CN107860460A - The feature extracting method of vibration signal under strong noise background - Google Patents
The feature extracting method of vibration signal under strong noise background Download PDFInfo
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Abstract
The present invention relates to the feature extracting method of vibration signal under strong noise background, comprise the following steps：Sampling obtains one section of mechanical oscillation signal A；Four even number periodic extensions more than cycle are made to signal A, obtain new time series B after continuation；More relevant treatments more than three times are done to time series B, obtain characteristic signal correlated series C and a constant term sum；EMD decomposition is carried out to sequence C, obtains each IMF components ciWith surplus rn, wherein, ciIt is designated as D；Cross-correlation calculation is carried out to each IMF components D and time series B, by result of calculation compared with the threshold value λ set, and screening for λ will be more than in result of calculation, be designated as E；Marginal spectrum analysis is carried out to E, forms marginal spectral curve, what amplitude protruded is the feature of vibration signal in marginal spectral curve.Analysis efficiency of the present invention is high, can carry out on-line checking to vibration signal and hiding characteristic signal and state representation signal can be extracted in the case where signal to noise ratio is low.
Description
Technical field
The present invention relates to mechanical system vibration signal processing, and specifically the feature of vibration signal carries under strong noise background
Take method.
Background technology
As high precision measurement equipment and advanced means of testing continue to bring out, to the analysis side of mechanical system vibration signal
Method proposes higher requirement.And some characteristic signals of mechanical system and potential state representation signal are often submerged in the strong back of the body
Among scape noise so that some nonterminal characters that mechanical system shows, as fault message, equipment state change information and
General performance information of system etc., it is impossible to by detecting for early stage, the operation to whole industrial system bring potential safety hazard and
Economic loss, or even cause casualties.
The existing processing method available for mechanical system vibration signal includes：Fourier transform；Short time discrete Fourier transform；
Wigner-Ville is analyzed；Modern spectral estimation method；Neural net method；Higher order statistic analysis；Wavelet analysis and Xi Er
Bert-Huang (Hilbert-Huang Translation:HHT) method.
In the above-mentioned methods, be wavelet analysis with the immediate prior art of the present invention, 1.5 dimension spectrums are analyzed and HHT methods.
Wavelet analysis method is that a kind of window size (i.e. window area) is fixed but its shape can change, time window and frequency
When window is all changeable-frequency partial analysis method.Under large scale, the low-frequency information (overall situation) of signal can be showed,
Under small yardstick, high frequency (part) feature of signal can be reflected.Wavelet analysis can be extracted effectively wink from signal
State abrupt information, multiple dimensioned (or more resolutions) refinement is carried out to signal by calculation functions such as flexible and translations and analyzes, solves
The indeterminable many difficult problems of Fourier transform.Therefore wavelet analysis has obtained widely should in the processing of Engineering Signal
With, and achieve good effect, it is considered to be the important breakthrough since Fourier transform in scientific method and instrument.
Substantial amounts of emulation and case history it has been shown that wavelet analysis in the practical application of vibration signal processing there is
Some shortcomings：(1) to singular points, wavelet transformation is very sensitive, and it is accurately fixed that the catastrophe point of singular signal can be given
Position, but be difficult to judge that those catastrophe points are points interested；(2) suitable time domain and frequency domain resolution is chosen in engineering not have
It is well solved；(3) wavelet analysis lacks effective fast algorithm, thus is difficult the requirement for meeting real-time；(4) it is small
The selection of wave conversion Wavelets with spectrum analyze in window function selection as, it is necessary to according to the characteristics of different application problem come
It is specific to consider, select suitable wavelet basis function extremely difficult specific engineering problem.
1.5 dimension spectrums are defined as the one dimensional fourier transform of third moment Diagonal Slice.Because it greatly reduces bispectrum
Amount of calculation, and save the property of some higher-order spectrums, thus applied in the signal transacting of mechanical system.Because
The particularity of 1.5 dimension spectrums, it has following several premium properties：(1) there is high-order statistic to suppress Gaussian noise and symmetrical point
The ability of cloth noise；(2) amount of calculation is minimum in higher-order spectrum, close with power spectrum；(3) fundamental frequency point of harmonic signal can be strengthened
Amount, in favor of extracting weaker fundamental frequency；(4) harmonic term of non-square phase-couple is can remove, extracts the feature in vibration signal
Amount.
1.5 dimension spectrums are when to signal analysis, due to being that more correlated serieses of signal are made with high-order Fourier conversion so that
In the signal characteristic composition that expression extracts, can due to Fourier is converted and cause the later stage be difficult to the harmonic wave that handles into
Point, the feature extraction to signal brings erroneous judgement；When doing more relevant treatments to vibration signal, noise signal is located in the lump
Reason so that this method has higher requirement to the signal to noise ratio of signal, it is difficult to meet under complex working conditions, vibration signal characteristics
The demand of extraction.
Hilbert-Huang conversion is developed in recent years, a kind of brand-new time series signal analysis method.Its
Core is empirical mode decomposition (Empirical Mode Decomposition:EMD), complexity signal decomposition into several
Intrinsic mode function (Intrinsic Mode Function:IMF)；Hilbert is carried out to obtained intrinsic mode function again
Conversion, and then instantaneous frequency and the amplitude that each intrinsic mode function changes over time are obtained, finally just obtain amplitude-frequency
The three-dimensional Spectral structure of rate-time.
Because empirical mode decomposition is adaptive, local orthogonal and complete, therefore it decomposes fast and flexible.And due to
Empirical mode decomposition is the localized variation based on signal, thus available for the analysis of non-linear and non-stationary process.With quick Fourier
The spectrum that leaf transformation obtains is compared, and the amplitude and frequency of each intrinsic mode function that HHT is obtained change over time, and eliminate
To express the monochromatic wave that non-linear, non-stationary process introduces.Compared with wavelet analysis method, HHT has the excellent of wavelet analysis
Point, the fuzzy and unintelligible of wavelet analysis is eliminated in resolution ratio, has and more accurately composes structure, thus HHT is non-in analysis
Linearly, there is very high application value in non-stationary process.HHT methods are because its validity to signal analysis, thus very
Many-side is applied.
Empirical mode decomposition is by multiple moving process to decompose to obtain intrinsic mode function one by one.In shifting each time
During dynamic, the local mean values of signal are calculated according to the upper and lower envelope of signal, wherein upper and lower envelope is by signal
Local maximum and minimum are provided by Based on Interpolating Spline, and this algorithm can bring error in analysis, particularly when each
Individual frequency component lean on it is close when, error is just bigger.Although clear and definite instantaneous frequency is capable of the instantaneous change of expression signal in HHT
Change situation, still, all it has been shown that when signal to noise ratio is smaller in emulation and engineer applied, HHT methods can not be effectively obtained letter
Characteristic component in number.HHT methods have that empirical mode decomposition stopping criterion is not perfect enough, it is false easily to be produced in decomposable process
The deficiency of the uncertainty of component and decomposition result etc..
In summary, a common issue existing for existing analysis of vibration signal method is to being mixed in characteristic signal composition
Folded noise is more sensitive so that when carrying out the analysis of mechanical system vibration signal, especially to shaking under strong noise background
During dynamic signal analysis, it is very restricted.Therefore, design analysis efficiency height, on-line checking can be carried out simultaneously to vibration signal
Vibration signal under the strong noise background of hiding characteristic signal and state representation signal can be extracted in the case where signal to noise ratio is low
Feature extracting method is very necessary.
The content of the invention
It is an object of the invention to provide a kind of analysis efficiency it is high, on-line checking can be carried out to vibration signal and can be in signal to noise ratio
The feature extraction side of vibration signal under the strong noise background of hiding characteristic signal and state representation signal is extracted in the case of low
Method.
To achieve the above object, the present invention adopts the following technical scheme that：The feature of vibration signal under a kind of strong noise background
Extracting method, comprise the following steps：
S1. sampling obtains the mechanical oscillation signal x (t) of a length of 0.8 minute to 1.2 minutes at one section, is designated as A；
S2. four even number periodic extensions more than cycle are made to signal A, obtains new time series x (t+ after continuation
τ), it is designated as B；
S3. more relevant treatments more than three times are done to time series B, obtain characteristic signal correlated series C and a constant term
Sum：
Rs(t, τ, τ)=Rx(t,τ,τ)+3σE{x(t)}+γ
In formula, Rx(t, τ, τ) is C, and 3 σ E { x (t) }+γ are constant；
S4. EMD decomposition is carried out to sequence C, obtains each IMF components ciWith surplus rn, wherein, ciIt is designated as D；
S5. cross-correlation calculation is carried out to each IMF components D and time series B, result of calculation is entered with the threshold value λ set
Row compares, and will be more than screening for λ in result of calculation, is designated as E；
S6. marginal spectrum analysis is carried out to E, forms marginal spectral curve, as vibrating for amplitude protrusion is believed in marginal spectral curve
Number feature.
Using the present invention, by carrying out more correlation analyses, empirical mode decomposition to mechanical oscillation signal time series, to this
Levy the screening of mode function, marginal spectrum analysis is carried out to the intrinsic mode function screened, obtain and vibrated under strong noise background
The feature of signal.
Analysis efficiency of the present invention is high, on-line checking can be carried out to vibration signal and can be extracted in the case where signal to noise ratio is low hidden
The characteristic signal and state representation signal of Tibetan.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the present invention；
Fig. 2 is a period of time sequence chart described in the embodiment of the present invention one by formula (15)；
Fig. 3 is that the time series provided by equation (15) is carried out handling resulting marginal spectrum using the present invention；
Fig. 4 is that the time series provided by equation (15) is carried out handling resulting marginal spectrum using wavelet analysis；
Fig. 5 is that the time series provided by equation (15) is carried out handling resulting marginal spectrum using dimension spectrum analysis；
Fig. 6 is that the time series provided by equation (15) is carried out handling resulting marginal spectrum using HHT analyses；
Fig. 7 is a period of time sequence chart described in the embodiment of the present invention two by formula (16)；
Fig. 8 is that the time series provided by equation (16) is carried out handling resulting marginal spectrum using the present invention；
Fig. 9 is that the time series provided by equation (16) is carried out handling resulting marginal spectrum using wavelet analysis；
Figure 10 is that the time series provided by equation (16) is carried out handling resulting marginal spectrum using dimension spectrum analysis；
Figure 11 is that the time series provided by equation (16) is carried out handling resulting marginal spectrum using HHT analyses.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail, but the embodiment should not be understood
For limitation of the present invention.
The feature extracting method of vibration signal, comprises the following steps under a kind of strong noise background：
S1. sampling obtains the mechanical oscillation signal x (t) of a length of 0.8 minute to 1.2 minutes at one section, is designated as A；
S2. four even number periodic extensions more than cycle are made to signal A, obtains new time series x (t+ after continuation
τ), it is designated as B；
S3. more relevant treatments more than three times are done to time series B, obtain characteristic signal correlated series C and a constant term
Sum：
Rs(t, τ, τ)=Rx(t,τ,τ)+3σE{x(t)}+γ
In formula, Rx(t, τ, τ) is C, and 3 σ E { x (t) }+γ are constant；
S4. EMD decomposition is carried out to sequence C, obtains each IMF components ciWith surplus rn, wherein, ciIt is designated as D；
S5. cross-correlation calculation is carried out to each IMF components D and time series B, result of calculation is entered with the threshold value λ set
Row compares, and will be more than screening for λ in result of calculation, is designated as E；
S6. marginal spectrum analysis is carried out to E, forms marginal spectral curve, as vibrating for amplitude protrusion is believed in marginal spectral curve
Number feature.
Specifically refinement is as follows for the above method：
1st, the more correlation analyses of mechanical oscillation signal time series
The correlation function (i.e. second-order correlation function) of mechanical oscillation signal time series { x (t), t ∈ T } is defined as
Rx(t, τ)=E { x (t) x (t+ τ) } (1)
E { } represents average statistical in formula.
This is imitated, correlation function is defined as three times for definition
Rx(t,τ1,τ2)=E { x (t) x (t+ τ1)x(t+τ2)} (2)
The correlation function of each order can be so defined successively, and (including three times) above correlation function is referred to as time sequence three times
The correlation more of row.
If the eigen vibration signal of analysis system is x (t), obtained random noise n (t) is measured to be independent identically distributed,
And it is separate with x (t).So, the time series signal s (t) tested can be expressed as
S (t)=x (t)+n (t) (3)
In order to simplify the calculating to correlation function three times, the diagonal slices τ of correlation function three times is taken1=τ2=τ, when such
Between sequence s (t) correlation function three times be expressed as
Rs(t, τ, τ)=E { s (t) s (t+ τ) s (t+ τ) }=E { [x (t)+n (t)] [x (t+ τ)+n (t+ τ)] [x (t+ τ)+n
(t+τ)]} (4)
To noise n (t) it is assumed that its second-order correlation function is expressed as more than
Equally, the correlation function three times of noise function is expressed as
So (4) formula expands into
Rs(t, τ, τ)=Rx(t,τ,τ)+Rx(t,0)E{n(t)}+2Rx(t,τ)E{n(t+τ)}+σE{x(t)+2x(t+τ)}
+γ (7)
For simplification (7) formula, and consider the feature of complex vibration signal, take out one section of typical vibration signal, this section is believed
Number do periodic extension.In general, in order that obtaining follow-up more correlated serieses has preferable analyticity, the sequence selected is done
Not less than the continuation in eight cycles.So, the vibration signal after periodic extension has below equation establishment
E { x (t) }=E { x (t+ τ) }；E { n (t) }=E { n (t+ τ) } (8)
So, can be turned to according to above-mentioned analysis and derivation, (7) formula
Rs(t, τ, τ)=Rx(t,τ,τ)+Rx(t,0)E{n(t)}+2Rx(t,τ)E{n(t)}+3σE{x(t)}+γ (9)
R in above formulax(t, 0)=E { x (t+ τ) x (t+ τ) }, and according to the applicable cases of reality, it can be assumed that system noise
Sound is zero-mean, so as to which (9) formula can be further simplified as
Rs(t, τ, τ)=Rx(t,τ,τ)+3σE{x(t)}+γ (10)
In above formula, E { x (t) } is the average for the vibration signal that sampling obtains, and the cycle that sample sequence is done is prolonged according to above-mentioned
Open up, so when analyzing complete cycle, E { x (t) } will be a constant, two 3 σ E { x behind the right in (10) formula in equation
(t) }+γ is a constant, that is to say, that the correlation function three times of sampling time sequence is equal to the three of system features vibration signal
Secondary correlation function and constant and.
2nd, empirical mode decomposition
Empirical mode decomposition is Huang et al. in the HHT proposed in 1998 core content, is at a kind of brand-new signal
Reason method, it has broken away from the dependence in signal characteristic abstraction to Fourier transform in traditional sense, avoided in signal characteristic abstraction
In harmonic component is introduced due to the mathematical meaning of Fourier transform so as to cause the possibility of erroneous judgement.
The core of empirical mode decomposition assumes that signal is made up of several intrinsic mode function components, wherein, eigen mode
State function must is fulfilled for two basic assumptions：(1) on whole data set, the number of extreme point across the number of zero point it is equal or
At most difference one；(2) at any point in time, the coenvelope that is defined by local maximum and defined down by local minimum
The average of envelope is zero.So, time series x (t) can be decomposed into several intrinsic mode function components ciWith more than one
Measure rnSum, i.e.,
Wherein, surplus rnFor an a monotonic function either constant.
Empirical mode decomposition and signal decomposition method (such as wavelet transformation) difference based on Fourier transform, it is not pre-
The decomposition base of first Setting signal, its decomposition to signal be based on signal in itself, also avoid to produce due to basic function
The possibility of false harmonic signal.And empirical mode decomposition process is adaptive, complete, local orthogonal, thus it
Suitable for non-linear, non-stationary signal the feature extraction of mechanical oscillation.
3rd, to the screening of intrinsic mode function
The intrinsic mode function that empirical mode decomposition obtains is selected using correlation function algorithm.
Known by the characteristics of empirical mode decomposition, sequences y (t) can be decomposed into each intrinsic mode letter with empirical mode decomposition
Number component diWith a surplus snSum, be expressed as
I-th of intrinsic mode function component d againiWith y (t) coefficient correlation μiDefinition be
In formula, M represents the data points for calculating.
By the intrinsic characteristic of empirical mode decomposition, chaff component will likely be produced in decomposable process.In order to avoid void
The misleading that false harmonic wave recognizes to vibration characteristics, intrinsic mode function component is selected using coefficient correlation.Known by Correlation Theory,
Real intrinsic mode function should be obtained from the data before decomposition, so the correlation of it and data before decomposition should have
By force, i.e., coefficient correlation μ value should be larger.An appropriate threshold value is set for this, when their value is less than this threshold value, just
It is considered that the intrinsic mode function is a false component caused by decomposition.
On threshold value λ determination, can be defined by following function
λi=max (μi)/η (14)
max(μi) represent to μiTake extreme value, η is the constant selected according to actual conditions, is typically taken between η=8~15
Integer, η=10 are taken herein.
4th, marginal spectrum analysis is carried out to the intrinsic mode function screened
The more relevant treatments of sequential are carried out to signal in advance, the influence of zero mean noise can be suppressed, highlight depositing for characteristic signal
Amplifying its local feature, good pre-processing data is provided for subsequent processes.By the intrinsic spy of empirical mode decomposition
Property, chaff component will likely be produced in decomposable process.In order to avoid the misleading that false harmonic wave recognizes to vibration characteristics, to decomposing
The each intrinsic mode function arrived carries out correlation analysis with the sequence before decomposing, and obtains corresponding each coefficient correlation μ.
Because really intrinsic mode function should be obtained from the data before decomposition, it with decompose before data
Correlation should have larger value.An appropriate threshold value is set for this, when their value is less than this threshold value, it is possible to recognize
It is a caused false component in decomposition for the intrinsic mode function.
Embodiment one
Object：s1(t)=[1+sin (5 π t)] cos [20 π t+0.2sin (10 π t)]+sin (80 π t) (15)
A period of time sequence chart of above formula (15) description is as shown in Figure 2.
To the time series provided by equation (15), using method provided by the invention, obtained marginal spectrum such as Fig. 3 institutes
Show.
From the Daubechies small echos in orthogonal wavelet as wavelet basis function, and use MATLAB wavelet toolboxes
In db10 5 layers of wavelet decomposition are done to the time series provided by equation (15), then obtained detail signal is carried out weight
Structure, then the signal obtained to reconstruct do marginal spectrum analysis, and the marginal spectrogram so obtained is as shown in Figure 4.
The spectrum analysis of 1.5 dimensions is done to the time series provided by equation (15), obtained spectrogram is as shown in Figure 5.
HHT analyses are done to the time series provided by equation (15), the Serial No. obtained first to sampling does Empirical Mode
State is decomposed, and obtains each intrinsic mode function component, then does Hilbert spectrum analyses to them, marginal spectrum obtained from entering is such as
Shown in Fig. 6.
From Fig. 3 to Fig. 6, the marginal spectrum that the method that the present invention provides obtains can accurately flutter the feature for grasping signal
Radio-frequency component；For the nonlinear properties of AM/FM amplitude modulation/frequency modulation, characteristic frequency that wavelet analysis can not be clearly in expression signal into
Point, obvious is at 40Hz, two spectral peaks occurs；1.5 dimension spectrum analyses, can give expression to signal to a certain extent
Characteristic component, but due to the characteristic of Fourier transform, occur some small harmonic components at 10Hz, this is follow-up point
Analysis brings difficulty；HHT is analyzed, its expression to AM/FM amplitude modulation/frequency modulation part and to the expression at 40Hz, is all perfectly clear, and
And according to the instantaneous frequency defined in HHT, the fluctuation situation of signal intermediate frequency rate has clearly been given expression to, thus in such case
Under, HHT methods are a kind of outstanding signal characteristic extracting methods.
Embodiment two
Object：s2(t)=[1+sin (5 π t)] cos [20 π t+0.2sin (10 π t)]+sin (80 π t)+n (t) (16)
The noise signal n (t) that the AM/FM amplitude modulation/frequency modulation signal that above formula is constructed by equation (15) adds zero-mean, variance is 15
Gained, a period of time sequence chart that it is described are as shown in Figure 7.
To the time series provided by equation (16), using method provided by the invention, obtained marginal spectrum such as Fig. 8 institutes
Show.
5 layers of wavelet decomposition are done to the time series provided by equation (16) using the db10 in MATLAB wavelet toolboxes,
Then obtained detail signal is reconstructed, then the signal obtained to reconstruct does marginal spectrum analysis, obtained marginal spectrogram is such as
Shown in Fig. 9.
The spectrum analysis of 1.5 dimensions is done to the sequence of the AM/FM amplitude modulation/frequency modulation of Noise, obtained spectrogram is as shown in Figure 10.
HHT analyses are done to the time series provided by equation (16), obtained marginal spectrum is as shown in figure 11.
From Fig. 8 to Figure 11, method of the invention can extract characteristic signal therein, and this shows, this method pair
Non-linear, non-stationary signal feature extraction has good adaptability；Wavelet analysis is because it is to Analysis of nonlinear signals
Invalid feature so that when to containing noisy AM/FM amplitude modulation/frequency modulation signal analysis, it appears completely helpless；1.5 dimension spectrum analyses
Contain noisy AM/FM amplitude modulation/frequency modulation signal by being then based on the one dimensional fourier transform of third moment diagonal slices, thus in analysis
When, there are more unknown harmonic components, so cannot be used for the feature extraction of the signal；HHT is due to strong background noise
Effect so that it cannot be used for the feature extraction of AM/FM amplitude modulation/frequency modulation signal.
The content not being described in detail in this specification, belong to prior art known to those skilled in the art.
Claims (1)
1. the feature extracting method of vibration signal, comprises the following steps under a kind of strong noise background：
S1. sampling obtains the mechanical oscillation signal x (t) of a length of 0.8 minute to 1.2 minutes at one section, is designated as A；
S2. four even number periodic extensions more than cycle are made to signal A, obtains new time series x (t+ τ) after continuation, note
For B；
S3. more relevant treatments more than three times are done to time series B, obtain characteristic signal correlated series C and a constant term sum：
Rs(t, τ, τ)=Rx(t,τ,τ)+3σE{x(t)}+γ
In formula, Rx(t, τ, τ) is C, and 3 σ E { x (t) }+γ are constant；
S4. EMD decomposition is carried out to sequence C, obtains each IMF components ciWith surplus rn, wherein, ciIt is designated as D；
S5. cross-correlation calculation is carried out to each IMF components D and time series B, result of calculation is compared with the threshold value λ set
Compared with, and screening for λ will be more than in result of calculation, it is designated as E；
S6. marginal spectrum analysis is carried out to E, forms marginal spectral curve, what amplitude protruded in marginal spectral curve is vibration signal
Feature.
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| CN108896975A (en) * | 2018-06-14 | 2018-11-27 | 上海交通大学 | Cross-correlation singularity Power Spectrum Distribution calculation method |
| CN111242366A (en) * | 2020-01-08 | 2020-06-05 | 广东技术师范大学 | EMD method and device for processing signals in real time |
| CN113158896A (en) * | 2021-04-21 | 2021-07-23 | 中国民航大学 | Method for extracting weak fault features of rolling element of rolling bearing under transmission path |
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| CN108896975A (en) * | 2018-06-14 | 2018-11-27 | 上海交通大学 | Cross-correlation singularity Power Spectrum Distribution calculation method |
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| CN111242366A (en) * | 2020-01-08 | 2020-06-05 | 广东技术师范大学 | EMD method and device for processing signals in real time |
| CN111242366B (en) * | 2020-01-08 | 2023-10-31 | 广东技术师范大学 | EMD method and device capable of being used for processing signals in real time |
| CN113158896A (en) * | 2021-04-21 | 2021-07-23 | 中国民航大学 | Method for extracting weak fault features of rolling element of rolling bearing under transmission path |
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