CN107121497B - The ultrasonic guided wave detecting method of accidental resonance characteristic based on Duffing system - Google Patents
The ultrasonic guided wave detecting method of accidental resonance characteristic based on Duffing system Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/04—Analysing solids
- G01N29/12—Analysing solids by measuring frequency or resonance of acoustic waves
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
Abstract
The invention discloses a kind of ultrasonic guided wave detecting methods of accidental resonance characteristic based on Duffing system, which comprises the Duffing system based on free vibration constructs the accidental resonance model of ultrasonic guided wave detecting；It is recorded under fixed input signal amplitude, change corresponding output signal amplitude when damping ratio in accidental resonance model, and output signal amplitude is drawn out with the change curve of damping ratio, select damping ratio optimal value of the parameter of the value of corresponding damping ratio at output signal amplitude maximum as accidental resonance model；After the damping ratio optimal value of the parameter of selection accidental resonance model, filtering using accidental resonance model realization to mixed signal, and the identification to mixed signal；Wherein, the mixed signal is the mixed signal of ultrasonic guided wave signals and noise signal.Whether the present invention can identify the Weak Ultrasonic guided wave signals in mixed signal, judge defective in pipeline, further improve the sensitivity of ultrasonic guided wave detecting defect of pipeline.
Description
Technical field
The present invention relates to a kind of ultrasonic guided wave detection technology, especially a kind of accidental resonance based on Duffing system is special
The ultrasonic guided wave detecting method of property, belongs to technical field of nondestructive testing.
Background technique
" supersonic guide-wave technology " is a kind of non-destructive testing new technology proposed based on the propagation characteristic of stress wave in solids,
Compared with conventional ultrasonic wave detection technique, supersonic guide-wave is excited along waveguiding structure length direction, detection range be " line " and
Non- " point ", detection range have become the important method of field of non destructive testing up to 50~100 meters.Currently, ultrasonic guided wave detecting
Technical application is extensively in the detection of slender structure, such as in rodlike, rod-shaped and plate structure non-destructive testing, especially
In pipeline especially for the practical pipeline such as some liquid-filling pipes, buried pipeline, high-temperature and pressure pipeline, oil-gas pipeline, rail, steel
In rope and hardened structure.The application illustrates the validity of proposed method for detecting the supersonic guide-wave propagated in pipeline.
Due to complex characteristics of the supersonic guide-wave in communication process, in actually detected inevitably it is examined away from
From, defect size, structure Service Environment and test macro error etc. influence, cause to receive signal and show as under very noisy
Weak signal feature greatly reduces defects detection efficiency.In order to improve the detection efficiency of supersonic guide-wave, extend detecting distance, state
Inside and outside researcher increasingly payes attention to the analysis and research to ultrasonic guided wave signals, and has developed many effectively methods.Such as
Traditional time-domain analysis, frequency-domain analysis (FFT transform) and Time-Frequency Analysis (wavelet transformation, Short Time Fourier Transform etc.), with
And Chaotic Detecting Method developed in recent years.Achieve certain achievement.Wherein in Chaotic Detecting Method, especially exist
It is had made intensive studies using many scholars on the method for detecting weak signals of Chaotic Duffing Oscillator.However this method is also deposited
Any frequency can not be detected for example, there are frequency, initial phases to limit for the detection of Duffing system in some problems to be solved
The guided wave signals of rate, arbitrary phase, influence detection efficiency.
Summary of the invention
The purpose of the present invention is to solve the defects of conventional ultrasonic wave detection technique, provide a kind of based on Duffing system
Weak Ultrasonic guided wave signals in pipeline echo can be enhanced in the ultrasonic guided wave detecting method of the accidental resonance characteristic of system, this method
Amplitude, so as to identify the Weak Ultrasonic guided wave signals in mixed signal, judge it is whether defective in pipeline, further
Improve the sensitivity of ultrasonic guided wave detecting defect of pipeline.
The purpose of the present invention can be reached by adopting the following technical scheme that:
The ultrasonic guided wave detecting method of accidental resonance characteristic based on Duffing system, which comprises
S1, the Duffing system based on free vibration, construct the accidental resonance model of ultrasonic guided wave detecting；
S2, it is recorded under fixed input signal amplitude, changes corresponding output signal when damping ratio in accidental resonance model
Amplitude, and output signal amplitude is drawn out with the change curve of damping ratio, select corresponding damping at output signal amplitude maximum
Damping ratio optimal value of the parameter of the value of ratio as accidental resonance model；
S3, selection accidental resonance model damping ratio optimal value of the parameter after, using accidental resonance model realization to mixing
The filtering of signal, and the identification of the mixed signal to unknown frequency；Wherein, the mixed signal be ultrasonic guided wave signals with make an uproar
The mixed signal of acoustical signal.
Further, the method also includes:
S4, selection accidental resonance model damping ratio optimal value of the parameter after, using accidental resonance model inspection in pipeline
In the echo-signal that is collected into, judge whether defective in pipeline.
Further, step S1 is specifically included:
S11, the Duffing system for choosing free vibration, expression formula are as follows:
Wherein, k is damping ratio, (- ax+bx3) it is nonlinear resilience item, corresponding potential function isAnd it modifies potential function and isAnd then it obtains improved
Duffing system is as follows:
S12, the ultrasonic guided wave signals expression formula modulated through Hanning window are as follows:
Wherein, A is ultrasonic guided wave signals amplitude, and n is the single audio frequency number selected, ωc=2 π fc, fcIt is super arbitrarily to survey
The centre frequency of guided Waves；
S13, the accidental resonance model for constructing ultrasonic guided wave detecting, as follows:
Wherein, s (t) is above-mentioned ultrasonic guided wave signals, and n (t) is pure noise signal De (t), and e (t) is to meet N (0,1) point
The white Gaussian noise of cloth, D are noise level；
S14, selection suitable parameter k, A, fcAnd D, when A is smaller, the movement of entire Duffing system is to surround
The linear osccilation of one of bifocal, oscillation angular frequency is exactly ω, and the displacement x output response form of Duffing system is as follows:
Wherein, the π of ω=2 f, f are the frequency of accidental resonance model output response, and B is the amplitude of output signal,For phase
Position, xnIt (t) is higher order harmonic wave；Formula (5) derivation can be obtained, speedThe centre frequency of output response signal be still f, angular frequency
Rate is ω, and assumes speedOutput signal amplitude be C；
S15, the centre frequency f for surveying supersonic guide-wavecRelationship between the frequency f of accidental resonance model output response is full
Foot:
fcΔ t=fh (6)
Wherein, Δ t is the sampling time interval of measured signal, and h is to solve Duffing using quadravalence-Runge Kutta method
The integration step of system meets f=f as h=Δ tc。
Further, step S2 is specifically included:
S21, noise item n (t)=0 in formula (4) is enabled, the amplitude A of fixed input signal s (t) changes damping in formula (4)
Value than k solves the solution of formula (4), that is, finds out the value of output signal amplitude B in formula (5) using quadravalence-Runge Kutta method；
S22, it draws out at fixed input signal amplitude A, change curve of the output signal amplitude B with k, and trade-off curve
On, when output signal amplitude B is maximized, the value of corresponding damping ratio k is the damping ratio optimal value of the parameter of accidental resonance model.
Further, step S3 is specifically included:
S31, selection accidental resonance model damping ratio optimal value of the parameter after, according to input signal amplitude A and noise water
The value of flat D finds out the displacement x and speed of formula (4)
S32, respectively to the mixed signal of input, output displacement signal x and output speed signalSequence carry out power
Spectrum analysis, to identify the ultrasonic guided wave signals in mixed signal；
S33, the value for changing input signal amplitude A and noise level D repeat step S31 and S32.
Further, step S4 is specifically included:
S41, in the duct excitation ultrasound guided wave signals, and the echo-signal in collection conduit return incidence wave and end face
Signal between wave inputs accidental resonance model；
S42, power spectrumanalysis is carried out to the output signal of accidental resonance model, if it exists with institute's excitation ultrasound guided wave signals
The consistent spectral line of frequency, then it is defective in pipeline, if without apparent characteristic frequency, zero defect in pipeline.
The present invention have compared with the existing technology it is following the utility model has the advantages that
1, the present invention constructs the accidental resonance model of ultrasonic guided wave detecting, selection by the Duffing system of free vibration
Damping ratio optimal value of the parameter of the value of corresponding damping ratio as accidental resonance model at output signal amplitude maximum, based on random
Resonance principle not only can be filtered noise reduction to the mixed signal of ultrasonic guided wave signals and noise, enable a part of noise
Amount can be transferred on signal, and the periodical output of enhancing Duffing system can also be realized to optional frequency in mixed signal
It is identified with the ultrasonic guided wave signals of unknown frequency, ultrasonic guided wave signals in pipeline echo can be enhanced in accidental resonance model
Amplitude can also identify even if the supersonic guide-wave in mixed signal is Weak Ultrasonic guided wave signals by accidental resonance model,
Improve the detection efficiency in actually detected.
2, the present invention select the value of corresponding damping ratio at output signal amplitude maximum as the resistance of accidental resonance model
After Buddhist nun is than optimal value of the parameter, the echo-signal that is collected into the duct using accidental resonance model inspection, it can be determined that in pipeline
It is whether defective, the small flaw detection sensitivity in pipeline is improved, there is innovative significance, have a wide range of applications.
Detailed description of the invention
Fig. 1 is the ultrasonic guided wave detecting method flow chart of the embodiment of the present invention 1.
Fig. 2 a is the time domain waveform of the original input signal of the embodiment of the present invention 2.
Fig. 2 b is the time domain waveform of the output displacement signal x of the embodiment of the present invention 2.
Fig. 2 c is the time domain waveform of the output speed signal y of the embodiment of the present invention 2.
Fig. 3 a is the power spectrum chart of the original input signal of the embodiment of the present invention 2.
Fig. 3 b is the power spectrum chart of the output displacement signal x of the embodiment of the present invention 2.
Fig. 3 c is the power spectrum chart of the output speed signal y of the embodiment of the present invention 2.
Fig. 4 is the output signal and original input signal time domain waveform amplitude comparison diagram of the embodiment of the present invention 2.
Fig. 5 is output signal amplitude B under the input signal amplitude A of the embodiment of the present invention 2 with the variation diagram of damping ratio k.
Fig. 6 a is original when being input signal amplitude A=0.00001, the noise level D=0.00001 of the embodiment of the present invention 2
The time domain waveform of input signal.
Fig. 6 b is exported when being input signal amplitude A=0.00001, the noise level D=0.00001 of the embodiment of the present invention 2
The time domain waveform of displacement signal x.
Fig. 6 c is exported when being input signal amplitude A=0.00001, the noise level D=0.00001 of the embodiment of the present invention 2
The time domain waveform of speed signal y.
Fig. 7 a is original when being input signal amplitude A=0.00001, the noise level D=0.00001 of the embodiment of the present invention 2
The power spectrum chart of input signal.
Fig. 7 b is exported when being input signal amplitude A=0.00001, the noise level D=0.00001 of the embodiment of the present invention 2
The power spectrum chart of displacement signal x.
Fig. 7 c is exported when being input signal amplitude A=0.00001, the noise level D=0.00001 of the embodiment of the present invention 2
The power spectrumanalysis figure of speed signal y.
Fig. 8 a is the original when embodiment of the present invention 2 identifies the ultrasonic guided wave signals of unknown frequency and the mixed signal of noise
The power spectrum chart of beginning input signal.
Fig. 8 b is defeated when the embodiment of the present invention 2 identifies the ultrasonic guided wave signals of unknown frequency and the mixed signal of noise
The power spectrum chart of speed signal y out.
Fig. 9 a is the original input signal and output speed that the detection numerical value simulated defect pipeline of the embodiment of the present invention 2 obtains
Signal y sequence time domain waveform comparing result figure.
Fig. 9 b is the original input signal and output speed that the detection numerical value simulated defect pipeline of the embodiment of the present invention 2 obtains
Signal y sequence power composes comparing result figure.
Figure 10 a is that the original input signal that the test experience defect tracking of the embodiment of the present invention 2 obtains and output speed are believed
Number y sequence time domain waveform comparing result figure.
Figure 10 b is the power spectrum chart for the original input signal that the test experience defect tracking of the embodiment of the present invention 2 obtains.
Figure 10 c is the power spectrum for the output speed signal y sequence that the test experience defect tracking of the embodiment of the present invention 2 obtains
Figure.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment 1:
As shown in Figure 1, present embodiments providing a kind of supersonic guide-wave inspection of accidental resonance characteristic based on Duffing system
Survey method, method includes the following steps:
S101, the Duffing system based on free vibration, construct the accidental resonance model of ultrasonic guided wave detecting, this is random
Resonance model is used to detect the Weak Ultrasonic guided wave signals of optional frequency；
Accidental resonance is in numerous nonlinear systems in nature (the present embodiment is Duffing system) by inner or outer noise
A kind of universal phenomenon induced, three fundamentals occurred are nonlinear system, small-signal and noise, that is to say, that when
When realizing synergistic effect between nonlinear system, small-signal and noise three, accidental resonance will occur, the letter of system output at this time
Number frequecy characteristic it is consistent with the frequency of input signal, and the amplitude of signal greatly enhances under the frequency；Accidental resonance utilizes non-
Linear system, under input signal and the synergistic effect of noise, the increase that the signal-to-noise ratio of system output will be with noise is presented
First increase the trend subtracted afterwards, and peak value occurs in a certain noise intensity；Stochastic Resonance Phenomenon is no longer simply to filter out noise letter
Number, but under the booster action of noise, noise is effectively utilized, enhances the output of weak signal, the basic principle is that non-thread
Property system under the action of a part of noise energy is transferred on signal so that faint signal strength increases greatly originally
By force, so as to cause nonlinear system enhancing periodically export；Stochastic Resonance Phenomenon enhances the faint week in output signal
The amplitude of phase signal, and the signal-to-noise ratio of former mixed signal is improved, Stochastic Resonance Phenomenon is applied to faint supersonic guide-wave and is believed
Number detection in, the frequency and spectral magnitude of the output signal by analyzing stochastic resonance system can identify former mixing letter
Whether contain ultrasonic guided wave signals in number；
S102, realize accidental resonance mode there are mainly two types of: on the one hand can pass through addition noise realize；Another party
Face can focus on adjusting the parameter of Duffing system by the structural parameters of adjusting nonlinear system, the present embodiment, main
If adjusting the value of damping ratio, specifically: it is recorded under fixed input signal amplitude, when changing damping ratio in accidental resonance model
Corresponding output signal amplitude, and output signal amplitude is drawn out with the change curve of damping ratio, select output signal amplitude most
Damping ratio optimal value of the parameter of the value of the corresponding damping ratio of general goal as accidental resonance model；
S103, after the damping ratio optimal value of the parameter of selection accidental resonance model, using accidental resonance model realization to mixed
The filtering of signal is closed, which is the mixed signal of ultrasonic guided wave signals and noise signal, can be mixed by observation input
The time domain waveform for closing signal, output displacement signal and output speed signal, in the wave of input mixed signal and output displacement signal
The ultrasonic guided wave signals that can not be observed in shape can be observed in the waveform of output speed signal, illustrate to play filtering drop
The effect made an uproar；Meanwhile the identification using accidental resonance model realization to mixed signal, by input mixed signal, output bit
The sequence of shifting signal and output speed signal carries out power spectrumanalysis, if input mixed signal, output displacement signal and output
One of power spectrum of speed signal have with the consistent frequency component of original periodic signal frequency, that is, have apparent spectral line,
Then there are the periodic signal of the frequency, i.e. ultrasonic guided wave signals, illustrates to recognize in mixed signal using accidental resonance model
The ultrasonic guided wave signals of unknown frequency；
S104, selection accidental resonance model damping ratio optimal value of the parameter after, using accidental resonance model inspection in pipe
The echo-signal being collected into road, judge it is whether defective in pipeline, specifically: selection accidental resonance model damping ratio most
After excellent parameter value, excitation ultrasound guided wave signals, and the echo-signal in collection conduit in the duct, by incidence wave and edge echo
Between signal input accidental resonance model；Power spectrumanalysis is carried out to the output signal of accidental resonance model, if it exists with institute
The consistent spectral line of excitation ultrasound guided wave signals frequency illustrates that there are ultrasonic guided wave signals in echo-signal, and the supersonic guide-wave is believed
It number is caused by the reflection of the defects of pipeline, to illustrate defective presence in pipeline, if illustrating back without apparent characteristic frequency
Without ultrasonic guided wave signals in wave signal, to illustrate that pipeline is intact, zero defect exists in pipeline.
Embodiment 2:
The present embodiment carries out the small defect recognition of supersonic guide-wave and positioning, tool to pipeline by taking specific experiment as an example, in laboratory
Body implementation process is as follows:
S1, the accidental resonance model for constructing ultrasonic guided wave detecting
S11, the Duffing system for choosing free vibration, expression formula are as follows:
Wherein, k is damping ratio, (- ax+bx3) it is nonlinear resilience item, corresponding potential function isThe present embodiment selects a=b=1, and modifies potential function and be
And then improved Duffing system is obtained, it is as follows:
The barrier height of modified potential function reduces, and the critical value for crossing the signal amplitude of potential well needs reduces, can be with
The comparison of the lower two kinds of potential functions of the signal-to-noise ratio of the signal of detection is as shown in table 1；
The different bistable potential function performance comparisons of table 1
S12, the ultrasonic guided wave signals expression formula modulated through Hanning window are as follows:
Wherein, A is ultrasonic guided wave signals amplitude, and n is the single audio frequency number selected, ωc=2 π fc, fcIt is super arbitrarily to survey
The centre frequency of guided Waves；
The centre frequency of the ultrasonic guided wave signals excited in general hollow steel pipe is 70kHz, therefore the present embodiment is with 70
It is inquired into for kHz, but can identify the guided wave signals of arbitrary centre frequency using this method；Due to accidental resonance mould
Type can only detect the signal of low frequency, therefore, the centre frequency of ultrasonic guided wave signals be converted, i.e., according to 70kHz=0.07
(1/ μ s), ω=ωc=2 π 0.07rad/ μ s ≈ 0.4398, wherein integration step is when utilizing quadravalence Runge-Kutta integration
0.02μs；
S13, the accidental resonance model for constructing ultrasonic guided wave detecting, as follows:
Wherein, s (t) is above-mentioned ultrasonic guided wave signals, and n (t) is pure noise signal De (t), and e (t) is to meet N (0,1) point
The white Gaussian noise of cloth, D are noise level；
S14, selection suitable parameter k, A, fcAnd D, when A is smaller, the movement of entire Duffing system is to surround
The linear osccilation of one of bifocal, oscillation angular frequency is exactly ω, and the displacement x output response form of Duffing system is as follows:
Wherein, the π of ω=2 f, f are the frequency of accidental resonance model output response, and B is the amplitude of output signal,For phase
Position, xnIt (t) is higher order harmonic wave, compared with the amplitude B of output signal, amplitude very little is not almost observed；Formula (5) is asked
Leading can obtain, speedThe centre frequency of output response signal be still fc, angular frequency ωc, and assume speedOutput signal
Amplitude be C；
In the present embodiment, simple in order to describe, it is enabled in the applicationSpeed responsive is replaced with alphabetical y
S15, the centre frequency f for surveying supersonic guide-wavecRelationship between the frequency f of accidental resonance model output response is full
Foot:
fcΔ t=fh (6)
Wherein, Δ t is the sampling time interval of measured signal, and h is to solve Duffing using quadravalence-Runge Kutta method
The integration step of system meets f=f as h=Δ tc。
The optimal value of the parameter of damping ratio in S2, selection accidental resonance model
S21, noise item n (t)=0 in formula (4) is enabled, the amplitude A of fixed input signal s (t) changes damping in formula (4)
Value than k solves the solution of formula (4), mainly finds out output signal amplitude B in formula (5) using quadravalence-Runge Kutta method
Value；
S22, with k=0.075, A=0.0001, n (t)=0, fcFor=0.07Hz, draws out be originally inputted letter respectively
Number (mixed signal of ultrasound waveguide and noise), the time domain waveform and power spectrum of output displacement signal x and output speed signal y
Figure, original input signal, output displacement signal x and output speed signal y time domain waveform are respectively as shown in Fig. 2 a~2c, Cong Tuzhong
As can be seen that the time domain waveform of output displacement signal x and output speed signal y is consistent with the time domain waveform of original input signal,
To illustrate, three's frequency is consistent, and phase is different, compared to original input signal, output displacement signal x and output speed signal
The amplitude of y increases；The power spectrum chart of original input signal, output displacement signal x and output speed signal y is respectively such as 3a~3c
It is shown；
S23, with k=0.075, A=0.0001, n (t)=0, fcFor=0.07Hz, further verification step S22 conclusion
Reliability, and the time domain waveform of original input signal, output displacement signal x and output speed signal y is compared, is marked
The value of corresponding A, B, C, as a result as shown in Figure 4；
S24, according to the mode for determining output signal amplitude B in step S24, determine under fixed input signal amplitude A, output
Signal amplitude B with k change curve, as a result as shown in figure 5, as can be seen from the figure k=0.075 when, B is maximized, i.e., defeated
Signal amplitude is maximum out, therefore, selects k=0.075, is the optimal value of the parameter of damping ratio.
S3, the filtering using accidental resonance model realization to mixed signal, and realize the identification to mixed signal
S31, after the damping ratio optimal value of the parameter of selection accidental resonance model, realize filtering to mixed signal, selection
The k value that step S24 is determined, i.e., with k=0.075, A=0.00001, D=0.00001, fcFor=0.07Hz, original is drawn respectively
The time domain waveform of beginning input signal, output displacement signal x and output speed signal y can from figure as shown in Fig. 6 a~6c
Out, the waveform for directly observing input signal and output displacement signal x can not observe ultrasonic guided wave signals, and observe output speed
The waveform of signal y is spent, it can be observed that apparent ultrasonic guided wave signals, which plays the work of filtering noise reduction
With；
S32, respectively by formula (3) input signal and output signal carry out power spectrumanalysis, obtained result such as Fig. 7 a
Shown in~7c, have on the power spectrum chart of the power spectrum of input signal and output signal x and y as we can clearly see from the figure with
The consistent frequency component of original periodic signal frequency has apparent spectral line, i.e. amplitude maximum at the frequency at 0.07Hz, right
Than Fig. 6 a~6c and 7a~7c, it is found that output signal sequence y is more more stable than output signal sequence x, next mainly using defeated
Signal sequence y carries out power spectrumanalysis out；
S33, the value for further changing input signal amplitude A and noise level D, reduce the signal-to-noise ratio of mixed signal, and ask
At this time under low signal-to-noise ratio, the power spectrum chart of Mixed design signal and output sequence y as shown in figure 8, it can be seen from the figure that due to
The influence of noise can not tell said frequencies component from input signal power spectrogram, and pass through the power of observation output signal y
Spectrogram illustrates the periodic signal for having the frequency, i.e. ultrasonic guided wave signals, says it can be found that there is an apparent spectral line at 0.07Hz
The detection of the bright faint guided wave signals that unknown frequency can be carried out using the Stochastic Resonance Detection System, the present embodiment is with 0.07Hz
For illustrate the reliability of method.
Whether S4, the echo-signal being collected into the duct using accidental resonance model inspection are judged defective in pipeline
After the damping ratio optimal value of the parameter of selection accidental resonance model, using accidental resonance model, numerical value is detected respectively
The flaw echoes between incidence wave and edge echo being collected into simulated defect pipeline and experimental defects pipeline, i.e., will be to
It surveys signal and inputs Duffing system, power spectrumanalysis is carried out to output signal；For detecting numerical value simulated defect pipeline, obtain
Power spectrumanalysis result as shown in figure 9b, wherein input signal and output signal sequence y time domain waveform are compared from such as Fig. 9 a institute
Show；For test experience defect tracking, obtained power spectrumanalysis result as illustrated in figures 10b and 10c, wherein input signal with it is defeated
The comparison of signal sequence y time domain waveform is from as shown in Figure 10 a out；As can be seen that it will be incident from Fig. 9 a~9b and Figure 10 a~10c
Flaw echoes between wave and edge echo input accidental resonance model, can identify in central defect echo exist with
The consistent frequecy characteristic of stimulating frequency, wherein actually detected middle excitation ultrasound guided wave signals centre frequency is 70kHz, that is, fc=
70kHz is divided into Δ t=0.00000002s between acquisition time, and integration step is h=0.02s in this example, therefore passes through formula
(6) calculate after obtain output signal frequency be 0.07Hz, i.e. f=0.07Hz, from power spectrumanalysis it is also seen that
There are apparent spectral lines at 0.07Hz.This illustrates existing characteristics ultrasonic guided wave signals in echo-signal, further relates to two detections
It is defective in pipeline (numerical simulation defect tracking and experimental defects pipeline), that is, there is damage.
In conclusion the present invention constructs the accidental resonance mould of ultrasonic guided wave detecting by the Duffing system of free vibration
Type selects damping ratio optimal value of the parameter of the value of corresponding damping ratio at output signal amplitude maximum as accidental resonance model,
Based on Stochastic Resonance Theory, not only noise reduction can be filtered to the mixed signal of ultrasonic guided wave signals and noise, so that one
Point noise energy can be transferred on signal, and the periodical output of enhancing Duffing system can also be realized in mixed signal
The ultrasonic guided wave signals of optional frequency and unknown frequency are identified that accidental resonance model can be enhanced ultrasound in pipeline echo and lead
The amplitude of wave signal can also by accidental resonance model even if the supersonic guide-wave in mixed signal is Weak Ultrasonic guided wave signals
To identify, the detection efficiency in actually detected is improved；In addition, being returned using what accidental resonance model inspection was collected into the duct
Wave signal, it can be determined that it is whether defective in pipeline, the small flaw detection sensitivity in pipeline is improved, there is innovative significance,
It has a wide range of applications.
The above, only the invention patent preferred embodiment, but the scope of protection of the patent of the present invention is not limited to
This, anyone skilled in the art is in the range disclosed in the invention patent, according to the present invention the skill of patent
Art scheme and its inventive concept are subject to equivalent substitution or change, belong to the scope of protection of the patent of the present invention.
Claims (4)
1. the ultrasonic guided wave detecting method of the accidental resonance characteristic based on Duffing system, it is characterised in that: the method packet
It includes:
S1, the Duffing system based on free vibration, construct the accidental resonance model of ultrasonic guided wave detecting；
S2, it is recorded under fixed input signal amplitude, changes corresponding output signal amplitude when damping ratio in accidental resonance model,
And output signal amplitude is drawn out with the change curve of damping ratio, select the value of corresponding damping ratio at output signal amplitude maximum
Damping ratio optimal value of the parameter as accidental resonance model；
S3, selection accidental resonance model damping ratio optimal value of the parameter after, using accidental resonance model realization to mixed signal
Filtering, and realize identification to mixed signal；Wherein, the mixed signal is the mixed of ultrasonic guided wave signals and noise signal
Close signal；
S4, selection accidental resonance model damping ratio optimal value of the parameter after, received in the duct using accidental resonance model inspection
Whether the echo-signal collected judges defective in pipeline；
Step S1, specifically includes:
S11, the Duffing system for choosing free vibration, expression formula are as follows:
Wherein, k is damping ratio, (- ax+bx3) it is nonlinear resilience item, corresponding potential function isAnd it modifies potential function and isAnd then it obtains improved
Duffing system is as follows:
S12, the ultrasonic guided wave signals expression formula modulated through Hanning window are as follows:
Wherein, A is ultrasonic guided wave signals amplitude, and n is the single audio frequency number selected, ωc=2 π fc, fcIt is led arbitrarily to survey ultrasound
The centre frequency of wave；
S13, the accidental resonance model for constructing ultrasonic guided wave detecting, as follows:
Wherein, s (t) is above-mentioned ultrasonic guided wave signals, and n (t) is pure noise signal De (t), and e (t) is to meet N (0,1) to be distributed
White Gaussian noise, D are noise level；
S14, selection suitable parameter k, A, fcAnd D, when A is smaller, the movement of entire Duffing system is around bifocal
One of linear osccilation, oscillation angular frequency is exactly ω, and the displacement x output response form of Duffing system is as follows:
Wherein, the π of ω=2 f, f are the frequency of accidental resonance model output response, and B is the amplitude of output signal,For phase, xn
It (t) is higher order harmonic wave；Formula (5) derivation can be obtained, speedThe centre frequency of output response signal be still f, angular frequency is
ω, and assume speedOutput signal amplitude be C；
S15, the centre frequency f for surveying supersonic guide-wavecRelationship between the frequency f of accidental resonance model output response meets:
fcΔ t=fh (6)
Wherein, Δ t is the sampling time interval of measured signal, and h is to solve Duffing system using quadravalence-Runge Kutta method
Integration step meet f=f as h=Δ tc。
2. the ultrasonic guided wave detecting method of the accidental resonance characteristic according to claim 1 based on Duffing system, special
Sign is: step S2 is specifically included:
S21, noise item n (t)=0 in formula (4) is enabled, the amplitude A of fixed input signal s (t) changes damping ratio k in formula (4)
Value solves the solution of formula (4), that is, finds out the value of output signal amplitude B in formula (5) using quadravalence-Runge Kutta method；
S22, draw out at fixed input signal amplitude A, output signal amplitude B with k change curve, and on trade-off curve,
When output signal amplitude B is maximized, the value of corresponding damping ratio k is the damping ratio optimal value of the parameter of accidental resonance model.
3. the ultrasonic guided wave detecting method of the accidental resonance characteristic according to claim 1 based on Duffing system, special
Sign is: step S3 is specifically included:
S31, selection accidental resonance model damping ratio optimal value of the parameter after, according to input signal amplitude A's and noise level D
Value, finds out the displacement x and speed of formula (4)
S32, respectively to the mixed signal of input, output displacement signal x and output speed signalSequence carry out power spectrum point
Analysis, to identify the ultrasonic guided wave signals in mixed signal；
S33, the value for changing input signal amplitude A and noise level D repeat step S31 and S32.
4. the ultrasonic guided wave detecting method of the accidental resonance characteristic according to claim 1 based on Duffing system, special
Sign is: step S4 is specifically included:
S41, in the duct excitation ultrasound guided wave signals, and the echo-signal in collection conduit, by incidence wave and edge echo it
Between signal input accidental resonance model；
S42, power spectrumanalysis is carried out to the output signal of accidental resonance model, if it exists with institute's excitation ultrasound guided wave signals frequency
Consistent spectral line, then it is defective in pipeline, if without apparent characteristic frequency, zero defect in pipeline.
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