CN112147225A - Nonlinear wave detection method for underwater gate - Google Patents

Nonlinear wave detection method for underwater gate Download PDF

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CN112147225A
CN112147225A CN202010795436.XA CN202010795436A CN112147225A CN 112147225 A CN112147225 A CN 112147225A CN 202010795436 A CN202010795436 A CN 202010795436A CN 112147225 A CN112147225 A CN 112147225A
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wave
frequency
waves
gate
transducer
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王子健
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Nanjing Smart Infrastructure Technology Research Institute Co ltd
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Nanjing Smart Infrastructure Technology Research Institute Co ltd
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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
    • G01N29/06—Visualisation of the interior, e.g. acoustic microscopy
    • 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
    • G01N29/06—Visualisation of the interior, e.g. acoustic microscopy
    • G01N29/0654—Imaging
    • 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
    • G01N29/06—Visualisation of the interior, e.g. acoustic microscopy
    • G01N29/0654—Imaging
    • G01N29/069—Defect imaging, localisation and sizing using, e.g. time of flight diffraction [TOFD], synthetic aperture focusing technique [SAFT], Amplituden-Laufzeit-Ortskurven [ALOK] technique
    • 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
    • G01N29/46—Processing the detected response signal, e.g. electronic circuits specially adapted therefor by spectral analysis, e.g. Fourier analysis or wavelet analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/01—Indexing codes associated with the measuring variable
    • G01N2291/015—Attenuation, scattering
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/023—Solids
    • G01N2291/0234—Metals, e.g. steel
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/028—Material parameters
    • G01N2291/0289—Internal structure, e.g. defects, grain size, texture
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/04—Wave modes and trajectories
    • G01N2291/044—Internal reflections (echoes), e.g. on walls or defects

Abstract

The invention discloses a nonlinear wave detection method of an underwater gate, which comprises the steps of firstly determining the relation of the group velocity of lamb waves and the product of the frequency plate thickness through wave velocity calculation, then carrying out coupling optimization, reducing the energy of lamb waves leaking into water, increasing the energy of lamb waves in a gate plate, adopting 7 transducers to excite the waves to simultaneously reach a focusing point, generating the maximum scattered waves at the focusing point, improving the signal-to-noise ratio, obtaining a detection signal, extracting integral frequency multiplication components of the excitation waves from a frequency spectrum, adding the frequency multiplication components to be used as the damage degree of the focusing point, and sequentially transforming the focusing point to form a damage image of the whole gate; the invention removes the linear wave scattered by the structure, and only adopts the nonlinear wave scattered by the damage to detect the gate, so that the lamb wave can detect the metal plate with a complex structure and can carry out detection without influencing the water retaining of the gate; the damage visualization of the whole gate can be realized, and the damage degree of each point can be quantitatively represented.

Description

Nonlinear wave detection method for underwater gate
Technical Field
The invention belongs to the technical field of nondestructive testing, and particularly relates to a nonlinear wave detection method for an underwater gate.
Background
The hydraulic gate is a thin-wall metal structure and is easily damaged by aging, freeze thawing, corrosion and cavitation. The method is characterized in that nondestructive testing is regularly carried out on the hydraulic gate under the condition of not influencing water retaining, is the key for guaranteeing engineering safety and realizing scientific maintenance, and therefore an integral, rapid and nondestructive testing method for the underwater gate needs to be developed.
The existing hydraulic gate detection mainly comprises coating and corrosion amount detection, and the gate safety is evaluated through the combination of the erosion residual thickness of the gate and stress calculation. The existing detection method only can detect point by point, cannot evaluate the overall safety of the gate, and has hidden danger on the safety of the gate. Particularly for deep water gates of high dam and large-span gates with span of nearly one hundred meters, the risk of structural failure is higher, and an integral detection method is more needed.
The current mature overall detection methods comprise A scanning, B scanning and C scanning. A, exciting and receiving ultrasonic waves by a point of a sweep aiming at a plate, wherein the abscissa is time, and the ordinate is an ultrasonic signal, so that the defect in the plate thickness direction can be detected; b, scanning a vertical section of the plate along the thickness direction, wherein the probe moves along a line, the abscissa is the displacement of the probe, and the ordinate is the thickness of the plate; c-scan a horizontal section to a fixed depth of the plate, as shown in fig. 13, the probe is moved across the surface of the plate to image a signal at a particular depth. Therefore, the scanning process requires moving the probe, which is time-consuming and labor-consuming.
For metal plates, one of the more common methods of bulk inspection is guided wave inspection. When the guided wave encounters damage, scattering occurs. By collecting and analyzing the scattered waves, the information such as whether the damage occurs, the position of the damage, the size of the damage and the like can be reversely calculated. The guided wave detection has the advantages that: during detection, the position of the probe does not need to be moved, and large-area integral detection can be realized through the propagation, scattering and return of the guided wave in the plate. Meanwhile, when water exists on one side of the metal plate, the wave guide method still has good detection capability.
However, the gate is not a smooth metal plate, and structures such as stiffening, riveting and the like are often provided on the surface of the gate, and since the structures also cause scattering of guided waves, the scattering of the structures may submerge and damage the scattering, so that damage cannot be identified. Indoor experiments show that only linear scattering waves of damage can be used to detect damage far away from a structure (in the moment, linear scattering of the damage is not submerged by structural scattering), a detection blind area exists, and real damage is likely to occur near the structure (such as fatigue cracks at an opening). Therefore, although lamb waves can well detect smooth metal plates, it is difficult to apply the lamb waves to gate detection having a complicated configuration. Meanwhile, common damages of the gate, such as corrosion, fatigue, bolt looseness and the like, are difficult to detect through linear scattered waves.
In essence, the damage scattering removes linear components, and also includes nonlinear components. Linear scattering of the lesion, whose frequency is the same as the frequency of the constructive scattered wave, and nonlinear scattering of the lesion, whose frequency is an integer multiple of the constructive scattered wave. By time-frequency analysis, linear scattering and nonlinear scattering can be separated. Because the nonlinear scattering can only come from damage, the damage can be detected, positioned and quantified only by considering nonlinear scattering waves, the interference of the constructed linear scattering waves can be avoided, and the lamb waves can be applied to the detection of components with complex structures, so that the problem of integral nondestructive detection of the underwater gate is solved.
Disclosure of Invention
In order to solve the problems, the invention discloses a nonlinear wave detection method for an underwater gate, which can realize the whole damage visualization of the gate, quantitatively represent the damage degree of each point, is not interfered by the complex structure of the gate, has no blind area in detection and improves the detection accuracy.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a nonlinear wave detection method for an underwater gate comprises the following steps:
(1) wave velocity calculation
Determining the length, width, thickness, elastic modulus and Poisson ratio of the gate panel by looking up engineering data, field measurement and inversion by combining monitoring data; solving a wave equation of lamb waves:
Figure BDA0002625439180000021
where ω is the angular frequency, cLIs the transverse wave velocity, cTDrawing a frequency dispersion curve of lamb waves, and determining the relation between the phase velocity of the lamb waves and the product of the frequency plate thickness;
according to the relationship between phase velocity and group velocity:
Figure BDA0002625439180000022
determining the relation of the group velocity of lamb waves and the product of frequency and plate thickness;
(2) coupling optimization
Modulating the sine function by using a window function m (t) to generate an excitation signal:
Figure BDA0002625439180000023
the window function modulation is to ensure that the excitation signal is at the central frequency omega0Peaks with energy, in the dispersion curve of lamb waves, by looking up ω0The propagation velocity of the excitation signal is obtained.
Decomposing displacement of gate panel into scalar potential function by Helmholtz decomposition
Figure BDA0002625439180000024
And the sum of the vector potential functions Ψ, assuming that water cannot transfer shear, its displacement is represented by a scalar potential only, resulting in the following equation of motion:
Figure BDA0002625439180000025
the waterless side of the gate panel is a free surface, the stress is 0, and the boundary condition is obtained:
Figure BDA0002625439180000026
Figure BDA0002625439180000031
the water retaining side of the gate panel has the conditions of stress balance and off-plane displacement continuity:
Figure BDA0002625439180000032
the united vertical type (4) - (6) solves the displacement of the water body, and represents the energy leaked into the water body by the lamb wave; the wave number in the metal plate and the water body has the following geometrical relationship:
Figure BDA0002625439180000033
the geometric relation (7) is used as a limiting condition, the conditional extreme value of the water displacement is solved through a Lagrange method, the optimal wave number kx and ky are found, the energy of lamb waves leaking into water is reduced, and the energy of the lamb waves in the gate plate is increased;
(3) single point focusing
On the water blocking surface, a linear array consisting of 7 transducers is pasted on the gate panel, and the serial numbers are 1-7 in sequence. The distance between every two transducers is equal, and the transducers can independently excite and receive lamb wave signals; selecting the center of the array as a coordinate origin O, and recording the coordinate of the focusing point as O', wherein
Figure BDA0002625439180000034
Where Δ t is the time for transducer i to excite earlier than transducer 4, and if Δ t is negative, it indicates that transducer i is delayed by Δ t than transducer 4. Setting the excitation time of each transducer according to the criterion, ensuring that excitation waves of each transducer simultaneously reach a focusing point, and generating maximum scattered waves at the focusing point;
(4) signal-to-noise ratio enhancement
After the excitation is completed, the transducers acquire the excitation of the adjacent 6 transducers; taking two adjacent transducers as an example, the distance between the two transducers is recorded as deltax; the waveform of the excitation signal after Δ x has been delivered is as follows:
Figure BDA0002625439180000035
when k is0，k1First two-stage Taylor expansion of A-mode wavenumberWhen the coefficient is calculated, the A mode direct wave excited by the transducer a is obtained;
when k is0，k1When the first two-order Taylor expansion coefficients of the S-mode wave number are taken, the S-mode direct wave excited by the transducer a is obtained;
removing direct waves of A and S modes from a signal received by the transducer b to obtain a detection signal of the transducer b;
(5) calculation of damage product
The detection signal contains two components, one is a linear wave, the frequency is equal to the excitation frequency and comes from damage linear scattering, structural scattering and edge scattering, and the other is a nonlinear wave, the frequency is an integral multiple of the excitation frequency and comes from damage nonlinear scattering; extracting frequency components of integral multiple frequency from the frequency spectrum, and adding the frequency spectrum energy of nonlinear waves to be used as the damage degree of the focusing point;
(6) lesion visualization
And (5) continuously changing the focus point, repeating the step 3-5 to obtain the damage degree of each point, and forming a damage image of the whole gate.
The invention has the beneficial effects that:
(1) detection can be carried out under the condition that the water retaining of the gate is not influenced;
(2) the device is not interfered by the complex structure of the gate, and has no blind area in detection;
(3) the damage visualization of the whole gate can be realized, and the damage degree of each point can be quantitatively represented;
(4) contact damage such as corrosion, bolt loosening, fatigue, etc. can be detected;
(5) the probe does not need to be moved during detection.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph showing the product of the phase velocity of lamb wave and the frequency plate thickness in step (1) of the present invention;
FIG. 3 is a graph showing the product of the group velocity of lamb waves and the frequency plate thickness in step (1) of the present invention;
FIG. 4 is a schematic diagram of the optimization of the excitation wavenumber in step (2) of the present invention;
FIG. 5 is a phase difference calculation chart of single-point focusing in step (3) of the present invention;
FIG. 6 is a schematic diagram of single point focusing in step (3) of the present invention;
FIG. 7 is a diagram of the original signal received by transducer b in step (4) of the present invention;
FIG. 8 shows the direct wave of the A-mode emitted from the transducer a in step (4) of the present invention;
FIG. 9 shows the S-mode direct wave emitted from the transducer a in step (4) of the present invention;
FIG. 10 is a diagram of the detection signal of the transducer b after the signal-to-noise ratio is increased in step (4) of the present invention;
FIG. 11 is a frequency spectrum of the detection signal of the transducer b in step (5) of the present invention;
FIG. 12 is an image of the damage of the entire gate in step (6) of the present invention;
FIG. 13 is a schematic diagram of the scanning methods A, B, and C in the background art.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
As shown in the figure, the nonlinear wave detection method of the underwater gate comprises the following steps:
(1) wave velocity calculation
The length, width, thickness, elastic modulus and Poisson ratio of the gate panel are determined by means of looking up engineering data, field measurement, monitoring data inversion and the like. Solving a wave equation of lamb waves:
Figure BDA0002625439180000051
where ω is the angular frequency, cLIs the transverse wave velocity, cTIs the longitudinal wave velocity, h is the half plate thickness, and k is the wave number. Drawing a frequency dispersion curve of the lamb wave, and determining the relation between the phase velocity of the lamb wave and the product of the frequency and the plate thickness, as shown in FIG. 2:
according to the relationship between phase velocity and group velocity:
Figure BDA0002625439180000052
the relationship between the group velocity of lamb waves and the product of frequency and plate thickness is determined, as shown in FIG. 3:
(2) coupling optimization
Modulating the sine function by using a window function m (t) to generate an excitation signal:
Figure BDA0002625439180000053
the purpose of the window function modulation is to ensure that the excitation signal has a peak with energy at the center frequency ω 0, and in the dispersion curve of the lamb wave, the propagation velocity of the excitation signal can be obtained by querying ω 0, as shown in fig. 4.
Decomposing displacement of gate panel into scalar potential function by Helmholtz decomposition
Figure BDA0002625439180000054
And the sum of the vector potential functions Ψ, assuming that water cannot transfer shear, its displacement is represented by a scalar potential only, resulting in the following equation of motion:
Figure BDA0002625439180000055
the waterless side of the gate panel is a free surface, the stress is 0, and the boundary condition is obtained:
Figure BDA0002625439180000056
the water retaining side of the gate panel has the conditions of stress balance and off-plane displacement continuity:
Figure BDA0002625439180000057
Figure BDA0002625439180000061
and (4) to (6) in a joint type, solving the displacement of the water body, and representing the energy of lamb wave leaking into the water body, wherein as shown in fig. 4, the metal plate and the wave number in the water body have the following geometrical relationship:
Figure BDA0002625439180000062
and (3) taking the geometric relation (7) as a limiting condition, solving the conditional extreme value of the water displacement by a Lagrange method, finding the optimal wave number kx and ky, reducing the energy leaked into the water by the lamb wave, and increasing the energy of the lamb wave in the gate plate.
(3) Single point focusing
On the water blocking surface, a linear array composed of 7 transducers (such as piezoelectric transducer and electromagnetic transducer) is pasted on the gate panel, and the serial numbers are 1-7. The distance between every two transducers is equal, and the transducers can independently excite and receive lamb wave signals. Selecting the center of the array as a coordinate origin O, and recording the coordinate of the focusing point as O', wherein
Figure BDA0002625439180000063
As shown in fig. 5, where Δ t is the time for transducer No. i to fire earlier than transducer No. 4, if Δ t is negative, it indicates that transducer No. i is delayed by Δ t than transducer No. 4. Setting the excitation time of each transducer according to the criterion can ensure that the excitation waves of each transducer simultaneously reach the focus point, and the maximum scattered waves are generated at the focus point, as shown in fig. 6.
(4) Signal-to-noise ratio enhancement
After the excitation is completed, the transducer will acquire the excitation of the adjacent 6 transducers. Due to the multi-modal phenomenon of lamb waves, the excitation of one transducer contains two wave packets of A and S, and the detection signal is very complex. Taking two adjacent transducers as an example, the received signal of one transducer is shown in FIG. 7
Let us note the separation of the two transducers as Δ x. The waveform of the excitation signal after Δ x has been delivered is as follows:
Figure BDA0002625439180000064
when k is0，k1When the first two-order Taylor expansion coefficients of the A-mode wave number are taken, the A-mode direct wave excited by the transducer a is obtained;
when k is0，k1When the first two-order Taylor expansion coefficients of the S-mode wave number are taken, the S-mode direct wave excited by the transducer a is obtained; in the signal received by the transducer b, the direct waves of the a and S modes are removed, and a detection signal of the transducer b is obtained, as shown in fig. 10.
Since the direct wave (linear wave) is removed, the energy ratio of the nonlinear wave is further improved in the detection signal. In the existing nonlinear wave extraction process, a great difficulty is that in a frequency spectrum, the peak value of a linear wave is too large, the energy is too high, so that the frequency spectrum peak of the nonlinear wave is not obvious, and the nonlinear wave cannot be extracted. The invention can highlight the frequency spectrum wave crest of the nonlinear wave through the operation of the step.
(5) Calculation of damage product
The detection signal contains two components, one is a linear wave with equal frequency and excitation frequency and comes from damage linear scattering, structural scattering and edge scattering, and the other is a nonlinear wave with integral multiple of the excitation frequency and comes from damage nonlinear scattering. Frequency components of an integral multiple of the frequency are extracted from the spectrum, and the spectral energy of the nonlinear wave is added as the degree of damage at the focusing point, as shown in fig. 11.
(6) Lesion visualization
And (5) continuously changing the focus point, and repeating the step 3-5 to obtain the damage degree of each point. The damage image shown in fig. 12 is formed, and the point with a high pixel is the damage position.
The invention removes the linear wave scattered by the structure, and only adopts the nonlinear wave scattered by the damage to detect the gate, so that the lamb wave can detect the metal plate with a complex structure and can carry out detection when the water retaining of the gate is not influenced; the damage visualization of the whole gate can be realized, and the damage degree of each point can be quantitatively represented.
The description of the points is as follows:
(1) the phased array may be not only linear, but also circular, annular, rectangular, and the like. The directional detection can be realized not only by a phase modulation method, but also by other methods such as frequency modulation, or by using a transducer capable of being directionally excited in hardware.
(2) By replacing Δ x in step 4 with the path length of the scattered waves through the edge of the shutter plate, the scattered waves at the edge of the shutter plate can also be removed, thereby further improving the composition ratio of the nonlinear waves. The method for improving the signal-to-noise ratio also comprises a plurality of signal processing methods such as wavelet transformation, Fourier transformation, duffing oscillator and the like, and can replace the method in the step 4.
(3) The invention is not only suitable for gates, but also suitable for thin-wall structures such as airplanes, ship shells, bridge decks, gas storage tanks, pipelines and the like, the structures can be made of metal materials or composite materials, and the structures can be filled with liquid and can also be wrapped by soil, concrete and water (such as seabed petroleum pipelines and underground buried pipes).
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.

Claims (1)

1. A nonlinear wave detection method of an underwater gate is characterized by comprising the following steps: the method comprises the following steps:
(1) wave velocity calculation
Determining the length, width, thickness, elastic modulus and Poisson ratio of the gate panel by looking up engineering data, field measurement and inversion by combining monitoring data; solving a wave equation of lamb waves:
Figure FDA0002625439170000011
whereinOmega is the angular frequency, cLIs the transverse wave velocity, cTDrawing a frequency dispersion curve of lamb waves, and determining the relation between the phase velocity of the lamb waves and the product of the frequency plate thickness;
according to the relationship between phase velocity and group velocity:
Figure FDA0002625439170000012
determining the relation of the group velocity of lamb waves and the product of frequency and plate thickness;
(2) coupling optimization
Modulating the sine function by using a window function m (t) to generate an excitation signal:
Figure FDA0002625439170000013
the window function modulation is to ensure that the excitation signal is at the central frequency omega0Peaks with energy, in the dispersion curve of lamb waves, by looking up ω0Obtaining the propagation speed of the excitation signal;
decomposing displacement of gate panel into scalar potential function by Helmholtz decomposition
Figure FDA0002625439170000017
And the sum of the vector potential functions Ψ, assuming that water cannot transfer shear, its displacement is represented by a scalar potential only, resulting in the following equation of motion:
Figure FDA0002625439170000014
the waterless side of the gate panel is a free surface, the stress is 0, and the boundary condition is obtained:
Figure FDA0002625439170000015
the water retaining side of the gate panel has the conditions of stress balance and off-plane displacement continuity:
Figure FDA0002625439170000016
Figure FDA0002625439170000021
Figure FDA0002625439170000022
the united vertical type (4) - (6) solves the displacement of the water body, and represents the energy leaked into the water body by the lamb wave; the wave number in the metal plate and the water body has the following geometrical relationship:
Figure FDA0002625439170000023
the geometric relation (7) is used as a limiting condition, the conditional extreme value of the water displacement is solved through a Lagrange method, the optimal wave number kx and ky are found, the energy of lamb waves leaking into water is reduced, and the energy of the lamb waves in the gate plate is increased;
(3) single point focusing
On the water retaining surface, a linear array consisting of 7 transducers is stuck on the gate panel, and the serial numbers are 1 to 7 in sequence; the distance between every two transducers is equal, and the transducers can independently excite and receive lamb wave signals; selecting the center of the array as a coordinate origin O, and recording the coordinate of the focusing point as O', wherein
Figure FDA0002625439170000024
Wherein, delta t is the time that the transducer I needs to excite earlier than the transducer 4, if delta t is a negative value, the transducer I needs to delay delta t than the transducer 4; setting the excitation time of each transducer according to the criterion, ensuring that excitation waves of each transducer simultaneously reach a focusing point, and generating maximum scattered waves at the focusing point;
(4) signal-to-noise ratio enhancement
After the excitation is completed, the transducers acquire the excitation of the adjacent 6 transducers; taking two adjacent transducers as an example, the distance between the two transducers is recorded as deltax; the waveform of the excitation signal after Δ x has been delivered is as follows:
Figure FDA0002625439170000025
when k is0，k1When the first two-order Taylor expansion coefficients of the A-mode wave number are taken, the A-mode direct wave excited by the transducer a is obtained;
when k is0，k1When the first two-order Taylor expansion coefficients of the S-mode wave number are taken, the S-mode direct wave excited by the transducer a is obtained;
removing direct waves of A and S modes from a signal received by the transducer b to obtain a detection signal of the transducer b;
(5) calculation of damage product
The detection signal contains two components, one is a linear wave, the frequency is equal to the excitation frequency and comes from damage linear scattering, structural scattering and edge scattering, and the other is a nonlinear wave, the frequency is an integral multiple of the excitation frequency and comes from damage nonlinear scattering; extracting frequency components of integral multiple frequency from the frequency spectrum, and adding the frequency spectrum energy of nonlinear waves to be used as the damage degree of the focusing point;
(6) lesion visualization
And (5) continuously changing the focus point, repeating the step 3-5 to obtain the damage degree of each point, and forming a damage image of the whole gate.
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CN114166942A (en) * 2021-11-25 2022-03-11 武汉大学 Laser ultrasonic-based method for measuring defect burying depth between metal additive manufacturing layers

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