CN109632309A - Based on the rolling bearing fault intelligent diagnosing method for improving S-transformation and deep learning - Google Patents
Based on the rolling bearing fault intelligent diagnosing method for improving S-transformation and deep learning Download PDFInfo
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Abstract
The invention discloses a kind of based on the rolling bearing fault intelligent diagnosing method for improving S-transformation and deep learning, change its Gauss function window width by way of window width regulatory factor is added to S-transformation, and then improve the time frequency resolution of S-transformation, the impact component that can be accurately detected in vibration signal, preferably to extract the fault signature of bearing vibration signal.This method does improvement S-transformation to the vibration signal of bearing fault, obtain the eigenmatrix of signal, eigenmatrix is launched into feature vector by column to be input in sparse autocoder model, utilize the characteristic of encoder, the further feature for further extracting data excavates artificial unrecognized some important implicit informations；And accurate classification is made to the feature extracted.The present invention can effectively improve the accuracy rate of rolling bearing fault diagnosis.
Description
Technical field
The present invention relates to rolling bearing fault diagnosis and Artificial technical field of intelligence, and in particular to one kind is based on changing
Into the Fault Diagnosis of Roller Bearings of S-transformation and deep learning.
Background technique
Rolling bearing is the Key basic parts and important rotating part of equipment manufacture, is known as mechanical pass
Section.It has the advantages that high-efficient, frictional resistance is small, and lubrication is easily realized, using very universal on rotating machinery.However it rolls
Bearing is also that the component most easily to break down in rotating machinery occupies very high ratio according to statistics in all kinds of failures,
About 30%.This is because rolling bearing is the component that operating condition is the most severe in mechanical equipment, played in mechanical equipment
The effect of load and posting load is born, its operating status directly influences the performance of whole mechanical equipment.Therefore, to bearing
Failure makes accurate diagnosis, there is huge realistic meaning.
The vibration signal for mainly passing through processing bearing to the diagnosis of bearing fault, extracts fault signature, then classify.Cause
This contains signal processing and pattern-recognition two parts among these.Traditional signal processing method such as Fourier transformation etc., cannot
It is well adapted for this non-stationary signal of bearing vibration signal.With the continuous improvement of production technology, industrial production also enters greatly
Data age, it is traditional to be applicable in well by artificial feature extracting method in face of huge data scale, because
This, be badly in need of it is a kind of intelligent, fault diagnosis field continue it is a kind of intelligent, can handle big data method occur.2006,
Machine learning authority Hinton publishes thesis at " Science " and proposes deep learning main points of view: the neural network tool of more hidden layers
Have an excellent feature learning ability, the feature learnt to data have it is more essential portray, thus be conducive to visualization or
Classification；Difficulty of the deep neural network in training can be overcome by " Level by level learning " Lai Youxiao, and Level by level learning passes through no prison
Educational inspector practises to realize.In short, compared with traditional feature extracting method, deep learning network by construct more hidden layers model and
Mass data training data learns more useful feature automatically, to finally promote the accuracy of classification or prediction.
Summary of the invention
In view of the above technical problems, the purpose of the present invention is to provide a kind of based on the rolling for improving S-transformation and deep learning
Dynamic bearing method for diagnosing faults.
To achieve the above object, the present invention is realized according to following technical scheme:
Kind is based on the Fault Diagnosis of Roller Bearings for improving S-transformation and deep learning, which is characterized in that including walking as follows
It is rapid:
Step S1: vibration signal of the rolling bearing under different faults state is obtained；
Step S2: doing improved S-transformation to vibration signal, improves its time domain point by way of window width regulatory factor is arranged
Resolution enhances its detection effect to impact signal, extracts the fault signature of signal, obtains vibration signal by improving S-transformation
Eigenmatrix；
Step S3: eigenmatrix is launched into input of the feature vector as neural network by column, is divided into no label data
And have two groups of label data, using no label data realize network pre-training, then with have label data fine tuning whole network join
Number, completes the building of sparse autocoder neural network model；
Step S4: new fault-signal to be measured is handled according to above-mentioned steps, is input to trained network model
In, realize the intelligent diagnostics of bearing fault.
In above-mentioned technical proposal, the Gauss function expression formula of S-transformation is σ (f)=1/f, and f is frequency, window width size with
Frequency is related, is not affected by other factors, and S-transformation is improved in the step S1 by the way that window width regulatory factor is added, makes window width table
Become σ (f)=g/f up to formula, after regulatory factor g is added, window function width is not only related with frequency, can also be by adjusting g's
Value changes window width, to reinforce the time domain of S-transformation or the resolution ratio of frequency domain, according to Heisenberg's uncertainty principle, time domain
It cannot be improved simultaneously with frequency domain resolution, therefore reduce window width, obtain higher time resolution, increased window width, can be promoted
Frequency domain resolution impacts the effective characterization failure feature of ingredient, therefore pass through setting for bearing vibration signal
The mode of window width regulatory factor promotes the time resolution of S-transformation, it is made to more precisely detect the impact in vibration signal
Component preferably extracts the fault signature of signal.
In above-mentioned technical proposal, the sparse autocoder network model building in step S3 is through the following steps that realize
:
Using unlabeled exemplars, single layer network is constructed using the unsupervised training algorithm of layer-by-layer greediness from bottom to top, every layer
Parameter learning is carried out using from encryption algorithm, one layer of adjustment every time successively adjusts, obtains the weight and threshold value of network；
Using supervised learning on the basis of the weight that the first step learns, pass through BP algorithm using the sample of tape label
From top to bottom, entire network parameter is finely tuned, the building of sparse autocoder neural network model is completed.
Compared with the prior art, the invention has the following advantages:
The present invention is first is that improving S-transformation can according to need by introducing window width regulatory factor by changing regulatory factor
Mode changes the window width of S-transformation Gauss function, to obtain higher time resolution and more accurately detect in signal
Impact component, preferably to extract the feature of bearing vibration signal.The eigenmatrix obtained after S-transformation is by signal
The information of time-domain and frequency-domain combines, more conducively the expression of signal characteristic.Second is that utilizing sparse autocoder neural network
Powerful learning ability, from simple to complex, by rudimentary to advanced, hidden feature of the depth ground inside mining data is greatly mentioned
The accuracy rate of classification is risen.Compare it is more acurrate for traditional artificial extraction characterization method, it is more rapidly, more stable, it is more intelligent.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
Other attached drawings are obtained according to these attached drawings.
Fig. 1 is a kind of rolling bearing fault testing method based on improvement S-transformation in conjunction with deep learning of the present invention
Flow chart.
Fig. 2 (a) is the three-dimensional figure for the eigenmatrix that S-transformation obtains；
Fig. 2 (b) is the time-frequency domain waveform diagram for the eigenmatrix that S-transformation obtains；
Fig. 2 (c) is the frequency-domain waveform figure for the eigenmatrix that S-transformation obtains；
Fig. 3 (a) is the effect contrast figure for improving S-transformation processing bearing impact signal g=0.5；
Fig. 3 (b) is the effect contrast figure for improving S-transformation processing bearing impact signal g=1；
Fig. 3 (c) is the effect contrast figure for improving S-transformation processing bearing impact signal g=25；
Fig. 4 is the structural schematic diagram of autocoder；
Fig. 5 is that rolling bearing data generate testing stand schematic diagram；
Fig. 6 is the column diagram of the classification accuracy under different neural network parameters.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.
The present invention is based on improve Fault Diagnosis of Roller Bearings flow chart such as Fig. 1 institute of the S-transformation in conjunction with deep learning
Show, includes the following steps:
Step S1: vibration signal of the rolling bearing under different faults state is obtained；
Step S2: doing improved S-transformation to vibration signal, improves its time domain point by way of window width regulatory factor is arranged
Resolution enhances its detection effect to impact signal, extracts the fault signature of signal, obtains vibration signal by improving S-transformation
Eigenmatrix；
Step S3: eigenmatrix is launched into input of the feature vector as neural network by column, is divided into no label data
And have two groups of label data, using no label data realize network pre-training, then with have label data fine tuning whole network join
Number, completes the building of sparse autocoder neural network model；
Step S4: new fault-signal to be measured is handled according to above-mentioned steps, is input to trained network model
In, realize the intelligent diagnostics of bearing fault.
Wherein, S-transformation is improved in step S2 by addition window width regulatory factor, and window width is changed by regulatory factor, from
And reinforce S-transformation for the ability of signal characteristic abstraction.
The present invention introduces improvement S-transformation first.
Step 1: introducing S-transformation principle.
S-transformation proposed that it was the basis in Short Time Fourier Transform and wavelet transformation in 1996 by Stockwell earliest
On grow up, also improve defect while both inheriting advantage.It is only that it inherits Short Time Fourier Transform unifrequency
The ability of vertical analysis and Multi-resolution analysis of wavelet transform, and it uses Gauss function, and the inverse of window width and frequency is at just
Than eliminating the selection of window function and the defect that window width is fixed, being very suitable to processing non-stationary signal.
The continuous S-transformation expression formula of signal x (t) is as follows:
In formula: ω (t- τ, f) is Gauss function；τ is shift factor, for controlling position of the Gaussian window on time shaft t
It sets；F is frequency.
It can be seen that S-transformation is different from Short Time Fourier Transform by (1) formula, the height and width of Gaussian window become with frequency
Change, the defect of Short Time Fourier Transform window height and equivalent width can be overcome in this way.If enabling τ=mT, f=n/NT, root
The discrete form that S-transformation can be obtained according to (1) formula is as follows:
The discrete Fourier transform that X [k] is time series x (m) in formula is as follows:
By (2) formula it is found that doing discrete S-transformation to signal as a result a matrix, wherein matrix column corresponds to sampled point
Time, row respective frequencies value, matrix element are plural number, and the information of amplitude and phase can be obtained from element.Need special attention
It is that frequency values after S-transformation need to carry out conversion according to sample frequency and sampling number could corresponding with actual frequency, converts
Mode is identical as discrete Fourier transform, and the actual frequency of each point is (fs/ N) * n, wherein fsFor sample frequency, N is sampled point
Number, n are the serial number of nth point.The result of S-transformation can use 3 dimensional drawing visual representation.To the west of store up university's rolling bearing inner ring
Failure does S-transformation, wherein 1000 sampled points of sample length for failure scale is 0.007 inch of fault data, samples
Frequency is 12kHz, and wherein frequency coordinate has been converted into actual frequency.The three-dimensional figure and time-frequency domain figure of eigenmatrix are shown in Fig. 2
(a) shown in-Fig. 2 (c).
Step 2: improved S-transformation.
According to above it will be appreciated that, the window width of the Gauss function of S-transformation is σ (f)=1/f, it follows that the window width of S-transformation
Inversely with frequency, one timing of frequency, window width is also fixation, then time frequency resolution is also fixed.The vibration of rolling bearing
Dynamic signal is non-stable sophisticated signal, and the feature on different frequency component is also different, in order to adapt to signal difference
The characteristics of frequency component, the present invention use improved S-transformation, and expression formula is as follows:
From the above equation, we can see that becoming window width from original σ (f)=1/f by the way that window width regulatory factor g is addedAt this moment window width is not only inversely proportional with frequency, also related with g, and the variation speed of window width can be adjusted by changing g
Degree.It is exactly common S-transformation as g=1, it is found that as 0 < g < 1, window width becomes the uncertainty principle proposed according to Heisenberg
Small, time resolution is improved, and as g > 1, window width becomes larger, and frequency domain resolution is improved.It is done for bearing impact signal
Improved S-transformation, and eigenmatrix is depicted as contour map expression.Take g=0.5 respectively, 1,25 changes window width, and then
To different time resolutions, it can be seen that as g=0.5, window width narrows, and time resolution is improved, impact signal peak
Gap portion between value and two adjacent peaks can be detected accurately.As g=1, window width broadens, under time resolution
Drop, although the peak value of impact signal can also be detected with peak value gap, precision is obviously not so good as high when g=0.5.Work as g
When=25, window width is most wide, and time resolution declines to a great extent, and can not detect peak value and the peak value gap of impact signal.Its
Shown in effect such as Fig. 3 (a)-Fig. 3 (c).
Can for bearing vibration signal, impact ingredient can have effectively characterization failure feature, accurately
Impact ingredient in identification vibration signal determines the effect of fault diagnosis.Therefore, believe with S-transformation processing bearing vibration
Number when, in order to more accurately detect the impact ingredient in vibration signal, need to be promoted time resolution, also just need to contract
Small window width regulatory factor, makes window width narrow.But if window width is narrow, according to Heisenberg uncertainty principle, time domain and frequency domain point
Resolution cannot improve simultaneously, therefore frequency domain resolution can become very low, by a large amount of experimental verification, choose window frame regulatory factor
G=0.5, both improves time resolution, also remains certain frequency domain resolution, can efficiently extract rolling bearing letter
Number feature.
Secondly, the present invention introduces sparse autocoder.
Step 1: introducing autocoder (Auto Encoder, AE) and sparse autocoder (Sparse
Auto Encode)。
Autocoder is the neural network comprising one layer of hidden layer, and the purpose is to allow output to be equal to input (i.e. y (i)=x
(i), wherein { x (1), x (2) ... x (n) } indicates input sample set), allow implicit spy in the automatic mining data of encoder
Sign.Autocoder structure is as shown in Figure 4.Autocoder attempts to establish an identity function by study and make the output of network
Equal to input, i.e.,When hidden layer neuron number is less than input number of layers, network can compress data, from
And find in it hiding feature, when hidden layer neuron more than input number of layers it is more when, can to network be added it is sparse
Property limitation excavate the feature of input data.
The input of neural network is x,The activity for indicating j-th of neuron of hidden layer, then hidden layer is neural
The average activity of first j may be expressed as:
To realize that sparsity requires the average activity of hidden layer neuron very small, enableP is sparsity
Parameter is one be in close proximity to 0 number, can be achieved with the sparsity of network in this way.In order to meetThis condition, palpus
Additional penalty factor is added in original Neural Network Optimization objective function:
T is the number of hidden layer neuron in formula, which also can be described as relative entropy:
In formula,Be one using p as mean value andFor the volume between two Bernoulli random variables of mean value
Relative entropy.It has following property, whenWhen, relative entropy 0, as p andWhen gap increases, relative entropy monotonic increase, so
It can achieve the purpose that sparse limitation by minimizing relative entropy.
Step 2: introducing the pre-training process and trim process learnt based on SAE model depth:
A, pre-training
Pre-training, i.e., using unsupervised learning from bottom to top.First with no label training sample data training first layer, obtain
To the connection weight and offset parameter of first layer.By sparse autocoder principle it is found that SAE model can learn to data sheet
The structure of body, to obtain the feature for having more expression ability than inputting.After study obtains the 1st layer, using 1 layer of output as
2nd layer of input, the 2nd layer of training, thus obtains the connection weight and offset parameter of the second layer, and so on, by successively coveting
Greedy unsupervised training method generates the initial weight and threshold value of sparse autocoder.
B, it finely tunes, i.e., top-down supervised learning.The sample of tape label is inputted into neural network, calculate reality output with
Error is transmitted from up to down, is finely adjusted to whole network parameter by the error of desired output, completes sparse autocoder mind
Building through network model to sum up, the training process of sparse autocoder neural network model can be divided into following two step:
Single layer network is constructed using the unsupervised training algorithm of layer-by-layer greediness from bottom to top, every layer using from encryption algorithm into
Row parameter learning, every time one layer of adjustment, successively adjusts, finally obtains the feature prior information of no label data；
Using supervised learning on the basis of the weight that the first step learns, pass through BP algorithm using the data of tape label
From top to bottom, entire network parameter is finely tuned.
Case study on implementation 1:
With certain university's bearing data instance, illustrate to examine based on rolling bearing fault of the improvement S-transformation in conjunction with deep learning
Disconnected implementation method.
(1) test data
As shown in figure 5, the rolling bearing experiment porch includes one 2 horsepowers of motor (left side) (1h=746w), one
Torque sensor (centre), a power meter (right side) and control electronics.The testing stand includes drive end bearing and fan
End bearing, acceleration transducer are separately mounted to the position at the driving end and 12 o'clock of fan end of electric machine casing.Vibration signal is
It is acquired by the DAT logger in 16 channels, drive end bearing fault data sample frequency is 12kHz.In this trial, originally
It is research object that driving end (bearing) is chosen in invention.In the case where motor load is 0 operating condition, choosing bearing fault mode respectively is inner ring
Three failure, outer ring failure and rolling element positions, failure scale are 0.007 inch, and 0.014 inch, 0.021 inch totally 9 kinds not
Same fault data.Every 100 sampling numbers of 9 kinds of operating conditions are divided into a sample by the present invention, and every kind of operating condition obtains 80 samples
This, preceding 60 groups of samples are chosen to be training sample, and rear 20 groups of samples are chosen to be test sample.List 1 is as follows
1 test sample Verbose Listing of table
| Fault type | Fault degree | Sample size (training sample/test sample) | Data number | Tag along sort |
| Inner ring failure | 0.007 | 60/20 | 105DE | 1 |
| Inner ring failure | 0.014 | 60/20 | 169DE | 2 |
| Inner ring failure | 0.021 | 60/20 | 209DE | 3 |
| Outer ring failure | 0.007 | 60/20 | 130DE | 4 |
| Outer ring failure | 0.014 | 60/20 | 197DE | 5 |
| Outer ring failure | 0.021 | 60/20 | 234DE | 6 |
| Rolling element failure | 0.007 | 60/20 | 118DE | 7 |
| Rolling element failure | 0.014 | 60/20 | 185DE | 8 |
| Rolling element failure | 0.021 | 60/20 | 222DE | 9 |
(2) it improves S-transformation and handles time domain vibration signal
To the S-transformation that the sample chosen in (1) improves, wherein window frame regulatory factor g=0.5.Become by improved S
It gets eigenmatrix in return, matrix is expanded into input of the feature vector as neural network by column.
(3) neural metwork training and classification
Neural network used by this case is 4 layer networks, and every layer of neuron number is 5000-1000-100-9,
Input layer character pair vector length, output layer correspond to failure modes number.Three first layers are that there are two the sparse of hidden layer for a tool
Autocoder is implemented in combination with classification feature with the last layer.By training sample obtained in above-mentioned steps (2) be input to without
In trained sparse autocoder neural network models, the pre-training and fine tuning of network are carried out, the building of network model is completed,
Finally test sample is input in trained network model and carries out experimental verification, checks classification results.
(4) analysis of experimental results
Experimental data is as stated earlier, and using Xi Chu university rolling bearing totally 9 class fault data, data are passed through S-transformation,
Eigenmatrix is obtained, uses eigenmatrix as the input of neural network, every kind of failure extracts 80 groups of data respectively, wherein 60 groups of works
For training data, 20 groups are used as test data.Optimal network parameter is chosen, classification experiments are carried out to the test sample of failure,
It is tested by 20 subseries, Average Accuracy reaches 98.14%.Table 2 is that this method and existing method are classified about bearing fault
The comparison of accuracy rate.
2 distinct methods fault diagnosis result of table
The cause for influencing neural network classification accuracy rate is known as very much, wherein more crucial is exactly the learning rate and sample of network
This frequency of training, learning rate is too small, and frequency of training is too low, is easy that network is made to fall into locally optimal solution；Learning rate is too big, training
Number is excessively high, and be easy to cause over-fitting.So best point could be obtained by choosing learning rate appropriate and frequency of training
Class effect.So experimental setup learning rate rises to 0.5 every 0.1 since 0.1, frequency of training is from 500 times every on 500 times
It is raised to 3000 times, is combined for totally 30 kinds by the learning rate for combining different with frequency of training, to find the optimized parameter of network, experiment
It proves, when frequency of training is 1000 times, and learning rate is 0.1, accuracy rate highest reaches 98.11%, shown in experimental result Fig. 6.
In conclusion based on Fault Diagnosis of Roller Bearings of the S-transformation in conjunction with deep learning is improved, first by changing
Obtain the eigenvalue matrix of signal into S-transformation, later by sparse autocoder neural network from simple to complex, by rudimentary
To the advanced substantive characteristics for automatically extracting input data, and energy automatic mining goes out the abundant information being hidden in given data,
The dependence to a large amount of signal processing technologies and diagnostic experiences is got rid of, the efficiency of fault signature extraction is improved, it is effective to improve
The accuracy rate of rolling bearing fault diagnosis.This method is of great significance to the intelligent trouble diagnosis of rolling bearing.
Specific embodiments of the present invention are described above.It is to be appreciated that the invention is not limited to above-mentioned
Particular implementation, those skilled in the art can make a variety of changes or modify within the scope of the claims, this not shadow
Ring substantive content of the invention.In the absence of conflict, the feature in embodiments herein and embodiment can any phase
Mutually combination.
Claims (3)
1. a kind of based on the Fault Diagnosis of Roller Bearings for improving S-transformation and deep learning, which is characterized in that including walking as follows
It is rapid:
Step S1: vibration signal of the rolling bearing under different faults state is obtained；
Step S2: doing improved S-transformation to vibration signal, improves the resolution of its time domain by way of window width regulatory factor is arranged
Rate enhances its detection effect to impact signal, extracts the fault signature of signal, obtains vibration signal by improving S-transformation
Eigenmatrix；
Step S3: eigenmatrix is launched into input of the feature vector as neural network by column, is divided into no label data and has
Two groups of label data, realize the pre-training of network using no label data, then with there is the entire network parameter of label data fine tuning, it is complete
At the building of sparse autocoder neural network model；
Step S4: new fault-signal to be measured is handled according to above-mentioned steps, is input in trained network model, real
The intelligent diagnostics of existing bearing fault.
2. a kind of Fault Diagnosis of Roller Bearings based on improvement S-transformation and deep learning according to claim 1,
Be characterized in that: the Gauss function expression formula of S-transformation is σ (f)=1/f, and f is frequency, and window width size is related with frequency, not by it
He influences factor, and S-transformation is improved in the step S1 by the way that window width regulatory factor is added, window width expression formula is made to become σ (f)=g/
F, after regulatory factor g is added, window function width is not only related with frequency, also changes window width by adjusting the value of g, thus plus
The strong time domain of S-transformation or the resolution ratio of frequency domain, according to Heisenberg's uncertainty principle, time-domain and frequency-domain resolution ratio cannot mention simultaneously
Height, therefore reduce window width and obtain higher time resolution, increase window width, frequency domain resolution is promoted, for bearing vibration
For signal, the effective characterization failure feature of ingredient is impacted, therefore is become in such a way that window width regulatory factor is set to promote S
The time resolution changed makes it detect the impact component in vibration signal, extracts the fault signature of signal.
3. a kind of Fault Diagnosis of Roller Bearings based on improvement S-transformation and deep learning according to claim 1,
Be characterized in that: sparse autocoder network model in step S3 building is through the following steps that realize:
Using unlabeled exemplars, single layer network, every layer of use are constructed using the unsupervised training algorithm of layer-by-layer greediness from bottom to top
Parameter learning is carried out from encryption algorithm, one layer of adjustment every time successively adjusts, obtains the weight and threshold value of network；
Using supervised learning on the basis of the weight that the first step learns, using the sample of tape label by BP algorithm from upper
Under and, entire network parameter is finely tuned, completes the building of sparse autocoder neural network model.
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| CN111539152A (en) * | 2020-01-20 | 2020-08-14 | 内蒙古工业大学 | Rolling bearing fault self-learning method based on two-stage twin convolutional neural network |
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| CN115030903A (en) * | 2022-06-16 | 2022-09-09 | 江苏大学镇江流体工程装备技术研究院 | On-line diagnosis method for early fault of rolling bearing in centrifugal pump |
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| CN113567131A (en) * | 2021-07-29 | 2021-10-29 | 沈阳建筑大学 | Bearing fault diagnosis method based on S transformation and miniature convolution neural network model |
| CN113567131B (en) * | 2021-07-29 | 2024-05-03 | 沈阳建筑大学 | Bearing fault diagnosis method based on S transformation and miniature convolutional neural network model |
| WO2023099849A1 (en) * | 2021-12-02 | 2023-06-08 | Safran Aircraft Engines | Method for automatically diagnosing a part |
| FR3130028A1 (en) * | 2021-12-02 | 2023-06-09 | Safran Aircraft Engines | Automatic part diagnostic method |
| CN115030903A (en) * | 2022-06-16 | 2022-09-09 | 江苏大学镇江流体工程装备技术研究院 | On-line diagnosis method for early fault of rolling bearing in centrifugal pump |
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