CN106908451A - Metal plate defect localization method based on laser Lamb wave frequency wavenumber analysis - Google Patents

Metal plate defect localization method based on laser Lamb wave frequency wavenumber analysis Download PDF

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CN106908451A
CN106908451A CN201710125692.6A CN201710125692A CN106908451A CN 106908451 A CN106908451 A CN 106908451A CN 201710125692 A CN201710125692 A CN 201710125692A CN 106908451 A CN106908451 A CN 106908451A
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laser
wave
defect
lamb wave
signal
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CN106908451B (en
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刘增华
冯雪健
陈洪磊
马春雷
何存富
吴斌
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Beijing University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84Systems specially adapted for particular applications
    • G01N21/88Investigating the presence of flaws or contamination
    • G01N21/95Investigating the presence of flaws or contamination characterised by the material or shape of the object to be examined
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01Arrangements or apparatus for facilitating the optical investigation
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84Systems specially adapted for particular applications
    • G01N21/88Investigating the presence of flaws or contamination
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01Arrangements or apparatus for facilitating the optical investigation
    • G01N2021/0106General arrangement of respective parts
    • G01N2021/0112Apparatus in one mechanical, optical or electronic block
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84Systems specially adapted for particular applications
    • G01N21/88Investigating the presence of flaws or contamination
    • G01N21/8851Scan or image signal processing specially adapted therefor, e.g. for scan signal adjustment, for detecting different kinds of defects, for compensating for structures, markings, edges
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2201/00Features of devices classified in G01N21/00
    • G01N2201/06Illumination; Optics
    • G01N2201/061Sources
    • G01N2201/06113Coherent sources; lasers

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  • Investigating Or Analyzing Materials By The Use Of Ultrasonic Waves (AREA)

Abstract

The invention discloses the metal plate defect localization method based on laser Lamb wave frequency wavenumber analysis, belong to laser-ultrasound field of non destructive testing.First, by laser pumping pop one's head on a metal plate fixed position encourage, laser pick-off popped one's head in defect line scanning receive, obtain N group Lamb wave data, obtain the time and space wave field on scanning pattern.Secondly, the N group Lamb wave data to collecting are respectively adopted the signal that the method for continuous wavelet transform is extracted under particular centre frequency, it is ensured that the analyticity of defect location result.Finally, spatial frequency wave number imaging is carried out using the algorithm of short empty two-dimensional Fourier transform to the wavefield signals after extraction, the feature according to wave-number spectrum on scanning pattern realizes the positioning of defect.The invention provides a kind of detection method of Entirely contactless formula, the action rule between Lamb wave and defect is disclosed in wave-number domain.

Description

Metal plate defect localization method based on laser Lamb wave frequency-wavenumber analysis
Technical field
The invention provides a kind of metal plate defect localization method based on laser Lamb wave frequency-wavenumber analysis, belong to Laser-ultrasound technical field of nondestructive testing.
Background technology
Plate profile structure or class plate profile structure have substantial amounts of application in aircraft industry and petrochemical industry, using lossless inspection Survey method carries out detection research to hardened structure not only has high scientific research value, and is anticipated with important economic and society Justice.
Mainly there are X-ray detection method, detection method of eddy, thermal imaging method, ultrasonic method etc. for large panel construction Non-Destructive Testing Deng.It is actually detected that these methods have been widely used in industry spot, but inevitably there are problems that.Such as X-ray With radiation effect, human body can be subject to more serious injury under the ray of high intensity for a long time;The result of EDDY CURRENT It is vector superposed between each variable, need to could obtains required result by various demodulation methods, and the technology is only used for The detection of conductive material;Thermal imaging method is only used for the detection of platy structure surface, near surface flaw.And laser Lamb wave is detected Technology combines the advantage of Laser Ultrasonic Technique and Lamb wave detection technique, and the defects detection for band large-scale metal plate structure has more Obvious advantage.(1) laser ultrasonic detection technology can realize at a distance, non-contact detecting can be applied to the poisonous particular field of high temperature Close;(2) there is laser ultrasonic detection technology high time-space resolution power can gather all-wave information;(3) laser pumping Lamb wave wideband, It is multi-modal conveniently to realize multi-modal, multi-frequency data fusion imaging.
At present, laser Lamb wave defect detecting technique is mainly based upon laser for the method for metal plate structure defects detection The defect detecting technique of sensor array.Determining for defect is realized with reference to different laser sensor array forms and all kinds of imaging algorithms Position.Because Lamb wave is multi-modal, frequency dispersion the characteristics of, cause the defect waves bag under Limited propagation space to be difficult in time domain identified Out.Although enabling defect information preferably to recognize in two dimensions of time and frequency using Time-Frequency Analysis Method, only Can judge that defect whether there is but cannot position.By taking elliptic imaging algorithm as an example, the method by having, zero defect signal make Difference, retains flaw echoes and realizes defect location.But for these reasons, whether there is direct wave letter after flaw indication subtracts each other Number and border reflected signal be difficult to be completely counterbalanced by, amplitude even be much larger than flaw indication, it is difficult to obtain pure flaw indication. Therefore, inevitably there is check frequency and artifact in the method.Based on using conventional time domain, frequency domain or time-frequency domain signal Processing method is difficult by the positioning that laser Lamb wave realizes defect, and some scholars have difference according to the Lamb wave of different modalities Spatial characteristic developed the defect inspection method of Lamb wave frequency-wavenumber domain analysis.Current the method is passed using piezoelectricity Sensor is encouraged, and laser vibration measurer receives multigroup Lamb wave signal in the scanning of diverse location line, based on frequency-wavenumber analysis method reality The positioning of existing defect.The Lamb wave of different center frequency is different to the susceptibility of defect, but piezoelectric excitation can only be encouraged every time Single centre frequency, it is impossible to conveniently realize multi-frequency defect imaging.Therefore, in order to realize real non-contact detecting, fully Laser time high, the advantage of spatial resolution are played, laser pumping is taken, the intensive scanning of laser receives the excitation of Lamb wave signal Reception mode, has developed the metal plate defect localization method based on laser-ultrasound and frequency-wavenumber analysis method, for industrial and commercial bank of army The noncontact of industry widely used band large-scale metal tabular structure, quick, comprehensive Non-Destructive Testing.
The content of the invention
To achieve the above object, the present invention proposes a kind of metallic plate based on laser Lamb wave frequency-wavenumber analysis and lacks Fall into localization method.By CF extraction algorithm, the frequency range in extraction wideband laser Lamb wave to weld defect control optimizes defect The sensitivity of detection and detection efficiency, have developed a kind of defect positioning method of Entirely contactless formula.
Realizing the detecting system of the method includes laser controller, pulse laser, laser pumping probe, digital oscillography Device, model to be checked, laser pick-off probe, continuous pulse laser, optical splitter, demodulator, computer.Laser-ultrasound driver unit Including laser controller, pulse laser, laser pumping probe.Laser controller provides energy excitation pulse to pulse laser Laser produces pulse laser, is then sent through laser pumping probe.Meanwhile, laser controller provides synchronous triggering to oscillograph Signal realizes the synchronization motivationtheory collection of laser ultrasound signal.Laser-ultrasound reception system include continuous pulse laser, optical splitter, Demodulator, laser pick-off probe.Continuous pulse laser exports continuous laser, and two beams are divided into after optical splitter.A branch of conduct ginseng Examine light and be directly inputted to demodulator;Another beam is irradiated to surface of aluminum plate through laser pick-off probe, then will be reflected through surface of aluminum plate The laser (flashlight) for carrying ultrasonic signal afterwards also enters into demodulator.Be tod using reference light and flashlight in demodulator Ultrasonic signal is demodulated to be gathered by oscillograph and shown.Finally, the ultrasound data for being collected using MATLAB treatment realizes defect Positioning.To avoid the influence of the air-shock wave docking collection of letters number produced by Thermoelastic regime, excitation and receiving transducer split aluminium sheet Both sides.
To achieve the above object, the present invention is adopted the following technical scheme that:
A kind of metal plate defect localization method based on laser Lamb wave frequency-wavenumber analysis is comprised the following steps:
Step one:Adjust laser ultrasonic detection system to optimum Working;
Hardened structure to be checked is set up first, it is ensured that plate Stability Analysis of Structures.Laser ultrasonic detection system is opened, continuous impulse is set and is swashed The output energy and the sampling parameter and passage triggering mode of oscillograph of light device.Between adjustable plate structure and laser pick-off probe Distance and angle, until system output amplitude it is high and stabilization AC signal.
Step 2:The excitation of Lamb wave signal is received;
Laser pumping probe is believed in the excitation of hardened structure fixed position, laser pick-off probe with step-length x pointwises collection Lamb wave Number fxT (), x is the distance between laser pick-off hot spot and laser pumping hot spot.Finally obtain the Lamb wave data square of M rows N row Battle array.M counts for spatial sampling, and N counts for time sampling.
Step 3:The extraction of wideband laser Lamb wave CF composition;
For the laser Lamb wave signal of wideband, set specific frequency signal is extracted using the method for continuous wavelet transform, be easy to Defect recognition.For any square-integrable function f (t), i.e. f (t) ∈ L2(R) continuous wavelet transform, is:
Wherein t is the time, and R is set of real numbers, L2(R) it is quadractically integrable function collection, ψ (t) is a wavelet or female small Ripple.Generating function ψ (t) can be obtained into wavelet sequence after flexible and translation:
Wherein:A is contraction-expansion factor, and b is shift factor.
Step 4:The construction of two-dimentional Hanning window function;
A two-dimentional Hanning window is constructed in MATLAB, the Lamb matrix signals to obtaining spatially are intercepted paragraph by paragraph.Should Dimension is consistent the Lamb wave signal gathered in window and step 2 in time, the wavelength of dimension spatially according to Lamb wave Determine.Two-dimentional window function W (t, x) expression formula is as follows:
Wherein x is locus, DxIt is the half-breadth of window.
Step 5:To extracting the adding window interception paragraph by paragraph of time-space wavefield signals u (t, x) after centre frequency, after interception Every section of time-space wavefield signals do two-dimensional Fourier transform;
The thought of Short Time Fourier Transform is used for reference, to extracting the time-space wavefield signals after centre frequency spatially Interception, enables spatial information to retain, then carry out two-dimensional Fourier transform to each section paragraph by paragraph.To ensure the accurate of wave number, two dimension The Spatial Dimension of Hanning window is greater than a wavelength.There is artifact to prevent the border in window, the part of adding window there will be weight twice It is folded.Said process is represented by:
(s, ω, k) are space-frequency-wave-number spectrum to wherein L, and s is locus index, and ω is angular frequency, and k is wave number;
Step 6:The one-dimensional space-wave number defect location.
Wave-number spectrum in all two-dimensional Fourier transform results that extraction step five is obtained under CF, combines in order Obtain space-wave-number spectrum.When zero defect in model to be measured, space-wave-number spectrum only exists positive wave-number spectrum;Have when in model to be measured Positive wave number spectrum is not only existed during defect, in space-wave-number spectrum and also there is negative wave-number spectrum.The end of negative wave-number spectrum and positive wave number are composed The position that existing energy is die-offed is exactly the position of defect.
Brief description of the drawings
Fig. 1 laser ultrasonic detection system schematic diagrames.
Fig. 2 aluminium sheets and defective locations schematic diagram.
Fig. 3 laser Lamb wave time-domain signals.
The excitation of Fig. 4 laser Lamb wave receives schematic diagram.
Fig. 5 laser Lamb wave time-space wavefield signals.
Fig. 6 extracts the time-domain signal near 160kHz frequencies.
Fig. 7 extracts the time-space wave field figure near 160kHz frequencies.
Fig. 8 two dimension Hanning windows.
Time-space wave field adding window interception result near Fig. 9 160kHz frequencies.
Figure 10 adding window wave field two-dimensional Fourier transform results.
Label is described as follows in figure:1- aluminium sheets, 2- defects, 3- excitation hot spots, 4- light spot receiveds, 5- flaw echos.
Specific embodiment
Following EXPERIMENTAL EXAMPLE is provided with reference to the content of the inventive method:
Fig. 1 is laser ultrasonic detection system, is divided into excitation and receives two parts.Laser-ultrasound driver unit includes laser control Device processed, pulse laser, laser pumping probe.Laser controller provides energy excitation pulse laser and produces to pulse laser Pulse laser, then sends through laser pumping probe.Meanwhile, laser controller provides synchronous triggering signal and realizes swashing to oscillograph The synchronization motivationtheory collection of light ultrasonic signal.Laser-ultrasound reception system includes continuous pulse laser, optical splitter, demodulator, swashs Light-receiving is popped one's head in.Continuous pulse laser exports continuous laser, and two beams are divided into after optical splitter.It is a branch of directly defeated as reference light Enter to demodulator;Another beam is irradiated to surface of aluminum plate through laser pick-off probe, is carried after then being reflected through surface of aluminum plate super The laser (flashlight) of acoustical signal is also entered into demodulator.Reference light and flashlight are used in demodulator by ultrasonic signal solution Recall to be gathered by oscillograph and show.Finally, the ultrasound data for being collected using MATLAB treatment realizes defect location.To avoid The influence of the air-shock wave docking collection of letters number produced by Thermoelastic regime, so excitation and receiving transducer split aluminium sheet in this example Both sides.
As shown in Fig. 2 lacking to process the through hole of 20mm × mmm on the aluminium sheet of 1000mm × 1000mmmm × 1mm in size Fall into, defect is away from upper surface 490mm, away from lower surface 490mm, away from left side 300mm, away from right side 698mm.
The present embodiment is comprised the following steps:
Step one:Adjust laser ultrasonic detection system to optimum Working;
Hardened structure to be checked is set up first, it is ensured that the stabilization of hardened structure.Laser controller is opened, laser controller is set to arteries and veins The energy for rushing laser offer is 3.8J.Regulation the distance between incentive probe and aluminium sheet and angle, distance is in embodiment 100mm, angle is 90o, excitation spot diameter is 1mm (focusing).Excitation hot spot is placed on the upper and lower center line of defect, away from defect right-hand member 150mm。
Laser-ultrasound reception system is opened, the output energy for setting continuous pulse laser is 150mW, by the straight of demodulator Stream output exports the passage 2 and passage 4 (other passages can also) that are respectively connected to oscillograph with exchange.It is triggering to set passage 2 Source, direct current triggering, channel impedance is 50 Ω.Mobile laser pick-off probe makes light spot received at 10.2mm on the left of excitation hot spot, Upper-lower position is consistent.The distance between regulation laser pick-off probe and aluminium sheet and angle make the direct current signal that passage 2 is received high It is in 500mV, embodiment 1.2V (no more than 3V).Switching channel 4 is trigger source, opens the high pressure on demodulator and calibration Switch, adjusts AC signal amplitude highest and stabilization that the triggering level of passage 4 is received up to passage 4.Now laser pick-off The distance of probe and surface of aluminum plate is about 40mm, and light spot received diameter is about 0.3mm (focusing).Calibration switch is closed, is selected again The trigger source that passage 2 is oscillograph is selected, the synchronous trigger source and passage 2 that laser controller is provided are connected.The direct current of demodulator Output is connected to another oscillograph, used as the reference voltage of ultrasonic signal amplitude.Oscilloscope sampling rate is set to 50MHz, sampling It is 10000 to count, to reduce data volume and prevent from adopting into border reflected signal.Single presses actuator buttons, is gathered by oscillograph The laser Lamb wave signal for arriving is as shown in Figure 3.
Step 2:Excitation receives Lamb wave signal;
Laser Lamb wave excitation reception mode is as shown in Figure 4.Excitation hot spot is placed on the upper and lower center line of defect, away from defect right-hand member 150mm fixed positions are encouraged.Excitation, light spot received upper-lower position are consistent, to encourage at the 10.2mm of hot spot left side as starting Position, with step-length 0.2mm pointwises collection Lamb wave signal fxT (), x is excitation the distance between hot spot and light spot received.This reality Apply and acquire 1301 groups of data altogether in example, obtain the data matrix of the row of 1301 row 10000, at that time m- space wave field such as Fig. 5 institutes Show.
Step 3:The extraction of wideband laser Lamb wave CF composition;
Using method foundation formula (1) of continuous wavelet transform (CWT) to 1301 groups of wideband laser Lamb in the present embodiment Ripple signal extraction centre frequency is easy to defect recognition for the signal of 160kHz.CWT is to one of which laser Lamb wave signal to carry Take, as a result as shown in fig. 6, can be clearly seen that defect reflection echo compared to time-domain signal before extracting.To laser Lamb wave Result is as shown in Figure 7 after time-space wave field extracts 160kHz centre frequencies using CWT.
Step 4:The construction of two-dimentional Hanning window;
A two-dimentional Hanning window is constructed in MATLAB, the Lamb wave matrix data to obtaining spatially does the Chinese and rather adjusts System.In time, the dimension of window is consistent with the Lamb wave signal gathered in step 2, is 10000.In the present embodiment, laser connects Receive probe primary recipient A0The Lamb wave (based on acoplanarity displacement) of mode, the A in 100kHz~400kHz frequency bands0On mode wavelength 17mm is limited to, undistorted to ensure wave number, window function dimension spatially elects 80mm as.Two-dimentional Hanning window is as shown in Figure 8.
Step 5:To extracting time-space wavefield signals u (t, x) the segmentation adding window interception after centre frequency, after interception Every section of time-space wavefield signals do two-dimensional Fourier transform;
Cut to being spatially segmented with the Hanning window that length is 80mm by the wavefield signals after CF constituents extraction Take.To be intercepted after the original position of Hanning window and data matrix alignment, then moving Hanning window every 0.2mm (ensures space essence Degree) continue to intercept until all interception is finished.Time-space wave field after being intercepted through two-dimentional Hanning window is as shown in Figure 9.To interception Each segment signal afterwards does two-dimensional Fourier transform according to (4) formula, obtains F-K spectra, as shown in Figure 10.Can be with from figure Find out that the result that obtains and theoretic frequency-wave number curve kissing merge the energy near 160kHz and be dominant, as a result with expected one Cause.
Step 6:The one-dimensional space-wave number defect location.
The wave-number spectrum under 160kHz is chosen in every section of result of windowed data two-dimensional Fourier transform, these data are pressed Sequencing during selection discharges obtain space-wave-number spectrum from left to right.When zero defect on scanning pattern, space-wave-number spectrum Only exist positive wave-number spectrum;Do not only exist positive wave number spectrum when defective on scanning pattern, in space-wave-number spectrum and occur negative Wave-number spectrum.The end of negative wave-number spectrum and positive wave number compose the position that the position that existing energy die-offs is exactly defect.

Claims (1)

1. the metal plate defect localization method based on laser Lamb wave frequency-wavenumber analysis, realizes the detecting system bag of the method Include laser controller, pulse laser, laser pumping probe, digital oscilloscope, model to be checked, laser pick-off probe, continuous arteries and veins Rush laser, optical splitter, demodulator, computer;Laser-ultrasound driver unit includes laser controller, pulse laser, laser Incentive probe;Laser controller provides energy excitation pulse laser and produces pulse laser to pulse laser, then through laser Incentive probe sends;Meanwhile, laser controller realizes that the synchronization of laser ultrasound signal swashs to oscillograph offer synchronous triggering signal Encourage collection;Laser-ultrasound reception system includes continuous pulse laser, optical splitter, demodulator, laser pick-off probe;Continuous impulse Laser exports continuous laser, and two beams are divided into after optical splitter;It is a branch of to be directly inputted to demodulator as reference light;Another Shu Jing Laser pick-off probe is irradiated to surface of aluminum plate, and the laser that ultrasonic signal is carried after then being reflected through surface of aluminum plate is also entered into In demodulator;Ultrasonic signal is demodulated to gather display by oscillograph using reference light and flashlight in demodulator;Finally, The ultrasound data collected using MATLAB treatment realizes defect location;It is the air-shock wave pair for avoiding being produced by Thermoelastic regime The influence of signal is received, excitation and receiving transducer split aluminium sheet both sides;
It is characterized in that:The method is comprised the following steps:
Step one:Adjust laser ultrasonic detection system to optimum Working;
Hardened structure to be checked is set up first, it is ensured that plate Stability Analysis of Structures;Laser ultrasonic detection system is opened, continuous pulse laser is set Output energy and oscillograph sampling parameter and passage triggering mode;Adjustable plate structure and laser pick-off probe between away from From and angle, until system output amplitude it is high and stabilization AC signal;
Step 2:The excitation of Lamb wave signal is received;
, in the excitation of hardened structure fixed position, laser pick-off probe is with step-length x pointwises collection Lamb wave signal f for laser pumping probex T (), x is the distance between laser pick-off hot spot and laser pumping hot spot;Finally obtain the Lamb wave data matrix of M rows N row;M For spatial sampling is counted, N counts for time sampling;
Step 3:The extraction of wideband laser Lamb wave CF composition;
For the laser Lamb wave signal of wideband, set specific frequency signal is extracted using the method for continuous wavelet transform, be easy to defect Identification;For any square-integrable function f (t), i.e. f (t) ∈ L2(R) continuous wavelet transform, is:
W f ( a , b ) = < f , &psi; a , b > = | a | - 1 / 2 &Integral; R f ( t ) &psi; &OverBar; ( t - b a ) d t - - - ( 1 )
Wherein t is the time, and R is set of real numbers, L2(R) it is quadractically integrable function collection, ψ (t) is a wavelet or morther wavelet;Will Generating function ψ (t) can obtain wavelet sequence after flexible and translation:
&psi; a , b ( t ) = 1 | a | &psi; ( t - b a ) a , b &Element; R ; a &NotEqual; 0 - - - ( 2 )
Wherein:A is contraction-expansion factor, and b is shift factor;
Step 4:The construction of two-dimentional Hanning window function;
A two-dimentional Hanning window is constructed in MATLAB, the Lamb matrix signals to obtaining spatially are intercepted paragraph by paragraph;The window and Dimension is consistent the Lamb wave signal gathered in step 2 in time, and dimension spatially is determined according to the wavelength of Lamb wave It is fixed;Two-dimentional window function W (t, x) expression formula is as follows:
Wherein x is locus, DxIt is the half-breadth of window;
Step 5:To extract centre frequency after time-space wavefield signals u (t, x) paragraph by paragraph adding window interception, to interception after it is every Section time-space wavefield signals do two-dimensional Fourier transform;
The thought of Short Time Fourier Transform is used for reference, it is spatially piecewise to extracting the time-space wavefield signals after centre frequency Interception, enables spatial information to retain, then carry out two-dimensional Fourier transform to each section;To ensure the accurate of wave number, the two-dimentional Chinese is peaceful The Spatial Dimension of window is greater than a wavelength;There is artifact to prevent the border in window, the part of adding window there will be overlap twice;On The process of stating is represented by:
L ( s , &omega; , k ) = &Integral; - &infin; &infin; &Integral; - &infin; &infin; u ( t , x ) W * ( t , x - s ) e - j ( k x - &omega; t ) d t d x - - - ( 4 )
(s, ω, k) are space-frequency-wave-number spectrum to wherein L, and s is locus index, and ω is angular frequency, and k is wave number;
Step 6:The one-dimensional space-wave number defect location;
Wave-number spectrum in all two-dimensional Fourier transform results that extraction step five is obtained under CF, in order combination is obtained Space-wave-number spectrum;When zero defect on scanning pattern, space-wave-number spectrum only exists positive wave-number spectrum;When defective on scanning pattern When, positive wave number spectrum is not only existed in space-wave-number spectrum and also there is negative wave-number spectrum;The end of negative wave-number spectrum and positive wave number compose existing energy The position that amount die-offs is exactly the position of defect.
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