IMPROVED DOMAIN TRANSFORMATION METHOD FOR DISPERSIVE ULTRASONIC GUIDED WAVE SIGNAL

Abstract

An improved domain transformation method for a dispersive ultrasonic guided wave signal, including the following steps: obtaining a dispersive wave number curve and a non-dispersive wave number curve corresponding to a mode of an ultrasonic guided wave signal; calculating an ultrasonic guided wave excitation waveform that is in distance domain and that has a reduced space width; obtaining an ultrasonic guided wave impulse response signal in distance domain; and calculating and obtaining a non-dispersive ultrasonic guided wave distance-domain signal whose resolution is enhanced.

Claims

1. An improved domain transformation method for a dispersive ultrasonic guided wave signal, comprising the following steps: (1) obtaining a dispersive wave number curve corresponding to a mode of an ultrasonic guided wave signal, wherein theoretically calculating, based on material parameters of a structure, or obtaining, through practical measurement by using an actuator and a sensor configured in the structure, an original dispersive curve K.sub.0() corresponding to the mode of the ultrasonic guided wave signal, wherein is an angular frequency; (2) calculating an ultrasonic guided wave excitation waveform in distance domain and having a reduced space width, performing a first frequency-domain interpolation on a spectrum of an ultrasonic guided wave excitation signal in a time domain to obtain the original ultrasonic guided wave excitation waveform .sub.a(r) in distance domain and having a reduced space width, wherein r is a distance variant; (3) obtaining an ultrasonic guided wave impulse response signal in a distance domain, performing a second frequency-domain interpolation on a spectrum of an ultrasonic guided wave impulse response signal h(t) in the time domain obtained in the structure, to obtain the ultrasonic guided wave impulse response signal h(r) in the distance domain, wherein h(t) and h(r) are respectively the ultrasonic guided wave impulse response signal in time domain and the ultrasonic guided wave impulse response signal in the distance domain, and t is a time variant; and (4) calculating and obtaining a non-dispersive ultrasonic guided wave distance-domain signal having an enhancing resolution, calculating an ultrasonic guided wave distance-domain signal (r) having an enhancing spatial resolution as (r)=.sub.a(r)*h(r), wherein * is a convolution operation.

2. The improved domain transformation method according to claim 1, wherein the actuator in step (1) is a piezoelectric wafer P.sub.A.

3. The improved domain transformation method according to claim 1, wherein the sensor in step (1) is a piezoelectric wafer P.sub.B.

4. The improved domain transformation method for a dispersive ultrasonic guided wave signal according to claim 1, wherein the step of calculating the ultrasonic guided wave excitation waveform in the distance domain and having the reduced space width in step (2) comprises the following steps: first determining a non-dispersive wave number curve $K_{\mathrm{non}}\left(\right)=\frac{m..Math.}{c_{g.Math..Math.0}},$ wherein is an angular frequency, c.sub.g0 is a group velocity of the mode of the ultrasonic guided wave signal at a central frequency, m is a distance-domain width scale factor of an ultrasonic guided wave excitation waveform, and m1; then calculating an interpolation mapping sequence .sub.non ()=K.sub.non.sup.1 (), wherein K.sub.non.sup.1() is an inverse function of K.sub.non (); further calculating a spectrum V.sub.a()=FT[.sub.a(t)] of the ultrasonic guided wave narrowband excitation signal in the time domain, wherein .sub.a (t) is the ultrasonic guided wave narrowband excitation signal in the time domain, and FT[ ] is a Fourier transform operation; and subsequently performing a third frequency-domain interpolation on the spectrum V.sub.a() of the narrowband excitation signal according to the interpolation mapping sequence .sub.non (), and then performing an inverse Fourier transform to calculate the ultrasonic guided wave excitation waveform .sub.a(r) in the distance domain and having the reduced space width as .sub.a(r)=IFT{V.sub.a[.sub.non ()]}, wherein IFT[ ] is an inverse Fourier transform operation.

5. The improved domain transformation method according to claim 1, wherein the step of obtaining the ultrasonic guided wave impulse response signal in the distance domain in step (3) comprises the following steps: first obtaining an ultrasonic guided wave impulse response time-domain signal h(t) by using the actuator and the sensor in the structure and through an impulse or a step pulse excitation, and calculating a transfer function H() corresponding to the propagation of the ultrasonic guided wave signal as H()=FT[h(t)]; then adjusting K.sub.0() to K.sub.1()=K.sub.0()K.sub.0(.sub.0)+K.sub.non(.sub.0), wherein .sub.0 is a central angular frequency, K.sub.0(.sub.0) is a value of a wave number of an original dispersive curve K.sub.0() at .sub.0, and K.sub.non(.sub.0) is a value of a wave number of a non-dispersive wave number curve K.sub.non() at .sub.0; further calculating an interpolation mapping sequence ()=K.sub.1.sup.1(), wherein K.sub.1.sup.1() is an inverse function of K.sub.1(), and K.sub.1() is a new dispersive curve obtained after the K.sub.0() is adjusted; and subsequently performing a fourth frequency-domain interpolation on the transfer function H() according to the interpolation mapping sequence (), and then performing inverse Fourier transform, to calculate the ultrasonic guided wave impulse response signal h(r) in the distance domain as h(r)=IFT{H[()]}.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] FIG. 1 is an implementation flowchart of an improved domain transformation method for a dispersive ultrasonic guided wave signal provided in an embodiment.

[0015] FIG. 2 is a schematic diagram of arrangement of piezoelectric wafers in an aluminum plate structure.

[0016] FIG. 3 is a diagram of a Lamb wave narrowband excitation signal.

[0017] FIG. 4 is a diagram of an original dispersive A.sub.0 mode Lamb wave sensor signal.

[0018] FIG. 5 is a diagram of an original dispersive wave number curve of A.sub.0 Lamb wave mode that is obtained through calculation.

[0019] FIG. 6 is a diagram of an interpolation mapping sequence for the frequency-domain interpolation performed on a Lamb wave narrowband excitation signal spectrum.

[0020] FIG. 7 is a diagram of a Lamb wave narrowband excitation signal that is in distance domain and that has a reduced space width.

[0021] FIG. 8 is a diagram of a Lamb wave narrowband excitation signal that is in distance domain and that has an unchanged space width.

[0022] FIG. 9 is a diagram of a Lamb wave impulse response time-domain signal.

[0023] FIG. 10 is a diagram of an adjusted dispersive wave number curve of an A.sub.0 Lamb wave mode.

[0024] FIG. 11 is a diagram of an interpolation mapping sequence obtained based on an adjusted dispersive wave number curve of an A.sub.0 Lamb wave mode.

[0025] FIG. 12 is a diagram of a Lamb wave impulse response distance-domain signal.

[0026] FIG. 13 is a diagram of a non-dispersive A.sub.0 mode Lamb wave distance-domain signal whose wave-packet space width is reduced.

[0027] FIG. 14 is a diagram of a non-dispersive A.sub.0 mode Lamb wave distance-domain signal whose wave-packet space width is unchanged.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer, the following clearly and completely describes the technical solutions of the present invention through implementations with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by a person of ordinary skills in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0029] In this embodiment, a typical ultrasonic guided wave, that is, an A.sub.0 mode Lamb waves propagating in an LY21 aluminum plate structure is used as a research object. A dimension of the aluminum plate is 1200 mm1000 mm1.5 mm. The plate material parameters are listed in table 1.

TABLE-US-00001 TABLE 1 Material parameters of the aluminum plate Thickness Elasticity d (mm) Density (kg/m.sup.3) Poisson's ratio modulus E (GPa) 1.5 2780 0.33 73.1

[0030] Two piezoelectric wafers P.sub.A and P.sub.B are configured in the aluminum plate structure to respectively serve as an actuator and a sensor, as shown in FIG. 2. A five-peak sinusoidal modulated signal with a central frequency of 70 kHz is selected as a narrowband excitation signal .sub.a(t), as shown in FIG. 3.

[0031] The narrowband excitation signal is generated with P.sub.A. An A.sub.0 mode Lamb wave sensor signal (t) is collected by the sensor P.sub.B, as shown in FIG. 4. It can be seen that due to dispersion and the resolution limitation of wave packets in the signal, the wave packets in the signal are no longer five-peak sinusoidal modulated signals, and extension and overlapping occur on all the wave packets, resulting in a relatively low resolution.

[0032] An improved domain transformation method for a dispersive ultrasonic guided wave signal according to this embodiment includes the following steps:

[0033] (1) Obtaining a dispersive wave number curve corresponding to a mode of an ultrasonic guided wave signal.

[0034] An original dispersive wave number curve K.sub.0() of A.sub.0 mode is obtained through a theoretical calculation by using the material parameters of the aluminum plate in table 1, as shown in FIG. 5.

[0035] (2) Calculating an ultrasonic guided wave excitation waveform that is in distance domain and that has a reduced space width.

[0036] First, a group velocity c.sub.g0 of A.sub.0 mode at the central frequency of 70 kHz is measured as 1933.5 m/s, a distance-domain width scale factor m is set to 2, and K.sub.non() is obtained through calculation based on

[00002]$K_{\mathrm{non}}\left(\right)=\frac{m..Math.}{c_{g.Math..Math.0}}.$

[0037] Then, an interpolation mapping sequence .sub.non() is obtained through calculation based on .sub.non()=K.sub.non.sup.1(), as shown in FIG. 6.

[0038] Subsequently, Fourier transform is performed on the narrowband excitation signal .sub.a(t), to obtain a narrowband excitation signal spectrum .sub.a(). Based on a formula .sub.a(r)=IFT{V.sub.a[.sub.non ()]}, frequency-domain interpolation is first performed on the excitation signal spectrum V.sub.a() according to the interpolation mapping sequence .sub.non(), and then inverse Fourier transform is performed, to calculate the ultrasonic guided wave excitation waveform .sub.a(r) that is in distance domain and that has a reduced space width, as shown in FIG. 7.

[0039] FIG. 8 shows an ultrasonic guided wave excitation waveform .sub.a(r) that is in distance domain and that has an unchanged space width, where the excitation waveform is obtained through calculation when m=1. It can be seen by comparing FIG. 7 and FIG. 8 that a distance-domain width of .sub.a(r) is half that of .sub.a(r), and a spatial resolution of the wave packet is also doubled accordingly.

[0040] (3) Obtaining an ultrasonic guided wave impulse response signal in distance domain.

[0041] First, the impulse excitation signal is generated with P.sub.A, and an impulse response time-domain signal h(t) is collected by P.sub.B, as shown in FIG. 9. Fourier transform is performed on h(t) to obtain a transfer function H() corresponding to the propagation of a Lamb wave signal.

[0042] Subsequently, K.sub.0() is adjusted to K.sub.1()=K.sub.0()K.sub.0(.sub.0)+K.sub.non(.sub.0), and a wave number curve K.sub.1() obtained after the adjustment is shown in FIG. 10. An interpolation mapping sequence () is obtained through calculation based on ()=K.sub.1.sup.1(), as shown in FIG. 11.

[0043] Based on a formula h(r)=IFT {H[()]}, frequency-domain interpolation is first performed on the transfer function H() according to the interpolation mapping sequence (), and then inverse Fourier transform is performed, to calculate the ultrasonic guided wave impulse response signal h(r) in distance domain, as shown in FIG. 12.

[0044] (4) Calculating and obtaining a non-dispersive ultrasonic guided wave distance-domain signal whose resolution is enhanced.

[0045] A non-dispersive ultrasonic guided wave distance-domain signal (r) whose wave-packet space width is reduced is finally obtained through calculation based on a formula (r)=.sub.a(r)*h(r), as shown in FIG. 13. FIG. 14 shows a non-dispersive ultrasonic guided wave distance-domain signal (r) whose wave-packet space width is unchanged, where the signal is obtained through calculation based on a formula (r)=.sub.a(r)*h(r). Compared with the original dispersive A.sub.0 mode sensor signal (t) in FIG. 4, all the wave packets in (r) and (r) are recompressed due to dispersion compensation. Because a space width of a wave packet in (r) is not reduced, severe overlapping occurs on the adjacent wave packets in (r) that have much close distance-domain locations, and the wave packets cannot be distinguished, as shown in two dashed boxes in FIG. 14. Because a space width of a wave packet in (r) is halved, the adjacent wave packets in (r) are obviously separated, and a location of the wave packet is consistent with a propagation distance, as shown in two dashed boxes in FIG. 13. It indicates that on the basis of recompressing an original dispersion-extended wave packet of the ultrasonic guided wave signal, the improved domain transformation dispersion compensation method for an ultrasonic guided wave signal provided in the present invention further improves the resolution of the ultrasonic guided wave signal by reducing the space width of the wave packet in the non-dispersive ultrasonic guided wave distance-domain signal, thereby further facilitating subsequent signal analysis and extraction of damage features.

[0046] A basic principle of the present invention is first transforming a dispersive ultrasonic guided wave signal from time domain to distance domain, so as to compensate the dispersion effect, thereby recompressing an original dispersion-extended wave packet in time domain, and improving the time-domain resolution of the wave packet. On this basis, by reducing a distance scale of an ultrasonic guided wave excitation waveform, the distance-domain widths of non-dispersive wave packets in the ultrasonic guided wave distance-domain signal are reduced, thereby further improving the spatial resolution of the signal.