A Fault Diagnosis Method for Wind Turbine Bearings Based on Mahalanobis Distance Compensation Factor

Abstract

The present invention provides a fault diagnosis method for a fan bearing based on a Mahalanobis distance compensation factor to solve the problems of inaccurate fault feature extraction and low efficiency improvement existing in traditional fault feature extraction methods. It includes the following steps: S100, obtaining the time-domain vibration signal of the fan rolling bearing; S200, mapping the time-domain vibration signal to the graphical domain in a Mahalanobis distance weighted manner to construct a graph signal and obtaining the value range of the Mahalanobis distance compensation factor; S300, using an optimization algorithm to optimize the value range of the Mahalanobis distance compensation factor and obtaining the optimal solution of the Mahalanobis distance compensation factor; S400, using the optimal solution of the Mahalanobis distance compensation factor to correct the Mahalanobis distance and reconstructing the graph signal according to step S200; S500, extracting the bearing fault feature index according to the reconstructed graph signal to obtain each bearing fault feature index data set; S600, performing clustering analysis on the bearing fault feature index data set through a clustering algorithm to complete the bearing fault classification and identification diagnosis.

Description

Technical Field

[0001] The present invention relates to the field of mechanical fault detection, especially the field of fan fault detection, and specifically provides a fan bearing fault diagnosis method based on the Mahalanobis distance compensation factor. Background Art

[0002] Rolling bearings are common and widely used important components in fans. Their failures will directly affect the operating status of mechanical equipment. In the lightest case, it will cause shutdown and production suspension, and in the worst case, it will lead to accidents, resulting in losses of life and property. During the periodic rotation of rolling bearings, when local damages occur on the inner ring, outer ring or rolling elements of the bearings, periodic impact pulses will be generated at the parts in contact with the damages, and the fault signals of the bearings are contained in the vibration signals. Therefore, it is of great practical significance to study the vibration signals of bearings. When the bearings are working, their state signals are often submerged by noise due to factors such as load and working environment. At the same time, factors such as the coupling of the external environment, the excitation of the vibration source and the response greatly increase the difficulty of feature extraction. Therefore, how to efficiently extract fault impact signals is one of the keys to bearing fault diagnosis.

[0003] Traditional fault feature extraction methods, such as synchronous extraction transformation, empirical mode decomposition, local mean decomposition, homologous dual-channel signal-to-noise blind source separation method, etc. However, these traditional methods often lead to inaccurate fault feature extraction due to phenomena such as modal aliasing and endpoint effects, and sometimes it is also difficult to achieve the purpose of efficiently extracting fault feature indicators. As an emerging signal extraction method, graph signal processing technology has the characteristic of studying data structures from the perspective of networks, providing a new idea for signal processing, and has gradually attracted the attention of scholars at home and abroad.

[0004] Graph signal processing technology is derived and developed from algebraic spectral graph theory, aiming to study the relationship between points inside the graph, rather than simply studying image data sets and images themselves, which is essentially different from image processing technology. Currently, graph signal processing technology is mainly used in the fields of image processing, chemistry, machine learning, etc. The key to graph signal processing technology lies in the construction of graph signals. However, constructing graph signals using Euclidean distance has problems of dimension influence and is greatly affected by weighting coefficients. Summary of the Invention

[0005] In view of the above problems, the present invention provides a fan bearing fault diagnosis method based on the Mahalanobis distance compensation factor, which can solve the problems of inaccurate fault feature extraction and low efficiency improvement existing in traditional fault feature extraction methods.

[0006] Its technical solution is that a fan bearing fault diagnosis method based on the Mahalanobis distance compensation factor is characterized in that it includes the following steps:

[0007] S100, Obtain the time-domain vibration signal of the fan rolling bearing:

[0008] S200, Map the time-domain vibration signal of the fan rolling bearing to the graphical domain in a way of Mahalanobis distance weighting to construct a graph signal and estimate the value range of the Mahalanobis distance compensation factor;

[0009] S300, Optimize the value range of the Mahalanobis distance compensation factor using an optimization algorithm and obtain the optimal solution of the Mahalanobis distance compensation factor;

[0010] S400, Correct the Mahalanobis distance using the optimal solution of the Mahalanobis distance compensation factor and reconstruct the graph signal according to step S200;

[0011] S500, Extract the bearing fault feature indicators from the reconstructed graph signal to obtain each bearing fault feature indicator dataset;

[0012] S600, Perform clustering analysis on the bearing fault feature indicator dataset through a clustering algorithm to complete the bearing fault classification and identification diagnosis.

[0013] Further, step S200 is specifically as follows: Define the graph as an undirected two-dimensional data structure. For an undirected, weighted graph G=(V, E), V represents a finite set of vertices and nodes in the graph (where the element v i represents the i-th vertex, and the number of vertices N = |V|), and E represents a finite set of connecting edges between points in the graph (where the element e ij represents the connecting edge between the i-th vertex and the j-th vertex, and the number of edges N = |E|); Use the signal values of the sampling points in the time-domain vibration signal of the fan rolling bearing as the vertices and nodes of the graph, and connect each signal value one by one according to the time series to form a non-branching path to form a graph signal; For an undirected, weighted graph, the adjacency matrix W represents the weights of the edges in the graph, where the element w ij represents the weighted value of the connecting edge e i between vertex v j and vertex v ij ; If there is no edge connection between vertex v i and vertex v j , then w ij = 0. If there is no edge connection between vertex v i and vertex v j , but vertex v i and vertex v j are adjacent, then w ij = -1; Use the Mahalanobis distance for weighting, that is, obtain the adjacency matrix

[0014]

[0015] In Equation (1), x i is the i-th data point, x j is the j-th data point, ∑ is the covariance matrix between data points, and σ is the Mahalanobis distance compensation factor;

[0016] The degree matrix of the graph is obtained from the adjacency matrix, where the element value d ii on the diagonal is equal to the algebraic sum of all elements in the corresponding column of its adjacency matrix, representing the number of edges emitted by the corresponding vertex and node v i in the graph, that is

[0017]

[0018] In Equation (2), N is the total number of vertices and nodes in the graph;

[0019] Based on the adjacency matrix W and the degree matrix D, the Laplace matrix L can be obtained. Numerically, the graph Laplace matrix L is the difference between the degree matrix D and the adjacency matrix W, that is

[0020] L = D - W (3)

[0021] It can be seen from the definition that the Laplace matrix of the graph is a real symmetric matrix. Therefore, the Laplace matrix is orthogonally similar diagonalized, that is

[0022]

[0023] In Equation (4), U is the eigenvector of the Laplace matrix;

[0024] Using formula (1) combined with the limit method, the value range of the Mahalanobis distance compensation factor σ is estimated to be between 0 and 1.

[0025] Furthermore, the optimization algorithm adopts any one of the genetic algorithm, the particle swarm algorithm, and the iterative method; when any of the above algorithms is used to optimize the Mahalanobis distance compensation factor, the Mahalanobis distance compensation factor σ is selected as the optimization variable, the objective function is the evaluation function for measuring the metric level of the characteristic index, the variance of the characteristic index is selected as the evaluation function, and the constraint condition is the value range of the Mahalanobis distance compensation factor; the fitness function in the optimization algorithm is the variance of the characteristic index. Let the characteristic index be x(t) = [x1, x2,..., n , then the specific calculation formula of the fitness function fit is

[0026]

[0027] In the formula, n is the total number of samples, x i is the characteristic index of the i-th sample, is the average value of all sample characteristic indices.

[0028] Furthermore, the bearing fault characteristic indexes described in step S500 include the total variation of the graph signal, the second graph energy index, the maximum value of the eigenvalues, and the graph structure connectivity index;

[0029] Among them, the total variation of the graph signal is used to measure the overall smoothness of the graph signal, and its value is the algebraic sum of the differences in signal values on each edge. For the signal x ∈ R on the graph N×1 , its Laplace matrix can be described as:

[0030]

[0031] In formula (6), N is the total number of signal vertices and nodes on the graph, and x i is the signal value of the i-th point;

[0032] The Laplace matrix can reflect the local smoothness of the graph. Summing up the local smoothness of all points on the graph, the total variation of the graph signal is obtained, that is

[0033]

[0034] In formula (7), e ij represents the connecting edge between the i-th vertex and the j-th vertex;

[0035] Let the eigenvalue diagonal matrix of the Laplace matrix be diag[λ1 λ2... λ N , then the Second Mohar index is defined as:

[0036]

[0037] The maximum value of the eigenvalues is:

[0038] ML = max(diag[λ1 λ2... λ N ) (9)

[0039] The graph structure connectivity index is:

[0040]

[0041] In formula (8), N is the total number of vertices and nodes in the graph.

[0042] Furthermore, the clustering algorithm in step S600 adopts any one of the K-median clustering algorithm, support vector machine, Gaussian process (GP) model, DBSCAN (Density-Based Spatial Clustering of Applications with Noise) density-based clustering algorithm, and machine learning.

[0043] The beneficial effects of the present invention are as follows: It adopts a graph signal processing method based on the Mahalanobis distance compensation factor. Compared with the fault feature extraction method in the time domain, this method can effectively extract the set of feature indicators characterizing the states of different fan rolling bearings and can accurately classify the fan rolling bearings in different states. After optimizing the Mahalanobis distance compensation factor by using the genetic algorithm, or the particle swarm algorithm or the iterative method and correcting the graph signal constructed based on the Mahalanobis distance, the graph signal can have better recognition, so that the extracted bearing fault feature indicators have a higher measurement level, thus further improving the accuracy of bearing fault diagnosis and recognition. And using the clustering algorithm can quickly and accurately classify the fault feature indicators, thereby greatly improving the efficiency of bearing fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is the flowchart of the fan bearing fault diagnosis when the genetic algorithm is used for the optimization algorithm in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0045] A fan bearing fault diagnosis method based on the Mahalanobis distance compensation factor according to the present invention is characterized in that it includes the following steps:

[0046] S100, using an acceleration sensor to obtain the time-domain vibration signal of the fan rolling bearing; in practical applications, other sensors may also be used to obtain it.

[0047] S200, mapping the time-domain vibration signal of the fan rolling bearing to the graph domain in a Mahalanobis distance weighted manner to construct a graph signal and estimating the value range of the Mahalanobis distance compensation factor.

[0048] S300, using an optimization algorithm to optimize the value range of the Mahalanobis distance compensation factor and obtaining the optimal solution of the Mahalanobis distance compensation factor.

[0049] S400, using the optimal solution of the Mahalanobis distance compensation factor to correct the Mahalanobis distance and reconstructing the graph signal according to step S200.

[0050] S500, extracting bearing fault feature indicators according to the reconstructed graph signal to obtain each bearing fault feature indicator data set.

[0051] S600, performing clustering analysis on the bearing fault feature indicator data set through a clustering algorithm to complete bearing fault classification and recognition diagnosis.

[0052] Among them, step S200 is specifically: defining the graph as an undirected two-dimensional data structure. For an undirected, weighted graph G=(V, E), V represents a finite set of vertices and nodes in the graph (where the element v irepresents the \(i\)-th vertex, and the number of vertices \(N = |V|\). \(E\) represents a finite set of connecting edges between points in the graph (where the element \(e\) ij represents the connecting edge between the \(i\)-th vertex and the \(j\)-th vertex, and the number of edges \(N = |E|\); the signal values of the sampling points in the time-domain vibration signal of the fan rolling bearing are used as the vertices and nodes of the graph, and each signal value is connected one by one according to the time series to form a non-branching path to form a graph signal; for an undirected, weighted graph, the adjacency matrix \(W\) represents the weights of the edges in the graph, where the element \(w\) ij represents vertex \(v\) i and vertex \(v\) j the weighted value of the connecting edge \(e\) ij between them; if there is no edge connection between vertex \(v\) i and vertex \(v\) j then \(w\) ij = 0, if there is no edge connection between vertex \(v\) i and vertex \(v\) j but vertex \(v\) i is adjacent to vertex \(v\) j then \(w\) ij = -1; weighted by the Mahalanobis distance, that is, the adjacency matrix

[0053]

[0054] In formula (1), \(x\) i is the \(i\)-th data point, \(x\) j is the \(j\)-th data point, \(\sum\) is the covariance matrix between data points, and \(\sigma\) is the Mahalanobis distance compensation factor;

[0055] The degree matrix of the graph is obtained according to the adjacency matrix, where the element value \(d\) ii on the diagonal is equal to the algebraic sum of all elements in the corresponding column of its adjacency matrix, representing the number of edges emitted by the corresponding vertex and node \(v\) i in the graph, that is

[0056]

[0057] In formula (2), \(N\) is the total number of vertices and nodes in the graph;

[0058] Based on the adjacency matrix \(W\) and the degree matrix \(D\), the Laplace matrix \(L\) can be obtained. Numerically, the graph Laplace matrix \(L\) is the difference between the degree matrix \(D\) and the adjacency matrix \(W\), that is

[0059] \(L = D - W\) (3)

[0060] It can be known from the definition that the Laplace matrix of the graph is a real symmetric matrix, so the Laplace matrix is orthogonally similar diagonalized, that is

[0061]

[0062] In Equation (4), U is the eigenvector of the Laplace matrix.

[0063] Using formula (1) combined with the limit algorithm, the value range of the Mahalanobis distance compensation factor σ is estimated to be between 0 and 1.

[0064] In the process of establishing graph signals using Mahalanobis distance weighting, the vibration signal value of the bearing is much smaller than the node and vertex serial numbers of the graph. This causes the weight value of the edge in the graph signal to approach the node and vertex serial numbers of the graph, making the distinguishability of the graph signal structures in different states of the gear small. Therefore, in this method, a distance compensation factor is used to correct the Mahalanobis distance; thus, selecting an appropriate distance compensation factor is the key to establishing graph signals.

[0065] The optimization algorithm in step S300 adopts any one of the genetic algorithm, particle swarm algorithm, and iterative method; when optimizing the Mahalanobis distance compensation factor using any of the above algorithms, the Mahalanobis distance compensation factor σ is selected as the optimization variable, the objective function is the evaluation function for measuring the metric level of the characteristic index, the variance of the characteristic index is selected as the evaluation function, and the constraint condition is the value range of the Mahalanobis distance compensation factor; the fitness function in the optimization algorithm is the variance of the characteristic index. Let the characteristic index be x(t) = [x1, x2,..., x n , then the specific calculation formula of the fitness function fit is

[0066]

[0067] In the formula, n is the total number of samples, x i is the characteristic index of the i-th sample, is the average value of the characteristic indices of all samples.

[0068] The bearing fault characteristic indices in step S500 include the total variation of the graph signal, the second graph energy index, the maximum value of the eigenvalues, and the graph structure connectivity index;

[0069] Among them, the total variation of the graph signal is used to measure the overall smoothness of the graph signal, and its value is the algebraic sum of the differences in the signal values on each edge. For the signal x ∈ R N×1 on the graph, its Laplace matrix can be described as:

[0070]

[0071] In Equation (6), N is the total number of vertices and nodes of the signal on the graph, and x i is the signal value of the i-th point;

[0072] The Laplace matrix can reflect the local smoothness of a graph. By summing up the local smoothness of all points on the graph, the total variation of the graph signal is obtained, that is

[0073]

[0074] In formula (7), e ij represents the connecting edge between the i-th vertex and the j-th vertex;

[0075] Let the eigenvalue diagonal matrix of the Laplace matrix be diag[λ1λ2...λ N , then the Second Mohar index is defined as:

[0076]

[0077] The maximum value of the eigenvalue is:

[0078] ML = max(diag[λ1λ2...λ N ) (9)

[0079] The graph structure connectivity index is:

[0080]

[0081] In formula (8), N is the total number of vertices and nodes in the graph.

[0082] Among them, the clustering algorithm in step S600 adopts any one of the K-median clustering algorithm, support vector machine, Gaussian process (GP) model, DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering algorithm, and machine learning. Among them, the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering algorithm is a density-based clustering algorithm; the above clustering algorithms are all existing algorithms in the field.

[0083] In the above method of the present invention, the genetic algorithm, particle swarm algorithm, iterative method, and K-median clustering algorithm in the optimization algorithm are all existing conventional algorithms in the field.

[0084] The above has described the specific implementation of the present invention in detail, but the content is only a preferred implementation of the present invention and cannot be considered as limiting the scope of implementation of the present invention. Any equivalent changes and improvements made according to the scope of the application of the present invention should still fall within the scope covered by the patent of the present invention.

Claims

1. A fault diagnosis method for a fan bearing based on a Mahalanobis distance compensation factor, characterized in that: It includes the following steps. S100: Obtain the time-domain vibration signal of the fan rolling bearing. S200: Map the time-domain vibration signal of the fan rolling bearing to the graphic domain in a way of Mahalanobis distance weighting to construct a graph signal and estimate the value range of the Mahalanobis distance compensation factor. S300: Use an optimization algorithm to optimize the value range of the Mahalanobis distance compensation factor and obtain the optimal solution of the Mahalanobis distance compensation factor. S400: Use the optimal solution of the Mahalanobis distance compensation factor to correct the Mahalanobis distance and reconstruct the graph signal according to step S200. S500: Extract the bearing fault feature indexes according to the reconstructed graph signal to obtain each bearing fault feature index data set. S600: Perform clustering analysis on the bearing fault feature index data set through a clustering algorithm to complete the bearing fault classification recognition and diagnosis. Step S200 is specifically as follows: Define the graph as an undirected two-dimensional data structure. For an undirected, weighted graph G = (V, E), V represents a finite set of vertices and nodes in the graph, and the element v in this finite set i represents the i-th vertex, and the number of vertices N = |V|. E represents a finite set of connecting edges between points in the graph, and the element e in this finite set ij represents the connecting edge between the i-th vertex and the j-th vertex, and the number of connecting edges N = |E|; Use the signal values of the sampling points in the time-domain vibration signal of the fan rolling bearing as the vertices and nodes of the graph, and connect each signal value one by one according to the time series to form a non-branching path to form a graph signal; For an undirected, weighted graph, the adjacency matrix W represents the weights of the edges in the graph, where the element w ij represents the vertex v i and the vertex v j The weighted value of the connecting edge e ij between them; If there is no edge connection between the vertex v i and the vertex v j , then w ij = 0. If there is no edge connection between the vertex v i and the vertex v j , but the vertex v i and the vertex v j are adjacent, then w ij = -1; Use the Mahalanobis distance for weighting, that is, obtain the adjacency matrix In Equation (1), x i is the i-th data point, x j is the j-th data point, Σ is the covariance matrix between the data points, and σ is the Mahalanobis distance compensation factor; Obtain the degree matrix of a graph according to the adjacency matrix, where the element value d on the diagonal ii is equal to the algebraic sum of all elements in the corresponding column i of its adjacency matrix, representing the corresponding vertex and node v in the graph i The number of edges emitted, that is In formula (2), N is the total number of vertices and nodes of the graph. Based on the adjacency matrix W and the degree matrix D, the Laplace matrix L of the graph is obtained. Numerically, the Laplace matrix L of the graph is the difference between the degree matrix D and the adjacency matrix W, that is L = D - W (3) It can be known through definition that the Laplace matrix of the graph is a real symmetric matrix. Therefore, orthogonal similarity diagonalization is performed on the Laplace matrix, that is In formula (4), U is the eigenvector of the Laplace matrix, and λ1…λ N are the eigenvalues of the Laplace matrix; Using formula (1) combined with the limit method, the value range of the Mahalanobis distance compensation factor σ is estimated to be between 0 and 1.

2. The method for diagnosing faults of a fan bearing based on a Mahalanobis distance compensation factor according to claim 1, wherein: The optimization algorithm adopts any one of the genetic algorithm, the particle swarm algorithm, and the iterative method; when optimizing the Mahalanobis distance compensation factor using any of the above algorithms, the Mahalanobis distance compensation factor σ is selected as the optimization variable, the objective function is an evaluation function for measuring the metric level of the characteristic index, the variance of the characteristic index is selected as the evaluation function, and the constraint condition is the value range of the Mahalanobis distance compensation factor; the fitness function in the optimization algorithm is the variance of the characteristic index. Let the characteristic index be x(t) = [x1, x2, …, x n , then the specific calculation formula of the fitness function fit is In the formula, n is the total number of samples, and x i is the characteristic index of the i-th sample, and is the average value of the characteristic indices of all samples.

3. A fault diagnosis method for a fan bearing based on a Mahalanobis distance compensation factor according to claim 1, characterized in that: The bearing fault feature indexes described in step S500 include the total variation of the graph signal, the second graph energy index, the maximum value of the eigenvalues, and the graph structure connectivity index. Among them, the total variation of the graph signal is used to measure the overall smoothness of the graph signal, and its value is the algebraic sum of the differences of the signal values on each edge. For the signal x ∈ R on the graph N×1 , its Laplace matrix is described as: In formula (6), N is the total number of signal vertices and nodes on the graph, and x i is the signal value of the i-th point; The Laplace matrix can reflect the local smoothness of the graph. Summing up the local smoothness of all points on the graph, the total variation of the graph signal is obtained, that is In formula (7), e ij represents the connecting edge between the i-th vertex and the j-th vertex; Let the diagonal matrix of the eigenvalues of the Laplace matrix be diag[λ1λ2…λ N , then the Second Mohar index is defined as: The maximum value of the eigenvalues is: ML = max(diag[λ1λ2...λ N ) (9) The graph structure connectivity index is: In formula (8), N is the total number of vertices and nodes in the graph.

4. A fault diagnosis method for a fan bearing based on a Mahalanobis distance compensation factor according to claim 1, characterized in that: The clustering algorithm in step S600 adopts any one of the K-median clustering algorithm, support vector machine, Gaussian process model, DBSCAN clustering algorithm (density-based clustering algorithm), and machine learning.

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