Multimodal bearing fault diagnosis method based on supervised antihyperbolic sine space learning

Abstract

The invention discloses a multi-modal bearing fault diagnosis method based on supervised antihyperbolic sine space learning, which mainly constructs a supervised antihyperbolic sine space learning model, so that multi-modal features of fault data can be learned in a supervised environment, and the accuracy of fault diagnosis in the supervised environment is effectively improved. The method specifically comprises the following steps: (1) constructing a supervised antihyperbolic sine space learning model by means of different manifold structures among fault sample data; (2) an analytic solution of an inverse hyperbolic sine space projection matrix in the model is optimized and solved; and (3) multi-modal fault features of the fault sample data are obtained on the basis of the inverse hyperbolic sine space projection matrix, and a fault diagnosis result is obtained by using a classifier. Compared with the prior art, the fault diagnosis method is more effective and robust.

Description

Technical Field

[0001] The present invention relates to technical fields such as spatial learning and fault diagnosis, and specifically to a multimodal bearing fault diagnosis method based on supervised inverse hyperbolic sine spatial learning, which can be applied to fields such as fault diagnosis and risk classification. Background Art

[0002] In the field of fault diagnosis, bearings are the core components of rotating machinery, which are used to support and reduce the friction between rotating parts. They can keep mechanical equipment running stably at high speed and extend the service life of the equipment. Since rotating machinery is a key equipment in modern industrial production, once a fault occurs, it may cause serious economic losses or even safety accidents. Therefore, how to extract the most valuable information from high-dimensional fault data and provide support for accurate fault diagnosis is the current key issue. Among all the methods to solve the problem, spatial learning is an effective method. However, the actual collected fault data usually contains noise and redundant information, which will cause the intra-class and inter-class sample covariance matrices to deviate from the true covariance matrix, limiting the further improvement of diagnostic accuracy. To this end, this invention uses the relevant theories of spatial learning and the inverse hyperbolic sine function to construct a supervised inverse hyperbolic sine space learning model, which can solve the problem of the intra-class and inter-class sample covariance matrices deviating from the true covariance matrix. In addition, the invention also derives the analytical solution of the model through the Lagrange multiplier method, and obtains multimodal fault features with good class separation through spatial projection, which can obtain better fault identification effect and higher accuracy. Summary of the invention

[0003] In order to better discover the internal structure of the data, the present invention constructs a supervised inverse hyperbolic sine space learning model based on the spatial learning theory, and theoretically derives the solution of the model, thereby solving the problem that the sample covariance matrix deviates from the true covariance matrix during the training process. The specific implementation steps of the present invention are as follows:

[0004] 1. Convert the training bearing fault diagnosis data into column vectors to form a bearing fault diagnosis training sample set Where Q i represents the characteristic dimension of the i-th data set, n represents the number of samples, and m is the number of fault modes.

[0005] 2. Construct a supervised inverse hyperbolic sine space learning model.

[0006] The specific steps for constructing the supervised inverse hyperbolic sine space learning model are as follows:

[0007] (2a) Construction of sample covariance matrix:

[0008] For training samples Assume that the sample is not centralized. represents the i-th (i=1,2,…,m) sample set F (i) The pth (p=1,2,…,n) sample in is the sample set F (i) The mean of the matrix H (ii) is the sample set F (i) The within-class covariance matrix of :

[0009]

[0010] Similarly, is the sample set F (j) The sample mean of (ij) is the sample set F (i) and F (j) The between-class covariance matrix of :

[0011]

[0012] (2b) Construction of the inverse hyperbolic sine covariance matrix:

[0013] In order to solve the problem that the sample covariance matrix deviates from the true covariance matrix during the training process, the present invention uses an inverse hyperbolic sine function to correct the singular values ​​of the sample covariance matrix, thereby forming an inverse hyperbolic sine covariance matrix. Taking the intra-class covariance matrix as an example, the sample intra-class covariance matrix H (ii) Perform singular value decomposition:

[0014] H (ii) =P (ii) Λ (ii) D (ii)T

[0015] Where P (ii) and D (ii) Respectively represent H (ii) The left and right singular matrices of (ii) = is a singular value diagonal matrix. The inverse hyperbolic sine function is used to correct the singular value matrix, and the inverse hyperbolic sine intra-class covariance matrix is ​​further constructed.

[0016]

[0017] in is a diagonal matrix of singular values.

[0018] The rank of the inverse hyperbolic sine covariance matrix is ​​equal to the rank of the sample covariance matrix, that is, The proof is as follows: If but when When therefore With H (ii) have the same rank, i.e. This shows that the inverse hyperbolic sine covariance matrix still has the basic properties of the sample covariance matrix. Similarly, the inverse hyperbolic sine inter-class covariance matrix is ​​defined as

[0019]

[0020] in, for The corresponding singular value diagonal matrix, P (ij) and D (ij) Respectively represent H (ij) The left singular matrix and right singular matrix of t ij H (ij) The rank of t ij =rank(H (ij) ).

[0021] (2c) Construction of supervised inverse hyperbolic sine space learning model:

[0022] Based on the solution of the inverse hyperbolic sine intra-class and inter-class covariance matrices and the spatial learning theory, a supervised inverse hyperbolic sine spatial learning model is proposed to solve the problem that the sample covariance matrix deviates from the true covariance matrix. (1) T,η (2)T ,…,η (m)T ) is F (i) Find the projection vector such that F (i)′ =η (i) TF (i) , i = 1, 2, ..., m reaches the maximum correlation, and defines the optimal model for supervised inverse hyperbolic sine space learning:

[0023]

[0024] 3. The rank of the covariance matrix does not change after singular value correction, that is, in the case of high dimensions and limited sample size, the inverse hyperbolic sine class covariance matrix may still be singular. When , the solution of the projection direction of the above optimization model remains unchanged, then the supervised inverse hyperbolic sine space learning model can be expressed by the following optimization problem:

[0025]

[0026] Constructing the Lagrange multiplier function L(η) for supervised inverse hyperbolic sine space learning model (i) ):

[0027]

[0028] Among them, λ is the Lagrange multiplier, L(η (i) ) for η (i) Find the partial derivative:

[0029]

[0030] make Zero gives:

[0031]

[0032] Finally, the optimization problem of supervised inverse hyperbolic sine space learning model transformation can be transformed into the following generalized eigenvalue equation:

[0033]

[0034] The generalized eigenvalue λ is the objective function value of the cross-modal inverse hyperbolic sine subspace optimization problem. Solve the above equation and get L = (η (1)T ,η (2)T ,…,η (m)T ) after which the training sample set can be (i) ′=η (i)T F (i) ,i=1,2,…,m spatial projection method is used to reduce the dimension.

[0035] 4. Use spatial projection to obtain the multimodal features of fault data, and use a classifier to classify the multimodal fault features to obtain the fault diagnosis results.

[0036] The method of the present invention has the following advantages:

[0037] (1) The present invention can grasp the intrinsic structure of multimodal bearing fault data, and based on this, learn the multimodal inverse hyperbolic sine space, effectively improving the class separation of multimodal bearing fault features;

[0038] (2) The present invention further constrains the learning of the spatial projection matrix by using the spatial learning related theory and the inverse hyperbolic sine function, which can reveal the authenticity of the covariance matrix in the more effective inverse hyperbolic sine space, obtain more comprehensive intrinsic identification information, and effectively improve the accuracy of fault diagnosis in a supervised environment;

[0039] (3) Through theoretical derivation, the present invention obtains an analytical solution of the supervised inverse hyperbolic sine space learning model, which can quickly obtain the multi-modal fault test features of the fault test samples, thereby achieving more accurate classification of fault types. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is the flow chart of the present invention, where q is the number of fault categories

[0041] Figure 2 is the classification accuracy of the random experiment DETAILED DESCRIPTION

[0042] The specific implementation steps of the present invention are as follows:

[0043] 1. Convert the training fault sample data into column vectors to form a fault sample set Where Q i represents the characteristic dimension of the i-th data set, n represents the number of samples, m is the number of fault modes, and the matrix H is defined as (ii) is the sample set F (i) The intra-class covariance matrix, H (ij) is the sample set F (i) and F (j) The between-class covariance matrix of , j = 1, 2, …, m.

[0044] 2. Based on the supervised inverse hyperbolic sine space learning model, By performing eigenvalue decomposition, we can obtain the eigenvector η corresponding to the maximum eigenvalue λ (i)T , where η (i)T That is the multimodal projection direction of the inverse hyperbolic sine space projection matrix, thereby obtaining the analytical solution of the inverse hyperbolic sine space projection matrix.

[0045] 3. For the fault training sample set Multimodal fault feature Z of the pth fault training sample p for Finally, the k-nearest neighbor classifier is used to classify the multimodal fault features through the trained classifier to obtain the final bearing fault diagnosis results.

[0046] The effect of the present invention is further verified by the following experiments:

[0047] The bearing fault sample data set consists of 1000 data samples. Three data modes are selected from the Paderborn data set for experimental verification, namely motor current signal, torque signal and vibration signal. In this experiment, the current, torque and vibration signals are divided into 250 samples with a sampling length of 1024. Figure 2 The accuracy of the bearing fault diagnosis classification for each random experiment is intuitively displayed. Figure 2 It can be seen that the method of the present invention still has good classification accuracy in a supervised environment, and the average diagnosis recognition rate of the random experiment reaches 100%, which also reveals that the method of the present invention is an effective bearing fault diagnosis classification method in a supervised environment.

Claims

1. The present invention discloses a multi-modal bearing fault diagnosis method based on supervised inverse hyperbolic sine space learning, comprising the following steps: (1) Convert the training bearing fault diagnosis data into column vectors to form a bearing fault diagnosis training sample set Where Q i represents the characteristic dimension of the i-th data set, n represents the number of samples, and m represents the number of fault modes; (2) Construct a supervised inverse hyperbolic sine space learning model; (3) Optimize and solve the inverse hyperbolic sine space projection matrix L = (η (1)T , η (2)T ,…,η (m)T ); (4) Use spatial projection to obtain the multimodal features of fault data, and use a classifier to classify the multimodal fault features to obtain the fault diagnosis results.

2. The multimodal bearing fault diagnosis method based on supervised inverse hyperbolic sine space learning according to claim 1 is characterized in that: The steps of constructing the supervised inverse hyperbolic sine space learning model in step (2) are as follows: (1) Convert the training fault diagnosis data into column vectors to form a fault diagnosis training sample set Where Q i represents the characteristic dimension of the i-th data set, n represents the number of samples, m is the number of fault modes, and the matrix H is defined as (ii) is the sample set F (i) The intra-class covariance matrix, H (ij) is the sample set F (i) and F (j) The inter-class covariance matrix of , j = 1, 2, …, m; (2) For training samples Assume that the sample is not centralized. represents the i-th (i=1,2,…,m) sample set F (i) The pth (p = 1, 2, ..., n) sample in the sine space is used to construct a supervised inverse hyperbolic sine space learning model: in F (i) Find the projection vector, and is the inverse hyperbolic sine intra-class and inter-class covariance matrix; Taking the inverse hyperbolic intra-class covariance matrix as an example, construct the inverse hyperbolic sine intra-class covariance matrix as follows: Where P (ii) and D (ii) Respectively represent H (ii) The left singular matrix and the right singular matrix of , use the inverse hyperbolic sine function to correct the singular value matrix, and then get the inverse hyperbolic sine class covariance matrix is a diagonal matrix of singular values, H (ii) The build is as follows: in is the sample set F (i) The mean value of H (ii) Perform singular value decomposition: H (ii) =P (ii) Λ (ii) D (ii)T in is a diagonal matrix of singular values; Similarly, construct the inverse hyperbolic sine inter-class covariance matrix as follows: in, for The corresponding singular value diagonal matrix, P (ij) and D (ij) Respectively represent H (ij) The left singular matrix and right singular matrix of t ij H (ij) The rank of t ij =rank(H (ij) ), the between-class covariance matrix H (ij) The build is as follows: in is the sample set F (j) The sample mean of H (ij) Perform singular value decomposition: H (ij) =P (ij) Λ (ij) D (ij)T in is a diagonal matrix of singular values; (3) The supervised inverse hyperbolic sine space learning model can be expressed as the following optimization problem: Among them, the constraints When , the solution of the projection direction of the above optimization model remains unchanged.

3. The multimodal bearing fault diagnosis method based on supervised inverse hyperbolic sine space learning according to claim 1 is characterized in that: The optimization solution of the inverse hyperbolic sine space projection matrix L=(η (1)T , η (2)T ,…,η (m)T ), the steps are as follows: (1) Construct the Lagrange multiplier function L(η) of the supervised inverse hyperbolic sine space learning model (i) ): Among them, λ is the Lagrange multiplier, L(α (i) ) for α (i) Find partial derivatives: make Zero gives: Finally, the optimization problem of supervised inverse hyperbolic sine space learning model transformation can be transformed into the following generalized eigenvalue equation: The generalized eigenvalue λ is the objective function value of the multi-modal inverse hyperbolic sine space optimization problem; Solve the above formula and get L = (η (1)T , η (2)T , …, η(m)T ) after which the fault diagnosis training sample set can be (i)′ =η (i)T F (i) , i = 1, 2, …, m shape dimensionality reduction.

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