Fault diagnosis method based on unsupervised cross-modal hyperbolic subspace

Abstract

The present invention discloses a fault diagnosis method based on unsupervised cross-modal hyperbolic subspace. The method mainly constructs an unsupervised cross-modal hyperbolic subspace learning model, thereby being able to learn the cross-modal features of fault data in an unsupervised environment and effectively improve the accuracy of fault diagnosis in an unsupervised environment. The specific implementation process is as follows: (1) constructing an unsupervised cross-modal hyperbolic subspace learning model with the help of different manifold structures between fault sample data; (2) optimizing and solving the analytical solution of the cross-modal hyperbolic subspace projection matrix in the model; (3) obtaining the cross-modal fault features of the fault sample data based on the cross-modal hyperbolic subspace projection direction, and using a classifier to obtain the classification results of the fault diagnosis. Compared with the existing technology, the fault diagnosis method of the present invention is more effective and accurate.

Description

Technical Field

[0001] The present invention relates to technical fields such as spatial learning and fault diagnosis, and specifically to a fault diagnosis method based on unsupervised cross-modal hyperbolic subspace, 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. Their health status has a significant impact on the performance, stability, and service life of mechanical equipment. Bearing vibration signals contain bearing fault information, and analysis and processing of these signals can identify the bearing's health status. Therefore, extracting the most discriminative features from large amounts of high-dimensional fault data to better perform fault diagnosis is a key issue.

[0003] Among all the methods to solve the problem, spatial learning is an effective method. However, the intrinsic structure of the data cannot be better discovered. Existing spatial learning technologies such as the fault diagnosis method of local preservation projection consider the intrinsic locality of fault data and propose a fault monitoring method based on manifold learning and big data analysis for fault diagnosis. However, this method can only process single-modal data, and the problem of Euclidean space manifold cannot be solved. To this end, this invention constructs a cross-modal hyperbolic subspace learning model with the help of local correlation theory and hyperbolic space learning. The model can perform cross-modal information fusion and solve the local distortion problem of Euclidean space manifold. In addition, the invention also derives the analytical solution of the model through the Lagrange multiplier method, and uses spatial projection to obtain cross-modal fault features with good class separation, which can achieve better fault identification effect and higher accuracy. Summary of the Invention

[0004] To better discover the intrinsic structure of data, the present invention constructs a cross-modal hyperbolic subspace learning model based on local correlation theory and theoretically derives an analytical solution to the model, thereby solving the problem of local distortion of the Euclidean space manifold during training. The specific implementation steps of the present invention are as follows:

[0005] 1. Collect data signals from mechanical equipment, extract the original data signal features from the time domain, frequency domain and time-frequency domain, and construct a high-dimensional fault feature set X = [x1,…,x n ]∈R p×n and Y=[y1,…,y n ]∈R q×n , where p, q represent the feature sample dimensions of X, Y, n represents the number of feature samples, (x, y) is derived from the feature sample set Any pair of samples.

[0006] 2. Construct a cross-modal hyperbolic subspace learning model.

[0007] The specific steps for constructing the cross-modal hyperbolic subspace learning model are as follows:

[0008] (1) Objective optimization function based on canonical correlation analysis:

[0009] For the training sample X=[x1,…,x n ]∈R p×n and Y=[y1,…,y n ]∈R q×n , and assume that the sample has not been centered, record is the mean of the observed sample, F and G are two sets of basis vectors found by X and Y, so that X = F T X, Y = G T The correlation between Y reaches its maximum, and the criterion function of the correlation is expressed as follows:

[0010]

[0011] where · is the matrix multiplication operator, Q xx ,Q yy ,Q xy Expand as follows:

[0012]

[0013] The optimization problem of the correlation criterion function can be described as a generalized multiple linear regression problem:

[0014]

[0015]

[0016] Similarly for the constraints, the following optimization problem can be derived:

[0017]

[0018]

[0019]

[0020] (2) Geodesic distance in the Poincare sphere model:

[0021] In order to solve the problem of local distortion of Euclidean space manifolds, in this paper, the hyperbolic geometric model of complex networks uses the extended Poincare disk model to represent the hyperbolic space. The geodesic distance in the Poincare sphere model is:

[0022]

[0023] where v i and v jrepresent the i-th sample vector and the j-th sample vector respectively.

[0024] The Poincaré disk model is a concrete manifestation of the Poincaré sphere model in two dimensions. The Poincaré disk model is angle-conservative, that is, the Euclidean angle between hyperbolas in the model is equal to its hyperbolic value; the distance in the Poincaré disk model is different from that in Euclidean space. The hyperbolic distance r from the center of the disk is h and Euclidean distance r e There is the following relationship between them:

[0025]

[0026] (3) Definition of similarity matrix:

[0027] For more complex nonlinear correlation problems, the assumption of linear correlation is only valid locally. i ,y i ), its local correlation can be expressed as F T ∑ j∈ne(i) (x i -x j )(y i -y j ) T G, where the symbol ne(i) represents x i (or y i ) is the local neighbor sample index set. Two assumptions are made about the data distribution: (1) the samples of X and Y are distributed on a continuous low-dimensional manifold; (2) the potential mapping relationship from X to Y is continuous. On this basis, the similarity matrix is ​​defined as and The matrix elements

[0028]

[0029] where ρ(x i ,x j )=d(v i ,v j ).

[0030]

[0031] Where ρ(y i ,y j )=d(v i ,v j ).

[0032] (4) Based on the local information of data distribution, it is further processed in hyperbolic space:

[0033] In the local hyperbolic space method of canonical correlation analysis, the eigenvectors of the cross-modal hyperbolic subspace are derived, and the Euclidean input features are mapped to the hyperbolic space to obtain the weight values ​​between samples. The canonical correlation analysis in the local neighborhood of the hyperbolic space can be defined as Therefore, a global nonlinear problem can be reduced to n local (quasi) linear subproblems in hyperbolic space. Conversely, the combination of these subproblems can be used as an approximation of the original problem. Therefore, after considering the local distribution characteristics of the data, the cross-modal hyperbolic subspace can be described as the following optimization problem:

[0034]

[0035]

[0036]

[0037] After derivation and simplification, the unsupervised cross-modal hyperbolic subspace learning model can be described as:

[0038] max F T XQ XY Y T G

[0039] F T XQ XX X T F=1

[0040] G T YQ YY Y T G=1

[0041] Here X=[x1,…,x n ],Y=[y1,…,y n ], symbol Represents an operator.

[0042] 3. Optimize the solution of the generalized eigenvalue equation across modal hyperbolic subspaces.

[0043] The generalized eigenvalue equation for optimizing the cross-modal hyperbolic subspace is as follows:

[0044]

[0045] The generalized eigenvalue λ is the objective function value of the optimization problem in the cross-modal hyperbolic subspace. After solving the above equation and obtaining the vector set (F, G), the original data can be obtained according to F T x and G T y in the form of dimensionality reduction.

[0046] 3. Use spatial projection to obtain cross-modal hyperbolic subspace features, and use the classifier to obtain the fault diagnosis classification results.

[0047] For the high-dimensional fault feature sample set X=[x1,…,x n ]∈R p×n and Y=[y1,…,y n ]∈R q×n , find the i-th sample pair (x i ,y i Finally, the fault training features and fault test features are classified using the k-nearest neighbor classifier to obtain the fault diagnosis classification results.

[0048] The method of the present invention has the following advantages:

[0049] (1) The present invention can fuse different modal fault data for cross-modal processing, and based on this, proposes a cross-modal hyperbolic subspace to effectively extract the discriminant information between different modal fault features;

[0050] (2) The present invention further constrains the learning of the spatial projection matrix by leveraging local correlation theory and hyperbolic space learning, which can reveal more effective local preservation structures and solve the local distortion problem of Euclidean space, thereby obtaining more comprehensive intrinsic identification information and effectively improving the accuracy of fault diagnosis in an unsupervised environment.

[0051] (3) Through theoretical derivation, the present invention obtains the analytical solution of the cross-modal hyperbolic subspace learning model, which can quickly obtain the cross-modal fault characteristics of fault samples and achieve more accurate fault classification. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of the present invention

[0053] Figure 2 is the classification accuracy of the random experiment DETAILED DESCRIPTION

[0054] The specific implementation steps of the present invention are as follows: The present invention proposes a fault diagnosis method based on unsupervised cross-modal hyperbolic subspace. The specific implementation methods and basic principles of the present invention are further explained below with reference to the accompanying drawings.

[0055] 1. Collect fault signals from mechanical equipment, collect different modal data of different faulty bearings, and divide the collected fault signals according to the sampling length;

[0056] 2. Extract statistical features in the time domain, frequency domain, and time-frequency domain from the collected data samples, and then obtain a two-modal fault feature set. The feature fault sample data set is divided into a training set and a test set in proportion;

[0057] 3. By combining hyperbolic space learning with local correlation theory, an unsupervised cross-modal hyperbolic subspace learning model is constructed. This model first maps fault samples into a hyperbolic space using hyperbolic distance. Hyperbolic space has a certain degree of angle-preserving property, which can reduce the impact of data distortion. Then, combined with local correlation theory, the two modal data are fused, taking into account the local structure of the samples, improving inter-modal complementarity while maximizing the extraction of sample discriminant features.

[0058] 4. Based on the unsupervised cross-modal hyperbolic subspace learning model, the optimization matrix is ​​obtained by the Lagrange multiplier method. Performing eigenvalue decomposition can obtain the eigenvector corresponding to the maximum eigenvalue λ, where the eigenvector is the cross-modal hyperbolic subspace projection direction of the hyperbolic subspace projection matrix, thereby obtaining an analytical solution for the cross-modal hyperbolic subspace projection matrix. The training set is sent to the unsupervised cross-modal hyperbolic subspace learning model for training to obtain the projection matrices F and G. Then, the fault features of the training and test samples are directly obtained through spatial projection. The projection matrix is ​​used to reduce the dimensionality of the test sample set to obtain a low-dimensional feature set.

[0059] 5. For the fault training sample set X=[x1,…,x n ]∈R p×n and Y=[y1,…,y n ]∈R q×n , the first (x i ,y i ) fault training samples is the cross-modal fault feature (F T x i ,G T y i ). Finally, the fault features are classified by the trained classifier to obtain the final fault diagnosis result. The effect of the present invention is further verified by the following experiments:

[0060] The experimental data is selected from the Paderborn bearing dataset, in which the artificial damage test bench consists of four modules, namely motor, torque measurement shaft, rolling bearing test module, flywheel and load motor. Two data modes are selected from the dataset for experimental verification. The fault data sampling frequency is 64KHz. All test bearing models are 6203 rolling bearings. Faulty bearings are divided into artificial damage and accelerated life test damage. This section selects two groups of artificial damage fault data, one type of accelerated life damage data and one type of fault-free data. The artificial damage is inner ring fault and outer ring fault, respectively, denoted as F1 and F2. Accelerated life damage is a mixed fault of the inner ring and outer ring, denoted as F3, and no fault data is denoted as F4. The fault signal is divided into 250 samples with a sampling length of 1024. At the same time, the ratio of training data and test data is divided. First, 10 data samples are selected as training data, and the rest are used as tests. In order to avoid experimental chance, the same random experiment is repeated ten times, and the average value of the ten times is used as the final average recognition rate. Figure 2 It is intuitively demonstrated that the fault diagnosis classification accuracy improves with each increase in training samples. As can be seen from Table 1, the method of the present invention has good classification accuracy, and the best random average experimental accuracy reaches 99.25%, which also reveals that the method of the present invention is an effective fault diagnosis classification method in an unsupervised environment.

Claims

1. A cross-modal hyperbolic subspace fault diagnosis method includes the following steps: Step 1: Install sensors on the faulty equipment to collect data signals. Use different faulty bearings to collect different types of fault signals. Divide the collected fault signals according to the sampling length. Bearing fault data is selected from the Paderborn bearing dataset. Faulty bearings are categorized into artificial damage failure, accelerated life damage failure, and no failure. Artificial damage is caused by inner ring failure and outer ring failure, respectively. Accelerated life damage is a mixed failure of the inner and outer rings. Step 2: Extract the original data signal features from the time domain, frequency domain and time-frequency domain respectively, and construct a high-dimensional fault feature set X = [x1,…,x n ]∈R p×n and Y=[y1,…,y n ]∈R q×n , where p, q represent the sample dimensions of X, Y, n represents the number of samples, (x, y) is derived from the feature sample set Any pair of samples; Step 3: An unsupervised cross-modal hyperbolic subspace learning model is constructed by combining local correlation theory and hyperbolic space learning. The constructed model is as follows: max F T XQ XY Y T G s.t.F T XQ XX X T F=1 G T YQ YY Y T G=1 In this model, the samples are centered and recorded is the mean of the observed sample, F and G are the two sets of feature projection vectors found by X and Y, and F T and G T is the transpose of the feature projection vectors F and G, so that x'=F T X, Y'=G T The correlation between Y is maximized; Q in the unsupervised cross-modal hyperbolic subspace learning model XY =D XY -Q X °Q Y , Q XX =Q XX -Q X °Q X , Q YY =D YY -Q Y °Q Y , the symbol ° represents the operator of matrix calculation, and For the matrix D XY and D YY It is the same expression, D XY 、D YY and D XX Is a diagonal matrix of size n×n, the similarity matrix and The following description can be made: among(x i ,x j )=d(x i ,x j ); d(x i ,y j ) is the geodesic distance in the Poincare sphere model. The hyperbolic geometric model of complex networks uses the extended Poincare disk model to represent the hyperbolic space, which is expressed as follows: where x i and y j denote sample vectors i and j respectively; the Poincare disk model is a two-dimensional embodiment of the Poincare sphere model. The Poincare disk model is angle-preserving, that is, the Euclidean angle between hyperbolas in the model is equal to its hyperbolic value; the distance in the Poincare disk model is different from that in Euclidean space. The hyperbolic distance r starting from the center of the disk is h and Euclidean distance r e There is relationship; Step 4: Optimize and solve the model constructed in step 2 to obtain the cross-modal hyperbolic subspace projection matrix (F, G). The generalized eigenvalue equation of the cross-modal hyperbolic subspace is optimized and solved as follows: The generalized eigenvalue λ is the objective function value of the optimization problem across the modal hyperbolic subspace. After solving the above equation and obtaining the projection matrix (F, G), the high-dimensional fault data sample can be obtained according to F T x and G T y form for dimensionality reduction; In step 5, the cross-modal features of the fault data are obtained using the hyperbolic subspace projection matrix of step 3, and the classification results of the fault data are obtained using the KNN classifier.

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