CN113670612B - Rolling bearing fault diagnosis method based on weighted combined envelope spectrum - Google Patents
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Abstract
The invention discloses a rolling bearing fault diagnosis method based on weighted combined envelope spectrum, which is characterized by comprising the following steps: s1: acquiring a vibration acceleration signal of a rolling bearing; s2: estimating the two-dimensional spectrum coherence of the vibration acceleration signal of the rolling bearing; s3: constructing an envelope spectrum slice weight function of the two-dimensional spectrum coherence; s4: obtaining a weighted combination envelope spectrum of the vibration acceleration signal according to the two-dimensional spectrum coherence and the envelope spectrum slice weight function; s5: analyzing the weighted combination envelope spectrum according to the related fault information of the rolling bearing to obtain an analysis result; s6: and diagnosing the rolling bearing fault according to the analysis result. The rolling bearing fault diagnosis method based on the weighted combined envelope spectrum can solve the problem that the bearing fault characteristic information cannot be effectively extracted when the existing fault diagnosis method analyzes the bearing vibration signal with multiple resonance frequency bands.
Description
Technical Field
The invention relates to the technical field of rolling bearing fault diagnosis, in particular to a rolling bearing fault diagnosis method based on weighted combination envelope spectrums.
Background
Surface damage to rolling bearing elements often provokes repetitive transient impacts, and correspondingly, vibration signals of rolling bearings often show transient impulses that occur periodically at certain characteristic frequencies. Therefore, the extraction of the periodic pulse characteristics is an important prerequisite for the fault diagnosis of the rolling bearing. Transient pulses caused by rolling bearing faults have second-order cyclostationarity, and an effective analysis method is spectral coherence. Because the spectral coherence is a two-dimensional representation of spectral frequency and cycle frequency, in application, the spectral coherence is often integrated along a spectral frequency axis to obtain an Enhanced Envelope Spectrum (Enhanced Envelope Spectrum), and fault detection and diagnosis of the rolling bearing are realized by analyzing the Enhanced Envelope Spectrum. However, the emphasis envelope spectrum is obtained by integrating spectral coherence over the whole spectral band (i.e. zero to nyquist frequency) and does not take into account the distribution difference of fault information over the whole frequency band, so that the influence of the interference components on the identification of fault characteristic frequencies cannot be effectively eliminated in the case of strong interference noise. An Improved Envelope Spectrum (Improved Envelope Spectrum) obtained by integrating spectral coherence in a resonance frequency band range can improve the fault detection capability of the Envelope Spectrum based on the spectral coherence, but the method usually selects only one resonance frequency band sensitive to faults for integration without considering other resonance frequency bands containing fault information, and bearing fault characteristic information cannot be effectively extracted when a bearing vibration signal with multiple resonance frequency bands is analyzed.
Disclosure of Invention
The invention aims to provide a rolling bearing fault diagnosis method based on a weighted combined envelope spectrum, and the method is used for solving the problem that the bearing fault characteristic information cannot be effectively extracted when the existing fault diagnosis method is used for analyzing bearing vibration signals with multiple resonance frequency bands.
The technical scheme for solving the technical problems is as follows:
the invention provides a rolling bearing fault diagnosis method based on a weighted combined envelope spectrum, which comprises the following steps:
s1: acquiring a vibration acceleration signal of a rolling bearing;
s2: estimating the two-dimensional spectrum coherence of the vibration acceleration signal of the rolling bearing;
s3: constructing an envelope spectrum slice weight function of the two-dimensional spectrum coherence;
s4: obtaining a weighted combination envelope spectrum of the vibration acceleration signal according to the two-dimensional spectrum coherence and the envelope spectrum slice weight function;
s5: analyzing the weighted combination envelope spectrum according to the related fault information of the rolling bearing to obtain an analysis result;
s6: and diagnosing the rolling bearing fault according to the analysis result.
Optionally, in step S1, a vibration acceleration signal of the rolling bearing is acquired by using a vibration acceleration sensor and a data acquisition device.
Optionally, in step S2, the two-dimensional spectrum coherence of the vibration acceleration signal of the rolling bearing is as follows:
wherein, γ x (α, f) is the two-dimensional spectral coherence of the acceleration signal, S x (alpha, f) is the spectral correlation of the vibration acceleration signal, alpha is the cycle frequency, f is the spectral frequency, S x (0,f) is the slice of the spectral correlation of the vibration acceleration signal at α =0, S x (0,f- α) is the result of a translation of the slice of the vibration acceleration signal at α =0 along the spectral frequency by α.
Alternatively, the spectral correlation of the vibration acceleration signal is expressed as:
wherein S is x (alpha, F) is the spectral correlation of the vibration acceleration signal, alpha is the cycle frequency, F is the spectral frequency, N is the sampling length of the vibration acceleration signal, F s Is the sampling frequency, R, of the vibration acceleration signal x (t n ,τ m ) Is an instantaneous autocorrelation function of the vibration acceleration signal, and
is the expectation operator, denotes the complex conjugate, t n ＝n/F s ，n＝0,1,2,…,N-1，τ m ＝m/F s ，m＝0,1,2,…N-1，t n And τ m Respectively representing the sampling instant and the time delay.
Optionally, in step S3, the two-dimensional spectrum coherent envelope spectrum slice weight function is:
wherein w (f) represents the envelope spectrum slice weight function of the two-dimensional spectrum coherence, represents the frequency domain signal-to-noise ratio measure of the envelope spectrum slice of the spectrum coherence at each spectrum frequency, and thres is a threshold.
Optionally, the frequency domain signal-to-noise ratio measure of the envelope spectral slice at each spectral frequency of the spectral coherence is expressed as:
wherein FDSNRM (f) represents the frequency domain signal-to-noise ratio measure of the envelope spectrum slice of the spectral coherence at each spectral frequency, H and L are the number of harmonics and the number of cyclic frequencies of the fault feature frequency in the envelope spectrum slice, respectively, γ x (α, f) is the two-dimensional spectral coherence of the acceleration signal, A h Denotes a frequency hf m A narrow band of centered cyclic frequencies and A h ＝{α|(h-δ)f m ≤α≤(h+δ)f m H =1,2, …, H, δ is a small positive number, f m Is the fault characteristic frequency of the rolling bearing, and alpha and f represent the cycle frequency and the spectrum frequency, respectively.
Optionally, the threshold is represented as:
thres＝μ(FDSNRM(f))+η·σ(FDSNRM(f))
where μ (-) and σ (-) are the mean and standard deviation operators, respectively, η is a non-negative coefficient used to adjust the threshold, and FDSNRM (f) represents the frequency-domain signal-to-noise ratio measure of the envelope spectral slice at each spectral frequency of the spectral coherence.
Optionally, in step S4, the weighted combination envelope spectrum of the vibration acceleration signal is represented as:
wherein WCES (alpha) is vibration acceleration signalWeighted combined envelope spectrum of signs, w (f) representing the envelope spectrum slice weight function of said two-dimensional spectral coherence, γ x (α, F) is the two-dimensional spectral coherence of the acceleration signal, F s For the sampling frequency of the vibration acceleration signal, alpha and f respectively represent the cycle frequency and the spectrum frequency, alpha i Denotes the ith discrete cycle frequency and alpha i ＝iF s N, N and F s Respectively, the sampling length and the sampling frequency of the vibration acceleration signal.
Optionally, the rolling bearing related fault information includes:
the size parameters and the rotating speed information of the rolling bearing; and/or
And obtaining the fault characteristic frequency of each element of the rolling bearing according to the size parameters and the rotating speed information of the rolling bearing.
The invention has the following beneficial effects:
the method provided by the invention does not need to divide the spectrum frequency bands with spectrum coherence, and the calculation process is simple and convenient; evaluating the distribution difference of fault characteristic information in the whole spectrum frequency band by adopting frequency domain signal-to-noise ratio measurement, and identifying envelope spectrum slices rich in fault information and dominant in interference components in spectrum coherence by introducing an information threshold; the constructed weight function can enhance the amplitude of the fault-related component and attenuate the influence of the disturbance component. The method can effectively reveal the fault characteristic information of the rolling bearing, and is an effective rolling bearing fault diagnosis method.
Drawings
FIG. 1 is a flowchart of a rolling bearing fault diagnosis method based on a weighted combination envelope spectrum according to an embodiment of the present invention;
fig. 2 shows vibration acceleration signals of an outer ring fault bearing of the rolling bearing fault diagnosis method based on the weighted combined envelope spectrum according to the embodiment of the present invention, and the spectrum coherence, the enhanced envelope spectrum, the frequency domain signal-to-noise ratio measurement, and the weighted combined envelope spectrum thereof;
fig. 3 shows vibration acceleration signals of an inner ring fault bearing of the rolling bearing fault diagnosis method based on the weighted combined envelope spectrum according to the embodiment of the present invention, and the spectrum coherence, the enhanced envelope spectrum, the frequency domain signal-to-noise ratio measurement, and the weighted combined envelope spectrum thereof.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth to illustrate, but are not to be construed to limit the scope of the invention.
Example 1
The invention provides a rolling bearing fault diagnosis method based on a weighted combined envelope spectrum, and a flow chart of the method is shown in figure 1. The method designs a frequency domain signal-to-noise ratio measure to quantitatively evaluate bearing fault characteristic information contained in each envelope spectrum slice of spectrum coherence, introduces an information threshold to identify the envelope spectrum slice rich in fault information and dominant in interference components in the spectrum coherence, and then constructs a weight function by the frequency domain signal-to-noise ratio measure and the information threshold to enhance the fault characteristic extraction and interference noise elimination capability of the envelope spectrum based on the spectrum coherence.
The technical scheme for solving the technical problems is as follows:
the invention provides a rolling bearing fault diagnosis method based on weighted combined envelope spectrum, which is shown in a reference figure 1 and comprises the following steps:
s1: acquiring a vibration acceleration signal of a rolling bearing;
s2: estimating the two-dimensional spectrum coherence of the vibration acceleration signal of the rolling bearing;
s3: constructing an envelope spectrum slice weight function of the two-dimensional spectrum coherence;
s4: obtaining a weighted combination envelope spectrum of the vibration acceleration signal according to the two-dimensional spectrum coherence and the envelope spectrum slice weight function;
s5: analyzing the weighted combination envelope spectrum according to the related fault information of the rolling bearing to obtain an analysis result;
s6: and diagnosing the rolling bearing fault according to the analysis result.
The invention has the following beneficial effects:
the method provided by the invention does not need to divide the spectrum frequency bands with spectrum coherence, and the calculation process is simple and convenient; evaluating the distribution difference of fault characteristic information in the whole spectrum frequency band by adopting frequency domain signal-to-noise ratio measurement, and identifying envelope spectrum slices rich in fault information and dominant in interference components in spectrum coherence by introducing an information threshold; the constructed weight function can enhance the amplitude of the fault-related component and attenuate the influence of the disturbance component. The method can effectively reveal the fault characteristic information of the rolling bearing, and is an effective rolling bearing fault diagnosis method.
Optionally, in step S1, a vibration acceleration signal of the rolling bearing is acquired by using a vibration acceleration sensor and a data acquisition device.
The data acquisition equipment refers to instrument equipment for acquiring vibration acceleration signals of the bearing, and comprises a data acquisition card, a computer provided with data acquisition software and the like.
Specifically, the mathematical sign of the vibration acceleration signal is: x (t) n )。
Wherein, t n ＝n/F s N =0,1, …, N-1 is the sampling instant, F s Is the sampling frequency and N is the signal sampling length.
Optionally, in the step S2, the two-dimensional Spectral Coherence (Spectral Coherence) of the vibration acceleration signal of the rolling bearing is as follows:
wherein, γ x (α, f) is the two-dimensional spectral coherence of the acceleration signal, S x (alpha, f) is the spectral correlation of the vibration acceleration signal, alpha is the cycle frequency, f is the spectral frequency, S x (0,f) is the slice of the spectral correlation of the vibration acceleration signal at α =0, S x (0,f- α) is the result of a translation of the slice of the vibration acceleration signal at α =0 along the spectral frequency by α.
Alternatively, the Spectral Correlation (Spectral Correlation) of the vibration acceleration signal is expressed as:
wherein S is x (alpha, F) is the spectral correlation of the vibration acceleration signal, alpha is the cycle frequency, F is the spectral frequency, N is the sampling length of the vibration acceleration signal, F s Is the sampling frequency, R, of the vibration acceleration signal x (t n ,τ m ) Is an instantaneous autocorrelation function of the vibration acceleration signal, an
Is an expectation operator, denotes the complex conjugate, t n ＝n/F s ，n＝0,1,2,…,N-1，τ m ＝m/F s ，m＝0,1,2,…N-1，t n And τ m Respectively representing the sampling instant and the time delay.
Optionally, in step S3, the two-dimensional spectrum coherent envelope spectrum slice weight function is:
wherein w (f) represents the envelope spectral slice weight function of the two-dimensional spectral coherence, FDSNRM (f) represents the frequency-domain signal-to-noise ratio measure of the envelope spectral slice at each spectral frequency of spectral coherence, thres is the threshold.
Alternatively, the Frequency-Domain Signal-to-Noise Ratio Measure (FDSNRM) of the envelope spectral slice of the spectral coherence at each spectral Frequency is expressed as:
wherein FDSNRM (f) represents the frequency domain signal-to-noise ratio measure of the envelope spectrum slice of the spectral coherence at each spectral frequency, H and L are the number of harmonics and the number of cyclic frequencies of the fault feature frequency in the envelope spectrum slice, respectively, γ x (α, f) is the two-dimensional spectral coherence of the acceleration signal,A h denotes a frequency hf m A narrow band of centered cyclic frequencies and A h ＝{α|(h-δ)f m ≤α≤(h+δ)f m H =1,2, …, H, δ is a small positive number, f m Is the fault characteristic frequency of the rolling bearing, alpha and f respectively represent the cycle frequency and the spectrum frequency, alpha i Denotes the ith discrete cycle frequency and i ＝iF s n, N and F s Respectively, the sampling length and the sampling frequency of the vibration acceleration signal.
Optionally, the threshold is represented as:
thres＝μ(FDSNRM(f))+η·σ(FDSNRM(f))
where μ (-) and σ (-) are the mean operator and the standard deviation operator, respectively, η is a non-negative coefficient used to adjust the threshold, and FDSNRM (f) represents the frequency-domain signal-to-noise ratio measure of the envelope spectral slice at each spectral frequency of the spectral coherence.
Optionally, in step S4, a Weighted Combined Envelope Spectrum (WCES) of the vibration acceleration signal is represented as:
wherein WCES (alpha) is a weighted combined envelope spectrum of the vibration acceleration signal, w (f) represents a slice weight function of the envelope spectrum of the two-dimensional spectrum coherence, gamma x (α, F) is the two-dimensional spectral coherence of the acceleration signal, F s For the sampling frequency of the vibration acceleration signal, α and f denote a cycle frequency and a spectrum frequency, respectively.
Optionally, the rolling bearing related fault information includes:
the size parameters and the rotating speed information of the rolling bearing; and/or
And obtaining the fault characteristic frequency of each element of the rolling bearing according to the size parameters and the rotating speed information of the rolling bearing.
Specifically, the fault characteristic frequency of each element of the rolling bearing is estimated according to the size parameter and the rotating speed information of the rolling bearing to be detected. And judging whether the fault characteristic frequency and the spectral line at the harmonic component thereof in the weighted combined envelope spectrum can be observed or not according to the fault characteristic frequency of the rolling bearing. If the fault characteristic frequency and the spectral line at the harmonic component of a certain element are very obvious, the existence of faults and the fault types of the rolling bearing can be judged.
The parameters of the method provided by the invention comprise the type of a window function, the window length, the maximum cycle frequency of observation, a threshold coefficient eta and a fault characteristic frequency f m . In the following embodiments, the window function is a Hanning (Hanning) window, the window length is 128 sampling points, and the threshold coefficient is 1.5; the maximum cycling frequency observed in example 2 was 250Hz, and the maximum cycling frequency observed in example 3 was 1200Hz; the failure characteristic frequency of example 2 was 66.42Hz, and the failure characteristic frequency of example 3 was 325.8Hz.
Example 2
Fig. 2 is a vibration acceleration signal of a rolling bearing with an outer ring fault and its spectral coherence, enhanced envelope spectrum, frequency domain signal-to-noise ratio measure and weighted combined envelope spectrum. The sampling frequency of the bearing vibration acceleration signal is 150kHz, and the length of the analyzed signal is 4s. The characteristic frequency f of the bearing outer ring fault cannot be observed in the spectrum coherence and the enhanced envelope spectrum shown in fig. 2 (b) and (c) o And the spectral lines corresponding to the harmonic waves of the rolling bearing cannot identify the outer ring fault of the rolling bearing. The frequency domain signal-to-noise ratio measure shown in fig. 2 (d) indicates that the bearing outer ring fault characteristic information is mainly distributed in a spectral frequency band near 47 kHz. The bearing outer ring fault characteristic frequency f can be clearly detected in the weighted combination envelope spectrum of the bearing vibration acceleration signal shown in FIG. 2 (e) o And its first 2 nd harmonic 2f o And 3f o And the spectral line can be judged as the fault of the bearing outer ring. Therefore, the method provided by the invention can effectively detect the fault of the outer ring of the rolling bearing.
Example 3
Fig. 3 is a vibration acceleration signal of a rolling bearing with inner ring failure and its spectral coherence, enhanced envelope spectrum, frequency domain signal-to-noise ratio measure and weighted combined envelope spectrum. The sampling frequency of the bearing vibration acceleration signal is 51.2kHz, and the length of the analyzed signal is 4s. The spectral coherence shown in FIG. 3 (b) cannot be obtainedClearly observing the characteristic frequency f of the bearing inner ring fault i And spectral lines corresponding to harmonic waves of the rolling bearing cannot identify the faults of the inner ring of the rolling bearing. The characteristic frequency f of the bearing inner ring fault can be observed in the enhanced envelope spectrum shown in FIG. 3 (c) i And its first 2 nd harmonic 2f i And 3f i The corresponding spectral lines. The frequency domain signal-to-noise ratio measure shown in fig. 3 (d) indicates that the bearing inner race fault characteristic information is mainly distributed in three spectral frequency bands near 7kHz, 11kHz and 17.5 kHz. The bearing inner ring fault characteristic frequency f can be clearly detected from the weighted combined envelope spectrum of the bearing vibration acceleration signal shown in fig. 3 (e) i And its first 2 nd harmonic 2f i And 3f i The spectral line can be judged as the bearing inner ring fault. Therefore, the method provided by the invention can effectively detect the inner ring fault of the rolling bearing.
The above description is only exemplary of the present invention and should not be taken as limiting the invention, and any modifications, equivalents, improvements and the like that are within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A rolling bearing fault diagnosis method based on weighted combination envelope spectrum is characterized by comprising the following steps:
s1: acquiring a vibration acceleration signal of a rolling bearing;
s2: estimating the two-dimensional spectrum coherence of the vibration acceleration signal of the rolling bearing;
s3: constructing an envelope spectrum slice weight function of the two-dimensional spectrum coherence;
s4: obtaining a weighted combination envelope spectrum of the vibration acceleration signal according to the two-dimensional spectrum coherence and the envelope spectrum slice weight function;
s5: analyzing the weighted combination envelope spectrum according to the related fault information of the rolling bearing to obtain an analysis result;
s6: diagnosing the rolling bearing fault according to the analysis result;
in step S4, the weighted combination envelope spectrum of the vibration acceleration signal is represented as:
wherein WCES (alpha) is a weighted combined envelope spectrum of the vibration acceleration signal, w (f) represents a slice weight function of the envelope spectrum of the two-dimensional spectrum coherence, gamma x (α, F) is a two-dimensional spectral coherence of the acceleration signal, F s A and f are sampling frequencies of the vibration acceleration signals and respectively represent a cycle frequency and a spectrum frequency;
in step S3, the envelope spectrum slice weight function of the two-dimensional spectrum coherence is:
wherein w (f) represents the envelope spectral slice weight function of the two-dimensional spectral coherence, FDSNRM (f) represents the frequency domain signal-to-noise ratio measure of the envelope spectral slice at each spectral frequency of spectral coherence, thres is a threshold;
the frequency domain signal-to-noise ratio measure of the envelope spectral slice of the spectral coherence at each spectral frequency is expressed as:
wherein FDSNRM (f) represents the frequency domain signal-to-noise ratio measure of the envelope spectrum slice of the spectral coherence at each spectral frequency, H and L are the number of harmonics and the number of cyclic frequencies of the fault feature frequency in the envelope spectrum slice, respectively, γ x (α, f) is the two-dimensional spectral coherence of the acceleration signal, A h Denotes a frequency hf m A narrow band of centered cyclic frequencies and A h ＝{α|(h-δ)f m ≤α≤(h+δ)f m H =1,2, …, H, δ is a small positive number, f m Is the fault characteristic frequency of the rolling bearing, alpha and f respectively represent the cycle frequency and the spectrum frequency, alpha i Denotes the ith discrete cycle frequency and alpha i ＝iF s * N, N and F s Respectively, the sampling length and the sampling frequency of the vibration acceleration signal.
2. The rolling bearing fault diagnosis method based on the weighted combination envelope spectrum according to claim 1, wherein in the step S1, a vibration acceleration signal of the rolling bearing is acquired by using a vibration acceleration sensor and a data acquisition device.
3. The rolling bearing fault diagnosis method based on the weighted combination envelope spectrum according to claim 1, wherein in the step S2, the two-dimensional spectrum coherence of the vibration acceleration signal of the rolling bearing is as follows:
wherein, γ x (α, f) is the two-dimensional spectral coherence of the acceleration signal, S x (alpha, f) is the spectral correlation of the vibration acceleration signal, alpha is the cycle frequency, f is the spectral frequency, S x (0,f) is the slice of the spectral correlation of the vibration acceleration signal at α =0, S x (0,f- α) is the result of a translation of the slice of the vibration acceleration signal at α =0 along the spectral frequency by α.
4. The rolling bearing fault diagnosis method based on the weighted combined envelope spectrum according to claim 3, wherein the spectral correlation of the vibration acceleration signal is represented as:
wherein S is x (alpha, F) is the spectral correlation of the vibration acceleration signal, alpha is the cycle frequency, F is the spectral frequency, N is the sampling length of the vibration acceleration signal, F s Is the sampling frequency, R, of the vibration acceleration signal x (t n ,τ m ) Is the vibrationInstantaneous autocorrelation function of acceleration signal, and
is an expectation operator, denotes the complex conjugate, t n ＝n*F s ，n＝0,1,2,…,N-1，τ m ＝m/F s ,m＝0,1,2,…t n And τ m Respectively representing the sampling instant and the time delay.
5. The rolling bearing fault diagnosis method based on the weighted combined envelope spectrum according to claim 1, wherein the threshold values are represented as:
thres＝μ(FDSNRM(f))+η·σ(FDSNRM(f))
where μ (-) and σ (-) are the mean operator and the standard deviation operator, respectively, η is a non-negative coefficient used to adjust the threshold, and FDSNRM (f) represents the frequency-domain signal-to-noise ratio measure of the envelope spectral slice at each spectral frequency of the spectral coherence.
6. The rolling bearing fault diagnosis method based on the weighted combination envelope spectrum according to any one of claims 1 to 5, wherein the rolling bearing-related fault information includes:
the size parameters and the rotating speed information of the rolling bearing; and/or
And obtaining the fault characteristic frequency of each element of the rolling bearing according to the size parameters and the rotating speed information of the rolling bearing.
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