CN106596737B - Multi-mode signal separation method based on Lamb wave structure - Google Patents

Multi-mode signal separation method based on Lamb wave structure Download PDF

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CN106596737B
CN106596737B CN201611090136.1A CN201611090136A CN106596737B CN 106596737 B CN106596737 B CN 106596737B CN 201611090136 A CN201611090136 A CN 201611090136A CN 106596737 B CN106596737 B CN 106596737B
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displacement
wave structure
time
lamb wave
lamb
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CN106596737A (en
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武湛君
周凯
周震寰
徐新生
杨正岩
赵祯
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Dalian University of Technology
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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
    • 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
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/023—Solids
    • 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

Abstract

The invention discloses a multi-mode signal separation method based on a Lamb wave structure, which extracts one or more modes in a multi-mode Lamb wave signal according to the structural features of different modes of the Lamb wave, can quantitatively analyze the information of each mode contained in the multi-mode Lamb wave signal, can be used for researching the reflection, transmission, mode conversion and other phenomena of each mode of the Lamb wave at the discontinuous part of a structure, and can be used for researching the amplitude problem of each mode of the Lamb wave excitation signal under different excitation conditions.

Description

Multi-mode signal separation method based on Lamb wave structure
Technical Field
The invention relates to a multimode signal separation method based on a Lamb wave structure.
Background
Many large structures such as airplane wings, long-distance oil pipelines, ocean platforms and the like have very complex and severe service environments, and are gradually damaged in the using process, so that the structures finally fail, and therefore, damage detection of the structures is very necessary. Because these are large structures, the traditional nondestructive testing method has low efficiency and is even difficult to realize, and therefore, the ultrasonic guided wave testing technology is required to be applied. The ultrasonic guided wave detection technology is characterized in that ultrasonic guided waves are excited in a structure, the ultrasonic guided waves are transmitted in the structure, reflection, transmission, mode conversion and the like can occur when the ultrasonic guided waves meet the discontinuity of the structure, and whether damage exists in the structure or not and the size, the position and the like of the damage can be judged through received ultrasonic guided wave signals. The ultrasonic guided wave detection technology receives extensive attention and intensive research in recent years, and because the ultrasonic guided wave has the characteristics of high propagation speed, long propagation distance, small attenuation, sensitivity to tiny cracks and the like, the ultrasonic guided wave has many advantages for detecting large-scale structural damage, such as convenient operation, large detection range, high detection efficiency, capability of detecting regions which are difficult to reach and the like, so that the ultrasonic guided wave propagation characteristic is very necessary to research.
For large thin-wall structures, Lamb waves are mainly used for detecting damage at present. Lamb waves are ultrasonic guided waves existing in plate structures, have multiple modes, and are different in different Lamb wave propagation speeds, wave structures and the like, so that signals are very complex. However, Lamb waves with different modes are sensitive to different damage characteristics, so that damage characteristics can be more accurately extracted and structural information can be acquired only by detecting damage with multiple modes, and therefore, separating single-mode signals contained in multi-mode Lamb wave signals has very important significance for simplifying signals and realizing the extraction of the damage characteristics in the structure.
Disclosure of Invention
According to the problems in the prior art, the invention discloses a multimode signal separation method based on a Lamb wave structure, which comprises the following specific steps:
s1, considering Lamb waves propagating in an isotropic plate, establishing a two-dimensional rectangular coordinate system (x, y), wherein x represents the Lamb wave propagation direction, y represents the plate normal direction, and a Lamb wave displacement vector u is equal to (ux,uy)TAnd stress vector σ ═ in the direction of propagation (σ)xx,τxy)TConstructing a vector ψ (u) ═ uT,σT)TWherein u isxAnd uyRespectively representing in-plane and out-of-plane displacements, [ sigma ]xxAnd τxyRespectively representing normal and shear stress.
S2, expanding the Lamb wave displacement vector and the stress vector according to each mode
Wherein c is+nAnd c-nRepresenting the expansion coefficients, + and-are propagation directions, and ω represents the angular frequency.
S3, proving that the normalized orthogonal relation exists between different modal displacement vectors and stress vectors
Wherein m and n are modal orders, and delta is a Crohn's function.
S4, establishing a two-dimensional plate structure model with the length of L and the wall thickness of h by using finite element software, dividing N units along the wall thickness direction, and arranging L distance ends1And arranging signal receiving points, wherein the receiving points are N +1 nodes along the wall thickness direction and are used for extracting Lamb wave structure information. Lamb wave signals are excited at the end part, and Lamb wave time domain displacement signals are extracted from the receiving point.
S5, selecting a signal receiving node, selecting a certain time domain signal area, and randomly selecting N0A time ti，i＝1,…,N0For each time tiAnd taking the in-plane displacement wave structure. The in-plane displacement wave structure corresponds to an out-of-plane displacement wave structure tiWave structure at time + Δ t, and satisfiesTwo Δ t satisfying this condition are set as Δ t1And Δ t2。
S6, for each moment tiExtracting tiThe in-plane displacement wave structure corresponding to the moment is extracted, and t is extractedi+Δt1And ti+Δt2The displacement wave structure at the moment and the out-of-plane displacement wave structure respectively form displacement vectorsAnd
s7, mixing tiThe two sets of displacement vectors at the time are respectively substituted into the expansion equation (1) to obtain
M represents the number of Lamb wave propagation modes existing at the frequency,to representOr
S8, establishing an equation set by utilizing the normalized orthogonal relation of the formula (2)
Where s is 1,2, …, M. The equation set contains 2M linear equations with 2M unknowns to be solved, and t can be obtained by solvingiEach modal coefficient at a time.
S9, for each tiTwo sets of coefficients are obtained at the time, and the two sets of coefficients respectively have delta t values corresponding to delta t1And Δ t2Reconstructing two groups of coefficients corresponding to the moment according to the formula (1) respectively to obtain reconstructed displacementAndis provided with The discrimination is carried out according to the following modes:
s10, for any of timing domain signal areasTime tjGet tjIn-plane displacement wave structure at time and tjAnd + delta t moment out-of-plane displacement wave structure, wherein delta t is obtained according to step S9, and the obtained in-plane displacement and out-of-plane displacement form a displacement vectorCalculating the available t according to the steps S7 and S8jEach modal coefficient of time is calculated by time-series { t }jAnd drawing curves for independent variables respectively to obtain waveform diagrams of the modal coefficients, which describe the waveforms of single-modal Lamb waves.
Due to the adoption of the technical scheme, the multi-mode signal separation method based on the Lamb wave structure, provided by the invention, separates the multi-mode Lamb wave signals into a single-mode situation according to the structural characteristics of the Lamb wave with different modes, can quantitatively analyze the multi-mode Lamb wave signals containing information of each mode, can be used for researching the phenomena of Lamb wave reflection, transmission, mode conversion and the like at the discontinuous part of the structure, and can be used for researching the amplitude problem of excitation signals of each mode of the Lamb wave under different excitation conditions; the finite element model adopted by the method is a simple two-dimensional plate structure model, the model is simple, the calculation time is short, and the result is reliable.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a method disclosed in the present invention;
FIG. 2 is a schematic diagram of the ABAQUS load application and signal receiving point locations;
FIG. 3 is a diagram of a shifted time domain signal extracted from group A of receiver points No. 1;
FIG. 4 is a diagram of a displacement time domain signal extracted from group B of receiving points No. 1;
fig. 5 is a diagram of mode separation of partial time domain signals of group a receiving points, fig. 5(a) is a diagram of partial displacement time domain signals extracted from group 1 receiving point, and fig. 5(b) is a diagram of mode separation of S0 and a 0;
fig. 6 is a diagram of mode separation of partial time domain signals of group B receiving points, fig. 6(a) is a diagram of partial shifted time domain signals extracted from group 1 receiving point, and fig. 6(B) is a diagram of mode separation of S0 and a 0.
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
as shown in fig. 1, a multi-mode signal separation method based on a Lamb wave structure,
example (b): the method disclosed by the invention is adopted for S in the isotropic aluminum plate0And A0The specific steps of the modal signal separation method are as follows: the method content of the invention is combined to provide a method for simulating S in an isotropic aluminum plate by using finite element software0And A0The specific steps of the modal signal separation method are as follows:
(1) establishing a two-dimensional plate structure model by using finite element software, wherein the length of the model is 300mm, the thickness of the model is 3mm, the selected material is aluminum, and the density of the model is 2700kg/m3Young's modulus was 70GPa, and Poisson's ratio was 0.33.
(2) And applying a 5-cycle sinusoidal displacement signal modulated by a Hanning window at the left end of the model as an excitation signal, wherein the center frequency f is 200 KHz. The excitation signal is a uniformly distributed displacement signal loaded along the wall thickness at an angle of 45 deg., as shown in fig. 2, and the amplitudes of both coordinate components of the excitation signal are 1 mm. At this frequency-thickness product, Lamb waves exist in only two modes, namely S0And A0。
(3) Adopting square grid division, setting grid size to be 0.2mm in length direction, dividing 8 units along wall thickness direction, setting two groups of receiving points at 50mm and 150mm away from left end of model, respectively called group A receiving points and group B receiving points, each group of receiving points respectively including 9 nodes along wall thickness direction for extracting calculation result, as shown in FIG. 2,
(4) the signal receiving points of the group A and the group B are respectively numbered from top to bottom as receiving points No. 1-9, and the calculated time domain information of the in-plane displacement and the out-of-plane displacement of the receiving point No. 1 is respectively extracted, as shown in fig. 3 and fig. 4. Taking group a as an example for explanation, the operations of group B and group a receiving points are completely the same and will not be described again. Selecting the first waveform of the time domain signal of the group A No. 1 receiving point, and randomly selecting N0A time ti，i＝1,…,N0For each time tiAnd taking the in-plane displacement wave structure.
(5) According to the phase relationship between the in-plane displacement and the out-of-plane displacement, andithere are two possibilities for the out-of-plane displacement time corresponding to the time, ti+Δt1And ti+Δt2And satisfyWhere ω 2 π f is the circle frequency. Respectively extracting the two moment out-of-plane displacement wave structures, and forming a displacement vector with the in-plane displacementAnd
(6) the two sets of displacement vectors are respectively brought into a displacement and stress expansion mode, namely
In the formulaTo representOrWhen M is 2.
(7) Construction of a system of linear equations from normalized orthogonal relationships
In the formula, s is 1,2, …, M, and each modal coefficient can be obtained by solving the linear equation system.
(8) Calculating the two linear equations to obtain two groups of coefficients, and isomorphic displacement vector using the two groups of coefficientsAndis provided with The discrimination is carried out according to the following modes:
(9) can be obtained by calculationFor the A group No. 1 node, for the determined signal region, for any time t in the regionjGet tjIn-plane displacement wave structure at time, take tjCalculating t by using the off-plane displacement wave structure at the moment of + delta tjTime-series { t } of each modal coefficient obtained by calculating the time-series of each modal coefficientjI draw curves respectively, the curves are waveform diagrams of various modal coefficients, the first wave packet modal separation condition of the group A receiving point time domain signals is shown in fig. 5, and the first two wave packet modal separation conditions of the group B receiving point time domain signals are shown in fig. 6. And reconstructing the Lamb wave time domain signal according to the propagation speed.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (1)

1. A multimode signal separation method based on a Lamb wave structure is characterized by comprising the following steps: the method comprises the following steps:
s1, considering Lamb waves propagating in an isotropic plate, establishing a two-dimensional rectangular coordinate system (x, y), wherein x represents the Lamb wave propagation direction, y represents the plate normal direction, and solving a Lamb wave displacement wave structure u-u (u-u)x,uy)TAnd stress wave structure sigma ═ s (sigma)xx,τxy)TWherein u isxAnd uyRespectively representing in-plane and out-of-plane displacements, [ sigma ]xxAnd τxyRespectively representing normal stress and shear stress; where T represents the transpose of a vector or matrix;
s2, expanding the displacement and stress of the real Lamb wave according to each mode
Wherein c is+nAnd c-nRepresents the expansion coefficients, + and-are propagation directions;
s3, obtaining a normalized orthogonal relation according to the property of the Lamb wave control equation
Wherein m and n are modal orders, 2h is plate thickness, and delta is a kronecker delta function;
s4, establishing a two-dimensional plate structure model with the length of L and the plate thickness of 2h, dividing N units along the plate thickness direction, and arranging L units at the distance end part1Arranging signal receiving points, wherein the receiving points are N +1 nodes along the plate thickness direction and are used for extracting Lamb wave time domain signals;
s5, selecting a signal receiving node, selecting a certain time domain signal area, and randomly selecting N0One hourMoment ti，i＝1,…,N0For each time tiTaking the in-plane displacement wave structure, and the out-of-plane displacement wave structure corresponding to the in-plane displacement wave structure is tiWave structure at time + Δ t, and satisfiesTwo Δ t satisfying this condition are set as Δ t1And Δ t2ω represents angular frequency;
s6, for each moment tiExtracting tiThe in-plane displacement wave structure corresponding to the moment is extracted, and t is extractedi+Δt1And ti+Δt2The time-off-plane displacement wave structure respectively forms displacement vectorsAnd
s7, mixing tiThe two sets of displacement vectors at the time are respectively substituted into the expansion equation (1) to obtain
M represents the number of Lamb wave propagation modes existing at the frequency,to representOr
S8, establishing an equation set by utilizing the normalized orthogonal relation of the formula (2)
Wherein s is 1,2, …, M, the equation set contains 2M linear equations, 2M unknowns to be solved, t can be obtained by solvingiEach modal coefficient at a moment;
s9, for each tiTwo sets of coefficients are obtained at the time, and the two sets of coefficients respectively have delta t values corresponding to delta t1And Δ t2Reconstructing two groups of coefficients corresponding to the moment according to the formula (1) respectively to obtain reconstructed displacementAndis provided with The discrimination is carried out according to the following modes:
wherein: b represents a plate thickness of 2h, α1,i，β1,iAnd alpha2,i，β2,iRespectively correspond toAndintermediate calculation coefficient of (a), gamma1And gamma2Is corresponding toAndthe discrimination coefficient of (1);
s10, for any time t of taking a timing domain signal areajGet tjIn-plane displacement wave structure at time and tjAnd + delta t moment out-of-plane displacement wave structure, wherein delta t is obtained according to step S9, and the obtained in-plane displacement and out-of-plane displacement form a displacement vectorCalculating the available t according to the steps S7 and S8jEach modal coefficient of time is calculated by time-series { t }jAnd drawing curves for independent variables respectively to obtain waveform diagrams of the modal coefficients, which describe the waveforms of single-modal Lamb waves.
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CN108459087B (en) * 2018-04-25 2020-09-29 大连理工大学 Multimode Lamb wave mode separation method applied to plate structure damage detection
CN108921113A (en) * 2018-07-10 2018-11-30 南京信息工程大学 Multi-mode Lamb wave signal separating method based on fractional order differential
CN110243521A (en) * 2019-07-02 2019-09-17 广东工业大学 A kind of sheet stress measurement method and sheet stress measuring system
CN110702785B (en) * 2019-09-24 2020-10-16 清华大学 Method and device for time-frequency domain modal decomposition and defect positioning of frequency dispersion Lamb wave polynomial
CN112014471B (en) * 2020-07-10 2023-09-01 北京工业大学 Plate structure multi-mode lamb wave topological gradient imaging method based on virtual sensor
CN111812207A (en) * 2020-07-21 2020-10-23 大连理工大学 Non-reference damage diagnosis imaging method based on ultrasonic guided wave conversion mode extraction
CN112179987B (en) * 2020-09-15 2022-07-15 河海大学 Nondestructive testing method for long-distance thin plate structure micro-defects
CN114088818B (en) * 2021-11-16 2024-03-22 南京工业大学 Ultrasonic guided wave method and system for identifying global rigidity

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