CN108491777A - A kind of Lamb wave spatial sampling signal fitting method based on Morlet morther wavelets - Google Patents
A kind of Lamb wave spatial sampling signal fitting method based on Morlet morther wavelets Download PDFInfo
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Abstract
The Lamb wave spatial sampling signal fitting method based on Morlet morther wavelets that the invention discloses a kind of, belongs to engineering structure health monitoring technical field.The centre frequency, sample frequency, sampling instant of Morlet morther wavelets is arranged in this method first；Then Lamb wave excitation emulation signal is built according to the pumping signal wave crest number of Lamb wave；Secondly according to the related coefficient of Morlet morther wavelets fitting waveform under different frequency bands width parameter and Lamb wave excitation emulation signal, the frequency bandwidth parameter of Morlet morther wavelets is sought；The error sum of squares of waveform and Lamb wave spatial sampling signal is finally fitted according to Morlet wavelet functions under different scale factors, shift factor, the fitting parameter of Morlet wavelet functions is sought, corresponding Morlet wavelet functions fitting waveform is the Morlet wavelet functions fitting waveform of Lamb wave spatial sampling signal at this time.The present invention improves the spatial resolution and length of Lamb wave spatial sampling signal, to peomote application of the space wave-number domain signal processing method in engineering structure health monitoring field.
Description
Technical field
The Lamb wave spatial sampling signal fitting method based on Morlet morther wavelets that the present invention relates to a kind of, belongs to engineering knot
Structure health monitoring technical field.
Background technology
Structure health monitoring method based on Lamb wave have damage monitoring high sensitivity, monitoring range it is big, can be online
Using can also apply offline, active damage monitoring can be carried out also can carry out passive Impact monitoring, metal structure can be monitored
The advantages that composite structure etc. can be monitored.Therefore, the structure health monitoring method based on Lamb wave receives both domestic and external wide
General research is one of current most promising structural health monitoring technology.In general, piezoelectric transducer is to realize Lamb wave excitation
With the main devices of sensing.For the structure health monitoring method based on Lamb wave, the method for early stage mainly passes through analysis
Lamb wave is damaged after effect, and signal is in time domain, frequency domain, the feature of time-frequency domain or mode conversion feature, such as flying for signal
Row time, amplitude, energy, major frequency components and its amplitude, time-frequency amplitude, singularity characteristics value etc. recognize damage
And characterization.But it since Lamb wave has the characteristic of multi-mode, that is to say under the same centre frequency, it may appear that Duo Gemo
The Lamb wave of the Lamb wave signal of formula, different mode uses routine in the time and apart from upper often mutually interspersed overlapping
Time domain, frequency domain or time-frequency domain signal processing method are difficult to be analyzed, and the Lamb wave signal of different mode is with different
Propagation characteristic, these will result in any of the above monitoring structural health conditions imaging method error based on Lamb wave and become larger, or even prison
It surveys difficult.For this purpose, researcher attempts to analyze Lamb wave signal in space-wave-number domain.Wherein there are many scholar's uses to sweep
The space wave information that the Lamb wave in formula laser doppler vibrometer acquisition structure is propagated is retouched, this mode is difficult to carry out structure
The on-line monitoring of damage.Some scholars are monitored on-line using piezoelectric sensor array acquisition Lamb wave space wave information,
It is limited to the size of piezoelectric transducer and the form of structure, the spatial resolution of this collected Lamb wave spacing wave of mode
Limited with length, this has seriously affected subsequent space-wave number domain signal processing method, and damage monitoring error is caused to become larger.
Invention content
To solve the above problems, to propose a kind of Lamb wave spatial sampling signal based on Morlet morther wavelets quasi- by the present invention
Conjunction method, this method fit Lamb wave spatial sampling signal using Morlet wavelet functions, are adopted to improve Lamb wave space
The spatial resolution and length of sample signal.
The present invention is to solve its technical problem to adopt the following technical scheme that：
Step 1：Initialize installation
1. the centre frequency that Morlet morther wavelets are arranged is c, sample frequency d, sampling instant t, sampling instant is differentiated
Rate is Δ t=1/d.
2. according to the pumping signal wave crest number n of Lamb wave, corresponding Lamb wave excitation emulation letter is built using formula (1)
Number s1, the centre frequency for emulating signal is c1=c, sample frequency d1=d, sampling instant t1=t.
In formula：c1The centre frequency of emulation signal, t are encouraged for Lamb wave1When encouraging the sampling of emulation signal for Lamb wave
It carves, n is the wave crest number of Lamb wave excitation emulation signal, and π is pi.
Step 2：Seek the frequency bandwidth parameter h of Morlet morther wavelets
1. the scanning range that the frequency bandwidth parameter h of Morlet morther wavelets is arranged is hs, scanning resolution is Δ h.
2. calculating the Morlet morther wavelets under each frequency bandwidth parameter according to Morlet mother wavelet functions (formula (2))
Function waveform f1(t), extraction Morlet mother wavelet function waveforms f1(t) imaginary part, and normalize, left and right overturning, obtain Morlet
Morther wavelet is fitted waveform s2。
In formula：f1For Morlet mother wavelet functions, t is sampling instant, and π is pi, and h is the frequency band of Morlet morther wavelets
Width parameter, e are natural constant, and i is imaginary unit, and c is the centre frequency of Morlet morther wavelets.
3. calculating Morlet morther wavelets fitting waveform s according to formula (3)2Emulation signal s is encouraged with Lamb wave1Phase relation
Number r.
In formula：R is s2With s1Related coefficient, Cov (s2,s1) it is s2With s1Covariance, Var [s2] it is s2Variance,
Var[s1] it is s1Variance.
4. finally obtaining the correlation coefficient r under each frequency bandwidth parameter, wherein corresponding frequency at correlation coefficient r maximum value
Frequency bandwidth parameter h of the bandwidth parameter as Morlet morther wavelets.
Step 3：Seek the Morlet wavelet functions fitting waveform s of Lamb wave spatial sampling signal3
1. the scanning range that the scale factor a of Morlet wavelet functions is arranged is as, scanning resolution is Δ a；Morlet
The scanning range of the shift factor b of wavelet function is bs, and scanning resolution is Δ b.
2. choosing a scale factor a and shift factor b, spatial sampling point x at this time is calculated according to formula (4).
In formula：G is the spatial sampling frequencies of Lamb wave spatial sampling signal.
3. calculating the Morlet wavelet function waveforms f under parameter current according to Morlet wavelet functions (formula (5))2(x),
Extract Morlet wavelet function waveforms f2(x) imaginary part, and normalize, left and right overturning, obtain Morlet wavelet functions fitting wave
Shape s3。
4. calculating Morlet wavelet functions fitting waveform s according to formula (6)3With spatial sampling signal s0Error sum of squares
k。
K=∑s (s3-s0)2 (6)
5. finally obtaining the error sum of squares k under each scale factor a and shift factor b, wherein error sum of squares k is minimum
Fitting parameters of the corresponding scale factor a and shift factor b as Morlet wavelet functions at value, corresponding Morlet is small at this time
Wave function is fitted waveform s3As Lamb wave spatial sampling signal s0Morlet wavelet functions be fitted waveform.
Beneficial effects of the present invention are as follows：
1, the spatial resolution of Lamb wave spatial sampling signal is improved；
2, the length of Lamb wave spatial sampling signal is increased；
3, hardware requirement of the space-wave number domain signal processing method to spatial sampling equipment is reduced；
4, reduce the arrangement quantity of Lamb wave spatial sampling sensor；
5, the damage monitoring error based on space-wave number domain signal processing method is reduced；
6, the present invention peomotes space-wave number domain signal processing method and is answered engineering structure health monitoring field
With.
Description of the drawings
Fig. 1 is the implementing procedure of the Lamb wave spatial sampling signal fitting method based on Morlet morther wavelets；
Fig. 2 is the schematic diagram of Specimen Shape, piezoelectric transducer position and two-dimensional Cartesian coordinate system in embodiment；
Fig. 3 is Lamb wave spatial sampling signal；
Fig. 4 is Lamb wave excitation emulation signal；
Fig. 5 is the related coefficient under each frequency bandwidth parameter；
Fig. 6 is Morlet morther wavelets fitting waveform；
Fig. 7 is the error sum of squares under each scale factor and shift factor；
Fig. 8 is Morlet wavelet functions fitting waveform and Lamb wave spatial sampling signal contrast.
Specific implementation mode
Below in conjunction with attached drawing, by specific embodiment, the present invention is further illustrated.
The centre frequency, sample frequency, sampling instant of Morlet morther wavelets is arranged in this method first；Then according to Lamb wave
Pumping signal wave crest number structure Lamb wave excitation emulation signal；Secondly small according to mother Morlet under different frequency bands width parameter
Wave is fitted the related coefficient of waveform and Lamb wave excitation emulation signal, seeks the frequency bandwidth parameter of Morlet morther wavelets；Finally
The error sum of squares of waveform and spatial sampling signal is fitted according to Morlet wavelet functions under different scale factors, shift factor,
The fitting parameter of Morlet wavelet functions is sought, corresponding Morlet wavelet functions fitting waveform is that Lamb wave space is adopted at this time
The Morlet wavelet functions of sample signal are fitted waveform.
Fig. 1 is the implementing procedure of the Lamb wave spatial sampling signal fitting method the present invention is based on Morlet morther wavelets：If
Set the centre frequency c, sample frequency d, sampling instant t of Morlet morther wavelets；According to the pumping signal wave crest number n structures of Lamb wave
Build Lamb wave excitation emulation signal s1；The scanning range hs and interval delta h of the frequency bandwidth parameter h of Morlet morther wavelets are set；
Select the scan values of a frequency bandwidth parameter；Calculate Morlet mother wavelet function waveforms f1(t)；Extract f1(t) imaginary part, and
Normalization, left and right overturning obtain Morlet morther wavelets fitting waveform s2；Calculate s2With s1Correlation coefficient r；Calculate each frequency band
Related coefficient under width parameter；Corresponding frequency bandwidth parameter is as Morlet morther wavelets at selection correlation coefficient r maximum value
Frequency bandwidth parameter h；The scanning range as and interval delta a of the scale factor a of Morlet wavelet functions are set, Morlet is set
The scanning range bs and interval delta b of the shift factor b of wavelet function；Select the scan values of a scale factor, a displacement because
The scan values of son；Calculate spatial sampling point x；Calculate Morlet wavelet function waveforms f2(x)；Extract f2(x) imaginary part, and normalizing
Change, left and right overturning, obtains Morlet wavelet functions fitting waveform s3；Calculate s3With spatial sampling signal s0Error sum of squares k；
Calculate the error sum of squares under each scale factor, shift factor；Choose corresponding scale factor a at error sum of squares minimum value
Fitting parameter with shift factor b as Morlet wavelet functions, the waveform of corresponding Morlet wavelet functions fitting at this time are
The Morlet wavelet functions of Lamb wave spatial sampling signal are fitted waveform.
Embodiment test specimen is one block of 100cm × 100cm × 0.2cm (length × width x thickness) aluminium alloy.Excitation/sensing element is
PZT-5A type piezoelectric transducers, a diameter of 0.8cm, the thickness 0.04cm of PZT-5A type piezoelectric transducers.Experimental facilities uses
Be certain university research and development structural healthy monitoring system.It is linear it to be evenly arranged 7 array elements in the underface centre position of test specimen
Piezoelectric sensor array, for acquiring the Lamb wave spacing wave in structure, between two neighboring piezoelectric transducer central point
Spacing is Δ x=0.9cm, and the distance between linear piezoelectric sensor array and aluminium alloy test specimen lower edge are 20cm.Range line
Exciting element of the piezoelectric transducer as Lamb wave is arranged at shape piezoelectric sensor array central point 30cm.With linear piezoelectricity
The axis of sensor array is x-axis, and the central point of linear piezoelectric sensor array is origin, and it is straight that two dimension is established in test specimen structure
Angular coordinate system, as shown in Figure 2.A five wave crest narrow band signal of 20kHz Sine Modulateds is generated using structural healthy monitoring system, it is defeated
Enter to exciting element.Linear piezoelectric sensor array is connected using structural healthy monitoring system, acquires the Lamb propagated in structure
Wave signal, Lamb wave spatial sampling signal s0As shown in Figure 3.
Embodiment includes the following steps：
Step 1：Initialize installation
1. the centre frequency that Morlet morther wavelets are arranged is c=1Hz, sample frequency d=50Hz, sampling instant t=
[- 70,70], sampling instant resolution ratio are Δ t=1/d.
2. according to the pumping signal wave crest number (five wave crest narrow band signal of Sine Modulated, n=5) of Lamb wave, formula is utilized
(1) corresponding Lamb wave excitation emulation signal s is built1, the centre frequency for emulating signal is c1=c=1Hz, sample frequency d1
=d=50Hz, sampling instant t1=t=[- 70,70], as shown in Figure 4.
In formula：c1The centre frequency of emulation signal, t are encouraged for Lamb wave1When encouraging the sampling of emulation signal for Lamb wave
It carves, n is the wave crest number of Lamb wave excitation emulation signal, and π is pi.
Step 2：Seek the frequency bandwidth parameter h of Morlet morther wavelets
1. the scanning range that the frequency bandwidth parameter h of Morlet morther wavelets is arranged is hs=[1.5,2.4], scanning resolution
For Δ h=0.0001.
2. calculating the Morlet morther wavelets under each frequency bandwidth parameter according to Morlet mother wavelet functions (formula (2))
Function waveform f1(t), extraction Morlet mother wavelet function waveforms f1(t) imaginary part, and normalize, left and right overturning, obtain Morlet
Morther wavelet is fitted waveform s2。
In formula：f1For Morlet mother wavelet functions, t is sampling instant, and π is pi, and h is the frequency band of Morlet morther wavelets
Width parameter, e are natural constant, and i is imaginary unit, and c is the centre frequency of Morlet morther wavelets.
3. calculating Morlet morther wavelets fitting waveform s according to formula (3)2Emulation signal s is encouraged with Lamb wave1Phase relation
Number r.
In formula：R is s2With s1Related coefficient, Cov (s2,s1) it is s2With s1Covariance, Var [s2] it is s2Variance,
Var[s1] it is s1Variance.
4. the correlation coefficient r under finally obtained each frequency bandwidth parameter is as shown in figure 5, wherein correlation coefficient r is maximum
Frequency bandwidth parameter h=of (0.9985) the corresponding frequency bandwidth parameter (1.9621) as Morlet morther wavelets at value
1.9621, corresponding Morlet morther wavelets fitting waveform s at this time2As shown in Figure 6.
Step 3：Seek the Morlet wavelet functions fitting waveform s of Lamb wave spatial sampling signal3
1. the scanning range that the scale factor a of Morlet wavelet functions is arranged is as=[10,30], scanning resolution is Δ
A=0.01；The scanning range of the shift factor b of Morlet wavelet functions is bs=[- 0.054,0.054], and scanning resolution is
Δ b=0.00009.
2. choosing a scale factor a and shift factor b, spatial sampling point x at this time is calculated according to formula (4).
In formula：G is the spatial sampling frequencies of Lamb wave spatial sampling signal, g=2 π/Δ x.
3. calculating the Morlet wavelet function waveforms f under parameter current according to Morlet wavelet functions (formula (5))2(x),
Extract Morlet wavelet function waveforms f2(x) imaginary part, and normalize, left and right overturning, obtain Morlet wavelet functions fitting wave
Shape s3。
4. calculating Morlet wavelet functions fitting waveform s according to formula (6)3With Lamb wave spatial sampling signal s0Error
Quadratic sum k.
K=∑s (s3-s0)2 (6)
5. finally obtaining the error sum of squares k under each scale factor a and shift factor b, the square-error after normalization
With k as shown in fig. 7, (0.1211) corresponding scale factor a (20.26) and shift factor b wherein at error sum of squares k minimum values
The fitting parameter of (- 0.00882) as Morlet wavelet functions, at this time corresponding Morlet wavelet functions fitting waveform s3As
Lamb wave spatial sampling signal s0Morlet wavelet functions be fitted waveform, as shown in Figure 8.From figure 8, it is seen that Morlet is small
Wave function fitting waveform greatly improves the spatial resolution and length of Lamb wave spatial sampling signal.
Although having shown and described the present invention referring particularly to its preferred embodiment, those skilled in the art can be with
Understand, model of the various changes in form and details without departing from the present invention described in the appended claims can be made
It encloses.It is described in detail above in association with specific embodiments of the present invention, but is not limitation of the present invention.It is every according to this hair
Any simple modification made to the above embodiment of bright technical spirit, still falls within the range of technical solution of the present invention.
Claims (10)
1. a kind of Lamb wave spatial sampling signal fitting method based on Morlet morther wavelets, which is characterized in that
The approximating method is as follows：
Step 1：Initialize installation constructs Lamb wave excitation emulation signal s1；
Step 2：The phase of emulation signal is encouraged with Lamb wave according to Morlet morther wavelets fitting waveform under different frequency bands width parameter
Relationship number seeks the frequency bandwidth parameter h of Morlet morther wavelets；
Step 3：According to Morlet wavelet functions fitting waveform and Lamb wave spatial sampling under different scale factors, shift factor
The error sum of squares of signal seeks the fitting parameter of Morlet wavelet functions, and corresponding Morlet wavelet functions are fitted wave at this time
Shape is the Morlet wavelet functions fitting waveform s of Lamb wave spatial sampling signal3。
2. the Lamb wave spatial sampling signal fitting method according to claim 1 based on Morlet morther wavelets, feature
It is,
The step 1 is specially：
(1) centre frequency of setting Morlet morther wavelets is c, sample frequency d, sampling instant t；
(2) corresponding Lamb wave excitation emulation signal s is built according to the pumping signal wave crest number n of Lamb wave1。
3. the Lamb wave spatial sampling signal fitting method according to claim 2 based on Morlet morther wavelets, feature
It is：
In formula：c1The centre frequency of emulation signal, t are encouraged for Lamb wave1For the sampling instant of Lamb wave excitation emulation signal, n is
The wave crest number of Lamb wave excitation emulation signal, π is pi, c1=c, t1=t.
4. the Lamb wave spatial sampling signal fitting method according to claim 1 based on Morlet morther wavelets, feature
It is,
The step 2 is specially：
(1) scanning range of the frequency bandwidth parameter h of setting Morlet morther wavelets is hs, and scanning resolution is Δ h；
(2) the Morlet mother wavelet function waveforms f under each frequency bandwidth parameter is calculated according to Morlet mother wavelet functions1
(t), extraction Morlet mother wavelet function waveforms f1(t) imaginary part, and normalize, left and right overturning, it is quasi- to obtain Morlet morther wavelets
Multiplex shape s2；
(3) Morlet morther wavelets fitting waveform s is calculated2Emulation signal s is encouraged with Lamb wave1Correlation coefficient r；
(4) correlation coefficient r under each frequency bandwidth parameter, wherein corresponding frequency band at correlation coefficient r maximum value are finally obtained
Frequency bandwidth parameter h of the width parameter as Morlet morther wavelets.
5. the Lamb wave spatial sampling signal fitting method according to claim 4 based on Morlet morther wavelets, feature
It is：
In formula：f1For Morlet mother wavelet functions, t is sampling instant, and π is pi, and h is the frequency bandwidth of Morlet morther wavelets
Parameter, e are natural constant, and i is imaginary unit, and c is the centre frequency of Morlet morther wavelets.
6. the Lamb wave spatial sampling signal fitting method according to claim 4 or 5 based on Morlet morther wavelets, special
Sign is：
In formula：R is s2With s1Related coefficient, Cov (s2,s1) it is s2With s1Covariance, Var [s2] it is s2Variance, Var
[s1] it is s1Variance.
7. the Lamb wave spatial sampling signal fitting method according to claim 1 based on Morlet morther wavelets, feature
It is,
The step 3 is specially：
(1) scanning range of the scale factor a of setting Morlet wavelet functions is as, and scanning resolution is Δ a；Morlet small echos
The scanning range of the shift factor b of function is bs, and scanning resolution is Δ b；
(2) a scale factor a and shift factor b is chosen, spatial sampling point x at this time is calculated；
(3) the Morlet wavelet function waveforms f under parameter current is calculated according to Morlet wavelet functions2(x), extraction Morlet is small
Wave function waveform f2(x) imaginary part, and normalize, left and right overturning, obtain Morlet wavelet functions fitting waveform s3；
(4) Morlet wavelet functions fitting waveform s is calculated3With Lamb wave spatial sampling signal s0Error sum of squares k；
(5) the error sum of squares k under each scale factor a and shift factor b, wherein error sum of squares k minimum values are finally obtained
Locate the fitting parameter of corresponding scale factor a and shift factor b as Morlet wavelet functions, at this time corresponding Morlet small echos
Function Fitting waveform s3As Lamb wave spatial sampling signal s0Morlet wavelet functions be fitted waveform.
8. the Lamb wave spatial sampling signal fitting method according to claim 7 based on Morlet morther wavelets, feature
It is：
In formula：X is spatial sampling point, and g is the spatial sampling frequencies of Lamb wave spatial sampling signal, and a is scale factor, and b is position
Move the factor.
9. the Lamb wave spatial sampling signal fitting method according to claim 7 based on Morlet morther wavelets, feature
It is：
In formula：f2For Morlet wavelet functions, π is pi, and h is the frequency bandwidth parameter of Morlet morther wavelets, and e is that nature is normal
Number, i are imaginary unit, and c is the centre frequency of Morlet morther wavelets, and a is scale factor, and b is shift factor.
10. the Lamb wave spatial sampling signal fitting method according to claim 7 based on Morlet morther wavelets, feature
It is：
Error sum of squares k=∑s (s3-s0)2。
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110018235A (en) * | 2019-03-12 | 2019-07-16 | 上海大学 | A kind of lack sampling Lamb wave wave number searching method based on time domain compensation |
| CN114397010A (en) * | 2021-12-29 | 2022-04-26 | 南京中科声势智能科技有限公司 | Transient signal acoustic imaging method based on wavelet decomposition |
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| CN105372326A (en) * | 2015-10-20 | 2016-03-02 | 南京航空航天大学 | Space-wavenumber filter based on Lamb wave wavenumber scanning |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110018235A (en) * | 2019-03-12 | 2019-07-16 | 上海大学 | A kind of lack sampling Lamb wave wave number searching method based on time domain compensation |
| CN110018235B (en) * | 2019-03-12 | 2021-07-13 | 上海大学 | Time domain compensation-based under-sampling Lamb wave number searching method |
| CN114397010A (en) * | 2021-12-29 | 2022-04-26 | 南京中科声势智能科技有限公司 | Transient signal acoustic imaging method based on wavelet decomposition |
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