A time–distance domain transform method for Lamb wave dispersion compensation considering signal waveform correction

Abstract

In Lamb wave identification, time–distance domain mapping (TDDM) is one of the most popular methods for dispersion compensation. However, it is found that the processed signal waveforms are easily deformed by TDDM. To improve the compensation effect, a time–distance domain transform (TDDT) method is presented in this paper. In TDDT, both dispersion removal and signal waveform correction are accomplished to result in more convenience of dispersive signal interpretation. Instead of the complex back-propagation concept, only the basic Fourier transform (FT) properties are used to study the principle of TDDT. The realization of TDDT under broadband excitation and narrowband excitation is discussed, in which the signal waveform maintenance is of particular interest and the reason for TDDM disturbance of the signal waveforms is also investigated. Numerical simulations on A0 or S0 mode signals are implemented for the primary validation of TDDT. Then, in association with the traditional delay-and-sum algorithm, a high spatial resolution imaging method based on TDDT is developed. An experimental study is finally arranged to demonstrate the efficiency of TDDT and the TDDT-based imaging method.

Signal Construction-Based Dispersion Compensation of Lamb Waves Considering Signal Waveform and Amplitude Spectrum Preservation

“…Using the plate material parameters in Table 1, the original nonlinear-dispersion wavenumber relations $K_{0}false(\omega false)$ of the two fundamental modes are theoretically derived from the Rayleigh-Lamb dispersion equation [23,28,30]. With Equations (6) and (9), the linearized wavenumber relations $K_{lin}false(\omega false)$ and $K_{non}false(\omega false)$ can be calculated.…”

“…Since the excitation signal $V_{a}false(\omega false)$ is known in a priori, from Equation (4), the crucial problem in signal construction is how to pursue the corresponding phase-delay factor. Its general expression can be rewritten in a composite function [28,30] $Efalse(r,\omega false)=E\left[r,Kfalse(\omega false)\right]=e^{-ikr}{|}_{k=K(\omega )}$ where the subfunction is the dispersion relation $Kfalse(\omega false)$ and the generating function $Efalse(r,kfalse)=e^{-ikr}$. For a given $r$, $Efalse(r,kfalse)$ is only a simple exponential function and irrespective of the exact variation relation of its independent variable $k$, i.e., $Kfalse(\omega false)$, which implies that $Efalse(r,\omega false)$ under various dispersion relations is subject to an identical $Efalse(r,kfalse)$.…”

“…The waveform deformation, similar to the frequency-shifting phenomenon is then produced to $v_{a}false(tfalse)$ and the final constructed signal [30]. Additionally, the more ${\mathrm{\Omega }}_{lin}false(\omega false)$ or ${\mathrm{\Omega }}_{non}false(\omega false)$ differs from $\omega$, the more serious deformation will occur to $v_{lin}^{\prime }false(tfalse)$ or $v_{non}^{\prime }false(tfalse)$.…”

“…It is necessary to conduct a comparison with the typical signal domain transform methods, i.e., TDDM and TDDT, the calculation formulas of which are respectively given as [23,30] $\begin{array}{cc}\hfill \tilde{v}false(rfalse)& =\mathrm{IFFT}\left\{V_0\left[\mathrm{normal\Omega }false(kfalse)\right]\right\}\hfill \\ & =\mathrm{IFFT}\left\{V_a\left[\mathrm{normal\Omega }false(kfalse)\right]\right\}\ast \mathrm{IFFT}\left\{H\left[\mathrm{normal\Omega }false(kfalse)\right]\right\}\hfill \end{array}$ $\begin{array}{cc}\hfill vfalse(rfalse)& =\mathrm{IFFT}\left\{V_a\left[{\mathrm{\Omega }}_{non}false(kfalse)\right]\right\}\ast \mathrm{IFFT}\left\{H\left[\mathrm{normal\Omega }false(kfalse)\right]\right\}\hfill \\ & =v_{a}false(rfalse)\ast \mathrm{IFFT}\left\{H\left[\mathrm{normal\Omega }false(kfalse)\right]\right\}\hfill \end{array}$ where $\mathrm{normal\Omega }false(kfalse)=K_0^{-1}false(\omega false)$, ${\mathrm{\Omega }}_{non}false(kfalse)=K_{non}^{-1}false(\omega false)$, the distance-domain excitation signal $v_{a}false(rfalse)=\mathrm{IFFT}\left\{V_a\left[{\mathrm{\Omega }}_{non}false(kfalse)\right]\right\}$ and $v_{a}false(rfalse)=v_a\left[c_{g}false({\omega }_{c}false)t\right]$ [30], $\tilde{v}false(rfalse)$ and $vfalse(rfalse)$ are...…”

A Signal Decomposition Method for Ultrasonic Guided Wave Generated from Debonding Combining Smoothed Pseudo Wigner-Ville Distribution and Vold–Kalman Filter Order Tracking

“…Kercel et al [8] used Bayesian parameter estimates to isolate multiple modes in GW signals collected from laser ultrasonic testing on a manufacturing assembly line. Cai et al [9] provided a timedistance domain transform (TDDT) method to interpret the dispersion of Lamb waves, which can result in high spatial resolution images of damage areas. Rizzo and di Scalea utilized Discrete Wavelet Transform (DWT) to extract wavelet domain features for enhanced defect characterization in multiwire strand structures [10].…”