CN108801630B - Gear fault diagnosis method for single-channel blind source separation - Google Patents
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Abstract
The invention discloses a gear fault diagnosis method for single-channel blind source separation, and relates to the technical field of gear fault diagnosis methods in a gear box. The method comprises the steps of collecting vibration signals of a gearbox by using a single accelerator sensor; performing wavelet soft threshold denoising on the acquired single-channel signal; performing CEEMD decomposition on the noise-reduced signal to obtain a plurality of IMF components and residual components; selecting a proper IMF component by adopting a method based on combination of kurtosis and a continuous mean square error rule; taking the selected IMF component and the source signal as input signals for blind source separation, and extracting a target signal by adopting a CICA method; and carrying out spectrum analysis on the extracted signal, and identifying the fault characteristics of the gear. The method is simple in principle and easy to implement, and can accurately utilize a single-channel measurement signal to diagnose the gear fault under strong noise.
Description
Technical Field
The invention relates to the technical field of gearbox fault diagnosis, in particular to a gear fault diagnosis method with single-channel blind source separation.
Background
The gear is widely applied to various rotary mechanical equipment and becomes one of the most critical parts of the equipment, so that the gear has important significance in fault diagnosis. At present, the main method for diagnosing gear faults is vibration signal analysis, but because fault signals are often submerged in a strong noise background, how to successfully extract fault characteristic information becomes the most critical step. The vibration signal of the gear is a non-stationary signal, which is often superimposed with strong noise, and classical filtering methods based on fourier transform are no longer effective in removing noise. The wavelet transform has the characteristics of good time-frequency localization and multi-resolution analysis, so that the wavelet transform is suitable for processing non-stationary signals and strong noise signals and has good noise reduction capability.
The EMD algorithm is intuitive and simple, the signal can be decomposed into a series of inherent mode functions, the mode functions can describe the input signal in different scales, and the EMD algorithm has the characteristics of orthogonality, completeness, adaptability and the like, and has great advantages in processing non-stationary signals. Although the EMD has many advantages, its decomposition is unstable, and there is a modal aliasing phenomenon, which causes a certain IMF component to contain signals of different scales, or similar scale signals exist in different IMF components, which makes the EMD decomposition very limited. EEMD is an improved method of EMD, and adds certain white noise to an original signal to enable the signal to have continuity on different scales. CEEMD is an improved algorithm based on EMD and EEMD, and auxiliary noise is added in a positive and negative pair form, so that residual auxiliary noise in a reconstructed signal can be well eliminated, the number of times of adding noise sets can be low, the calculation efficiency is high, and the phenomenon of modal aliasing is further weakened.
ICA is a separation method for separating individual source signals having independent statistical characteristics from a mixed signal. Because the prior information of the independent source signal required in the separation process is very little and the separation effect is obvious, the ICA has wide application in the fields of wireless communication, voice processing, mechanical fault diagnosis and the like. In practical application, the application of the method in the gear fault feature extraction is limited because the source signal sequence uncertainty and the number are not easy to determine and the like. In recent years, the algorithm of the cic developed on the basis of the ICA is improved, so that the problem is effectively solved, and the cic firstly utilizes the prior information to generate a reference signal and further extracts an interested independent component without knowing the number of source signals.
Disclosure of Invention
The invention aims to solve the technical problem of how to provide a fault diagnosis method which can effectively extract a gear fault signal in a gearbox by using a single-channel gearbox vibration signal.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: single-channel blind source separation
The gear fault diagnosis method is characterized by comprising the following steps:
performing wavelet soft threshold denoising on the acquired single-channel vibration signal of the gearbox;
performing CEEMD decomposition on the noise-reduced signal to obtain a plurality of IMF components and residual components;
selecting a proper IMF component by adopting a method based on combination of kurtosis and a continuous mean square error rule;
taking the selected IMF component and the source signal as input signals of a blind source component, and extracting a target signal by adopting a CICA method;
and carrying out frequency spectrum analysis on the extracted target signal, identifying fault characteristics and finishing the diagnosis of the gear fault.
The further technical scheme is that the method further comprises the following steps: a single acceleration sensor is used to acquire gearbox vibration signals.
The further technical scheme is that the method for performing wavelet soft threshold denoising comprises the following steps:
selection of wavelet basis functions and number of decomposition layers: selecting a wavelet basis function according to the characteristics of a signal, wherein the regularity of the wavelet basis function and the structural similarity of the waveform and data influence the signal denoising effect, and the symN wavelet basis is similar to a mechanical vibration waveform, so that the symN wavelet basis function is selected to perform wavelet soft threshold denoising; the noise reduction effect is different for different decomposition layer numbers, and the decomposition layer number is reasonably selected;
selecting a threshold and determining a threshold function: the wavelet coefficient under each decomposition scale is compared with the threshold value, and the purified coefficient value is obtained after processing;
wavelet reconstruction: and reconstructing the wavelet low-frequency coefficient and the decomposed high-frequency coefficients of each layer to obtain a denoised signal.
The further technical scheme is that the CEEMD decomposition of the noise-reduced signal comprises the following steps:
adding n groups of auxiliary white noises into the signals subjected to noise reduction preprocessing, wherein the auxiliary noises are added in a positive and negative pair mode, so that two sets of IMF components are generated:
wherein: s is a signal after noise reduction pretreatment; n is white noise conforming to normal distribution; m1、M2Respectively adding positive and negative paired noise signals;
EMD decomposition is carried out on each signal in the set respectively, each signal obtains a group of IMF components, wherein the jth IMF component of the ith signal is represented as cij；
The decomposition results are obtained by means of a combination of multicomponent quantities:
wherein: c. CjRepresents the j-th IMF component finally obtained by CEEMD decomposition, and n represents the group number of the auxiliary white noise.
The further technical scheme is that the method based on the combination of kurtosis and continuous mean square error criteria is as follows:
calculating the kurtosis of each IMF, wherein when the gearbox normally runs, the amplitude distribution of the collected vibration signals is similar to normal distribution, so that the kurtosis value is equal to 3, and when the gear has a fault, the kurtosis value is increased;
the criterion for Continuous Mean Square Error (CMSE), namely:
wherein H is the total length of the signal, and r is the number of decomposed IMFs;
the critical IMF component is determined according to the following two principles:
if the CMSE has a local minimum value in front of the overall minimum value, adding 1 to the position corresponding to the first local minimum value;
if the local minimum value does not exist, adding 1 to the position corresponding to the overall minimum value, wherein the position containing more fault information is the critical IMF component and the IMF components after the critical IMF component, and combining the kurtosis to select the effective IMF component.
The further technical scheme is that the method for extracting the target signal by adopting the CICA method comprises the following steps:
constructing a reference pulse signal r (t) based on the fault signal characteristic frequency of the gear, and defining a distance function of a target signal y to be extracted and the reference signal r (t) as epsilon (y, r) for representing the proximity degree of the target signal and the reference signal; epsilon (y, r) is measured by mean square error epsilon (y, r) ═ E { (y-r) }, and the mathematical model of the cic a algorithm is shown in equation (4) and equation (5):
an objective function:
max J(y)≈ρ{E[G(y)]-E[G(v)]} (4)
constraint conditions are as follows:
wherein rho is a normal number, G (-) is a nonlinear function, v is a Gaussian variable with a covariance matrix the same as y, ξ is a threshold value, equation (5) is solved by a Lagrange multiplier method to obtain the optimal estimation of a source signal, and the required signal is extracted.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the method uses the wavelet soft threshold value to perform denoising processing, can effectively improve the signal-to-noise ratio, and enables blind source separation to have good effect. The method comprises the steps of obtaining a multi-channel virtual channel through CEEMD decomposition, selecting a proper IMF component by a method based on combination of kurtosis and a continuous mean square error criterion, taking the IMF component and a source signal as input signals for blind source separation, extracting a target vibration signal through a CICA method, and identifying fault characteristics.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a method according to an embodiment of the invention;
FIG. 2 is a block diagram of a DDS experimental bench in an embodiment of the present invention;
FIG. 3 is a diagram of a gearbox drive train in an embodiment of the present invention;
FIG. 4 is a diagram of a failed gear position in an embodiment of the present invention;
FIG. 5 is a gear diagram with partially broken teeth in an embodiment of the invention;
FIG. 6a is a time domain plot of the original acquired signal;
FIG. 6b is a time domain plot of the original acquired signal after wavelet de-noising;
FIG. 7a is a signal magnitude spectrum after wavelet de-noising;
FIG. 7b is a signal envelope spectrum after wavelet de-noising;
FIG. 8 is a kurtosis value for each IMF;
FIG. 9 is the CMSE for each IMF;
FIG. 10 is a selection of suitable IMF components;
FIG. 11 is a time domain waveform of a reference signal and an extracted fault signal;
FIG. 12 is an amplitude spectrum of an extracted fault signal;
fig. 13 is an envelope spectrum of an extracted fault signal.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
As shown in fig. 1, the embodiment of the invention discloses a gear fault diagnosis method for single-channel blind source separation, and the specific implementation method comprises the following steps:
and 5, performing frequency spectrum analysis on the extracted target signal, identifying fault characteristics and finishing diagnosis of the gear fault.
In step 1, the wavelet soft threshold denoising method comprises the following steps:
1-1) selection of wavelet basis functions and number of decomposition levels: selecting a wavelet basis function according to the characteristics of a signal, wherein the regularity of the wavelet basis function and the structural similarity of the waveform and data influence the signal denoising effect, and the symN wavelet basis is similar to a mechanical vibration waveform, so that the symN wavelet basis function is selected to perform wavelet soft threshold denoising; and the noise reduction effect is different for different decomposition layer numbers, and the decomposition layer number is reasonably selected.
1-2) selecting a threshold and determining a threshold function: and (3) comparing the wavelet coefficients under each decomposition scale with the threshold value, and processing to obtain the purified coefficient value.
1-3) wavelet reconstruction: and reconstructing the wavelet low-frequency coefficient and the decomposed high-frequency coefficients of each layer to obtain a denoised signal.
In the step 2, the signal decomposition by CEEMD comprises the following steps:
adding n groups of auxiliary white noises into the signals subjected to noise reduction preprocessing, wherein the auxiliary noises are added in a positive and negative pair mode, so that two sets of IMF components are generated:
wherein: s is a signal after noise reduction pretreatment; n is white noise conforming to normal distribution; m1、M2Respectively adding positive and negative paired noise signals;
EMD decomposition is carried out on each signal in the set respectively, each signal obtains a group of IMF components, wherein the jth IMF component of the ith signal is represented as cij；
The decomposition results are obtained by means of a combination of multicomponent quantities:
wherein: c. CjRepresenting the j-th IMF component finally obtained by CEEMD decomposition; n denotes the number of sets of auxiliary white noise.
In step 3, the method based on the combination of kurtosis and continuous mean square error criterion is as follows:
and calculating the kurtosis of each IMF, wherein when the gearbox runs normally, the amplitude distribution of the collected vibration signals is similar to normal distribution, so that the kurtosis value is equal to 3, and when the gear has a fault, the kurtosis value is increased.
The criterion for Continuous Mean Square Error (CMSE), namely:
where H is the total length of the signal and r is the number of IMFs decomposed.
The critical IMF component is determined according to the following two principles: if the CMSE has a local minimum value in front of the overall minimum value, adding 1 to the position corresponding to the first local minimum value; and if the local minimum value does not exist, adding 1 to the position corresponding to the overall minimum value, wherein more fault information is the critical IMF component and the IMF component after the critical IMF component. Selecting an effective IMF component in combination with the kurtosis;
the extraction of the target signal by the CICA method adopted in the step 4 comprises the following steps:
and constructing a reference pulse signal r (t) based on the fault signal characteristic frequency of the gear, and defining a distance function of the target signal y to be extracted and the reference signal r (t) as epsilon (y, r) to represent the proximity degree of the target signal and the reference signal. Epsilon (y, r) can be measured by mean square error epsilon (y, r) ═ E { (y-r) }, and the mathematical model of the cic a algorithm is shown in equation (4) and equation (5):
an objective function:
max J(y)≈ρ{E[G(y)]-E[G(v)]} (4)
constraint conditions are as follows:
wherein rho is a normal number, G (-) is a nonlinear function, v is a Gaussian variable with a covariance matrix the same as y, ξ is a threshold value, equation (5) is actually a constraint optimization problem, and the optimal estimation of a source signal can be obtained by solving the constraint optimization problem through a Lagrange multiplier method, so that a target source signal is extracted.
Example 1:
in order to verify the effectiveness of the method, a fault diagnosis comprehensive experiment table (DDS) which is designed by SpectraQuest and can simulate industrial power transmission is adopted for experimental analysis, and the figure is shown in figure 2. The power transmission system of the experiment table consists of a 1-stage planetary gearbox, a 2-stage parallel shaft gearbox, a bearing load and a programmable magnetic brake, and the transmission system diagram of the gearbox is shown in figure 3.
The method researches and sets the local gear fault at the driving wheel Z6 position of the output stage Z6/Z7 of the dead axle gearbox, such as the position shown in FIG. 4, and the other positions have no fault on the gears (including the planetary gearbox) and all bearings. The single failure of the fixed axis gearbox gear Z6 was set to a partial tooth break failure, where the width of the broken tooth was approximately 30% of the tooth width, as shown in fig. 5; the input rotating speed of the motor is 40Hz (2400r/min), the rotating frequency transmitted to the intermediate shaft of the parallel gearbox is 2.537Hz, the number of teeth is 36, and the meshing frequency is 91.35 Hz. Data are collected by using a DASP data collector, the sampling frequency is 5120Hz, and the total sampling time length is 10 s.
Acquiring single-channel vibration data of a gearbox, firstly, performing wavelet soft threshold denoising and preprocessing to improve the signal-to-noise ratio, and acquiring a time domain source signal and a denoised signal in the diagrams 6 a-6 b; fig. 7a-7b are amplitude spectra and envelope spectra after preprocessing, from the amplitude spectra, an obvious peak value of 39.86Hz can be seen, the frequency is close to the motor input frequency of 40Hz, and a peak value of 91.18Hz close to the meshing frequency of the gear on the intermediate shaft can also be seen, but no obvious side band occurs, and the influence of other frequencies is also present, and the frequency of the shaft where the gear fault is located in the envelope spectra is still indistinguishable, so that a certain noise reduction effect can be achieved by using wavelet soft threshold, but the fault characteristic of the gear cannot be directly and effectively distinguished.
And further performing CEEMD decomposition on the single-channel signal subjected to the preliminary noise reduction to obtain 10 IMF components and a residual component. Kurtosis values and CMSE values for each IMF were calculated as shown in FIGS. 8 and 9. The kurtosis graphs show that the kurtosis values of IMF3, IMF5 and IMF6 are relatively large; the appropriate IMF is selected from the CMES map as the component after IMF3 using the principles described herein. In general, it is finally judged that the IMFs 3, 5, and 6 belong to vibration mode components, as shown in fig. 10. The reference signal and the target extraction signal obtained by using the selected IMF component and the source signal as input signals of the CICA through the CICA are shown in fig. 11.
The extracted gear fault signal is subjected to amplitude spectrum analysis, and as shown in fig. 12, the meshing frequency (theoretical value 91.35Hz) of the fault gear and the side frequency of the fault gear, which is modulated by the conversion frequency of 2.53Hz, can be clearly observed; by analyzing the envelope spectrum, as shown in fig. 13, the rotation frequency (theoretical value 2.53Hz) of the intermediate shaft where the fault gear is located and the frequency doubling component thereof can be obviously seen.
The test data processing result in the embodiment of the invention verifies the effectiveness of the method.
Claims (5)
1. A gear fault diagnosis method for single-channel blind source separation is characterized by comprising the following steps:
performing wavelet soft threshold denoising on the acquired single-channel vibration signal of the gearbox;
performing CEEMD decomposition on the noise-reduced signal to obtain a plurality of IMF components and residual components;
selecting a proper IMF component by adopting a method based on combination of kurtosis and a continuous mean square error rule;
the method based on the combination of kurtosis and continuous mean square error criteria is as follows:
calculating the kurtosis of each IMF, wherein when the gearbox normally runs, the amplitude distribution of the collected vibration signals is similar to normal distribution, so that the kurtosis value is equal to 3, and when the gear has a fault, the kurtosis value is increased;
the criterion for Continuous Mean Square Error (CMSE), namely:
wherein H is the total length of the signal, and r is the number of decomposed IMFs;
the critical IMF component is determined according to the following two principles:
if the CMSE has a local minimum value in front of the overall minimum value, adding 1 to the position corresponding to the first local minimum value;
if the local minimum value does not exist, adding 1 to the position corresponding to the overall minimum value, wherein the position containing much fault information is the critical IMF component and the IMF components behind the critical IMF component, and taking the IMF component obtained based on the kurtosis and the common IMF component of the IMF components judged by the continuous mean square error criterion as the effective IMF component;
taking the selected IMF component and the source signal as input signals of a blind source component, and extracting a target signal by adopting a CICA method;
and carrying out frequency spectrum analysis on the extracted target signal, identifying fault characteristics and finishing the diagnosis of the gear fault.
2. The method for gear fault diagnosis with single channel blind source separation according to claim 1, characterized in that the method further comprises: a single acceleration sensor is used to acquire gearbox vibration signals.
3. The single channel blind source separation gear fault diagnosis method of claim 1, characterized in that the method for performing wavelet soft threshold denoising comprises the steps of:
selection of wavelet basis functions and number of decomposition layers: selecting a wavelet basis function according to the characteristics of a signal, wherein the regularity of the wavelet basis function and the structural similarity of the waveform and data influence the signal denoising effect, and the symN wavelet basis is similar to a mechanical vibration waveform, so that the symN wavelet basis function is selected to perform wavelet soft threshold denoising; the noise reduction effect is different for different decomposition layer numbers, and the decomposition layer number is reasonably selected;
selecting a threshold and determining a threshold function: the wavelet coefficient under each decomposition scale is compared with the threshold value, and the purified coefficient value is obtained after processing;
wavelet reconstruction: and reconstructing the wavelet low-frequency coefficient and the decomposed high-frequency coefficients of each layer to obtain a denoised signal.
4. The method for gear fault diagnosis with single-channel blind source separation according to claim 1, wherein the CEEMD decomposition of the noise-reduced signal comprises the following steps:
adding n groups of auxiliary white noises into the signals subjected to noise reduction preprocessing, wherein the auxiliary noises are added in a positive and negative pair mode, so that two sets of IMF components are generated:
wherein: s is a signal after noise reduction pretreatment; n is white noise conforming to normal distribution; m1、M2Respectively adding positive and negative paired noise signals;
EMD decomposition is carried out on each signal in the set respectively, each signal obtains a group of IMF components, wherein the jth IMF component of the ith signal is represented as cij；
The decomposition results are obtained by means of a combination of multicomponent quantities:
wherein: c. CjRepresents the j-th IMF component finally obtained by CEEMD decomposition, and n represents the group number of the auxiliary white noise.
5. The single channel blind source separated gear fault diagnosis method of claim 1, characterized by: the method for extracting the target signal by adopting the CICA method comprises the following steps:
constructing a reference pulse signal r (t) based on the fault signal characteristic frequency of the gear, and defining a distance function of a target signal y to be extracted and the reference signal r (t) as epsilon (y, r) for representing the proximity degree of the target signal and the reference signal; epsilon (y, r) is measured by mean square error epsilon (y, r) ═ E { (y-r) }, and the mathematical model of the cic a algorithm is shown in equation (3) and equation (4):
an objective function:
max J(y)≈ρ{E[G(y)]-E[G(v)]} (3)
constraint conditions are as follows:
wherein rho is a normal number, G (-) is a nonlinear function, v is a Gaussian variable with a covariance matrix the same as y, ξ is a threshold value, and equation (4) is solved by a Lagrange multiplier method to obtain the optimal estimation of a source signal and extract a required signal.
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| CN111079710B (en) * | 2019-12-31 | 2023-04-18 | 江苏理工学院 | Multilayer noise reduction method based on improved CEEMD rolling bearing signal |
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| CN112945546B (en) * | 2021-01-20 | 2023-07-25 | 南京航空航天大学 | Precise diagnosis method for complex faults of gearbox |
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