CN109342091A - Vibration fault extracting method based on self-adaptive harmonics detection and improvement EMD - Google Patents
Vibration fault extracting method based on self-adaptive harmonics detection and improvement EMD Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M17/00—Testing of vehicles
- G01M17/08—Railway vehicles
- G01M17/10—Suspensions, axles or wheels
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
Abstract
The invention discloses a kind of based on self-adaptive harmonics detection and improves the vibration fault extracting method of EMD.This method are as follows: acquisition trajectory vibration signal first;Construct adaptive morphology junction filter, be filtered to signal: selection structural element calculates the length of structural element, calculates the height of structural element, constructs Multi-structure elements collection, determine optimum structure element;Then the EMD that signal improves is decomposed, by calculating the related coefficient of signal and the kurtosis value of signal, screens IMF component;Hilbert transformation finally is carried out to IMF component, calculates the Hilbert marginal spectrum of IMF component.Vibration fault extracting method of the present invention, it is simple and easy, easily and effectively, it can be realized the efficient diagnosis of vibration fault.
Description
Technical field
The invention belongs to city railway train wheelset failure monitoring technical fields, especially a kind of to be filtered based on adaptive morphology
Involve the vibration fault extracting method for improving EMD.
Background technique
The signal measured in Practical Project usually contains many noises and impact signal, and traditional filtering algorithm can not be accomplished
All noises are filtered out, difficulty will be brought to the analysis that is further processed of signal in this way.
The common extracting method of Vibration Fault Signal includes EMD, EEMD etc., and EMD is as classical signal processing algorithm, energy
Mode function different in signal is enough isolated, however there is modal overlap, prevent some mode signals are from by just
Really separate.EEMD gathers empirical mode decomposition by addition white noise, has improvement to modal overlap problem, however but deposits
The problem of noise remains.
Summary of the invention
That the purpose of the present invention is to provide a kind of methods is simple, real-time is good based on self-adaptive harmonics detection and improvement
The vibration fault extracting method of EMD, to realize the efficient diagnosis of vibration fault.
Realizing the technical solution of the object of the invention is: a kind of vibration based on self-adaptive harmonics detection and improvement EMD
Failure extracting method, comprising the following steps:
Step 1, acquisition trajectory vibration signal;
Step 2, adaptive morphology junction filter is constructed, signal is filtered;
Step 3, the EMD that signal improves is decomposed;
Step 4, the related coefficient of signal and the kurtosis value of signal are calculated, IMF component is screened;
Step 5, Hilbert transformation is carried out to IMF component, calculates the Hilbert marginal spectrum of IMF component.
Further, building adaptive morphology junction filter, specific steps described in step 2 are as follows:
Step 2.1, selection structural element;
Step 2.2, the length L for calculating structural elements;
Step 2.3, the height H for calculating structural elementj;
Step 2.4, construction Multi-structure elements collection;
Step 2.5 determines optimum structure element.
Further, EMD improved to signal described in step 3 is decomposed, specific steps are as follows:
Step 3.1, using EMD algorithm to adding the signal x after making an uproar(i)=x ± β0w(i)It is decomposed, obtains the 1st improvement
The IMF component of EMD:
Wherein, w(i)For equal value zero, the white noise of unit variance;βkFor white noise intensity, k=0,1,2 ..., K, I is to add
Noise number;X is original signal;x(i)To add the signal after making an uproar;Ek() is k-th of the IMF component obtained after EMD is decomposed;E1+
For component, the E that positive white noise is added1-For the component that negative white noise is added;
Step 3.2, the residual error r for calculating the 1st IMF component1:
r1=x-imf1
Step 3.3, using EMD decomposition computation r1±β1E1(w(i)) first mode, and be defined as improve EMD decompose
2nd IMF component imf2:
Step 3.4 works as k=1,2 ... K, calculates k-th of residual error rk:
rk=xk-1-imfk
Wherein K is the IMF component number that original signal decomposes;
Step 3.5, using EMD decomposition computation rk±βkEk(w(i)) the 1st modal components, and be defined as improving EMD
+ 1 IMF component imf of kthk+1:
Step 3.6 enables k be incremented by 1, repeats step 3.4~step 3.5, calculates next IMF component, stop when k=K
Only.
Further, the related coefficient of signal and the kurtosis value of signal are calculated described in step 4, specific as follows:
The cross-correlation coefficient ρ of definition signal x (n) and y (n)xyAre as follows:
The kurtosis value Kurtosis of signal is normalized m rank central moment, is defined as follows:
In formula, x={ x1,x2,…,xN}={ xiIt is Discrete signal, i=1,2 ..., N, N is sample point number, x
For the mean value of signal x.
Further, Hilbert transformation is carried out to IMF component described in step 5, calculates the limit Hilbert of IMF component
Spectrum, specific as follows:
Hilbert transformation is done to IMF component, obtains the instantaneous frequency and instantaneous amplitude of each component, by each component
Instantaneous frequency and instantaneous amplitude are superimposed together, and obtain the Hilbert amplitude spectrum H (ω, t) of IMF component are as follows:
Wherein, akIt (t) is the instantaneous amplitude of k-th of IMF component, ωk(t) instantaneous frequency of k-th of IMF component, K are original
The IMF component number that signal decomposition obtains;
By the Hilbert spectrogram of IMF component to time integral, the Hilbert marginal spectrum h (ω) of IMF component is obtained:
Wherein, T is the length of original signal;The Hilbert marginal spectrum of IMF component reflects instantaneous frequency in all frequencies
On size and variation.
Compared with prior art, the present invention its remarkable advantage is: (1) adaptive Mathematical Morphology Filtering method is proposed, to letter
Number have well filtering processing ability;(2) by acquisition train rail vibration acceleration signal, self-adaptive harmonics detection is utilized
And signal processing carries out processing analysis to vibration signal, in signal processing modal overlap and noise residue problem carry out
Optimization;(3) calculation method is simple, has good practical value.
Detailed description of the invention
Fig. 1 is the flow chart the present invention is based on self-adaptive harmonics detection and the vibration fault extracting method for improving EMD.
Fig. 2 is that track vibration signal original waveform figure is surveyed in the embodiment of the present invention.
Fig. 3 is filter effect quantization figure in the embodiment of the present invention, wherein (a) is modified opening operator structural element depth map,
(b) it is form closed operation structural element depth map, (c) is form opening and closing operation structural element depth map, (d) is transported for form make and break
Calculate structural element depth map.
Fig. 4 is track vibration signals measured figure after filtering in the embodiment of the present invention.
Fig. 5 is that actual measurement track vibration signal improves EMD exploded view in the embodiment of the present invention.
Fig. 6 is each rank IMF related coefficient and kurtosis value figure in the embodiment of the present invention, wherein (a) is IMF related coefficient figure,
It (b) is kurtosis value figure.
Fig. 7 is the limit the Hilbert spectrogram of IMF component in the embodiment of the present invention, wherein (a) is first IMF component
The limit Hilbert spectrogram is (b) limit the Hilbert spectrogram of second IMF component, is (c) third IMF component
The limit Hilbert spectrogram is (d) limit the Hilbert spectrogram of the 4th IMF component.
Fig. 8 is the Hilbert spectrogram of sensitivity IMF component in the embodiment of the present invention, wherein (a) is first IMF component
Hilbert spectrogram, (b) be second IMF component Hilbert spectrogram, (c) be the 4th IMF component Hilbert
Spectrogram.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawing.
The not smoother fault signature of the city rail vehicle wheel overall situation can be transmitted to the vibration of track by the coupling of wheel and track
On dynamic, failure-frequency has also correspondingly been transmitted on track.The present invention uses self-adaptive harmonics detection and improves the vibration event of EMD
Hinder method for extracting signal, track vibration signal is decomposed, Vibration Fault Signal can be extracted, effectively EMD, which is decomposed, exists
Modal overlap problem and EEMD existing for noise residue problem.
In conjunction with Fig. 1, the Vibration Fault Signal extracting method based on self-adaptive harmonics detection and improvement EMD, firstly, acquisition rail
Road vibration signal, building adaptive morphology junction filter are filtered signal;Then filtered signal is improved
EMD decompose, pass through and calculate related coefficient and signal kurtosis value, screen IMF component;Hilbert change finally is carried out to IMF component
It changes, calculates the Hilbert marginal spectrum of IMF component.Specific step is as follows:
Step 1, acquisition trajectory vibration signal;
Step 2, adaptive morphology junction filter is constructed, signal is filtered;It is specific as follows:
Step 2.1, selection structural element
Under normal conditions, linear structure does not consider height, only considers its width;Semicircular structure element mathematic(al) representation is such as
Shown in formula (1), shown in triangular structure mathematic(al) representation such as formula (2):
Wherein, i is data amount check, and H is height, and L is length, and H, L are two characteristic parameters of structural element.
Step 2.2, the length L for calculating structural elements
Setting signal time series is x={ xi| i=1,2 ..., N }, maximum position is PE={ PEi| i=1,
2,…,NLB, minimum position is NA={ NAi| i=1,2 ..., NLS, wherein NLB、NLSRespectively maximum in original signal
Number and minimum number.
According to Min-max position sequence, the adjacent spaces of local maximum are calculated, as a result as shown in formula (3), are calculated
The adjacent spaces of local minimum, as a result as shown in formula (4):
According to the features of shape of triangle element and semicircle element, length dimension L is determinedSMaximum value is minimum shown in (5)
Value is shown in (6):
Lsmax=ceil (max ([max (dpi)+1]/2,[max(dNi)-1]/2)) (5)
Lsmin=fix (min ([min (dpi)-1]/2,[max(dNi)-1]/2)) (6)
Wherein, ceil is to round up, and fix is to be rounded downwards;
According to formula (5) and formula (6), obtain shown in length dimension such as formula (7):
Ls={ Lsmin,Lsmin+1,L,Lsmax-1,Lsmax} (7)
Step 2.3, the height H for calculating structural elementj
Signal time sequence is x={ xi| i=1,2 ..., N }, by calculating its available local maximum value sequence are as follows:
LB={ LBi| i=1,2 ..., NLB}
Wherein NLBIndicate local maximum number;
Local minimum is calculated, as a result are as follows:
LS={ LSi| i=1,2 ..., NLS}
Wherein NLSIndicate local minimum number;
According to above-mentioned position sequence, the adjacent spaces of local maximum are calculated, as a result as shown in formula (8), local minimum
Adjacent spaces such as formula (9) shown in:
The maximum value H of elevational dimension then can be obtainedmax:
Hmax=max (max (AMP),max(AMN)) (10)
Thus, structural element length is as height:
Step 2.4, construction Multi-structure elements collection
Large-scale structure element has good filter effect for impacting biggish noise, on the contrary, small-scale structure is first
Element has good effect for impacting lesser noise, therefore, constructs with flowering structure collection:
Shown in linear structure element set such as formula (12):
G1(N)={ zeros (2Lsmin+1),zeros(2(Lsmin+1)+1),L,zeros(2Lsmax+1)} (12)
Shown in three-legged structure element set such as formula (13):
Shown in semi-circular structure collection such as formula (14):
In formula, n=-Ls... 0 ..., Ls, j=1,2 ... Lsmax-Lsmin,Ls=Lsmin,…,Lsmax。
Step 2.5, optimum structure element determine
Under different structural element processing, signal can have different size of characteristic frequency coefficient, be carried out according to size
Sequence selects optimum structure element, and is combined, and obtains optimum combination filter, characteristic frequency intensity size mathematical definition
Are as follows:
Wherein, FCi(i=1,2,3) indicates each frequency multiplication amplitude of characteristic frequency in signal spectrum, Fj(j=1,2 ..., N-1)
Indicate frequency amplitude.
Step 3, the EMD that signal improves is decomposed;It is specific as follows:
Enable Ek() is obtained k-th of IMF component after EMD is decomposed, and enabling w (i) is equal value zero, unit variance it is white
Noise, original signal x, adding the signal after making an uproar is x(i), K is the IMF component number that original signal decomposes, and I is plus noise
Number, βiFor white noise intensity.
Step 3.1, using EMD algorithm to adding the signal x after making an uproar(i)=x ± β0w(i)It is decomposed, obtains the 1st improvement
The IMF component of EMD:
Wherein, w(i)For equal value zero, the white noise of unit variance;βkFor white noise intensity, k=0,1,2 ..., K, I is to add
Noise number;X is original signal;x(i)To add the signal after making an uproar;Ek() is k-th of the IMF component obtained after EMD is decomposed;E1+
For component, the E that positive white noise is added1-For the component that negative white noise is added;
Step 3.2, the residual error for calculating the 1st IMF component:
r1=x-imf1 (17)
Step 3.3, using EMD decomposition computation r1±β1E1(w(i)) first mode, and be defined as improve EMD decompose
2nd IMF component:
Step 3.4 works as k=1,2 ... K, calculates k-th of residual error rk:
rk=xk-1-imfk (19)
Wherein K is the IMF component number that original signal decomposes;
Step 3.5, using EMD decomposition computation rk±βkEk(w(i)) the 1st modal components, and be defined as improving EMD
+ 1 IMF component of kth:
Step 3.6 enables k be incremented by 1, repeats step 3.4~step 3.5, calculates next IMF component, stop when k=K
Only.
Step 4, the related coefficient of signal and the kurtosis value of signal are calculated, IMF component is screened;It is specific as follows:
The cross-correlation coefficient ρ of definition signal x (n) and y (n)xyAre as follows:
The kurtosis value Kurtosis of signal is normalized m rank central moment, is defined as follows:
In formula, x={ x1,x2,…,xN}={ xiIt is Discrete signal, i=1,2 ..., N, N is sample point number, x
For the mean value of signal x.In one embodiment, m=4.
According to calculated result, IMF component is screened by the standard deviation of related coefficient and the threshold value of signal kurtosis.
Step 5, Hilbert transformation is carried out to IMF component, calculates the Hilbert marginal spectrum of IMF component.
Hilbert transformation is done to IMF component, obtains the instantaneous frequency and instantaneous amplitude of each component, is added to one
It rises, obtains the Hilbert amplitude spectrum H (ω, t) of IMF component are as follows:
Wherein, akIt (t) is the instantaneous amplitude of k-th of IMF component, ωk(t) instantaneous frequency of k-th of IMF component, K are original
The IMF component number that signal decomposition obtains;
By the Hilbert spectrogram of IMF component to time integral, the Hilbert marginal spectrum h (ω) of IMF component can be obtained:
Wherein, T is the length of original signal;The Hilbert marginal spectrum of IMF component reflects instantaneous frequency in all frequencies
On size and variation.
Embodiment 1
Certain metro company license number that this example uses scene to measure passes through track vibration when acquisition system for 8788 train
Dynamic signal carries out mathematical morphology filter to it and improves EMD to decompose, to verify the engineering feasibility of mentioned method.Signal
Sample frequency is 10kHz, train running speed 60km/h.
According to the mathematical morphology filter filtering principle of proposition, the knot of signal is calculated according to signal to be processed first
Structure parameter, the length dimension sequence L for obtaining the structural element of signal is [3,16], and the signal height scale of processing to be filtered is
[0,0.8355] carries out basic morphologic filtering to the track vibration signal that collection in worksite obtains, including form is opened, form
Close, form open-close, form close-opening operation, calculate different structure element filtering processing after signal characteristic frequency intensity value, press
Size is obtained according to intensity value to be ranked up, and chooses the maximum structural element of intensity value and operation operator.
In conjunction with the waveform diagram for the track vertical vibration signal that Fig. 1 collection in worksite arrives, duration 2s is sampled, totally 20000 samplings
Point, it can be seen that live track vibration signal is affected by noise very big from the waveform diagram of signal, normal signal has all been flooded
In noise signal, in order to which subsequent more preferable earth signal is decomposed, the failure-frequency in stick signal needs first to shake to live track
Dynamic signal is filtered, to reach preferably discomposing effect.
1 optimum structure element of table
From Fig. 3 (a)~(d) it can be seen that form open-close and form close-the frequency intensity coefficient of opening operation most very much not surpasses
0.04 is crossed, and it has been more than 0.04 that form, which is opened with the frequency intensity coefficient maximum of form closed operation, illustrates that morphology is opened and morphology
Closed operation has better filter effect to signal.Based on the above analysis, length is used to form broad sense for 15 linear structure element
Morphologic filters are filtered original vibration signal.Fig. 4 is filtered track vibration signal, it is known that by filtering
Treated, and track vibration signal is more smooth, significantly reduces the interference of noise, and shock point signal is relatively more clear.
In order to further analyze processing actual measurement track vibration signal, now using improved EMD decomposition method to noise reduction process after
Track vibration signal carry out decomposition analysis.Parameter setting are as follows: white noise acoustic amplitude is 0.05 times of fault vibration signal standards difference,
Adding number is 100, maximum screening iteration 1000 times.The IMF component such as Fig. 5 institute decomposed using improved EMD decomposition method
Show, it is known that impact signal ingredient caused by failure is concentrated mainly in preceding 8 rank IMF component.
To the IMF component that improvement EMD decomposition algorithm decomposes, its correlation coefficient value with original signal and each rank are calculated
The signal kurtosis value of IMF component, shown in calculated result such as Fig. 6 (a)~(b).The related coefficient and kurtosis value of each rank IMF component are each
It is not identical, and the variation tendency that related coefficient presentation is successively decreased, and signal kurtosis value first increases and then decreases.According to IMF selection principle,
IMF related coefficient standard deviation is that 0.2234, IMF kurtosis value threshold value is 8, and screening obtains IMF1, IMF2, IMF3, IMF4 this four
Intrinsic mode function.The Hilbert envelope spectrum for calculating four IMF components, as shown in Fig. 7 (a)~(d).
The frequency of impact that can be clearly seen that IMF1 from Fig. 7 is 13.13Hz, and the frequency of impact of IMF2 is 14.38Hz,
The frequency of impact of IMF3 is 46.88Hz, and the frequency of impact of IMF4 is 13.13Hz.It can be found that containing in IMF1, IMF2, IMF4
There is the frequency of impact of 13Hz or so.According to speed 60km/h, wheel diameter 840mm, wheel circumference 2.64m, available wheel
Rotational frequency be 6.31Hz, 13Hz frequency and the not smoother theoretical failure-frequency of the 2 rank wheel overall situations more connect for 12.62Hz
Closely, the IMF component obtained contains the characteristic frequency in original signal, thereby increases and it is possible to containing wheel fault, need further to pass through
Signal analysis and processing is determined.
The Hilbert spectrogram of IMF1, IMF2, IMF4 are calculated, such as
Shown in Fig. 8 (a)~(c), lateral ribbon distribution spectrogram can be significantly seen from figure, and frequency is in 13Hz
Up and down, it is closer to the 2 not smoother theoretic frequencies of the rank wheel overall situation, therefore by self-adaptive harmonics detection and improves EMD decomposition
Afterwards, the IMF component obtained is correctly extracted the fault characteristic frequency in original signal.
Claims (5)
1. a kind of vibration fault extracting method based on self-adaptive harmonics detection and improvement EMD, which is characterized in that including following step
It is rapid:
Step 1, acquisition trajectory vibration signal;
Step 2, adaptive morphology junction filter is constructed, signal is filtered;
Step 3, the EMD that signal improves is decomposed;
Step 4, the related coefficient of signal and the kurtosis value of signal are calculated, IMF component is screened;
Step 5, Hilbert transformation is carried out to IMF component, calculates the Hilbert marginal spectrum of IMF component.
2. the vibration fault extracting method according to claim 1 based on self-adaptive harmonics detection and improvement EMD, feature
It is, building adaptive morphology junction filter, specific steps described in step 2 are as follows:
Step 2.1, selection structural element;
Step 2.2, the length L for calculating structural elements;
Step 2.3, the height H for calculating structural elementj;
Step 2.4, construction Multi-structure elements collection;
Step 2.5 determines optimum structure element.
3. the vibration fault extracting method according to claim 1 based on self-adaptive harmonics detection and improvement EMD, feature
It is, EMD improved to signal described in step 3 is decomposed, specific steps are as follows:
Step 3.1, using EMD algorithm to adding the signal x after making an uproar(i)=x ± β0w(i)It is decomposed, obtains the 1st improvement EMD's
IMF component:
Wherein, w(i)For equal value zero, the white noise of unit variance;βkFor white noise intensity, k=0,1,2 ..., K, I is plus noise
Number;X is original signal;x(i)To add the signal after making an uproar;Ek() is k-th of the IMF component obtained after EMD is decomposed;E1+To be added
Component, the E of positive white noise1-For the component that negative white noise is added;
Step 3.2, the residual error r for calculating the 1st IMF component1:
r1=x-imf1
Step 3.3, using EMD decomposition computation r1±β1E1(w(i)) first mode, and be defined as improve EMD decompose the 2nd
A IMF component imf2:
Step 3.4 works as k=1,2 ... K, calculates k-th of residual error rk:
rk=xk-1-imfk
Wherein K is the IMF component number that original signal decomposes;
Step 3.5, using EMD decomposition computation rk±βkEk(w(i)) the 1st modal components, and be defined as improve EMD kth+1
A IMF component imfk+1:
Step 3.6 enables k be incremented by 1, repeats step 3.4~step 3.5, calculates next IMF component, stop when k=K.
4. the vibration fault extracting method according to claim 1 based on self-adaptive harmonics detection and improvement EMD, feature
It is, the related coefficient of signal and the kurtosis value of signal is calculated described in step 4, specific as follows:
The cross-correlation coefficient ρ of definition signal x (n) and y (n)xyAre as follows:
The kurtosis value Kurtosis of signal is normalized m rank central moment, is defined as follows:
In formula, x={ x1,x2,…,xN}={ xiIt is Discrete signal, i=1,2 ..., N, N is sample point number, and x is signal
The mean value of x.
5. the vibration fault extracting method according to claim 1 based on self-adaptive harmonics detection and improvement EMD, feature
It is, Hilbert transformation is carried out to IMF component described in step 5, calculates the Hilbert marginal spectrum of IMF component, specific as follows:
Hilbert transformation is done to IMF component, obtains the instantaneous frequency and instantaneous amplitude of each component, by the instantaneous of each component
Frequency and instantaneous amplitude are superimposed together, and obtain the Hilbert amplitude spectrum H (ω, t) of IMF component are as follows:
Wherein, akIt (t) is the instantaneous amplitude of k-th of IMF component, ωk(t) instantaneous frequency of k-th of IMF component, K are original signal
Decompose obtained IMF component number;
By the Hilbert spectrogram of IMF component to time integral, the Hilbert marginal spectrum h (ω) of IMF component is obtained:
Wherein, T is the length of original signal;The Hilbert marginal spectrum of IMF component reflects instantaneous frequency in all frequencies
Size and variation.
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CN113501028B (en) * | 2021-07-07 | 2022-08-09 | 中国铁道科学研究院集团有限公司 | Method and device for diagnosing poor welded joint of heavy-duty railway steel rail |
CN114580460A (en) * | 2022-01-17 | 2022-06-03 | 西南交通大学 | Railway vehicle wheel rail fault diagnosis method based on morphological filtering and HHT conversion |
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