leibler (KL) divergence to measure the distribution differences between data. Based on the feature data of the bearing in the normal state in the source and target domains, the MMD of the marginal probability distribution between the two is calculated. Therefore, the MMD value sequence of D types of feature data between the source and target domains can be obtained:

[0077] S MMD ={M(1),M(2),…,M(D)} (7)

[0078] KL divergence is often used in probability theory and information theory to describe the distribution difference between probability distributions. Given the marginal probability distribution of the source domain and the target domain is P S and P T , then P S and P T The KL divergence between is defined as:

[0079]

[0080] In the formula, p(x i ) is the target distribution; q(x i ) is the matching distribution; x i is a discrete random variable; L is the length of the probability distribution. Similarly, the feature data of the bearing in the normal state in the source and target domains are used to calculate the KL divergence of the marginal probability distribution between the two. Therefore, the KL divergence value sequence of D types of feature data between the source and target domains can be obtained:

[0081] S KLD ={D KL (1),D KL (2),…,D KL(D)} (9)

[0082] (3) Construction of domain adaptation feature selection indicators

[0083] Based on the discriminative performance evaluation of feature classification accuracy and the inter-domain difference evaluation based on multiple distance indicators, a new domain adaptation feature selection indicator, the Ratio of Classification Accuracy and Differences between Domains (RCD), is constructed. Its expression is as follows:

[0084]

[0085] Where CA(d) represents the classification accuracy of the d-th feature, M(d) represents the MMD value of the d-th feature data between the source domain and the target domain, and D KL (d) represents the KL divergence between the marginal probability distributions of the d-th feature data in the source domain and the target domain.

[0086] For D features, based on formula (10), the corresponding RCD sequence can be obtained as follows:

[0087] S R ={R(1),R(2),…,R(D)} (11)

[0088] It can be seen that when the RCD value of a feature is larger, it indicates that the feature has both discriminative performance and cross-domain invariance, which is more beneficial to domain adaptation processing and fault pattern recognition and classification. Therefore, the RCD sequence of each statistical feature is calculated and sorted in descending order. The top-ranked features are selected to construct a new domain adaptation feature set for subsequent domain adaptation processing and cross-domain fault diagnosis model training.

[0089] Furthermore, in step (3), in order to solve the problems of traditional feature-based transfer learning methods that are prone to feature distortion in the original feature space, insufficient consideration of data distribution differences between different domains, and insufficient consideration of source domain sample category information and neighborhood relations, this paper proposes a new transfer learning method based on domain adaptation with neighborhood relation preservation and manifold embedding distribution alignment. This method integrates manifold subspace learning, adaptive dynamic distribution alignment, and neighborhood relation preservation between class data, and mainly includes three steps:

[0090] Step S31: Grassmann manifold feature learning;

[0091] Step S32: adaptive dynamic distribution alignment;

[0092] Step S33: Cross-domain classifier learning under the principle of structural risk minimization.

[0093] Suppose a method to transform fault diagnosis knowledge from labeled source domain samples D S ={X S ,Y S} and unlabeled target domain normal state samples Transfer learning to unlabeled target domain samples D T ={X T}domain adaptation task;

[0094] Among them D S and D T The data were collected under specific working conditions and different working conditions respectively. represents a dataset containing m samples, is the kth sample k=1,2,…m; X S The corresponding category label set is is the kth sample label; represents a sample set containing n samples, is the jth sample (j=1,2,…n); D S and D T The marginal probability distribution and conditional probability distribution of are different, that is, P(X S )≠P(X T ) and Q(Y S |X S )≠Q(Y T |X T ).

[0095] Grassmann manifold feature learning in step S31

[0096] Manifold learning is a classic data dimensionality reduction method that aims to explore the structural characteristics of low-dimensional data embedded in a high-dimensional observation space. Unlike traditional dimensionality reduction analysis methods, manifold learning assumes that the existing data is uniformly sampled in a high-dimensional Euclidean space and has an underlying low-dimensional manifold structure. Manifold learning discovers underlying patterns in the data in the high-dimensional observation space by reconstructing the manifold structure in the high-dimensional sample data. Unsupervised manifold learning methods are widely used in mechanical fault diagnosis, and results have shown that manifold learning can effectively capture the inherent manifold characteristics associated with mechanical fault information.

[0097] In the original Euclidean space, if we directly S ={X S ,Y S} and target domain D T ={X T} Perform data migration, X SIt will cause data distortion. The literature Wang, J., Feng, W., Chen, Y., Yu, H., & Yu, PS (2018). Visual domain adaptation with manifold embedded distribution alignment. In ACM Multimedia (pp. 402-410) proposed that feature distortion refers to the deformation or distortion of the data representation in the feature space. It is usually difficult to overcome the problem of feature distortion by aligning the distribution in the original feature space. s and D t The features in are mapped into the Grassmann manifold space respectively. The shortest path between two points φ0 and φ1 in the manifold space should be composed of geodesic flow {Φ(p):0≤p≤1}.

[0098] The manifold characteristic u can be expressed as u = g(x) = Φ(p) T x represents; where g(x) represents the manifold transformation result of the original feature data x, g represents the manifold feature learning function, Φ(p) T x represents the product of the transpose of the geodesic flow and the original feature data x.

[0099] Calculate the original Euclidean space eigenvector x i and x j Projection v on Φ(p) i , v j , use v i and v j The inner product of defines the geodesic flow kernel function G:

[0100]

[0101] Based on formula (12), where dt is the differential with respect to t, the original feature data can be projected into the subspace of the Grassmann manifold space.

[0102] In step S32, adaptive dynamic distribution alignment

[0103] (1) Marginal probability distribution alignment

[0104] Given two feature datasets Z S and Z T , which represent the source domain and target domain features on G(d), respectively, and can align the two marginal probability distributions P(Z S ) and P(Z T ). P(Z S ) and P(Z T ) is defined as:

[0105]

[0106] Where H is the reproducing kernel Hilbert space (RKHS), n S and n T Z S and Z T , tr(·) represents the trace of the matrix, and the matrix K is defined as follows:

[0107]

[0108] Among them, K S,S ,K S,T and K T,T Z S , cross-domain, Z T The kernel matrix in . The matrix L0 is defined as follows:

[0109]

[0110] K can be decomposed into an empirical kernel map using the matrix Features can be mapped to a low-dimensional space. The kernel matrix K can be calculated as follows:

[0111]

[0112] Where W is the transformation matrix, W T is the transpose of the W matrix. P(Z S ) and P(Z T ) can be further expressed as:

[0113] MMD 2 (P S ,P T )=tr(W T KL0KW) (17)

[0114] The optimization goal of edge distribution adaptation is to obtain an optimal transformation matrix so that after transformation P(Z S ) and P(Z T ) reaches its minimum value.

[0115] (2) Conditional Probability Distribution Alignment

[0116] In order to improve the effect of domain adaptation, it is also necessary to consider minimizing the conditional probability distribution Q S (Y S |Z S ) and Q T (Y T |Z TSince the target domain has no label information, the conditional probability distribution Q cannot be directly obtained. T (Y T |Z T ). To this end, the base classifier trained with labeled source domain data can be used to predict the target domain data category and obtain the category pseudo label. S (Y S |Z S ) and Q T (Y T |Z T ) is too complicated to calculate directly, so we use Q S (Z S |Y S =c) and Q T (Z T |Y T =c) to solve, c∈[1,2,,C], representing each class in the label set (C is the number of categories of feature data). S (Z S |Y S =c) and Q T (Z T |Y T =c) is defined as:

[0117]

[0118] Where: Φ(z i ) indicates zi Perform nonlinear mapping, which can make the conditional probability distribution Q S (Y S |Z S ) and Q T (Y T |Z T ) have the smallest distribution difference.

[0119] and are the source and target data samples belonging to category c, respectively. Represents the target data z i Pseudo labels. and are the number of source and target data samples belonging to class c respectively. The MMD matrix L c It can be calculated by the following expression:

[0120]

[0121] By minimizing formula (18), in the new representation and Under this condition, the conditional probability distribution between the two is narrowed.

[0122] (3) Adaptive dynamic distribution alignment

[0123] In order to dynamically adapt the conditional probability distribution and marginal probability distribution between data in different domains, the adaptive factor α is introduced. By combining the conditional probability distribution and the conditional probability distribution difference expression, the adaptive dynamic distribution difference expression is constructed as follows:

[0124]

[0125] Where α∈[0,1] is the adaptive factor. When α→1, the data similarity between the source and target domains is high, so the marginal probability distribution alignment is given a higher weight. When α→0, the data distribution difference between the source and target domains is large, in which case the conditional probability distribution alignment is given a higher weight. To dynamically solve the adaptive factor, the A-distance metric method is used to solve the optimal adaptive factor α.

[0126] (4) Maintaining neighborhood relationships

[0127] In order to consider the influence of the class information and neighborhood relationship of feature data in the process of adaptive dynamic distribution alignment, a new local neighborhood discriminant matrix L is designed based on the principle of local Fisher discriminant analysis. N , integrated into the adaptive dynamic distribution alignment goal, L N The expression is as follows:

[0128]

[0129] Among them, S w and They are the intra-class scatter matrix and the inter-class scatter matrix, respectively, and their expressions are as follows:

[0130]

[0131] in,

[0132]

[0133] In formulas (24) and (25), n, l, n l and C are the number of feature samples, feature sample categories, the number of samples in the first category and the total number of sample categories, respectively. and p ij Construct the weight matrix. ij for and p ij The adjustment parameter ranges from 0 to 1. i and z j The closer the distance, the ijThe larger the value, the greater the inter-class divergence and the greater the boundary distance between samples of different classes. i and z j The farther the distance, the greater the ij The smaller the , the smaller the intra-class divergence is, and the more cohesive the samples of the same class are. Finally, the separability between samples of different classes is improved. Based on equations (17), (18), (20) and (21), the adaptive dynamic distribution difference expression with neighborhood relationship preservation is constructed:

[0134]

[0135] Where α is the optimal adaptive factor obtained by using the A-distance measurement method, and λ is the adjustment parameter, which ranges from 0 to 1.

[0136] Step S33: cross-domain classifier learning under the principle of structural risk minimization;

[0137] After Grassmann manifold feature learning and adaptive dynamic distribution alignment, based on the principle of structural risk minimization, Z S , And mean square error to learn the domain invariant classifier f, which is expressed as follows:

[0138]

[0139] Where H K is the reproducing kernel Hilbert space, η and λ f are regularization parameters. Based on the fact that the regularization functional in high or even infinite dimensions can be represented by the finite-dimensional space spanned by data samples, the classifier f can be expanded as follows:

[0140]

[0141] in Therefore, formula (27) can be further expressed as:

[0142]

[0143] In the formula, ||·|| F is the Frobenious norm, is the kernel matrix, Is a diagonal domain indicator matrix, if i∈Z S , then A ii =1, otherwise A ii = 0. The expression of matrix L is as follows:

[0144] L=(1-α)L c +αL0+μL N (30)

[0145] yes ZS and ZT The category label matrix of . The solution to the optimization problem of formula (29) can be transformed into the following expression:

[0146] W * =((A+λL)K+ηI) -1 AY T (31)

[0147] To verify the effectiveness and advantages of the proposed method, cross-domain fault diagnosis tasks under different working conditions were set based on the bearing fault dataset of Case Western Reserve University, and comparative experiments were carried out. The results show that: (1) The cross-domain fault diagnosis performance of the BFD-NRMMEDA model constructed based on the proposed method is significantly better than that of other models. Based on the fault data of Case Western Reserve University, the maximum accuracy of all cross-domain fault diagnosis tasks is not less than 98%, and can reach 100% at most; based on the own bearing fault data, the cross-domain fault diagnosis accuracy can reach up to 95.17%, which is significantly better than the fault diagnosis model based on classic feature transfer learning; (2) The domain adaptation method based on transfer learning, combined with the domain adaptation feature selection method DFERD proposed in this paper, can significantly improve the accuracy of cross-domain fault diagnosis.

[0148] Although this specification is described according to implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0149] Therefore, the above description is only a preferred embodiment of the present application and is not intended to limit the scope of implementation of the present application; that is, all equivalent modifications made according to the scope of the claims of the present application are within the scope of protection of the claims of the present application.

Claims

1. A bearing fault diagnosis method that integrates neighborhood relations and maintains alignment with manifold embedding distribution, characterized in that: It includes the following four steps: (1) Signal processing and time-frequency statistical feature extraction The vibration signals of bearings with known working conditions and bearing vibration signals with unknown working conditions are obtained. Based on the bearing vibration signals with known working conditions, a variety of time-frequency domain statistical feature data are extracted as a labeled source domain feature set. Based on the bearing vibration signals with unknown working conditions, a variety of time-frequency domain statistical feature data are extracted as an unlabeled target domain feature set. The vibration signals of bearings with known working conditions and bearing vibration signals with unknown working conditions are processed using empirical mode decomposition (EMD) to extract intrinsic mode components, calculate time-frequency domain statistical features, and construct an original feature set. (2) Domain Adaptation Feature Selection Based on the original feature set obtained in step (1), the naive Bayes classification algorithm is used to process each feature data in the source domain to obtain the classification accuracy CA of the feature. The classification accuracy CA is also used as the classification accuracy CA of the corresponding class statistical feature data in the target domain feature set. The classification accuracy CA represents the discriminative ability of each statistical feature data in the source domain feature set and the target domain feature set; Then, based on the feature data in the source and target domains under normal conditions, the maximum mean difference and KL divergence of the marginal probability of the features between different domains are calculated to characterize the cross-domain stability of the features. Finally, the domain adaptation feature selection index RCD is constructed based on the fault classification accuracy, the maximum mean difference of marginal probability and KL divergence; (3) Domain adaptation based on neighborhood relationships to maintain alignment with the manifold embedding distribution For the domain adaptation feature selection index obtained in step (2), features are selected from the source domain and the target domain to construct a subset and perform domain adaptation processing; The Grassmann manifold subspace is learned for the feature subsets of the source and target domains. In the learned manifold subspace, the adaptive dynamic distribution alignment process is performed, taking into account the category label information and the neighborhood relationship between samples, thereby reducing the distribution difference between the source and target domains while improving the separability of the feature data. (4) Training and testing of bearing cross-domain fault diagnosis model After the adaptive dynamic distribution alignment in step (3), the source domain and target domain feature sets are used for training and testing the cross-domain fault diagnosis model respectively; based on the labeled source domain feature data, the fault pattern recognition classifier is trained under the principle of structural risk minimization to obtain the cross-domain fault diagnosis model of the bearing; then, the unlabeled target domain feature data is input into the trained classifier to predict the category label and obtain the cross-domain fault diagnosis result.

2. The bearing fault diagnosis method according to claim 1, wherein: In step (1), EMD, as a time-frequency analysis method, can decompose the signal according to its own time scale characteristics, and decompose the complex original signal into the sum of several complete and almost orthogonal intrinsic mode function components and residual components. Each IMF component corresponds to a vibration mode of a specific signal of a discrete frequency. After decomposing the intrinsic mode function components containing each resonant frequency band based on the EMD algorithm, envelope detection is implemented through Hilbert transform; the envelope signal filters the frequency components of high-frequency attenuated vibration and retains the low-frequency components containing fault characteristic information. The envelope signal is subjected to spectral analysis, and the characteristic information reflecting the rolling bearing fault is extracted from the IMF component and its envelope spectrum, respectively, to form the original time-frequency statistical feature set for subsequent processing.

3. The bearing fault diagnosis method according to claim 1, wherein: In step (2), the naive Bayesian classification algorithm is used to process the feature data in the source domain to obtain the classification accuracy CA of the feature. Given a source domain feature set containing D feature samples, Among them, the dth feature The expression is as follows: Where, is the nth feature sample of the kth fault category, K is the number of fault categories in the source domain feature data, and N is the total number of feature samples; the naive Bayesian classification algorithm is used to obtain the CA of D features in the source domain, forming a feature importance score sequence S IS as follows: S IS ={CA(1),CA(2),…,CA(P)} When the CA value of a feature is larger, the discriminant performance of the feature is better and the feature is more suitable for fault classification.

4. The bearing fault diagnosis method according to claim 3, wherein the fusion neighborhood relationship is kept aligned with the manifold embedding distribution, The inter-domain difference evaluation based on multiple distance indicators in step (2) is as follows: The maximum mean difference and (KL) divergence are used to measure the distribution difference between data. Based on the feature data of the bearing in the normal state in the source domain and the target domain, the MMD of the marginal probability distribution between the two is calculated. The MMD value sequence of D types of feature data between the source domain and the target domain can be obtained: S MMD ={M(1),M(2),…,M(D)} KL divergence is often used in probability theory and information theory to describe the distribution difference between probability distributions. Given the marginal probability distribution of the source domain and the target domain is P S and P T , then P S and P T The KL divergence between is defined as: Where, p(xi) is the target distribution; q(xi) is the matching distribution; xi is a discrete random variable; L is the length of the probability distribution; the characteristic data of the bearing in the normal state in the source domain and the target domain are also used to calculate the KL divergence of the marginal probability distribution between the two. Therefore, the KL divergence value sequence of D types of characteristic data between the source domain and the target domain can be obtained: S KLD ={D KL (1),D KL (2),…,D KL (D)}。 5. The bearing fault diagnosis method according to claim 4, wherein the fusion neighborhood relationship is kept aligned with the manifold embedding distribution, Based on the above-mentioned discriminative performance evaluation of feature classification accuracy and the inter-domain difference evaluation based on multiple distance indicators, a new domain adaptation feature selection indicator, the ratio of feature classification accuracy to inter-domain difference (RCD), is constructed. Its expression is as follows: For D features, the corresponding RCD sequence can be obtained as follows: S R ={R(1),R(2),…,R(D)}。 6. The bearing fault diagnosis method according to claim 1, wherein the fusion neighborhood relationship is kept aligned with the manifold embedding distribution, When performing adaptive dynamic distribution alignment and maintaining the neighborhood relationship between class data in step (3), it mainly includes three steps: Step S31: Grassmann manifold feature learning; Step S32: adaptive dynamic distribution alignment; Step S33: Cross-domain classifier learning under the principle of structural risk minimization.

7. The bearing fault diagnosis method according to claim 6, wherein the fusion neighborhood relationship is kept aligned with the manifold embedding distribution, Suppose a method to transform fault diagnosis knowledge from labeled source domain samples D S ={X S ,Y S } and unlabeled target domain normal state samples Transfer learning to unlabeled target domain samples D T ={X T }domain adaptation task; Among them D S and D T The data were collected under specific working conditions and different working conditions respectively. represents a dataset containing m samples, is the kth sample k=1,2,…m; X S The corresponding category label set is is the kth sample label; represents a sample set containing n samples, is the jth sample (j=1,2,…n); D S and D T The marginal probability distribution and conditional probability distribution of are different, that is, P(X S )≠P(X T ) and Q(Y S |X S )≠Q(Y T |X T ); Manifold learning can effectively capture the inherent manifold features related to mechanical fault information; In the original Euclidean space, if we directly S ={X S ,Y S } and target domain D T ={X T } Perform data migration, X S Will cause data distortion; D s and D t The features in are mapped into the Grassmann manifold space respectively; The shortest path between two points φ0 and φ1 in the manifold space should be composed of a geodesic flow {Φ(p):0≤p≤1}; The manifold characteristic u can be expressed as u = g(x) = Φ(p) T x indicates; Calculate the original Euclidean space eigenvector x i and x j Projection v on Φ(p) i , v j , use v i and v j The inner product of defines the geodesic flow kernel function G: Based on the above formula, the original feature data can be projected into the subspace of the Grassmann manifold space.

8. The bearing fault diagnosis method according to claim 7, wherein the fusion neighborhood relationship is kept aligned with the manifold embedding distribution, Step S32 includes edge probability distribution alignment and conditional probability distribution alignment. In order to achieve dynamic adaptation of conditional probability distribution and edge probability distribution between different domain data, an adaptive factor is introduced, and the conditional probability distribution and conditional probability distribution difference are combined to construct an adaptive dynamic distribution difference.

9. The bearing fault diagnosis method according to claim 8, wherein the fusion neighborhood relationship is kept aligned with the manifold embedding distribution, After Grassmann manifold feature learning and adaptive dynamic distribution alignment, based on the principle of structural risk minimization, the feature dataset of the source domain, the adaptive dynamic distribution difference with neighborhood relationship preservation and the mean squared error are utilized to learn a domain-invariant classifier.

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