An Adaptive Sparse Graph Learning Bearing Life Prediction Method Based on a Digital Twin Dictionary

Abstract

The present invention discloses an adaptive sparse graph learning bearing life prediction method based on a digital twin dictionary. This method establishes an extended exponential model and a linear piecewise model, generates a digital twin dictionary covering various degradation behaviors, designs a new graph learning optimization objective function, introduces a sparse regularization method to reduce the model complexity and parameter sensitivity, adaptively obtains the accurate topological structure of the data, and realizes the accurate prediction of the remaining service life based on the constructed digital twin dictionary and adaptive sparse graph learning.

Description

Technical Field

[0001] The present invention belongs to the technical fields of mechanical fault prediction and health management, and signal processing, and relates to a bearing life prediction method based on adaptive sparse graph learning using a digital twin dictionary. Background Art

[0002] Supporting and transmission parts of mechanical equipment such as bearings, gears, and rotating shafts are key components. Once these components fail, the mechanical equipment may not work properly at best, or serious safety accidents may occur at worst, both of which will cause huge losses to production and life. If faults can be detected as early as possible, or even the occurrence of faults can be predicted, it has more practical application value. Since rolling bearings are widely used in rotating machinery and are prone to failure, more and more attention has been paid to the research on predicting the remaining service life of rolling bearings.

[0003] Current methods for predicting the remaining service life mainly fall into two categories, namely model-based methods and data-driven methods. Model-based methods have a common feature that a complex degradation model needs to be established in advance, and there are many model parameters to be estimated. Since these methods are based on statistical principles, they are easily affected by abnormal behaviors in the degradation data, resulting in biased parameter estimation. Data-driven methods have the ability to process massive data, but they also have obvious disadvantages, that is, a large amount of training data is required. In practice, it is time-consuming and expensive to obtain a large amount of performance degradation data of rolling bearings throughout their life cycle. In addition, it is generally not allowed for mechanical equipment to fail, so it is even more difficult to obtain data on running to failure. In addition, deep learning models usually also face problems of training and parameter tuning, which are often time-consuming and have poor model generalization ability.

[0004] In summary, there are two problems to be solved in predicting the remaining service life of rolling bearings. One is how to obtain a large amount of training data covering more degradation behaviors to improve the prediction accuracy; the other is to propose an adaptive prediction method with a simple architecture, easy to implement, and low dependence on parameter adjustment. Therefore, the present invention proposes a bearing life prediction method based on adaptive sparse graph learning using a digital twin dictionary. Summary of the Invention

[0005] The purpose of the present invention is to provide a bearing life prediction method based on adaptive sparse graph learning using a digital twin dictionary to solve the problems existing in the prediction of rolling bearing life.

[0006] To achieve the above object, the technical solution adopted by the present invention is an adaptive sparse graph learning bearing life prediction method based on a digital twin dictionary. This method establishes an extended exponential model and a linear piecewise model, generates a digital twin dictionary covering various degradation behaviors, designs a new graph learning optimization objective function, introduces a sparse regularization method to reduce the model complexity and parameter sensitivity, adaptively obtains the accurate topological structure of the data, and realizes the accurate prediction of the remaining service life based on the constructed digital twin dictionary and adaptive sparse graph learning.

[0007] S1 Digital twin dictionary construction;

[0008] Establish an extended exponential function model and a linear piecewise model to characterize various degradation processes of rolling bearings:

[0009] Extended exponential model:

[0010]

[0011] where τ is the time delay coefficient, b is the translation coefficient, a is the base of the exponential model, M is the number of calculation points, and by changing the specific values of parameters a, b, and τ, a series of evolution trend lines can be obtained;

[0012] Extended linear piecewise model:

[0013]

[0014] where int represents taking the integer, a represents the starting value of the first linear model, b represents the inflection point value of the two linear models, c represents the end value of the second linear model, τ is the time delay coefficient, and by changing the specific values of parameters a, b, c, and τ, a series of evolution trend lines can be obtained;

[0015] S2 Adaptive sparse graph learning;

[0016] A large number of training samples are constructed in the way of S1 digital twin, and the training samples and the current test samples together form N nodes of the topological graph. A simple undirected, weighted, connected graph can be represented as Matrix represents N nodes of the graph, and vector x i is the node value. The adjacency matrix where w ij represents the weight of the edge connecting nodes i and j. For a graph, the most important thing is to determine its adjacency relationship:

[0017] Consider the following newly constructed optimization objective:

[0018]

[0019]

[0020] Let \(D\) ij =\(\|x\) i -\(x\) j \|^2\), and write the above optimization objective in matrix form:

[0021]

[0022] Establish a sparse regularization version of the above optimization objective:

[0023]

[0024] where \(\alpha\) is the regularization coefficient;

[0025] The optimization problem can be solved using the method of Lagrange multipliers:

[0026]

[0027] where, denotes the Moore-Penrose pseudoinverse. Given an arbitrary initial value of \(\beta\), the diagonal matrix form \(diag(w\) i \) of the calculated \(w\) i ) is used as the \(\beta\) for the next iteration. Repeat this iteration until the stopping condition for iteration is reached, and thus the adjacency matrix \(w\) of the data is obtained;

[0028] Define the degree matrix where, is the degree of node \(i\). Thus, the graph Laplacian matrix can be defined as Obviously, this matrix is a real symmetric matrix, so it has a set of complete orthogonal eigenvectors The corresponding eigenvalues are \(e = \{\lambda_1, \lt \lambda_2, \lt \cdots \lt, \lambda\) N \};

[0029] For the graph Given its known nodes and unknown nodes Calculate its Laplacian matrix Take the matrix that only contains the rows and columns of the unknown nodes to form the submatrix Calculate of the eigenvalues, and denote the minimum value as Then, for signals with eigenvalues less than \(\lambda\) min , they can all be predicted from the known node values:

[0030] Take the eigenvectors of the Laplacian matrix where the corresponding eigenvalues are less than \(\lambda\) min of the part, denoted as The graph learning framework can be expressed as:

[0031]

[0032] where Y = {y i}, i ∈ [1, N] is the life label vector;

[0033] Solving for the minimum variance solution, we can obtain:

[0034]

[0035] Then the life label of the unknown node can be estimated as:

[0036]

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention proposes a new adaptive sparse graph learning method based on a digital twin dictionary to predict the remaining useful life of rolling bearings. An extended exponential model and a linear piecewise model are established to generate a digital twin dictionary covering various degradation behaviors, solving the problem of insufficient training samples; a new graph learning optimization objective function is designed, and a sparse regularization method is introduced to reduce the model complexity and parameter sensitivity, adaptively obtaining the accurate topological structure of the data, avoiding inaccurate adjacency relationships caused by inappropriate parameters, and obtaining better prediction results without parameter adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of the adaptive sparse graph learning bearing life prediction method based on a digital twin dictionary.

[0040] Figure 2 is a schematic diagram of the digital twin dictionary construction principle.

[0041] Figure 3 is the constructed digital twin dictionary.

[0042] Figure 4 is the real-time remaining useful life prediction result. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0044] (1) Measured accelerated performance degradation data of rolling bearings, taking the accelerated performance degradation experimental data of rolling bearings publicly available at the University of Cincinnati in the United States as an example. The rotating shaft is supported by 4 Rexhord ZA-2115 double-row rolling bearings, and sensors are installed on the bearing housing of each bearing to collect data simultaneously. A load of 6000 lbs is applied radially to accelerate the bearing degradation process. Data is collected every 10 minutes, with 20480 data points (about 1 second) sampled each time. The performance degradation experiment was carried out 3 times. After the first experiment, the effective samples of each bearing were 2156 groups, among which the inner ring of the 3rd bearing (denoted as bearing 1) failed, and the rolling elements and outer ring of the 4th bearing (denoted as bearing 2) failed. After the second experiment, the effective samples of each bearing were 982 groups, among which the outer ring of the 1st bearing (denoted as bearing 3) failed. After the third experiment, the effective samples of each bearing were 6323 groups, among which the outer ring of the 3rd bearing (denoted as bearing 4) failed.

[0045] (2) First, based on Figure 2 the digital twin dictionary construction principle shown, a large number of digital simulation degradation data were generated, as Figure 3 shown, as the training dictionary for life prediction.

[0046] (3) Subsequently, based on Figure 1 the complete prediction method proposed, the remaining useful life of the bearing was predicted, as Figure 4 shown. It can be seen that the prediction result is very close to the true life and has a high accuracy.

Claims

1. An adaptive sparse graph learning bearing life prediction method based on a digital twin dictionary, characterized in that: This method establishes an extended exponential model and a linear piecewise model, generates a digital twin dictionary covering various degradation behaviors, designs a new graph learning optimization objective function, introduces a sparse regularization method to reduce the model complexity and parameter sensitivity, adaptively obtains the accurate topological structure of the data, and realizes the accurate prediction of the remaining useful life based on the constructed digital twin dictionary and adaptive sparse graph learning; S1 Digital twin dictionary construction; Based on the collected multiple groups of bearing acceleration signals, vibration signals, and radial load signals, an extended exponential function model and a linear piecewise model are established to characterize various degradation processes of rolling bearings: Extended exponential model: where τ is the time delay coefficient, b is the translation coefficient, a is the base of the exponential model, M is the number of calculation points, and a series of evolution trend lines can be obtained by changing the specific values of parameters a, b, and τ; Extended linear piecewise model: where int represents taking the integer, p represents the starting value of the first linear model, q represents the inflection point value of the two linear models, c represents the end value of the second linear model, τ is the time delay coefficient, and a series of evolution trend lines can be obtained by changing the specific values of parameters a, b, c, and τ; S2 Adaptive sparse graph learning; A large number of training samples are constructed in the way of S1 digital twins, and the training samples and the current test samples together form N nodes of the topological graph; a simple undirected, weighted, connected graph can be expressed as matrix represents N nodes of the graph, and the vector x i is the node value; the adjacency matrix where, w ij represents the weight of the edge connecting nodes i and j. For a graph, the most important thing is to determine its adjacency relationship: Consider the following newly constructed optimization objective: Let S ij = ||x i - x j ||², and write the above optimization objective in matrix form: Establish a sparse regularization version of the above optimization objective: where α is the regularization coefficient; Solve the optimization problem using the Lagrange multiplier method: Among them, represents the generalized inverse. Given any initial value of β, the calculated w i in the form of a diagonal matrix diag(w i ) is used as the β for the next iteration. This iteration is repeated until the stopping condition for iteration is reached, and thus the adjacency matrix w of the data is obtained; Define the degree matrix where is the degree of node i; Define the graph Laplacian matrix Obviously, this Laplacian matrix is a real symmetric matrix. Therefore, it has a set of completely orthogonal eigenvectors u = {u i}, and the corresponding eigenvalues are e = {λ1, <λ2, <…<, λ N} For the figure Given its known nodes and unknown nodes calculate its Laplacian matrix Take the matrix that only contains the unknown nodes in rows and columns to form a submatrix Calculate the eigenvalues of, and take the minimum value and denote it as Then for the signals corresponding to the eigenvalues less than λ min are predicted by the known node values: Take the Laplacian matrix of the eigenvectors in which the corresponding eigenvalues are less than λ min and denote it as Then the graph learning framework is expressed as: where Y = {y i}, i ∈ [1, N] is the lifetime label vector; Solve for the minimum variance solution to obtain: Then the life label estimation of the unknown node is:

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