Method for inspecting wall-thinned portion of pipe

Abstract

To provide an inspection method capable of easily evaluating a thinned part of a pipe by using electromagnetic waves.SOLUTION: The method includes a step of acquiring a reflection parameter of an electromagnetic wave with respect to a pipe in a frequency domain, a conversion step of converting the reflection parameter into a converted reflection parameter in a conversion domain corresponding to the frequency domain by Fourier transform, a calculation step of performing a band extraction process on the converted reflection parameter to acquire a converted band reflection parameter, an inverse conversion step of inversely converting the converted band reflection parameter from the conversion domain to the band reflection parameter in the frequency domain by inverse Fourier transform, and an analysis step of analyzing a dimension of a thinned portion from a beat waveform of the inversely converted reflection parameter.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present invention relates to a method for inspecting a pipe for thinning using electromagnetic waves. [Background technology]

[0002] Piping is used to transport oil, gas, and various other fluids. If a pipe has a thinned section, it can lead to accidents such as leaks, so early detection and evaluation of thinned sections is extremely important for the operation of the pipe. Patent Document 1 discloses a method for inspecting pipes by irradiating the pipes with gamma rays from outside and detecting Compton scattering. However, this method requires the inspection device to be moved in order to inspect the entire pipe.

[0003] Metallic piping can also be considered a waveguide for electromagnetic waves, and Patent Document 2 discloses a method for evaluating thinning by injecting electromagnetic waves into the piping and detecting the resonant frequency. However, it does not disclose a method for inspecting the location of local thinning areas or the amount of thinning (length, amount of change in thickness).

[0004] For this reason, a method has been proposed for evaluating localized thinning in pipes using electromagnetic waves. Because thinning changes impedance, it is thought that it is possible to inspect thinning by measuring the reflection of electromagnetic waves from the thinning. Theoretically, the location and dimensions of the thinning can be identified by multiplying the signal of the reflected wave in the time domain by the propagation velocity. However, because the propagation speed changes depending on the frequency of the electromagnetic wave, dispersion compensation is required to evaluate thinning areas. In long pipes, the amount of calculation required for dispersion compensation is large, making it difficult to apply.

[0005] Non-Patent Documents 1 and 2 disclose methods to avoid the computational burden of dispersion compensation. A vector network analyzer is used to inspect pipes using electromagnetic waves. One of the S parameters measured and output by the vector network analyzer is S 11The ratio of incident and reflected electromagnetic waves (reflected wave / incident wave) is a function of frequency. That is, S 11 is displayed in the frequency domain. The evaluation methods for thinned parts disclosed in Non-Patent Document 1 and Non-Patent Document 2 are 11 is converted from the frequency domain to the wavenumber domain using the group velocity, and h(z) is calculated as a function of the propagation distance z in the spatial domain.Then, the location of the thinned area is identified from h(z) displayed in the spatial domain, and the length and amount of thinning (i.e., change in thickness) of the thinned area are calculated by analyzing the signal from the thinned area. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent No. 6299033 [Patent Document 2] Japanese Patent Application Laid-Open No. 2008-224666 [Non-patent literature]

[0007] [Non-Patent Document 1] Weiying Cheng, Yijun Guo, Hidetoshi Hashizume;Localizing, identification and sizing of inner surface pipe wall thinning by means of domain transformation and spectral analysis,Mechanical Systems and Signal Processing 188 (2023) 110024 [Non-patent document 2] Cheng, Weiying, Guo, Yijun, Hashizume, Hidetoshi; Identification of location and size evaluation of wall thinning in pipes by domain conversion from frequency to wavenumber and spectrum analysis of microwave measurement signals, 31st MAGDA Conference in Kagoshima Summary of the Invention [Problem to be solved by the invention]

[0008] However, the generation of other modes during microwave propagation is inevitable. Since the propagation velocity differs for each mode, when multiple modes are mixed, determining which 'group velocity' to use for conversion to the wavenumber domain becomes a challenge. Therefore, the methods described in Non-Patent Documents 1 and 2 are difficult to apply to propagation involving multiple modes. Furthermore, group velocity varies nonlinearly with frequency. Therefore, the inverse Fourier transform, which converts from the wavenumber domain to the spatial domain, requires special processing to interpolate the signal displayed in the wavenumber domain. Therefore, a processing method that is not dependent on the propagation velocity is desired.

[0009] In view of the above problems, an object of the present invention is to provide an inspection method that uses electromagnetic waves to easily evaluate the location and dimensions of thinned parts in pipes. [Means for solving the problem]

[0010] The inspection method according to the present invention comprises: This is a method for inspecting thinned parts of pipes. acquiring a reflection parameter S(ω) of the electromagnetic wave with respect to the pipe in the frequency domain (ω domain); a transformation step of transforming the reflection parameters S(ω) into transformed reflection parameters F(Ω) in a transformed pair domain (Ω domain) corresponding to the frequency domain (ω domain) by a Fourier transform FT; The transformed reflection parameter F(Ω) is subjected to band extraction processing to obtain the transformed band reflection parameter F band A calculation step to obtain (Ω); The inverse Fourier transform (IFT) is used to obtain the transformed banded reflectance parameters F band (Ω) from the pair domain to the frequency domain banded reflection parameters S band an inverse transformation step of transforming back into (ω); The banded reflection parameter S band An analysis process to analyze the dimensions of the thinned part from the beat waveform of (ω) The present invention is characterized by comprising:

[0011] This method of inspecting pipe thinning can detect thinning on the inside of a pipe using electromagnetic waves. Furthermore, analysis using group velocity is no longer necessary, making inspection easier.

[0012] In addition, the inspection method according to the present invention includes: The band extraction may extract a component caused by the thinned portion.

[0013] This method of inspecting pipe thinning removes components that become noise in the analysis of the thinning, making it easier to analyze the thinning. Therefore, band extraction can also be applied to remove noise caused by reflections other than those in the thinning.

[0014] In addition, the inspection method according to the present invention includes: In the analyzing step, the reflection parameter S band The amount of thinning of the thinned portion may be calculated from the maximum value of the beat waveform (ω).

[0015] By using this method for inspecting thinned portions of pipes, the amount of thinning in the thinned portions can be easily evaluated.

[0016] In addition, the inspection method according to the present invention includes: In the analyzing step, the reflection parameter S band The amount of thinning of the thinned portion may be calculated from the maximum value of (ω), and the length of the thinned portion may be calculated from the beat frequency.

[0017] By using such a method for inspecting a pipe for thinned portions, the amount of thinning (change in thickness) and the length of the thinned portion can be easily detected.

[0018] In addition, the inspection method according to the present invention includes: In the calculation step, the position of the thinned portion may be calculated from the waveform of the transformed reflection parameter F(Ω).

[0019] By using this method for inspecting pipes for thinning portions, the location of the thinning portion can be easily detected.

[0020] In addition, the inspection method according to the present invention includes: The electromagnetic wave may be in TM01 mode.

[0021] This method of inspecting thinned parts of pipes makes it possible to evaluate thinning all around the pipe.

[0022] In addition, the inspection method according to the present invention includes: This is a method for inspecting thinned parts of pipes. The reflection parameter S for the electromagnetic wave incident on the pipe 11 a reflection parameter acquisition step of acquiring the reflection parameters in the frequency domain; a shape analysis step, The shape analysis step includes: Model reflection parameters due to the thinned portion m S 11 The absolute value of the low-order model reflection parameters | m S| lw and the absolute value of the model reflection parameter | m S 11 | and the low-order model reflection parameters | m S| lw The higher-order model reflection parameters, which are the difference between | m S| hi and the thickness reduction amount ΔR and central angle θ that specify the cross-sectional shape of the thickness reduction portion are calculated based on the low-order model reflection parameters | m S| lw a first contour map showing a correlation between the amount of wall thinning, the central angle, and the high-order model reflection parameter | m S| hi a second contour map showing a correlation between the maximum peak value of the The reflectance parameter S obtained for the pipe 11 from the absolute value of the low-order reflection parameter |S| lw and the absolute value of the reflection parameter |S 11 | and the low-order reflection parameter |S| lw and the higher-order reflection parameter |S| hi and constructing the low-order reflection parameters |S|lw selecting a first contour from the first contour map based on a peak value of |S|; and hi selecting a second contour from the second contour map based on a maximum peak value of and calculating the amount of wall thinning ΔR and the central angle θ of the pipe based on the first contour line and the second contour line.

[0023] This pipe inspection method makes it possible to calculate the amount of thinning and the central angle that characterize the cross-sectional shape of the thinned portion.

[0024] In addition, the inspection method according to the present invention includes: The low-order reflection parameter |S| lw The length of the thinned portion may be calculated from the beat frequency.

[0025] By using this type of pipe inspection method, it is possible to calculate the length of the thinned portion.

[0026] In addition, the inspection method according to the present invention includes: The low-order reflection parameter |S| lw The average thickness reduction amount <ΔR> of the thinned portion may be calculated from the peak value of

[0027] This type of pipe inspection method makes it possible to easily determine whether or not there is thinning in the pipe wall.

[0028] In addition, the inspection method according to the present invention includes: The incident electromagnetic wave may be in TM01 mode, and the high-order reflection parameters may be due to reflection by an electromagnetic wave having a cutoff frequency higher than the cutoff frequency of the TM01 mode.

[0029] By analyzing the reflection characteristics of electromagnetic waves in different modes, it is possible to calculate the amount of thinning and the central angle that characterize the shape of the thinned part.

[0030] In addition, the inspection method according to the present invention includes: The low-order reflection parameters may be constructed by singular spectrum analysis.

[0031] By using non-parametric spectral analysis, the reflection parameter S 11 From the above, the low-order reflection parameters |S| with smooth waveforms are lw It becomes easy to build a [Effects of the Invention]

[0032] According to the present invention, it is possible to provide an inspection method that can easily evaluate thinned portions of pipes using electromagnetic waves. [Brief explanation of the drawings]

[0033] [Figure 1] FIG. 1(A) shows the configuration of an inspection pipe 1 for explaining a method for measuring thinning portions, and FIG. 1(B) qualitatively shows the behavior of electromagnetic waves incident on a model pipe 2. [Figure 2] Figure 2(A) models the occurrence of thinning in the center of a standard pipe. The thinned area is indicated by PWT, and the standard pipe sections before and after the thinned area are indicated by SG1 and SG2. Note that since the system is axially symmetric, Figure 2(A) is a half-axial cross section. Figure 2(B) is a graph showing the frequency dependence of parameter S11. The horizontal axis of Figure 2(B) is frequency (f). [Figure 3] Figures 3(A) and (B) show the results of measuring the parameter S11 using a VNA for the test pipe 1 with a thinned portion PWT (indicated as 'with PWT' in the figure) and the reference pipe without a thinned portion PWT (indicated as 'NO PWT' in the figure). Figure 3(A) shows the real part of the parameter S11, and Figure 3(B) shows the imaginary part of the parameter S11. The horizontal axis of Figures 3(A) and (B) is frequency f (Frequency). [Figure 4]F(Ω) is obtained by Fourier transforming S(ω). Figures 4(A) and (B) show the dependence of F(Ω) on the ohm number, especially in the low ohm number region where the ohm number is less than 30. Figure 4(C) shows the real (Re) and imaginary (Im) parts of S(ω) obtained by inverse Fourier transform of F(Ω) for ohm numbers less than 30. Figure 4(D) shows the real (Re) and imaginary (Im) parts of the measured parameter S(ω) for the test pipe 1. Figure 4(E) shows the real (Re) and imaginary (Im) parts of S(ω) obtained by inverse Fourier transform of F(Ω) for ohm numbers less than 30 from the measured signal of the VNA for the reference pipe, after removing S(ω). Figure 4(F) shows the real (Re) and imaginary (Im) parts of S(ω) obtained by inverse Fourier transform of F(Ω) for ohm numbers less than 30 for the pipe 1 with the PWT inserted, after removing S(ω). The horizontal axis in Figures 4(C), (D), (E), and (F) is frequency f. [Figure 5] Figures 5(A), (B), (C), and (D) show F(Ω), which is the Fourier transform of S(ω) shown in Figures 4(E) and (F), and show the Ω-number dependence of Fband (Ω number ≥ 30) in the high Ω-number region where Ω number is 30 or higher. Figures 5(A) and (B) show F(Ω), which is the Fourier transform of S(ω) shown in Figure 4(E), and Figures 5(C) and (D) show F(Ω), which is the Fourier transform of S(ω) shown in Figure 4(F). These figures show the Ω-number dependence of Fband (Ω number ≥ 30) in the high Ω-number region where Ω number is 30 or higher. Figures 5(C) and (D) show Fband(Ω), which is divided into several subbands (subbands I, II, III, and IV) in the high Ω-number region where Ω number is ≥ 30. [Figure 6] Figures 6(A), (B), (C), and (D) show graphs in which Fband(Ω) is converted to S(ω) by inverse Fourier transform in each subband shown in Figures 5(C) and (D). The horizontal axis of Figures 6(A), (B), (C), and (D) is frequency (f). [Figure 7] Fig. 7(A) is a conceptual diagram illustrating a method for extracting the signal Sband(ω) required for PWT analysis from the measurement signal S(ω) via F(Ω), and Fig. 7(B) is a conceptual diagram illustrating a method for obtaining the PWT dimensions from the extracted Sband(ω). [Figure 8]Figure 8(A) shows a graph of Sband(ω) obtained by inverse Fourier transform of Fband(Ω) (Ω number ≧ 30) in the Ω band, which reflects the influence of the PWT, for the test pipe 1 using a PWT with W = 50 [mm] and dR = 1.0 [mm]. Figure 8(B) shows a graph plotting the envelope of Sband(ω) obtained by inverse Fourier transform of Fband(Ω) (1100 ≧ Ω number ≧ 763, including bands I, II, and III), which reflects the influence of the PWT, for the test pipe 1 using a PWT with W = 100 [mm] and dR = 1 [mm]. The horizontal axis of Figures 8(A) and (B) is frequency (f). [Figure 9] Fig. 9(A) is a graph showing a comparison between the calculated thickness change dR (vertical axis) and the actual thickness change dR (horizontal axis), and Fig. 9(B) is a graph showing a comparison between the calculated length W (vertical axis) and the actual length W (horizontal axis). [Figure 10] Figure 10 shows the spatial domain representation h(z) of the parameter S11 measured for a standard pipe without a PWT. [Figure 11] FIG. 11 shows a flow diagram for evaluating PWT using a computing device with a storage device such as a computer. [Figure 12] Figure 12(A) shows a cross section of the model pipe 2'' in the longitudinal direction (Z-axis direction), and Figure 12(B) shows a cross section perpendicular to the longitudinal direction of the model pipe 2''. Figure 12(C) shows the results of two-dimensional modal analysis for a cross section with wall thinning of ΔR = 1 [mm], and Figure 12(D) shows the results of two-dimensional modal analysis for a cross section with wall thinning of ΔR = 2 [mm], showing the relationship between frequency and propagation constant. [Figure 13] FIG. 13 shows the results of simulating the frequency dependence of the reflection parameter S11 obtained by irradiating electromagnetic waves in the TM01 mode from the end of the model pipe 2''. [Figure 14]Figure 14(A) shows the frequency dependence of Slow and Shi when the thickness reduction amount ΔR = 2 [mm] and the central angle θ = 270 [°], and Figure 14(B) shows the frequency dependence of the absolute value of Slow |Slow| when the thickness reduction amount ΔR = 1 [mm] and the central angle θ = 45 to 360 [°]. Figure 14(C) shows the relationship between the peak value of the beat waveform in the low frequency range and the average thickness reduction amount <ΔR>. [Figure 15] Figure 15(A) shows the eigenvalue γi of |S| when ΔR = 2 [mm] and θ = 90 [°]. Figure 15(B) shows the frequency (f) dependence of |S|, |S|lw, and |S|hi when θ = 270, 180, and 90 [°]. [Figure 16] Fig. 16(A) shows the relationship between the value |Slw|pk (peak value) at the peak point of |S|lw and the average amount of metal loss <ΔR>. Fig. 16(B) shows a contour map showing the correlation between the peak value |Slw|pk and the amount of metal loss ΔR and the central angle θ. Fig. 16(C) shows a contour map showing the correlation between the maximum value |Shi|mx of the peak of |S|hi and the amount of metal loss ΔR and the central angle θ. [Figure 17] Fig. 17(A) is a diagram illustrating the cross-sectional shape analysis process for calculating the amount of wall thinning ΔR and the central angle θ of the pipe to be inspected. Fig. 17(B) shows the frequency (f) dependence of |S|lw and |S|hi. Fig. 17(C) shows the first and second contour lines selected from the first and second contour maps. DETAILED DESCRIPTION OF THE INVENTION

[0034] Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the following embodiments are not intended to limit the scope of the present invention. Furthermore, the same or similar components will be designated by the same reference numerals, and their description may be omitted.

[0035] Furthermore, terms used in this specification that specify shapes, geometric conditions, and their degrees, such as "parallel," "orthogonal," and "identical," as well as values ​​of lengths and angles, are not to be construed as being bound by strict meanings, but rather as including a range within which similar functions can be expected.

[0036] (Embodiment 1) This paper describes a method for measuring thinning portions on the inner surface of a pipe using electromagnetic waves. The pipe to be inspected is conductive, for example, made of metal, and can be regarded as a waveguide for electromagnetic waves. Figure 1(A) shows the structure of an inspection pipe 1 to explain the method for measuring thinning areas, and Figure 1(B) qualitatively shows the behavior of electromagnetic waves incident on a model pipe 2. The inspection pipe 1 is made of metal and forms a cylindrical waveguide for electromagnetic waves. The same applies to the other pipes described below.

[0037] The test pipe 1 was made by connecting ten standard pipes, each 1.5 m long with flanges on both ends and with an inner radius (1 / 2 of the inner diameter) a1, and the thinned section (hereinafter sometimes referred to as PWT) was simulated by a short pipe (referred to as a simulated thinned short pipe) with a length W and an inner radius a1 + dR (= a2), which was inserted between the standard pipes. The inner radius a1 of the standard pipe is 9.5 mm, and the combinations of dR and W are shown in the table in Figure 1(A). The dimensions of the pipe to be inspected are not limited to those described above.

[0038] A mode converter is inserted into the test port, which is one end of the inspection pipe 1, and the mode converter is connected to a vector network analyzer (hereinafter sometimes referred to as VNA). The end of the inspection pipe 1 is open. A simulated wall-thinning short pipe with a length W and an inner radius a1 + dR is placed at the seventh position, i.e., Lwt = 7 × 1.5 m = 10.5 m from one end of the inspection pipe 1. Therefore, the simulated wall-thinning short pipe is located in the range of 10.5 [m] to 10.5 + W [m] from the input end of the electromagnetic wave. Using a VNA, an electromagnetic wave is incident from the test port, and the parameter S, which is one of the S parameters (scattering parameters) related to the reflected signal, is measured. 11 Measure the parameter S 11 is defined as the ratio of the reflected wave to the incident wave (reflected wave / incident wave). In this specification, the parameter S 11 To distinguish it from other S parameters, it is sometimes called a reflection parameter. It should be noted that a commercially available known device can be used as the VNA.

[0039] The VNA measures the parameter S by sweeping the frequency of the electromagnetic wave. 11 Measure. The electromagnetic wave in TEM mode was converted to TM01 mode via a mode converter and then incident on the test port. TM01 mode is advantageous for detecting thinning all around the circumference. In a standard pipe with an inner radius of 9.5 mm, the cutoff frequency of electromagnetic waves in TM01 mode is 12.087 GHz, so the VNA sweeps the electromagnetic waves (microwaves) in the range of 12.1 to 21.1 GHz at intervals of 1,406,250 Hz, and inputs electromagnetic waves of a total of 6,401 frequencies into the test port at one end of the inspection pipe 1. The electromagnetic wave is not limited to the TM01 mode. The mode can be selected according to the purpose of the inspection and measurement can be performed.

[0040] FIG. 1(B) shows the behavior of electromagnetic waves incident on the model pipe 2 from the test port. The model pipe 2 simulates the test pipe 1, and has a wall-thinned portion (PWT) in the middle and an open end. Impedance mismatch occurs at the wall-thinned portion and the end. The incident electromagnetic wave (incident wave) is partially reflected at the thinned portion and partially transmitted. The transmitted electromagnetic wave (transmitted wave) is partially reflected at the end portion. In this way, the incident wave is multiple-reflected within the model pipe 2 and returns to the test port.

[0041] The parameters measured by the VNA are as follows: 11 This paper describes a new method for processing and evaluating thinning portions. Therefore, new terms will be defined as necessary in this specification.

[0042] <The influence of reflected waves from thinned parts - theoretical considerations> Figure 2(A) is an axial cross-sectional view of a model pipe 2' with a thinned part PWT in the center of a standard pipe (a half model is shown because of axisymmetric). Figure 2(B) shows the parameter S 11 10 is a graph showing the frequency dependence of . The inner radius of the standard pipe is a1, and the length and inner radius of the thinned part PWT are w and a1 + dR (= a2), respectively. The model pipe 2' can be regarded as a waveguide for electromagnetic waves. The pipe to be inspected has a thinned part PWT as a geometrical and electromagnetic discontinuity.

[0043] As shown in FIG. 2(A), if the longitudinal direction of the model pipe 2' is the z-axis, the electromagnetic wave is incident on the model pipe 2' from z=-L. Standard piping has a characteristic impedance Z a1 The thinned part PWT has a different characteristic impedance Z a2 Therefore, an impedance mismatch occurs at the boundary between the standard pipe and the thinned part PWT, and part of the electromagnetic wave is reflected and part is transmitted. As a result, the electromagnetic wave is multiple-reflected.

[0044] The reflection coefficient Γ of an electromagnetic wave can be defined as the ratio of the electric field of the electromagnetic wave propagating in the -z direction (the direction in which the electromagnetic wave is reflected) to the electric field of the electromagnetic wave propagating in the z direction (the direction in which the electromagnetic wave is incident). The reflection coefficient Γ is a function of z. The parameter S 11 is given by the reflection coefficient Γ at z=-L. Since the proof of theoretical calculation is not the purpose of this specification, details will be omitted, but the electric field and the like can be calculated by solving Maxwell's equations using a cylindrical coordinate system for an axisymmetric cylindrical pipe.

[0045] Figure 2(B) shows the parameter S 11 The vertical axis shows the frequency dependence of the parameter S 11 The horizontal axis indicates the frequency (f=ω / 2π) of the electromagnetic wave incident on the model pipe 2'. "Re" is the parameter S 11 The real part of "Im" is the parameter S 11Also, "Abs" indicates the value of the imaginary part of the parameter S 11 The envelope of the absolute value of is shown, where ω is the angular frequency.

[0046] Since the inner diameter of the standard pipe and the thinned part PWT are different, multiple reflections occur. 11 The waveform of shows that the electromagnetic waves from multiple reflections overlap each other, causing a beat phenomenon. 11 It can be seen that the absolute value of varies periodically depending on the frequency. In addition, the parameter S 11 The point where the absolute value (or envelope) of is minimum is defined as a beat point, and the frequency of the beat point is defined as a beat frequency. A waveform where the beat phenomenon is confirmed is called a beat waveform.

[0047] It is possible to theoretically calculate the reflection coefficient Γ when electromagnetic waves in TM01 mode are incident on model pipe 2'. Because electromagnetic waves undergo multiple reflections, which are repeatedly reflected and transmitted, the reflection coefficient Γ at z=0 when electromagnetic waves in TM01 mode are incident can be found by the sum of an infinite geometric series. Using the relational expression transmittance = 1 + reflectance, the reflection coefficient Γ at z=0 can be calculated using Equation 1. TIFF2026036661000002.tif1454 (Formula 1) where Γ 12 is the absolute value of the reflection coefficient of the electromagnetic wave incident on the thinned part PWT from the standard pipe, w is the length of the PWT, and "j" indicates the imaginary unit.

[0048] Furthermore, β is a propagation parameter and is defined by the following equation 2. TIFF2026036661000003.tif1873 (Formula 2) Here, kc is the cutoff wave number, k and f are the wave number and frequency of the electromagnetic wave, c is the speed of the electromagnetic wave in a vacuum, and p 01 is the first root of the 0th order Bessel function of the first kind (2.405), and a is the inner radius of the waveguide. As can be seen from Eq. 2, the cutoff wave number k c are the inner radius a and p 01and (k c =p 01 / a). The index "2" of "β2" in Equation 1 indicates that it is the propagation parameter β2 of the thinning portion PWT.

[0049] Equation 1 states that when 1-exp(-j2β2W)=0, the reflection coefficient Γ z=0 = 0, that is, when 2β2W = 2π × n, the reflection coefficient Γ z=0 =0. A set of propagation parameters β2 that satisfies 2β2W=2π×n is defined as β 2(i) where i is a natural number and β 2(i) W = π × i. β 2(i) Using this, the length W can be calculated using Equation 3. TIFF2026036661000004.tif1544 (Formula 3) In addition, β 2(i) In Equation 2, the inner radius is a2, and the frequency is the beat frequency f i It can be calculated by substituting

[0050] Also, in Equation 1, Γ 12 < 1, and Γ 12 2 ≪If 1, TIFF2026036661000005.tif962 (Formula 4) It can be approximated as Γ z=0 is maximized when exp(-j2β2W)=-1. Therefore, the parameter S 11 The maximum absolute value of is Γ 12 It is twice as much.

[0051] Characteristic impedance Z of standard piping a1 and the characteristic impedance Z of the thinned part PWT a2 Using the reflection coefficient Γ at z=0 12z=0 teeth, TIFF2026036661000006.tif1650 (Formula 5) This becomes: x=Za2 / Z a1 Then, TIFF2026036661000007.tif1662 (Formula 6) Therefore, Γ 12z=0 Once is found, x can be calculated. If the specific impedance is Z0, TIFF2026036661000008.tif1144 (Formula 7) TIFF2026036661000009.tif1145 (Formula 8) where k is the wave number and F is a constant. a1 is the inner radius of the standard pipe and a2 is the inner radius of the PWT.

[0052] Therefore, the cutoff wave number of the standard piping and PWT is k c1 and k c2 Then, x can be calculated using the following equation 9. TIFF2026036661000010.tif2662 (Formula 9) Since the inner radius a1 of the standard piping is known, if the value of x is known, the inner radius a2 (= a1 + dR) of the PWT can be calculated from Equation 9. Once the inner radius a2 of the PWT is determined, the length W of the PWT can be determined using Equations 2 and 3. Therefore, the length W of the PWT and the amount of thinning dR can be determined.

[0053] Thus, the parameter S measured by the VNA 11 The length W of the PWT and the amount of thinning dR can be calculated from the periodicity and maximum value of the

[0054] (Measurement results) Figures 3(A) and (B) show the parameter S for the test pipe 1 with a thinned part PWT of w=50[mm] and dR=1.0[mm] (therefore, inner radius = 9.5 + 1.0 = 10.5[mm]) and the reference pipe without a thinned part PWT. 11 The results measured by VNA are shown below. In Fig. 3, "NOPWT" indicates the measurement result of the reference pipe without PWT, and "withPWT" indicates the measurement result of the test pipe 1 with PWT. 11 The graph in Figure 3(B) shows the real part of the parameter S 11 The horizontal axis of the graphs in Figures 3(A) and (B) represents frequency (f=ω / 2π). Note that frequency f and angular frequency ω are essentially the same, differing only by the multiplier 2π. Therefore, in this specification, angular frequency and frequency may be collectively referred to as "frequency." For example, the parameter S output from the VNA 11 is a function of frequency f, but can be easily transformed into a function of angular frequency ω, and the parameter S 11 can be considered to be output as a function of angular frequency ω. In the following calculations, it is easy to replace angular frequency ω with frequency f.

[0055] In Figure 3, the parameter S 11 Regardless of whether PWT is used or not, a sinusoidal waveform with a large amplitude and a long period is observed with respect to ω. Furthermore, it can be confirmed that a short-period waveform with a small amplitude (called a ripple) is superimposed on the long-period waveform. The parameter S for the two pipes shown in Figure 3 11 It is difficult to determine whether or not there is a PWT from the waveform, and it is difficult to directly obtain information on the thinned area. Below, the parameter S 11 Extraction of thinning signals and the extracted S 11 The periodicity of ω, i.e., the parameter S related to metal thinning with ω as a variable 11 A method for analyzing the frequency components of the above will be described.

[0056] (Method for evaluating thinning areas - signal processing method) The following describes the parameter S measured by VNA after injecting electromagnetic waves into the pipe under inspection. 11 We will explain the signal processing method to extract the signal related to PWT from the parameter S measured by the VNA and evaluate the PWT. 11is a function of the angular frequency ω (or a function of the frequency f). The parameter S defined as a function of ω 11 , the parameter S shown in the ω domain 11 For simplicity, the parameter S is expressed in the ω domain. 11 is written as S(ω). The VNA uses the parameter S 11 is output in the angular frequency domain (or frequency domain).

[0057] As shown in Figure 3, S(ω) has a long-period component with a large amplitude and a short-period component with a small amplitude. As mentioned above, no dependency on the presence or absence of thinning is observed in the long-period component. The following explains how to obtain information on thinned parts by removing low Ω number components from F(Ω), which is the transformation of S(ω) into the Ω domain, and extracting high Ω number components.

[0058] To analyze the frequency components of S(ω) with respect to ω, a Fourier transform is performed on S(ω). TIFF2026036661000011.tif855 (Formula 10) By the Fourier transform, the ω domain is transformed into the Ω domain, and S(ω) is transformed into F(Ω) defined in the Ω domain. Note that F(Ω) defined as a function of Ω number is expressed as the parameter S 11 It is sometimes referred to as. Furthermore, the Ω domain is transformed into the ω domain by the inverse Fourier transform, and F(Ω) is transformed into S(ω).

[0059] Ω and ω are paired with each other in the Fourier transform, and S(ω) and F(Ω) are paired with each other in the Fourier transform. Therefore, in this specification, the Ω domain is sometimes referred to as the domain that is the transform pair (or dual domain) of the ω domain, and the ω domain is sometimes referred to as the domain that is the transform pair (or dual domain) of the Ω domain. Furthermore, F(Ω) is the transform pair of S(ω) and is sometimes referred to as the transformed reflection parameter. Ω reflects the periodicity of the S(ω) waveform when S(ω) is considered as a function of ω. Therefore, in this specification, Ω is sometimes referred to as the transform-to-frequency for angular frequency ω.

[0060] Note that the actual S(ω) is measured by sweeping the frequency at a predetermined interval, so it is a discrete value S(ω i ) can be obtained. Therefore, in practice, the discrete fast Fourier transform (or discrete Fourier transform) is used to calculate S(ω i ) is the F(Ω) of the Ω domain i ) TIFF2026036661000012.tif649 (Formula 11) Here, DFFT stands for Discrete Fast Fourier Transform. Also, F(Ω i ) is obtained by inverse discrete fast Fourier transform (or inverse discrete Fourier transform) as S(ω i ) Hereinafter, "Fourier transform" includes "discrete Fourier transform" and "discrete fast Fourier transform", and "inverse Fourier transform" includes "inverse discrete Fourier transform" and "inverse discrete fast Fourier transform".

[0061] F(Ω) can be obtained by Fourier transforming S(ω) shown in Figure 3. Figures 4(A) and (B) show the Ω-number dependence of F(Ω), especially in the low Ω-number region where the Ω number is less than 30. Figure 4(C) shows S, which is the inverse Fourier transform of F(Ω) for Ω numbers less than 30 (Ω number ≦ 30). low 11 (ω). The solid line in Figure 4(C) indicates S 11 The dotted line indicates the real part of S 11 Fig. 4(D) shows the imaginary part of the parameter S 11 The real part (Re) and imaginary part (Im) of the parameter S of the inspection pipe 1 shown in Figures 3(A) and 3(B) are shown. 11 The real and imaginary parts of are shown on one diagram. The vertical axis of the graphs in Figures 4(A) and (B) represents F (Ω), and the horizontal axis represents the number of Ω. Figure 4(A) shows S 11is a graph of the real part of F(Re(S 11 )) Figure 4(B) shows S 11 The imaginary part of F(Im(S 11 )) F(Ω) is a complex number, and each F(Ω) has a real part (Re) and an imaginary part (Im). Figure 4(E) shows the S (Ω) obtained by inverse Fourier transform of F(Ω) from the measured signal of the VNA in the reference pipe where the Ω number is less than 30. 11 S with (ω) removed 11 Figure 4(F) shows the real part (Re) and imaginary part (Im) of (ω). Figure 4(F) shows the S 11 S with (ω) removed 11 (ω) are the real part (Re) and the imaginary part (Im).

[0062] As shown in Figures 4(A) and (B), a large peak at approximately 1500 is observed when the Ω number is 6. As shown in Figure 4(C), F(Ω) in the low Ω number region is inversely transformed to the ω domain by inverse Fourier transform, S low 11 (ω) is a long-period waveform with no short-period ripples. S shown in Figure 4(C) 11 The waveform of the real part of reproduces the long-period component of the real part of Figure 4(D), and S 11 The waveform of the imaginary part of Fig. 4(D) reproduces the long-period component of the imaginary part of the waveform of Fig. 4(D). Therefore, it can be confirmed that a specific periodic component of the S(ω) waveform can be extracted using F(Ω), which is defined as a function of the Ω number in the Ω domain.

[0063] Figures 5(A), (B), (C), and (D) show F(Ω), which is the Fourier transform of S(ω) shown in Figure 3. F in the high Ω number region (Ω number is 30 or more) band (Ω number ≧ 30) where F band (Ω number < 30) was set to 0. Figures 5(A), (B), (C), and (D) show the F bandThe real part of (Ω) (denoted as "Re" in the figure) and F band The imaginary part of (Ω) (denoted as "Im" in the figure) is plotted.

[0064] Figure 5(A) shows the S(ω) remaining after removing the long-period components of S(ω) for the reference pipe without a PWT. hi The real part of F(ω) (Fig. 4(E)) is converted to F(Ω) (Fig. 5(A) on the vertical axis, F(Re(S hi 11 ) is shown. Figure 5(B) shows the F obtained by converting the imaginary part of S(ω) for the reference pipe without PWT. band (Ω) (Figure 5(B) vertical axis is F(Im(S hi 11 ) is shown. Figure 5(C) shows the S(ω) remaining after the long-period component of S(ω) of the test pipe 1 with the PWT is removed. hi The real part of (ω) (Fig. 4(F)) is transformed into F(Ω) (Fig. 5(C) on the vertical axis, F(Re(S hi 11 ) is shown. Figure 5(D) shows the S(ω) remaining after the long-period component of S(ω) of the test pipe 1 with the PWT is removed. hi (ω) (F obtained by converting the imaginary part of Figure 4(F) band (Ω) (Figure 5(D) on the vertical axis F(Im(S hi 11 ) is written as ). ) is written as .

[0065] In all of Figures 5(A), (B), (C), and (D), F(Ω) rises sharply at the Ω number value of 1100, and a waveform that extends over a wide range is observed in the Ω number range above 1100. This waveform is observed regardless of whether a PWT is used, and can be understood as a waveform that reflects the influence of the end of the pipe and the re-propagation and reflection of the reflected wave from the end.

[0066] As shown in Figure 5(C) and (D), the region of Ω number values ​​from 763 to 1100 can be divided into three subbands with peaks: the first subband I, the second subband II, and the third subband III. bandIn the first subband I, it can be seen that F(Ω) rises sharply at the point where the Ω number is 763. The waveform in this region is observed only in the test pipe 1 having the PWT, and can be understood to be a waveform related to the PWT. F band The sudden change in the waveform of (Ω) is due to the effect of the discontinuity. F band The Ω number where a sudden change in Ω occurs reflects the location information of the discontinuity (piping). The subband with a peak in the region where the Ω number is 1100 or more is referred to as the fourth subband IV. As mentioned above, the subband with the largest Ω number reflects the influence of the end of the pipe and the propagation thereafter. However, the number of subbands is not limited to 4. The number and positions of the subbands in the Ω domain vary depending on the shape, position, etc. of the PWT.

[0067] Figure 6 shows the F in each subband I, II, III, and IV of Ω shown in Figures 5(C) and 5(D). band The graph shows the result of converting (Ω) to S(ω) using the inverse Fourier transform. FIG. 6(A) shows the first subband I, FIG. 6(B) shows the second subband II, FIG. 6(C) shows the third subband III, and FIG. 6(D) shows the F of the region where the Ω number is 1100 or more (referred to as the fourth subband IV). band The graph shows the result of transforming S(ω) into S(ω) by inverse Fourier transform. The vertical axis is the transformed S(ω), and since the low Ω number component is removed from the transformed S(ω), the vertical axis shows S 11 hi The horizontal axis represents frequency f.

[0068] The S(ω) corresponding to Ω of the fourth subband IV shows a broad waveform over a wide range of ω, whereas the S(ω) corresponding to F(Ω) of the first subband I, the second subband II, and the third subband III have waveforms that are separated from each other (compared to the S(ω) of the fourth subband IV).

[0069] By performing an inverse Fourier transform on F(Ω) where the Ω number is 30 or more, the long-period components of the S(ω) waveform as shown in Figure 3 can be removed, and the ripple, which is a short-period component, can be analyzed. However, as shown in Figure 6(D), in the region where the Ω number is 1100 or more, F(Ω) is strongly affected by multiple reflections, where microwaves returning from the end of the pipe to the incident point are propagated and reflected again, making PWT analysis difficult. Therefore, it is preferable to perform an inverse Fourier transform on F(Ω) in the region where the Ω number is 763 to 1100, where only primary reflection occurs in the PWT, and calculate S(ω), which is most related to PWT. In this way, by calculating S(ω) displayed in the ω domain obtained from the VNA via its transformed counterpart F(Ω) displayed in the Ω domain, it is possible to remove unnecessary noise components and extract components that more clearly reflect the PWT, enabling detailed analysis.

[0070] FIG. 7 is a schematic diagram for explaining a method for removing unnecessary periodic components from the measured S(ω) and analyzing the PWT. FIG. 7(A) is a conceptual diagram for explaining a method for extracting periodic components necessary for analyzing the PWT from S(ω) via F(Ω). FIG. 7(B) shows the extracted S band FIG. 10 is a conceptual diagram illustrating a method for acquiring PWT information from (ω). In FIG. 7(A), FT stands for Fourier transform, and IFT stands for inverse Fourier transform. Hereinafter, with reference to FIG. 7(A), a method for extracting and analyzing a specific periodic component from S(ω) obtained as a function of ω in the ω domain using a VNA will be described. FIG. 7B will be described later.

[0071] The following steps can also be performed automatically by a computer, etc. For example, generation of an envelope (such as interpolation of maximum values), detection of peak values, detection of minimum values, detection of waveform rising edges, etc. may be performed by a computer, etc. A flow diagram for evaluating PWT using a calculation device equipped with a storage device such as a computer is shown in Figure 11. The calculation device can input S(ω) measured by the VNA directly via wired or wireless communication, or via a storage medium (see S1 in Figure 11). The program to be executed is stored in the storage device. The calculation device can also store the total length of the pipe in the storage device.

[0072] Step 0 First, an electromagnetic wave is incident on the pipe to be inspected, and the reflection parameter S(ω) is obtained in the ω domain using a VNA. In the following steps, processing is performed on the obtained S(ω).

[0073] Step 1 In Figure 7(A), as shown by the upward arrow labeled "FT," S(ω), which is a function of ω in the ω domain, is Fourier transformed and converted into F(Ω), which is a function of the Ω number in the Ω domain (see S2 in Figure 11).

[0074] Step 2 Thereafter, as shown by the dotted arrow pointing from left to right in FIG. 7(A), calculations are performed on F(Ω) in the Ω domain. Specifically, the region of F(Ω) corresponding to the long-period components of S(ω) (Ω number is 30 or less, but is not limited to 30) is excluded. Note that the region of F(Ω) corresponding to the long-period components of the S(ω) waveform is significantly higher (several tens of times) than the F(Ω) of the short-period components, as shown in Figures 4(A) and (B), and is clearly distinguishable. By utilizing this, it is possible to determine the region of low Ω number that should be removed by the calculation device (see S3 in Figure 11). Then, the envelope of F(Ω) is generated by a known method, analyzed, and the positions of the maximum point (peak), minimum point, and rising point of the envelope, as well as the number of Ω, are determined, and F(Ω) is divided into subbands, i.e., multiple Ω bands (see FIG. 5). For example, the width of the Ω subband can be determined by the width from one minimum point to the next minimum point. The position (terminal position) of the subband with the largest Ω number (fourth subband IV in FIG. 5) corresponding to the end of the pipe may be identified (see S4 in FIG. 11), and then the subbands (first, second, and third subbands I, II, and III in FIG. 5) before the end position (regions with a smaller Ω number than the end position) may be identified (see S5 in FIG. 11). The order in which the subbands are identified is arbitrary and is not limited to the above, but if there is no PWT in the piping, only the end position is identified.

[0075] If the only subband present is the fourth subband IV (if the number of subbands is one), it can be determined that there is no PWT in the piping. In this case, the following steps 3 and 4 are unnecessary (see S6 and S14 in Figure 11). The envelope may be determined by the maximum values ​​of the real and imaginary parts of F(Ω), or by the absolute value of F(Ω). It is not necessary to calculate the envelope. The width of the Ω subband may be determined from the waveform of F(Ω).

[0076] If the number of subbands is greater than 1, the position of the PWT can be calculated in the step of dividing the signal into subbands, as will be described later (see S7 in FIG. 11).

[0077] Next, extract F(Ω) corresponding to the subband. The extracted F(Ω) is denoted as F band This is written as (Ω). (See S8 in Figure 11.) Also, as mentioned above, Ω is a discrete value Ω i For example, if i is an integer greater than or equal to 0, then for simplicity, F(Ω i ) and F band (Ω i ) as F(i) and F band This is written as (i). Ω i F in the range of N1 to N2 band To extract (i), the following calculations can be performed on F(i): TIFF2026036661000013.tif1660 (Formula 12) N max is Omega i For example, the parameter S shown in Figure 3 is 11 The measurement result is 3201 (=(6401-1) / 2+1). 5(C) and (D), N1 is the Ω number value (minimum value) of 763 indicating the beginning of the smallest first subband I, and N2 is the Ω number value (minimum value) of 1100 indicating the beginning of the largest fourth subband IV. The region N1≦i≦N2 corresponds to the Ω number component mainly caused by PWT. In this specification, F(Ω) is used to calculate the F of the subband. band Extracting (Ω) is called band extraction. band (Ω) is sometimes referred to as the transformation banded reflection parameter.

[0078] F band To extract (Ω), the window function WD(Ω) is defined to be 1 only in the region corresponding to the subband (N1≦i≦N2) and 0 elsewhere, and F band (Ω) = F(Ω) × WD(Ω), so F band (Ω) can also be found. For example, when Ω is a discrete value, the window function WD(i) is defined so that WD(i) = 1 in the range of N1 ≤ i ≤ N2 and WD(i) = 0 in other ranges, and F band (i) = F(i) × WD(i) = F band (i) may be sought.

[0079] Step 3 Then, conjugate the negative Ω number region (-N max F in (i<0) band (i) is constructed and the (-N max ≦i≦N max ) in F band In Fig. 7(A), as shown by the downward arrow labeled "IFT", the F band (i) (or Fband (Ω)) in the ω domain band (i) (or S band (ω) (see S9 in Figure 11). S band (i) is the parameter S for a specific Ω number range with respect to ω. 11 Shows. In addition, S band (i) is sometimes called the banded reflection parameter.

[0080] As described above, it is possible to extract a specific range of Ω number components for S(ω) defined in the ω domain via F(Ω) defined in the Ω domain.

[0081] Step 4 As shown in Figure 7(B), the unnecessary noise components are removed. band The amount of thinning dR and length W of the PWT can be calculated from the beat waveform (ω).

[0082] The measured parameters S 11 A method for calculating the dimensions of the PWT will now be specifically described.

[0083] (Measurement of thickness loss) Figure 8(A) shows the S(Ω) obtained by converting F(Ω) (Ω number ≥ 30) from which components with an Ω number of 30 or less have been removed into the ω domain. hi The graph shows the parameter S (ω) obtained for test pipe 1 using a PWT with W = 50 [mm] and dR = 1.0 [mm]. 11 is used. The vertical axis is S band (ω)(S hi 11 ) and the horizontal axis represents frequency.

[0084] As mentioned above, S band The maximum absolute value of (ω) is Γ z=0 The effect of PWT is extracted as S band From the beat waveform of (ω), S bandThe maximum absolute value of (ω) can be found (see S10 in FIG. 11). Furthermore, x can be calculated using Equation 6. The maximum value may be obtained from the maximum value of the waveform between beat points, for example.

[0085] The radius a1 of the standard pipe is known, and the cutoff wave number k of the standard pipe is c1 can be calculated from the radius a1. Also, the cutoff wave number k c2 is determined by the radius a2. Therefore, the radius a2 of the PWT can be calculated from Equation 9, and the amount of thinning dR can be calculated as a2-a1 (see S11 in Figure 11).

[0086] (Measurement of thinning length) In Figure 8(A), as indicated by the arrow, beat points are observed where the envelope of S(ω) (the envelope at the upper end) becomes a minimum. The beat frequency can be calculated from the beat points (see S12 in Figure 11). As mentioned above, the radius a2 of the PWT can be calculated, and the radius a2 and the beat frequency f i From this, β 2(i) can be obtained. Therefore, the obtained series of β 2(i) Using the above, the length W of the PWT can be calculated using Equation 3 (see S13 in FIG. 11).

[0087] Figure 8(B) shows the results of a similar analysis performed on test pipe 1 with PWTs of different sizes (W = 100 mm, dR = 1 mm) within bands I, II, and III. Specifically, by using Fourier transform and inverse Fourier transform, specific periodic components of the S(ω) waveform in the ω domain were extracted via F(Ω) in the Ω domain, and an envelope was formed. It should be noted that it is not always necessary to form an envelope as shown in FIG. 8(A).

[0088] Figure 8(B) shows the F of the Ω domain, which reflects the influence of PWT, excluding the low and high Ω number regions. band(Ω) is inverse Fourier transformed to obtain S band The vertical axis is the envelope of S band (ω)(S hi 11 ) expressed in decibels. As indicated by the arrows, beat points where the envelope of S(ω) becomes a minimum are observed. S band The maximum value of (ω) can be found from point P indicated by the dotted arrow. As a result, the inner radius a2 of the PWT can be found. Furthermore, the beat frequency can be determined from the beat points, and the length W of the PWT can be calculated. In FIG. 8(B), the second maximum value (the maximum point between the first beat point and the second beat point) can be selected as point P.

[0089] A similar analysis was performed on the test pipe 1 with PWTs under other conditions. band (ω) was obtained, and it was confirmed that it was possible to measure the amount and length of thinning of the PWT.

[0090] Figure 9 shows the reflection parameter S 11 The PWT size (thinning amount dR and length W) calculated from the measurement results is compared with the actual values. FIG. 9(A) is a graph showing a comparison between the calculated amount of wall-thickness reduction dR and the actual amount of wall-thickness reduction dR. The calculated dR value on the vertical axis is the reflection parameter S 11 The horizontal axis is the actual value of the metal loss dR ("actual dR value" in the figure). FIG. 9B is a graph showing a comparison between the calculated length W and the actual length W. The calculated value of W on the vertical axis is calculated by the above analysis method using the reflection parameter S 11 The horizontal axis is the actual value of the length W ("actual W value" in the figure).

[0091] As shown in Figure 9(A), PWTs with different lengths W (40, 50, 90, 100 mm) and thickness reduction amounts were investigated, and it can be seen that the calculated thickness reduction amount dR reproduces the actual thickness reduction amount dR.

[0092] As shown in Figure 9(B), when PWTs with different thickness reduction amounts dR (0.5, 1, 1.5, 2 mm) were investigated, it can be seen that the calculated length W reproduces the actually measured length W.

[0093] Reflectance parameter S 11 It can be seen that the absolute values ​​of the PWT size (thinning amount dR and length W) can be measured by the measurement.

[0094] (PWT position detection) Using F(Ω), it is possible to detect the position of the PWT. As shown in Figures 5(A) and (B), signals indicating the influence of the pipe end are confirmed from Ω number = 1100, and as shown in Figures 5(C) and (D), signals indicating the influence of PWT are confirmed from Ω number = 763. The total length of the pipe is 1.5×10=15 [m], and the Ω value of 1100 corresponds to a length of 15 [m]. The Ω value 763 corresponds to the location where the influence of the PWT is detected. Therefore, the number of Ω = 763 corresponds to the length 763 / 1100 × 15 [m] = 10.4 [m], which is the same as the actual distance to the PWT of 10.5 [m]. Since the total length of the pipe to be inspected can be actually measured, it is possible to calculate the position of the PWT from the waveform of F(Ω). In this way, the position of the PWT can be calculated from the value of Ω at the rising point of the first (smallest) peak in the first subband I (see S5 in FIG. 11).

[0095] The correspondence between Ω and distance can also be confirmed by another method. In detail, as described in Non-Patent Documents 1 and 2, S(ω) is transformed into the spatial domain to correspond the signal of S(ω) to the distance from the incident point of the electromagnetic wave. In the spatial domain, S(ω) is given by the following Fourier transform as a function of the propagation distance z: TIFF2026036661000014.tif12119 (Formula 13) where V gr is the group velocity and V gr =(λ0 / λ)c, where λ0 and λ are the wavelengths of the electromagnetic wave in a vacuum and in a pipe, respectively, and c is the propagation speed of the electromagnetic wave in a vacuum.

[0096] Figure 10 shows the parameter S measured for a standard pipe without a PWT. 11 is expressed in the spatial domain as h(z). The parameter S 11 was measured by sweeping the electromagnetic wave frequency range of 12.1 to 21.1 GHz at intervals of 1406250 Hz using a VNA. The vertical and horizontal axes of the graph in FIG. 10 represent the absolute value of h(z) and the propagation distance z, respectively. 10, the white arrows correspond to the ends of the standard pipes that make up the pipe, and the black arrow indicates the end of the test pipe 1. Also, FD, indicated by a white triangle, is the total propagation distance z, and FD = 87.4194 [m].

[0097] h(z) in the spatial domain corresponds to F(Ω) in the Ω domain, with z corresponding to Ω. By sweeping at equal intervals using the VNA described above, the discrete number of Ω becomes 6401, which corresponds to the total propagation distance FD (87.4194 [m]). Therefore, an Ω value of 1100 corresponds to a distance of 87.4194 x 1100 / 6400 = 15.0 m, which is equal to the total length of a standard pipe. The Ω value of 763 corresponds to a distance of 87.4194 × 763 / 6400 = 10.4 m, which is approximately the same as the actual distance to the PWT of 10.5 m. From the above, it was confirmed that the analytical results using h(z) in the spatial domain and the analytical results using F(Ω) in the Ω domain are consistent.

[0098] In addition, the group velocity V gr varies depending on the mode, and in a signal with a large number of mixed modes, the group velocity V gr It is difficult to convert using the group velocity V gr If h(z) is calculated using However, F(Ω) can be obtained by applying the usual known Fourier transform to S(ω).

[0099] From the above results, the reflection parameter S 11 The position of the PWT can be detected from the waveform of F(Ω) by converting (S(ω)) into F(Ω) in the Ω domain using a Fourier transform. Furthermore, F(Ω) is processed to extract F(Ω) for a specific region of Ω, and the S converted into the ω domain using an inverse Fourier transform is band The amount of thinning and length of the PWT can be evaluated from (ω).

[0100] (Embodiment 2) In the first embodiment, it is possible to evaluate the amount of thinning in a thinned portion where thinning has occurred over the entire circumference of a pipe. In the second embodiment, an inspection method is provided that makes it possible to evaluate the amount of thinning in a thinned portion where thinning has occurred only in a part of the pipe rather than over the entire circumference, and also to detect the amount of thinning and the central angle of the thinned portion that characterize the shape of the thinned portion. In contrast to the full-circumferential wall thinning in the first embodiment, wall thinning occurring in a part of the pipe is referred to as partial circumferential wall thinning.

[0101] Figures 12(A) and (B) show the configuration of a model pipe 2'' for explaining a method for inspecting thinned parts. Figure 12(A) shows a longitudinal cross section (Z-axis direction) of the model pipe 2'', and Figure 12(B) is a cross section (AA line cross section) perpendicular to the longitudinal direction of the model pipe 2'', showing a cross section of the thinned part. The model pipe 2'' is a simulation of an inspection pipe having a partial circumferential thinned part along the way, is conductive, functions as a waveguide for electromagnetic waves, and has an open end. Figures 12(C) and (D) show the effect of thinned sections on the frequency dependence of the propagation constant. The horizontal axis is frequency, and the vertical axis is the propagation constant. Figure 12(C) shows the results of a two-dimensional modal analysis performed on a cross section (see Figure 12(B)) with a thinning amount of ΔR=1 [mm], and Figure 12(D) shows the results of a two-dimensional modal analysis (inner radius R0=9.5 [mm]) on a cross section with a thinning amount of ΔR=2 [mm] (see Figure 12(B)). In Figure 12(C), "0" indicates no thinning, and "1-45", "1-90", "1-180", and "1-270" indicate data for ΔR=1 [mm] and central angle θ=45, 90, 180, and 270 [°], respectively. In Figure 12(D), "0" indicates no thinning, and "2-45", "2-90", "2-180", and "2-270" indicate data for ΔR=2 [mm] and central angle θ=45, 90, 180, and 270 [°], respectively. The propagation constant (rad / m) was calculated over the frequency range of 12.1 to 21.1 GHz with a step size of 0.2 GHz. In the following analysis, unless otherwise specified, the inner radius R0 was set to 9.5 mm. In order to distinguish it from the thickness reduction amount dR, which is the thickness change amount of the full circumferential thinning, the thickness reduction amount ΔR of the partial circumferential thinning is sometimes referred to as the partial thickness reduction amount.

[0102] As shown in FIG. 12(A), the inner radius of the normal part of the model pipe 2'' (i.e., the inner radius of the standard pipe) is R0, and the thinned part has a length W and a thinned amount ΔR. As shown in Figure 12(B), the model pipe 2'' has partial circumferential thinning in the thinned area within the range of the central angle θ. Hereinafter, partial circumferential thinning will be referred to as PCPWT (partial-circumferential pipe wall thinning). The amount of thinning ΔR and the central angle θ are parameters that specify the cross-sectional shape of the partial circumferential thinning. The end of the PCPWT is located at a distance L (Z=0) from the end of the model pipe 2'' (Z=-L), and the PCPWT is located in the range from Z=0 to Z=w in the Z-axis direction.

[0103] In Figures 12(C) and (D), the frequency at which the propagation constant becomes positive corresponds to the cutoff frequency. It can be seen that the cutoff frequencies increase in the order of TE11 mode, TM01 mode, TE21 mode, and TE01 / TM11 mode. The cutoff frequencies of the TE11 mode and TM01 mode are below the lower frequency limit of 12.1 GHz. It can also be seen that the cutoff frequencies of the TE21 mode and TE01 / TM11 mode are higher than that of the TM01 mode. In the example shown in Figure 12, it can be seen that the higher modes TE21 mode and TE01 / TM11 mode do not occur in the low frequency range below 13 [GHz], the TE21 mode occurs in the intermediate frequency range from 13 [GHz] or more to below 16 [GHz], but the TE01 / TM11 mode does not occur, and the TE01 / TM11 mode occurs in the high frequency range above 16 [GHz]. The TM01 mode, which is the electromagnetic wave (sometimes referred to as the incident electromagnetic wave) incident on the model pipe 2'', is sometimes referred to as the lower mode (or fundamental mode), and the mode of the electromagnetic wave with a higher cutoff frequency than the TM01 mode is sometimes referred to as the higher mode. As described above, the TEM mode-TM01 mode converter causes TM01 mode electromagnetic waves (sometimes referred to as incident electromagnetic waves) to be incident on the model pipe 2''. Therefore, the TM01 mode, which is the dominant mode, is sometimes referred to as a lower-order mode, and electromagnetic wave modes with a cutoff frequency higher than that of the TM01 mode are sometimes referred to as higher-order modes. As shown in Figures 12(C) and (D), the cutoff frequency of the TE11 mode electromagnetic wave is lower than that of the TM01 mode electromagnetic wave and can propagate across the entire frequency range, so PCPWT information cannot be obtained from the TE11 mode electromagnetic wave. Therefore, the TE11 mode is not used in PCPWT analysis.

[0104] It can also be seen that the cutoff frequencies of the TE21 mode and the TE01 / TM11 mode decrease as the central angle θ increases, and the cutoff frequency for a metal loss ΔR of 2 mm is lower than the cutoff frequency for a metal loss ΔR of 1 mm. It can also be seen that the cutoff frequencies of the TE21 mode and the TE01 / TM11 mode are significantly affected by the metal loss ΔR and the central angle θ.

[0105] Figure 13 shows the reflection parameter S obtained by irradiating electromagnetic waves in TM01 mode from the end (Z=0) of the model pipe 2''. 11 The horizontal axis is frequency, and the vertical axis is reflection parameter S 11 The conditions for PCPWT are: position L = 100 [mm], length w = 40 [mm], thickness reduction ΔR = 2 [mm], and central angle θ = 360, 270, 180, 90, 45 [°]. For simplicity, the reflection parameter S 11 Simply use the parameter S 11 It is sometimes referred to as.

[0106] When the central angle θ=360° corresponding to the full circumference thinning, the parameter S 11 It can be observed that the waveform of varies smoothly and regularly with frequency. On the other hand, when the central angles are 270, 180, 90, and 45°, which correspond to partial circumferential thinning, the parameter S 11 It can be observed that the smooth waveform of the waveform becomes discontinuous as the frequency increases, and outliers become more pronounced. In this way, the effect of partial circumferential thinning is expressed by the parameter S 11 It can be seen that these appear as outliers in the smooth waveform of the waveform, and are particularly noticeable in the higher frequency region than the smooth waveform region.

[0107] According to the inspection method shown in the first embodiment, the parameter S shown in FIG. 11 S low 11 (ω)S hi (ω). For simplicity, S low 11 (ω) to S low , S hi (ω) to S hi It is written as follows. Figure 14(A) shows the S when the thickness reduction amount ΔR=2[mm] and the central angle θ=270[°]. low and S hi The frequency dependence of S at thickness reduction ΔR=1[mm] and central angle θ=45~360[°] is shown in Fig. 14(B). low Absolute value of |S low The frequency dependence of | is shown. 11 S constructed from low is F(Ω i ) (-30≦i≦30). The legend in FIG. 14(B) indicates the correspondence between the symbols and the central angle θ.

[0108] As shown in the dashed line in Figure 14(A), the S 11 Built from S hi It can be seen that the TE21 mode occurs in the mid-frequency region and the TM11 mode occurs in the high-frequency region. On the other hand, S low In the low frequency range, especially in the frequency range below 16 GHz, the S low It can be seen that the same beat pattern is obtained.

[0109] As shown in FIG. 14(B), in the frequency range below 16 GHz, |S low It can be seen that the peak value of | changes depending on the central angle θ (see the area surrounded by the dashed line in Figure 14(B)). The average thickness loss <ΔR> is defined as <ΔR> = ΔRθ / 360, and the correlation between the average thickness loss <ΔR> and the peak value of the beat waveform in the low frequency range is investigated. The results are shown in Figure 14(C). It can be seen that there is a linear relationship between the peak value and the average thickness loss <ΔR>. In Figure 14(C), the symbol "◆ (diamond)" indicates partial circumferential thinning with a thickness reduction of ΔR = 1 [mm], the symbol "▲ (triangle)" indicates partial circumferential thinning with a thickness reduction of ΔR = 2 [mm], and the symbol "×" indicates a central angle θ of 360 [°], which corresponds to full circumferential thinning. It can be seen that the full circumferential thinning and the average partial circumferential thinning have the same linear relationship with respect to the peak value.

[0110] The cross-sectional area A of the PCPWT having the thickness reduction amount ΔR and the central angle θ is calculated as follows: A=πR0 2 +π[(R0+ΔR) 2 -R0 2 ]θ / 360 (Equation 14) ΔR is sufficiently small compared to R0, and if the contribution of the square of ΔR is ignored, the cross section A can be approximated as follows: A=π(R0+<ΔR>) 2 (Formula 15) The linear relationship shown in Figure 14(C) is the cross-sectional area A = π(R0 + <ΔR>) 2 This is consistent with the correlation between the maximum value of the beat waveform and the amount of metal loss for the entire circumference of the thinning. Therefore, instead of the inner radius a1 and the amount of thinning dR, it is possible to apply the analysis of embodiment 1 to a circumferential thinning having a pseudo inner radius R0 and an average amount of thinning <ΔR>. Therefore, even in the case of partial circumferential thinning, it is possible to calculate the position L of the thinned part and the length w and average amount of thinning <ΔR> as the dimensions of the thinned part. Therefore, it is possible to confirm whether or not there is a thinned part with an average amount of thinning <ΔR>.

[0111] However, the average thickness reduction amount <ΔR> is ΔRθ / 360, and since the thickness reduction amount ΔR and the central angle θ cannot be detected separately, the cross-sectional shape of the partial circumferential thickness reduction cannot be identified. In order to separately obtain ΔR and θ, the parameter S 11 The electromagnetic wave components of the higher order modes of the waveform are analyzed. An inspection method that can separately detect ΔR and θ will be described below.

[0112] As shown in Figure 13, the parameter S 11 In this case, the influence of higher modes appears as outliers. As shown in Figure 14(B), outliers are observed at frequencies around 18 GHz. It can also be seen that the outliers are at their maximum when the central angle θ is 180°, and it is believed that these outliers contain information about the central angle θ. (See the area surrounded by the dashed line in Figure 14(B).) In addition, |S low As can be seen from the waveform of |, the parameter S 11 Constructed from |S low | has ripples, making outlier detection difficult. To extract outliers, the parameter S measured using a VNA 11 Singular Spectral Analysis (SSA), a non-parametric spectral analysis, can be applied to the signal. By using this type of spectral analysis, it is possible to extract various parameters S 11 It is possible to extract a smooth waveform that eliminates ripple components. In addition, the parameter S 11 is output in the frequency domain or the angular frequency domain. The frequency and angular frequency differ only by a multiplier of 2π and are equivalent to each other, and are sometimes collectively referred to as the frequency domain. In the following description, the parameter S 11 Although an example in which is output in the angular frequency (ω) domain is shown, it may also be output in the frequency (f) domain.

[0113] Parameter S displayed in the angular frequency (ω) domain 11The absolute value of |S 11 | is the absolute value |S| of the slowly oscillating component caused by pseudo full - circumference meat reduction having an average meat reduction amount <ΔR>. lw And |S| is a residual component reflecting the influence of high - order modes due to the nature of partial - circumference meat reduction. hi It is decomposed into these two. Here, |S| hi is the difference between |S 11 | and |S| lw and is defined by the following formula 16. |S| hi =|S 11 |-|S| lw (Formula 16) Note that the parameter S 11 may be expressed as S(ω i )(i = 1~N) to clarify the angular frequency dependence.

[0114] Based on the method of singular - spectrum analysis, the absolute value |S(ω i )| of S(ω i ) is embedded in an M - dimensional vector space. Here, the window width M is greater than 1 and less than N (1 < M < N). As the value of M, for example, M = N / 5 can be set. When N = 361, N = 72. Let K = N - M + 1 and form a trajectory matrix G of an M×K matrix. G=[G1:···:G k (Formula 17) Here, G i =(g i ,···,g i+M-1 ) T (1≦i≦K) is a lagged vector of size M, g[[ID=5^1]] i is the value of |S i | for the angular frequency ω 11 and g i =|S(ω i )|.

[0115] Next, perform singular - value decomposition (Singular Value Decomposition) on the trajectory matrix G. Y = GG T The eigenvalues γ i(i=1, , M) and calculate the eigenvalue γ i The eigenvector U corresponding to i (i=1, ,M) is obtained. Note that the eigenvalue γ i are sorted in order of magnitude. Figure 15(A) shows the |S 11 eigenvalue γ of | i The first four eigenvalues ​​γ i (i=1, 2, 3, 4) are the other eigenvalues ​​γ i (i≧5), accounting for more than 90% of the total. i (i=1, 2, 3, 4) are sometimes called principal eigenvalues. Four principal eigenvalues ​​γ i The eigenvector U corresponding to i (i=1, 2, 3, 4) and |S 11 |S|, which is the main part of | lw The principal eigenvalue γ i The eigenvector U corresponding to i is sometimes called the principal eigenvector.

[0116] Figure 15(B) shows |S for θ=270, 180, and 90°. 11 |, |S| lw and |S| hi In Fig. 15(B), the solid line indicates the frequency (f) dependence of |S 11 |, dashed line indicates |S| lw , the dashed line is |S| hi and the symbols "*" and "×" indicate |S| lw The peak and beat points of |S| are shown. lw The beat frequency can be calculated from the difference between the two beat points, and the length of the thinned portion w can be calculated based on Equation 3. |S| lw has a smooth curve with outliers separated, and is constructed from low Ω numbers |S low It shows the same trend as |S| lw is S 11 Low Ω component S low This can be interpreted as reflecting the The reflection parameter S11 For |S| lw are sometimes called "low-order reflection parameters". 11 | and |S| lw The difference between |S| hi are sometimes called "higher-order reflection parameters". |S| lw contains the information of the reflection of the TM01 mode, which is mainly the incident electromagnetic wave, and |S| hi is considered to contain information on the reflection of higher mode electromagnetic waves.

[0117] In addition, |S 11 This does not preclude the use of other mathematical methods, such as neural networks (NNs) and empirical dynamic modeling (EDMs), as analytical methods for reproducing the principal smooth waveforms of |. In the case of singular spectrum analysis, the number of principal eigenvalues ​​can also be determined appropriately from the obtained eigenvalues.

[0118] Figure 16(A) shows that |S| lw Peak value at the peak point of |S lw | pk and the average thickness reduction amount <ΔR>. Here, the symbols "◆ (diamond)", "■ (square)", "▲ (triangle)", and "× (cross)" indicate examples of PCPWT thickness reduction amount ΔR = 0.5, 1, 1.5, and 2 [mm], respectively. For any thickness reduction amount ΔR, the peak value |S lw | pk and the average thickness loss <ΔR> are in a linear relationship, and it can be confirmed that the linear relationship in Figure 14(C) is reproduced. Peak value |S lw | pk Since it is possible to detect the average amount of thinning <ΔR> from the above, it is possible to determine whether or not thinning has occurred from the value of the average amount of thinning <ΔR>.

[0119] To calculate the amount of thinning ΔR and the central angle θ, information on electromagnetic waves in higher modes (TE21 mode and TE01 / TM11 mode) is further utilized. Figure 16(B) shows the peak value |S lw | pkFIG. 16(C) is a contour map (referred to as a first contour map) showing the correlation between |S| and the thickness reduction amount ΔR and the central angle θ in the high frequency region above 16 [GHz]. hi The maximum value of the peak |S hi | mx 10 shows a contour map (referred to as a second contour map) showing the correlation between the thickness reduction amount ΔR and the central angle θ.

[0120] In order to create the first contour map and the second contour map, for example, the thickness reduction amount ΔR is changed in the range of 0.5 to 2 [mm] and the central angle θ is changed in the range of 30 to 360 [°], and |S 11 Calculate | and |S 11 | to peak value |S lw | pk and maximum peak value |S hi | mx In this way, the peak value |S lw | pk and maximum peak value |S hi | mx 16B and the second contour map shown in FIG. 16C can be obtained. S in Figure 14(A) hi Referring to the waveform of FIG. 1, the first contour map and the second contour map are considered to reflect the influence of different electromagnetic wave modes.

[0121] Hereinafter, the first contour map and the second contour map are used to measure the reflection parameter S 11 Next, a method for detecting the amount of thinning ΔR and the central angle θ will be described. FIG. 17(A) is a diagram illustrating a cross-sectional shape analysis process for detecting the amount of wall thinning ΔR and the central angle θ of the pipe to be inspected using a first contour map and a second contour map prepared in advance.

[0122] The first and second contour maps are prepared by simulation. Since the inner radius R of a normal pipe is known, electromagnetic simulation is performed for the estimated range of wall thinning ΔR and central angle θ to obtain the reflection parameter S 11 The calculated reflection parameter S 11 The absolute value of the low-order reflection parameter |S| is calculated by singular spectrum analysis. lw and high-order reflection parameters |S| hi Then, |S| lw Peak value of |S lw | pk and |S| hi Maximum peak value of |S hi | mx Calculate the thickness reduction amount ΔR and the central angle θ for |S lw | pk The first contour map of |S hi | mx A second contour map of the The reflection parameter S 11 To distinguish between the first and second contour maps, the reflectance parameter S 11 The model reflection parameters ( m S 11 ) and the model reflection parameters m S 11 The low-order reflection parameters and high-order reflection parameters constructed from the m S| lw ) and higher-order model reflection parameters (| m S| hi ) is sometimes referred to as

[0123] A method for analyzing the cross-sectional shape of a PCPWT will be specifically described below with reference to Fig. 17(A). The cross-sectional shape analysis process shown in Fig. 17(A) can be performed using an arithmetic device equipped with a storage device such as a computer. To verify this method, the reflection parameters S of a PCPWT with length w = 40 [mm], ΔR = 1.8 [mm], and θ = 270° are as follows:11 was calculated by simulation and used. Figure 17(B) shows the reflection parameter |S 11 |, |S 11 Built on |S| lw and |S| hi 17(C) shows the frequency (f) dependence of the frequency (f). Figure 17(C) shows contour lines selected from the first contour map and the second contour map of Figures 16(B) and 16(C) (referred to as the first contour line and the second contour line, respectively), where the dashed lines indicate the selected first specific contour lines and the solid lines indicate the selected second specific contour lines.

[0124] (Step 0): Contour map preparation step As described above, the first contour map and the second contour map are generated by simulation. The created first contour map and second contour map can be stored as data in a storage device or the like. The first contour map and the second contour map can be generated by the same method as steps 1 to 3 below. Therefore, the part enclosed by the dashed line in FIG. 17(A) is executed when the data is created and when the actual measurement is performed. However, in step 1, the model reflection parameters m S 11 Use the model reflection parameters m S 11 can be generated by simulation, but in practice, PCPWTs with various known thickness reduction amounts ΔR and central angles θ are artificially manufactured, and the model reflection parameters are calculated by actual measurements using a VNA as described in Step 1. m S 11 may be obtained.

[0125] (Step 1): Reflection parameter S 11 Acquisition Steps The electromagnetic wave in TM01 mode is incident on the pipe to be inspected, and the reflection parameter S is measured using the VNA. 11 The measured reflection parameter S 11is input to the arithmetic unit.

[0126] (Step 2): Low-order reflection parameters |S| lw Construction steps The measured reflectance parameter S 11 (Specifically, the absolute value of the reflection parameter |S 11 |) based on the low-order reflection parameters |S| lw Build. (Step 2-1): Peak value |S lw | pk Acquisition Steps |S| lw Peak value of |S lw | pk For example, |S| shown in FIG. lw In the example, the peak value |S lw | pk and get "0.46868". In addition, the peak value |S lw | pk is sometimes referred to as the first peak value. (Step 2-2): First contour selection step Peak value |S for the thickness reduction amount ΔR and central angle θ prepared in advance lw | pk From the first contour map of |S lw | pk Select the first contour line corresponding to Specifically, the contour line having the first peak value "0.46868" from the first contour map is selected as the first contour line. Since the contour lines of the first contour map are finite, the first contour lines may be reconstructed and selected by an interpolation method such as interpolation, and the same applies to the second contour lines of the second contour map.

[0127] (Step 3): High-order reflection parameters |S| hi Construction steps |S 11 | and |S| lw By subtracting from the higher-order reflection parameter |S|hi (=|S 11 |-|S| lw ) to build a (Step 3-1): Maximum peak value |S hi | mx Acquisition Steps |S| hi Maximum peak value of |S hi | mx For example, |S| shown in FIG. hi In this case, the maximum peak value |S hi | mx and get "0.34351". The maximum peak value |S hi | mx is sometimes referred to as the second peak value. (Step 3-2): Second contour selection step The maximum peak value |S for the thickness reduction amount ΔR and central angle θ prepared in advance hi | mx The maximum peak value obtained from the second contour map of |S hi | mx Select the second contour line corresponding to

[0128] (Step 4): Step to determine the amount of thinning and the central angle (step to identify the cross-sectional shape) The amount of thinning ΔR and the central angle θ corresponding to the intersection point between the first specific contour line and the second specific contour line (the point indicated by the symbol "◇ (diamond)" in Figure 17(C)) are determined (see the dashed line in Figure 17(C)). Through the above steps, it is possible to uniquely determine the thickness reduction amount ΔR and the central angle θ that satisfy both the values ​​of the first specific contour line and the second specific contour line, thereby detecting the cross-sectional shape of the PCPWT.

[0129] Thus, the measured reflectance parameter S 11 By analyzing the higher-order mode electromagnetic wave components contained in the PCPWT, it is possible to separate and calculate the thickness reduction amount ΔR and the central angle θ of the PCPWT. The thickness reduction amount ΔR and the central angle θ are parameters that reflect the cross-sectional shape of the PCPWT, and as a result, it is possible to analyze the cross-sectional shape of the PCPWT. The piping to be inspected is a conductive electromagnetic wave waveguide, and is not limited to the shapes shown in FIG. 1 or FIG. [Industrial Applicability]

[0130] According to the present invention, by irradiating an electromagnetic wave and analyzing reflection parameters, it is possible to quantitatively detect the position, amount and length of a thinned portion of a pipe in a non-destructive manner. Reflection parameters can be measured using a commercially available vector network analyzer, and well-known Fourier transform and inverse Fourier transform techniques can be used. Conductive piping can be inspected non-destructively, and the present invention has great industrial applicability. [Explanation of symbols]

[0131] 1 Inspection piping 2, 2', 2'' model piping PWT thinning area VNA Vector Network Analyzer SG1, SG2 standard piping

Claims

1. This is a method for inspecting thinned parts of pipes. obtaining reflection parameters of electromagnetic waves from the piping in the frequency domain; a transforming step of transforming said reflectance parameters into transformed reflectance parameters in a transform-to-domain corresponding to said frequency domain by a Fourier transform; a calculation step of performing band extraction processing on the transformed reflection parameters to obtain transformed band reflection parameters; an inverse transform step of transforming the transformed banded reflection parameters back from the transformed pair domain to the frequency domain banded reflection parameters by an inverse Fourier transform; an analysis step of analyzing the dimensions of the thinned portion from the beat waveform of the banded reflection parameters; An inspection method comprising:

2. 2. The inspection method according to claim 1, wherein the band extraction extracts a component caused by the thinned portion.

3. 3. The inspection method according to claim 1, wherein the analyzing step calculates the amount of thinning of the thinned portion from the maximum value of the beat waveform of the reflection parameter.

4. 3. The inspection method according to claim 1, wherein the analyzing step calculates the amount of thinning of the thinned portion from the maximum value of the reflection parameter, and calculates the length of the thinned portion from the beat frequency.

5. 3. The inspection method according to claim 1, wherein the calculation step calculates the position of the thinned portion from the waveform of the converted reflection parameter.

6. 3. The inspection method according to claim 1, wherein the electromagnetic wave is in TM01 mode.

7. This is a method for inspecting thinned parts of pipes. a reflection parameter acquisition step of acquiring reflection parameters of an electromagnetic wave incident on the pipe in a frequency domain; a shape analysis step, The shape analysis step includes: constructing low-order model reflection parameters from absolute values ​​of model reflection parameters due to the thinned portion and high-order model reflection parameters which are differences between the absolute values ​​of the model reflection parameters and the low-order model reflection parameters, and preparing in advance a first contour map which indicates a correlation between the amount of thinning and central angle which specify a cross-sectional shape of the thinned portion and the peak value of the low-order model reflection parameters, and a second contour map which indicates a correlation between the amount of thinning and central angle and the maximum peak value of the high-order model reflection parameters; constructing the low-order reflection parameters from the absolute values ​​of the reflection parameters acquired for the pipe and the high-order reflection parameters which are the differences between the absolute values ​​of the reflection parameters and the low-order reflection parameters, selecting a first contour line from the first contour map based on the peak value of the low-order reflection parameters, and selecting a second contour line from the second contour map based on the maximum peak value of the high-order reflection parameters; and calculating the amount of wall thinning and the central angle of the pipe based on the first contour line and the second contour line.

8. 8. The inspection method according to claim 7, wherein the length of the thinned portion is calculated from the beat frequency of the low-order reflection parameter.

9. 8. The inspection method according to claim 7, wherein an average amount of thinning of the thinned portion is calculated from the peak value of the low-order reflection parameter.

10. 8. The inspection method according to claim 7, wherein the incident electromagnetic wave is in TM01 mode, and the high-order reflection parameters are due to reflection by an electromagnetic wave having a cutoff frequency higher than the cutoff frequency of the TM01 mode.

11. 8. The method of claim 7, wherein the low-order reflectance parameters are constructed by singular spectrum analysis.

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