Low-frequency ultrasonic scanning imaging quantitative detection method for large-depth submillimeter defects

Abstract

The invention discloses a low-frequency ultrasonic scanning imaging quantitative detection method for large-depth submillimeter-level defects, and belongs to the technical field of ultrasonic nondestructive testing. The method comprises the following steps: acquiring A-type ultrasonic signals p0 (t) of multiple groups of position codes by adopting an ultrasonic detector, calculating a synthetic aperture length and an apodization coefficient according to a sound field distribution rule of an ultrasonic probe, synthesizing a signal ps (t) of each coding position by adopting a delay superposition rule, decomposing the ps (t) into N sub-signals by adopting a split spectrum analysis method with variable center frequency fi and variable bandwidth, and calculating the position code of the A-type ultrasonic signals p0 (t); sub-signals with the same center frequency are combined with coding information to generate a scanning image Imi, the defect size di in the Imi is measured according to a-6dB method, a sound field directivity function is adopted to fit a change curve of di along with fi, and di corresponding to the slope k of the recognition curve =-0.01 is the defect size. According to the method, the problems that the resolution of a traditional synthetic aperture focusing method is limited by the size of a probe and the signal-to-noise ratio of multi-resolution scanning imaging is low are solved, and high-signal-to-noise-ratio and high-precision quantitative detection of submillimeter defect sizes in a large depth range can be realized by adopting low-frequency ultrasound.

Description

Technical Field

[0001] The invention discloses a quantitative detection method of deep sub-millimeter-level defects by low-frequency ultrasonic scanning imaging, belonging to the technical field of ultrasonic non-destructive testing. Background Art

[0002] During the manufacturing or service process of new materials such as additively manufactured high-temperature alloys, high-entropy alloys, and carbon fiber composites, due to the combined effects of the material's own characteristics, parameter settings during the production process, and external environmental conditions, "hidden" micro-defects such as pores, cracks, and unfused parts are easily generated inside. The size is mostly tens of microns to hundreds of microns, which seriously affects the tensile strength, ductility, and fatigue strength of parts. As key equipment has higher and higher requirements for the performance of parts, the defect detection standards are becoming more and more stringent, and the accuracy requirements for defect positioning and quantitative detection have also been increased from millimeters to sub-millimeter levels. Therefore, quantitative non-destructive testing of sub-millimeter defects is crucial to ensure the comprehensive performance indicators of key components.

[0003] Ultrasonic testing has high sensitivity, intuitive results, high efficiency, and a wide range of applications. It can be used for the automated characterization and evaluation of defects. It is currently widely used in the detection of defects of millimeter size and above. However, when ultrasonic testing of submillimeter defects of parts and components is performed, the echo signal amplitude caused by submillimeter defects is usually weak due to the inhomogeneity and anisotropy of the material structure. Moreover, when the defect size is less than half the wavelength or less than the diameter of the sound beam, it is easily submerged by structural noise, resulting in defect leakage. Many scholars have conducted in-depth research on ultrasonic testing of submillimeter defects of parts and components, mainly by expanding the probe aperture and optimizing the threshold algorithm to improve the defect detection effect. Chen Jiaming et al. proposed an improved synthetic aperture focusing technique (SAFT) for the internal defect detection of additively manufactured titanium alloys, which can improve the signal-to-noise ratio of the detection signal of rough surface samples. The improved SAFT improves the resolution of the detection system. The experimental results show that the SAFT of ultrasonic signals can detect artificial defects with a diameter of 0.2 mm to 0.75 mm in the sample. Qin et al. developed a threshold determination method based on the statistical theory of noise extreme values ​​for alloy parts with strong scattering effects, and proposed a time-domain two-dimensional synthetic aperture C-scan (SAFT-C) imaging method to realize ultrasonic C-scan identification of micro defects inside strongly scattering alloy components. The 9.8 MHz water immersion point focusing probe was used to effectively identify all flat-bottom hole defects with a diameter of not less than 0.2 mm in 304 stainless steel test blocks. The above work is also mainly focused on improving the quantification of millimeter-level defects and the detection rate of submillimeter defects (0.1~0.8 mm). At present, the ultrasonic quantitative detection of defect sizes below 0.8 mm still faces huge challenges and needs to be further studied.

[0004] Traditional phased array ultrasonic or ultrasonic C-scan detection can improve the lateral resolution of scanning imaging to a certain extent by increasing the probe aperture, increasing the probe frequency, optimizing the threshold and other methods, and improve the detection capability and quantitative accuracy of submillimeter defects. However, it is still difficult to accurately quantify submillimeter defects smaller than the resolution, and it will also introduce new problems such as reduced signal-to-noise ratio, insufficient detection depth, and poor quantitative accuracy of defects far from the focus. The present invention aims at the key technical difficulties of ultrasonic quantitative detection of submillimeter defect sizes within a large depth range of parts, proposes an adaptive variable bandwidth split spectrum analysis method, and develops a multi-resolution C-scan quantitative detection technology (Synthetic aperture focusing multi-resolution C-scan, SAF-MRC) that integrates ultrasonic synthetic aperture focusing, so as to achieve high signal-to-noise ratio and high-precision quantitative detection of submillimeter defect sizes within a large depth range of parts. Summary of the invention

[0005] The present invention proposes a method for quantitative detection of deep submillimeter defects with low-frequency ultrasonic scanning imaging, which overcomes the contradiction between the lateral resolution and detection depth of traditional ultrasonic C-scan imaging technology, and solves the problem that the low probe frequency and large aperture size of phased array ultrasonic imaging detection lead to the difficulty in quantitatively detecting the size of hundreds of micrometer-level defects. Under the premise of ensuring the signal-to-noise ratio, this method effectively improves the detection depth and resolution, and realizes quantitative detection of micrometer-level defects. It has a wider scope of application, is simple and easy to apply in engineering, and can be applied to all ultrasonic scanning imaging detection technologies, with great economic and social benefits.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a quantitative detection method of deep sub-millimeter defect low-frequency ultrasonic scanning imaging, the method comprising the following steps:

[0007] (1) Calibrate the ultrasonic detector, low-frequency ultrasonic probe, and step encoder, perform coded scanning detection on the object to be inspected, and collect M groups of coded ultrasonic A-type ultrasonic signals p0(t), where t represents the time information of the ultrasonic signal;

[0008] (2) Based on the acoustic field distribution law of the ultrasonic probe and the acoustic field position of the target area to be inspected, the effective synthetic aperture length L and the apodization coefficient w (ΔL) are calculated, where ΔL represents the horizontal distance from the central axis of the acoustic field;

[0009] (3) According to the target point position Q0 in the target area to be inspected and combined with the effective synthetic aperture length L, determine the positions Q of all participating points used for synthetic aperture focusing I , calculate the acoustic delay τ corresponding to each moment in the depth direction z from all participating points to the target point;

[0010] (1)

[0011] Where τ is the sound delay, unit is s;

[0012] (4) The number of reconstructed positions in the depth direction is equal to the number of ultrasonic signal sampling. The signals at all depths are “delayed and superimposed” according to the acoustic delay τ to obtain the reconstructed ultrasonic signal p at the target point position Q0. s (t):

[0013] (2)

[0014] where w(ΔL) is the apodization coefficient within the synthetic aperture, x j Indicates the sampling location;

[0015] (5) The signal p synthesized in step (4) s (t) Perform fast Fourier transform to obtain its amplitude spectrum A(f), and identify the effective frequency band corresponding to half the amplitude of A(f) [f l , f u ], the effective frequency band is divided into N center frequencies f i The filter band of , i is a natural number from 1 to N;

[0016] (6) Use bandpass filtering method with center frequency f i P s (t) The signal is split spectrum analyzed to obtain signals with different center frequencies f i The sub-signal p i (t), filter bandwidth b i According to the sub-signal energy E i The total energy E of the sum signal satisfies 10lg(E / E i ) <Signal to noise ratio relationship is determined;

[0017] (7) Different coding positions with the same center frequency f i The sub-signal p i (t) Perform amplitude imaging to obtain N scanning images Im with different frequency characteristics and multiple resolutions i ;

[0018] (8) Scan the image Im for each resolution i The "-6dB method" is used to detect the defect size d i , and draw N detected defect sizes d i Follow i The change curve of

[0019] (9) Analyze the directivity function of the ultrasonic probe based on the principle of acoustic reciprocity c , that is, the sound field distribution function, the directivity function of the ultrasonic probe D cIt can also be pre-determined by numerical simulation, such as formula (3), where D is the probe size, in mm, λ is the wavelength in the inspected component, in mm, and θ is the sound wave diffusion angle, in radians;

[0020] D c =function(D, λ, θ) (3)

[0021] (10) At a specific depth z of a component with a sound velocity of v, according to the ultrasonic probe directivity function D c The theoretical beam width is determined by reducing the maximum amplitude by half, which is the detection defect size d of the ultrasonic scanning image at each resolution. i , according to λf=v, the detection defect size d is derived i With the center frequency f i The quantitative formula (4);

[0022] d i =function(D, f i , v, z) (4)

[0023] (11) Substitute the known ultrasonic probe size D and the component sound velocity v into formula (4), and calculate the defect size d determined in step (10) i Follow i Linear fitting is performed based on the changing rules;

[0024] (12) Then take the derivative of the fitting curve with respect to frequency f and determine the d corresponding to the slope k = -0.01 of the fitting curve. i This is the quantitative size of the actual defect.

[0025] The effects and benefits of the present invention are as follows: the present invention proposes a quantitative detection method for sub-millimeter defects at great depth using low-frequency ultrasonic scanning imaging. It is only necessary to use a low-frequency ultrasonic probe for coded scanning detection, combine synthetic aperture focusing and split spectrum analysis to obtain a multi-resolution scanning image and detect the defect size in each resolution scanning image, and accurately quantify the size of all detected defects according to the directivity function of the ultrasonic probe. The method can achieve high signal-to-noise ratio and high-precision quantitative detection of tiny defects at great detection depth using low-frequency ultrasound. It overcomes the limitations of the traditional "-6dB method" that requires the probe resolution to be smaller than the defect size and the "equivalent method" that requires a large number of comparison test blocks, and also overcomes the limitations of the high-frequency focusing probe's large attenuation, low signal-to-noise ratio, and insufficient detection depth. It is also not limited by the size, shape, and scanning imaging method of the ultrasonic probe, and has extremely strong engineering applicability. It has a wide range of applications, is simple and easy to apply in engineering, and can be extended to all ultrasonic scanning imaging detection technologies, with great economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1It is a schematic diagram of an ultrasonic C-scan detection system.

[0027] Figure 2 It is the position-coded ultrasonic A-type echo signal p0(t) collected by the ultrasonic detection system.

[0028] Figure 3 This is a schematic diagram of the probe sound field distribution when the defocus distance is 8 mm.

[0029] Figure 4 is the ultrasonic signal p reconstructed by the synthetic aperture of the nominal Φ400 μm defect s (t) Comparison with the original signal.

[0030] Figure 5 is the amplitude spectrum of the synthetic signal of Φ400 μm defect.

[0031] Figure 6 This is a scanned image of a defect with a nominal size of Φ400 μm when the center frequency of the filter band is 16 MHz.

[0032] Figure 7 The defect size of Φ400 μm is d i Follow i Change curve.

[0033] Figure 8 It is a schematic diagram of the probe sound field distribution at the focal position.

[0034] Fig. 9 is the amplitude spectrum of the synthetic signal of Φ200 μm defect.

[0035] Fig.10 This is a scanned image of a defect with a nominal size of Φ200 μm when the center frequency of the filter band is 31 MHz.

[0036] Fig.11 The defect size of Φ200 μm is d i Follow i Change curve.

[0037] Figure 1 In: 1. 3D printed nickel-based high-temperature alloy specimen, 2. Low-frequency ultrasonic probe, 3. XYZ three-dimensional stepping encoder, 4. Ultrasonic detector, 5. Computer with signal processing software. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] Figure 1 The schematic diagram of the ultrasonic C-scan detection system is shown in FIG. 1 , which includes a 3D printed nickel-based high-temperature alloy sample 1, a GEUSIP 40 ultrasonic detector 4, a low-frequency ultrasonic probe 2, an XYZ three-dimensional stepping encoder 3, and a computer 5 with signal processing software. The detection steps adopted by the detection method are as follows:

[0040] Example 1

[0041] The ultrasonic C-scan detection system used in this embodiment includes a 3D printed nickel-based high-temperature alloy sample 1, a low-frequency ultrasonic probe 2 (a water immersion point focusing probe with a nominal frequency of 20 MHz), an XYZ three-dimensional stepping encoder 3, a GE USIP 40 ultrasonic detector 4, and a computer 5 with signal processing software, such as Figure 1 As shown, the 3D printed nickel-based high-temperature alloy specimen is a specimen containing a pore-type defect with a nominal diameter of Φ400 μm, and the detection steps used are as follows:

[0042] (1) The GE USIP 40 ultrasonic detector, the water immersion point focusing probe with a nominal frequency of 20 MHz, and the XYZ three-dimensional stepping encoder were calibrated to perform encoding scanning on the 3D printed nickel-based high-temperature alloy sample to be inspected. The ultrasonic detection system was used to collect 60×60 sets of position-encoded ultrasonic A-type echo signals p0(t) of a Φ400 μm defect with an 8 mm defocus in the non-focal column area, see Figure 2 .

[0043] (2) Sound field distribution based on low-frequency focused probe, such as Figure 3 As shown, the effective synthetic aperture length L located in the non-focal column area with a focus deviation of 8 mm is calculated to be 0.45 mm.

[0044] (1)

[0045] Where z is the depth in mm, and a is the diffusion angle of the probe in radians.

[0046] (3) According to the target point position (x0, y0) in the target area and the effective synthetic aperture length L = 0.45 mm in the non-focal area, determine all participating points (x i , y j ). Calculate the acoustic delay τ at each depth from all synthetic aperture participating points to the target point.

[0047] (2)

[0048] (4) The number of reconstructed positions in the depth direction is equal to the number of samples. The amplitudes at all depths are combined to reconstruct 60×60 groups of ultrasonic signals. Ultrasonic signal p after synthetic aperture reconstruction of Φ400 μm defect s (t) Compared with the original signal Figure 4 shown.

[0049] (3)

[0050] where w(ΔL) is the apodization coefficient within the synthetic aperture, x j Indicates the sampling location.

[0051] (5) The signal p synthesized in step (4) s (t) Perform fast Fourier transform to obtain its amplitude spectrum A(f), as Figure 5 As shown in the figure, identify the effective frequency band [10.2 MHz, 29.4 MHz] corresponding to half the amplitude of A(f), and divide the effective frequency band into 9 center frequencies f i filter band.

[0052] (6) Using split spectrum analysis with center frequency f i P s (t) The signal is band-pass filtered to obtain signals with different center frequencies f i The sub-signal p i (t), filter bandwidth b i According to the sub-signal energy E i The total energy E of the sum signal satisfies 10lg(E / E i ) <21.8dB confirmed.

[0053] (7) The center frequency f of different encoding positions i The sub-signal p i (t) Perform amplitude imaging to obtain 9 scanning images Im with different frequency characteristics and multiple resolutions i , where the scanning image of a defect with a nominal size of Φ400 μm when the filter band center frequency is 16 MHz is as follows Figure 6 shown.

[0054] (8) Scan the image Im for each resolution i The "-6dB method" is used to detect the defect size d i , and plot the defect size d detected by ultrasonic scanning imaging at 9 resolutions i Follow i The change curve is as Figure 7 shown.

[0055] (9) Analyze the directivity function of the ultrasonic probe based on the principle of acoustic reciprocity c , that is, the sound field distribution function, the directivity function of the ultrasonic probe D c It can also be pre-determined by numerical simulation, such as formula (4), where D is the probe size, in mm, λ is the wavelength of the component to be tested, in mm, and θ is the sound wave diffusion angle, in radians.

[0056] (4)

[0057] (10) At a specific depth z of a component with a sound velocity of v, according to D c The theoretical beam width is determined by reducing the maximum amplitude by half, which is the defect size d detected by ultrasonic scanning images at each resolution. i , according to λf=v, the defect size d is derived i With the center frequency f i The quantitative formula (6):

[0058] (5)

[0059] (6)

[0060] (11) Substitute the known ultrasonic probe size D = 6 mm and the sound velocity v = 5720 m / s of the object under test into formulas (5) and (6), and calculate the defect size d measured in step (10) i Follow i Linear fitting is performed on the changing rules.

[0061] (12) Then the fitting curve is differentiated with respect to frequency f, and the slope k = -0.01 corresponds to d i The actual defect is 405 μm. The actual diameter of each defect is quantified using a laser confocal microscope, and the size of the Φ400 μm defect is Φ389 μm. The relative error between the quantitative size and the actual size is 4.1%. This shows that synthetic aperture multi-resolution ultrasonic C-scan imaging technology can accurately quantify the size of defects in non-focal areas.

[0062] Example 2

[0063] The ultrasonic C-scan detection system used in this embodiment includes a 3D printed nickel-based high-temperature alloy sample 1, a low-frequency ultrasonic probe 2 (a water immersion point focusing probe with a nominal frequency of 20 MHz), an XYZ three-dimensional stepping encoder 3, a GE USIP 40 ultrasonic detector 4, and a computer 5 with signal processing software, such as Figure 1 As shown, the 3D printed nickel-based high-temperature alloy specimen is a specimen containing pore-type defects with a nominal diameter of Φ200 μm, and the detection steps used are as follows:

[0064] (1) The GE USIP 40 ultrasonic detector, the water immersion point focusing probe with a nominal frequency of 20 MHz, and the XYZ three-dimensional stepping encoder were calibrated. The 3D printed nickel-based high-temperature alloy sample to be inspected was coded and scanned. The ultrasonic detection system was used to collect 30×30 groups of position-coded ultrasonic A-type echo signals p0(t) of Φ200 μm defects in the focal column area.

[0065] (2) Sound field distribution based on low-frequency focused probe, such as Figure 8 As shown, the effective synthetic aperture length L of Φ200 μm in the focal column area is calculated to be 0.21 mm.

[0066] (1)

[0067] (3) According to the position of the target point (x0, y0), combined with the effective synthetic aperture length L = 0.21 mm in the focal area, determine all participating points (x i , y j ). Calculate the acoustic delay τ at each depth from all synthetic aperture participating points to the target point.

[0068] (2)

[0069] (4) The number of reconstructed positions in the depth direction is equal to the number of samples. The amplitudes at all depths are combined to reconstruct 30×30 groups of ultrasonic signals.

[0070] (3)

[0071] where w(ΔL) is the apodization coefficient within the synthetic aperture, x j Indicates the sampling location.

[0072] (5) The signal p synthesized in step (4) s (t) Perform fast Fourier transform to obtain its amplitude spectrum A(f), as Fig. 9 As shown in the figure, identify the effective frequency band [8.2 MHz, 33.6 MHz] corresponding to half the amplitude of A(f), and divide the effective frequency band into 13 center frequencies f i filter band.

[0073] (6) Using split spectrum analysis with center frequency f i P s (t) The signal is band-pass filtered to obtain signals with different center frequencies f i The sub-signal p i (t), filter bandwidth b i According to the sub-signal energy E i The total energy E of the sum signal satisfies 10lg(E / Ei ) <17.8dB confirmed.

[0074] (7) The center frequency f of different encoding positions i The sub-signal p i (t) Perform amplitude imaging to obtain 13 scanning images Im with different frequency characteristics and multiple resolutions i , where the scanning image of a defect with a nominal size of Φ200 μm when the filter band center frequency is 31 MHz is as follows Fig.10 shown.

[0075] (8) Scan the image Im for each resolution i The "-6dB method" is used to detect the defect size d i , and plot the defect size d detected by ultrasonic scanning imaging at 9 resolutions i Follow i The change curve is as Fig.11 shown.

[0076] (9) Analyze the directivity function of the ultrasonic probe based on the principle of acoustic reciprocity c , that is, the sound field distribution function, the directivity function of the ultrasonic probe D c It can also be pre-determined by numerical simulation, such as formula (4), where D is the probe size, in mm, λ is the wavelength of the component to be tested, in mm, and θ is the sound wave diffusion angle, in radians.

[0077] (4)

[0078] (10) At a specific depth z of a component with a sound velocity of v, according to D c The theoretical beam width is determined by reducing the maximum amplitude by half, which is the defect size d detected by ultrasonic scanning images at each resolution. i , according to λf=v, the defect size d is derived i With the center frequency f i The quantitative formula (5):

[0079] (5)

[0080] (6)

[0081] (11) Substitute the known ultrasonic probe size D = 6 mm and the sound velocity v = 5720 m / s of the object under test into formulas (5) and (6), and calculate the defect size d measured in step (10) i Follow i Linear fitting is performed on the changing rules.

[0082] (12) Then the fitting curve is differentiated with respect to frequency f, and the slope k = -0.01 corresponds to d i The actual defect is 212 μm. The actual diameter of each defect is quantified using a laser confocal microscope, and the size of a Φ200 μm defect is Φ196 μm. The relative error between the quantitative size and the actual size is 8.1%. This shows that the synthetic aperture multi-resolution ultrasonic C-scan imaging technology can accurately quantify the size of defects in the focal area.

Claims

1. A quantitative detection method of deep sub-millimeter defects by low-frequency ultrasonic scanning imaging, characterized by: The detection method includes an ultrasonic detection system consisting of an object to be detected, an ultrasonic detector, a low-frequency ultrasonic probe, a stepping encoder and signal processing software. The method includes the following steps: (1) Calibrate the ultrasonic detector, low-frequency ultrasonic probe, and step encoder, perform coded scanning detection on the object to be inspected, and collect M groups of coded ultrasonic A-type ultrasonic signals p0(t), where t represents the time information of the ultrasonic signal; (2) Based on the acoustic field distribution law of the ultrasonic probe and the acoustic field position of the target area to be inspected, the effective synthetic aperture length L and the apodization coefficient w (ΔL) are calculated, where ΔL represents the horizontal distance from the central axis of the acoustic field; (3) According to the target point position Q0 in the target area to be inspected and combined with the effective synthetic aperture length L, determine the positions Q of all participating points used for synthetic aperture focusing I , calculate the acoustic delay τ corresponding to each moment in the depth direction z from all participating points to the target point; (1)； Where τ is the sound delay, unit is s; (4) The number of reconstructed positions in the depth direction is equal to the number of ultrasonic signal sampling. The signals at all depths are "delayed and superimposed" according to the acoustic delay τ to obtain the reconstructed ultrasonic signal p at the target point position Q0. s (t): (2)； where w(ΔL) is the apodization coefficient within the synthetic aperture, x j Indicates the sampling location; (5) The signal p synthesized in step (4) s (t) Perform fast Fourier transform to obtain its amplitude spectrum A(f), and identify the effective frequency band corresponding to half the amplitude of A(f) [f l , f u ], the effective frequency band is divided into N center frequencies f i The filter band of , i is a natural number from 1 to N; (6) Use bandpass filtering method with center frequency f i P s (t) The signal is split spectrum analyzed to obtain signals with different center frequencies f i The sub-signal p i (t), filter bandwidth b i According to the sub-signal energy E i The total energy E of the sum signal satisfies 10lg(E / E i ) < The relationship between signal-to-noise ratio is determined; (7) Different coding positions with the same center frequency f i The sub-signal p i (t) Perform amplitude imaging to obtain N scanning images Im with different frequency characteristics and multiple resolutions i ; (8) Scan the image Im for each resolution i The "-6dB method" is used to detect the defect size d i , and draw N detected defect sizes d i Follow i The change curve of (9) Analyze the directivity function of the ultrasonic probe based on the principle of acoustic reciprocity c , that is, the sound field distribution function, the directivity function of the ultrasonic probe D c It can also be pre-determined by numerical simulation, such as formula (3), where D is the probe size, in mm, λ is the wavelength in the inspected component, in mm, and θ is the sound wave diffusion angle, in radians; D c =function(D, λ, θ) (3); (10) At a specific depth z of a component with a sound velocity of v, according to the ultrasonic probe directivity function D c The theoretical beam width is determined by reducing the maximum amplitude by half, which is the detection defect size d of the ultrasonic scanning image at each resolution. i , according to λf=v, the detection defect size d is derived i With the center frequency f i The quantitative formula (4); d i =function(D, f i , v, z) (4); (11) Substitute the known ultrasonic probe size D and the component sound velocity v into formula (4), and calculate the defect size d determined in step (10) i Follow i Linear fitting is performed based on the changing rules; (12) Then take the derivative of the fitting curve with respect to frequency f and determine the d corresponding to the slope k = -0.01 of the fitting curve. i This is the quantitative size of the actual defect.

Images