CN105181334A - Rolling bearing fault detection method based on cascade multistable stochastic resonance and empirical mode decomposition (EMD) - Google Patents
Rolling bearing fault detection method based on cascade multistable stochastic resonance and empirical mode decomposition (EMD) Download PDFInfo
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Abstract
The present invention relates to a rolling bearing fault detection method based on cascade multistable stochastic resonance and EMD. The method comprises the steps of calculating the fault characteristic frequency of a to-be-diagnosed mechanical device, extracting the vibration data of the to-be-diagnosed mechanical device as the input of a cascade multistable stochastic resonance system, wherein the output of the cascade multistable stochastic resonance system is used as a vibration data result corresponding to the vibration data; carrying out the Fourier transform on the extracted vibration data result to obtain the frequency spectrum of an original signal, and determining the frequency components contained in the frequency spectrum; optimally selecting the parameters of the multistable stochastic resonance system, and introducing a vibration signal in the cascade multistable stochastic resonance system; taking the output of the last-level of the cascade multistable stochastic resonance system as the output of the cascade multistable stochastic resonance system, carrying out the EMD on the output of the system, extracting the frequency components contained in the signals and according with the prescient fault characteristic frequency, and determining whether the rolling is faulted and the faulted parts according to an EMD result.
Description
Technical field
The present invention relates to rolling bearing fault diagnosis technical field, particularly a kind of rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD.
Technical background
Rolling bearing is one of most widely used mechanical component, and be also hold one of flimsy element most in plant equipment, its operation conditions directly affects the function of whole equipment simultaneously.According to incompletely statistics, in the rotating machinery using rolling bearing, the mechanical fault of nearly 30% is all caused by bearing.The reason that bearing produces fault has fatigue flake, wearing and tearing, plastic yield, corrosion, fracture, gummed and retainer damage etc.If diagnose bearing initial failure not in time, machinery and equipment will be caused to produce catastrophic failure, thus cause huge economic loss.Therefore, diagnose out the fault features of bearing to the generation avoiding catastrophic failure, ensure that the normal operation of plant equipment has major and immediate significance.But the feature of initial failure itself is very faint, and the extraction realizing initial failure Weak characteristic has challenge.
In bearing failure diagnosis field, utilizing modern signal processing method to process bearing fault, accurately extract fault characteristic signals from containing noisy signal, is one of focus of current failure diagnosis.Existing feature extracting method is go out to send detection failure feature from the angle of stress release treatment mostly, extract at Weak characteristic and show excellent characteristic in fault diagnosis, but for the Weak characteristic signal of noise serious pollution, although noise reduction simply reduces noise to a certain extent, but also weaken characteristic signal, effect is undesirable.
Accidental resonance be a kind of noise that utilizes to strengthen the new theory of feeble signal, it is that medium causes weak periodic signal and non-linear synergistic non-linear phenomena with noise, as a kind of Weak characteristic extracting method, is applied to Detection of Weak Signals field.Compared with classic method, it strengthens Weak characteristic while attenuating noise, improves signal to noise ratio (S/N ratio), realizes the detection of feeble signal.But, only at input signal, meet certain matching condition between noise and nonlinear system, could Stochastic Resonance Phenomenon be produced, realize the extraction of Weak characteristic.
During the actual feeble signal extremely low in process signal to noise ratio (S/N ratio), the effect of single accidental resonance can not reach our re-set target, can affect to the accuracy of diagnostic result.
Summary of the invention
The present invention overcomes above-mentioned the deficiencies in the prior art, and provide a kind of rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD, technical scheme of the present invention is as follows:
A kind of rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD, the method is based on the multistable stochastic resonance system of a kind of cascade, the multistable stochastic resonance system of described cascade comprises multiple multistable stochastic resonance system, wherein, the output of the multistable stochastic resonance system of the first order is as the input of the multistable stochastic resonance system in the second level, the output of the multistable stochastic resonance system in the second level is as the input of the multistable stochastic resonance system of the third level, by that analogy, the output of the multistable stochastic resonance system of afterbody is the output of the multistable stochastic resonance system of cascade; The method content comprises the following steps:
(1) fault characteristic frequency treating diagnostic machine tool equipment is calculated, extract and treat the input of the vibration data of diagnostic machine tool equipment as the multistable stochastic resonance system of cascade, the output of the multistable stochastic resonance system of cascade is as the vibration data result corresponding to vibration data; Fourier transform is carried out to the vibration data result extracted, obtains the frequency spectrum of original signal, and determine frequency content contained in frequency spectrum;
(2) optimal choice is carried out to the parameter of multistable stochastic resonance system, vibration signal is introduced a multistable stochastic resonance system of cascade; Described multistable stochastic resonance system is described by Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t);
In formula, U (x) is multistable stochastic resonance system potential-energy function,
wherein a, b, c are parameter; S (t) is feeble signal; η (t) is average is 0, variance is 1, intensity is the white noise of D; Regulate its parameter a, b, c make it and inputted vibration signal reaches optimum matching and with there is Stochastic Resonance Phenomenon;
(3) Fourier transform is carried out to every one-level output signal of the multistable stochastic resonance system of cascade, get its frequency spectrum, observe in every one-level frequency spectrum whether have fault characteristic frequency composition; For making the process of extraction characteristic signal definitely, Fourier transform being carried out to the output of the multistable stochastic resonance system of every one-level, observes the frequency content in its frequency spectrum;
(4) using the output of the output of multistable for cascade stochastic resonance system afterbody as the multistable stochastic resonance system of cascade, system is exported and carries out empirical mode decomposition, extract contain in each signal and to conform to frequency content with the fault characteristic frequency of precognition, rule of thumb Mode Decomposition result judges the position whether this rolling bearing exists fault and break down.
In step (4), described using the output of the output of multistable for cascade stochastic resonance system afterbody as the multistable stochastic resonance system of cascade, export system and carry out empirical mode decomposition, the process of its empirical mode decomposition comprises the steps:
A, original signal is decomposed into limited intrinsic mode functions:
in formula, x (t) represents original signal; c
irepresent i-th intrinsic mode function component; r
nt () is for extracting the residual volume after n mode component;
Wherein each Intrinsic mode functions represents the characteristic signal of the Different time scales comprised in original signal, namely a progressive simple signal, and residual volume represents the trend amount information in raw data;
B, carry out Hilbert conversion by decomposing intrinsic mode functions out, when obtaining-frequently combine spectrogram, the Hilbert conversion of x (t) can be expressed as the convolution of x (t) and 1/ π t:
in formula, ρ. ν. represent the main value getting integration.
Owing to adopting technique scheme, a kind of rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD provided by the invention, compared with prior art there is such beneficial effect: the present invention utilizes multistable stochastic resonance system to the good characteristic of time domain waveform noise reduction, first export there being noise cancellation signal to carry out the multistable accidental resonance of cascade, energy gradually by high frequency to while low-frequency transfer, signal is made to obtain noise reduction, wherein, the output of the multistable accidental resonance of previous stage is as the input of rear stage, then the characteristic signal of bearing fault is extracted further, empirical mode decomposition is carried out to the signal after noise reduction, make the physical significance of EMD definitely, achieve the efficient diagnosis of bearing mechanical fault.Instant invention overcomes the problem of weak signal extraction difficulty under strong noise background, the Weak fault information by noise floods is amplified, significant to the Incipient Fault Diagnosis of rolling bearing.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of a kind of rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD of the present invention;
Fig. 2 is time domain waveform and the spectrogram of original signal;
Fig. 3 is that original signal directly carries out EMD decomposition result;
Fig. 4 is the multistable stochastic resonance system design sketch of cascade;
Fig. 5 is the EMD decomposition result that 1 grade of multistable accidental resonance of cascade exports;
Fig. 6 is the EMD decomposition result that 2 grades of multistable accidental resonances of cascade export;
Fig. 7 is the EMD decomposition result that 3 grades of multistable accidental resonances of cascade export.
Embodiment
Below in conjunction with accompanying drawing, the present invention is further detailed explanation.
The inventive method is based on the multistable stochastic resonance system of a kind of cascade, the multistable stochastic resonance system of described cascade comprises multiple stochastic resonance system, wherein, the output of the multistable stochastic resonance system of the first order is as the input of second level stochastic resonance system, the output of the multistable stochastic resonance system in the second level is as the input of third level stochastic resonance system, by that analogy, the output of the multistable stochastic resonance system of afterbody is the output of cascade stochastic resonance system.
As shown in Figure 1, the method specifically comprises the following steps a kind of rolling bearing fault testing method flow chart of steps based on the multistable accidental resonance of cascade and EMD of the present invention:
(1) calculate the fault characteristic frequency treating diagnostic machine tool equipment, extract and treat the input of the vibration data of diagnostic machine tool equipment as the multistable stochastic resonance system of cascade, the output of the multistable stochastic resonance system of cascade is as the data result corresponding to vibration data;
Fourier transform is carried out to the vibration data result extracted, obtains the frequency spectrum of original signal, and determine frequency content contained in frequency spectrum;
(2) carry out optimal choice to the parameter of multistable stochastic resonance system, the size of regulating parameter a, b, c makes itself and input signal reach optimum matching;
(3) Fourier transform is carried out to the multistable stochastic resonance system output signal of every one-level, get its frequency spectrum, observe in every one-level frequency spectrum whether have fault characteristic frequency composition;
In order to make the process of extraction characteristic signal definitely, Fourier transform being carried out to the output of the multistable stochastic resonance system of every one-level, observes the frequency content in its frequency spectrum.
(4) using the output of the output of multistable for afterbody stochastic resonance system as cascade stochastic resonance system, system is exported and carries out empirical mode decomposition, judge according to EMD result the position whether this swivel bearing exists fault and break down.The process of described empirical mode decomposition is as follows:
A, original signal is decomposed into limited intrinsic mode functions:
in formula, x (t) represents original signal; c
irepresent i-th intrinsic mode function component; r
nt () is for extracting the residual volume after n mode component;
Wherein each Intrinsic mode functions represents the characteristic signal of the Different time scales comprised in original signal, namely a progressive simple signal, and residual volume represents the trend amount information in raw data;
B, carry out Hilbert conversion by decomposing intrinsic mode functions out, when obtaining-frequently combine spectrogram, the Hilbert conversion of x (t) can be expressed as the convolution of x (t) and 1/ π t:
in formula, ρ. ν. represent the main value getting integration.
Embodiment one:
Rolling bearing is generally made up of inner ring, outer ring, rolling body and retainer four part, if rolling bearing breaks down, its failure-frequency is predictable.Suppose that the outer ring of rolling bearing is fixed, inner ring rotates with working shaft, working shaft rotating speed is N (r/min), bearing pitch diameter is D (mm), rolling body diameter is d (mm), contact angle is β (rad), and rolling body number is n, then its different faults characteristic frequency is as follows:
Characteristic frequency during bearing outer ring defectiveness:
Characteristic frequency during bearing inner race defectiveness:
Characteristic frequency during single rolling body defectiveness:
Mill frequency is touched in retainer and outer ring:
Be the bearing of SKF6205 for model, rotating speed is 1797r/min (29.95Hz), and sample frequency is 12kHz.The pitch diameter of this bearing is 39.04mm, and rolling body diameter is 7.94mm, and rolling body number is 9, and contact angle is 0 °.
For the rolling bearing of this model, as shown in table 1 through can be calculated its fault characteristic frequency.
Table 1 bearing fault characteristics frequency
| Inner ring failure-frequency | 162Hz |
| Outer ring failure-frequency | 107Hz |
| Rolling body failure-frequency | 141Hz |
| Retainer failure-frequency | 12Hz |
First, gathering bearing signal, as Fig. 2, is time domain waveform and the spectrogram of this bearing inner race fault-signal.The vibration of obvious periodic impulse is there is from the time domain waveform of Fig. 2 (a) visible signal, and in spectrogram 2 (b), spectrum energy is distributed in a very wide frequency range, and there is large spectrum peak group within the scope of 1kHz ~ 2kHz, this is the single order natural mode of vibration vibration of parts of bearings, but can't see obvious vibration performance in the low-frequency range of original spectrum.If directly carry out EMD decomposition to this signal, as shown in Figure 3, the EMD number of plies is many for decomposition result, and the IMF frequency of occurrences aliasing decomposited, concrete frequency content is differentiated unclear.Therefore, before EMD, need to carry out necessary noise reduction process to signal.
Secondly, the rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD is utilized to detect, bearing original signal is input in the multistable stochastic resonance system of cascade, cascade number is 3, here three-stage cascade is selected to be because after the multistable stochastic resonance system of third level cascade exports, first Intrinsic mode functions that EMD decomposites is characteristic frequency.Every one-level chooses separately optimum systematic parameter to its process data, and 1 grade here, 2 grades and 3 grades of cascade parameters are: b=0.72, c=-0.3, d=0.08.Using the input of the output of first order accidental resonance as second level accidental resonance, using the input of the output of second level accidental resonance as third level accidental resonance, the output of the output very cascade stochastic resonance system of third level accidental resonance.
Fig. 4 is the output of original signal after the multistable resonator system of cascade, as can be seen from Fig. 4 (b), (d) and (f), after the multistable resonator system of cascade, in original spectrum, the HFS of single order principal oscillation mode is by complete " filtering ", occurs obvious characteristic frequency f in frequency spectrum
cand frequency multiplication composition, particularly by after 3 grades of multistable resonator systems of cascade, because high-frequency energy is constantly to low-frequency transfer, in Fig. 4 (f), stay characteristic frequency f clearly
c.
Finally, EMD is carried out to the multistable stochastic resonance system of every one-level cascade, as Fig. 5,6,7, after 1 grade of multistable output of cascade, as shown in Figure 5, because HFS is weakened, the 1st IMF decomposited, the 2nd IMF and the 3rd IMF are still containing radio-frequency component, comparison of ingredients is complicated, but the 3rd IMF obviously can find out characteristic frequency f
cfrequency multiplication composition.After 2 grades and 3 grades of cascaded-outputs, because high-frequency energy is constantly to low-frequency transfer, high frequency interference gradually by filtering, fault characteristic frequency f
cmore and more clear.In Fig. 6 after 2 grades of cascaded-outputs, the 2nd the IMF mainly characteristic frequency f that empirical mode decomposition goes out
clow order frequency multiplication, and clearly can find out characteristic frequency f in the 3rd IMF
c.And in Fig. 7, after 3 grades of cascade accidental resonances, the 1st Intrinsic mode functions decomposited is exactly characteristic frequency f
c.
In sum, the method multistable for cascade stochastic resonance system combined with EMD, to extract feature feeble signal, optimizes the physical significance of EMD while removing high frequency noise, and then realizes the efficient diagnosis to mechanical fault.This method overcomes the problem of weak signal extraction difficulty under strong noise background, and the Weak fault information by noise floods is amplified, significant to the Incipient Fault Diagnosis of rolling bearing.
Above-described embodiment is only be described the preferred embodiment of the present invention; not scope of the present invention is limited; under not departing from the present invention and designing the prerequisite of spirit; the various distortion that those of ordinary skill in the art make technical scheme of the present invention and improvement, all should fall in protection domain that claims of the present invention determines.
Claims (2)
1. the rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD, it is characterized in that: the method is based on the multistable stochastic resonance system of a kind of cascade, the multistable stochastic resonance system of described cascade comprises multiple multistable stochastic resonance system, wherein, the output of the multistable stochastic resonance system of the first order is as the input of the multistable stochastic resonance system in the second level, the output of the multistable stochastic resonance system in the second level is as the input of the multistable stochastic resonance system of the third level, by that analogy, the output of the multistable stochastic resonance system of afterbody is the output of the multistable stochastic resonance system of cascade, the method content comprises the following steps:
(1) fault characteristic frequency treating diagnostic machine tool equipment is calculated, extract and treat the input of the vibration data of diagnostic machine tool equipment as the multistable stochastic resonance system of cascade, the output of the multistable stochastic resonance system of cascade is as the vibration data result corresponding to vibration data; Fourier transform is carried out to the vibration data result extracted, obtains the frequency spectrum of original signal, and determine frequency content contained in frequency spectrum;
(2) optimal choice is carried out to the parameter of multistable stochastic resonance system, vibration signal is introduced a multistable stochastic resonance system of cascade; Described multistable stochastic resonance system is described by Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t);
In formula, U (x) is multistable stochastic resonance system potential-energy function,
wherein a, b, c are parameter; S (t) is feeble signal; η (t) is average is 0, variance is 1, intensity is the white noise of D; Regulate its parameter a, b, c make it and inputted vibration signal reaches optimum matching and with there is Stochastic Resonance Phenomenon;
(3) Fourier transform is carried out to every one-level output signal of the multistable stochastic resonance system of cascade, get its frequency spectrum, observe in every one-level frequency spectrum whether have fault characteristic frequency composition; For making the process of extraction characteristic signal definitely, Fourier transform being carried out to the output of the multistable stochastic resonance system of every one-level, observes the frequency content in its frequency spectrum;
(4) using the output of the output of multistable for cascade stochastic resonance system afterbody as the multistable stochastic resonance system of cascade, system is exported and carries out empirical mode decomposition, extract contain in each signal and to conform to frequency content with the fault characteristic frequency of precognition, rule of thumb Mode Decomposition result judges the position whether this rolling bearing exists fault and break down.
2. a kind of rolling bearing fault testing method based on the multistable accidental resonance of cascade and EMD according to claim 1, it is characterized in that: in step (4), described using the output of the output of multistable for cascade stochastic resonance system afterbody as the multistable stochastic resonance system of cascade, export system and carry out empirical mode decomposition, the process of its empirical mode decomposition comprises the steps:
A, original signal is decomposed into limited intrinsic mode functions:
In formula, x (t) represents original signal; c
irepresent i-th intrinsic mode function component; r
nt () is for extracting the residual volume after n mode component;
Wherein each Intrinsic mode functions represents the characteristic signal of the Different time scales comprised in original signal, namely a progressive simple signal, and residual volume represents the trend amount information in raw data;
B, carry out Hilbert conversion by decomposing intrinsic mode functions out, when obtaining-frequently combine spectrogram, the Hilbert conversion of x (t) can be expressed as the convolution of x (t) and 1/ π t:
In formula, ρ. ν. represent the main value getting integration.
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| CN106203325A (en) * | 2016-07-07 | 2016-12-07 | 燕山大学 | Based on strengthening the Weak fault signal characteristic extracting methods cascading multistable accidental resonance |
| CN107870005A (en) * | 2016-09-27 | 2018-04-03 | 重庆邮电大学 | The normalization random resonant weak signal detection of empirical mode decomposition under over-sampling |
| CN108444698A (en) * | 2018-06-15 | 2018-08-24 | 福州大学 | Epicyclic gearbox Incipient Fault Diagnosis method based on TEO demodulation accidental resonances |
| CN110487547A (en) * | 2019-07-31 | 2019-11-22 | 中国特种设备检测研究院 | Fault Diagnosis of Roller Bearings under variable working condition based on vibrorecord and transfer learning |
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| CN106203325A (en) * | 2016-07-07 | 2016-12-07 | 燕山大学 | Based on strengthening the Weak fault signal characteristic extracting methods cascading multistable accidental resonance |
| CN107870005A (en) * | 2016-09-27 | 2018-04-03 | 重庆邮电大学 | The normalization random resonant weak signal detection of empirical mode decomposition under over-sampling |
| CN113383215A (en) * | 2018-04-30 | 2021-09-10 | 通用电气公司 | System and process for mode-matched bearing vibration diagnostics |
| CN108444698A (en) * | 2018-06-15 | 2018-08-24 | 福州大学 | Epicyclic gearbox Incipient Fault Diagnosis method based on TEO demodulation accidental resonances |
| CN108444698B (en) * | 2018-06-15 | 2019-07-09 | 福州大学 | Epicyclic gearbox Incipient Fault Diagnosis method based on TEO demodulation accidental resonance |
| CN110487547A (en) * | 2019-07-31 | 2019-11-22 | 中国特种设备检测研究院 | Fault Diagnosis of Roller Bearings under variable working condition based on vibrorecord and transfer learning |
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| CN116223043A (en) * | 2023-03-29 | 2023-06-06 | 哈尔滨理工大学 | Rolling bearing weak signal detection method based on VMD and cascade stochastic resonance combination |
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