CN121027337A - Phase group velocity matching dispersion removal method - Google Patents

Phase group velocity matching dispersion removal method

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Publication number
CN121027337A
CN121027337A CN202511230809.8A CN202511230809A CN121027337A CN 121027337 A CN121027337 A CN 121027337A CN 202511230809 A CN202511230809 A CN 202511230809A CN 121027337 A CN121027337 A CN 121027337A
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frequency
spectrum
signal
dispersion
wavenumber
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穆为磊
刘家辰
赵春旭
杨昊
周宇
朱晨旭
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Ocean University of China
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Ocean University of China
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    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/4454—Signal recognition, e.g. specific values or portions, signal events, signatures

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Abstract

The invention belongs to the technical field of nondestructive testing, and relates to a phase-group velocity matching frequency dispersion removing method. The method comprises the steps of S1, exciting signals in a propagation medium, collecting the propagation signals, removing the frequency spectrums of the excitation signals in the propagation signals, carrying out normalization processing, S2, solving nonlinear frequency-wave number spectrums, S3, carrying out linear mapping according to a propagation medium frequency dispersion curve to obtain a linear frequency-wave number corresponding relation, S4, setting equidistant wave number vectors, carrying out linear mapping from the nonlinear wave number spectrums to obtain a linear wave number spectrum, S5, converting the linear wave number spectrum into a new normalized frequency spectrum according to the wave number-frequency corresponding relation, adding excitation signal frequency spectrum components to obtain a frequency spectrum of a non-dispersion propagation signal, and S6, calculating to obtain a reconstructed time domain signal without dispersion. The method can extract and separate the wave packet of the target mode, restore the dispersion signal into the non-dispersion signal, improve the signal quality and accuracy, and is suitable for the scenes such as structural health of ultrasonic detection.

Description

Phase group velocity matching dispersion removing method
Technical Field
The invention belongs to the technical field of nondestructive testing, relates to frequency dispersion removal of ultrasonic guided wave frequency dispersion signals, and particularly relates to a phase group velocity matching frequency dispersion removal method.
Background
The ultrasonic guided wave technology has the inherent advantages of long propagation distance, small attenuation, high sensitivity to small defects, full thickness coverage and the like, and is widely focused in the fields of structural health monitoring and nondestructive detection. The important research direction is how to analyze and process the ultrasonic signal better and extract useful information from the received signal when performing ultrasonic guided wave nondestructive detection.
In the guided wave signal processing process, the phenomenon of frequency dispersion can lead to distortion of signals in the propagation process, and the accuracy and reliability of the signals are affected. For the original dispersion signal, how to remove the dispersion effect and reconstruct the dispersion-free signal is always the key point and the difficulty of research. When the existing signal processing method processes the dispersion signal, the problems of low processing precision, high computational complexity, limited application range and the like often exist, and the requirement of high-quality signal processing in practical application is difficult to meet.
Therefore, there is a need for an efficient and accurate method for processing a dispersion signal to realize a reconstruction of a target modal wave packet without a dispersion signal.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a phase-group velocity matching frequency dispersion removing method. The invention provides a non-dispersive signal reconstruction method based on dispersive signal processing, which can extract and separate wave packets of a target mode, recover dispersive signals into non-dispersive signals, improve signal quality and accuracy, and is suitable for scenes such as structural health of ultrasonic detection.
The technical scheme of the invention is as follows:
The invention provides a phase group velocity matching frequency dispersion removing method, which comprises the following steps:
S1, exciting signals in a propagation medium and collecting the propagation signals at a certain distance, calculating the frequency spectrums of the propagation signals and the excitation signals, removing the frequency spectrums of the excitation signals in the propagation signals, and carrying out normalization processing on the part without the frequency spectrums of the excitation signals;
s2, calculating a propagation medium dispersion curve and solving a nonlinear frequency-wave number spectrum;
S3, performing linear mapping according to the propagation medium dispersion curve to obtain a linear frequency-wave number corresponding relation;
S4, setting equidistant 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 spectrum according to the wave number-frequency correspondence, and adding excitation signal spectrum components into the new normalized spectrum to obtain a spectrum of the non-dispersion propagation signal;
S6, calculating to obtain a reconstructed time domain signal without dispersion.
Further, in the step S1, the spectrums of the excitation signal and the propagation signal are calculated by using fast fourier transform, respectively:
then, the frequency spectrum of the excitation signal in the propagated signal is removed using equation (3):
S(ω)=G(ω)/Vin(ω) (3);
finally, adopting normalization calculation to eliminate attenuation information in the wave propagation process:
Wherein V in (t) is an excitation signal, G (t) is a propagation signal, V in (ω) is a frequency spectrum of the excitation signal, G (ω) is a frequency spectrum of the propagation signal, For normalized spectrum, ω is angular frequency, i 2 = 1, and t is sampling time.
Further, in the step S2, a nonlinear frequency-wave number curve is solved by using the formula (5):
k=ω/cp (5)
wherein c p is the phase velocity of the corresponding mode guided wave;
Expanding the solved nonlinear frequency-wavenumber curve by using a taylor series to obtain a formula (6):
k=K(ω)=k0+k1(ω-ω0)+k2(ω-ω0)2+... (6)
wherein, k 0＝ω0/cp(ω0), Omega 0 is the center frequency of the excitation signal.
Further, the step S3 specifically includes:
S3.1, neglecting a high-order infinitely small part in a Taylor series expansion of the wave numbers, and mapping a nonlinear frequency wave number relation into a linear frequency wave number relation to obtain a formula (7):
k=k 1(ω)＝k0+k1(ω-ω0) (7) S3.2, removing the constant term in the taylor series, changing the frequency-wave number relationship into an oblique line passing through the origin, wherein the group velocity and the phase velocity corresponding to each frequency component of the signal wave packet propagating according to the relationship are the same, called phase velocity matching, and the frequency-wave number relationship of the phase velocity matching is expressed as formula (8):
k=K2(ω)＝k1(ω-ω0) (8)。
further, the step S4 specifically includes:
setting equidistant wavenumber vectors Interpolation is carried out according to the frequency-wave number relation in the nonlinear wave number spectrum to obtain the frequency-wave number relation matched with the group velocity, and equidistant wave number vectors are obtainedFrequency corresponding to each wave number value in (a)And amplitude value
Further, in the step S5, the phase group velocity matching frequency-wave number-amplitude relationship obtained in the step S4 is first determinedReassigning to obtain a new normalized frequency spectrum
Then, the spectrum of the propagation signal without dispersion and phase change is obtained using equation (9):
further, in the step S6, an inverse fourier transform is used to transform the spectrum of the propagation signal without dispersion and phase change into a time domain signal, so as to obtain a reconstructed time domain signal:
The invention has the beneficial effects that:
(1) The invention discloses a phase group velocity matching frequency dispersion removing method, which is used for carrying out non-frequency dispersion signal reconstruction based on a frequency dispersion signal. The method comprises the steps of calculating a propagation signal spectrum and an excitation signal spectrum, removing the excitation signal spectrum by a formula, normalizing the frequency spectrum, obtaining a linear frequency-wave number relation by a frequency dispersion curve, determining a wave value, obtaining a linear wave number spectrum and a new normalized frequency spectrum by interpolation, calculating a new signal spectrum, and obtaining a time domain signal by inverse Fourier transform. The method can effectively remove the dispersion effect, improve the signal quality and accuracy, is suitable for the scenes such as structural health of ultrasonic detection, provides a reliable scheme for signal processing and related application, and can accurately identify signal characteristics and analyze scene problems by aid of assistance.
(2) According to the phase group velocity matching dispersion removing method provided by the invention, the dispersion waveform is compressed into the incident waveform through linear mapping, so that the method has extremely strong recovery capability for complex dispersion signals with known modes.
Drawings
FIG. 1 is a five-cycle sinusoidal modulation excitation signal provided in embodiment 1 of the present invention;
fig. 2 is a block diagram of a received dispersion signal in embodiment 1 of the present invention;
FIG. 3 is a spectrum of the excitation signal in embodiment 1 of the present invention;
FIG. 4 is a spectrum of a propagated signal in example 1 of the present invention;
FIG. 5 is a spectrum of the propagation signal after removal of the excitation signal in example 1 of the present invention;
FIG. 6 is a normalized spectrum of example 1 of the present invention;
FIG. 7 is a graph of calculated dispersion;
FIG. 8 is a plot of frequency versus wavenumber for the S0 mode in example 1 of the present invention;
FIG. 9 is a plot of frequency versus wavenumber for the A0 mode in example 1 of the present invention;
FIG. 10 is a diagram showing the correspondence between nonlinear frequency and wave number in embodiment 1 of the present invention;
FIG. 11 is a diagram showing the conversion of phase group velocity matching frequency-wavenumber relationship in example 1 of the present invention;
Fig. 12 is a signal reconstructed by the group velocity matching dispersion removal method according to embodiment 1 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For a further understanding of the present invention, reference will now be made to the drawings and examples.
A phase group velocity matching frequency dispersion removing method comprises the following steps:
Step S1, firstly, exciting signals in a propagation medium and collecting the signals at a certain distance;
The propagation medium has a dispersion characteristic or the propagation medium needs to be satisfied that a dispersion curve can be obtained through measurement or theoretical calculation, and then a signal v in (t) is excited at a designated position A (x 1,y1) and a propagation signal g (t) is acquired at a designated position B (x 2,y2).
Then, calculating the frequency spectrums of the propagation signal and the excitation signal;
The signal spectrum is calculated by fourier transformation: where f (t) is the time domain signal and ω is the angular frequency. Further, the spectra of the excitation signal v in (t) and the propagation signal g (t) are calculated using a fast fourier transform, respectively:
Where V in (ω) is the frequency spectrum of the excitation signal, G (ω) is the frequency spectrum of the propagation signal, ω is the angular frequency, i 2 =1, and t is the sampling time.
Then, the frequency spectrum of the excitation signal in the propagated signal is removed. The formula is as follows:
S(ω)=G(ω)/Vin(ω);
Where G (ω) is the spectrum of the propagating signal and V in (ω) is the spectrum of the excitation signal.
At this time, S (ω) includes only the phase information and the attenuation information.
Finally, normalization processing is adopted for the part without the excitation signal spectrum. Normalization only affects the phase change in the propagation process, and attenuation information in the wave propagation process is eliminated by adopting normalization calculation, wherein normalization operation is as follows:
Wherein, the Is the normalized spectrum.
And S2, calculating a propagation medium dispersion curve and solving a nonlinear frequency-wave number spectrum.
Acquiring the dispersion characteristics of the ultrasonic guided waves of the corresponding modes according to the propagation medium, and solving a frequency-wave number curve:
k=ω/cp;
wherein c p is the phase velocity of the guided wave of the corresponding mode.
Expanding the solved nonlinear frequency-wave number relationship by using a taylor series:
k=K(ω)=k0+k1(ω-ω0)+k2(ω-ω0)2+···;
wherein, k 0＝ω0/cp(ω0), Omega 0 is the center frequency of the excitation signal.
And S3, performing linear mapping according to the propagation medium dispersion curve to obtain a linear frequency-wave number corresponding relation.
The adopted linear mapping method is a linear interpolation or spline interpolation algorithm.
The method comprises the following steps:
step S3.1, neglecting a high-order infinite small part in a Taylor series expansion of wave numbers, mapping a nonlinear frequency wave number relation into a linear frequency wave number relation, and enabling phase velocities corresponding to each frequency component of a received propagation signal wave packet to be the same:
k=K1(ω)＝k0+k1(ω-ω0)。
Step S3.2, removing constant items in the Taylor series, changing the frequency wave number relation into an oblique line passing through an origin, wherein the group velocity and the phase velocity corresponding to each frequency component of the signal wave packet propagated according to the relation are the same, namely phase velocity matching, the time delay reaching the same position is the same and no phase change exists, and the frequency-wave number relation of the phase velocity matching is expressed as:
k=K2(ω)＝k1(ω-ω0)。
s4, setting equidistant wave number vectors and performing linear mapping from the nonlinear wave number spectrum to obtain a linear wave number spectrum;
the adopted linear mapping method is a linear interpolation or spline interpolation algorithm. And establishing a functional relation between the frequency domain amplitude and the wave number of the signal through the angular frequency.
Further, in the frequency spectrumSetting equal interval frequency vector [ omega 1,ω2,…,ωn ] to obtain wave number [ k 1,k2,…,kn ] and amplitude [ a 1,a2,…an ] corresponding to each frequency value, wherein the wave number and frequency are in nonlinear relationship, thus the wave number intervals are different, and setting equal interval wave number vectorInterpolation is carried out according to the frequency-wave number relation in the nonlinear wave number spectrum to obtain the frequency-wave number relation matched with the group velocity, and equidistant wave number vectors are obtainedFrequency corresponding to each wave number value in (a)And amplitude valueThe wave number at this time becomes a linear relationship with frequency.
S5, converting the linear wave number spectrum into a new normalized spectrum according to the wave number-frequency correspondence, and adding excitation signal spectrum components into the new normalized spectrum to obtain a spectrum of the non-dispersion propagation signal.
And establishing a functional relation between the frequency domain amplitude and the wave number of the signal through the angular frequency.
Specifically, the phase velocity matching frequency-wave number-amplitude relationship obtained in step S4 willReassigning to obtain a new normalized frequency spectrum
Then, the spectrum of the non-dispersive propagating signal is obtained using the following formula:
Wherein, the To obtain a new normalized spectrum.
Further, multiplying the new normalized spectrum with the original excitation signal spectrum V in (ω) yields a spectrum of the propagated signal without dispersion and phase variation:
S6, calculating the time domain representation of the non-dispersion propagation signal to obtain a reconstructed time domain signal without dispersion.
The method comprises the steps of converting a frequency spectrum of a propagation signal without dispersion and phase change into a time domain signal by adopting inverse Fourier transform to obtain a reconstructed time domain signal:
The phase group velocity matching dispersion removing method disclosed by the invention compresses the dispersion waveform into the incident waveform through linear mapping, and has extremely strong recovery capability for complex dispersion signals with known modes.
Example 1
In the embodiment, taking the scenario of ultrasonic guided wave detection of a metal structural member as an example, the method disclosed by the invention is used for processing ultrasonic guided wave signals containing dispersion and reconstructing non-dispersion signals. It should be noted that, the application scenario of the present invention is not limited to the field of the present embodiment, such as structural health monitoring, which relates to the processing of the dispersion signal, and the application scenario can be implemented with reference to the logic of the present embodiment, and the following specific steps are developed.
In step S1, the propagation medium is a 6061 aluminum alloy flat plate with the thickness of 6mm, the excitation signal is a five-period sine modulation signal, the center frequency is 200kHz, and the time domain waveform is shown in figure 1. In this example denoted v in (t). The propagation signal was acquired 0.5 meters from the excitation location, as shown in fig. 2, with both S0 and A0 mode signals. In this example denoted g (t).
The frequency spectrum of the excitation signal v in (t) and the propagation signal g (t) are respectively calculated by adopting fast Fourier transformation:
Where V in (ω) is the frequency spectrum of the excitation signal, as shown in fig. 3, and G (ω) is the frequency spectrum of the propagation signal, as shown in fig. 4.
The frequency spectrum of the excitation signal is removed from the propagation signal by a division operation:
S(ω)=G(ω)/Vin(ω);
The removed spectrum is shown in fig. 5.
Finally, for the single-mode single-path wave packet, adopting normalization calculation to eliminate attenuation information in the wave propagation process:
The normalized spectrum obtained is shown in fig. 6.
In step S2, the density of the aluminum plate is 2810kg/m 3, the elastic modulus is 71GPa, the Poisson ratio is 0.33, and the dispersion curve is calculated according to the information of the 6061 aluminum plate, and is shown in FIG. 7. According to the dispersion curve, the frequency-wave number curves of the S0 mode and the A0 mode are respectively obtained by the following formulas:
Wherein, the The phase velocity of the guided wave for the S0 mode,The phase velocity of the guided wave is the A0 mode. Respectively expanding the three to Taylor series:
step S3 comprises the steps of:
step S3.1, neglecting a high-order infinite small part in a Taylor series expansion of the wave numbers, and mapping a nonlinear frequency wave number relation into a linear frequency wave number relation:
The phase velocity corresponding to each frequency component of the propagation signal wave packet corresponding to the linear frequency-wave number relationship is the same;
Step S3.2, removing constant items in the Taylor series, changing the frequency wave number relation into an oblique line passing through an origin, wherein the group velocity and the phase velocity corresponding to each frequency component of the signal wave packet propagated according to the relation are the same, namely phase velocity matching, the time delay reaching the same position is the same and no phase change exists, and the frequency-wave number relation of the phase velocity matching is expressed as:
In order to more clearly show the frequency-wavenumber relationship under different conditions, FIG. 8 shows the S0 mode K S, FIG. 9 shows the A0 mode of K A,A curve.
In the present embodiment, in step S4, the frequency spectrum is in the frequency range of 0-400KHzThe frequency vector [ omega 1,ω2,…,ωn ] with the interval of 2KHz is set to obtain the wave number [ k 1,k2,…,kn ] and the amplitude value [ a 1,a2,…an ] corresponding to each frequency value, and the wave number and the frequency at the moment are in nonlinear relation, so that the wave number intervals are different, as shown in fig. 10.
K 2 (ω) is set to equally spaced wavenumber vectors in the range of K 1～kn according to the sampling frequencyInterpolation is carried out according to the frequency-wave number relation in the nonlinear wave number spectrum (namely K (omega)) to obtain the frequency-wave number relation matched with the phase group velocity, and equidistant wave number vectors are obtainedFrequency corresponding to each wave number value in (a)And amplitude valueThe wave number at this time becomes a linear relationship with frequency as shown in fig. 11.
In step S5In (a)The amplitude corresponding to the frequency band is replaced byObtaining a new normalized frequency spectrum
Multiplying the new normalized spectrum with the original excitation signal spectrum to obtain a spectrum of the propagated signal without dispersion and phase variation:
in step S6, for Performing inverse Fourier transform to obtain a reconstructed time domain signal:
The results of this example are shown in FIG. 12.
The foregoing description is only a preferred embodiment of the present invention and is not intended to limit the present invention, but although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the technical solutions described in the foregoing embodiments, or that equivalents may be substituted for part of the technical features thereof. Any modification, equivalent replacement, variation, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1.一种相群速度匹配频散移除方法，其特征在于，包括以下步骤：1. A phase group velocity matching dispersion removal method, characterized by comprising the following steps: S1、在传播介质中激发信号并在一定距离处采集传播信号；计算传播信号和激励信号的频谱，同时去除传播信号中激励信号的频谱，对无激励信号频谱的部分采用归一化处理；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、计算传播介质频散曲线并求解非线性频率-波数谱；S2. Calculate the dispersion curve of the propagation medium and solve the nonlinear frequency-wavenumber spectrum; S3、根据传播介质频散曲线进行线性映射得到线性的频率-波数对应关系；S3. Obtain a linear frequency-wavenumber correspondence by performing a linear mapping based on the dispersion curve of the propagation medium; S4、设置等间隔波数向量并从非线性波数谱中进行线性映射得到线性波数谱；S4. Set equally spaced wavenumber vectors and perform linear mapping from the nonlinear wavenumber spectrum to obtain a linear wavenumber spectrum; S5、将线性波数谱按波数-频率对应关系转换为新的归一化频谱，在新的归一化频谱中添加激励信号频谱成分得到无频散传播信号的频谱；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、计算得到无频散的重构时域信号。S6. Calculate the reconstructed time-domain signal without dispersion. 2.根据权利要求1所述的相群速度匹配频散移除方法，其特征在于，所述步骤S1中，采用快速傅里叶变换分别计算激励信号和传播信号的频谱：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 respectively using Fast Fourier Transform: 然后，利用公式(3)去除传播信号中激励信号的频谱：Then, the spectrum of the excitation signal in the propagation signal is removed using formula (3): S(ω)＝G(ω)/Vin(ω) (3)；S(ω)=G(ω)/V in (ω) (3); 最后，采用归一化计算消除波传播过程中的衰减信息：Finally, normalization calculations are used to eliminate attenuation information during wave propagation: 其中，vin(t)为激励信号，g(t)为传播信号，Vin(ω)为激励信号的频谱，G(ω)为传播信号的频谱，为归一化频谱，ω为角频率，i2＝1，t为采样时间。Where vin (t) is the excitation signal, g(t) is the propagation signal, Vin (ω) is the spectrum of the excitation signal, and G(ω) is the spectrum of the propagation signal. The spectrum is the normalized spectrum, ω is the angular frequency, i2 = 1, and t is the sampling time. 3.根据权利要求1所述的相群速度匹配频散移除方法，其特征在于，所述步骤S2中，采用公式(5)求解非线性频率-波数曲线：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/cp (5)k＝ω/c p (5) 其中，cp为对应模态导波的相速度；Where c<sub>p</sub> is the phase velocity of the corresponding mode guided wave; 利用泰勒级数将求解的非线性频率-波数曲线展开，得到公式(6)：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)k＝K(ω)＝k 0 +k 1 (ω-ω 0 )+k 2 (ω-ω 0 ) 2 +… (6) 其中，k0＝ω0/cp(ω0),ω0为激励信号的中心频率。Among them, k 0 =ω 0 /c p (ω 0 ), ω0 is the center frequency of the excitation signal. 4.根据权利要求1所述的相群速度匹配频散移除方法，其特征在于，所述步骤S3具体为：4. The phase group velocity matching dispersion removal method according to claim 1, wherein step S3 specifically comprises: S3.1、忽略波数的泰勒级数展开式中的高阶无穷小部分，将非线性的频率波数关系映射为线性的频率波数关系，得到公式(7)：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)k＝K 1 (ω)＝k 0 +k 1 (ω-ω 0 ) (7) S3.2、将泰勒级数中的常数项去掉，频率波数关系变为一条过原点的斜线，按照这种关系传播的信号波包的每个频率分量对应的群速度和相速度相同，称为相群速度匹配；相群速度匹配的频率-波数关系表示为公式(8)：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)。k=K 2 (ω)=k 1 (ω-ω 0 ) (8). 5.根据权利要求1所述的相群速度匹配频散移除方法，其特征在于，所述步骤S4具体为：5. The phase group velocity matching dispersion removal method according to claim 1, wherein step S4 specifically comprises: 设置等间隔波数向量按照非线性波数谱中的频率-波数关系插值得到相群速度匹配的频率-波数关系，得到等间隔波数向量中每一个波数值对应的频率和幅值 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.根据权利要求1所述的相群速度匹配频散移除方法，其特征在于，所述步骤S5中，先按照步骤S4得到的相群速度匹配的频率-波数-幅值关系将进行重新分配，得到新的归一化频谱 6. The phase group velocity matching dispersion removal method according to claim 1, characterized in that, in step S5, the phase group velocity matching frequency-wavenumber-amplitude relationship obtained in step S4 is first adjusted... The spectrum is redistributed to obtain a new normalized spectrum. 然后，采用公式(9)得到无频散和相位变化的传播信号的频谱：Then, the spectrum of the propagating signal without dispersion and phase change is obtained using formula (9): 7.根据权利要求1所述的相群速度匹配频散移除方法，其特征在于，所述步骤S6中，采用逆傅里叶变换将无频散和相位变化的传播信号的频谱转为时域信号，得到重构时域信号：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 a reconstructed time-domain signal:
CN202511230809.8A 2025-08-30 2025-08-30 Phase group velocity matching dispersion removal method Pending CN121027337A (en)

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