CN104833729A - Ultrasonic guided-wave based calculation method for separating flexural mode reflected signal - Google Patents

Abstract

The present invention discloses a calculation method for separating symmetric and flexural mode wave packet and extracting weak signal of the bending mode. Based on the wave structure characteristic theory of axisymmetric mode and bending mode, the method uses finite element software to establish correlative model, extracts transient displacement signal of signal acquisition nodes of a guided-wave monitoring surface, and conducts delay superimposing on the collected signals on the frequency domain in accordance with relative formula; then the superimposed frequency domain signal is subjected to the inverse Fourier transform to obtain guided-wave mode wave packet of each order after separation; and Hilbert-Huang envelope is employed to calculate reflection coefficient for each mode. The method uses secondary development function of finite element software to compile the secondary development program, quantitatively analyze the influence degree of the parameters such as characteristics of defect size, location distribution, the number of defects and the center excitation frequency on the amplitude value of the flexural mode reflection echo generated from the defect locations through modal conversion, thereby integrally utilize reflection coefficients of axisymmetric mode and bending mode to evaluate the distribution of defect locations.

Description

Based on the computing method that the mode of flexural vibration reflected signal of supersonic guide-wave is separated

Technical field

The present invention relates to the computing method of supersonic guide-wave and the defect mechanism of action quantitative test of propagating in a kind of tubular waveguide, espespecially utilize the wave structure feature of axisymmetry mode and mode of flexural vibration, be separated symmetrical and mode of flexural vibration ripple bag, extract mode of flexural vibration feeble signal, utilize the yellow envelope of Hilbert to obtain each mode reflection coefficient, the reflection coefficient fully utilizing axisymmetry mode and mode of flexural vibration thus evaluates defective locations distribution

Background technology

The tubular steel structure that the ratio that thick-walled pipe refers to external diameter and wall thickness is less than 20.Thick-walled pipe is widely used in fields such as oil, chemical industry and thermal power generation, because pipeline to be operated in high temperature and high pressure environment and the easy contact corrosion medium of pipe inside and outside wall, in use easily there is various ways lost efficacy and caused leakage accident, cause Heavy environmental pollution accident and heavy economic losses.Therefore, find a kind of reliable, efficient, the low cost defect detecting technique that are applicable to posted sides pipeline, tiny flaw in Timeliness coverage posted sides pipeline, avoid or reduce related accidents seeming very important.Supersonic guide-wave has the advantages that a place excites long distance to detect, be used widely in plate, rail, pipeline and other industrial structure detect, in addition the efficient advantage fast of ultrasonic guided wave detection technology makes its testing cost much lower compared with conventional ultrasound lossless detection method, and therefore ultrasonic guided wave detection technology is subject to concern and the research of domestic and international many scholars as a kind of Novel lossless detection method.

Can interact with defect when supersonic guide-wave is propagated in pipe, not only produce the scattering phenomenons such as reflection, transmission, also can produce MODAL TRANSFORMATION OF A phenomenon.This is also the mechanism of supersonic guide-wave for defects detection.But ultrasonic guided wave detection technology often only considers the un-flexed mode guided wave of reflection and transmission at present, the mode of flexural vibration produced for utilizing MODAL TRANSFORMATION OF A is seldom paid close attention to, and mode of flexural vibration signal comprises abundant defect information is thus separated symmetrical mode and mode of flexural vibration signal to promoting ultrasonic guided wave detection technology important in inhibiting.In supersonic guide-wave and pipe, asymmetric defect effect can produce mode of flexural vibration, produce mode of flexural vibration can because defect size characteristic change and change, thus, study a kind of computing method being separated mode of flexural vibration, extract the signal of reflective symmetry mode and reflection mode of flexural vibration, supersonic guide-wave is quantitatively detected and just seems particularly important.

Summary of the invention

The object of the invention is to, be separated symmetrical mode and mode of flexural vibration ripple bag by providing a kind of and extract the computing method of mode of flexural vibration feeble signal, utilize the detected parameters such as Finite Element Method quantitative test flaw size feature, position distribution, defect number and center-driven frequency to from fault location through MODAL TRANSFORMATION OF A from the influence degree of mode of flexural vibration reflection echo amplitude produced, obtain the variation relation curve of longitudinal bending guided wave reflection coefficient with detected parameters, and then utilize the depth and place of axisymmetry mode and mode of flexural vibration reflection coefficient Comprehensive Assessment defect.

The method utilizes finite element software ABAQUS python to carry out parametric programming to the defective pipeline model of band, and automatically extract finite element simulation time domain waveform, then carry out phase delay to signal collected and superpose on frequency domain, and then being separated the mode of flexural vibration ripple bag in reflected signal.The inventive method comprises the following steps:

1.1. the pipeline three-dimensional entity model that length is L is set up, at distance pipeline model end L ₁place arranges the hole shape defect along the distribution of pipeline circumference, the defect center angle of hole shape defect and unit: degree, wherein, D _defectfor the diameter of hole defect, r _innerfor the internal diameter of pipeline; At distance pipeline model end L ₂place arranges N number of equally spaced node as Signal reception point along pipeline circumference, N>=8, for extracting the supersonic guide-wave reflected signal produced from fault location; At the pipeline model other end, N number of equally spaced node is set along pipeline circumference and encourages node as signal, N>=8, L>=3L _1,l>=3/2L ₂; Finite element discretization being carried out to model, requiring that grid cell size is not less than for asking 1/10 of highest frequency corresponding wavelength;

1.2. result of finite element is extracted, by what collect from N number of Signal reception point with according to formula process, obtain the circumferential transient Displacements of N number of Signal reception point m=1,2,3 ... N, wherein for the circumferential displacement of m Signal reception point under local coordinate system, for the x direction output displacement of m Signal reception point under global coordinate system, for the y direction output displacement of m Signal reception point under global coordinate system, α ^mbe the circumferential angle of m Signal reception point and reference point, wherein said reference point is present position on bus, defect center, now α ^m=0;

1.3. the circumferential transient Displacements X of N number of Signal reception point will obtained in step 1.2 _mt () carries out Fast Fourier Transform (FFT), then on frequency domain, carry out phase delay according to the following formula and superpose, obtaining frequency-region signal,

$B_n\left(f\right)=\underset{m=1}{\overset{N}{\mathrm{\Σ}}}\left|\mathrm{FFT}\right[X_m\left(t\right)\left]\right|e^{j(\mathrm{\φ}\left(\mathrm{FFT}\right[X_m\left(t\right)\left]\right)-n{\mathrm{\α}}^m/2\mathrm{\π})}$

α ^mbe the circumferential angle of m Signal reception point and reference point, wherein said reference point is present position on bus, defect center, now α ^m=0; M=1,2,3 ... N, φ (FFT [X _m(t)] be X _mthe phase place of (t), N is Signal reception point number; N is the exponent number of supersonic guide-wave mode, for rotational symmetry T (0,1) mode or L (0,2) mode, n=0, for asymmetric modes F (1,2) mode and F (1,3) mode, n=1, for asymmetric modes F (2,2) mode, n=2; J is imaginary number;

1.4. by the frequency-region signal B in step 1.3 _nf () carries out inverse fast Fourier transform, obtain the reconstruct time-domain signal A of the axisymmetry mode after being separated ripple bag and mode of flexural vibration _n(t):

$A_n\left(t\right)=\frac{\mathrm{IFFT}\left(B_n\left(f\right)\right)}{N}$

N is the exponent number of supersonic guide-wave mode, works as n=0, A _nt time-domain signal that () is axisymmetry mode; Work as n>=1, A _nt time-domain signal that () is mode of flexural vibration;

1.5. utilize Hilbert-Huang transform to the reconstruct time-domain signal A in step 1.4 _nt () carries out envelope drafting, extract the envelope maximum value of incident rotational symmetry guided wave signals and each mode guided wave reflected signal;

1.6. the envelope maximum value of incident rotational symmetry guided wave signals step 1.5 obtained and each mode guided wave reflected signal is according to reflection coefficient formula process, the rotational symmetry guided wave reflection coefficient produced when calculating rotational symmetry guided wave and defect effect and mode of flexural vibration reflection coefficient, as n=0, wherein, R ⁿfor rotational symmetry guided wave reflection coefficient; As n>=1, wherein, R ⁿfor mode of flexural vibration reflection coefficient; for the envelope maximum value of incident rotational symmetry guided wave signals, for the envelope maximum value of each mode guided wave reflected signal;

1.7. change flaw size, obtain rotational symmetry guided wave reflection coefficient and the mode of flexural vibration reflection coefficient of different size defect; For two defect, change defect relative position, obtain rotational symmetry guided wave reflection coefficient and the mode of flexural vibration reflection coefficient of defect; Change center-driven frequency, obtain the rotational symmetry guided wave reflection coefficient under different center-driven frequency and mode of flexural vibration reflection coefficient; Above-mentioned reflection coefficient is depicted as curve respectively, obtains rotational symmetry guided wave reflection coefficient and mode of flexural vibration reflection coefficient according to curve, for evaluating ducted Defect Equivalent size and judging defect present position.

beneficial effect:

The invention provides the method being separated the mode of flexural vibration ripple bag together with being aliasing in rotational symmetry guided wave ripple bag, compared with existing supersonic guide-wave pulse reflection method, method provided by the invention can quantitative test MODAL TRANSFORMATION OF A phenomenon, obtain the reflection coefficient of mode of flexural vibration, and then non-axis symmetry defect is identified.

1) can quantitative test MODAL TRANSFORMATION OF A phenomenon, obtain the reflection coefficient of mode of flexural vibration, and then non-axis symmetry defect is identified.

2) compared with experiment, can effectively save human and material resources, financial resources, and the secondary development merit of finite element software can be utilized to carry out parametric programming, calculate the mode of flexural vibration reflection coefficient of a large amount of defect, obtain reflection coefficient chart, to instruct experimental study and the technology establishment of ultrasonic guided wave detection technology.

3) the result precision calculated is higher, and easy to implement.

Accompanying drawing explanation

Fig. 1 is the step block diagram being separated mode of flexural vibration guided wave signals ripple bag computing method;

Fig. 2 is three-dimensional tube finite element model, and caliber is 76.2mm, wall thickness 5.5mm;

Fig. 3 be external diameter 76.2mm and the group velocity dispersion curve of wall thickness 5.5mm steel pipe and 65kHz time each modal waves structural drawing, Fig. 3 (a) group velocity; (b) T (0,1) mode; (c) F (1,2) mode; (d) F (1,3) mode; (e) F (2,2) mode;

Fig. 4 is the circumferential displacement of 90 monitoring points extractions along the distribution of pipeline circumference;

Fig. 5 is 0 rank mode signals after Signal separator;

Fig. 6 is the single order mode signals after Signal separator;

Fig. 7 is the second-order modal signal after Signal separator;

Fig. 8 (a) for the circular hole degree of depth account for wall thickness 50% time, the relation that double circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle; Fig. 8 (b) is corresponding piping schematic.Center-driven frequency is 65kHz;

Fig. 9 is circular hole degree of depth when accounting for wall thickness 100%, the relation that double circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle.Center-driven frequency is 65kHz;

Figure 10 (a) for the circular hole degree of depth account for wall thickness 100% time, the relation that three circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle; Figure 10 (b) is corresponding piping schematic.Center-driven frequency is 65kHz;

Figure 11 is circular hole degree of depth when accounting for wall thickness 100%, the relation that three circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle.Center-driven frequency (a) 40kHz; (b) 50kHz; (c) 60kHz; (d) 70kHz; (e) 80kHz.

Embodiment

Content in conjunction with the inventive method provides the computing method example of (0, the 1) mode of diplopore defect T in following pipe and mode of flexural vibration reflection coefficient, concrete steps as shown in Figure 1:

1) set up three-dimensional tube model as shown in Figure 2, model length is 3000mm, and external diameter is 76.2mm, and wall thickness is 5.5mm, and radius-thickness ratio is 13.85, and density is 7843kg/m ³, Young modulus is 210GPa, and Poisson ratio is 0.28; Pipe end outer shroud arranges 90 excitation nodes; Holding 2000mm place apart from signal excitation, arrange the circular hole defect in circumference distribution, the diameter of circular hole is 5.5mm, and the angle of two center of circular holes must be greater than 10 degree; Signal monitoring identity distance defect center 1000mm, monitoring surface arranges 90 equally spaced signal acquisition point along pipeline circumference; C3D8 grid is utilized to carry out discretize to the intact region of model, defect area utilizes C3D6 grid to carry out discretize, frequency range elects 40-80kHz as, pipeline wall thickness direction grid units is of a size of 1.83mm, pipeline axial direction grid units is of a size of 2.5mm, and the grid units of fault location is of a size of 1.5mm; Utilize local coordinate to tie up on 90 excitation nodes at pipeline excitation end and load circumferential displacement; Signal function expression formula in the present invention is as follows:

$f\left(t\right)=\left\{\begin{array}{cc}0.5(1-\cos \left(\frac{2\mathrm{\&pi;ft}}{n}\right)\sin \left(2\mathrm{\&pi;ft}\right)& 0<t\&le;\mathrm{\&tau;}\\ 0& t>\mathrm{\&tau;}\end{array}\right.$

Wherein τ is the burst length of signal, and n is recurrence interval number, and f is excitation frequency; Low periodicity signal can obtain the shorter duration, is beneficial to the resolving power improved in time domain; The narrow-band of multicycle number signal is conducive to the frequency dispersion effect reducing guided wave; Consider in the implementation case, excitation frequency scope is 40-80kHz, and periodicity is 5.

2) result of finite element is extracted, by what collect from 90 Signal reception points with according to formula process, obtain the circumferential transient Displacements of N number of Signal reception point m=1,2,3 ..., 90, wherein for the circumferential displacement of m Signal reception point under local coordinate system, for the x direction output displacement of m Signal reception point under global coordinate system, for the y direction output displacement of m Signal reception point under global coordinate system, α ^mbe the circumferential angle of m Signal reception point and reference point, wherein said reference point is present position on bus, defect center, now α ^m=0; Fig. 4 is the circumferential transient Displacements of 90 Signal reception points extractions along the distribution of pipeline circumference;

3) to step 2) 90 time-domain signal X obtaining _mt () carries out Fast Fourier Transform (FFT), then on frequency domain according to formula carry out phase delay and superpose; α ^mbe the circumferential angle of m Signal reception point and reference point, wherein said reference point is present position on bus, defect center, now α ^m=0; M=1,2,3 ... N, φ (FFT [X _m(t)] be X _mthe phase place of (t), N is Signal reception point number; N is the exponent number of supersonic guide-wave mode, for rotational symmetry T (0,1) mode or L (0,2) mode, n=0, for asymmetric modes F (1,2) mode and F (1,3) mode, n=1, for asymmetric modes F (2,2) mode, n=2; J is imaginary number.

4) by step 3) in frequency-region signal carry out inverse fast Fourier transform, then can obtain the axisymmetry mode after being separated ripple bag and mode of flexural vibration time-domain signal fig. 5 is the incident and reflected signal of T (0,1) mode after Signal separator; Fig. 6 is mode of flexural vibration F (1,3) after Signal separator and F (1,2) reflected signal; Fig. 7 is mode of flexural vibration F (2, the 2) reflected signal after Signal separator;

5) utilize Hilbert-Huang transform to the reconstruct time-domain signal A in step 1.4 _nt () carries out envelope drafting, extract the envelope maximum value of envelope maximum value axisymmetry mode guided wave reflected signal and the envelope maximum value of mode of flexural vibration guided wave reflected signal of incident rotational symmetry guided wave signals; Dotted line in Fig. 5 is the envelope of signal;

6) will in step 5) in the envelope maximum value of incident rotational symmetry guided wave signals, axisymmetry mode guided wave reflected signal and mode of flexural vibration guided wave reflected signal that obtains according to formula process, just the torsion T (0 produced when rotational symmetry guided wave and defect (double circular hole defect center is at a distance of 180 °) act on can be calculated, 1) mode reflection coefficient, mode of flexural vibration F (1,3) reflection coefficient, F (1,2) reflection coefficient and F (2,2) reflection coefficient; As shown in Figure 8, when defect center angle is 180 ° at a distance of angle, T (0,1) mode reflection coefficient is 0.0162, mode of flexural vibration F (1,3) reflection coefficient and F (1,2) reflection coefficient is all 0.0103 close to 0, F (2,2) reflection coefficient;

7) utilize the secondary development function of abaqus python, parametric programming is carried out to three-dimensional tube model, change the relative position of circular hole defect, at this with defect center circumference angle for variable, only need to change just the guided wave reflection coefficient of the double circular hole defect of different relative position can be calculated; Fig. 8 is circular hole degree of depth when accounting for wall thickness 50%, when T (0,1) mode incides in pipeline with 65kHz, and the relation that double circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle.For all defect (the circular hole degree of depth accounts for wall thickness 50%) center circumference angle, T (0,1) mode reflection coefficient is about 1.6%, swings trend with variable angle in microseism.F (1,2) and F (1,3) mode reflection coefficient are monotone decreasing trend with angle; F (2,2) mode reflection coefficient first in monotone decreasing trend with angle, until 90 degree reach minimum value, then increases with angle and increases, reaching maximal value 180 degree time; Single T (0,1) mode reflection coefficient is difficult to determine the distribution of circular hole in pipeline circumference, and is but easy to evaluate the distribution of circular hole defective locations in conjunction with the reflection coefficient of T (0,1) mode and mode of flexural vibration.

In addition, circular hole depth of defect and center-driven frequency can also be changed, obtain the guided wave reflection coefficient variation relation figure of the double circular hole defect in different detected parameters situation.Fig. 9 is circular hole degree of depth when accounting for wall thickness 100%, the relation that double circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle.Non-through hole (the circular hole degree of depth accounts for wall thickness 50%) has similar rule with the reflection coefficient of through hole defect (the circular hole degree of depth accounts for wall thickness 100%), but the reflection coefficient of non-through hole only has about 0.4 of through hole, this illustrate reflection coefficient not with hole depth linearly funtcional relationship.

Figure 10 is circular hole degree of depth when accounting for wall thickness 100%, the relation that three circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle.T (0,1), the F (1,2) in three holes, F (1,3) and F (2,2) reflection coefficient have similar Changing Pattern to the reflection coefficient of holes.T (0,1) the mode reflection coefficient in three holes is about 6.75%, and diplopore and single hole be respectively 4.5% and 2.25%; This mean the circular hole number that circumferentially distributes in pipe circumference and T (0,1) mode reflection coefficient linear; Hole count often increases by one, and its reflection coefficient just increases by 2.25%.

Figure 11 be under different center-driven frequency condition and the circular hole degree of depth accounts for wall thickness 100% time, the relation that three circular hole T (0,1) mode and mode of flexural vibration reflection coefficient change with defect center circumference variable angle.Center-driven frequency (a) 40kHz; (b) 50kHz; (c) 60kHz; (d) 70kHz; (e) 80kHz.

Result shows: utilize the torsion T (0 calculated, 1) mode reflection coefficient, mode of flexural vibration F (1,3) reflection coefficient, F (1,2) reflection coefficient and F (2,2) reflection coefficient can evaluate the degree of depth of the relative position of circumferentially many circular holes defect, circular hole number and hole defect; Make up the deficiency that conventional Ultrasound guided wave pulse reflection method can only be located; The method solves the result that obtains ultrasonic guided wave detection technology Related Experimental Study and engineer applied can provide useful reference.

Last it is noted that above embodiment only in order to illustrate the present invention and and unrestricted technical scheme described in the invention; Therefore, although this instructions with reference to each above-mentioned embodiment to present invention has been detailed description, those of ordinary skill in the art should be appreciated that and still can modify to the present invention or equivalent to replace; And all do not depart from technical scheme and the improvement thereof of the spirit and scope of invention, it all should be encompassed in the middle of right of the present invention.

Claims (1)

1., based on the computing method that the mode of flexural vibration reflected signal of supersonic guide-wave is separated, it is characterized in that comprising following steps:

1.1. the pipeline three-dimensional entity model that length is L is set up, at distance pipeline model end L ₁place arranges the hole shape defect along the distribution of pipeline circumference, the defect center angle of hole shape defect and unit: degree, wherein, D _defectfor the diameter of hole defect, r _innerfor the internal diameter of pipeline; At distance pipeline model end L ₂place arranges N number of equally spaced node as Signal reception point along pipeline circumference, N>=8, for extracting the supersonic guide-wave reflected signal produced from fault location; At the pipeline model other end, N number of equally spaced node is set along pipeline circumference and encourages node as signal, N>=8, L>=3L ₁, L>=3/2L ₂; Finite element discretization being carried out to model, requiring that grid cell size is not less than for asking 1/10 of highest frequency corresponding wavelength;

1.2. result of finite element is extracted, by what collect from N number of Signal reception point with according to formula process, obtain the circumferential transient Displacements of N number of Signal reception point m=1,2,3 ... N, wherein for the circumferential displacement of m Signal reception point under local coordinate system, for the x direction output displacement of m Signal reception point under global coordinate system, for the y direction output displacement of m Signal reception point under global coordinate system, α ^mbe the circumferential angle of m Signal reception point and reference point, wherein said reference point is present position on bus, defect center, now α ^m=0;

1.3. the circumferential transient Displacements X of N number of Signal reception point will obtained in step 1.2 _mt () carries out Fast Fourier Transform (FFT), then on frequency domain, carry out phase delay according to the following formula and superpose, obtaining frequency-region signal, specific as follows:

$B_n\left(f\right)=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\left|\mathrm{FFT}\right[X_m\left(t\right)|e^{j(\mathrm{\&phi;}\left(\mathrm{FFT}\right[X_m\left(t\right)\left]\right)-n{\mathrm{\&alpha;}}^n/2\mathrm{\&pi;})}$

α ^mbe the circumferential angle of m Signal reception point and reference point, wherein said reference point is present position on bus, defect center, now α ^m=0; M=1,2,3 ... N, φ (FFT [X _m(t)] be X _mthe phase place of (t), N is Signal reception point number; N is the exponent number of supersonic guide-wave mode, for rotational symmetry T (0,1) mode or L (0,2) mode, n=0, for asymmetric modes F (1,2) mode and F (1,3) mode, n=1, for asymmetric modes F (2,2) mode, n=2; J is imaginary number;

1.4. by the frequency-region signal B in step 1.3 _nf () carries out inverse fast Fourier transform, obtain the reconstruct time-domain signal A of the axisymmetry mode after being separated ripple bag and mode of flexural vibration _n(t):

$A_n\left(t\right)=\frac{\mathrm{IFFT}\left(B_n\left(f\right)\right)}{N}$

N is the exponent number of supersonic guide-wave mode, works as n=0, A _nt reconstruct time-domain signal that () is axisymmetry mode; Work as n>=1, A _nt reconstruct time-domain signal that () is mode of flexural vibration;

1.5. utilize Hilbert-Huang transform to the reconstruct time-domain signal A in step 1.4 _nt () carries out envelope drafting, extract the envelope maximum value of envelope maximum value axisymmetry mode guided wave reflected signal and the envelope maximum value of mode of flexural vibration guided wave reflected signal of incident rotational symmetry guided wave signals;

1.6. result step 1.5 obtained, according to reflection coefficient formula process, the rotational symmetry guided wave reflection coefficient produced when calculating rotational symmetry guided wave and defect effect and mode of flexural vibration reflection coefficient, as n=0, wherein, R ⁿfor rotational symmetry guided wave reflection coefficient; As n>=1, wherein, R ⁿfor mode of flexural vibration reflection coefficient; for the envelope maximum value of incident rotational symmetry guided wave signals, as n=0, for the envelope maximum value of axisymmetry mode guided wave reflected signal, as n>=1, for the envelope maximum value of mode of flexural vibration guided wave reflected signal;

1.7. change flaw size, obtain rotational symmetry guided wave reflection coefficient and the mode of flexural vibration reflection coefficient of different size defect; For two defect, change defect relative position, obtain rotational symmetry guided wave reflection coefficient and the mode of flexural vibration reflection coefficient of defect; Change center-driven frequency, obtain the rotational symmetry guided wave reflection coefficient under different center-driven frequency and mode of flexural vibration reflection coefficient; Above-mentioned reflection coefficient is depicted as curve respectively, obtains rotational symmetry guided wave reflection coefficient and mode of flexural vibration reflection coefficient according to curve, for evaluating ducted Defect Equivalent size and judging defect present position.