CN101982943A - Time domain rearrangement based ultra-phonic guided wave frequency dispersion compensation and multi-mode separating algorithm - Google Patents
Time domain rearrangement based ultra-phonic guided wave frequency dispersion compensation and multi-mode separating algorithm Download PDFInfo
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Abstract
The invention belongs to the ultrasonic technical field and particularly relates to a time domain rearrangement based ultra-phonic guided wave frequency dispersion compensation and multi-mode separating algorithm. The algorithm of the invention comprises three parts: the first part is the positive simulating algorithm of the ultrasonic guided wave frequency dispersion which can solve the delay parameters of different frequency components under the condition of a known waveguide medium theory frequency dispersion curve so as to acquire any impelled multi-mode ultrasonic waveguide time domain signal, the second part is reverse frequency dispersion compensation algorithm which can utilize the frequency dispersion relation to modify the delay at different degrees of the single mode waveguide frequency components so as to compress the long-term frequency dispersion mode type energy into instant impact, simplify the waveform of the guide wave and simply analyze, and the third part can realize the ultrasonic guided wave multi-mode separation based on the reverse frequency dispersion compensation algorithm.
Description
Technical Field
The invention belongs to the technical field of ultrasound, and particularly relates to an ultrasonic guided wave frequency dispersion signal simulation, compensation and mode separation algorithm based on time domain rearrangement.
Background
In the last decade, the application research of ultrasonic guided waves in long-distance nondestructive detection is receiving great attention. In actual propagation, ultrasonic waves often interact with the boundary of the waveguide in a reflection and refraction mode, and conversion between longitudinal waves and transverse waves occurs, so that the generated guided waves are sensitive to all information of a propagation medium, and the method can be widely applied to the nondestructive testing fields of industrial pipelines, industrial plates, railway tracks, long bone diagnosis and the like.
Guided waves have been successfully applied for long-range defect detection based on ultrasonic axial transmission techniques. However, the problem of guided waves is relatively complex, and generally, guided waves propagate in a medium in a multimode form, and due to different dispersion characteristics of the guided wave modes, most of the received guided waves are mixed signals of the multimode, which brings difficulty to further data analysis.
By applying the frequency dispersion compensation method, the time domain expansion of the guided wave signal caused by frequency dispersion can be compensated, so that the original signal with longer duration is compressed into the impact signal with shorter duration. Wilcox et al propose that the surface stress displacement distribution of a certain guided wave mode at a certain time can be effectively located by compensating time domain data in the propagation distance domain using a known wave number frequency curve [ reference 1 ]. On the basis, Toiyama1 and the like propose an improved pulse compression algorithm and apply the improved pulse compression algorithm to frequency dispersion compensation, and the calculation result of guided wave L (0,1) mode experimental signals shows that the algorithm can effectively inhibit guided wave frequency dispersion while improving the signal-to-noise ratio [ reference 2 ]. In addition, a polynomial mapping technique is also applied to the fitting of a wavenumber-frequency curve, that is, a polynomial is used to approximate a single-mode guided-wave wavenumber dispersion curve, thereby realizing time-domain compensation of the mode [ reference 3 ].
[ reference 1] Wilcox P D. A rapid signal processing technique to remove the effect of dispersion from guided wave signals. IEEE Trans. UFFC, 2003; 50(4): 419—427.
[ reference 2] Toiyama1 K, Hayashi T. Pulse compression technique considering velocity dispersion of guided wave. AIP Conf. Proc., 2008; 975: 587—593.
[ reference 3]] Liu L, Yuan F G. A linear mapping technique for dispersion removal of Lamb waves. Structural Health Monitoring, 2010; 9(1): 75—86.
The main limitation of the above method is that it can only compensate for the dispersion of a single guided wave mode with a narrow frequency band. In fact, the received guided wave is usually a multimode signal, and the method for exciting a guided wave signal in a single mode is not yet mature, and cannot be generally applied. Particularly, in some medical ultrasonic guided wave analysis fields including long bone detection, the morphological structure of a research object is complex, and single guided wave mode excitation is more difficult to realize. Therefore, the multi-mode guided wave compensation and separation has important practical value.
Disclosure of Invention
The invention aims to provide an ultrasonic guided wave frequency dispersion signal simulation, compensation and mode separation algorithm based on time domain rearrangement.
The ultrasonic guided wave frequency dispersion signal simulation, compensation and mode separation algorithm based on time domain rearrangement provided by the invention can be divided into three parts: applying a dispersion signal simulation algorithm to obtain a self-defined excited broadband signal dispersion result; the single mode guided wave frequency dispersion compensation is realized by applying a frequency dispersion compensation algorithm; for the multi-mode guided waves, a mode separation algorithm is applied on the basis of effective frequency dispersion compensation to obtain each single guided wave mode. The method comprises the following specific steps:
ultrasonic guided wave frequency dispersion simulation algorithm
(1) The group delay is excited for a certain time, and the calculation formula for calculating the group delay corresponding to each harmonic component of a certain guided wave mode is as follows:
wherein,
d is the distance between the transmitting transducer and the receiving transducer,
is the relationship between group velocity and frequency for a certain guided wave mode.
(2) And obtaining a frequency dispersion transfer function corresponding to the guided wave mode according to the group delay, wherein the expression of the frequency dispersion transfer function is as follows:
wherein the signal
Is the initial value of the integral.
(3) The forward simulation algorithm of the ultrasonic guided wave frequency dispersion solves the output of the excitation signal passing through the frequency dispersion system according to the frequency dispersion transfer function, and then the simulation signal corresponding to the excitation in a certain mode is obtained. If the frequency of the excitation signal isThen receiving the signal spectrum
The formula is as follows:
(4) and (4) respectively solving different guided wave modes by the method of the steps (1) to (3) through multi-guided wave mode superposition, and superposing multi-mode signals.
Ultrasonic guided wave frequency dispersion compensation
(5) Inverse function of frequency dispersion transfer function to realize frequency dispersion compensation of corresponding mode, and solving transfer function obtained in step (2)
The inverse function, whose expression is:
(6) guided wave mode dispersion compensation the dispersion compensation is achieved for a certain mode by the above equation (4). If the frequency spectrum of the dispersive signal is
The method is specifically realized as follows:
Ultrasonic guided wave multi-mode separation algorithm
(7) The compensation mode energy separation separates out the mixed signal of the compensation mode instantaneous excitation and the under compensation mode on the frequency dispersion compensation result. The specific realization of energy separation can use two sets of schemes, 1) if excitation can be measured in advance, the excitation is directly removed to obtain a residual mode signal; 2) if the excitation is not predictable, all signal energy near zero time of the compensation result can be separated out to be calculated as compensation mode energy, and the rest is under-compensation mode energy.
(8) Inverse dispersion compensation the result of the separation in step (7) is inversely compensated for the recoverable signal pattern. The counter compensation is realized by the following steps:
whereinAs a result of the separation in the step (7),
for a mode of guided wave dispersion signals,
is a transfer function expression for the guided wave mode.
(9) Repeating steps (6) - (8) for the remaining guided wave modes to separate all modes.
Drawings
Fig. 1 is a schematic block diagram of an ultrasonic guided wave dispersion simulation algorithm.
FIG. 2 is a schematic block diagram of an ultrasonic guided wave multi-mode separation algorithm.
FIG. 3 is a graph showing the dispersion of a 1mm steel plate having a uniform thickness.
Fig. 4 shows an excitation signal, a) a time domain waveform, b) a frequency spectrum.
FIG. 5 is a drawing showingA 0 ，A 1 AndS 0 three-mode frequency dispersion signal simulation results, a) time domain waveform, b) time frequency distribution after short-time Fourier transform.
FIG. 6 is a drawing showingA 0 ，A 1 AndS 0 simulation result of three-mode frequency dispersion signalA 1 The result after mode dispersion transfer function compensation, a) time domain waveform, b) time frequency distribution after short time Fourier transform.
FIG. 7 is a schematic representation of a partially separatedA 1 Mode a) time domain waveform, b) short time Fourier transformAnd (4) later time-frequency distribution.
FIG. 8 shows the removalA 1 The residual signal after the model a) is a time domain waveform, b) is a time frequency distribution after short time Fourier transform.
FIG. 9 is a schematic representation of a partially separatedA 0 Mode a) time domain waveform, b) time frequency distribution after short time Fourier transform.
FIG. 10 shows the result after separationS 0 Mode a) time domain waveform, b) time frequency distribution after short time Fourier transform.
FIG. 11 shows experimental signals of a steel plate with a uniform thickness of 1mm, which mainly includes a modelA 0 AndS 0 a) time domain waveform, b) time frequency distribution after short time Fourier transform.
FIG. 12 is a signal passing model of an experiment for a steel plate with a uniform thickness of 1mmS 0 The result after the frequency dispersion transfer function compensation, a) time domain waveform, b) time frequency distribution after short time Fourier transform.
FIG. 13 shows the signal pattern separation results of an experiment for a steel plate of 1mm uniform thickness, a) patternS 0 Time domain waveform, b) modeS 0 Time-frequency distribution after short-time Fourier transform, c) modeA 0 Time domain waveform, d) modeA 0 And (3) time-frequency distribution after short-time Fourier transform.
Detailed Description
The invention is further described below by way of examples.
Steel plate ultrasonic guided wave frequency dispersion simulation example
The whole simulation algorithm implementation process is described below by taking a steel plate model with uniform thickness of 1mm as an example. The steel plate has the relevant parameter of density 7.932g/cm 3Velocity of transverse wave 3200m/sVelocity 5960 of longitudinal wavem/s. By guiding wavesThe theory can be solved to obtain a dispersion curve, as shown in fig. 3. Signal source for use in simulationh(t)Has a center frequency of 0.65MHz and a 3dB bandwidth of about 0.4MHz, and has a time domain waveform and a frequency spectrum as shown in fig. 4. As can be seen from FIG. 1, if this signal is used as excitation, the corresponding dispersion signal will containA 0 ，A 1 AndS 0 three modes. Signal source for applying the above simulation methodh(t)GeneratingA 0 ，A 1 AndS 0 the results of the three-mode mixing of the frequency dispersion signals are shown in FIG. 5(a), and the results of the time-frequency distribution obtained by short-time Fourier transform are shown in FIG. 5(b) (note that the time-frequency distribution is obtained by short-time Fourier transform, and the expression of the time-frequency distribution is not specifically explained), wherein the curve represents the theoretical frequency dispersion curve, and the window of the short-time Fourier transform is 6.25μsThe gaussian window of (a). Comparing the theoretical dispersion curve with the time-frequency distribution diagram,A 0 ，A 1 andS 0 most of the energy of the three modes is concentrated around a theoretical frequency dispersion curve, and the results show that the simulation of the multi-mode signals can be realized by applying a frequency dispersion algorithm.
Steel plate ultrasonic guided wave simulation signal mode compensation and separation example
The inverse dispersion transfer function is applied to each of the above modes to compensate and separate them by a dispersion compensation analysis method. Firstly, according to the formulas (4) and (5), the three modes in the mixed waveform shown in FIG. 5 are processedA 1 The pattern is compensated and the result is shown in figure 6. FIG. 6(b) the area in the ellipse shows the spectrum compensatedA 1 The energy corresponding to the mode, the above results showA 1 The pattern energy is fully compensated back to the beginning of time. Removing the excitation signal therefromA 1 The mode energy is removed. Since the excitation signal is known in this example, the pattern separation algorithm is used to separate the first pattern in step (7)A 1 The mode energy. Then, using the algorithm (8) to respectively perform dispersion compensation on the separation results,A 1 result of pattern separationAs shown in fig. 7, fig. 7(a) is a time domain waveform, and fig. 7(b) is a time-frequency distribution. FIG. 8 shows the removalA 1 The residual under-compensated signal after the mode, wherein fig. 8(a) is a time domain waveform, and fig. 8(b) is a corresponding time frequency distribution. From fig. 7 and 8, the algorithm can be appliedA 1 Mode fromA 0 ，A 1 AndS 0 and separating the three modes of simulation signals.
Repeating the above steps for the remainderS 0 AndA 0 mixed mode signal first useS 0 OrA 0 And compensating the frequency dispersion transfer function, separating the mode energy, and performing inverse compensation on the frequency dispersion of the separation result to obtain a final result. FIG. 9 is a schematic representation of a partially separatedA 0 Mode, in which fig. 9(a) is a time domain waveform, and fig. 9(b) is a time-frequency distribution result; FIG. 10 shows the result after separationS 0 Mode, where fig. 10(a) is a time domain waveform and fig. 10(b) is a time-frequency distribution result.
Looking at fig. 7, 9 and 10, comparing the original and separated modes, the separated result and the original result keep better consistency. Therefore, the theoretical dispersion curve is applied, the complete compensation of the dispersion of each guided wave mode can be realized, and the separation of multi-mode signals can be realized based on the mode compensation principle.
Steel plate ultrasonic guided wave experimental signal mode compensation and separation example
The frequency dispersion compensation and mode separation are realized on the ultrasonic guided wave signals of the 1mm steel plate experiment by using a frequency dispersion compensation analysis method. The experimental signals are shown in FIG. 11 and mainly include patternsA 0 AndS 0 fig. 10(a) shows a time domain waveform, and fig. 10(b) shows a time-frequency distribution. Warp modeS 0 The result after the frequency dispersion transfer function compensation is shown in FIG. 12, in which FIG. 12(a) is a time domain waveform, FIG. 12(b) is a time-frequency distribution, and the original mode with a longer duration (about 0.11 ms) can be seenS 0 Is compressed into a pulse signal with a short duration (about 0.02 ms), andin time and modeA 0 Without overlap, dual mode separation can be achieved with time window clipping. Further patterns for separation resultsS 0 The inverse compensation of the dispersion transfer function is shown in FIG. 13, in which FIGS. 13(a) (b) are modesS 0 Time domain waveform and its time-frequency distribution, 13(c) (d) are modes respectivelyA 0 Time domain waveforms and their time-frequency distribution. As can be seen from FIG. 13, the patternsA 0 AndS 0 through the algorithm of this patent, guided wave mode separation has been realized.
Claims (1)
1. An ultrasonic guided wave frequency dispersion compensation and multi-mode separation algorithm based on time domain rearrangement is characterized by comprising the following specific steps:
ultrasonic guided wave frequency dispersion simulation algorithm
(1) Calculating group delay for a certain excitation, and calculating the group delay corresponding to each harmonic component of a certain guided wave mode by the following formula (1):
wherein,
d is the distance between the transmitting transducer and the receiving transducer,
the relation between the group velocity and the frequency of a certain guided wave mode;
(2) solving a frequency dispersion transfer function according to the group delay, and solving a frequency dispersion transfer function corresponding to a guided wave mode, wherein the expression is as follows:
（2）
wherein the signal
Is an integral initial value;
(3) the forward simulation of ultrasonic guided wave frequency dispersion solves the output of the excitation signal passing through the frequency dispersion system according to the frequency dispersion transfer function, namely the simulation signal corresponding to the excitation in a certain mode is obtained, if the frequency of the excitation signal is
Then receiving the signal spectrum
The formula is as follows:
(4) respectively solving different guided wave modes by the method of the steps (1) to (3) through multi-guided wave mode superposition, and superposing multi-mode signals;
ultrasonic guided wave frequency dispersion compensation
(5) Solving the inverse function of the dispersion transfer function to realize the dispersion compensation of the corresponding mode, and solving the transfer function obtained in the step (2)The inverse function, whose expression is:
（4）
(6) the guided wave mode frequency dispersion compensation realizes the frequency dispersion compensation on a certain mode by the above formula (4), if the frequency spectrum of a dispersion signal is
Then, the dispersion compensation formula is:
ultrasonic guided wave multi-mode separation algorithm
(7) Separating a mixed signal of a compensation mode instantaneous excitation and an under-compensation mode from a frequency dispersion compensation result by compensation mode energy separation; the energy separation method comprises the following steps: 1) if the excitation can be measured in advance, directly removing the excitation to obtain a residual mode signal; 2) if the excitation can not be measured in advance, all signal energy of the compensation result near the zero moment is separated and calculated as compensation mode energy, and the rest part is under-compensation mode energy;
(8) the frequency dispersion inverse compensation restores the signal mode to the inverse compensation of the separation result in the step (7); the specific formula of the inverse compensation is as follows:
wherein
As a result of the separation in the step (7),
for a mode of guided wave dispersion signals,
a transfer function expression corresponding to the guided wave mode;
(9) repeating steps (6) - (8) for the remaining guided wave modes until all modes are separated.
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Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102354343A (en) * | 2011-10-21 | 2012-02-15 | 北京工业大学 | Method for calculating ultrasonic guided wave frequency dispersion relationship based on characteristic frequency method |
| CN102565201A (en) * | 2011-10-25 | 2012-07-11 | 中国人民解放军理工大学 | Lamb wave frequency dispersion compensation method based on wave number curve measurement |
| CN105301117A (en) * | 2015-10-14 | 2016-02-03 | 浙江大学 | Method for detecting peripheral defect of hollow cylinder by ultrasonic frequency dispersion compensation principle |
| CN105510444A (en) * | 2015-11-27 | 2016-04-20 | 华南理工大学 | Two-way time reversal damage imaging method based on ultrasonic guided-wave |
| CN106354949A (en) * | 2016-08-30 | 2017-01-25 | 电子信息系统复杂电磁环境效应国家重点实验室 | Data compensation method based on Mallat algorithm and predistortion technology |
| CN107807175A (en) * | 2017-10-12 | 2018-03-16 | 南京航空航天大学 | A kind of improved frequency dispersion ultrasonic guided wave signals domain transform method |
| CN108514430A (en) * | 2018-05-07 | 2018-09-11 | 南京大学 | A kind of array multifrequency point ultrasonic bone density measuring technique |
| CN109856252A (en) * | 2019-02-01 | 2019-06-07 | 南京信息工程大学 | A kind of multi-mode Lamb wave separation method based on dispersion compensation and blind separation |
| CN112464524A (en) * | 2020-11-07 | 2021-03-09 | 西南交通大学 | Method for determining guided wave propagation characteristics of turnout variable cross-section steel rail |
| CN113218320A (en) * | 2021-05-06 | 2021-08-06 | 山东大学 | OFDR (offset-field-of-view) large strain measurement method based on distance domain compensation |
| CN114487117A (en) * | 2022-02-18 | 2022-05-13 | 浙江大学 | Non-recursive high-efficiency imaging method for ultrasonic phased array full matrix data |
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| CN102354343B (en) * | 2011-10-21 | 2014-01-08 | 北京工业大学 | Method for calculating ultrasonic guided wave frequency dispersion relationship based on characteristic frequency method |
| CN102354343A (en) * | 2011-10-21 | 2012-02-15 | 北京工业大学 | Method for calculating ultrasonic guided wave frequency dispersion relationship based on characteristic frequency method |
| CN102565201A (en) * | 2011-10-25 | 2012-07-11 | 中国人民解放军理工大学 | Lamb wave frequency dispersion compensation method based on wave number curve measurement |
| CN102565201B (en) * | 2011-10-25 | 2013-09-25 | 中国人民解放军理工大学 | Lamb wave frequency dispersion compensation method based on wave number curve measurement |
| CN105301117A (en) * | 2015-10-14 | 2016-02-03 | 浙江大学 | Method for detecting peripheral defect of hollow cylinder by ultrasonic frequency dispersion compensation principle |
| CN105301117B (en) * | 2015-10-14 | 2017-11-10 | 浙江大学 | A kind of method that hollow cylinder circumferential defect is detected with ultrasonic frequency dispersion compensation principle |
| CN105510444A (en) * | 2015-11-27 | 2016-04-20 | 华南理工大学 | Two-way time reversal damage imaging method based on ultrasonic guided-wave |
| CN105510444B (en) * | 2015-11-27 | 2018-04-13 | 华南理工大学 | Two-way time reversal damage imaging method based on supersonic guide-wave |
| CN106354949B (en) * | 2016-08-30 | 2019-10-25 | 电子信息系统复杂电磁环境效应国家重点实验室 | Compensation data method based on Mallat algorithm and pre-distortion technology |
| CN106354949A (en) * | 2016-08-30 | 2017-01-25 | 电子信息系统复杂电磁环境效应国家重点实验室 | Data compensation method based on Mallat algorithm and predistortion technology |
| CN107807175A (en) * | 2017-10-12 | 2018-03-16 | 南京航空航天大学 | A kind of improved frequency dispersion ultrasonic guided wave signals domain transform method |
| CN107807175B (en) * | 2017-10-12 | 2019-04-23 | 南京航空航天大学 | A kind of improved frequency dispersion ultrasonic guided wave signals domain transform method |
| CN108514430A (en) * | 2018-05-07 | 2018-09-11 | 南京大学 | A kind of array multifrequency point ultrasonic bone density measuring technique |
| CN109856252A (en) * | 2019-02-01 | 2019-06-07 | 南京信息工程大学 | A kind of multi-mode Lamb wave separation method based on dispersion compensation and blind separation |
| CN109856252B (en) * | 2019-02-01 | 2021-03-16 | 南京信息工程大学 | Multimode lamb wave separation method based on frequency dispersion compensation and blind separation |
| CN112464524A (en) * | 2020-11-07 | 2021-03-09 | 西南交通大学 | Method for determining guided wave propagation characteristics of turnout variable cross-section steel rail |
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