Rolling bearing fault diagnosis method based on complex manifold embedding learning

Abstract

The present invention discloses a rolling bearing fault diagnosis method based on complex manifold embedding learning, which solves the problem that traditional data-driven fault diagnosis methods cannot fully reveal the complex high-order relationships between fault samples, thereby effectively improving the accuracy of fault diagnosis. The implementation process is as follows: (1) extracting the time-frequency domain features of the original fault vibration signal and constructing a high-dimensional feature fault set; (2) based on hypergraph theory, using the supervision information of the sample and the intra-class and inter-class neighbor relationships, an intra-class hypergraph and an inter-class hypergraph are proposed, and a manifold tangent structure graph is constructed using a sparse affine tangent structure combination. After constructing the complex manifold embedding model, the optimized projection direction of the model is obtained through an iterative solution method, thereby obtaining low-dimensional fault features of the high-dimensional fault data; (3) the low-dimensional fault features are input into a classifier for fault identification, thereby obtaining the final fault diagnosis result. Experimental results show that the method of the present invention is an effective fault diagnosis method.

Description

Technical Field

[0001] The invention relates to a rolling bearing fault diagnosis method based on complex manifold embedding learning, which belongs to the field of pattern recognition and fault diagnosis. Background Art

[0002] Rolling bearings are widely used in industrial production equipment and play a vital role in manufacturing. They are one of the most important components in industrial equipment. The working environment of rolling bearings is relatively complex, and they are often faced with working conditions such as high temperature, high speed, and high load. Complex working conditions lead to frequent rolling bearing failures. If the faults are not detected in time, the damaged rolling bearing components will directly affect the performance of the equipment. To avoid huge casualties and property losses, a series of data-driven bearing health monitoring methods have been developed. In these methods, fault types are usually identified by extracting time domain features, frequency domain features, or time-frequency features. However, the high-dimensional multi-domain complex features make fault identification very difficult.

[0003] In recent years, rolling element bearing fault diagnosis methods based on manifold embedding have been extensively studied and widely applied in the field of fault diagnosis. Manifold embedding methods can effectively reveal the inherent geometric structure of data, mapping the high-dimensional nonlinear data of the original samples into a low-dimensional space and extracting feature information from the low-dimensional space. Traditional graph embedding algorithms include isometric mapping, locally linear embedding, locality-preserving projection, and neighborhood-preserving embedding. Isometric mapping uses geodesic distances to solve the adjacency graph between sample points and employs multi-dimensional scaling (MDS) to solve the projected matrix. As a global algorithm, isometric mapping requires calculating geodesic distances between all sample points in the dataset, which is computationally complex. Locally linear embedding uses the K nearest neighbors of a sample to obtain linear relationships between data points. When projecting high-dimensional space data into a low-dimensional space, the linear relationships between data points within the neighborhood are preserved. Locality-preserving projection defines a similarity matrix based on the neighborhood relationships between fault samples, preserving the geometric structure of the samples before and after the mapping. Neighborhood-preserving embedding uses the neighborhood data of each point to construct a nearest neighbor optimization function, and then solves the optimization function with the help of the least squares problem to obtain the projection matrix. The main purpose of the above-mentioned related graph embedding methods is to preserve the local neighborhood structure of fault data. They have achieved good diagnostic results in specific practical environments. However, the rolling bearing fault diagnosis method based on a single graph embedding structure cannot fully utilize the high-order relationships between multiple fault samples, which greatly reduces the accuracy of fault diagnosis. In recent years, in order to capture richer fault structure information, scholars have proposed many rolling bearing fault diagnosis methods that consider both global and local information of fault data, such as global local preserving projection, elasticity preserving projection, and Fisher discriminant global local preserving projection. Compared with the single graph embedding rolling bearing fault diagnosis method that only considers the global or local information, it can improve the accuracy of rolling bearing fault diagnosis to a certain extent.

[0004] All of the aforementioned rolling bearing fault diagnosis methods utilize simple graph structures to describe the geometric relationships between rolling bearing fault data. However, these graph structures are unable to effectively extract fault characteristic information when diagnosing multiple faults under complex operating conditions. Furthermore, the characteristic information of rolling bearing data samples is generally described using radial information. However, radial information alone cannot fully reveal the inherent structure of the high-dimensional manifold, making it difficult to achieve the complementarity of multi-angle information, which reduces the accuracy of rolling bearing fault diagnosis. Therefore, a more effective rolling bearing fault diagnosis method is urgently needed in practical applications. Summary of the Invention

[0005] This paper discloses a rolling bearing fault diagnosis method based on complex manifold embedding learning to solve the problem that traditional fault diagnosis algorithms cannot fully reveal complex high-order relationships and retain rich fault characteristics. The specific method steps are as follows:

[0006] 1. Collect the operating data of rolling bearing faults through sensors, extract relevant statistical features of multiple rolling bearing fault data from the perspectives of time domain, frequency domain and time-frequency domain, and construct a high-dimensional feature data set X = [x1, x2, ..., x n ]∈R M ×n , where N is the number of samples and M is the sample dimension; divide the fault data into training set X according to the proportion train and the test set X test .

[0007] 2. By constructing and optimizing a complex manifold embedding learning model, we can obtain a low-dimensional representation of high-dimensional fault features. The specific implementation is as follows:

[0008] (2a) Construct intra-class hypergraph, inter-class hypergraph and manifold tangent graph, and further give the objective functions corresponding to the three different graph structures. The specific implementation process is as follows:

[0009] ① Intra-class hypergraph G hw Defined as: G hw ={V hw ,E hw ,W hw}, where V hw is the vertex set of the intra-class hypergraph, E hw is the hyperedge set, W hw is the weight matrix. The objective function of the intra-class hypergraph is:

[0010]

[0011] in,(·) -1 Indicates the inverse operation, L hw =D hvw -H hw W hw (D hew ) -1 (H hw ) T is the intra-class hypergraph Laplacian matrix.

[0012] D hvw is the degree matrix of the vertices within the class, D hew is the degree matrix of the intra-class hyperedge, which are defined as:

[0013]

[0014] H hwis the intra-class point-edge relationship matrix, defined as:

[0015]

[0016] W hw is the weight matrix of the intra-class hyperedge, defined as:

[0017]

[0018] ②Inter-class hypergraph G hb Defined as: G hb ={V hb ,E hb ,W hb}, where V hb is the vertex set of the inter-class hypergraph, E hb is the hyperedge set, W hb is the weight matrix. The objective function of the inter-class hypergraph is:

[0019]

[0020] Among them, L hb =D hvb -H hb W hb (D heb ) -1 (H hb ) T is the inter-class hypergraph Laplacian matrix. hvb is the degree matrix of the inter-class vertices, D heb is the degree matrix of the inter-class hyperedge, which is defined as:

[0021]

[0022] H hb is the point-edge relationship matrix between classes, defined as:

[0023]

[0024] W hb is the weight matrix of the inter-class hyperedge, defined as:

[0025]

[0026] ③The manifold tangent graph is defined as: G t ={V tl ,W tl},in is the tangent vector vertex set of the original fault sample, is the similarity weight between vertices. The tangential structure f(x i ) c Defined as:

[0027]

[0028] Among them, l(x i ) is x i Tag information, Represents x i k nearest neighbors of s ij is x i and the affine coefficients of the k nearest neighbors, and In the tangential structure f(x i ) c In the equation, the affine coefficient s ij The solution can be performed based on the idea of ​​sparse representation. According to sparse representation, the tangential structure can be adaptively expressed through a constraint. And in solving s ij A sparse weighted norm representation model is used. The weighted norm can obtain a more accurate tangential structure by applying different weights to each neighbor vector. Therefore, the optimization function of the tangential graph is expressed as follows:

[0029]

[0030] Where Λ=diag(d1,d2,…,d n ) is a diagonal matrix, and the diagonal line contains the weight information between the sample and its neighbors. i =[s ij ] j is the sparse coefficient of the tangent vector, reflecting the similarity relationship between the two tangent vectors. i is the normalized tangent vector structure representation of the sample.

[0031] In order to further balance the selected neighbor samples, the local sparse coefficients are obtained by using local samples for construction. Therefore, the optimization function of the manifold tangent graph is as follows:

[0032]

[0033] Among them, the local normalized tangential structure and weight coefficient Λ l It is expressed as follows:

[0034]

[0035] The objective function of manifold tangent structure graph embedding is expressed as follows:

[0036]

[0037] in, L tl =D tl -W tlis the manifold tangent graph Laplace matrix, is the diagonal matrix. tl is the edge weight information of the manifold tangent graph, which is defined as follows:

[0038]

[0039] (2b) Constructing a unified target model for complex manifold embedding learning:

[0040]

[0041] sA T (βXL hb X T +QL tl Q T )A=I

[0042] This objective model unifies the objective functions of three different structures, where β represents the balance parameter used to control the relative weights of intra-class hypergraph structure information and inter-class structure information;

[0043] (2c) Iteratively solve the relevant projection direction of the complex manifold embedding learning target model:

[0044] According to the Lagrange multiplier method, the following equation can be obtained:

[0045]

[0046] Where λ is the Lagrange multiplier.

[0047] Taking the partial derivative of L(A,λ) with respect to A yields:

[0048]

[0049] make Replace λ(βXL in Eq. (37) hb X T +QL tl Q T ) to the right side of the new equation and multiply the left side of the new equation by (βXK hb X T +QL tl Q T ) -1 , we can get the following generalized characteristic equation:

[0050] (βXL hb X T +QL tl Q T ) -1 XL hw X T A=λA

[0051] Among them, λ is the eigenvalue and A is its corresponding eigenvector.

[0052] (2d) Through Y = A T X obtains the low-dimensional representation Y of high-dimensional features train and Y test ;

[0053] 3. Use the support vector machine classifier to classify the low-dimensional representation of high-dimensional features to obtain the classification results of fault data.

[0054] The present invention has the following beneficial effects: Based on hypergraph theory, it utilizes sample supervision information and intra-class and inter-class neighbor relationships to propose intra-class and inter-class hypergraphs. These hypergraph structures can reveal more complex high-order relationships between samples and preserve richer fault characteristics. By establishing a tangent graph to learn tangential information within the manifold, it overcomes the problem that single radial information cannot fully reveal the manifold's intrinsic structure, achieving the complementarity of multi-angle information. Furthermore, a manifold tangent structure graph is constructed using a sparse affine tangent structure combination. Experimental results demonstrate that this method can extract more effective fault discrimination features and improve the accuracy of fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The present invention will be further described below with reference to the accompanying drawings and examples.

[0056] Figure 1 is a flow chart of the method of the present invention;

[0057] Figure 2 It is a three-dimensional data distribution diagram after the rolling bearing fault data is projected by the method of the present invention;

[0058] Figure 3 This is the diagnosis result of the rolling bearing fault data by the method of the present invention. DETAILED DESCRIPTION

[0059] The specific implementation steps of the present invention are as follows:

[0060] 1. Collect the operating data of rolling bearing faults through sensors, extract multiple fault data related statistical features from the time domain, frequency domain and time-frequency domain perspectives, and construct a high-dimensional feature data set X = [x1, x2, ..., x N ]∈R M×N , where N is the number of samples and M is the sample dimension; divide the fault data into high-dimensional training feature sets X train and a high-dimensional test feature set X test ;

[0061] 2. Input the high-dimensional training feature set into the complex manifold embedding learning model

[0062]

[0063] sA T (βXL hb X T +QL tl Q T )A=I

[0064] To solve the projection direction A=(α1,α2,..,α k ), obtain high-dimensional fault features X by projection direction train and X test The low-dimensional representation Y train and Y test ;

[0065] 3. Use the classifier to classify the low-dimensional representation of the high-dimensional features to obtain the classification results of the fault data.

[0066] The effect of the present invention can be further verified by the following experiments:

[0067] For the problem of rolling bearing fault diagnosis, the present invention uses the rolling bearing data set of Western Reserve University as an example to conduct experiments. The data used are 12Khz sampling frequency, rotation speed of 1772r / min, nine types of drive end faults under damage radius of 0.1778mm, 0.3556 and 0.5334, and one type of fault-free data under the same working conditions, for a total of ten fault types. The rolling bearing type is SKF6205, and the faults are all single-point damage caused by manual electric spark machining. For each type of data in this experiment, 1024 sampling points are used as a sample, and a total of 1100 samples are obtained. Then, the time-frequency domain features of the original data are obtained to construct a high-dimensional feature set, and the feature set is randomly divided into a training set and a test set in proportion, and input into the proposed method for training, and the random experiment is repeated ten times.

[0068] Figure 2 The three-dimensional data distribution of rolling bearing fault data after projection is intuitively displayed. Figure 2 It can be observed that the low-dimensional representation extracted by the method of the present invention has good intra-class aggregation and inter-class separation. Figure 3 The fault diagnosis results of the method of the present invention are shown. Figure 3 It can be observed that accurate fault diagnosis can be achieved on the ten fault data of the drive end bearing at a sampling frequency of 12kHz and a rotation speed of 1772. The experimental results prove that the method disclosed in the present invention is an effective rolling bearing fault diagnosis method.

Claims

1. A rolling bearing fault diagnosis method based on complex manifold embedding learning, characterized by The method comprises the steps of: (1) The operating data of rolling bearing faults are collected by sensors, and multiple statistical features related to fault data are extracted from the time domain, frequency domain and time-frequency domain to construct a high-dimensional feature data set X = [x1, x2, ..., x N ]∈R M×N , where N is the number of samples and M is the sample dimension; divide the fault data into high-dimensional training feature sets X train and a high-dimensional test feature set X test ; (2) By constructing and optimizing the complex manifold embedding learning model, a low-dimensional representation of high-dimensional fault features is obtained. The specific implementation method is as follows: (2a) Construct intra-class hypergraph, inter-class hypergraph and manifold tangent graph, and further give the objective functions corresponding to the three different graph structures. The specific implementation process is as follows: ① Intra-class hypergraph G hw Defined as: G hw ={V hw ,E hw ,W hw }; Among them, V hw is the vertex set of the intra-class hypergraph, E hw is the set of hyperedges, W hw is the weight matrix; the objective function of the intra-class hypergraph is: in,(·) -1 Indicates the inverse operation, L hw =D hvw -H hw W hw (D hew ) -1 (H hw ) T is the intra-class hypergraph Laplacian matrix; D hvw is the degree matrix of the vertices within the class, D hew is the degree matrix of the intra-class hyperedge, which are defined as: H hw is the intra-class point-edge relationship matrix, defined as: W hw is the weight matrix of the intra-class hyperedge, defined as: ②Inter-class hypergraph G hb Defined as: G hb ={V hb ,E hb ,W hb }; Among them, V hb is the vertex set of the inter-class hypergraph, E hb is the hyperedge set, W hb is the weight matrix; the objective function of the inter-class hypergraph is: Among them, L hb =D hvb -H hb W hb (D heb ) -1 (H hb ) T is the inter-class hypergraph Laplacian matrix; D hvb is the degree matrix of the inter-class vertices, D heb is the degree matrix of the inter-class hyperedge, which is defined as: H hb is the point-edge relationship matrix between classes, defined as: W hb is the weight matrix of the inter-class hyperedge, defined as: ③The manifold tangent graph is defined as: G t ={V tl ,W tl },in is the tangent vector vertex set of the original fault sample, is the similarity weight between vertices; the tangential structure f(x i ) c Defined as: Among them, l(x i ) is x i Tag information, Represents x i k nearest neighbors of s ij is x i and the affine coefficients of the k nearest neighbors, and In the tangential structure f(x i ) c In the equation, the affine coefficient s ij It can be solved based on the idea of ​​sparse representation; based on sparse representation, the tangential structure can be adaptively expressed through a constraint; and in solving s ij A sparse weighted norm representation model is used. The weighted norm can obtain a more accurate tangential structure by applying different weights to each neighbor vector. Therefore, the optimization function of the tangential graph is expressed as follows: Where Λ=diag(d1,d2,…,d n ) is a diagonal matrix, and the diagonal line contains the weight information between the sample and its neighbors; s i =[s ij ] j is the sparse coefficient of the tangent vector, reflecting the similarity relationship between the two tangent vectors; T i is the normalized tangent vector structure representation of the sample; In order to further balance the selected neighbor samples, the local sparse coefficients are obtained by using local samples for construction. Therefore, the optimization function of the manifold tangent graph is as follows: Among them, the local normalized tangential structure and weight coefficient Λ l It is expressed as follows: The objective function of manifold tangent structure graph embedding is expressed as follows: in, L tl =D tl -W tl is the manifold tangent graph Laplace matrix, is the diagonal matrix; W tl is the edge weight information of the manifold tangent graph, which is defined as follows: (2b) Constructing a unified target model for complex manifold embedding: s.t.A T (βXL hb X T +QL tl Q T )A=I This objective model unifies the objective functions of three different structures, where β represents the balance parameter used to control the relative weights of intra-class hypergraph structure information and inter-class structure information; (2c) Iteratively solve the relevant projection direction of the complex manifold embedded in the target model: According to the Lagrange multiplier method, the following equation can be obtained: Where λ is the Lagrange multiplier; taking the partial derivative of L(A,λ) with respect to A yields: make Replace λ(βXL in Eq. (37) hb X T +QL tl Q T )A is moved to the right side of the new equation and multiplied by (βXL on the left side of the new equation hb X T +QL tl Q T ) -1 , we can get the following generalized characteristic equation: (βXL hb X T +QL tl Q T ) -1 XL hw X T A=λA Among them, λ is the eigenvalue and A is its corresponding eigenvector; (2d) Through Y = A T X obtains the low-dimensional representation Y of high-dimensional features train and Y test .

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