Rolling bearing fault diagnosis method based on density domain sensitive space learning

Abstract

The present invention discloses a rolling bearing fault diagnosis method based on density domain sensitive space learning, which solves the problem that the Euclidean distance in nonlinear space learning will lead to potential manifold loss and neglect of density structure, thereby effectively improving the accuracy of rolling bearing fault diagnosis. The implementation process is: (1) extracting the time-frequency domain features of the original fault vibration signal to construct a high-dimensional fault sample set; (2) with the help of density constraints between high-dimensional fault samples, constructing a local density constraint map, a global density constraint map, an intra-class density constraint map and an inter-class density constraint map, and on this basis, a density domain sensitive space learning model is proposed; (3) solving the projection matrix of the model, and using spatial projection to obtain low-dimensional fault features; (4) with the help of a classifier, the low-dimensional fault features are fault identified to obtain the final fault diagnosis result. Experimental results show that the method of the present invention is an effective rolling bearing fault diagnosis method.

Description

Technical Field

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

[0002] In recent years, due to the increasing number and scale of modern factories, modern mechanical equipment is developing towards high efficiency, high automation and high complexity. At the same time, the relationship between equipment is becoming closer and closer. Due to the complex relationship between equipment, even a small fault may trigger a chain reaction, resulting in a destructive failure of the entire mechanical equipment. This will not only cause huge economic losses, but also endanger the safety of personnel. Therefore, efficient and accurate fault diagnosis is the key to ensuring the smooth and safe operation of industrial processes. For rolling bearing faults, the current fault diagnosis methods are mainly divided into three categories: analytical model-based, knowledge-based and data-driven methods. Among them, in the data-driven method, it is easy to collect signals and determine the fault type through sensors and various measuring instruments. However, the collected signals are often non-stationary and nonlinear, and neither the time domain nor the frequency domain features can fully express the signals. Therefore, time-frequency features are usually used to describe the energy distribution and time-varying characteristics of the signal. So how to maintain the local and global structure and category information in the feature space.

[0003] In recent years, rolling bearing fault diagnosis methods based on spatial learning methods have been deeply studied and widely used in the field of fault diagnosis. The core idea is how to maintain the local global structure when projecting to the feature space while retaining the original spatial sample structure information. The most classic spatial learning algorithms, principal component analysis and independent component analysis, both only focus on the global information between samples and ignore the local information. Therefore, many methods based on manifold learning have emerged. Local preserving projection is a method to solve the local popular structure and sample distribution restrictions. It reduces the local popular structure of samples in the original space to a low-dimensional space, but ignores the global manifold structure of the samples. In order to make full use of the local popular structure and global popular structure of samples, many popular structure algorithms based on local preserving projection have been proposed in recent years. A discriminant preserving projection is proposed. This method integrates sample category information and improves the inter-class separability and intra-class aggregation between low-dimensional samples. In order to maximize the inter-class scatter and digest the local aggregation, a local preserving projection based on the maximum margin criterion is proposed. This algorithm can locally maintain the range of inter-class scatter and intra-class scatter. However, the above methods do not utilize the global structural information of the samples. Combining geometric information with discriminant information, a new discriminant orthogonal elasticity-preserving projection is proposed. This method fuses discriminant information with global-local information, and adds the maximum margin criterion and projection orthogonality constraint, which not only makes full use of discriminant information but also maintains the elastic structure between samples. The reconstruction graph structure takes class global and class local as the starting point, and proposes an orthogonal discriminant projection based on local-global balance. This method effectively extracts global feature information while maintaining the internal popular structure of high-dimensional fault sample sets by capturing local information within the class, local information between classes, non-local information within the class, and non-local information between classes.

[0004] However, in existing dimensionality reduction methods, Euclidean distance is widely used as a similarity measurement method. However, when samples are in a high-density neighborhood, the information they carry cannot be ignored, so using Euclidean distance as a similarity measurement method alone will cause the graph structure to lose the information carried by the samples, resulting in poor classification results. Summary of the invention

[0005] The present invention discloses a rolling bearing fault diagnosis method based on density domain sensitive space learning, so as to solve the problem that the traditional fault diagnosis algorithm cannot fully reveal the complex high-order relationship and retain rich fault characteristics. The specific method steps are as follows:

[0006] 1. The vibration monitoring signals of rolling bearings in mechanical equipment are collected by sensors, and multiple fault data-related statistical features are extracted from the time domain, frequency domain and time-frequency domain to construct a high-dimensional fault sample set. The high-dimensional fault sample set is divided into a high-dimensional fault training sample set X = [x1, x2, …, x N ]∈R M×N and high-dimensional fault test sample sets Where M is the sample dimension, N is the number of training samples, is the number of test samples, x i is the i-th high-dimensional fault training sample of X, for The i-th high-dimensional fault test sample.

[0007] 2. By constructing and optimizing the density domain sensitive space learning model, a low-dimensional representation of high-dimensional fault features is obtained. The specific implementation method is as follows:

[0008] (2a) Construct density domain constraints, and based on this, further give objective functions corresponding to four different graph structures. The specific implementation process is as follows:

[0009] x i and x j Represents a high-dimensional fault sample and calculates the asymmetric sorting distance r(x i ,x j ) is expressed as:

[0010]

[0011] in For x i In the mth nearest neighbor point sorted by distance, Represents x i In x j The position in the distance sorting table, thus Represents the sample point In x j Finally, the asymmetric distance is normalized to obtain the symmetric x i and x j The sorting distance R(x i ,x j )for:

[0012]

[0013] Density constraint D of high-dimensional fault samples w for:

[0014]

[0015] Where K represents the local neighbor parameter, m samlpex Represents the density median of the sample. Based on the density constraint, we construct the local density constraint graph, global density constraint graph, intra-class density constraint graph and inter-class density constraint graph, and their corresponding four different graph structure objective functions. The specific implementation process is as follows:

[0016] ①Define the local density constraint graph G ld(X,S ld ), where X is a high-dimensional fault training sample set, S ld is the weight matrix of the local density constraint graph, S ld The (i,j),i=1,2,…,N,j=1,2,…,N,element of element is defined as follows:

[0017]

[0018] Where t is the thermal nuclear parameter, ρ = R(x i ,x j )+D w Where N k (x j ) is the jth high-dimensional fault training sample x in X j The first k nearest neighbor sample set of k (x i ) is x in X i The first k nearest neighbor sample set of ld Local density constraint scatter matrix Defined as:

[0019]

[0020] in The following equivalent deduction can be performed

[0021]

[0022] Where L ld =X(D ld -S ld )X T , D ld is a diagonal matrix, and the elements on the diagonal are The column sum, that is Therefore, the local density constraint function is:

[0023]

[0024] ②Define the global density constraint graph G gd (X,W gd ), where X is a high-dimensional fault training sample set, W gd is the weight matrix of the global density y bundle graph, W gd The (i,j),i=1,2,…,N,j=1,2,…,N,element of element is defined as follows:

[0025]

[0026] In Figure G gd The global density constraint scatter matrix Defined as:

[0027]

[0028] in The following equivalent deductions can be made:

[0029]

[0030] Where L gd =X(D gd -S gd )X T , D gd is a diagonal matrix, and the elements on the diagonal are The column sum, that is Therefore, the global density constraint function is:

[0031]

[0032] ③Define the intra-class density constraint map Where X is a high-dimensional fault training sample set, is the weight matrix of the intra-class density constraint graph, The (i,j),i=1,2,…,N,j=1,2,…,N,element of element The definition of is as follows:

[0033]

[0034] in is the intra-class density constraint weight, is the intra-class density constraint weight. i and l j x i and x j The class label of . The intra-class density-constrained scatter matrix Defined as:

[0035]

[0036] in The following equivalent deductions can be made:

[0037]

[0038] in D ad is a diagonal matrix, and the elements on the diagonal are The column sum, that is Therefore, the intra-class density constraint function is:

[0039]

[0040] ④Define the inter-class density constraint map Where X is a high-dimensional fault training sample set, is the weight matrix of the inter-class density constraint graph, The (i,j),i=1,2,…,N,j=1,2,…,N,element of The elements is defined as follows:

[0041]

[0042] in is the inter-class density discrimination weight. The density-constrained scatter matrix between classes Defined as:

[0043]

[0044] in The following equivalent deductions can be made:

[0045]

[0046] in D ed is a diagonal matrix, and the elements on the diagonal are The column sum, that is Therefore, the inter-class density constraint function is:

[0047]

[0048] (2b) Through the above four different graph structure objective functions, a density domain sensitive spatial learning model is constructed:

[0049]

[0050] sP T P=I

[0051] where P is the projection matrix, I is the identity matrix, tr(·) is the trace operation of the matrix, and α and β are adjustment factors.

[0052] (2c) Solve the projection matrix of the model and use spatial projection to obtain low-dimensional fault features. The specific implementation method is as follows:

[0053] Construct the Lagrange multiplier function L(P) of the density domain sensitive spatial learning model:

[0054]

[0055] Where λ is the Lagrange multiplier; by setting the partial derivative of L(P) with respect to the projection matrix P to zero, the optimization problem of density domain sensitive spatial learning model transformation can be transformed into the following generalized eigenvalue decomposition problem:

[0056] X(L ge -L la )X T P=λP

[0057] Where X T is the matrix transpose of X, In this generalized eigenvalue decomposition problem, the Lagrange multiplier λ is also called the eigenvalue, and the projection direction P is composed of the eigenvectors corresponding to the first d largest eigenvalues, that is, P = [p1, p2, ..., p d ]∈R M×d , where d is the projection parameter of the projection direction, p i is the eigenvector corresponding to the i-th maximum eigenvalue; finally, the low-dimensional fault feature Y of the high-dimensional fault training sample set X and the high-dimensional fault test sample set are obtained by using spatial projection and projection matrix Low-dimensional fault signature in P T is the matrix transpose of P.

[0058] 3. Use classifiers to classify low-dimensional fault features Perform fault identification to obtain the final fault diagnosis result.

[0059] The beneficial effects of the present invention are: constructing a density domain sensitive space model, integrating density constraints into local structure, global structure, intra-class structure and inter-class structure, and density constraints can mine potential manifold information between samples and retain richer fault features. It solves the problem that the Euclidean metric cannot fully reveal the intrinsic structure of the manifold, and realizes the complementarity of multi-angle information. Experimental results show that this method can extract more effective fault discrimination features and improve the accuracy of fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0061] Figure 1 is a flow chart of the method of the present invention;

[0062] Figure 2 It is a two-dimensional data distribution diagram after the method of the present invention projects the high-dimensional fault data of the rolling bearing;

[0063] Figure 3 It is the confusion matrix of the method of the present invention for classifying high-dimensional fault data of rolling bearings. DETAILED DESCRIPTION

[0064] The specific implementation steps of the present invention are as follows:

[0065] 1. Collect the operating data of mechanical equipment failures through sensors, extract multiple fault data related statistical features from the time domain, frequency domain and time-frequency domain to construct a high-dimensional fault sample set, and divide the high-dimensional fault sample set into a high-dimensional fault training sample set X = [x1, x2, …, x N ]∈R M×N and high-dimensional fault test sample sets

[0066] 2. Input the high-dimensional fault training sample set into the density-domain sensitive space learning model,

[0067]

[0068] sP T P=I

[0069] To solve the projection direction P = [p1, p2, ..., p d ], and obtain the high-dimensional fault feature X by the projection direction train and X test The low-dimensional fault feature Y train and Y test ;

[0070] 3. Use the support vector machine classifier to classify the low-dimensional representation of the high-dimensional features to obtain the classification results of the fault data.

[0071] The effect of the present invention can be further verified by the following experiments:

[0072] For the problem of rolling bearing fault diagnosis, the present invention uses the rolling bearing data set of Case Western Reserve University in the United States. The bearing used in the experiment is 6205-RS JEM SKF deep groove ball bearing. The sensor is an acceleration sensor. The sensor is placed on the motor, torque sensor and dynamometer, and then the sensor collects the bearing vibration data set. The driving end bearing vibration signal with a sampling frequency of 12kHz and a rotation speed of 1750r / min is selected. Four vibration samples are collected, namely normal samples, inner ring faults, outer ring faults, and steel ball defect faults. The faults are all single-point damage caused by artificial electrospark machining. For each type of data in this experiment, 1024 sampling points are used as a sample, and a total of 100 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.

[0073] Figure 2 The two-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 classification results of the method of the present invention are shown. Figure 3 It can be observed that accurate fault diagnosis can be achieved on four high-dimensional fault data of the drive end bearing at a sampling frequency of 12kHz and a speed of 1750r / min. 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 density domain sensitive space learning, characterized in that The method comprises the following steps: (1) The vibration monitoring signals of rolling bearings in mechanical equipment are collected by sensors, and multiple fault data-related statistical features are extracted from the time domain, frequency domain, and time-frequency domain to construct a high-dimensional fault sample set. The high-dimensional fault sample set is divided into a high-dimensional fault training sample set X = [x1, x2, …, x N ]∈R M×N and high-dimensional fault test sample sets Where M is the sample dimension, N is the number of training samples, is the number of test samples, x i is the i-th high-dimensional fault training sample of X, for The i-th high-dimensional fault test sample; (2) Construct a density-domain sensitive spatial learning model. The specific implementation method is as follows: Density constraint D of high-dimensional fault samples w for: Where K represents the local neighbor parameter, m samlpex Represents the density median of the sample, R(x i ,x j ) is a high-dimensional fault sample x i and x j With the help of the density constraints of high-dimensional fault samples, local density constraint graphs, global density constraint graphs, intra-class density constraint graphs and inter-class density constraint graphs are constructed, and a density domain sensitive space learning model is proposed based on this: s.t.P T P=I Where P is the projection matrix, I is the identity matrix, tr(·) is the trace operation of the matrix, and α and β are adjustment factors. Where L gd =X(D gd -W gd )X T , W gd is the weight matrix of the global density constraint graph, W gd The (i,j),i=1,2,…,N,j=1,2,…,N,element of D gd is a diagonal matrix, and the elements on the diagonal are The column sum, that is The specific calculation is as follows: Where ρ = R(x i ,x j (+D w , t is the thermal core parameter; in this model Where L ed =X(D ed -W ed )X T , W ed is the weight matrix of the inter-class density constraint graph, W ed The (i,j),i=1,2,…,N,j=1,2,…,N,element of D ed is a diagonal matrix, and the elements on the diagonal are The column sum, that is The specific calculation is as follows: Where N k (x j ) is the jth high-dimensional fault training sample x in X j The first k nearest neighbor sample set of k (x i ) is x in X i The first k nearest neighbor sample set of i and l j x i and x j The class label of Where L ld =X(D ld -S ld )X T , S ld is the weight matrix of the local density constraint graph, S ld The (i,j),i=1,2,…,N,j=1,2,…,N,element of D ld is a diagonal matrix, and the elements on the diagonal are The column sum, that is The specific calculation is as follows: In this model in is the weight matrix of the intra-class density constraint graph, The (i,j),i=1,2,…,N,j=1,2,…,N,element of D ad is a diagonal matrix, and the elements on the diagonal are The column sum, that is The specific calculation is as follows: (3) Solve the projection matrix of the model and use spatial projection to obtain low-dimensional fault features. The specific implementation method is as follows: Construct the Lagrange multiplier function L(P) of the density-domain sensitive spatial learning model: Where λ is the Lagrange multiplier; by setting the partial derivative of L(P) with respect to the projection matrix P to zero, the optimization problem of density domain sensitive spatial learning model transformation can be transformed into the following generalized eigenvalue decomposition problem: X(L ge -IT la )X T P=λP Where X T is the matrix transpose of X, In this generalized eigenvalue decomposition problem, the Lagrange multiplier λ is also called the eigenvalue, and the projection direction P is composed of the eigenvectors corresponding to the first d largest eigenvalues, that is, P = [p1, p2, ..., p d ]∈R M×d , where d is the projection parameter of the projection direction, p i is the eigenvector corresponding to the i-th maximum eigenvalue; finally, the low-dimensional fault feature Y of the high-dimensional fault training sample set X and the high-dimensional fault test sample set are obtained by using spatial projection and projection matrix Low-dimensional fault signature Where Y = P T X, P T is the matrix transpose of P; (4) Using the classifier, low-dimensional fault features Perform fault identification to obtain the final fault diagnosis result.

Images