Bearing Fault Diagnosis Method Based on Relative Rank Space Topology Preserving Projection

Abstract

This invention discloses a bearing fault diagnosis method based on relative rank granular space topology-preserving projection, which solves the problems of difficulty in global structure mining of fault data and distortion of local similarity measurement, and effectively improves the accuracy of fault diagnosis. The specific implementation process is as follows: (1) A global constraint graph of granules is formed by constructing a neighborhood granular module and a globally complementary rank local constraint graph is formed by constructing a relative rank distance module, and a relative rank granular topology-preserving projection model is formed by combining spatial learning-related theories; (2) The analytical solution of the granular topology projection direction is derived to obtain the projection matrix of the low-dimensional topology space; (3) Randomly selected fault test samples are directly obtained by topological space projection to obtain granular topology fault features with good discriminative power, and the granular topology fault features are input into the classifier to obtain the final bearing fault diagnosis result. Compared with the prior art, the bearing fault diagnosis method of this invention is more accurate and robust.

Description

Technical Field

[0001] This invention relates to a bearing fault diagnosis method based on relative rank-granular space topology-preserving projection, which belongs to the field of pattern recognition and fault diagnosis. Background Technology

[0002] Bearings, as an indispensable key component in modern mechanical design, support loads, reduce friction, ensure precise positioning of moving parts, reduce relative displacement between mechanical components, lower equipment wear, reduce heat generation, extend equipment lifespan, effectively support high-speed rotating or moving parts, and improve the overall rotational efficiency of mechanical systems. Due to the strong interrelationships between equipment, a bearing failure can trigger a chain reaction, causing significant equipment damage or even safety accidents. Therefore, efficient and accurate bearing fault diagnosis is a critical issue. Spatial learning, as a fault diagnosis method, has a strong theoretical foundation and practical feasibility. However, since the original fault data is usually high-dimensional data with redundant information and noise, this leads to difficulties in global structure mining and distortion of local similarity measurements. To address this, this invention utilizes spatial theory to construct a granular topology-preserving space through data granulation. Within this space, it constructs weighted representations between neighboring granular vectors and relative rank weighted representations for local complementarity, forming a relative rank granular topology-preserving projection model. This model can deeply mine the global data structure and solve the problem of local similarity measurement distortion using relative rank. Through theoretical derivation of the model, analytical solutions for the particle topology projection direction are obtained. Based on the particle topology projection direction, particle topology fault characteristics with good discriminative power can be directly obtained, which effectively improves the accuracy of fault diagnosis. Summary of the Invention

[0003] To address the challenges of global data structure mining and the distortion of local similarity measurements, this invention constructs a relative rank-preserving granular topology projection model based on spatial learning theory. Analytical solutions for the granular topology projection direction are derived theoretically, and granular topology fault features with good discriminative power are directly obtained based on the granular topology projection direction. The specific implementation steps of this invention are as follows:

[0004] 1. Bearing vibration signals are collected by sensors, and 17 time-domain features, 4 frequency-domain features, and 7 time-frequency-domain features are obtained through feature extraction. A bearing fault data sample set X = {x1, x2, ... x} is constructed. n}∈R M×n Where M represents the sample dimension, n represents the number of samples, and x i Let i represent the i-th sample, i = 1, 2, ..., n; divide the fault data into a training set (train) and a test set (test) according to the proportion, and randomize the test set data for each experiment.

[0005] 2. Construct neighborhood granular modules through data granulation.

[0006] The specific construction steps of the neighborhood granular module are as follows:

[0007] (2a) The high-dimensional dataset samples can be divided into C classes according to their categories, C = [C1, C2, ..., C2]. h ], where C h Let x represent the h-th class of samples; for sample x n M = {m1, m2, ... m} q}, m q For sample x n The q-th dimension of the data, and N samples of the same dimension, where N = {n1, n2, ..., n} p},n p Let N be the p-th data point;

[0008] (2b) To eliminate scale differences between different features and ensure that subsequent similarity measurements are not affected by different feature scales, the data is normalized. For a dataset n p ∈N, n p The dimension data of the dimension is m q ∈M, its normalized result is defined as:

[0009]

[0010] Where n i_max In dimension m q The maximum value among all the data, n i_min In dimension m q Find the minimum value of all the data below.

[0011] For those belonging to the same dimension m q Different data n i n j Its distance is defined as:

[0012] D m (n i ,n j )=|v(n i ,m q )-v(n j ,m q )|

[0013] Where v(n) i ,m q ) represents data n i In dimension m q The value after normalization.

[0014] For those belonging to the same dimension m q Different data ni n j If the neighborhood parameter is set to σ, then n is defined. i n j The discriminant function for determining whether something is a neighborhood is:

[0015]

[0016] in n i With n j Between in the same dimension m q They are neighboring regions. n i With n j Between in the same dimension m j Not adjacent.

[0017] For those belonging to the same dimension m q The following data n p Its neighborhood particles are defined as:

[0018] g q (n p )={l1,l2,…l n}

[0019] in That is, n i With all n j Adjacency relationships ∈ N.

[0020] For a high-dimensional dataset X = {x1, x2, ... x} n}∈R M×N x n In M = {m1, m2, ... m} q The domain granular vector of} is defined as:

[0021] G M (x n )=(g1(n p ),g2(n p ),…g q (n p )) T

[0022] Where g q (n p ) represents data n p In dimension m q The neighboring particles constructed above.

[0023] The neighborhood particle module contains neighborhood particles and neighborhood particle vectors. For sample data, neighborhood particles are constructed in the same dimension, and neighborhood particle vectors are constructed in the entire space.

[0024] 3. Construct a relative rank-granular topology-preserving projection model to obtain granular topology fault characteristics.

[0025] The specific construction steps of the relative rank-granular topology-preserving projection model are as follows:

[0026] (3a) Construction of the global constraint graph of granules in the granular space:

[0027] For different data x1 and x2, their neighborhood particle vectors are represented as follows:

[0028] G M (x1)=(g1(n1),g2(n1),…g q (n1)) T

[0029] G M (x2)=(g1(n2),g2(n2),…g q (n2)) T

[0030] The absolute distance between two neighboring particle vectors is defined as:

[0031]

[0032] Where |M|=q, |N|=p.

[0033] At this point, the global graph W of the granular spatial data is... Gij Defined as:

[0034]

[0035] When i = j, W Gij =0.

[0036] (3b) Construction of the lower-rank local constraint graph of relative rank distance:

[0037] First, sort the Euclidean distances between the samples. The sorted index matrix is ​​defined as follows:

[0038]

[0039] Where ED(x) i ,x k ) represents the sample x i The Euclidean distance between the k nearest samples, index(i,j) specifically means: the element closest to the i-th element at the j-th position is the element at index(i,j).

[0040] Based on the sorted index matrix index(i,j), its relative rank is defined as:

[0041]

[0042] Where RR(i,j) represents the relative rank of sample i in the ranking of sample j, it can be seen that this is the sum of the ranking differences between sample i and sample j.

[0043] Next, we construct our relative rank distance, which is defined as:

[0044] Where a = RR(i,j), b = RR(index(i,j), find(index(index(i,j),:)==i)), a+b is the sum of the ranking distances of the two samples, and the purpose of the denominator min(a,b) is to normalize the distance. RRD(i,j) calculates the ratio of the ranking distances between the two samples, which is used to measure the relative positional relationship between them.

[0045] For RRD(i,j), according to the k-nearest neighbor principle, only the distances of its first k nearest neighbors are retained, and the distances of the remaining neighbors are set to 0. This distance is defined as:

[0046]

[0047] To mitigate the impact of outliers on the overall sample, we define the local average distance of each sample point as:

[0048]

[0049] To illustrate the difference between the local average distance of each sample and the total number of samples, we define its relative average distance as:

[0050] rad(i) = ad - lad(i)

[0051] Where ad = median(lad(i)), representing the median. This calculation compares the local variance of a sample with the "standard" variance of the entire sample, yielding a bias that reflects the density difference between each sample and its neighborhood. If a sample has high local variance, the value of rad(i) will be small; conversely, if a sample is located in a sparse region, its local variance will be large.

[0052] At this point, the local constraint diagram W of the lower rank distance relative to the rank is... Lij Defined as:

[0053]

[0054] Where θ is the average of the sum of distances for all samples, adjusted to the distance scale for each sample, and α is a hyperparameter used to control the smoothness of the distance metric.

[0055] (3c) Construction of the relative rank-grained topology-preserving projection model:

[0056] Based on the construction of the granular spatial granular global constraint graph and the relative rank distance lower-rank local constraint graph, as well as related spatial learning theories, a relative rank granular topology-preserving projection model is constructed to address the difficulties in global data structure mining and the distortion of local similarity measurement.

[0057]

[0058] For any vector x, we have:

[0059]

[0060] The objective function, using the Laplace matrix, is transformed as follows:

[0061]

[0062] Based on constraint information, the relative rank-granular topology-preserving projection model is defined as:

[0063]

[0064] 4. The model is theoretically derived to obtain the analytical solution for the particle topological projection direction. By randomly sampling test set data, the original dataset is projected into a low-dimensional topological space according to the particle topological projection direction to directly obtain particle topological fault features with good discriminative power. Finally, a classifier is used for classification to obtain fault diagnosis results.

[0065] The method of the present invention has the following advantages:

[0066] (1) This invention can construct neighborhood particles in the same dimension and neighborhood particle vectors in different dimensions through data granulation, deeply search for potential connections between data, and form a particle global constraint graph based on this, fully mining the original space global potential structural information.

[0067] (2) This invention constructs a rank local constraint graph under relative rank distance, retains the nonlinear structure of granular data as a complement to global information, effectively solves the problem of local similarity measurement distortion, and constructs a relative rank granular topology-preserving projection model in combination with the granular global constraint graph, realizes global feature association and local pattern recognition, and significantly improves the robustness and accuracy of fault diagnosis.

[0068] (3) This invention obtains an analytical solution for the relative rank granular topology-preserving projection model through theoretical derivation. By randomly sampling test set data, granular topology fault features with good discriminative power are directly obtained in the projected subspace. By minimizing local information association, the inter-class separability under relative rank distance is enhanced; by maximizing the global difference in granular space, the interference between different categories in the granular space is reduced, thereby accurately obtaining the granular topology fault features of the test samples and achieving more accurate fault diagnosis. Attached Figure Description

[0069] The present invention will be further described below with reference to the accompanying drawings and examples.

[0070] Figure 1 This is a flowchart of the present invention, where r is the number of sensors and h is the number of fault categories.

[0071] Figure 2 It is the classification accuracy of a randomized experiment. Detailed Implementation

[0072] The specific implementation steps of this invention are as follows:

[0073] 1. Bearing vibration signals are collected by sensors, and 17 time-domain features, 4 frequency-domain features, and 7 time-frequency-domain features are obtained through feature extraction. A bearing fault data sample set X = {x1, x2, ... x} is constructed. n}∈R M×n Where M represents the sample dimension, n represents the number of samples, and x i Let i represent the i-th sample, i = 1, 2, ..., n; divide the fault data into a training set (train) and a test set (test) according to the proportion, and randomize the test set data for each experiment.

[0074] 2. Based on the relative rank-granular topology-preserving projection model, the model is as follows:

[0075]

[0076] The analytical solution of the model is transformed into a generalized eigenvalue problem, which is solved by constructing the Lagrange equation. The resulting column vector P = {p1, p2, ... p d} is X[(1-α)W L +αL G ]X T The d largest generalized eigenvectors are also the directions of the particle topological projection.

[0077] 3. A low-dimensional training sample feature set is obtained from the bearing fault data through topological space projection. Fault test samples are randomly extracted, and the extracted samples are then directly projected through topological space to obtain granular topological fault features with good discriminative power. Finally, a classifier is used for classification to obtain the fault diagnosis results.

[0078] The effectiveness of this invention was further verified through the following experiments:

[0079] Data from the Case Western Reserve bearing dataset at different rotational speeds with a sampling frequency of 12 kHz were selected for experimental verification. In this experiment, the selected bearing fault data had a sampling length of 1024, generating 110 samples per class. The experiment selected four different vibration data types: normal condition, inner ring fault, outer ring fault, and steel ball defect. Figure 2 The classification accuracy of bearing fault diagnosis in each random experiment is visually demonstrated. From Figure 2 As can be seen, the accuracy of the method of this invention increases with the increase of the number of training samples, and the stability is also good. Experimental results show that the method disclosed in this invention is an accurate and effective method for bearing fault diagnosis.

Claims

1. A bearing fault diagnosis method based on topologically preserving projection of relative rank-granular space, characterized in that, The method includes the following steps: (1) Bearing vibration signals were collected by sensors, and 17 time-domain features, 4 frequency-domain features and 7 time-frequency-domain features were obtained through feature extraction to construct a bearing fault data sample set. ,in To represent a sample, Indicates the sample dimension. This means that, for the number of samples in the same dimension, the fault data is divided into training sets proportionally. and test set And randomize the test set data for each experiment; (2) Construct neighborhood granular modules through data granulation; (3) Constructing a relative rank-granular topology-preserving projection model, characterized by the following steps: (3a) Combining the neighborhood particle module, construct a relative rank-preserving topology projection model: in yes of The largest generalized eigenvector is also the direction of the granular topological projection. It is the Laplacian matrix of the granular global constraint graph. , It is the degree matrix of the granular global constraint graph. It is a global sample weight representation based on the neighborhood granular module, after the sample data has been granulated. Its definition is: in Represents the absolute distance between two neighboring particle vectors, when hour, The absolute distance is defined as: in , , Represents a neighboring particle. Represents the neighborhood particle vector; (3b) It is a representation of the local positional relationship of samples under relative rank distance, which is complementary to the global sample weight representation. It is defined as follows: in It calculates the average of the sum of distances across all samples. These are hyperparameters that are set to control the smoothness of the distance metric. Its relative average distance is defined as: in , representing the median, The local average distance between sample points is defined as: in It is the nearest neighbor parameter. Defined as: in It calculates the ratio of the ranking distance between two samples, used to measure their relative positional relationship, and is defined as: in , , It is the sum of the ranking distances of the two samples, and the denominator is... The purpose is to standardize this distance. Represents the sample In the sample The relative rank in a sorting algorithm is defined as: in The specific meaning is: (related to the first) The element of the first The closest is the first One element, Defined as: in Representation and Sample Recent Euclidean distance between samples; (4) The model is theoretically derived to obtain the analytical solution of the particle topology projection direction. Based on the particle topology projection direction, the particle topology fault characteristics with good discriminativeness are directly obtained, and the classifier is used for classification to obtain the fault diagnosis results.

2. The fault diagnosis method for a bearing based on relative rank-granular space topological preservation projection as described in claim 1, characterized in that... Step (2) involves constructing neighborhood granular modules through data granulation, and the steps are as follows: (2a) High-dimensional dataset samples can be classified into categories. kind, ,in Indicates the first Class of samples, for samples , , For its dimension, , For the data points; (2b) For high-dimensional datasets , build In dimensions Neighborhood particle vector: in Representative data In dimensions The neighboring particles constructed above; For those belonging to the same dimension The following data Constructing neighborhood particles: in ,Right now With all Adjacency relationship; Indicates belonging to the same dimension Different data below , Define a discriminant function to determine whether it is a neighborhood. express and Between in the same dimension They are neighboring regions. express and Between in the same dimension Not adjacent; the discriminant function is: in For the set neighborhood parameters, Indicates belonging to the same dimension Different data below , The distance between them Defined as: in Representing data In dimensions The value after normalization, the normalization formula is: in Indicates in dimension The maximum value among all the data below. Indicates in dimension Find the minimum value of all the data below.

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