Phase group velocity matching frequency dispersion removal method

Abstract

The invention belongs to the technical field of nondestructive testing, and relates to a phase group velocity matching frequency dispersion removal method. The method comprises the following steps: S1, exciting a signal in a propagation medium, collecting a propagation signal, removing a frequency spectrum of an excitation signal in the propagation signal, and carrying out normalization processing; s2, solving a nonlinear frequency-wave number spectrum; s3, performing linear mapping according to the propagation medium frequency dispersion curve to obtain a linear frequency-wave number corresponding relation; s4, setting equal-interval wave number vectors, and performing linear mapping from the nonlinear wave number spectrum to obtain a linear wave number spectrum; s5, converting the linear wave number spectrum into a new normalized frequency spectrum according to a wave number-frequency corresponding relation, and adding an excitation signal frequency spectrum component to obtain a frequency spectrum of a non-dispersion propagation signal; and S6, performing calculation to obtain a frequency-dispersion-free reconstructed time domain signal. According to the method, the wave packet of the target mode can be extracted and separated, the frequency dispersion signal is recovered to the non-frequency dispersion signal, the signal quality and accuracy are improved, and the method is suitable for scenes such as structure health of ultrasonic detection.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of nondestructive testing, and relates to dispersion removal of an ultrasonic guided wave dispersion signal, in particular to a phase group velocity matching dispersion removal method. BACKGROUND

[0002] The ultrasonic guided wave technology has been widely concerned in the fields of structural health monitoring and nondestructive testing due to its inherent advantages such as long propagation distance, small attenuation, high sensitivity to small defects and full thickness coverage. Among them, a more important research direction is how to better analyze and process the ultrasonic signal and how to extract useful information from the received signal when performing ultrasonic guided wave nondestructive testing.

[0003] In the guided wave signal processing process, the dispersion phenomenon will cause distortion of the signal in the propagation process, affecting the accuracy and reliability of the signal. For the original dispersion signal, how to remove the dispersion effect and reconstruct the non-dispersion signal has always been the focus and difficulty of research. The existing signal processing methods often have problems such as low processing accuracy, high computational complexity or limited application range when processing dispersion signals, which is difficult to meet the demand for high-quality signal processing in actual application.

[0004] Therefore, an efficient and accurate dispersion signal processing method is needed to reconstruct the target modal wave packet non-dispersion signal. SUMMARY

[0005] The purpose of the present application is to solve the above-mentioned problems existing in the prior art, and a phase group velocity matching dispersion removal method is proposed. The present application provides a non-dispersion signal reconstruction method based on dispersion signal processing, which can extract and separate the wave packet of the target mode, restore the dispersion signal to a non-dispersion signal, improve the signal quality and accuracy, and is suitable for structural health and other scenarios of ultrasonic detection.

[0006] The technical scheme of the present application is:

[0007] The present application provides a phase group velocity matching dispersion removal method, comprising the following steps:

[0008] S1, exciting a signal in a propagation medium and collecting a propagation signal at a certain distance; calculating the frequency spectrum of the propagation signal and the excitation signal, removing the frequency spectrum of the excitation signal in the propagation signal, and normalizing the part without excitation signal spectrum;

[0009] S2, calculating the dispersion curve of the propagation medium and solving the nonlinear frequency-wave number spectrum;

[0010] S3, linear mapping according to the dispersion curve of the propagation medium to obtain a linear frequency-wave number corresponding relationship;

[0011] S4. Set equally spaced wavenumber vectors and perform linear mapping from the nonlinear wavenumber spectrum to obtain a linear wavenumber spectrum;

[0012] S5. Convert the linear wavenumber spectrum into a new normalized spectrum according to the wavenumber-frequency correspondence, and add the excitation signal spectrum component to the new normalized spectrum to obtain the spectrum of the dispersion-free propagation signal.

[0013] S6. Calculate the reconstructed time-domain signal without dispersion.

[0014] Furthermore, in step S1, the spectra of the excitation signal and the propagation signal are calculated using Fast Fourier Transform (FFT):

[0015]

[0016] Then, the spectrum of the excitation signal in the propagation signal is removed using formula (3):

[0017] S(ω)=G(ω) / V in (ω) (3);

[0018] Finally, normalization calculations are used to eliminate attenuation information during wave propagation:

[0019]

[0020] Among them, v in (t) is the excitation signal, g(t) is the propagation signal, and V in G(ω) is the spectrum of the excitation signal, and G(ω) is the spectrum of the propagation signal. The spectrum is the normalized frequency, ω is the angular frequency, and i 2 =1, where t is the sampling time.

[0021] Furthermore, in step S2, the nonlinear frequency-wavenumber curve is solved using formula (5):

[0022] k=ω / c p (5)

[0023] Among them, c p This represents the phase velocity of the corresponding modal guided wave;

[0024] Expanding the solved nonlinear frequency-wavenumber curve using Taylor series yields formula (6):

[0025] k=K(ω)=k0+k1(ω-ω0)+k2(ω-ω0)2+… (6)

[0026] Where, k0=ω0 / c p (ω0), ω0 is the center frequency of the excitation signal.

[0027] Furthermore, step S3 specifically includes:

[0028] S3.1 Ignoring the higher-order infinitesimal parts in the Taylor series expansion of the wavenumber, the nonlinear frequency-wavenumber relationship is mapped to a linear frequency-wavenumber relationship, resulting in formula (7):

[0029] k=K1(ω)=k0+k1(ω-ω0) (7)S3.2、Removing the constant term in the Taylor series, the frequency-wavenumber relationship becomes an oblique line passing through the origin. The group velocity and phase velocity corresponding to each frequency component of the signal wave packet propagating according to this relationship are the same, which is called phase-group velocity matching; the frequency-wavenumber relationship of phase-group velocity matching is expressed as formula (8):

[0030] k=K2(ω)=k1(ω-ω0) (8).

[0031] Furthermore, step S4 specifically includes:

[0032] Set equally spaced wavenumber vectors The frequency-wavenumber relationship for phase group velocity matching is obtained by interpolation based on the frequency-wavenumber relationship in the nonlinear wavenumber spectrum, resulting in an equally spaced wavenumber vector. The frequency corresponding to each wave value and amplitude

[0033] Furthermore, in step S5, the frequency-wavenumber-amplitude relationship of the phase group velocity matching obtained in step S4 is first used to... The spectrum is redistributed to obtain a new normalized spectrum.

[0034] Then, the spectrum of the propagating signal without dispersion and phase change is obtained using formula (9):

[0035]

[0036] Furthermore, in step S6, the spectrum of the propagation signal without dispersion and phase change is converted into a time-domain signal using inverse Fourier transform to obtain the reconstructed time-domain signal:

[0037]

[0038] The beneficial effects of this invention are:

[0039] (1) This invention discloses a phase group velocity matching dispersion removal method, which reconstructs a dispersion-free signal based on a dispersion signal. The method includes: calculating the spectra of the propagation signal and the excitation signal; removing the excitation signal spectrum using a formula; normalizing the spectrum; obtaining a linear frequency-wavenumber relationship from the dispersion curve and determining the wavenumber value; interpolating to obtain the linear wavenumber spectrum and the new normalized spectrum; calculating the new signal spectrum; and obtaining the time-domain signal through inverse Fourier transform. Using this method can effectively remove dispersion effects, improve signal quality and accuracy, and is applicable to scenarios such as structural health detection in ultrasound. It provides a reliable solution for signal processing and related applications, helping to accurately identify signal features and analyze scenario problems.

[0040] (2) The phase group velocity matching dispersion removal method provided by the present invention compresses the dispersion waveform into the incident waveform through linear mapping, and has a strong recovery capability for relatively complex dispersion signals with known modes. Attached Figure Description

[0041] Figure 1 This is the five-cycle sinusoidal modulation excitation signal provided in Embodiment 1 of the present invention;

[0042] Figure 2 The dispersive signal received in Embodiment 1 of the present invention;

[0043] Figure 3 This is the spectrum of the excitation signal in Embodiment 1 of the present invention;

[0044] Figure 4 This is the spectrum of the propagating signal in Embodiment 1 of the present invention;

[0045] Figure 5 The spectrum of the propagation signal after removing the excitation signal in Embodiment 1 of the present invention;

[0046] Figure 6 This is the normalized spectrum in Embodiment 1 of the present invention;

[0047] Figure 7 The calculated dispersion curve;

[0048] Figure 8 The frequency-wavenumber curve of the S0 mode in Embodiment 1 of the present invention;

[0049] Figure 9 The frequency-wavenumber curve of mode A0 in Embodiment 1 of the present invention;

[0050] Figure 10 This is a schematic diagram showing the nonlinear frequency-wavenumber relationship in Embodiment 1 of the present invention;

[0051] Figure 11 This is a schematic diagram of the phase group velocity matching frequency-wavenumber relationship conversion in Embodiment 1 of the present invention;

[0052] Figure 12 This is the signal reconstructed using the phase group velocity matching dispersion removal method in Embodiment 1 of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] To further understand the present invention, it will be further described in conjunction with the accompanying drawings and embodiments.

[0055] A phase group velocity matching dispersion removal method includes the following steps:

[0056] Step S1: First, excite the signal in the propagation medium and collect it at a certain distance;

[0057] Among these, the propagation medium must possess dispersion characteristics, or in other words, the propagation medium must satisfy the requirement that its dispersion curve can be obtained through measurement or theoretical calculation, and then the excitation signal v is applied at a specified location A(x1,y1). in (t) and the propagation signal g(t) is collected at the specified location B(x2,y2).

[0058] Then, the spectra of the propagation signal and the excitation signal are calculated;

[0059] The signal spectrum is calculated using Fourier transform: Where f(t) is the time-domain signal and ω is the angular frequency. Furthermore, the excitation signal v is calculated using Fast Fourier Transform. in The spectra of g(t) and the propagation signal g(t):

[0060]

[0061] Among them, V in G(ω) is the spectrum of the excitation signal, G(ω) is the spectrum of the propagation signal, ω is the angular frequency, and i 2 =1, where t is the sampling time.

[0062] Next, the spectrum of the excitation signal is removed from the propagating signal. The formula is as follows:

[0063] S(ω)=G(ω) / V in (ω);

[0064] Where G(ω) is the spectrum of the propagating signal, V in (ω) represents the spectrum of the excitation signal.

[0065] At this point, S(ω) contains only phase information and attenuation information.

[0066] Finally, the portion of the spectrum of the unexcited signal is normalized. Normalization only affects the phase change during propagation. Normalization is used to eliminate attenuation information during wave propagation. The normalization operation is as follows:

[0067]

[0068] in, This is the normalized spectrum.

[0069] Step S2: Calculate the dispersion curve of the propagation medium and solve the nonlinear frequency-wavenumber spectrum.

[0070] Based on the propagation medium, the dispersion characteristics of the corresponding mode of ultrasonic guided wave are obtained, and the frequency-wavenumber curve is solved:

[0071] k=ω / c p ;

[0072] Among them, c p This represents the phase velocity of the corresponding modal guided wave.

[0073] The nonlinear frequency-wavenumber relationship obtained above can be expanded using Taylor series:

[0074] k=K(ω)=k0+k1(ω-ω0)+k2(ω-ω0) 2 +···;

[0075] Where, k0=ω0 / c p (ω0), ω0 is the center frequency of the excitation signal.

[0076] Step S3: Obtain a linear frequency-wavenumber correspondence by performing a linear mapping based on the dispersion curve of the propagation medium.

[0077] The linear mapping method used is either linear interpolation or spline interpolation algorithm.

[0078] Includes the following steps:

[0079] Step S3.1: Ignoring the higher-order infinitesimal parts in the Taylor series expansion of the wavenumber, the nonlinear frequency-wavenumber relationship is mapped to a linear frequency-wavenumber relationship, ensuring that the phase velocity corresponding to each frequency component of the received propagation signal wave packet is the same:

[0080] k = K1(ω) = k0 + k1(ω - ω0).

[0081] Step S3.2: Remove the constant term from the Taylor series. The frequency-wavenumber relationship becomes a slanted line passing through the origin. Each frequency component of a signal packet propagating according to this relationship corresponds to the same group velocity and phase velocity, which is called phase-group velocity matching. The time delays to reach the same position are the same, and there is no phase change. The frequency-wavenumber relationship of phase-group velocity matching is expressed as:

[0082] k = K2(ω) = k1(ω-ω0).

[0083] S4: Set equally spaced wavenumber vectors and perform linear mapping from the nonlinear wavenumber spectrum to obtain a linear wavenumber spectrum;

[0084] The linear mapping method used is either linear interpolation or spline interpolation algorithm. A functional relationship is established between the signal frequency domain amplitude and wavenumber using angular frequency.

[0085] Furthermore, in the spectrum Set equally spaced frequency vectors [ω1, ω2, ..., ω n ], to obtain the wavenumber [k1,k2,…,k] corresponding to each frequency value. n ] and amplitude [a1,a2,…a n At this point, the relationship between wavenumber and frequency is non-linear, therefore, different wavenumber intervals require the setting of equally spaced wavenumber vectors. The frequency-wavenumber relationship for phase group velocity matching is obtained by interpolation based on the frequency-wavenumber relationship in the nonlinear wavenumber spectrum, resulting in an equally spaced wavenumber vector. The frequency corresponding to each wave value and amplitude At this point, the wavenumber and frequency become linearly related.

[0086] S5: Convert the linear wavenumber spectrum into a new normalized spectrum according to the wavenumber-frequency correspondence, and add the excitation signal spectrum component to the new normalized spectrum to obtain the spectrum of the dispersion-free propagation signal.

[0087] The frequency domain amplitude of the signal is established as a function relationship with the wavenumber by using angular frequency.

[0088] Specifically, the frequency-wavenumber-amplitude relationship of the phase group velocity matching obtained in step S4 will be used to... The spectrum is redistributed to obtain a new normalized spectrum.

[0089] Next, the spectrum of the dispersion-free propagating signal is obtained using the following formula:

[0090]

[0091] in, To obtain the new normalized spectrum.

[0092] Furthermore, the new normalized spectrum is compared with the original excitation signal spectrum V. in Multiplying by (ω) yields the spectrum of the propagating signal without dispersion or phase change:

[0093] S6: Calculate the time-domain representation of the dispersion-free propagating signal to obtain the dispersion-free reconstructed time-domain signal.

[0094] The method used to convert the spectrum of the propagating signal without dispersion and phase change into a time-domain signal is the inverse Fourier transform, resulting in the reconstructed time-domain signal:

[0095]

[0096] The phase group velocity matching dispersion removal method disclosed in this invention compresses the dispersion waveform into the incident waveform through linear mapping, and has a strong recovery capability for relatively complex dispersion signals with known modes.

[0097] Example 1

[0098] This embodiment uses ultrasonic guided wave testing of metal structural components as an example. It utilizes the method of this invention to process the dissipative ultrasonic guided wave signal and reconstruct a dissipation-free signal. It should be noted that the application scenarios of this invention are not limited to this embodiment. Fields involving dissipative signal processing, such as structural health monitoring, can also refer to the logic of this embodiment for implementation. The specific steps are described below.

[0099] In step S1, the propagation medium is a 6mm thick 6061 aluminum alloy plate, the excitation signal is a five-cycle sinusoidal modulation signal with a center frequency of 200kHz, and the time-domain waveform is as follows. Figure 1 As shown. In this embodiment, it is denoted as v. in (t). The propagation signal is collected at a distance of 0.5 meters from the excitation location, such as... Figure 2 As shown, both S0 and A0 modes exist simultaneously. In this embodiment, they are denoted as g(t).

[0100] The excitation signal v was calculated using Fast Fourier Transform. in The spectra of g(t) and the propagation signal g(t):

[0101]

[0102] Among them, V in (ω) is the spectrum of the excitation signal, such as Figure 3 As shown, G(ω) is the spectrum of the propagating signal, as... Figure 4 As shown.

[0103] The spectrum of the excitation signal is removed from the propagation signal using a division operation:

[0104] S(ω)=G(ω) / Vin (ω);

[0105] The spectrum after removal is as follows Figure 5 As shown.

[0106] Finally, for single-mode, single-path wave packets, normalization is used to eliminate attenuation information during wave propagation:

[0107]

[0108] The obtained normalized spectrum is as follows Figure 6 As shown.

[0109] In step S2, the density of the 6061 aluminum plate is found to be 2810 kg / m³. 3 With an elastic modulus of 71 GPa and a Poisson's ratio of 0.33, its dispersion curve was calculated as follows: Figure 7 As shown. The frequency-wavenumber curves of the S0 mode and A0 mode are obtained from the dispersion curve using the following formula:

[0110]

[0111] in, Let S0 be the phase velocity of the guided wave. Let be the phase velocity of the A0 mode guided wave. Expand them into Taylor series:

[0112]

[0113] Step S3 includes the following steps:

[0114] Step S3.1: Ignoring the higher-order infinitesimal parts in the Taylor series expansion of the wavenumber, the nonlinear frequency-wavenumber relationship is mapped to a linear frequency-wavenumber relationship:

[0115]

[0116] At this point, the phase velocity corresponding to each frequency component of the propagating signal wave packet in the linear frequency-wavenumber relationship is the same.

[0117] Step S3.2: Remove the constant term from the Taylor series. The frequency-wavenumber relationship becomes a slanted line passing through the origin. Each frequency component of a signal packet propagating according to this relationship corresponds to the same group velocity and phase velocity, which is called phase-group velocity matching. The time delays to reach the same position are the same, and there is no phase change. The frequency-wavenumber relationship of phase-group velocity matching is expressed as:

[0118]

[0119] To more clearly illustrate the frequency-wavenumber relationship under different conditions, Figure 8The K of the S0 mode is given. S , curve, Figure 9 The K of mode A0 is given. A , curve.

[0120] In this embodiment, in step S4, the spectrum in the 0-400kHz frequency band... Set a frequency vector [ω1,ω2,…,ω] with an interval of 2kHz. n ], to obtain the wavenumber [k1,k2,…,k] corresponding to each frequency value. n ] and amplitude [a1,a2,…a n At this point, the wavenumber and frequency have a non-linear relationship, therefore the wavenumber intervals are different, such as... Figure 10 As shown.

[0121] Based on the sampling frequency, in k1~k n Within the range, K2(ω) is set as an equally spaced wavenumber vector. The frequency-wavenumber relationship for phase group velocity matching is obtained by interpolation based on the frequency-wavenumber relationship in the nonlinear wavenumber spectrum (i.e., K(ω)), resulting in an equally spaced wavenumber vector. The frequency corresponding to each wave value and amplitude At this point, the wavenumber and frequency become linearly related, such as... Figure 11 As shown.

[0122] In step S5, middle Replace the amplitude corresponding to the frequency band with A new normalized spectrum is obtained

[0123] Multiplying the new normalized spectrum by the original excitation signal spectrum yields the spectrum of the propagating signal without dispersion or phase change:

[0124]

[0125] In step S6, for The inverse Fourier transform is performed to obtain the reconstructed time-domain signal:

[0126]

[0127] The results of this embodiment are as follows: Figure 12 As shown.

[0128] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, alterations, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A phase group velocity matching dispersion removal method, characterized in that, Includes the following steps: S1. Excite a signal in the propagation medium and collect the propagation signal at a certain distance; calculate the spectrum of the propagation signal and the excitation signal, and remove the spectrum of the excitation signal from the propagation signal. Normalize the part of the spectrum without the excitation signal. S2. Calculate the dispersion curve of the propagation medium and solve the nonlinear frequency-wavenumber spectrum; S3. Obtain a linear frequency-wavenumber correspondence by performing a linear mapping based on the dispersion curve of the propagation medium; S4. Set equally spaced wavenumber vectors and perform linear mapping from the nonlinear wavenumber spectrum to obtain a linear wavenumber spectrum; S5. Convert the linear wavenumber spectrum into a new normalized spectrum according to the wavenumber-frequency correspondence, and add the excitation signal spectrum component to the new normalized spectrum to obtain the spectrum of the dispersion-free propagation signal. S6. Calculate the reconstructed time-domain signal without dispersion.

2. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, In step S1, the spectra of the excitation signal and the propagation signal are calculated using Fast Fourier Transform (FFT). Then, the spectrum of the excitation signal in the propagation signal is removed using formula (3): S(ω)=G(ω) / V in (oh) (3); Finally, normalization calculations are used to eliminate attenuation information during wave propagation: Among them, v in (t) is the excitation signal, g(t) is the propagation signal, and V in G(ω) is the spectrum of the excitation signal, and G(ω) is the spectrum of the propagation signal. The spectrum is the normalized frequency, ω is the angular frequency, and i 2 =1, where t is the sampling time.

3. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, In step S2, the nonlinear frequency-wavenumber curve is solved using formula (5): k=ω / c p (5) Among them, c p This represents the phase velocity of the corresponding modal guided wave; Expanding the solved nonlinear frequency-wavenumber curve using Taylor series yields formula (6): k=K(ω)=k0+k1(ω-ω0)+k2(ω-ω0) 2 +… (6) Where, k0=ω0 / c p (ω0), ω0 is the center frequency of the excitation signal.

4. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, Step S3 specifically involves: S3.1 Ignoring the higher-order infinitesimal parts in the Taylor series expansion of the wavenumber, the nonlinear frequency-wavenumber relationship is mapped to a linear frequency-wavenumber relationship, resulting in formula (7): k=K1(ω)=k0+k1(ω-ω0) (7) S3.

2. Removing the constant term from the Taylor series, the frequency-wavenumber relationship becomes a slant line passing through the origin. The group velocity and phase velocity corresponding to each frequency component of the signal wave packet propagating according to this relationship are the same, which is called phase-group velocity matching; the frequency-wavenumber relationship of phase-group velocity matching is expressed as formula (8): k=K2(ω)=k1(ω-ω0) (8).

5. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, Step S4 specifically involves: Set equally spaced wavenumber vectors The frequency-wavenumber relationship for phase group velocity matching is obtained by interpolation based on the frequency-wavenumber relationship in the nonlinear wavenumber spectrum, resulting in an equally spaced wavenumber vector. The frequency corresponding to each wave value and amplitude 6. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, In step S5, the frequency-wavenumber-amplitude relationship of the phase group velocity matching obtained in step S4 is first applied to... The spectrum is redistributed to obtain a new normalized spectrum. Then, the spectrum of the propagating signal without dispersion and phase change is obtained using formula (9):

7. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, In step S6, the spectrum of the propagation signal without dispersion and phase change is converted into a time-domain signal using inverse Fourier transform to obtain the reconstructed time-domain signal:

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