CN107607628A - A kind of supersonic guide-wave frequency dispersion compensation method and its application based on rarefaction representation - Google Patents
A kind of supersonic guide-wave frequency dispersion compensation method and its application based on rarefaction representation Download PDFInfo
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Abstract
The invention discloses a kind of supersonic guide-wave frequency dispersion compensation method based on rarefaction representation and its application, belong to ultrasonic technique field.The method of the invention includes：(1) the frequency dispersion response signal under the Dispersion Characteristics prior information generation different propagation distance of the supersonic guide-wave in structure；(2) set up frequency dispersion and propagate dictionary；(3) dictionary is propagated using the frequency dispersion and rarefaction representation is carried out to frequency dispersion signal to be compensated as signal base, established sparse representation model and solve, obtain rarefaction representation coefficient of the signal to be compensated under the signal base constructed；(4) non-frequency dispersion processing is carried out to original wave number, generates non-frequency dispersion response signal, and set up nondispersive propagation dictionary；(5) gained rarefaction representation coefficient and nondispersive propagation dictionary are utilized, non-frequency dispersion reconstruct is carried out to former frequency dispersion signal.The present invention can effectively realize dispersion compensation to single mode and multi-modal supersonic guide-wave, and the distortion of ripple bag is small, can improve the time frequency concentration degree of ultrasonic guided wave signals.
Description
Technical field
The invention belongs to ultrasonic technique field, and in particular to a kind of ultrasonic guided wave signals processing method, more particularly to it is a kind of
Supersonic guide-wave frequency dispersion compensation method and its application based on rarefaction representation.
Background technology
In recent years, as the reliability requirement of the Grand Equipments such as the fuselage wing to aircraft, blade of wind-driven generator is continuous
Improve, monitoring structural health conditions have obtained extensive research and development with fault diagnosis technology.Supersonic guide-wave is supervised as structural health
Survey with fault diagnosis field most one of instrument of prospect and receive significant attention.Monitoring structural health conditions based on supersonic guide-wave
A kind of active monitoring and diagnostic techniques with fault diagnosis technology, have to by the crackle equivalent damage in geodesic structure it is sensitive,
Can propagate in the structure it is longer apart from the advantages that, be structural health detection and the important development direction of field of non destructive testing it
One.Supersonic guide-wave has Dispersion and multimode step response, wherein, Dispersion is due between the wave number and frequency of supersonic guide-wave
Non-linear relation so that group velocity, phase velocity turn into the function of frequency, are embodied in ripple bag in the signal and extend in the time domain
Decline with amplitude；Multimode step response refers to, under any driving frequency, two or more guided wave modal in structure at least be present, different
There is different frequency dispersion and propagation characteristic between mode.It is multi-modal so that dispersion compensation is more difficult.Frequency dispersion makes with multimode step response
The easily mutual aliasing of ripple bag of supersonic guide-wave is obtained, difficulty is caused to echo-bearing, non-destructive tests etc..For multi-modal supersonic guide-wave
Signal carries out dispersion compensation, has important engineering significance and practical value.
In existing supersonic guide-wave frequency dispersion technology, time reversal is lost guided wave signals while dispersion compensation
Flight time, and the flight time is important characteristic parameter, loses flight-time information and is caused to subsequent insult positioning etc.
Extreme difficulties；Other method, the linear interpolation method proposed such as Wilcox when m- distance domain reflection method, Liu and the Yuan proposed,
Inflection frequency converter technique based on group velocity that Marchi et al. is proposed etc., both for the guided wave signals of single mode, to more
The dispersion compensation of mode guided wave signals is no longer applicable, and the ripple bag distortion that these methods are larger because the reasons such as interpolation are present, frequency dispersion
Effect is difficult to be fully compensated for.
The content of the invention
To overcome the shortcomings of existing supersonic guide-wave dispersion compensation technology, it is an object of the invention to provide one kind based on sparse
The supersonic guide-wave frequency dispersion compensation method of expression, it can be achieved to single mode or the dispersion compensation of multi-modal guided wave signals.
To reach above-mentioned purpose, the present invention uses following technical scheme：
A kind of supersonic guide-wave frequency dispersion compensation method based on rarefaction representation, is specifically included：
Step 1：Frequency dispersion under the Dispersion Characteristics prior information generation different propagation distance of supersonic guide-wave in structure
Response signal；
Using encouraging centre frequency fcThe group velocity c at placeg(fc) discretization is carried out to propagation distance, calculation formula is as follows：
Wherein, xiFor the propagation distance of frequency dispersion response signal, cg(fc) it is excitation centre frequency fcThe group velocity at place, i 0
To the integer between N-1, tiFor the propagation time of signal, fsFor the sample frequency of signal, N is the sampling number of signal；
Frequency dispersion response signal corresponding to the A0 mode that wave number is k is：
Wherein, F (ω) is pumping signal, and j is unit imaginary number, and ω is angular frequency, and t is time variable, and k is A0 mode guided waves
Wave number；
Step 2：Set up frequency dispersion and propagate dictionary；
Frequency dispersion is set up by row to the response signal obtained under different propagation distance and propagates dictionary, and carries out 2 norms by row and returns
One change is handled, and the frequency dispersion obtained under the target modalities that wave number is k propagates dictionary
U=[u0,u2,…,ui,…uN-1]D-1,
Wherein, D is that a diagonal element is Di,i=| | ui||2Diagonal matrix；
Step 3：Dictionary U is propagated using the frequency dispersion rarefaction representation is carried out to frequency dispersion signal to be compensated as signal base, established dilute
Dredge and represent model and solve；
Dictionary U is propagated come to frequency dispersion signal s to be compensated using the compound frequency dispersion built in the step 20Carry out sparse table
Show, structure coefficient table representation model s0=Ua+w,
Wherein, vectorial a is corresponding rarefaction representation coefficient, and w is noise item；
Above formula is converted into convex optimization problem to be solved, obtained：
Wherein, λ is penalty term parameter,To solve gained rarefaction representation coefficient vector；
Step 4：Non- frequency dispersion processing is carried out to original wave number, generates non-frequency dispersion response signal, and set up nondispersive propagation word
Allusion quotation；
The non-frequency dispersion of wave number k progress to target modalities handles to obtain k', and substitutes k, repeat step 1 and step 2 with k', obtains
To nondispersive propagation dictionary U'；
Step 5：Using gained rarefaction representation coefficient and nondispersive propagation dictionary, non-frequency dispersion weight is carried out to former frequency dispersion signal
Structure；
By the rarefaction representation vector in the nondispersive propagation dictionary U' tried to achieve in the step 4 and the step 3It is multiplied,
Obtain signal after dispersion compensation
The frequency dispersion, which propagates dictionary U, includes frequency dispersion propagation dictionary U corresponding to A0 modeA0With S0 mode corresponding to frequency dispersion propagate
Dictionary US0；
It is single mode dictionary or multi-modal compound dictionary that the frequency dispersion, which propagates dictionary U,；When signal to be compensated only includes single mode
During state guided wave, it is single mode dictionary that the frequency dispersion, which propagates dictionary U,；When signal to be compensated includes multi-modal guided wave, the frequency dispersion
It is multi-modal compound dictionary to propagate dictionary U；
The analytic modell analytical model that supersonic guide-wave in the step 1 is propagated in the structure is：
Wherein, kpFor the wave number of p-th of mode, Ap,jIt is x to correspond to propagation distance in p-th of modejGuided wave amplitude,
ω is angular frequency, and F (ω) is the frequency domain representation of pumping signal；
Non- frequency dispersion processing in the step 4 is to be linearized original wave number,
Wherein, k'(ω) for non-frequency dispersion processing after wave number, cgFor the group velocity of supersonic guide-wave；
The ripple bag distortion of signal is small after the dispersion compensation, and ripple bag is in A0 mode and S0 mode no longer aliasing, in time domain
It is middle to realize separation.
Present invention also offers a kind of application of the supersonic guide-wave frequency dispersion compensation method based on rarefaction representation.
A kind of application of the supersonic guide-wave frequency dispersion compensation method based on rarefaction representation, it is characterised in that utilize methods described
Dispersion compensation is carried out to damage scattered signal, the positioning to metal and Solid non-metallic damage position can be achieved；
Further, the metal includes aluminium alloy plate；
Further, the Solid non-metallic includes carbon fiber enhancement resin base composite material laminate.
Brief description of the drawings
Fig. 1 is the present embodiment by the physical dimension of geodesic structure and sensor arrangement schematic diagram；
Fig. 2 is the system structure diagram for being used to implement supersonic guide-wave frequency dispersion compensation method in the present embodiment；
Fig. 3 is the 3 crest Hanning windows modulation sine pulse signal schematic representation that the centre frequency of the present embodiment is 150kHz；
Fig. 4 is the frequency dispersion signal schematic representation to be compensated containing two kinds of guided wave modals of A0 and S0 of the present embodiment；
Fig. 5 is a kind of supersonic guide-wave frequency dispersion compensation method flow chart based on rarefaction representation that the present embodiment provides；
Fig. 6 (a)-Fig. 6 (b) is that the supersonic guide-wave corresponding with A0 mode of the present embodiment propagates dictionary schematic diagram；
Wherein, Fig. 6 (a) is that frequency dispersion corresponding with A0 mode propagates dictionary schematic diagram, and Fig. 6 (b) is corresponding with A0 mode
Nondispersive propagation dictionary schematic diagram；
Fig. 7 is the signal schematic representation after dispersion compensation of the present embodiment；
Fig. 8 is the damage imaging result figure obtained using signal after dispersion compensation of the present embodiment；
Fig. 9 is that embodiment applies obtained damage imaging result in carbon fiber enhancement resin base composite material laminate
Figure.
Embodiment
Technical scheme is described in detail with reference to the accompanying drawings and examples.
Reference picture 1 is the embodiment of the present invention by the physical dimension of geodesic structure and sensor arrangement schematic diagram.The present embodiment
Aluminium alloy plate using model 6061 is as treating geodesic structure, and preferred size is 1000mm × 1000mm × 2mm, its material parameter
For：Density p=2690kg/m3, Young's modulus E=68.9GPa, Poisson ratioσ=0.33.In the structure at a distance of two of 600mm
Position is respectively arranged a piezoelectric patches, and one is used as driver, and another is used as receiver.
Reference picture 2, the system structure diagram for implementing supersonic guide-wave frequency dispersion compensation method, including NI to be used in the present embodiment
Control system, NI PXI-5412 excitations board, PIEZO EPA-104 amplifiers, NI PXI-5122 analog input cards, signal condition
Device and Fig. 1 are shown by geodesic structure.Wherein, NI PXI-5412 encourage board, PIEZO EPA-104 amplifiers to be used to realize ultrasound
Generation of the guided wave signals in by geodesic structure.
Pumping signal employed in the present embodiment be a centre frequency be 150kHz Hanning window modulation 3 crests just
String pulse signal, its waveform are as shown in Figure 3.
Reference picture 4, it is the frequency dispersion signal schematic representation to be compensated containing two kinds of guided wave modals of A0 and S0 of the present embodiment.Fig. 3 institutes
After showing that pumping signal is excited by system, propagate in the structure, received device obtains signal as shown in Figure 4, the present embodiment after receiving
In, signal sampling frequencies fsPreferably 10MHz, sampling number N are preferably 30k., can be with according to measured material parameter prior information
Solved by supersonic guide-wave direct problem, obtain guided wave frequency dispersion prior information corresponding with structure, as frequency-wavenumber curve, frequency-
Group velocity curve, frequency-phase velocity curve etc..In the present embodiment, according to priori and excitation centre frequency, it is known that obtain
Frequency dispersion response signal in include 2 kinds of guided wave modals：A0 mode and S0 mode.
Reference picture 5, the present embodiment provide a kind of supersonic guide-wave frequency dispersion compensation method based on rarefaction representation, including following step
Suddenly：
Step 1：Frequency dispersion under the Dispersion Characteristics prior information generation different propagation distance of supersonic guide-wave in structure
Response signal.
Using encouraging centre frequency fcThe group velocity c at placeg(fc) discretization is carried out to propagation distance, calculation formula is as follows：
Wherein, xiFor the propagation distance of frequency dispersion response signal, cg(fc) it is excitation centre frequency fcThe group velocity at place, i 0
To the integer between N-1, tiFor the propagation time of signal, fsFor the sample frequency of signal, N is the sampling number of signal；
To the A0 mode that wave number is k, under pumping signal F (ω) as shown in Figure 3, corresponding propagation distance is xiFrequency dispersion
Response signal is：
Wherein, F (ω) is pumping signal, and j is unit imaginary number, and ω is angular frequency, and t is time variable, and k is A0 mode guided waves
Wave number；
In addition, the analytic modell analytical model that supersonic guide-wave is propagated in the structure is：
Wherein, kpFor the wave number of p-th of mode, Ap,jIt is x to correspond to propagation distance in p-th of modejGuided wave amplitude,
ω is angular frequency, and F (ω) is the frequency domain representation of pumping signal.
Step 2：Set up frequency dispersion and propagate dictionary U.
Frequency dispersion is set up by row to the A0 modal responses signal obtained under different propagation distance and propagates dictionary, and 2 are carried out by row
Norm normalized, frequency dispersion propagation dictionary corresponding to the A0 mode that wave number is k is obtained, as shown in Fig. 6 (a), calculation formula is：
UA0=[u0,u2,…,ui,…uN-1]D-1 (4)
Wherein, D is that a diagonal element is Di,i=| | ui||2Diagonal matrix.
The present embodiment includes A0 and S0 both modalities which, and the A0 mode wave numbers in said process are replaced with into S0 mode wave numbers,
Obtain frequency dispersion corresponding with S0 mode and propagate dictionary US0=[u0,u2,…,ui,…uN-1]D-1.By gained A0 and S0 both modalities which
Under frequency dispersion propagate dictionary combination, obtain frequency dispersion and propagate dictionary U, calculation formula is as follows：
U=[UA0,US0]=[u0,u2,…,ui,…uN-1]D-1 (5)
In the present embodiment, it is single mode dictionary or multi-modal compound dictionary that frequency dispersion, which propagates dictionary, depending on signal to be compensated
Included in mode number：When signal to be compensated only includes single mode guided wave, dictionary is the single mode dictionary；When to be compensated
When signal includes multi-modal guided wave, dictionary is corresponding multi-modal compound dictionary；
Step 3：Dictionary U is propagated using the frequency dispersion rarefaction representation is carried out to frequency dispersion signal to be compensated as signal base, established dilute
Dredge and represent model and solve.
By frequency dispersion signal s to be compensated0Deposited by row and carry out 2 norm normalizeds, answered with what is built in the step 2
Sum of fundamental frequencies, which dissipates propagation dictionary U, to be come to signal s0Rarefaction representation is carried out, and considers the influence of noise, builds following sparse representation model：
s0=Ua+w, (6)
Wherein, vectorial a is corresponding rarefaction representation coefficient, and w is noise item.According to sparse representation theory, above formula is converted
Solved, obtained for convex optimization problem：
Wherein, λ is penalty term parameter, and in the present embodiment, λ values are preferably max | 2UTs0|/10,It is sparse to solve gained
Represent coefficient vector.
Step 4：Non- frequency dispersion processing is carried out to original wave number, generates non-frequency dispersion response signal, and set up nondispersive propagation word
Allusion quotation.
The non-frequency dispersion of wave number k progress to target modalities handles to obtain k', and substitutes k, repeat step 1 and step 2 with k', obtains
To nondispersive propagation dictionary U', as shown in Fig. 6 (b).
In the present embodiment, non-frequency dispersion processing is to be linearized original wave number, and calculation formula is：
Wherein, k'(ω) for non-frequency dispersion processing after wave number, cgFor the group velocity of supersonic guide-wave.
Step 5：Using gained rarefaction representation coefficient and nondispersive propagation dictionary, non-frequency dispersion weight is carried out to former frequency dispersion signal
Structure.
By the rarefaction representation vector in the non-frequency dispersion dictionary U' in the step 4 and the step 3It is multiplied, obtains frequency dispersion
Signal after compensationCalculation formula is as follows：
Reference picture 7, it is the signal schematic representation after dispersion compensation of the present embodiment.As shown in fig. 7, signal after dispersion compensation
Time frequency concentration degree get a promotion, ripple coating compensate back and pumping signal almost consistent waveform, and ripple bag distorts small, and different moulds
Ripple bag no longer aliasing between state, realizes the separation of ripple bag in the time domain.
Reference picture 8, for the damage imaging result figure obtained using signal after compensation of the present embodiment.In above-mentioned aluminium sheet knot
In structure, sensor array is rearranged, lesion mimic is carried out using sticking Quality block, Lamb is gathered respectively before and after damage is introduced
Ripple response signal, using introduce damage after signal subtract before introducing damage to induction signal, obtain damaging scattered signal.Utilize figure
Method shown in 5 carries out dispersion compensation to damage scattered signal, and therefrom extracts A0 mode signals, using delay-and-sum method to aluminium
Plate center 500mm × 500mm region carries out damage imaging, obtains result as shown in Figure 8.In fig. 8,8 white point generations
The sensor array that table is made up of 8 piezoelectric patches, the position of black "×" symbology actual damage, the value generation of pixel in figure
Table damages possibility size：Pixel point value is higher (white portion), and damage probability is bigger.It can be seen that actual damage position and damage
Imaging gained damage position has higher uniformity, further demonstrates this method and is damaged in supersonic guide-wave in diagnostic application
Validity.
Reference picture 9, the damage imaging obtained for the present invention in the application of carbon fiber enhancement resin base composite material laminate
Figure.The physical dimension of the composite laminated plate is 400mm × 400mm × 2mm, is combined by 16 layers of lamina, wing flapping
Spend for [0/45/-45/90] 2s.In dispersion compensation, this composite laminated plate is handled by quasi-isotropic material, with 0 °
The dispersion curve in direction inputs as dispersion compensation feature, and to frequency dispersion signal, step compensates as described in Figure 5.Described in Fig. 8
It is similar, sensor array is set up by 8 piezoelectric patches, lesion mimic is carried out using sticking Quality block, obtains damage scattered signal.
After dispersion compensation is carried out to damage scattered signal, A0 mode signals are therefrom extracted, using delay-and-sum method to the tested knot
Structure carries out damage imaging, obtains result as shown in Figure 9.The result has carried out normalized, institute to the image after damage imaging
The value for having pixel normalizes to 0-1 scopes.In fig.9,8 white points represent the sensor array being made up of 8 piezoelectric patches,
The position of black "×" symbology actual damage, the value of pixel represents damage possibility size in figure：Pixel point value is higher
(white portion), damage probability is bigger.It can be seen that damage position obtained by actual damage position and damage imaging have it is higher consistent
Property, further demonstrate the validity that this method is damaged in diagnostic application in supersonic guide-wave.
Claims (9)
1. a kind of supersonic guide-wave frequency dispersion compensation method based on rarefaction representation, is specifically included：
Step 1：Frequency dispersion response under the Dispersion Characteristics prior information generation different propagation distance of supersonic guide-wave in structure
Signal；
Using encouraging centre frequency fcThe group velocity c at placeg(fc) discretization is carried out to propagation distance, calculation formula is as follows：
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Frequency dispersion response signal corresponding to the A0 mode that wave number is k is：
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Wherein, F (ω) is pumping signal, and j is unit imaginary number, and ω is angular frequency, and t is time variable, and k is the ripple of A0 mode guided waves
Number；
Step 2：Set up frequency dispersion and propagate dictionary；
Frequency dispersion is set up by row to the response signal obtained under different propagation distance and propagates dictionary, and 2 norm normalization are carried out by row
Processing, the frequency dispersion obtained under the target modalities that wave number is k propagate dictionary
U=[u0,u2,…,ui,…uN-1]D-1,
Wherein, D is that a diagonal element is Di,i=| | ui||2Diagonal matrix；
Step 3：Dictionary U is propagated using the frequency dispersion rarefaction representation is carried out to frequency dispersion signal to be compensated as signal base, establish sparse table
Representation model simultaneously solves；
Dictionary U is propagated come to frequency dispersion signal s to be compensated using the compound frequency dispersion built in the step 20Carry out rarefaction representation, structure
Build coefficient table representation model s0=Ua+w,
Wherein, vectorial a is corresponding rarefaction representation coefficient, and w is noise item；
Above formula is converted into convex optimization problem to be solved, obtained：
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Wherein, λ is penalty term parameter,To solve gained rarefaction representation coefficient vector；
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The non-frequency dispersion of wave number k progress to target modalities handles to obtain k', and substitutes k, repeat step 1 and step 2 with k', obtains non-
Frequency dispersion propagates dictionary U '；
Step 5：Using gained rarefaction representation coefficient and nondispersive propagation dictionary, non-frequency dispersion reconstruct is carried out to former frequency dispersion signal；
By the rarefaction representation vector in the nondispersive propagation dictionary U ' tried to achieve in the step 4 and the step 3It is multiplied, obtains
Signal after dispersion compensation
2. according to the method for claim 1, it is characterised in that preferable, the frequency dispersion, which propagates dictionary U, includes A0 mode pair
The frequency dispersion answered propagates dictionary UA0With S0 mode corresponding to frequency dispersion propagate dictionary US0。
3. method according to claim 1 or 2, it is characterised in that it is single mode dictionary or more that the frequency dispersion, which propagates dictionary U,
The compound dictionary of mode；When signal to be compensated only includes single mode guided wave, it is single mode dictionary that the frequency dispersion, which propagates dictionary U,；When
When signal to be compensated includes multi-modal guided wave, it is multi-modal compound dictionary that the frequency dispersion, which propagates dictionary U,.
4. according to the method for claim 1, it is characterised in that what the supersonic guide-wave in the step 1 was propagated in the structure
Analytic modell analytical model is：
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Wherein, kpFor the wave number of p-th of mode, Ap,jIt is x to correspond to propagation distance in p-th of modejGuided wave amplitude, ω is
Angular frequency, F (ω) are the frequency domain representation of pumping signal.
5. according to the method for claim 1, it is characterised in that the non-frequency dispersion processing in the step 4 is by original wave number
Linearized,
Wherein, k'(ω) for non-frequency dispersion processing after wave number, cgFor the group velocity of supersonic guide-wave.
6. according to the method for claim 1, it is characterised in that the ripple bag distortion of signal is small after the dispersion compensation, and ripple
Bag is in A0 mode and S0 mode no longer aliasing, in the time domain realization separation.
7. a kind of application of method as claimed in claim 1, it is characterised in that carried out using methods described to damage scattered signal
Dispersion compensation, the positioning to metal and Solid non-metallic damage position can be achieved.
8. application according to claim 7, it is characterised in that the metal includes aluminium alloy plate.
9. application according to claim 7, it is characterised in that the Solid non-metallic is answered including carbon fiber enhancement resin base
Condensation material laminate.
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