Method for multi-modal bearing fault diagnosis based on supervised hyperbolic cosine space learning

Abstract

The application discloses a multi-modal bearing fault diagnosis method based on supervised inverse hyperbolic sine space learning, mainly constructs a supervised inverse hyperbolic sine space learning model, thereby can learn multi-modal features of fault data under a supervised environment, effectively improves the accuracy of fault diagnosis under the supervised environment, and the specific implementation process is as follows: (1) with the aid of different manifold structures among fault sample data, a supervised inverse hyperbolic sine space learning model is constructed; (2) the analytical solution of the inverse hyperbolic sine space projection matrix in the model is optimized and solved; (3) on the basis of the inverse hyperbolic sine space projection matrix, multi-modal fault features of the fault sample data are obtained, 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 core components of rotating machinery, used to support and reduce friction between rotating parts. They enable mechanical equipment to maintain stable operation at high speeds and extend its service life. As rotating machinery is a key piece of equipment in modern industrial production, a failure can lead to serious economic losses or even safety accidents. Therefore, extracting the most valuable information from high-dimensional fault data to support accurate fault diagnosis is a key issue. Among all approaches to solving this problem, spatial learning is an effective approach. However, actual collected fault data often contains noise and redundant information, which causes the intra-class and inter-class sample covariance matrices to deviate from the true covariance matrix, limiting further improvements in diagnostic accuracy. To this end, this paper utilizes relevant spatial learning theories and the inverse hyperbolic sine function to construct a supervised inverse hyperbolic sine spatial learning model. This model can address the problem of intra-class and inter-class sample covariance matrices deviating from the true covariance matrix. Furthermore, the invention derives an analytical solution to the model using the Lagrange multiplier method and obtains multimodal fault features with good class separation through spatial projection, resulting in better fault identification 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 spatial learning model based on spatial learning theory and theoretically derives the solution of this model, thereby solving the problem of the sample covariance matrix deviating 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. Build 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 pth sample in the ith sample set F (i) represents the mean of the sample set F (i) , the matrix H (ii) is defined as the within-class covariance matrix of the sample set F (i) :

[0009]

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

[0011]

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

[0013] In order to solve the problem that the sample covariance matrix deviates from the true covariance matrix in the training process, the present application adopts the inverse hyperbolic cosine function to correct the singular value of the sample covariance matrix, and further forms the inverse hyperbolic cosine covariance matrix. Taking the within-class covariance matrix as an example, the singular value decomposition of the sample within-class covariance matrix H (ii) is carried out:

[0014] H (ii) = P (ii) Λ (ii) D (ii)T

[0015] Where P (ii) and D (ii) represent the left singular matrix and the right singular matrix of H (ii) , respectively, Λ (ii) = is a singular value diagonal matrix, the singular value matrix is corrected by using the inverse hyperbolic cosine function, and the inverse hyperbolic cosine within-class covariance matrix

[0016]

[0017] Where is a singular value diagonal matrix.

[0018] The rank of the inverse hyperbolic cosine covariance matrix is equal to the rank of the sample covariance matrix, that is, The proof is as follows: if , then When ​If Therefore With H (ii) The same rank, that is This shows that the inverse hyperbolic cosine covariance matrix still has the basic properties of the sample covariance matrix, and by analogy, the inverse hyperbolic cosine inter-class covariance matrix is defined as

[0019]

[0020] Where, For The corresponding singular value diagonal matrix, P (ij) And D (ij) Respectively, H (ij) The left singular matrix and the right singular matrix of t ij The rank of H (ij) , that is, t ij = rank(H (ij) ).

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

[0022] Based on the above inverse hyperbolic cosine intra-class and inter-class covariance matrix solution and space learning theory, in view of the problem that the sample covariance matrix deviates from the true covariance matrix, a supervised inverse hyperbolic cosine space learning model is proposed, L = (η (1) T,η (2)T ,…,η (m)T ) is the projection vector sought by F (i) , so that F (i)′ = η (i) TF (i) The correlation between i = 1, 2, …, m reaches the maximum, and the optimization model of supervised inverse hyperbolic cosine space learning is defined as:

[0023]

[0024] 3. The rank of the covariance matrix does not change after the singular value is corrected, that is, in the case of high dimension and limited sample size, the inverse hyperbolic cosine intra-class covariance matrix may still be singular, and when the constraint The solution of the projection direction of the above optimization model is unchanged, then the supervised inverse hyperbolic cosine space learning model can be represented by the following optimization problem:

[0025]

[0026] The Lagrange multiplier function L(η (i) ) of the supervised inverse hyperbolic cosine space learning model is constructed:

[0027]

[0028] where λ is a Lagrange multiplier, and partial derivative of L(η (i) ) with respect to η (i) is taken as follows:

[0029]

[0030] Letting be zero, we have:

[0031]

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

[0033]

[0034] The generalized eigenvalue λ is the objective function value of the cross-modal hyperbolic cosine inverse subspace optimization problem. After solving the above equation and obtaining L=(η (1)T ,η (2)T ,…,η (m)T ), the training sample set can be projected in the space of F (i) ′=η (i)T F (i) , i=1, 2, …, m for dimension reduction.

[0035] 4. The multi-modal features of the fault data are obtained by using the space projection, and the multi-modal fault features are classified by using the classifier, so that the diagnosis result of the fault is obtained.

[0036] The method has the following advantages:

[0037] (1) The method can grasp the internal structure of the multi-modal bearing fault data, and learn the multi-modal hyperbolic cosine inverse space based on the same, so that the class separation of the multi-modal bearing fault features is effectively improved;

[0038] (2) The method further constrains the learning of the space projection matrix by means of the space learning related theory and the hyperbolic cosine inverse function, can reveal the authenticity of the covariance matrix in the more effective hyperbolic cosine inverse space, obtain more comprehensive internal discriminant information, and effectively improve the accuracy of fault diagnosis in a supervised environment;

[0039] (3) The method obtains the analytical solution of the supervised hyperbolic cosine inverse space learning model through theoretical derivation, can quickly obtain the multi-modal fault test features of the fault test sample, and thus realizes more accurate classification of the fault types. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is a flowchart of the present application, wherein 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 group of data sets, n represents the number of samples, m is the number of fault modes, and the matrix H is defined (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.

[0044] 2. Based on the supervised inverse hyperbolic sine space learning model, Perform eigenvalue decomposition to 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 p-th 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 dataset consists of 1,000 data samples. Three data modalities were selected from the Paderborn dataset for experimental verification: motor current, torque, and vibration signals. In this experiment, the current, torque, and vibration signals were each divided into 250 samples, with a sampling length of 1,024. Figure 2 The accuracy of bearing fault diagnosis and classification for each random experiment is intuitively shown. 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 diagnostic recognition rate of the random experiment reaches 100%, which also reveals that the method of the present invention is an effective bearing fault diagnosis and classification method in a supervised environment.

Claims

1. A multimodal bearing fault diagnosis method based on supervised inverse hyperbolic sine space learning, comprising the following steps: (1) The training bearing fault diagnosis data is converted into a column vector. The training bearing fault diagnosis data comes from the Paderborn bearing fault dataset, from which three data modes are selected for experimental verification, namely motor current signal, torque signal and vibration signal, 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; (2) For multimodal bearing fault data of bearing fault diagnosis, a supervised inverse hyperbolic sine space learning model is constructed to correct the intra-class and inter-class sample covariance matrix deviation of bearing fault data. The model is constructed according to the following steps: (2a) Converting the training fault diagnosis data into a column vector, wherein the training fault diagnosis data is multimodal bearing fault data collected during the operation of the bearing, including motor current signal, torque signal, and vibration signal, to form a fault diagnosis training sample set where Q i Represents the characteristic dimension of the i-th group of data sets, n represents the number of samples, m is the number of fault modes, and the matrix H is defined (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; (2b) For training samples Assume that the sample is not centralized. represents the i-th (i=1,2,…,m) sample set F (i) The p-th (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: Among them, 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 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 and right singular matrices of t ij H (ij) The rank of t ij =rank(H (ij) ), the inter-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; (2c) The supervised inverse hyperbolic sine space learning model can be formulated as the following optimization problem: Among them, the constraints When , the solution of the projection direction of the above optimization model remains unchanged; (3) Optimize and solve the inverse hyperbolic sine space projection matrix L = (η (1) T,η (2) T,…,η (m)T ); (4) The multimodal features of the fault data are obtained by spatial projection, and the multimodal fault features are classified by a classifier to obtain the diagnosis results of the bearing fault.

2. 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) Constructing 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 the partial derivative: make Zero gives: Finally, the optimization problem of the 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 multimodal inverse hyperbolic sine space optimization problem; solve the above formula and get L = (η (1)T ,η (2)T ,…,η (m)T ) after the fault diagnosis training sample set can be pressed F (i)' =η (i)T F (i) ,i=1,2,…,m shape dimension reduction, the fault diagnosis training sample set is constructed based on multi-modal bearing fault data during the bearing operation process.

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