CN109883704A - A kind of extracting method of the Rolling Bearing Fault Character based on EEMD and K-GDE - Google Patents

A kind of extracting method of the Rolling Bearing Fault Character based on EEMD and K-GDE Download PDF

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CN109883704A
CN109883704A CN201910179215.7A CN201910179215A CN109883704A CN 109883704 A CN109883704 A CN 109883704A CN 201910179215 A CN201910179215 A CN 201910179215A CN 109883704 A CN109883704 A CN 109883704A
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李康强
冯志鹏
神克常
孙宏图
张建伟
徐阳
郭艳利
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Ludong University
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Abstract

The invention discloses a kind of extracting method of Rolling Bearing Fault Character based on EEMD and K-GDE, S1. measures bearing vibration using acceleration transducer and collector;S2. EEMD decomposition is carried out to bearing vibration signal;S3. the kurtosis index of each essential modular function itself is calculated;S4. the related coefficient between each essential modular function and original signal is calculated;S5. the sensitive simple component of kurtosis index and the maximum essential modular function of related coefficient as next step analysis in all essential modular functions is selected;S6. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;S7. Fourier is carried out to envelope range value to convert to obtain k-GDE envelope spectrum, by match peak frequency and Rolling Bearing Fault Character frequency, realize fault diagnosis.For the extracting method of the Rolling Bearing Fault Character of the invention based on EEMD and K-GDE on calculating amplitude envelope, it is accurately reliable to reach algorithm as a result, calculates simple and effective.

Description

A kind of extracting method of the Rolling Bearing Fault Character based on EEMD and K-GDE
Technical field
The present invention relates to fault signatures to extract field more particularly to a kind of rolling bearing fault based on EEMD and K-GDE The extracting method of feature.
Background technique
For rolling bearing as one of the most frequently used part of rotating machinery, running quality often determines the workability of whole system Energy.The vibration signal generated in operational process often has multi -components and non-stationary property, while adjoint typical modulating action, Frequency spectrum shows as the sideband that resonant frequency two sides are formed to the modulation of resonant frequency, and side in practical bearing vibration signals spectrograph Band is often non-symmetrical.In addition, multi-source noise and the unstability of vibration transfer path etc. in Practical Project test Deng all bringing difficulty to rolling bearing fault diagnosis.
It is varied for the method for rolling bearing diagnosis in engineering, such as: analysis of vibration signal method, acoustic-emission, magnetic Property method and iron spectrometry etc..All multi-methods are each has something to recommend him, and wherein analysis of vibration signal method is simple and efficient with it is used widely. On this basis, following Method for Bearing Fault Diagnosis has been developed in recent years: then extracting failure spy by first decomposing multi -components Sign, such as the rolling bearing early detection side of the Hilbert vibration decomposition based on EMD (empirical mode decomposition) and related coefficient Method, the rolling bearing fault diagnosis research based on EMD and Teager energy operator.These methods are the development of rolling bearing diagnosis Provide more approach.But it is the methods of above-mentioned there are also some defects, EMD method first may be produced when decomposing multi -components The problems such as raw modal overlap and end effect, secondly, such decomposition, which often only selects first, decomposites the essential modular function come Next step analysis is carried out, without considering that preferentially selection includes maximum fault characteristic information from multiple simple components after decomposition Simple component next step analysis is carried out as sensitive component, therefore above-mentioned various methods are in practical applications it is possible that accidentally Sentence even diagnostic error etc., in addition its specific diagnosis calculating process is also comparable cumbersome, and efficiency is lower.
Summary of the invention
The purpose of the present invention: in terms of decomposing multi -components, eliminate tradition EMD bring modal overlap the problem of;It is selecting Analyze on object, select include maximum fault characteristic information component as sensitive component progress next step analysis;It is calculating In amplitude envelope, it is accurately reliable to reach algorithm, calculates simple and effective.
In order to solve the above technical problems, the technical scheme adopted by the invention is that:
The extracting method of Rolling Bearing Fault Character of the one kind based on EEMD and K-GDE (K value generates the differential equation), packet It includes:
S1. bearing vibration is measured using acceleration transducer and collector, obtains bearing vibration signal;
S2. EEMD decomposition is carried out to bearing vibration signal, obtains several essential modular functions (english abbreviation IMF) With a residual components;
S3. the kurtosis index of each essential modular function itself is calculated;
S4. the related coefficient between each essential modular function and original signal is calculated;
S5. selection kurtosis index and related coefficient are better than other IMF, specifically, select kurtosis index and related coefficient The sum of maximum IMF as next step analysis sensitive simple component;This is because rolling bearing local damage failure can generate punching Hit, impact is more obvious that then kurtosis index is higher, therefore using kurtosis index can measure wherein comprising buckles number;And it is essential Between mode function and original signal related coefficient reflection wherein comprising the true ingredient of signal number.It therefore, can be according to each The size of matter mode function kurtosis index and related coefficient preferably goes out the essential modular function to Fault-Sensitive.
S6. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;K value model Enclose forWherein fsFor the sample frequency taken when acquisition bearing vibration signal, f is carrier frequency;
S7. Fourier is carried out to envelope range value to convert to obtain k-GDE envelope spectrum, pass through match peak frequency and the axis of rolling Fault characteristic frequency is held, realizes fault diagnosis.
Based on the above technical solution, the present invention can also be improved as follows.
Preferably, the step S2 include it is following step by step:
S21. original signal x (t) is defined, setting needs to decompose obtained IMF quantity Ns;The number of white noise is added in setting Nc;
S22. white noise is added into x (t), obtains noisy acoustical signalWherein subscript j indicates that white noise is added in jth time Sound;White noise acoustic amplitude is 0.2 times of the standard deviation of x (t);
S23. it findsIn all Local modulus maxima and minimum point;
S24. use cubic spline curve be fitted respectively all Local modulus maxima and minimum point as coenvelope line and Lower envelope line;The average value m for calculating envelope up and down, with noisy acoustical signalEnvelope average value m up and down is subtracted to obtain
If h meets two conditions of IMF, step S25 is executed;
If h is unsatisfactory for the condition of IMF, it is regarded asStep S23 is jumped back to, until obtained h meets the item of IMF Part;
S25. it obtains jth time and decomposes i-th of IMF component:
It obtains jth time and decomposes the i-th rank residual components:
Whether judge i < Ns;If so, using rjiInstead ofExecute step S23;
It is no to then follow the steps S26;
S26. do you judge j < Nc? if so, withInstead of x (t), step S22 is executed, it is no to then follow the steps S27;
S27. the sequencing of the IMF gone out according to each Cycle-decomposition, will decompose i-th obtained of IMF every timejiCollection merges It is average, i-th of IMF of EEMD decomposition is obtained, i.e.,
Preferably, the step S3 include it is following step by step:
S31. the time series for defining discrete signal is x1,x2,x3,x4,……xN
S32. the root-mean-square value of discrete signal is
S33. the kurtosis value of discrete signal is
S34. kurtosis index is the ratio between 4 powers of kurtosis and root-mean-square value, is
Preferably, the step S4 include it is following step by step:
S41. two discrete signals for defining related coefficient to be asked first are respectively X and Y;X is derived from rolling
Bear vibration original signal, Y are derived from IMFi
S42. the average value of X and Y are sought respectively,
S43. the related coefficient of two discrete signals is
Preferably, the step S6 include it is following step by step:
S61. basic status function is defined first,WhereinIt is displacement signal x clock synchronization Between t first differentialIndicate speed variables;It is second-order differential of the signal x to time tRepresent acceleration change Amount.And function of state δxIt can be expressed as the change rate of displacement signal x,It representsChange rate, kxConstant is expressed as two The product of person;
S62. for simple component amplitude-modulation frequency-modulation signalFor, wherein A (t) is amplitude modulation function, and ω is Frequency,For initial phase.Signal can be considered as the form of a solution of second order differential equation, and second order differential equation can be by base This function of state is constituted, and form isWherein δAAnd kAFor amplitude modulation function A (t) function of state.δωFor the function of state of frequencies omega;
S63. in general, the variation of modulated signal wants much slower compared to the variation of carrier signal, amplitude modulation item and frequency modulation item at this time Modulating frequency relative to the carrier frequency of signal be gradual, therefore can be approximated to be constant.Substituting into can in the formula in S62 Release envelope range value formula be
S64. for discrete signal x (n)=Acos (ω n+ θ), wherein A is vibration amplitude, and ω is intrinsic frequency, and θ is first Beginning phase, n are the discrete point of discrete signal.Construct its 3 points k value discrete signal, x (n-k)=Acos [ω (n-k)+θ], x (n) =Acos (ω n+ θ), x (n+k)=Acos [ω (n+k)+θ];
S65. the first differential in n point can be released by the combinations of three point K value discrete signal formula isSecond-order differential is
S66. envelope range value, which can be released, in the formula substituted into S63 is
S67. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;K value model Enclose forWherein fsFor the sample frequency taken when acquisition bearing vibration signal, f is carrier frequency.
Preferably, the step S67 selects multiple K values to carry out pre-demodulating point at equal intervals in K value value range first Analysis is selected the highest K value of characteristic frequency amplitude in pre-demodulating analysis result, the amplitude packet of sensitive component is sought based on K-GDE method Network.
Compared with prior art, the present invention has the following technical effect that
The extracting method of Rolling Bearing Fault Character based on EEMD and K-GDE of the invention calculate amplitude envelope on, It is accurately reliable to reach algorithm, calculates simple and effective.
Detailed description of the invention
Fig. 1 is the GB6220 deep-groove ball rolling bearing schematic diagram taken in the embodiment of the present invention;
Fig. 2 is the flow chart of extracting method of the invention;
Fig. 3 is the subdivision flow chart of step 2 of the present invention;
Fig. 4 is the time domain waveform of the housing washer fault vibration signal acquired in embodiment;
Fig. 5 is the first six IMF after EEMD is decomposed;
Fig. 6 is the related coefficient of each IMF and original signal;
Fig. 7 is the kurtosis index of each IMF;
Fig. 8 is the result for taking different K values to carry out pre-demodulating analysis;
Fig. 9 is the amplitude envelope of the sensitive component acquired when taking K=2 based on K-GDE method;
Figure 10 is to carry out Fourier to the envelope in Fig. 9 to convert to obtain k-GDE envelope spectrum;
In the accompanying drawings, list of designations represented by each label is as follows:
1., outer ring;2., ball;3., inner ring;D, sphere diameter
Specific embodiment
The principle and features of the present invention will be described below with reference to the accompanying drawings, and the given examples are served only to explain the present invention, and It is non-to be used to limit the scope of the invention.
Experiment use model GB6220 deep-groove ball rolling bearing, bearing schematic diagram as shown in Figure 1, by outer ring 1., ball 2., 3. inner ring forms;The detail parameters of rolling bearing are as shown in table 1.
1 rolling bearing GB6220 basic parameter of table
In order to simulate the local fault of each component part in rolling bearing, processing a diameter in bearing outer ring is 2mm, depth are the pit of 1mm, and processing method is electrical discharge machining.In an experiment, motor speed is set as 444r/min, by adding The amplification of mounted mechanism power, the load being applied on rolling bearing is 15.68kN, and data sampling frequency is set as 10kHz.Root According to the parameter of rolling bearing, the fault characteristic frequency of each element of bearing is calculated separately, as shown in table 2.
2 Rolling Bearing Fault Character frequency (Hz) of table
Shown in referring to figure 2., the extracting method of the Rolling Bearing Fault Character based on EEMD and K-GDE includes:
S1. bearing vibration is measured using acceleration transducer and collector, obtains bearing vibration signal;
The present embodiment is chosen outer ring fault vibration signal and is analyzed, shown referring to figure 4., and Fig. 4 is to utilize acceleration The Acceleration pulse that the housing washer of sensor and collector strategy vibrates.
S2. EEMD decomposition is carried out to bearing vibration signal, obtains several essential modular functions and a residual components; White noise can be added in EEMD facture on the basis of original signal first, and the white noise amplitude of addition is set as practical bearing vibration 0.2 times of the standard deviation of signal cycle-index 100 times, then carries out EMD screening again and decomposes;Shown in referring to figure 5., Fig. 5 is warp The first six IMF essence modular function after EEMD decomposition.
S3. the kurtosis index of each essential modular function itself is calculated;As shown in fig. 7, to count counted each IMF essence modular function Kurtosis index;
S4. the related coefficient between each essential modular function and original signal is calculated;As shown in fig. 6, outside for each IMF and original Enclose the related coefficient of fault-signal;
S5. selection kurtosis index and related coefficient are better than others IMF, specifically, select kurtosis index and phase relation Sensitive simple component of the maximum IMF of the sum of number as next step analysis;This is because rolling bearing local damage failure can generate Impact, impact are more obvious that then kurtosis index is higher, thus using kurtosis index can measure wherein comprising buckles number;And this Between matter mode function and original signal related coefficient reflection wherein comprising the true ingredient of signal number.It therefore, can be according to each The size of essential modular function kurtosis index and related coefficient preferably goes out the essential mode function to Fault-Sensitive.From Fig. 6 and Fig. 7 In as can be seen that the component kurtosis index of IMF2 and the value of related coefficient are larger for other IMF, therefore be selected as quick Component is felt as analysis in next step.
S6. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;K value model Enclose forWherein fsFor the sample frequency taken when acquisition bearing vibration signal, f is carrier frequency;
Selection different K values first carry out pre-demodulating analysis, as shown in Figure 8, it can be seen that after being decomposed using EEMD, different K There are the amplitude Characteristics outstanding for meeting characteristic frequency in the calculated result of value, wherein feature frequency in the method calculated result of K=2 Rate amplitude highest, therefore K=2 is selected, the amplitude envelope of sensitive component is sought based on K-GDE method.
S7. Fourier is carried out to envelope range value to convert to obtain k-GDE envelope spectrum, pass through match peak frequency and the axis of rolling Fault characteristic frequency is held, realizes fault diagnosis.As shown in Figure 10, it can be seen that frequency amplitude very outstanding corresponds respectively to roll 1~4 frequency multiplication of moving axis bearing outer-ring fault characteristic frequency, it was demonstrated that failure occurs in outer ring, and diagnosis effect is clearly.
Preferably, the step S2 include it is following step by step:
S21. original signal x (t) is defined, setting needs to decompose obtained IMF quantity Ns;The number of white noise is added in setting Nc;
S22. white noise is added into x (t), obtains noisy acoustical signalWherein subscript j indicates that white noise is added in jth time Sound;White noise acoustic amplitude is 0.2 times of the standard deviation of x (t);
S23. it findsIn all Local modulus maxima and minimum point;
S24. use cubic spline curve be fitted respectively all Local modulus maxima and minimum point as coenvelope line and Lower envelope line;The average value m for calculating envelope up and down, with noisy acoustical signalEnvelope average value m up and down is subtracted to obtain
If h meets two conditions of IMF, step S25 is executed;
If h is unsatisfactory for the condition of IMF, it is regarded asStep S23 is jumped back to, until obtained h meets IMF's Condition;
S25. it obtains jth time and decomposes i-th of IMF component:
It obtains jth time and decomposes the i-th rank residual components:
Whether judge i < Ns;If so, using rjiInstead ofExecute step S23;
It is no to then follow the steps S26;
S26. do you judge j < Nc? if so, withInstead of x (t), step S22 is executed, it is no to then follow the steps S27;
S27. the sequencing of the IMF gone out according to each Cycle-decomposition, will decompose i-th obtained of IMF every timejiCollection merges It is average, i-th of IMF of EEMD decomposition is obtained, i.e.,
Preferably, the step S3 include it is following step by step:
S31. the time series for defining discrete signal is x1,x2,x3,…,xn
S32. the root-mean-square value of discrete signal is
S33. the kurtosis value of discrete signal is
S34. kurtosis index is the ratio between 4 powers of kurtosis and root-mean-square value, is
Preferably, the step S4 include it is following step by step:
S41. two discrete signals for defining related coefficient to be asked first are respectively X and Y;
S42. the average value of X and Y are sought respectively,
S43. the related coefficient of two discrete signals is
Preferably, the step S6 include it is following step by step:
S61. basic status function is defined first,WhereinIt is displacement signal x clock synchronization Between t first differentialIndicate speed variables;It is second-order differential of the signal x to time tRepresent acceleration change Amount.And function of state δxIt can be expressed as the change rate of coherent signal xRepresent correlation functionChange rate, kxConstant It is expressed as the product of the two;
S62. for simple component amplitude-modulation frequency-modulation signalFor, wherein A (t) is amplitude modulation function, and ω is Frequency,For initial phase.Signal can be considered as the form of a solution of second order differential equation, and second order differential equation can be by base This function of state is constituted, and form isWherein δAAnd kAFor amplitude modulation function A (t) function of state.δωFor the function of state of frequencies omega;
S63. in general, the variation of modulated signal wants much slower compared to the variation of carrier signal, amplitude modulation item and frequency modulation item at this time Modulating frequency relative to the carrier frequency of signal be gradual, therefore can be approximated to be constant.Substituting into can in the formula in S62 Release envelope range value formula be
S64. for discrete signal x (n)=Acos (ω n+ θ), wherein A is vibration amplitude, and ω is intrinsic frequency, and θ is first Beginning phase, n are the discrete point of discrete signal.Construct its 3 points k value discrete signal, x (n-k)=Acos [ω (n-k)+θ], x (n) =Acos (ω n+ θ), x (n+k)=Acos [ω (n+k)+θ];
S65. the first differential in n point can be released by the combinations of three point K value discrete signal formula isSecond-order differential is
S66. envelope range value, which can be released, in the formula substituted into S63 is
S67. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;K value model Enclose forWherein fsFor the sample frequency taken when acquisition bearing vibration signal, f is carrier frequency.
The extracting method of Rolling Bearing Fault Character based on EEMD and K-GDE of the invention.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.

Claims (6)

1. a kind of extracting method of the Rolling Bearing Fault Character based on EEMD and K-GDE characterized by comprising
S1. bearing vibration is measured using acceleration transducer and collector, obtains bearing vibration signal;
S2. EEMD decomposition is carried out to bearing vibration signal, obtains several essential modular functions and a residual components;
S3. the kurtosis index of each essential modular function itself is calculated;
S4. the related coefficient between each essential modular function and original signal is calculated;
S5. the maximum essential modular function of the sum of kurtosis index and related coefficient in all essential modular functions is selected to divide as next step The sensitive simple component of analysis;
S6. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;K value range isWherein fsFor the sample frequency taken when acquisition bearing vibration signal, f is carrier frequency;
S7. Fourier is carried out to envelope range value to convert to obtain k-GDE envelope spectrum, pass through match peak frequency and rolling bearing event Hinder characteristic frequency, realizes fault diagnosis.
2. the extracting method of the Rolling Bearing Fault Character according to claim 1 based on EEMD and K-GDE, feature exist In, the step S2 include it is following step by step:
S21. original signal x (t) is defined, setting needs to decompose obtained IMF quantity Ns;The times N c of white noise is added in setting;
S22. white noise is added into x (t), obtains noisy acoustical signalWherein subscript j indicates that white noise is added in jth time; White noise acoustic amplitude is 0.2 times of the standard deviation of x (t);
S23. it findsIn all Local modulus maxima and minimum point;
S24. cubic spline curve is used to be fitted all Local modulus maxima and minimum point respectively as coenvelope line and lower packet Winding thread;The average value m for calculating envelope up and down, with noisy acoustical signalEnvelope average value m up and down is subtracted to obtain
If h meets two conditions of IMF, step S25 is executed;
If h is unsatisfactory for the condition of IMF, it is regarded asStep S23 is jumped back to, until obtained h meets the condition of IMF;
S25. it obtains jth time and decomposes i-th of IMF component:
It obtains jth time and decomposes the i-th rank residual components:
Whether judge i < Ns;If so, using rjiInstead ofExecute step S23;
It is no to then follow the steps S26;
S26. do you judge j < Nc? if so, withInstead of x (t), step S22 is executed, it is no to then follow the steps S27;
S27. the sequencing of the IMF gone out according to each Cycle-decomposition, will decompose i-th obtained of IMF every timejiCollection merges flat , i-th of IMF of EEMD decomposition is obtained, i.e.,
3. the extracting method of the Rolling Bearing Fault Character according to claim 1 or 2 based on EEMD and K-GDE, special Sign is, the step S3 specifically:
S31. the time series for defining discrete signal is x1,x2,x3,x4,……xN
S32. the root-mean-square value of discrete signal is
S33. the kurtosis value of discrete signal is
S34. kurtosis index is the ratio between 4 powers of kurtosis and root-mean-square value, is
4. the extracting method of the Rolling Bearing Fault Character according to claim 1 or 2 based on EEMD and K-GDE, special Sign is, the step S4 include it is following step by step:
S41. two discrete signals for defining related coefficient to be asked first are respectively X and Y;X is derived from the original letter of bearing vibration Number, Y is derived from IMFi
S42. the average value of X and Y are sought respectively,
S43. the related coefficient of two discrete signals is
5. the extracting method of the Rolling Bearing Fault Character according to claim 1 or 2 based on EEMD and K-GDE, special Sign is, the step S6 include it is following step by step:
S61. basic status function is defined first,Wherein x is displacement signal, corresponding step Collected bearing vibration signal in S1,It is first differential of the displacement signal x to time tIndicate speed variables;It is second-order differential of the signal x to time tRepresent acceleration variable;Function of state δxIndicate the variation of displacement signal x Rate,It representsChange rate, kxThe constant product for being expressed as the two;
S62. for simple component amplitude-modulation frequency-modulation signalFor, wherein A (t) is amplitude modulation function, and ω is frequency Rate,For initial phase;Signal can be considered as the form of a solution of second order differential equation, and second order differential equation can be by basic Function of state is constituted, and form isWherein δAAnd kAFor amplitude modulation function A (t) Function of state;δωFor the function of state of frequencies omega;
S63. in general, the variation of modulated signal wants much slower compared to the variation of carrier signal, the tune of amplitude modulation item and frequency modulation item at this time Frequency processed is gradual relative to the carrier frequency of signal, therefore can be approximated to be constant;It can be released in the formula substituted into S62 The formula of envelope range value is
S64. for discrete signal x (n)=Acos (ω n+ θ), wherein A is vibration amplitude, and ω is intrinsic frequency, and θ is initial phase Position, n are the discrete point of discrete signal;Construct its 3 points k value discrete signal, x (n-k)=Acos [ω (n-k)+θ], x (n)= Acos (ω n+ θ), x (n+k)=Acos [ω (n+k)+θ];
S65. the first differential in n point can be released by the combinations of three point K value discrete signal formula isSecond-order differential is
S66. envelope range value, which can be released, in the formula substituted into S63 is
S67. k value is chosen in value range, and the envelope range value of sensitive simple component is calculated based on k-GDE method;K value range isWherein fsFor the sample frequency taken when acquisition bearing vibration signal, f is carrier frequency.
6. the extracting method of the Rolling Bearing Fault Character according to claim 5 based on EEMD and K-GDE, feature exist In the step S67 selects multiple K values to carry out pre-demodulating analysis at equal intervals in K value value range first, selects pre- solution The highest K value of characteristic frequency amplitude in analysis result is adjusted, the amplitude envelope of sensitive component is sought based on K-GDE method.
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李康强等: "基于生成微分方程的行星齿轮箱故障振动信号解调分析", 《振动与冲击》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111985315A (en) * 2020-07-10 2020-11-24 合肥工业大学 Bearing fault signal intrinsic mode function decomposition and extraction method and device
CN113418704A (en) * 2021-06-18 2021-09-21 北京控制工程研究所 Bearing fault judgment method based on micro-vibration kurtosis improvement
CN113418705A (en) * 2021-07-23 2021-09-21 燕山大学 Early fault diagnosis method for rolling bearing
CN114486256A (en) * 2021-08-22 2022-05-13 北京燃气绿源达清洁燃料有限公司 Fault feature extraction method for CNG compressor rolling bearing
CN114486256B (en) * 2021-08-22 2023-10-31 北京燃气绿源达清洁燃料有限公司 CNG compressor rolling bearing fault feature extraction method

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Application publication date: 20190614