CN110907177A - Bearing fault diagnosis method based on layered extreme learning machine - Google Patents

Bearing fault diagnosis method based on layered extreme learning machine Download PDF

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CN110907177A
CN110907177A CN201911258077.8A CN201911258077A CN110907177A CN 110907177 A CN110907177 A CN 110907177A CN 201911258077 A CN201911258077 A CN 201911258077A CN 110907177 A CN110907177 A CN 110907177A
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learning machine
extreme learning
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贾利民
左亚昆
王志鹏
王宁
秦勇
陈欣安
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Beijing Jiaotong University
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    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention provides a bearing fault diagnosis method based on a layered extreme learning machine, which belongs to the technical field of fault diagnosis of mechanical parts and comprises the steps of decomposing a vibration acceleration signal into a plurality of modal components through a VMD algorithm; selecting the first four modes which are ordered according to the size of the central frequency, extracting features through an SVD algorithm, mapping input feature data into a random sparse hidden layer space, acquiring hidden information among training samples, and randomly mapping the feature data processed in the previous layer again through a sparse automatic encoder in each hidden layer; optimal neural network weights are obtained by a fast iterative shrinkage algorithm (FISTA) such that the actual output is close to the specified label data. The invention simultaneously realizes noise reduction and accurate classification, and can improve the identification precision and the utilization rate of characteristic information under the condition of a layered extreme learning machine; compared with the original extreme learning machine, the fault diagnosis of the rolling bearing signal can achieve higher identification precision and faster training speed.

Description

Bearing fault diagnosis method based on layered extreme learning machine
Technical Field
The invention relates to the technical field of fault diagnosis of mechanical parts, in particular to a fault diagnosis method based on a layered extreme learning machine.
Background
Bearing fault diagnosis is an effective technology for guaranteeing stable operation of a rotating machine. Therefore, rapid identification of failure states plays an important role in social production life. However, in the existing bearing fault diagnosis algorithm, the precision and the speed are two research problems which are difficult to be considered at the same time, and how to find an algorithm which ensures the identification precision and the identification speed at the same time has important significance in real life. However, the traditional methods such as the BP neural network, the legacy algorithm and the like only ensure the precision in the practical use, but sacrifice a great deal of operation time. The Extreme Learning Machine (ELM) is an algorithm with a speed having a significant advantage in the diagnosis of the rolling bearing failure compared with other neural network algorithms. However, it has the disadvantage of unstable learning effect, and the improved composite extreme learning (ML-ELM), deep extreme learning machine (AE _ ELM), etc. have the sacrifice of accuracy and speed.
Disclosure of Invention
The invention aims to provide a bearing fault diagnosis method based on a layered extreme learning machine, which can simultaneously ensure the identification precision and the identification speed, so as to solve at least one technical problem in the background technology.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a bearing fault diagnosis method based on a layered extreme learning machine, which comprises the following steps:
step S110: decomposing the vibration acceleration signal into a plurality of modal components through a VMD algorithm;
step S120: selecting the first four modes of the decomposed modal components according to the central frequency for feature extraction through an SVD algorithm to obtain feature data;
step S130: inputting the characteristic data into a layered extreme learning machine for training and learning, and outputting a bearing fault identification result; mapping input feature data into a random sparse hidden layer space to obtain hidden information among training samples, wherein each layer of hidden layer carries out random mapping again on the feature data processed by the previous layer through a sparse automatic encoder; then, N-layer learning is performed on the hidden layers to obtain advanced sparse features, and the output of each hidden layer i can be expressed as:
Hi=g(Hi-1·β)
wherein g is an activation function, and β is a table hidden layer weight;
wherein, the optimization model of the sparse automatic encoder is as follows:
Figure BDA0002310861660000021
Oβfor β value minimizing the right equation, X represents sparse mapping of characteristic data, and l1 represents penalty period during training;
finally, the optimal neural network weights β are obtained by a fast iterative shrinkage algorithm (FISTA) such that the actual output is close to the specified label data:
Figure BDA0002310861660000022
wherein, f (x) is the actually output label, h (x) is the eigenvalue mapped to the sparse hidden layer space, G is the label matrix, and λ is the random positive value.
Preferably, the fast iterative shrinkage algorithm comprises the following specific steps:
calculating the gradient of the smooth convex function ▽ p and a Leptozetz constant gamma;
let y1=β0∈Rn,t 11, when j (j ≧ 1), the following iteration is performed:
Figure BDA0002310861660000023
Figure BDA0002310861660000031
Figure BDA0002310861660000032
wherein, β0For the random initialization quantity of the algorithm, t1Is a variable with a unique initial value, and j is the iteration number.
The invention has the beneficial effects that: the feature extraction method based on the VMD-SVD and the layered extreme learning machine are combined to realize excellent effect on fault diagnosis of rolling bearing signals, compared with a single algorithm, the method has the effects of noise reduction and accurate classification, and can improve the identification precision and the utilization rate of feature information under the condition of the layered extreme learning machine; compared with the original extreme learning machine, the fault diagnosis of the rolling bearing signal can achieve higher identification precision and faster training speed.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flowchart illustrating steps of a bearing fault diagnosis method based on a hierarchical extreme learning machine according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of performing spectrum analysis on an original vibration signal according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a mode of performing VMD decomposition on a normal vibration signal according to an embodiment of the present invention.
Fig. 4 is a schematic mode diagram of a VMD decomposed vibration signal of an inner ring fault according to an embodiment of the present invention.
Fig. 5 is a schematic mode diagram of a vibration signal of an outer ring fault after VMD decomposition according to an embodiment of the present invention.
Fig. 6 is a schematic mode diagram of a vibration signal of a rolling element fault after VMD decomposition according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of an identification result of identifying a bearing fault by using a hierarchical extreme learning machine according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of an identification result of identifying a bearing fault by using an extreme learning machine according to an embodiment of the present invention.
Detailed Description
The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or modules, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, modules, and/or groups thereof.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding of the embodiments of the present invention, the following description will be further explained by taking specific embodiments as examples with reference to the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
It will be understood by those of ordinary skill in the art that the figures are merely schematic representations of one embodiment and that the elements or devices in the figures are not necessarily required to practice the present invention.
Example 1
As shown in fig. 1, an embodiment of the present invention provides a bearing fault diagnosis method based on a hierarchical extreme learning machine, which first decomposes a vibration signal of a bearing into a plurality of modes through a VMD, so as to achieve the purposes of noise reduction and feature extraction; secondly, performing secondary feature extraction and data compression on the data subjected to noise reduction and feature extraction through an SVD algorithm; and finally, learning through a novel layered extreme learning machine technology to achieve the purpose of fault diagnosis. The method specifically comprises the following steps:
firstly, decomposing vibration signal data into K modes by utilizing a VMD (variational mode decomposition) algorithm. The number of each modal sampling point is consistent with that of the original vibration signal, after VMD decomposition, irregular noise is removed, and the modal sampling points are converged around respective central frequency, so that the modal vibration signal has good identification.
Firstly, carrying out spectrum analysis on data to be decomposed so as to determine the number K of modes to be decomposed;
for each IMF modal component function μk (t)Performing Hilbert transform to obtain an analytic signal of IMF modal component, wherein the expression is
Figure BDA0002310861660000051
Wherein σtDenotes a unit pulse function, j ═ 1, 2.... k);
estimating the center frequency of the analytic signal of each IMF modal component
Figure BDA0002310861660000052
Mixing, modulating the frequency spectrum of each IMF modal component to a corresponding base frequency band,
Figure BDA0002310861660000053
calculating the square L of the gradient of the analytic signal of each IMF modal component determining the fundamental frequency band2Norm to obtain corresponding IMF modeThe component is expressed as
Figure BDA0002310861660000054
Wherein,
Figure BDA0002310861660000055
denotes a partial derivative, and μ K ═ { μ 1, μ 2.. μ K } denotes K IMF modal components obtained by decomposition, ωkRepresenting the center frequency of the IMF modal components, and f represents the sum of all IMF modal components;
introducing a secondary penalty factor α and a Lagrang multiplier lambda to obtain an expanded Lagrange algorithm, wherein the expression is,
Figure BDA0002310861660000061
and (4) solving the saddle point of the expanded Lagrange expression by using an alternative direction multiplier Algorithm (ADMM) to obtain K IMF modal components.
Finding the saddle points of the extended Lagrange expression includes:
the method comprises the following steps: initializing muk 1,ωk 1,λ1
Step two: and (3) executing a loop: n is n + 1;
step three: updating muk:
Figure BDA0002310861660000062
Updating omegak:
Figure BDA0002310861660000063
Step four: updating lambda:
Figure BDA0002310861660000064
step five: repeating the first step to the fourth step until the iteration stop condition is met
Figure BDA0002310861660000065
And finishing the iteration to obtain the saddle point of the expanded Lagrange expression.
And secondly, performing secondary processing on the extracted feature data by using an SVD (singular value decomposition) algorithm, and filtering data with unobvious features, so that secondary extraction of the features and compression of a sample space are realized, and the training speed is improved. Specifically, the method comprises the following steps:
constructing a signal data m multiplied by n order matrix H by K IMF modal components
Figure BDA0002310861660000066
Wherein U is E.Rm×mAnd V ∈ Rn×nAre all orthogonal matrices and are all provided with a matrix,
Figure BDA0002310861660000071
Ar=diag(σ12,…,σr),σi(i ═ 1,2, …, r) denotes the singular value of H, and σ denotes1≥…≥σrR is equal to or more than 0 and represents the rank of H, mui、νiAre respectively square arrays HHTAnd HTH ith feature vector.
And step three, processing and learning the feature data after secondary extraction by using a hierarchical extreme learning machine, and achieving the purpose of rapidly and accurately identifying the fault.
In the embodiment of the invention, the extreme learning machine of the artificial intelligence algorithm of the single-layer feedforward network is improved into the layered extreme learning machine, so that the precision and the operation speed are improved. The method is used for identifying the rolling bearing signals, and achieves good effect.
Example 2
The embodiment 2 of the invention provides a method for performing feature extraction by combining VMD-SVD and finally realizing fault diagnosis of a rolling bearing by using a hierarchical extreme learning machine.
The method comprises the following specific steps:
step one, decomposing a bearing vibration signal into a plurality of modes constrained at a central frequency through a VMD.
And step two, selecting the first four items of the decomposed modes to perform SVD respectively.
And step three, inputting the features after the secondary extraction into a hierarchical extreme learning machine for training to realize fault diagnosis.
The layered extreme learning machine is a multilayer nested improved algorithm of the extreme learning machine, and in the extreme learning machine algorithm, after input and output data and the classification type (0 regression or complex classification) of the data are specified, the weight and the threshold of a neural network can be automatically adjusted, so that the input data and the output data are matched as much as possible, and unsupervised learning is realized; meanwhile, the weight and the threshold value are both enabled to meet the orthogonal condition when being adjusted, the whole network is divided into two independent subsystems, namely a hidden layer system for carrying out multilayer sparse mapping on characteristic data and an original ELM system for learning data processed by multilayer hidden layers, and therefore parallelism can be considered in a more comprehensive mode. Parallelism is considered in a more comprehensive manner.
In particular, the method comprises the following steps of,
inputting the characteristic data into a layered extreme learning machine for training and learning, and outputting a bearing fault identification result; mapping input feature data into a random sparse hidden layer space to obtain hidden information among training samples, wherein each layer of hidden layer carries out random mapping again on the feature data processed by the previous layer through a sparse automatic encoder; then, N-layer learning is performed on the hidden layers to obtain advanced sparse features, and the output of each hidden layer i can be expressed as:
Hi=g(Hi-1·β)
wherein g is an activation function, and β is a table hidden layer weight;
wherein, the optimization model of the sparse automatic encoder is as follows:
Figure BDA0002310861660000081
Oβto minimize the right equationThe transformed β value is taken, X represents the sparse mapping of the characteristic data, and l1 represents the penalty period during training;
finally, the optimal neural network weights β are obtained by a fast iterative shrinkage algorithm (FISTA) such that the actual output is close to the specified label data:
Figure BDA0002310861660000082
wherein, f (x) is the actually output label, h (x) is the eigenvalue mapped to the sparse hidden layer space, G is the label matrix, and λ is the random positive value.
2. The bearing fault diagnosis method based on the hierarchical extreme learning machine as claimed in claim 1, wherein the fast iterative shrinkage algorithm comprises the following specific steps:
calculating the gradient of the smooth convex function ▽ p and a Leptozetz constant gamma;
let y1=β0∈Rn,t 11, when j (j ≧ 1), the following iteration is performed:
Figure BDA0002310861660000083
Figure BDA0002310861660000091
Figure BDA0002310861660000092
wherein, β0For the random initialization quantity of the algorithm, t1Is a variable with a unique initial value, and j is the iteration number.
In embodiment 2 of the present invention, rolling bearing data of the university of kessensch, usa was used as verification data of the failure diagnosis method. The tested bearing is an SFK bearing, a single-point fault is arranged on the bearing by using an electric spark machining technology, the fault diameter is selected to be 0.007mils, and the rotating speed is 1772 rpm. In embodiment 2 of the present invention, data in four states, namely, a normal state, an inner ring fault, an outer raceway fault, and a rolling unit fault of a rolling bearing under a sampling frequency of 12khz is selected for analysis, and 120000 test points are selected for each state, half of the test points are used as training data, and half of the test points are used as test data for verification.
First, a spectrogram of a processed signal is shown in fig. 2, from which it can be known that the number of dominant spectra is 4, and the number of modes should be determined as 5 by adding clutter, and the number is substituted into a VMD algorithm together with an original signal to obtain a waveform after noise reduction and decomposition, as shown in fig. 3 to fig. 6.
As shown in fig. 7 and 8, the number of test points was found to be less than 40 during the test. The difference between the number of the H-ELM points and the traditional ELM precision is not large, the H-ELM points and the traditional ELM precision can both keep the precision of more than 95%, and the error is less than 3%. Therefore, 50 eigenvalues are selected for each group, and 200 points are selected to establish the feature matrix. Then, the hilbert matrix established in each mode is substituted into the SVD algorithm to perform secondary decompression, and features with lower importance are filtered out to achieve the purpose of secondary feature extraction and sample space reduction, and the obtained result is as shown in table 1 by way of example, it can be seen that there is an obvious numerical difference between different states, which indicates that the feature extraction effect is good. And finally, inputting the data into a layered extreme learning machine for training and recognition.
Table 1:
Figure BDA0002310861660000093
Figure BDA0002310861660000101
experiments show that the H-ELM has good performance when the number of layers is 3, and then the number of hidden nodes of each layer of the neural network is adjusted by adopting a stepping method. And (5) carrying out cyclic training on the number of each node, wherein the number is from 10 to 100, and finding out the optimal solution. According to the test, the dimensions of the input random matrix are respectively 200x12, 200x30 and 200x35 (namely, the number of hidden nodes in the traditional ELM is respectively 12, 30 and 35), the cycle test precision is 97.5%, the single training time is 0.0023087s, and the test time is 0.00078823 s. When the activation function is tribas and the hidden node number is 300, the ELM test precision is 91.5%, and the total time of a single training is 0.0938 s. The pair ratio with the conventional extreme learning machine is shown in table 2 below:
table 2:
Figure BDA0002310861660000102
in summary, the bearing fault diagnosis method based on the hierarchical extreme learning machine according to the embodiment of the present invention is based on the multi-layer nesting mode of the extreme learning machine, and in the extreme learning machine series algorithm, after the input data and the output data are specified and the classification type (0 regression or complex classification) of the data is specified, it can automatically adjust the weight and the threshold of the neural network, thereby achieving the purpose of fast and accurate learning. Meanwhile, after VMD (variational modal decomposition) and SVD (singular value decomposition) are used as the feature extraction method in a matching way, more feature information can be reserved for identification on the premise of not sacrificing precision and speed, and the method has advantages in developing deeper fault information, so that the method is suitable for the field of fault diagnosis.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. A bearing fault diagnosis method based on a layered extreme learning machine is characterized by comprising the following steps:
step S110: decomposing the vibration acceleration signal into a plurality of modal components through a VMD algorithm;
step S120: selecting the first four modes of the decomposed modal components according to the central frequency for feature extraction through an SVD algorithm to obtain feature data;
step S130: inputting the characteristic data into a layered extreme learning machine for training and learning, and outputting a bearing fault identification result; mapping input feature data into a random sparse hidden layer space to obtain hidden information among training samples, wherein each layer of hidden layer carries out random mapping again on the feature data processed by the previous layer through a sparse automatic encoder; then, N-layer learning is performed on the hidden layers to obtain advanced sparse features, and the output of each hidden layer i can be expressed as:
Hi=g(Hi-1·β)
wherein g is an activation function, and β is a table hidden layer weight;
wherein, the optimization model of the sparse automatic encoder is as follows:
Figure FDA0002310861650000011
Oβfor β value minimizing the right equation, X represents sparse mapping of characteristic data, and l1 represents penalty period during training;
finally, the optimal neural network weights β are obtained by a fast iterative shrinkage algorithm (FISTA) such that the actual output is close to the specified label data:
Figure FDA0002310861650000012
wherein, f (x) is the actually output label, h (x) is the eigenvalue mapped to the sparse hidden layer space, G is the label matrix, and λ is the random positive value.
2. The bearing fault diagnosis method based on the hierarchical extreme learning machine as claimed in claim 1, wherein the fast iterative shrinkage algorithm comprises the following specific steps:
calculating the gradient of the smooth convex function ▽ p and a Leptozetz constant gamma;
let y1=β0∈Rn,t11, when j (j ≧ 1), the following iteration is performed:
Figure FDA0002310861650000021
Figure FDA0002310861650000022
Figure FDA0002310861650000023
wherein, β0For the random initialization quantity of the algorithm, t1Is a variable with a unique initial value, and j is the iteration number.
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CN113138080A (en) * 2021-04-22 2021-07-20 东北大学 Rolling bearing intelligent fault diagnosis method based on vibration twinning and extreme learning

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