A virtual time reversal method for space-coupled Lamb waves based on chirp signal technology

Abstract

The present invention relates to a virtual time reversal method for air-coupled Lamb waves based on chirp signal technology, and belongs to the field of communication signal technology. The method solves the problem that in the process of calculating the transfer function of a traditional narrowband pulse signal, the existence of an amplitude zero point or a point close to zero within the frequency band will cause a numerical error in the transfer function, thereby affecting the waveform accuracy of the inverted focus signal. Step 1: Input a chirp signal to excite the target structure and calculate the transfer function of the detection system; Step 2: Apply the transfer function to excite the narrowband signal, perform a virtual time reversal on the narrowband pulse signal, and obtain an inverted focus signal. This avoids the numerical error in the structure transfer function caused by the existence of a point zero or close to zero in the frequency amplitude of the narrowband pulse signal, and improves the accuracy of the inverted focus signal.

Description

Technical Field

[0001] The invention relates to a virtual time reversal method based on signal technology, belonging to the technical field of communication signals. Background Art

[0002] The development of nondestructive testing technologies for thin-walled structures (such as pipes, wind turbine blades, aircraft fuselages, pressure vessels, and ship hulls) has attracted great interest from contemporary researchers due to its application prospects and challenges. In recent years, ultrasonic guided wave technology, as a cutting-edge nondestructive testing and structural health monitoring method, has shown broad application prospects in the field of evaluation of plate-like structural components. In particular, guided wave propagation technology based on Lamb waves has the advantage of being able to propagate over relatively long distances while maintaining sensitivity to small changes in the structure, and has the advantage of detecting small damage (larger than half a wavelength). In addition, guided wave propagation technology based on Lamb waves can easily generate ultrasonic waves using low-cost piezoelectric transducers and minimal energy, and its implementation cost is relatively low, so it is widely used for defect detection in thin plate structures such as metals and composite materials.

[0003] The traditional baseline-based air-coupled Lamb detection method is easily affected by factors such as differences in the external environment and operating conditions, which results in large errors when comparing this method with baseline data. To address this issue, as well as the difficulty in obtaining baseline data, many studies have been conducted on baseline-free detection methods based on guided waves. The Lamb wave time reversal method has been widely studied as a baseline-free damage detection method. Compared with the time reversal method, the virtual time reversal method only performs a single forward physical pitch capture configuration, because the backward transmission process is actually replaced by computer signal operations, which greatly simplifies the detection steps.

[0004] In order to ensure that the ultrasonic transducer can effectively transfer mechanical energy to the sample, traditional contact ultrasonic detection methods often use water, glycerin and vaseline as coupling agents. However, the use of coupling agents will greatly reduce the detection efficiency and cause contamination to the material being tested. Air-coupled ultrasonic detection technology uses air as a coupling medium, which has the characteristics of non-contact and pollution-free. However, there is currently no solution for virtual time reversal of air-coupled ultrasonic detection. In addition, in the current virtual time reversal experiments, since the virtual time reversal of broadband signals will cause reversal failure due to the amplitude dispersion of different frequency components, most of them use narrowband pulse signals as excitation signals. However, there are some frequency amplitudes in the narrowband pulse signal that are close to or equal to 0, which will produce numerical errors in the process of calculating the transfer function, limiting the accuracy of the focused signal obtained by virtual time reversal. For example: suppose the time domain signal V of the first excitation is e (t) The corresponding frequency domain signal is V e (ω), the first received time domain signal Vr (t) The corresponding frequency domain signal is V r (ω), the second excitation signal V' e (t) The corresponding frequency domain signal is V' e (ω), the second received signal V' r (t) The corresponding frequency domain signal is V' r (ω). Since the time domain signal flip in the time domain is equal to the frequency domain conjugate, assuming that the transfer function of the frequency domain signal is G(r,ω), the relationship can be obtained:

[0005] V e (ω)=FT(V e (t)) (13)

[0006] V r (t) = FT(V r (ω)) (14)

[0007] V r (ω)=V e (ω)G(r,ω) (15)

[0008]

[0009] V r '(ω)=V e '(ω)G(r,ω) (17)

[0010] The combined equations (13) to (17) yield

[0011] V r '(t)=IFT(V r '(ω)) (18)

[0012] If there is no defect, due to the linear relationship of the virtual time reversal algorithm process, the reconstructed V' r (ω) will be normalized to V e (t) is completely equal; if there is a defect, the time reversibility will be destroyed, the reconstruction will fail, and the reconstructed signal V' r (ω) and V e Therefore, the core of the virtual time reversal algorithm is to accurately reproduce the transfer function. The accuracy of the transfer function will affect the waveform of the inverted focused signal. In the process of calculating the transfer function of traditional narrowband pulse signals, the existence of zero amplitude or near-zero amplitude points within the frequency band will cause numerical errors in the transfer function, affecting the waveform accuracy of the inverted focused signal.

[0013] Therefore, it is urgent to propose a space-coupled Lamb wave virtual time reversal method based on chirp signal technology to solve the above technical problems. Summary of the Invention

[0014] To address the above issues, a space-coupled Lamb wave virtual time reversal method based on chirp signal technology is provided. A brief overview of the invention is provided below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive overview of the invention. It is not intended to identify key or important aspects of the invention, nor is it intended to limit the scope of the invention.

[0015] The technical solution of the present invention:

[0016] A chirp signal-based space-coupled Lamb wave virtual time reversal method (CRVTR) is implemented using chirp signal technology. The chirp signal is used to excite a structure with high bandwidth characteristics to obtain a structural transfer function under the chirp signal. The transfer function is then used to perform virtual time reversal under narrowband signal excitation. The method comprises the following steps:

[0017] Step 1: Generate a chirp signal (a signal whose frequency varies with time) with high bandwidth characteristics, input the generated chirp signal to stimulate the target structure, and calculate the transfer function of the detection system;

[0018] Step 2: Apply the transfer function to excite the narrowband signal, perform virtual time reversal on the narrowband pulse signal, and obtain the inverted focusing signal.

[0019] Preferably: in step one, the detection system includes an air-coupled transducer A and an air-coupled transducer B, the target structure is a thin-walled structure or a thin plate structure, the air-coupled transducer A applies an excitation signal to the target structure, and the air-coupled transducer B receives the signal. The distance between the air-coupled transducer A and the target structure to be measured can be a fixed value or a variable value, and the distance between the air-coupled transducer B and the target structure to be measured can be a fixed value or a variable value.

[0020] Preferably: In step 1, the input chirp signal is set to S e (t), the corresponding frequency domain signal is S e (ω), the received time domain signal is S r (t), the corresponding frequency domain signal is S r (ω), then the transfer function of the entire detection system is calculated according to the following formula;

[0021] S r (ω)=G A (ω)G B (ω)S e (ω)G AB (r,ω)e -2αh (1)

[0022] Where r is the propagation distance of Lamb wave, ω is the angular frequency, α is the attenuation coefficient of ultrasonic wave in air, h is the distance between the air-coupled ultrasonic transducer and the thin plate to be measured, G A (ω) is the transfer function of exciting the air-coupled transducer A, G B (ω) is the transfer function of the receiving air-coupled transducer B, G AB (r,ω) is the structural transfer function from the excitation point A to the excitation point B in the plate structure;

[0023] The relationship is established through Fourier transform, so the transfer function of the detection system is:

[0024]

[0025] Where e is the base of the natural logarithm in the exponential function, which is used to describe the complex exponential form of the signal in the frequency domain.

[0026] Preferably, in step 2, the transfer function is a broadband transfer function, which can be applied to multiple different frequencies; then, based on the transfer function G(ω), a virtual time reversal of the narrowband pulse signal is performed, and the time domain signal V of the first excitation is set to e (t) The corresponding frequency domain signal is V e (ω), the first received time domain signal V r (t) The corresponding frequency domain signal is V r (ω), the second excitation signal V' e (t) The corresponding frequency domain signal is V' e (ω), the second received signal V' r (t) The corresponding frequency domain signal is V' r (ω); In the above signal, the original input signal V is known e (t) The corresponding frequency domain signal is V e (ω), then from the above transfer function, we can get the following relationship:

[0027] V r (ω)=V e (ω)G(ω) (3)

[0028]

[0029] In order to perform time reversal, V r (t) Perform complex conjugate operation to obtain the inverted signal V' r (t), where '*' represents the complex conjugate operation;

[0030] In the above formula, the final time-reversed signal is V' r (t), the signal converges to the main mode.

[0031] Preferably: in step 1, the structural transfer function of the entire detection system is calculated according to formula (2); the transducer transfer function is integrated into the structural transfer function to simplify the derivation process of the transfer function;

[0032] S r (ω)=S e (ω)G(r,ω)e -2αh (7)

[0033] Among them, G(r,ω) is G AB (r,ω), represents the transfer function from the excitation point A to the excitation point B in the detection system;

[0034] When the distance between air-coupled transducers A and B and the target structure to be measured is a constant, the attenuation of ultrasonic waves in the air is constant, which does not affect the virtual time reversal process of Lamb waves and has no effect on the transfer function. Therefore, the transfer function of the detection system can be further written as:

[0035]

[0036] Preferably: in step 2, Figure 3 As shown, let a five-cycle sinusoidal signal modulated by a Hanning window be V e (t), the corresponding frequency domain signal is V e (ω), according to the transfer function, the first received time domain signal V is obtained. r (t), the corresponding frequency domain signal is V r (ω);

[0037] V r (ω)=V e (ω)G(ω) (9)

[0038]

[0039] The received signal V r (t) Perform time domain inversion, which is equivalent to the complex conjugate operation in the frequency domain; obtain the second excitation signal V' e (t), the corresponding frequency domain signal is V' e (ω), and then the second excitation signal is transmitted through the air-coupled transducer A along the same path and received by the air-coupled transducer B to obtain the second received signal V' r (t), the corresponding frequency domain signal is V' r (t); as formula (22);

[0040]

[0041] When there is no damage on the path, the focus signal V' is inverted r(t) can reconstruct the original input signal V e Even if there is amplitude dispersion that cannot be eliminated, the waveform of (t) can at least reconstruct the shape of the original input signal. When there is damage on the path, the time reciprocity of the detection path will be destroyed, resulting in the inverted focused signal being unable to completely reconstruct the original input signal. This property can be used to perform baseline-free detection of Lamb waves.

[0042] Preferred: A chirp signal technology-based air-coupled Lamb wave virtual time reversal method is applied to non-destructive testing of thin-walled structures.

[0043] The present invention has the following beneficial effects:

[0044] In the time reversal calculation process, the present invention uses the broadband transfer function of the chirp signal instead of the traditional narrowband transfer function, avoiding the numerical error of the structural transfer function caused by the existence of zero or near-zero points in the frequency amplitude of the narrowband pulse signal, and greatly improving the accuracy of the inverted focus signal.

[0045] The present invention avoids the inability to reconstruct the original input signal when using the broadband signal itself for time reversal;

[0046] The transfer function obtained by the present invention also has a certain bandwidth and can be applied to baseline-free measurement of Lamb waves of multiple frequencies simultaneously, without the need for repeated signal acquisition, thereby improving efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is the principle diagram of virtual time reversal of narrowband pulse signal.

[0048] Figure 2 This is the experimental principle diagram of using chirp signals to obtain transfer functions.

[0049] Figure 3 This is a schematic diagram of the principle of using chirp signals to achieve virtual time reversal of narrowband pulse signals. G(r,ω) is the structural transfer function from the excitation signal to the received signal.

[0050] Figure 4 It uses the structural transfer function and the corresponding excitation signal spectrum restored by traditional VTR.

[0051] Figure 5 Comparison of inverted focus signals: (a) traditional virtual time reversal (VTR), (b) virtual time reversal using chirp signal technology (CRVTR). DETAILED DESCRIPTION

[0052] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0053] Specific implementation method 1: Combination Figure 1-5 This embodiment is described. This embodiment is an air-coupled Lamb wave virtual time reversal method based on chirp signal technology. The chirp signal technology is used to implement a virtual time reversal method (CRVTR). The chirp signal is used to excite a characteristic with high bandwidth characteristics to obtain a structural transfer function under the chirp signal. The transfer function is then used to perform virtual time reversal under narrowband signal excitation. Virtual time reversal refers to a process in which, for a one-transmit-one-receive mode, the effective signal received by the receiving probe is intercepted, and then the signal is flipped end to end on the time axis to become a new signal that is excited from the transmitting probe and received by the receiving probe again. The virtual time reversal method proposed in the present invention is based on this and uses the chirp signal to obtain a transfer function to simulate the above process. The method includes the following steps:

[0054] Step 1: Generate a chirp signal (a signal whose frequency varies with time) with high bandwidth characteristics, input the generated chirp signal to stimulate the target structure, and calculate the transfer function of the detection system;

[0055] In step 1, the detection system includes transducer A and transducer B. Both transducer A and transducer B are air-coupled transducers (air-coupled transducers). The target structure is a thin-walled structure or a thin plate structure. Air-coupled transducer A applies an excitation signal to the target structure, and air-coupled transducer B receives the signal. The distance between air-coupled transducer A and the target structure to be measured can be a fixed value or a variable value, and the distance between air-coupled transducer B and the target structure to be measured can be a fixed value or a variable value.

[0056] In step 1, let the input chirp signal be S e (t), the corresponding frequency domain signal is S e (ω), the received time domain signal is S r (t), the corresponding frequency domain signal is S r (ω), then the transfer function of the entire detection system is calculated according to the following formula;

[0057] S r (ω)=G A (ω)G B (ω)S e (ω)G AB (r,ω)e -2αh(1)

[0058] Where r is the propagation distance of Lamb wave, ω is the angular frequency, α is the attenuation coefficient of ultrasonic wave in air, h is the distance between the air-coupled ultrasonic transducer and the thin plate to be measured, G A (ω) is the transfer function of exciting the air-coupled transducer A, G B (ω) is the transfer function of the receiving air-coupled transducer B, G AB (r,ω) is the structural transfer function from the excitation point A to the excitation point B in the plate structure;

[0059] The relationship is established through Fourier transform, so the transfer function of the detection system is:

[0060]

[0061] Where e is the base of the natural logarithm in the exponential function, which is used to describe the complex exponential form of the signal in the frequency domain;

[0062] Step 2: Apply the transfer function to excite the narrowband signal, perform virtual time reversal on the narrowband pulse signal, and obtain the inverted focusing signal;

[0063] In step 2, the transfer function is a broadband transfer function that can be applied to multiple different frequencies. Then, based on the transfer function G(ω), a virtual time reversal of the narrowband pulse signal is performed. Let the time domain signal V of the first excitation be e (t) The corresponding frequency domain signal is V e (ω), the first received time domain signal V r (t) The corresponding frequency domain signal is V r (ω), the second excitation signal V' e (t) The corresponding frequency domain signal is V' e (ω), the second received signal V' r (t) The corresponding frequency domain signal is V' r (ω); In the above signal, the original input signal V is known e (t) The corresponding frequency domain signal is V e (ω), then from the above transfer function, we can get the following relationship:

[0064] V r (ω)=V e (ω)G(ω) (3)

[0065]

[0066] In order to perform time reversal, V r (t) Perform complex conjugate operation to obtain the inverted signal V' r(t), where '*' represents the complex conjugate operation, i and t are introduced by the inverse Fourier transform, i is an imaginary number, and t represents time. It has no specific meaning here and only represents the time domain signal V(t) corresponding to V(ω);

[0067] In the above formula, the final time-reversed signal is V' r (t), the signal converges to the main mode, so this signal is also called the inverted focusing signal. In the calculation process of time reversal, the broadband transfer function of the chirp signal is used instead of the traditional narrowband transfer function, which avoids the numerical error of the structural transfer function caused by the existence of zero or near-zero points in the frequency amplitude of the narrowband pulse signal, which ultimately affects the accuracy of the inverted focusing signal. At the same time, it can also avoid the inability to reconstruct the original input signal when using the broadband signal itself for time reversal. In addition, due to the high bandwidth characteristics of the chirp signal, the transfer function obtained by this method also has a certain bandwidth, which can be applied to the baseline-free measurement of multiple frequency Lamb waves (plate waves) at the same time without the need to repeatedly acquire signals.

[0068] The present invention proposes a virtual time reversal method (CRVTR) using chirp signal technology. The chirp signal is used to excite the high-bandwidth characteristics to obtain the structural transfer function under the chirp signal, and then the transfer function is used to perform virtual time reversal under narrowband signal excitation. This method not only avoids the error generated in calculating the structural transfer function due to the presence of points with frequency amplitudes of 0 or close to 0 in the narrowband pulse signal, but also utilizes the high-bandwidth characteristics of the chirp so that the obtained transfer function can simultaneously realize the virtual time reversal of multiple narrowband pulse signals of different frequencies, effectively improving the detection efficiency.

[0069] Specific implementation method 2: Combination Figure 1-5 This embodiment describes a method for virtual time reversal of an air-coupled Lamb wave based on chirp signal technology, including the following steps:

[0070] Step 1: Calculate the structural transfer function of the entire detection system according to formula (2); integrate the transducer transfer function into the structural transfer function to simplify the derivation process of the transfer function;

[0071] S r (ω)=S e (ω)G(r,ω)e -2αh (7)

[0072] Among them, G(r,ω) is G AB (r,ω), represents the transfer function from the excitation point A to the excitation point B in the detection system;

[0073] When the distance between air-coupled transducers A and B and the target structure to be measured is a constant, the attenuation of ultrasonic waves in the air is constant, which does not affect the virtual time reversal process of Lamb waves and has no effect on the transfer function. Therefore, the transfer function of the detection system can be further written as:

[0074]

[0075] In step 2, if Figure 3 As shown, let a five-cycle sinusoidal signal modulated by a Hanning window be V e (t), the corresponding frequency domain signal is V e (ω), according to the transfer function, the first received time domain signal V is obtained. r (t), the corresponding frequency domain signal is V r (ω);

[0076] V r (ω)=V e (ω)G(ω) (9)

[0077]

[0078] The received signal V r (t) Perform time domain inversion, which is equivalent to the complex conjugate operation in the frequency domain; obtain the second excitation signal V' e (t), the corresponding frequency domain signal is V' e (ω), and then the second excitation signal is transmitted through the air-coupled transducer A along the same path and received by the air-coupled transducer B to obtain the second received signal V' r (t), the corresponding frequency domain signal is V' r (t);

[0079]

[0080] When there is no damage on the path, the focus signal V' is inverted r (t) can reconstruct the original input signal V e Even if there is amplitude dispersion that cannot be eliminated, the waveform of (t) can at least reconstruct the shape of the original input signal. When there is damage on the path, the time reciprocity of the detection path will be destroyed, resulting in the inverted focused signal being unable to completely reconstruct the original input signal. This property can be used to perform baseline-free detection of Lamb waves.

[0081] Example 1:

[0082] The present invention proposes to use chirp signals to calculate the transfer function G(r,ω), apply the transfer function G(r,ω) to the virtual time reversal process of narrowband pulse signals, and accurately reproduce the transfer function G(r,ω);

[0083] like Figure 2 As shown, when the excitation voltage V is applied to the air-coupled transducer A e At (t), the response signal V received by the air-coupled transducer B is r (t) The corresponding frequency domain signal V r (ω) is:

[0084] V r (ω)=G A (ω)G B (ω)V e (ω)G AB (r,ω)e -2αh (19)

[0085] Among them, r or r AB is the propagation distance of Lamb wave, ω is the angular frequency, α is the attenuation coefficient of ultrasonic wave in air, h is the distance between the air-coupled ultrasonic transducer and the thin plate to be measured, G A (ω) is the transfer function of exciting the air-coupled transducer A, G A (ω) is the transfer function of the receiving air-coupled transducer B, G AB (r,ω) is the structural transfer function from the excitation point A to the excitation point B in the plate structure; in the thin plate structure, the guided wave modes of the low-frequency signal are mainly A0 and S0 modes; G AB (r,ω) can be further expressed as:

[0086]

[0087] Where A(r,ω) is the amplitude-frequency response of the received Lamb wave signal, k(ω) is the wave number, r AB Indicates that the distance here is equal to the distance from the air-coupled transducer A to the air-coupled transducer B; when the distance h between the air-coupled ultrasonic transducer and the thin plate to be measured is a constant, the propagation attenuation of the ultrasonic wave in the air is e -αh is a constant and has no effect on the time reversal process, and the following formula is obtained:

[0088] V r (ω)=G A (ω)G B (ω)V e (ω)A(r,ω)e -ik(ω)r (twenty one)

[0089] The received signal is inverted in the time domain, that is, conjugate processing in the frequency domain. The inverted signal can be expressed as:

[0090]

[0091] Among them, '*' represents the complex conjugate operation, G ABrepresents the Lamb propagation r in the plate structure AB Structural transfer function of distance;

[0092] The V' obtained in the formula A (ω) is loaded on the air-coupled transducer B as the excitation signal. At this time, the air-coupled transducer A, as the receiving transducer, receives the Lamb wave signal as follows:

[0093]

[0094] Among them, A(r AB , w) indicates that when Lamb wave propagates r AB Distance, the amplitude-frequency response of the Lamb wave at the receiving point;

[0095] Let K = G A (ω)G B (ω) is the transfer function of the air-coupled ultrasonic transducer in the system, let Γ=|A(r,ω)| 2 is the time reversal operator; then the structural transfer function from the excitation end A to the receiving end B is G(r,ω)=K·Γ; where the transducer transfer function K is determined by the characteristics of the transducer itself and has nothing to do with the excitation signal, and Γ is generated by the propagation of Lamb waves in the plate structure;

[0096] Due to e -ik(ω)r During the calculation process, it is eliminated by time reversal, as shown in formula (20), so both intra-mode dispersion and multi-mode dispersion are compensated. However, A(r,ω) indicates that there is still amplitude dispersion in the reconstructed signal. Signal components of different frequencies are unevenly amplified during the time reversal process, making it impossible to perfectly reconstruct the original broadband signal when using broadband signals for virtual time reversal. Signals of different frequencies are unevenly scaled and superimposed, which ultimately leads to reconstruction failure. Therefore, broadband signals cannot be used directly for time reversal. Instead, the transfer function calculated from the broadband signal is applied to the narrowband pulse signal. This can solve the problem of inaccurate transfer function of narrowband pulse signal reproduction (such as Figure 4 As shown), it can also avoid the inability to reconstruct the original input signal when using the broadband signal itself for time reversal; the inverted focus signal achieved by the traditional VTR method and the CRVTR method proposed in the present invention is as follows Figure 5 In addition, due to the high bandwidth characteristics of the chirp signal, the transfer function obtained using the CRVTR method also has a certain bandwidth and can be applied to the baseline-free measurement of Lamb waves of multiple frequencies at the same time. There is no need to repeatedly acquire signals, which can effectively improve the detection efficiency.

[0097] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutations and combinations. Therefore, the present invention will no longer describe the technical solutions after permutations and combinations one by one, but it should be understood that the technical solutions after permutations and combinations have been disclosed by the present invention.

[0098] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for virtual time reversal of air-coupled Lamb waves based on chirp signal technology, characterized by: The following steps are involved: Step 1: Input chirp signal to stimulate the target structure and calculate the transfer function of the detection system; In step 1, the detection system includes transducer A and transducer B. Transducer A applies an excitation signal to the target structure, and transducer B receives the signal. In step 1, the input chirp signal is S e ( t ), the corresponding frequency domain signal is S e ( ω ), the received time domain signal is S r ( t ), the corresponding frequency domain signal is S r ( ω ); in, r is the propagation distance of Lamb waves, ω is the angular frequency, α is the attenuation coefficient of ultrasound in air, h is the distance between the air-coupled ultrasonic transducer and the thin plate to be measured, G A ( ω ) is the transfer function of the excitation transducer A, G B ( ω ) is the transfer function of the receiving transducer B, G AB ( r , ω ) is the structural transfer function from the excitation point A to the excitation point B in the plate structure; The transfer function of the detection system is: Step 2: Apply the transfer function to excite the narrowband signal, perform virtual time reversal on the narrowband pulse signal, and obtain the inverted focusing signal.

2. The method of claim 1 for virtual time reversal of air-coupled Lamb waves based on chirp signal technology, characterized in that: In step 2, in the transfer function G ( ω ) is used to perform virtual time reversal of the narrowband pulse signal. The time domain signal of the first excitation is assumed to be V e ( t ) corresponds to the frequency domain signal: V e ( ω ), first receiving the time domain signal V r ( t ) corresponds to the frequency domain signal: V r ( ω ), the second excitation signal V’ e ( t ) corresponds to the frequency domain signal: V’ e ( ω ), receiving the signal for the second time V’ r ( t ) corresponds to the frequency domain signal: V’ r ( ω ); the following relationship can be obtained; Where, '*' represents the complex conjugate operation; The time-reversed signal obtained is V’ r ( t ), the signal converges to the main mode.

3. The method of virtual time reversal of air-coupled Lamb waves based on chirp signal technology according to claim 2, characterized in that: In step 1, the structural transfer function of the detection system is calculated according to formula (2) to simplify the derivation process of the transfer function; When the distance between transducer A, transducer B and the target structure to be measured is a constant, the attenuation of ultrasonic waves in the air is constant, which does not affect the virtual time reversal process of Lamb waves and has no effect on the transfer function. Therefore, the transfer function of the detection system can be further written as:

4. The method of claim 3 for virtual time reversal of air-coupled Lamb waves based on chirp signal technology, characterized in that: In step 2, the first received time domain signal is obtained according to the transfer function V r ( t ), the corresponding frequency domain signal is V r ( ω ); 5. The method of virtual time reversal of air-coupled Lamb waves based on chirp signal technology according to claim 4, characterized in that: A space-coupled Lamb wave virtual time reversal method based on chirp signal technology is applied to non-destructive testing of thin-walled structures.

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