CN116337445B - Bearing fault extraction method based on multi-scale permutation entropy and kurtosis value fusion factors - Google Patents
Bearing fault extraction method based on multi-scale permutation entropy and kurtosis value fusion factors Download PDFInfo
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Abstract
The application belongs to the field of aeroengine design, and discloses a bearing fault extraction method based on multi-scale arrangement entropy and kurtosis value fusion factors, which comprises the steps of collecting fault bearing vibration signals to form a data set; then intercepting data in a certain time in the data set, calculating the theoretical characteristic frequency of the fault of the inner ring of the bearing, and obtaining a spectrogram of the fault bearing through Fourier transformation; performing wavelet packet decomposition and wavelet packet reconstruction on the vibration signals in the spectrogram to form a plurality of different wavelet bases, then performing cost function calculation on the original vibration signals according to the different wavelet bases, and selecting an optimal wavelet base to perform three-layer wavelet decomposition on the original signals; performing secondary screening on the eight decomposed WPC components, and performing SG smoothing filtering; and obtaining an optimal time domain signal, and finally obtaining fault bearing frequency domain information by utilizing Hilbert envelope demodulation, and identifying a bearing fault. The method can inhibit noise signals to a great extent, improve the signal-to-noise ratio of vibration signals and identify the fault characteristics of the rolling bearing.
Description
Technical Field
The application belongs to the field of aeroengine design, and particularly relates to a bearing fault extraction method based on multi-scale permutation entropy and kurtosis value fusion factors.
Background
Rolling bearings are critical components of various rotating machine systems, and their operating conditions can have an impact on the stability, accuracy and safety of the overall machine system operation. The rolling bearing is used as a key component of an aeroengine, and the fault diagnosis problem of the rolling bearing is one of the front-edge problems of the actual application of the current engineering. The method for diagnosing the faults of the rolling bearing comprises a method for diagnosing and identifying low signal-to-noise ratio signals based on a wavelet packet decomposition and optimized envelope spectrum combination mode and a method for diagnosing the faults of the rolling bearing based on SNDCNN, and has good capability of identifying the faults of the rolling bearing with different rotating speeds and fault types. By constructing the simulation casing, a complex transmission path of the vibration signal is simulated, and fault characteristic information is identified by using empirical mode decomposition and envelope spectrum technology. However, when the rolling bearing fails, the vibration signal contains a lot of noise, and the failure characteristic information of the rolling bearing is difficult to identify from the original vibration signal.
Therefore, how to accurately and efficiently extract the fault characteristics of the rolling bearing is a problem to be solved.
Disclosure of Invention
The purpose of the application is to provide a bearing fault extraction method based on multi-scale arrangement entropy and kurtosis value fusion factors, so as to solve the problem that the fault characteristics of the rolling bearing in the prior art are difficult to extract.
The technical scheme of the application is as follows: a bearing fault extraction method based on multi-scale permutation entropy and kurtosis value fusion factors comprises the following steps:
performing a rolling bearing fault test, collecting fault bearing vibration signals to form a data set, and sorting data in the data set according to time;
intercepting data in a certain time in a data set, calculating the theoretical characteristic frequency of the fault of the inner ring of the bearing, forming a vibration signal time domain diagram of the fault bearing, and obtaining a spectrogram of the fault bearing through Fourier transformation;
performing wavelet packet decomposition and wavelet packet reconstruction on the vibration signals in the spectrogram to form a plurality of different wavelet bases, performing cost function calculation on the original vibration signals according to the different wavelet bases, selecting an optimal wavelet base to perform three-layer wavelet decomposition on the original signals, and obtaining eight WPC components;
calculating correlation coefficients of all the WPC components, and eliminating the smallest and next smallest components in the correlation coefficients to finish one-time screening of the WPC components; calculating the correlation between each WPC component and an original signal, calculating characteristic factors of each WPC component, respectively calculating kurtosis values and multi-scale permutation entropy, performing secondary screening by using a theta value criterion to obtain a reconstructed and noise-reduced time domain signal, and performing SG smoothing filtering;
performing Hilbert envelope demodulation on the time domain signals subjected to secondary screening to obtain frequency spectrum information, and obtaining fault characteristic frequency and frequency multiplication of a fault bearing and coordination frequency formed by superposition of partial characteristic frequency and motor frequency conversion according to the frequency spectrum information to finish fault data extraction.
Preferably, the wavelet base decomposition formula is:
in the method, in the process of the invention,and->Wavelet coefficients that are wavelet transforms; z is a scale parameter, Z e Z + The method comprises the steps of carrying out a first treatment on the surface of the m and k are translation parameters, m and k belong to Z; j is a frequency parameter, j e {2 } j -1,2 j -2,…,0}；h k-2m Is a low pass filter; g k-2m Is a high pass filter;
the wavelet packet reconstruction formula is as follows:
in the method, in the process of the invention,coefficients reconstructed for the wavelet packet; h is a m-2k Reconstructing the low-pass filter; g m-2k And reconstructing the high-pass filter.
Preferably, when wavelet decomposition is performed on the wavelet base, the adopted double-scale equation is:
in the formula, { V m (t) }, m.epsilon.Z is defined by the basis function V m Wavelet packet determined by =φ (t), g k And h k A high-pass filter and a low-pass filter with a length of 2n, respectively, n representing the order of the wavelet packets and k being a panning parameter.
Preferably, when the wavelet basis is calculated by a cost function, the current cost function satisfies:
the wavelet base is determined to be the best wavelet base.
Preferably, the 8 WPC components are WPC-1 to WPC-8, respectively, and if two signal data are M and N, respectively, the correlation coefficient is:
wherein PCC (M, N) is the correlation coefficient of two signals; cov (M, N) is the covariance of the two signals;variance of M; />Variance of N;
sorting the 8 WPC components according to the magnitude of the correlation coefficient, and respectively calculating characteristic factors of the 6 WPC components after eliminating the smallest and next smallest WPC components, wherein the calculation formula is as follows:
wherein n=1, 2, …, z, z is the number of WPC components; kappa (kappa) n The kurtosis value is the n-th order WPC component kurtosis value; omega n Entropy values are multi-scale arranged for the nth order WPC component.
Preferably, the formula for calculating the WPC component kurtosis value is:
wherein E (Y) is the mathematical expectation of Y; η is the signal mean; sigma is the standard deviation of the signal;
the signal sequence x= { X with length N 1 ,x 2 ,…,x N Coarse-grained treatment, and reconstructing the treated sequence to obtain:
Y l (s)＝{y l (s),y (l+1) (s),…,y (l+(m-1)μ) (s)}
where m is the embedding dimension, μ is the delay time, l is the reconstruction component l=1, 2, …, N- (m-1) μ;
the reconstruction time sequence is arranged in an ascending order to obtain S (r) = (j) 1 ,j 2 ,…,j m ) R=1, 2, …, R, (r.ltoreq.m ≡! ) Obtaining probability P of symbol sequence occurrence r (r＝1,2,…,R)；
Then calculating the permutation entropy value of each coarse-grained sequence, namely:
preferably, the SG smoothing filter formula is:
in the method, in the process of the invention,to smooth the coefficient, x k+1 Is a signal sequence.
According to the bearing fault extraction method based on the multi-scale permutation entropy and kurtosis value fusion factor, a data set is formed by collecting fault bearing vibration signals; then intercepting data in a certain time in the data set, calculating the theoretical characteristic frequency of the fault of the inner ring of the bearing, and obtaining a spectrogram of the fault bearing through Fourier transformation; performing wavelet packet decomposition and wavelet packet reconstruction on the vibration signals in the spectrogram to form a plurality of different wavelet bases, then performing cost function calculation on the original vibration signals according to the different wavelet bases, and selecting an optimal wavelet base to perform three-layer wavelet decomposition on the original signals; performing secondary screening on the eight decomposed WPC components, and performing SG smoothing filtering; and obtaining an optimal time domain signal, and finally obtaining fault bearing frequency domain information by utilizing Hilbert envelope demodulation, and identifying a bearing fault. The method can inhibit noise signals to a great extent, improve the signal-to-noise ratio of vibration signals and identify the fault characteristics of the rolling bearing. Compared with the existing literature method, the method provided by the application reserves more complete bearing fault information on the basis of noise suppression, can accurately identify the bearing fault information and diagnose the bearing fault.
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In order to more clearly illustrate the technical solutions provided by the present application, the following description will briefly refer to the accompanying drawings. It will be apparent that the figures described below are only some embodiments of the present application.
FIG. 1 is a schematic overall flow chart of the present application;
FIG. 2 is a time domain diagram of a fault bearing vibration signal of the present application;
FIG. 3 is a spectrum diagram of the present application;
FIG. 4 is a block diagram of 8 WPC component signals of the present application;
FIG. 5 is a graph of the correspondence between WPC components and feature factors of the present application;
FIG. 6 is a time domain waveform diagram after smoothing filtering of SG of the present application;
FIG. 7 is a spectrum diagram obtained by Hilbert envelope demodulation of the present application;
fig. 8 is a schematic diagram of a partial detail of an envelope spectrum of the present application.
Detailed Description
In order to make the purposes, technical solutions and advantages of the implementation of the present application more clear, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application.
A bearing fault extraction method based on multi-scale permutation entropy and kurtosis value fusion factors selects a 6205-2RSJEM SKF type deep groove ball bearing as an analyzed bearing, and a rolling bearing laboratory consists of a motor, a torque sensor, a power tester and an electronic controller. The type of the bearing is 6205-2RS JEM SKF deep groove ball bearing, and the fault mode is single-point fault preset by the electric spark machining technology of the inner ring and the outer ring. The data set comprises fault vibration signal data of different forms of rolling bearings, the measuring point positions are vertical positions of bearing supports at the ends of the motor, the pitting diameter is 0.007 inches, the sampling frequency is 12kHz, and the data under the working conditions of the rotating speed of 1797r/min are selected for analysis.
As shown in fig. 1, the method comprises the following steps:
step S100, performing a rolling bearing fault test, acquiring fault bearing vibration signals by using a vibration sensor to form a data set, and sorting data in the data set according to time so as to facilitate calling, wherein the data acquired by different test batches are registered by using different labels;
step S200, intercepting data within a certain time, preferably 1S, in a data set, calculating a theoretical characteristic frequency of a bearing inner ring fault, forming a fault bearing vibration signal time domain diagram, and obtaining a frequency spectrum diagram of the fault bearing through Fourier transformation;
in a specific example, the theoretical characteristic frequency of the bearing inner ring fault is 162Hz through calculation, the time domain diagram of the fault bearing vibration signal is shown in fig. 2, the frequency spectrum diagram after Fast Fourier Transform (FFT) is shown in fig. 3, and it can be seen from the original time domain signal that the bearing vibration signal contains a large amount of noise. In fig. 3, the characteristic frequency of the bearing inner ring fault appears at 162Hz, but the amplitude is lower and the interference information is obvious, so that it is difficult to judge the bearing fault and the fault form from the time domain and the frequency spectrum information.
Step S300, carrying out wavelet packet decomposition and wavelet packet reconstruction on the vibration signals in the spectrogram to form a plurality of different wavelet bases, then carrying out cost function calculation on the original vibration signals according to the different wavelet bases, selecting an optimal wavelet base to carry out three-layer wavelet decomposition on the original signals to obtain eight WPC components, as shown in fig. 4;
the wavelet transformation is a local transformation of time and frequency of an input signal, and random noise signals in an original vibration signal of a bearing can be effectively restrained through function operation. The wavelet decomposition is used for decomposing the low-frequency information of the vibration signal, and the wavelet packet decomposition is used for optimizing the decomposition frequency band on the basis of the wavelet decomposition. The wavelet packet decomposition simultaneously decomposes the low-frequency information and the high-frequency information of the vibration signal, optimizes the time resolution of the low-frequency information and the frequency resolution of the high-frequency information, and has stronger time-frequency signal local analysis capability. The optimal wavelet basis wavelet packet analysis is selected, the wavelet basis is needed to decompose the vibration signal, and a group of orthogonal basis which can be formed by extracting from the wavelet packet is one wavelet packet basis. Common wavelet functions include Daubechies (db), biorthogonal (bior), symlets (sym) and the like, and the selection of different wavelet bases can have different decomposition results on vibration signals, and the results can reflect different signal characteristics.
The wavelet base decomposition formula is:
in the method, in the process of the invention,and->Wavelet coefficients that are wavelet transforms; z is a scale parameter, Z e Z + The method comprises the steps of carrying out a first treatment on the surface of the m and k are translation parameters, m and k belong to Z; j is a frequency parameter, j e {2 } j -1,2 j -2,…,0}；h k-2m Is a low pass filter; g k-2m Is a high pass filter;
the wavelet packet reconstruction formula is as follows:
in the method, in the process of the invention,coefficients reconstructed for the wavelet packet; h is a m-2k Reconstructing the low-pass filter; g m-2k And reconstructing the high-pass filter.
When the wavelet base is subjected to wavelet decomposition, the adopted double-scale equation is as follows:
in the formula, { V m (t) }, m.epsilon.Z is defined by the basis function V m Wavelet packet determined by =φ (t), g k And h k A high-pass filter and a low-pass filter of length 2n, respectively, n representing the order of the wavelet packets.
While the slave wavelet packet {2 (j-k)/2 V m (2 j-k t-h),m＝2 k The energy component L extracted from +n, h.epsilon.Z 2 A set of orthogonal groups of (R) is L 2 A wavelet packet of (R). Common wavelet functions include Daubechies (db), biorthogonal (bior), symlets (sym) and the like, and the selection of different wavelet bases can have different decomposition results on vibration signals, and the results can reflect different signal characteristics.
The value can reflect the signal regularity, and in order to ensure that the required signal contains more bearing fault information, a wavelet packet base with the minimum cost function (entropy) value is selected as a decomposition standard.
When the wavelet basis is calculated through the cost function, the current cost function satisfies the following conditions:
the wavelet base is determined to be the best wavelet base and S (0) is called an additive cost function.
The Wavelet Packet Decomposition (WPD) is used for simultaneously decomposing the low-frequency information and the high-frequency information of the vibration signal, so that the time resolution of the low-frequency information and the frequency resolution of the high-frequency information are optimized, and the device has strong capability of locally analyzing the time-frequency signal.
Step S400, calculating correlation coefficients of all the WPC components, and eliminating the smallest and next smallest components in the correlation coefficients to finish one-time screening of the WPC components; calculating the correlation between each WPC component and an original signal, calculating characteristic factors of each WPC component, respectively calculating kurtosis values and multi-scale permutation entropy, performing secondary screening by using a theta value criterion to obtain a reconstructed and noise-reduced time domain signal, and performing SG smoothing filtering;
the correlation coefficient criterion may characterize the degree of correlation of two sequences, where the pearson correlation coefficient removes the influence of two variable dimensions, i.e. the covariance normalized by M and N, reflecting a linear correlation coefficient with a value between-1 and 1. The original signal is subjected to wavelet packet decomposition to obtain a plurality of components, and the correlation coefficient between the components and the original vibration signal is calculated, so that the components containing a large amount of noise and interference can be effectively filtered, and fault information is reserved.
The 8 WPC components are WPC-1 to WPC-8 respectively, and if two signal data are M and N respectively, the correlation coefficient is:
wherein PCC (M, N) is the correlation coefficient of two signals; cov (M, N) is the covariance of the two signals;variance of M; />Variance of N; the larger the correlation coefficient is, the two components are relatedThe stronger the association.
And sorting the 8 WPC components according to the magnitude of the correlation coefficient, and eliminating the WPC-5 component and the WPC-6 component with the smallest correlation number and the next smallest correlation number to finish one-time screening of the WPC components.
The characteristic factors of the 6 retained WPC components are calculated according to a formula (9), and as shown in FIG. 5, the characteristic factors of the WPC-3, the WPC-7 and the WPC-8 can be seen to be larger than other components and are all larger than 1.5, and the characteristic factors of the WPC are calculated, specifically, the calculation is carried out through kurtosis values and multi-scale arrangement entropy respectively.
The characteristic factor criterion kurtosis is a dimensionless parameter which can embody impact components in bearing signals, and is sensitive to bearing fault information. When the rolling bearing has no fault, the vibration signal is normally distributed, and the kurtosis value is within 3; when the rolling bearing breaks down, the probability density of impact signals caused by the faults can be increased, kurtosis values can be increased, the more fault impact information contained in the vibration signals is used for keeping bearing fault characteristic information when the WPC component (wavelet packet node component) is selected, and a plurality of components with larger kurtosis values can be selected for reconstruction. The formula for calculating the kurtosis value of the WPC component is as follows:
wherein E (Y) is the mathematical expectation of Y; η is the signal mean; sigma is the standard deviation of the signal. In order to keep bearing fault characteristic information when the WPC component is selected, a plurality of components with larger kurtosis values can be selected for reconstruction.
The permutation entropy can detect the complexity and randomness of the time sequence on a single scale, the multiscale permutation entropy optimizes the complexity and randomness, and can detect the characteristic information contained in the time sequence on multiple scales.
The signal sequence x= { X with length N 1 ,x 2 ,…,x N Coarse-grained treatment, and reconstructing the treated sequence to obtain:
Y l (s)＝{y l (s),y (l+1) (s),…,y (l+(m-1)μ) (s)} (7)
where m is the embedding dimension, μ is the delay time, l is the reconstruction component l=1, 2, …, N- (m-1) μ;
the reconstruction time sequence is arranged in an ascending order to obtain S (r) = (j) 1 ,j 2 ,…,j m ) R=1, 2, …, R, (r.ltoreq.m ≡! ) Obtaining probability P of symbol sequence occurrence r (r＝1,2,…,R)；
The permutation entropy value, i.e. MPE value, of each coarsening sequence is then calculated:
in order to avoid the problem that the filtering of the WPC component by a single parameter possibly leads to the filtering of the component containing fault information, the kurtosis value is fused with the multi-scale permutation entropy, the WPC component is filtered again by the same specific gravity, and the calculation formula of the theta value is as follows:
wherein n=1, 2, …, z, z is the number of WPC components; kappa (kappa) n The kurtosis value is the n-th order WPC component kurtosis value; omega n Entropy values are multi-scale arranged for the nth order WPC component.
Carrying out signal reconstruction on the WPC component subjected to secondary screening by using a theta value criterion; in order to increase the signal-to-noise ratio of the vibration signal, the reconstructed signal is subjected to secondary noise reduction by using SG smoothing filter, and finally the optimal time domain waveform is obtained as shown in fig. 6. It can be seen that the periodic impact component of the reconstructed time domain signal is more obvious, and the fault information is more prominent.
The SG filtering is a filtering method based on local polynomial least square fitting in the time domain, and is characterized in that noise can be filtered and the shape and width of the signal can be ensured not to be changed. The SG smoothing filter formula is:
in the method, in the process of the invention,to smooth the coefficient, x k+1 Is a signal sequence.
Step S500, hilbert envelope demodulation is performed on the time domain signal after the secondary screening to obtain spectrum information, as shown in FIG. 7, the spectrum information can be seen to be located in a frequency band [0,1000 ]]Can clearly extract the fault characteristic frequency F of the bearing inner ring i =162 Hz, and frequency multiplication thereof 2F i ＝323Hz、3F i ＝485Hz、4F i ＝647Hz、5F i =808 Hz and 6F i =970 Hz, and the fault signature frequency is [0,1000]The frequency peak value in the frequency band can clearly identify the rolling bearing fault. The local details of the envelope spectrum are shown in FIG. 8, at [0,400 ]]Besides the fault characteristic frequency and the frequency multiplication thereof, the frequency band can be seen to have a harmonic frequency formed by overlapping part of the characteristic frequency and the motor frequency, the part of harmonic components are because the inner ring can synchronously run along with the rotating shaft in the working process of the bearing system, the fault position of the bearing changes along with the running of the rotating shaft, and the periodic change occurs, and the part of harmonic components are also important reference information for diagnosing the faults of the rolling bearing.
The method comprises the steps of collecting vibration signals of a fault bearing to form a data set; then intercepting data in a certain time in the data set, calculating the theoretical characteristic frequency of the fault of the inner ring of the bearing, and obtaining a spectrogram of the fault bearing through Fourier transformation; performing wavelet packet decomposition and wavelet packet reconstruction on the vibration signals in the spectrogram to form a plurality of different wavelet bases, then performing cost function calculation on the original vibration signals according to the different wavelet bases, and selecting an optimal wavelet base to perform three-layer wavelet decomposition on the original signals; performing secondary screening on the eight decomposed WPC components, and performing SG smoothing filtering; and obtaining an optimal time domain signal, and finally obtaining fault bearing frequency domain information by utilizing Hilbert envelope demodulation, and identifying a bearing fault. The method can inhibit noise signals to a great extent, improve the signal-to-noise ratio of vibration signals and identify the fault characteristics of the rolling bearing. Compared with the existing literature method, the method provided by the application reserves more complete bearing fault information on the basis of noise suppression, can accurately identify the bearing fault information and diagnose the bearing fault.
The foregoing is merely specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily conceivable by those skilled in the art within the technical scope of the present application should be covered in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (5)
1. A bearing fault extraction method based on a multi-scale permutation entropy and kurtosis value fusion factor is characterized by comprising the following steps:
performing a rolling bearing fault test, collecting fault bearing vibration signals to form a data set, and sorting data in the data set according to time;
intercepting data in a certain time in a data set, calculating the theoretical characteristic frequency of the fault of the inner ring of the bearing, forming a vibration signal time domain diagram of the fault bearing, and obtaining a spectrogram of the fault bearing through Fourier transformation;
performing wavelet packet decomposition and wavelet packet reconstruction on the vibration signals in the spectrogram to form a plurality of different wavelet bases, performing cost function calculation on the original vibration signals according to the different wavelet bases, selecting an optimal wavelet base to perform three-layer wavelet decomposition on the original signals, and obtaining eight WPC components;
calculating correlation coefficients of all the WPC components, and eliminating the smallest and next smallest components in the correlation coefficients to finish one-time screening of the WPC components; calculating the correlation between each WPC component and an original signal, calculating characteristic factors of each WPC component, respectively calculating kurtosis values and multi-scale permutation entropy, performing secondary screening by using a theta value criterion to obtain a reconstructed and noise-reduced time domain signal, and performing SG smoothing filtering;
performing Hilbert envelope demodulation on the time domain signals subjected to secondary screening to obtain frequency spectrum information, and obtaining fault characteristic frequency and frequency multiplication of a fault bearing and coordination frequency formed by superposition of partial characteristic frequency and motor frequency conversion according to the frequency spectrum information to finish fault data extraction;
the 8 WPC components are WPC-1 to WPC-8 respectively, and if two signal data are M and N respectively, the correlation coefficient is:
wherein PCC (M, N) is the correlation coefficient of two signals; cov (M, N) is the covariance of the two signals;variance of M;variance of N;
sorting the 8 WPC components according to the magnitude of the correlation coefficient, and respectively calculating characteristic factors of the 6 WPC components after eliminating the smallest and next smallest WPC components, wherein the calculation formula is as follows:
wherein n=1, 2, …, z, z is the number of WPC components; kappa (kappa) n The kurtosis value is the n-th order WPC component kurtosis value; omega n Entropy values are arranged for the n-th order WPC component in a multi-scale mode;
the formula for calculating the kurtosis value of the WPC component is as follows:
wherein E (Y) is the mathematical expectation of Y; η is the signal mean; sigma is the standard deviation of the signal;
the signal sequence x= { X with length N 1 ,x 2 ,…,x N Coarse-grained treatment, and reconstructing the treated sequence to obtain:
Y l (s)＝{y l (s),y (l+1) (s),…,y (l+(m-1)μ) (s)}
where m is the embedding dimension, μ is the delay time, l is the reconstruction component l=1, 2, …, N- (m-1) μ;
the reconstruction time sequence is arranged in an ascending order to obtain S (r) = (j) 1 ,j 2 ,…,j m ) R=1, 2, …, R, (r.ltoreq.m ≡! ) Obtaining probability P of symbol sequence occurrence r (r＝1,2,…,R)；
Then calculating the permutation entropy value of each coarse-grained sequence, namely:
2. the bearing fault extraction method based on the multi-scale permutation entropy and kurtosis value fusion factor of claim 1, wherein the wavelet base decomposition formula is:
in the method, in the process of the invention,and->Wavelet coefficients that are wavelet transforms; z is a scale parameter, Z e Z + The method comprises the steps of carrying out a first treatment on the surface of the m and k are translation parameters, m and k belong to Z; j is a frequency parameter, j e {2 } j -1,2 j -2,…,0}；h k-2m Is a low pass filter; g k-2m Is a high pass filter;
the wavelet packet reconstruction formula is as follows:
in the method, in the process of the invention,for wavelet packet weightThe constructed coefficients; h is a m-2k Reconstructing the low-pass filter; g m-2k And reconstructing the high-pass filter.
3. The bearing fault extraction method based on the multi-scale permutation entropy and kurtosis value fusion factor according to claim 1, wherein the adopted double-scale equation is:
in the formula, { V m (t) }, m.epsilon.Z is defined by the basis function V m Wavelet packet determined by =φ (t), g k And h k A high-pass filter and a low-pass filter with a length of 2n, respectively, n representing the order of the wavelet packets and k being a panning parameter.
4. The bearing fault extraction method based on the multi-scale permutation entropy and kurtosis value fusion factor according to claim 1, wherein when the wavelet basis is calculated through the cost function, the current cost function satisfies:
the wavelet base is determined to be the best wavelet base.
5. The bearing fault extraction method based on the multi-scale permutation entropy and kurtosis value fusion factor of claim 1, wherein the SG smoothing filter formula is:
in the method, in the process of the invention,to smooth the coefficient, x k+i Is a signal sequence.
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| CN108375472A (en) * | 2018-02-12 | 2018-08-07 | 武汉科技大学 | Based on the Method for Bearing Fault Diagnosis and system and device for improving experience wavelet transformation |
| JP2021018818A (en) * | 2019-07-18 | 2021-02-15 | 浙江大学Ｚｈｅｊｉａｎｇ Ｕｎｉｖｅｒｓｉｔｙ | Propeller cavitation state detection method based on wavelet and principal component analysis |
| CN113780056A (en) * | 2021-07-22 | 2021-12-10 | 山东科技大学 | Rolling bearing fault diagnosis method based on vibration signal |
| CN113834658A (en) * | 2021-10-27 | 2021-12-24 | 沈阳航空航天大学 | Early fault identification method for rolling bearing based on WPD-KVI-Hilbert |
| JP2022087010A (en) * | 2020-11-30 | 2022-06-09 | ▲広▼州大学 | Time varying structure instantaneous frequency determination method, system, device, and storage medium |
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| US11188065B2 (en) * | 2017-09-23 | 2021-11-30 | Nanoprecise Sci Corp. | System and method for automated fault diagnosis and prognosis for rotating equipment |
| CN108388860B (en) * | 2018-02-12 | 2020-04-28 | 大连理工大学 | Aero-engine rolling bearing fault diagnosis method based on power entropy spectrum-random forest |
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| CN108375472A (en) * | 2018-02-12 | 2018-08-07 | 武汉科技大学 | Based on the Method for Bearing Fault Diagnosis and system and device for improving experience wavelet transformation |
| JP2021018818A (en) * | 2019-07-18 | 2021-02-15 | 浙江大学Ｚｈｅｊｉａｎｇ Ｕｎｉｖｅｒｓｉｔｙ | Propeller cavitation state detection method based on wavelet and principal component analysis |
| JP2022087010A (en) * | 2020-11-30 | 2022-06-09 | ▲広▼州大学 | Time varying structure instantaneous frequency determination method, system, device, and storage medium |
| CN113780056A (en) * | 2021-07-22 | 2021-12-10 | 山东科技大学 | Rolling bearing fault diagnosis method based on vibration signal |
| CN113834658A (en) * | 2021-10-27 | 2021-12-24 | 沈阳航空航天大学 | Early fault identification method for rolling bearing based on WPD-KVI-Hilbert |
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