CN115235769A - Fan bearing fault diagnosis method based on Mahalanobis distance compensation factor - Google Patents

Abstract

The invention provides a method for diagnosing a fan bearing fault based on a Mahalanobis distance compensation factor, which aims to solve the problems of inaccurate fault feature extraction and low efficiency improvement of the traditional fault feature extraction method. The method comprises the following steps of S100, acquiring a time domain vibration signal of a fan rolling bearing: s200, mapping the time domain vibration signal to a graph domain by adopting a Mahalanobis distance weighting mode to construct a graph signal and obtain a value range of a Mahalanobis distance compensation factor; s300, optimizing the value range of the Mahalanobis distance compensation factor by adopting an optimization algorithm, and obtaining the optimal solution of the Mahalanobis distance compensation factor; s400, correcting the Mahalanobis distance by using the optimal solution of the Mahalanobis distance compensation factor, and reconstructing a picture signal according to the step S200; s500, extracting bearing fault characteristic indexes according to the reconstructed graph signals to obtain a bearing fault characteristic index data set; s600, carrying out clustering analysis on the bearing fault characteristic index data set through a clustering algorithm to finish bearing fault classification, identification and diagnosis.

Description

A fault diagnosis method for fan bearings based on Mahalanobis distance compensation factor

technical field

The invention relates to the field of mechanical fault detection, in particular to the field of fan fault detection, in particular to a fan bearing fault diagnosis method based on a Mahalanobis distance compensation factor.

Background technique

Rolling bearings are a common and widely used important component in fans, and their failures will directly affect the operation of mechanical equipment, ranging from shutdown to production, or accidents, resulting in loss of life and property. During the periodic rotation of the rolling bearing, when the inner ring, outer ring or rolling element of the bearing is partially damaged, the parts in contact with the damage will generate periodic shock pulses, and the fault signal of the bearing is contained in the vibration signal. Therefore, it is of great practical significance to study the vibration signal of the bearing. The bearing is affected by factors such as load and working environment during operation, and its state signal is often submerged by noise. At the same time, factors such as the external environment, excitation and response of the vibration source are coupled with each other, which greatly increases the difficulty of feature extraction. Therefore, how to efficiently extract the fault impact signal is one of the keys to bearing fault diagnosis.

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., but these traditional methods often occur due to modal aliasing, end-point effects and other phenomena This leads to the problem of inaccurate extraction of fault features, and sometimes it is difficult to achieve the purpose of efficiently extracting fault feature indicators; as an emerging signal extraction method, graph signal processing technology has the characteristics of studying data structure from the perspective of the network, providing signal processing A new way of thinking has gradually attracted the attention of scholars at home and abroad.

Graph signal processing technology, derived from the algebraic spectrogram theory, aims to study the relationship between points and points in the graph, rather than simply studying the image data set and the image itself, which is fundamentally different from image processing technology. At present, graph signal processing technology is mainly used in image processing, chemistry, machine learning and other fields. The key of graph signal processing technology lies in the construction of graph signal, but the use of Euclidean distance to construct graph signal has the problem of dimensional influence, and the influence of weight coefficient is greater.

SUMMARY OF THE INVENTION

Aiming at the above problems, the present invention provides a fault diagnosis method for fan bearings based on Mahalanobis distance compensation factor, which can solve the problems of inaccurate fault feature extraction and low efficiency improvement in traditional fault feature extraction methods.

The technical solution is, 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, using the Mahalanobis distance weighting method to map the time domain vibration signal of the fan rolling bearing to the graphic domain to construct the formed graphic signal and estimate 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 obtain an optimal solution of the Mahalanobis distance compensation factor;

S400, correcting the Mahalanobis distance by using the optimal solution of the Mahalanobis distance compensation factor, and reconstructing the graph signal according to step S200;

S500, extracting the bearing fault characteristic index according to the reconstructed graph signal, and obtaining a data set of each bearing fault characteristic index;

S600: Perform cluster analysis on the bearing fault characteristic index data set through a clustering algorithm, so as to complete the bearing fault classification, identification and diagnosis.

Further, step S200 is specifically as follows: 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 _i Represents the i-th vertex, the number of vertices N=|V|), E represents the finite set of connecting edges between points in the graph (where element e _ij represents the i-th vertex and the j-th vertex The connecting edges between the vertices, 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 taken as the vertices and nodes of the graph, and the signal values are connected one by one according to the time series to form A path without branches forms a graph signal; for an undirected, weighted graph, the adjacency matrix W represents the weights of the edges in the graph, and the element w _ij represents the weighted value of the connecting edge e _ij between the vertex v _i and the vertex v _j ; 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 Mahalanobis distance for weighting, that is, get the adjacency matrix

In formula (1), x _i is the i-th data point, x _j is the j-th data point, ∑ is the covariance matrix between the data points, and σ is the Mahalanobis distance compensation factor;

The degree matrix of the graph is obtained according to the adjacency matrix, wherein 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, which represents the number of edges emitted by the corresponding vertices and nodes _vi in the graph, 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 can be obtained. The graph Laplace matrix L is numerically the difference between the degree matrix D and the adjacency matrix W, that is,

L=D-W (3)

It can be seen from the definition that the Laplace matrix of the graph is a real symmetric matrix, so the orthogonal similar diagonalization of the Laplace matrix is performed, that is,

In formula (4), U is the eigenvector of Laplace matrix;

The value range of the Mahalanobis distance compensation factor σ is estimated from formula (1) combined with the limit method, which ranges from 0 to 1.

Further, the optimization algorithm adopts any one of genetic algorithm, particle swarm algorithm, and iterative method; when using any of the above algorithms to optimize the Mahalanobis distance compensation factor, the Mahalanobis distance compensation factor σ is selected as the optimization variable. , the objective function is an evaluation function that measures the measurement level of the feature index, the variance of the feature index is selected as the evaluation function, and the constraints are the value range of the Mahalanobis distance compensation factor; the fitness function in the optimization algorithm is the variance of the feature index , set the feature index to be x(t)=[x ₁ , x ₂ ,..., x _n ], then the specific calculation formula of the fitness function fit is:

为所有样本特征指标的平均值。In the formula, n is the total number of samples, x _i is the characteristic index of the ith sample,

is the average value of all sample feature indicators.

Further, the bearing fault characteristic index in step S500 includes the total variation of the graph signal, the second graph energy index, the maximum value of the characteristic value, 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 ^N×1 on the graph, its Laplace A matrix can be 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 ith point;

The Laplace matrix can reflect the local smoothness of the graph, and the local smoothness of all points on the graph is summed to obtain the total variation of the graph signal, that is

In formula (7), e _ij represents the connecting edge between the ith vertex and the jth vertex;

Let the eigenvalue diagonal matrix of the Laplace matrix be diag[λ ₁ λ ₂ ...λ _N ], then the Second Mohar index is defined as:

The maximum value of the eigenvalue is:

ML=max(diag[λ ₁ λ ₂ ...λ _N ]) (9)

The graph structure connectivity index is:

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

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

The beneficial effect of the present invention is that: it adopts the graph signal processing method based on Mahalanobis distance compensation factor, and compared with the fault feature extraction method in the time domain, the method can effectively extract the feature index set representing the state of different fan rolling bearings, And it can accurately classify the fan rolling bearings in different states; after using the genetic algorithm, particle swarm algorithm or iterative method to optimize the Mahalanobis distance compensation factor, the graph signal constructed based on the Mahalanobis distance is corrected, which can make the graph signal It has better identification, so that the extracted bearing fault characteristic index has a higher measurement level, so it can further improve the accuracy of bearing fault diagnosis and identification; and the clustering algorithm can quickly and accurately classify the fault characteristic index, This greatly improves the efficiency of bearing fault diagnosis.

Description of drawings

FIG. 1 is a flowchart of the fault diagnosis of the fan bearing in which the optimization algorithm adopts the genetic algorithm in the present invention.

Detailed ways

A fault diagnosis method for a fan bearing based on the Mahalanobis distance compensation factor of the present invention is characterized in that: it comprises the following steps:

S100, the acceleration sensor is used to obtain the time-domain vibration signal of the fan rolling bearing; in practical applications, other sensors may also be used to obtain it;

S200, using the Mahalanobis distance weighting method to map the time domain vibration signal of the fan rolling bearing to the graphic domain to construct the formed graphic signal and estimate 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 obtain an optimal solution of the Mahalanobis distance compensation factor;

S400, correcting the Mahalanobis distance by using the optimal solution of the Mahalanobis distance compensation factor, and reconstructing the graph signal according to step S200;

S500, extracting the bearing fault characteristic index according to the reconstructed graph signal, and obtaining a data set of each bearing fault characteristic index;

S600: Perform cluster analysis on the bearing fault characteristic index data set through a clustering algorithm, so as to complete the bearing fault classification, identification and diagnosis.

Wherein, 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 (wherein element v _i represents is the i-th vertex, the number of vertices N=|V|), E represents the finite set of connecting edges between points in the graph (where element e _ij represents the i-th vertex and the j-th vertex Connecting edges between vertices, 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 taken as the vertices and nodes of the graph, and the signal values are connected one by one according to the time series to form a line A path without branches forms a graph signal; for an undirected, weighted graph, the adjacency matrix W represents the weights of the edges in the graph, and the element w _ij represents the weighted value of the connecting edge e _ij between the vertex v _i and the vertex v _j ; 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 Mahalanobis distance for weighting, that is, get the adjacency matrix

In formula (1), x _i is the i-th data point, x _j is the j-th data point, ∑ is the covariance matrix between the data points, and σ is the Mahalanobis distance compensation factor;

The degree matrix of the graph is obtained according to the adjacency matrix, wherein 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, which represents the number of edges emitted by the corresponding vertices and nodes _vi in the graph, 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 can be obtained. The graph Laplace matrix L is numerically the difference between the degree matrix D and the adjacency matrix W, that is

L=D-W (3)

It can be seen from the definition that the Laplace matrix of the graph is a real symmetric matrix, so the orthogonal similar diagonalization of the Laplace matrix is performed, that is,

In formula (4), U is the eigenvector of the Laplace matrix.

The value range of the Mahalanobis distance compensation factor σ is estimated from formula (1) and the limit algorithm.

In the process of using Mahalanobis distance weighting to build a graph signal, the vibration signal value of the bearing is much smaller than the value of the node and vertex serial numbers of the graph, which causes the weights of the edges in the graph signal to approach the node and vertex serial numbers of the graph. Therefore, in this method, the distance compensation factor is used to correct the Mahalanobis distance; therefore, choosing an appropriate distance compensation factor is the key to building a graph signal.

The optimization algorithm of step S300 adopts any one of genetic algorithm, particle swarm algorithm, and 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, and the target The functions are all evaluation functions to measure the measurement level of the feature index, and the variance of the feature index is selected as the evaluation function, and the constraints are the value range of the Mahalanobis distance compensation factor; the fitness function in the optimization algorithm is the variance of the feature index, set The characteristic index is x(t)=[x ₁ , x ₂ ,..., x _n ], then the specific calculation formula of the fitness function fit is:

为所有样本特征指标的平均值。In the formula, n is the total number of samples, x _i is the characteristic index of the ith sample,

is the average value of all sample feature indicators.

In step S500, the bearing fault characteristic index includes the total variation of the graph signal, the second graph energy index, the maximum value of the eigenvalue, 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 ^N×1 on the graph, its Laplace matrix can be 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 ith point;

The Laplace matrix can reflect the local smoothness of the graph, and the local smoothness of all points on the graph is summed to obtain the total variation of the graph signal, that is

In formula (7), e _ij represents the connecting edge between the ith vertex and the jth vertex;

Let the eigenvalue diagonal matrix of the Laplace matrix be diag[λ ₁ λ ₂ ...λ _N ], then the Second Mohar index is defined as:

The maximum value of the eigenvalue is:

ML=max(diag[λ ₁ λ ₂ ...λ _N ]) (9)

The graph structure connectivity index is:

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

Wherein, the clustering algorithm in step S600 adopts any one of 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, The DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering algorithm is a density-based clustering algorithm; the above-mentioned clustering algorithms are all existing algorithms in the field.

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

The specific implementation of the present invention has been described in detail above, but the content is only a preferred embodiment of the present invention, and cannot be considered to limit the implementation scope of the present invention. All equivalent changes and improvements made according to the scope of the application of the invention should still fall within the scope of the patent of the present invention.

Claims (5)

1. a fan bearing fault diagnosis method based on Mahalanobis distance compensation factor, is characterized in that: it comprises the following steps, S100, obtain the time-domain vibration signal of the fan rolling bearing: S200, using the Mahalanobis distance weighting method to map the time domain vibration signal of the fan rolling bearing to the graphic domain to construct the formed graphic signal and estimate 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 obtain an optimal solution of the Mahalanobis distance compensation factor; S400, correcting the Mahalanobis distance by using the optimal solution of the Mahalanobis distance compensation factor, and reconstructing the graph signal according to step S200; S500, extracting the bearing fault characteristic index according to the reconstructed graph signal, and obtaining a data set of each bearing fault characteristic index; S600: Perform cluster analysis on the bearing fault characteristic index data set through a clustering algorithm, so as to complete the bearing fault classification, identification and diagnosis. 2. The method for diagnosing fan bearing faults based on Mahalanobis distance compensation factor according to claim 1, wherein step S200 is specifically: the definition graph is an undirected two-dimensional data structure, and for an undirected, weighted graph G=(V, E), V represents a finite set of vertices and nodes in the graph (where element vi represents the _i -th vertex, and the number of vertices is N=|V|), E represents the point in the graph A finite set of connecting edges with points (where the element e _ij represents the connecting edge between the ith vertex and the jth vertex, the number of edges N=|E|); the time domain vibration of the fan rolling bearing The signal values of the sampling points in the signal are used as the vertices and nodes of the graph, and the signal values are connected one by one according to the time series to form a path without branches to form a graph signal; for undirected and weighted graphs, the adjacency matrix W represents the edge of the graph. Weight, where element w _ij represents the weighted value of the connecting edge e _ij between vertex v _i and vertex v _j ; if there is no edge connection between vertex v _i and vertex v _j , then w _ij =0, if vertex v _i There is no edge connection with vertex v _j , but vertex v _i and vertex v _j are adjacent, then w _ij =-1; use Mahalanobis distance for weighting, that is, get the adjacency matrix

In formula (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; The degree matrix of the graph is obtained according to the adjacency matrix, wherein 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, which represents the number of edges emitted by the corresponding vertices and nodes _vi in the graph, 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 can be obtained. The graph Laplace matrix L is numerically the difference between the degree matrix D and the adjacency matrix W, that is, L=D-W (3) It can be seen from the definition that the Laplace matrix of the graph is a real symmetric matrix, so the orthogonal similar diagonalization of the Laplace matrix is performed, that is,

In formula (4), U is the eigenvector of Laplace matrix; The value range of the Mahalanobis distance compensation factor σ is estimated from formula (1) combined with the limit method. 3. A kind of fan bearing fault diagnosis method based on Mahalanobis distance compensation factor according to claim 1, is characterized in that: described optimization algorithm adopts any one in genetic algorithm, particle swarm algorithm, iterative method; When any of the above algorithms optimize the Mahalanobis distance compensation factor, the Mahalanobis distance compensation factor σ is selected as the optimization variable, the objective function is an evaluation function to measure the measurement level of the feature index, and the variance of the feature index is selected as the evaluation function. The conditions are the value range of the Mahalanobis distance compensation factor; the fitness function in the optimization algorithm is the variance of the characteristic index, and if the characteristic index is x(t)=[x ₁ ,x ₂ ,...,x _n ], then the adaptation The specific calculation formula of the degree function fit is:

In the formula, n is the total number of samples, x _i is the characteristic index of the ith sample,

is the average value of all sample feature indicators. 4 . The method for diagnosing fan bearing faults based on Mahalanobis distance compensation factor according to claim 1 , wherein the characteristic indicators of bearing faults in step S500 include the total variation of the map signal, the second map energy index , the maximum value of 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 ^N×1 on the graph, its Laplace A matrix can be 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 ith point; The Laplace matrix can reflect the local smoothness of the graph, and the local smoothness of all points on the graph is summed to obtain the total variation of the graph signal, that is

In formula (7), e _ij represents the connecting edge between the ith vertex and the jth vertex; Let the eigenvalue diagonal matrix of the Laplace matrix be diag[λ ₁ λ ₂ …λ _N ], then the Second Mohar index is defined as:

The maximum value of the eigenvalue is: ML=max(diag[λ ₁ λ ₂ ...λ _N ]) (9) The graph structure connectivity index is:

In formula (8), N is the total number of vertices and nodes in the graph. 5. The fault diagnosis method for fan bearings based on Mahalanobis distance compensation factor according to claim 1, characterized in that: the clustering algorithm in the step S600 adopts K-median clustering algorithm, support vector machine, Gaussian Any of the process (GP) model, DBSCAN (Density-Based Spatial Clustering of Applications with Noise) density-based clustering algorithm, and machine learning.

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