CN112179995B - Ultrasonic guided wave signal reconstruction method based on transfer function - Google Patents

Ultrasonic guided wave signal reconstruction method based on transfer function Download PDF

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CN112179995B
CN112179995B CN202010976496.1A CN202010976496A CN112179995B CN 112179995 B CN112179995 B CN 112179995B CN 202010976496 A CN202010976496 A CN 202010976496A CN 112179995 B CN112179995 B CN 112179995B
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杨志勃
朱明峰
陈雪峰
严如强
张兴武
王诗彬
李明
刘一龙
田绍华
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Xian Jiaotong University
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Abstract

The utility model discloses an ultrasonic guided wave signal reconstruction method based on transfer function, which comprises the following steps: applying a certain step signal epsilon (t) to an ultrasonic guided wave detection system for excitation, and collecting a step response signal r (t) generated by the ultrasonic guided wave detection system under the excitation of the step signal epsilon (t); performing Fourier transform on the step response signal R (t) to obtain a frequency domain step response signal R (omega), and further obtaining a transfer function H (omega) for representing the transfer relationship between the step response signal epsilon (t) and the step response signal R (t); and applying an arbitrary signal S (omega) to excite the ultrasonic guided wave detection system, multiplying the arbitrary signal S (omega) with a transfer function H (omega) in a frequency domain to obtain a frequency domain reconstruction response signal C (omega), and performing inverse Fourier transform on the frequency domain reconstruction response signal C (omega) to obtain a time domain reconstruction response signal C (t).

Description

Ultrasonic guided wave signal reconstruction method based on transfer function
Technical Field
The disclosure belongs to the technical field of ultrasonic guided wave, and particularly relates to an ultrasonic guided wave signal reconstruction method based on a transfer function.
Background
The structural health monitoring is vital to guarantee the safe and stable operation of major equipment, can reduce the maintenance cost of equipment, and is not limited by the strategy of regular maintenance of traditional equipment diagnosis. Meanwhile, the method has important significance for ensuring the life safety of people and the like. The ultrasonic guided wave is widely applied to structural health monitoring, such as Lamb waves, has the characteristics of long propagation distance and small attenuation, is very sensitive to micro damage, and is an important tool in guided wave monitoring. The ultrasonic guided wave structure health monitoring mode is an active health monitoring mode, and the traditional health monitoring mode is passive, so that the active ultrasonic guided wave structure health monitoring mode has great research significance and is an important development direction in the field of structure health monitoring.
In the field of ultrasound guided wave structure health monitoring, signals of various periods and frequencies are often required to be excited to acquire internal characteristics of a monitoring structure, such as cracks, layers, cavities, bolt looseness and the like. However, different excitation signals have different reaction capabilities to the structural feature, and therefore, it is important to quickly determine which excitation signal is optimal for the structural feature extraction.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the defects in the prior art, the disclosed method for reconstructing ultrasonic guided wave signals based on the transfer function can realize the rapid reconstruction of response signals under any excitation in an ultrasonic guided wave detection system by calculating the transfer function between excitation signals and response signals, avoids the complex steps of repeatedly acquiring the response signals through experiments under the common condition, reduces the time and labor cost, and realizes the rapid acquisition of target experiment signals.
In order to achieve the above purpose, the present disclosure provides the following technical solutions:
a method for reconstructing ultrasonic guided wave signals based on a transfer function comprises the following steps:
s100: applying a certain step signal epsilon (t) to an ultrasonic guided wave detection system for excitation, and collecting a step response signal r (t) generated by the ultrasonic guided wave detection system under the excitation of the step signal epsilon (t);
s200: performing Fourier transform on the step response signal r (t) to obtain a frequency domain step response signal B (omega), and further obtaining a transfer function H (omega) for representing the transfer relationship between the step response signal epsilon (t) and the step response signal r (t);
s300: and applying an arbitrary signal S (omega) to excite the ultrasonic guided wave detection system, multiplying the arbitrary signal S (omega) with a transfer function H (omega) in a frequency domain to obtain a frequency domain reconstruction response signal C (omega), and performing inverse Fourier transform on the frequency domain reconstruction response signal C (omega) to obtain a time domain reconstruction response signal C (t).
Preferably, step S200 includes the steps of:
s201: multiplying the frequency domain step response signal R (omega) by the angular frequency omega to obtain a transform frequency step response signal T (omega);
s202: the step response T (omega) signal of the conversion frequency and unit imaginary number
Figure BDA0002684927310000021
Multiplication is performed to obtain the transfer function H (ω).
Preferably, the transformation frequency step response signal T (ω) is represented by:
Figure BDA0002684927310000031
where ω is the angular frequency, e is the natural logarithmic sign, i is the imaginary unit, and dt is the first derivative of time t.
Preferably, in step 202, the transfer function H (ω) is represented as:
Figure BDA0002684927310000032
where Re (-) represents the real part of ". cndot.", and Im (-) represents the imaginary part of ". cndot.".
Preferably, in step S300, the frequency domain reconstruction response signal C (ω) is represented by:
C(ω)=S(ω)H(ω)=S(ω)·Re(H(ω))+S(ω)·Im(H(ω))
where Re (-) represents the real part of ". cndot.", and Im (-) represents the imaginary part of ". cndot.".
Preferably, in step S100, after the step response signal r (t) is acquired, the step response signal r (t) needs to be subjected to 0 compensation processing, specifically, the processing is performed in the following manner:
Figure BDA0002684927310000033
wherein, N is the original length of the step response signal r (t), and the length after 0 complementing is 9N.
Preferably, the method further comprises step S400: removing redundant signals in the reconstructed response signal c (t) to obtain a real reconstructed response signal d (t), where the real reconstructed response signal d (t) is represented as:
Figure BDA0002684927310000034
wherein M is the length of the real reconstructed response signal, and M and N satisfy N ═ 1.5M.
Preferably, the sampling time length of the step response signal r (t) is greater than the time length of the real reconstructed response signal d (t).
The present disclosure also provides a system for implementing a method for ultrasonic guided wave signal reconstruction, comprising:
a signal excitation unit for generating an excitation signal of an arbitrary waveform;
a signal amplification unit for amplifying the excitation signal;
the signal loading unit is used for loading the amplified excitation signal to the ultrasonic guided wave detection system;
and the signal acquisition unit is used for acquiring a response signal generated by the ultrasonic guided wave detection system under the action of the excitation signal.
Preferably, the excitation frequency of the signal excitation unit is 20MHz, and the collection frequency of the signal collection unit is 10 MHz.
Compared with the prior art, the beneficial effect that this disclosure brought does: the method can reconstruct the response signal under any excitation in the ultrasonic guided wave detection system by utilizing the transfer function, can avoid obtaining the response signal through repeated experiments, reduces the time and labor cost, and can ensure that the reconstructed response signal has the same accuracy as the response signal obtained through experimental means while realizing the quick obtaining of the response signal.
Drawings
Figure 1 is a flow chart of a method for reconstructing an ultrasonic guided wave signal based on a transfer function according to an embodiment of the present disclosure;
FIG. 2 is a waveform diagram of a time domain response under step excitation of an ultrasonic guided wave signal reconstruction method based on a transfer function according to another embodiment of the disclosure;
FIG. 3 is a waveform diagram of a frequency domain response under step excitation of an ultrasonic guided wave signal reconstruction method based on a transfer function according to another embodiment of the disclosure;
FIG. 4 is a time domain diagram of a 3-cycle 50KHz center frequency tone burst excitation signal of an ultrasonic guided wave signal reconstruction method based on a transfer function according to another embodiment of the present disclosure;
FIG. 5 is a time domain diagram of an experimental acquisition signal excited by a 3-cycle 50KHz center frequency of an ultrasonic guided wave signal reconstruction method based on a transfer function according to another embodiment of the present disclosure;
FIG. 6 is a time domain diagram of a reconstructed signal excited by a center frequency of 50KHz with a period of 3 according to an ultrasonic guided wave signal reconstruction method based on a transfer function provided by another embodiment of the disclosure;
FIG. 7 is a time domain diagram of a 5-cycle 70KHz center frequency tone burst excitation signal of a method for reconstructing an ultrasonic guided wave signal based on a transfer function according to another embodiment of the present disclosure;
FIG. 8 is a time domain diagram of an experimental acquisition signal excited by a central frequency of 70KHz with a period of 5 cycles according to an ultrasonic guided wave signal reconstruction method based on a transfer function provided by another embodiment of the present disclosure;
FIG. 9 is a time domain diagram of a reconstructed signal excited by a center frequency of 70KHz with a period of 5 according to an ultrasonic guided wave signal reconstruction method based on a transfer function provided by another embodiment of the disclosure;
figure 10 is a schematic structural diagram of a system for implementing a method for reconstructing an ultrasonic guided wave signal according to another embodiment of the present disclosure.
Detailed Description
Specific embodiments of the present disclosure will be described in detail below with reference to fig. 1 to 10. While specific embodiments of the disclosure are shown in the drawings, it should be understood that the disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present disclosure is to be determined by the terms of the appended claims.
To facilitate an understanding of the embodiments of the present disclosure, the following detailed description is to be considered in conjunction with the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present disclosure.
In one embodiment, as shown in fig. 1, a method for reconstructing an ultrasonic guided wave signal based on a transfer function includes the following steps:
s100: applying a certain step signal epsilon (t) to an ultrasonic guided wave detection system for excitation, and collecting a step response signal r (t) generated by the ultrasonic guided wave detection system under the excitation of the step signal epsilon (t);
s200: performing Fourier transform on the step response signal r (t) to obtain a frequency domain response step signal B (omega), and further obtaining a transfer function H (omega) for representing the transfer relationship between the step signal epsilon (t) and the step response signal r (t);
s300: and applying an arbitrary signal S (omega) to excite the ultrasonic guided wave detection system, multiplying the arbitrary signal S (omega) with a transfer function H (omega) in a frequency domain to obtain a frequency domain reconstruction response signal C (omega), and performing inverse Fourier transform on the frequency domain reconstruction response signal C (omega) to obtain a time domain reconstruction response signal C (t).
It can be seen that the above embodiments approximate a structural health monitoring system using guided waves to a linear system, and thus, the response of the monitored structure can be obtained by multiplying the excitation by the transfer function. Further, it can be understood that: the response under any excitation can be reconstructed as long as the transfer function between input and output is obtained. This turns the problem to how to obtain a transfer function between the monitoring system input and output.
The transfer function is the unit impulse response of the system, therefore, ideally, the impulse signal can be excited to obtain the transfer function of the system, which is actually limited by the performance of the device, and the impulse excitation is not easily obtained, but provides a guiding idea for the above-mentioned embodiment to obtain the transfer function. Therefore, as long as the transfer function is obtained, it is not necessary to rely on experiments to obtain the guided wave response under any excitation.
Based on this, the above embodiments provide a method for reconstructing an ultrasonic guided wave signal based on a transfer function.
In another embodiment, step S100 may specifically include the following steps: after the step response signal r (t) is acquired, the step response signal r (t) needs to be subjected to 0 complementing processing.
In this embodiment, the matching between the reconstructed response signal and the response signal obtained by the subsequent experimental means can be made better by the 0 complementing process. The accuracy of the reconstructed response signal is related to the frequency resolution of the transfer function (i.e. the distance between adjacent frequency points), the higher the frequency resolution, the more accurate the detailed characterization of the reconstructed response signal. Wherein, frequency resolution equals sampling frequency and divides the number of sampling points, and sampling frequency is fixed, increases the number of sampling points and can improve frequency resolution, however can not a large amount of increase sampling points, and this can occupy a large amount of data storage space, and redundant signal is too much, consequently can short sampling, and 0 increases frequency resolution again by complementing, and concrete mode is as follows:
Figure BDA0002684927310000081
wherein, N is the original length of the step response signal r (t), and the length after 0 complementing is 9N.
In another embodiment, step S200 may specifically include the following steps:
s201: multiplying the frequency domain step response signal R (omega) by the angular frequency omega to obtain a transform frequency step response signal T (omega);
in this step, the transform frequency step response signal T (ω) is represented as:
Figure BDA0002684927310000082
where ω is the angular frequency, e is the natural logarithmic sign, i is the imaginary unit, and dt is the first derivative of time t.
S202: the step response T (omega) signal of the conversion frequency and unit imaginary number
Figure BDA0002684927310000083
Multiplication is performed to obtain the transfer function H (ω).
In this step, the transfer function H (ω) is expressed as:
Figure BDA0002684927310000084
where Re (-) represents the real part of ". cndot.", and Im (-) represents the imaginary part of ". cndot.".
In another embodiment, in step S300, the frequency domain reconstruction response signal C (ω) is represented as:
C(ω)=S(ω)H(ω)=S(ω)·Re(H(ω))+S(ω)·Im(H(ω))
where Re (-) represents the real part of ". cndot.", and Im (-) represents the imaginary part of ". cndot.".
In another embodiment, the method further comprises step S400: removing redundant signals in the reconstructed response signal c (t) to obtain a real reconstructed response signal d (t), where the real reconstructed response signal d (t) is represented as:
Figure BDA0002684927310000091
wherein M is the length of the real reconstructed response, and M and N satisfy N ═ 1.5M.
In this embodiment, the redundant signal needs to be removed because it comes from the data point of the complement 0 used to improve the frequency resolution of the transfer function, rather than from the actual step response signal.
In another embodiment, the sampling time length of the step response signal r (t) (step response signal before 0 is compensated) is longer than the time length of the real reconstructed response signal d (t).
In this embodiment, limited by the performance of system hardware, the step signal ∈ (t) cannot be triggered at time 0, and there is a time delay, which may cause the step response signal r (t) to move backward on the time scale, so the time length of the step response signal r (t) (the step response signal before compensating for 0) should be greater than the time length of the real reconstructed response signal d (t), so as to compensate for the backward movement time.
Referring to fig. 2, the time domain response waveform shown in the figure has a time length of 1500us, and can reconstruct a signal with a time length of less than 1500us, and data close to 1500us is not available due to out-of-range, and the reconstructed signal has a time length of 1000us in the embodiment.
Referring to fig. 3, according to the nyquist sampling theorem, only the transfer function in the frequency range below half the sampling frequency, which is 10MHz in this case, is accurate, so that signals in the frequency band range as shown in fig. 3, i.e. the 5MHz frequency band range, can be used for reconstructing the signal, and the reconstructed signal beyond the 5MHz frequency band will be aliased.
In order to further illustrate that the method can accurately reconstruct signals, and verify the adaptability and reliability of the method to different excitation signal frequencies and periods, the following adopts different excitation signals to verify the technical scheme provided by the present disclosure.
Comparing the shape of the reconstructed response signal with the shape of the response signal obtained by experiment is the most intuitive and explanatory comparison method for verifying the method. Fig. 4 is a time domain diagram of a tone burst excitation signal with a cycle number of 3 and a center frequency of 50KHz, an experimental response signal when the signal of fig. 4 is used as an excitation is shown in fig. 5, a reconstructed response signal is shown in fig. 6, and it can be seen that the shapes of the reconstructed response signal of fig. 6 and the experimental response signal of fig. 5 have high similarity. At the same time, the curve of the reconstructed signal of fig. 6 is smoother than the experimental signal, since the transfer function has a filtering effect. Fig. 7 is a time domain diagram of a tone burst excitation signal having a cycle number of 5 and a center frequency of 70KHz, and an experimental response signal and a reconstructed response signal corresponding to the excitation signal of fig. 7 are shown in fig. 8 and fig. 9, respectively. The same experimental phenomena as the experimental response and the reconstructed response under the excitation signal of fig. 4 occur, i.e., the reconstructed signal and the experimental response signal can still maintain good similarity under the conditions of the variable period and the central frequency excitation signal.
Through the comparison, the technical scheme provided by the disclosure has the capability of accurately reconstructing the response signal, can replace the response signal obtained through experiments, does not need to execute complicated experiments to obtain the response signals under various excitation signals, and thus can save a large amount of time and labor cost.
In another embodiment, as shown in fig. 10, the present disclosure also provides a system for implementing a method for ultrasonic guided wave signal reconstruction, including:
a signal excitation unit for generating an excitation signal of an arbitrary waveform;
a signal amplification unit for amplifying the excitation signal;
the signal loading unit is used for loading the amplified excitation signal to the ultrasonic guided wave detection system;
and the signal acquisition unit is used for acquiring a response signal generated by the ultrasonic guided wave detection system under the action of the excitation signal.
Based on the system provided by the embodiment, the guided wave response signal of any central frequency and periodic excitation signal can be reconstructed without repeatedly adopting experimental means, the accuracy same as that of an experimental target signal can be obtained, and the labor and time costs are reduced.
In another embodiment, the excitation frequency of the signal excitation unit is 20MHz, and the collection frequency of the signal collection unit is 10 MHz.
The foregoing describes the general principles of the present disclosure in conjunction with specific embodiments, however, it is noted that the advantages, effects, etc. mentioned in the present disclosure are merely examples and are not limiting, and they should not be considered essential to the various embodiments of the present disclosure. Furthermore, the foregoing disclosure of specific details is for the purpose of illustration and description and is not intended to be limiting, since the foregoing disclosure is not intended to be exhaustive or to limit the disclosure to the precise details disclosed.

Claims (8)

1. A transfer function solving and ultrasonic guided wave signal reconstruction method based on step excitation comprises the following steps:
s100: applying a certain step signal epsilon (t) to an ultrasonic guided wave detection system for excitation, and collecting a step response signal r (t) generated by the ultrasonic guided wave detection system under the excitation of the step signal epsilon (t);
s200: performing a fourier transform on the step response signal R (t) to obtain a frequency-domain step response signal R (ω), and further obtaining a transfer function H (ω) representing a transfer relationship between the step response signal R (t) and the step response signal R (t), wherein the transfer function H (ω) is obtained by:
s201: multiplying the frequency domain step response signal R (omega) by the angular frequency omega to obtain a transform frequency step response signal T (omega);
s202: the step response T (omega) signal of the conversion frequency and unit imaginary number
Figure FDA0003222360600000011
Multiplying to obtain a transfer function H (ω), said transfer function H (ω) being expressed as:
Figure FDA0003222360600000012
wherein Re (·) represents the real part of "·", and Im (·) represents the imaginary part of "·";
s300: and applying an arbitrary signal S (omega) to excite the ultrasonic guided wave detection system, multiplying the arbitrary signal S (omega) with a transfer function H (omega) in a frequency domain to obtain a frequency domain reconstruction response signal C (omega), and performing inverse Fourier transform on the frequency domain reconstruction response signal C (omega) to obtain a time domain reconstruction response signal C (t).
2. The method according to claim 1, wherein in step S201, the transform frequency step response signal T (ω) is represented as:
Figure FDA0003222360600000021
where ω is the angular frequency, e is the natural logarithmic sign, i is the unit imaginary number, and dt is the first differential of time t.
3. The method according to claim 1, wherein in step S300, the frequency domain reconstruction response signal C (ω) is represented as:
C(ω)=S(ω)H(ω)=S(ω)·Re(H(ω))+S(ω)·Im(H(ω))
where Re (-) represents the real part of ". cndot.", and Im (-) represents the imaginary part of ". cndot.".
4. The method according to claim 1, wherein in step S100, after acquiring the step response signal r (t), the step response signal r (t) needs to be subjected to 0 complementing processing, specifically by:
Figure FDA0003222360600000022
wherein, N is the original length of the step response signal r (t), and the length after 0 complementing is 9N.
5. The method according to claim 1, wherein the method further comprises a step S400 of: removing redundant signals in the reconstructed response signal c (t) to obtain a real reconstructed response signal d (t), where the real reconstructed step response signal d (t) is represented as:
Figure FDA0003222360600000023
wherein M is the length of the real reconstructed response signal, and M and N satisfy N ═ 1.5M.
6. The method according to claim 1, wherein the sampling time length of the acquired step response signal r (t) is larger than the time length of the real reconstructed response signal d (t).
7. A system for implementing the method of claim 1, comprising:
a signal excitation unit for generating an excitation signal of an arbitrary waveform;
a signal amplification unit for amplifying the excitation signal;
the signal loading unit is used for loading the amplified excitation signal to the ultrasonic guided wave detection system;
and the signal acquisition unit is used for acquiring a response signal generated by the ultrasonic guided wave detection system under the action of any excitation signal.
8. The system of claim 7, wherein the excitation frequency of the signal excitation unit is 20MHz and the acquisition frequency of the signal acquisition unit is 10 MHz.
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