Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.     

Experimental detection and focusing in shallow water by decomposition of the time reversal operator

A rigid 24-element source-receiver array in the 10-15 kHz frequency band, connected to a programmable electronic system, was deployed in the Bay of Brest during spring 2005. In this 10- to 18-m-deep environment, backscattered data from submerged targets were recorded. Successful detection and focusing experiments in very shallow water using the decomposition of the time reversal operator (DORT method) are shown. The ability of the DORT method to separate the echo of a target from reverberation as well as the echo from two different targets at 250 m is shown. An example of active focusing within the waveguide using the first invariant of the time reversal operator is presented, showing the enhanced focusing capability. Furthermore, the localization of the scatterers in the water column is obtained using a range-dependent acoustic model.     

Revisiting iterative time reversal processing: application to detection of multiple targets

The iterative time reversal processing represents a high speed and easy way to self-focus on the strongest scatterer in a multitarget medium. However, finding weaker scatterers is a more difficult task that can be solved by computing the eigenvalue and eigenvector decomposition of the time reversal operator, the so-called DORT method. Nevertheless, as it requires the measurement of the complete interelements response matrix and time-consuming computation, the separation of multiple targets may not be achieved in real time. In this study, a new real time technique is proposed for multitarget selective focusing that does not require the experimental acquisition of the time reversal operator. This technique achieves the operator decomposition using a particular sequence of filtered waves propagation instead of computational power. Due to its simplicity of implementation, this iterative process can be achieved in real time. This high speed selective focusing is experimentally demonstrated by detecting targets through a heterogeneous medium and in a speckle environment. A theoretical analysis compares this technique to the DORT formalism.     

Spatio-temporal invariants of the time reversal operator

The decomposition of the time reversal operator, known by the French acronym DORT, is a technique to extract point scatterers' monochromatic Green's functions from a medium. It is used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. A limitation of the method arises from its single-frequency nature, when the signals used in acoustics are often broadband. Reconstruction of the broadband Green's functions from the single-frequency Green's functions can be very difficult when numerous scatterers are present in the medium. Moreover, the method does not take advantage of the axial resolution associated with broadband signals. Time domain methods are investigated here as an answer to these problems. It is shown that the time reversal operator in the time domain takes the form of a tensor. The properties of the invariants are discussed. It is shown they do not have all the expected properties. Another method is proposed that requires a priori information on the medium.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

Wideband imaging of extended targets with the decomposition of the time reversal operator

The weighted wideband imaging approach of full signal subspaces is proposed based on the decomposition of the time reversal operator(DORT). Although each singular vector of nonzero singular values does not correspond to one of the extended targets any more, the conventional approach of selective time reversal focusing still chooses one of the signal subspaces for imaging. Simultaneously, the time-reversal MUSIC imaging is carried out at a single frequency for wideband signal. The imaging of both...     

Time reversal technique for health monitoring of metallic structure using Lamb waves

Time reversal active sensing using Lamb waves is investigated for health monitoring of a metallic structure. Experiments were conducted on an aluminum plate to study the time reversal behavior of A₀ and S₀ Lamb wave modes under narrow band and broad band pulse excitation. Damage in the form of a notch was introduced in the plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. Time–frequency analysis of the time reversed signal was carried out to extract the damage information. A measure of damage based on wavelet transform was derived to quantify the hidden damage information in the time reversed signal. It has been shown that time reversal can be used to achieve temporal recompression of Lamb waves under broadband signal excitation. Further, the broad band excitation can also improve the resolution of the technique in detecting closely located defects. This is demonstrated by picking up the reflection of waves from the edge of the plate, from a defect close to the edge of the plate and from defects located near to each other. This study shows the effectiveness of Lamb wave time reversal for temporal recompression of dispersive Lamb waves for damage detection in health monitoring applications.     

宽带扩展性目标时反算子分解成像

在时反算子分解技术的基础上,提出了宽带全信号子空间加权成像方法。虽然扩展性目标与时反算子的特征向量不再是一一对应关系,传统的时反选择性聚焦仍然选择某一特定的信号子空间成像,而时反MUSIC只利用某一频点成像,导致定位结果背景起伏较高。为克服这些缺陷,利用时反算子的特征值判断信号子空间的个数,以广义散射系数为加权系数,实现全宽带和全信号子空间成像。结果表明,此方法的旁瓣水平明显下降。      

Propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms

The present study aims to investigate the propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms. Time-reversed Lamb waves could be successfully launched in 6 acrylic tubes with wall thicknesses from 2 to 12 mm by using a modified time reversal method. The group velocities of the time-reversed Lamb waves in the acrylic tubes were measured by using the axial transmission technique. They decreased very slightly with increasing wall thickness, showing good agreement with the theoretical group velocity of the A0 Lamb wave in the acrylic plate. These results suggest that the time-reversed Lamb waves in the acrylic tubes would essentially behave as the A0 Lamb wave, consistent with the behavior of the slow guided wave in long cortical bones. It is expected that the application of the time-reversed Lamb waves in long bones would enhance clinical potential of ultrasonic technologies for the diagnosis of osteoporosis.     

Imaging in the presence of grain noise using the decomposition of the time reversal operator

In this paper, we are interested in detecting and imaging defects in samples of cylindrical geometry with large speckle noise due to the microstructure. The time reversal process is an appropriate technique for detecting flaws in such heterogeneous media as titanium billets. Furthermore, time reversal can be iterated to select the defect with the strongest reflectivity and to reduce the contribution of speckle noise. The DORT (the French acronym for Decomposition of the Time Reversal Operator) method derives from the mathematical analysis of the time reversal process. This detection technique allows the determination of a set of signals to be applied to the transducers in order to focus on each defect separately. In this paper, we compare three immersion techniques on a titanium sample, standard transmit/receive focusing, the time reversal mirror (TRM), and the DORT method. We compare the sensitivity of these three techniques, especially the sensitivity to a poor alignment of the array with the front face of the sample. Then we show how images of the sample can be obtained with the TRM and the DORT method using backpropagation algorithm.     

A time reversal damage imaging method for structure health monitoring using Lamb waves

This paper investigates the Lamb wave imaging method combining time reversal for health monitoring of a metal-lic plate structure.The temporal focusing effect of the time reversal Lamb waves is investigated theoretically.It demonstrates that the focusing effect is related to the frequency dependency of the time reversal operation.Numerical simulations are conducted to study the time reversal behaviour of Lamb wave modes under broadband and narrowband excitations.The results show that the reconstructed time reversed wave exhibits close similarity to the reversed nar-rowband tone burst signal validating the theoretical model.To enhance the similarity,the cycle number of the excited signal should be increased.Experiments combining finite element model are then conducted to study the imaging method in the presence of damage like hole in the plate structure.In this work,the time reversal technique is used for the recompression of Lamb wave signals.Damage imaging results with time reversal using broadband and narrowband excitations are compared to those without time reversal.It suggests that the narrowband excitation combined time reversal can locate and determine the size of structural damage more precisely,but the cycle number of the excited signal should be chosen reasonably.     

Backscattering of transients by tilted truncated cylindrical shells: time-frequency identification of ray contributions from measurements

Impulse backscattering measurements by a thick-walled finite cylindrical shell are examined in the time-frequency domain to identify and characterize individual ray contributions from generalized Lamb waves excited on the shell. Previous experiments and analysis in the frequency-aspect angle domain [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)] indicate that large backscattering enhancements occur in the midfrequency region for the shell tilted at large angles. Presently this experimental data is examined in the time-frequency domain for selected angles of incidence. Individual ray contributions are evident and their evolution over aspect angle is discussed. The most prominent contribution is due to the meridional ray of the a0 leaky Lamb wave. This feature distinctly highlights the truncation of the shell and is found over a range of aspect angles spanning 200 degrees for the frequencies examined. Also observed are periodic features corresponding to end-reflected helical waves of the a0-. These scattering features are significantly different from those reported for thin-walled finite cylinders at low frequencies. The present results may be useful for target identification and localization and as a comparison tool for high-frequency computational scattering models.     

Transient Lamb waves: comparison between theory and experiment

This paper presents an experimental investigation of the generation of transient Lamb waves inside an immersed plate by a time limited signal. The transient Lamb waves are the solutions of the characteristic equation of the plate for complex frequency and real slowness, in contrast to the leaky Lamb waves, for which the slowness is complex and the frequency is real. By using a large transducer in agreement with the real slowness assumption, the excitation of these transient Lamb waves is observed experimentally both in reflection and transmission for a tone burst excitation. Particular attention is paid to the A0 mode for which the amplitude increases exponentially in time. As a result, the total reflected waveform contains in this case a transient contribution, coming from the generation of the A0 mode, that precedes the forced regime. It is shown that there is a very good agreement between the theoretical and the experimental time exponential amplitude variations of the transient Lamb waves. For the A0 mode, the transient signal is qualitatively explained by a group velocity higher than the phase velocity.     

Re-radiation of acoustic waves from the A0 wave on a submerged elastic shell

We consider evacuated thin semi-infinite shells immersed in a fluid, which may be either of cylindrical shape with a hemispherical shell endcap, or formed two-dimensionally by semi-infinite parallel plates joined together by a semi-cylinder. The connected shell portions are joined in a manner to satisfy continuity but with a discontinuous radius of curvature. Acoustic waves are considered incident along the axis of symmetry (say the z axis) onto the curved portion of the shell, where they, at the critical angle of coincidence, generate Lamb and Stoneley-type waves in the shell. Computations were carried out using a code developed by Cao et al. [Chinese J. Acoust. 14, 317 (1995)] and was used in order to computationally visualize the waves in the fluid that have been re-radiated by the shell waves a the critical angle. The frequency range was below that of the lowest Lamb wave, and only the A0 wave (and partly the S0 wave) was observed to re-radiate into the fluid under our assumptions. The results will be compared to experimental results in which the re-radiated waves are optically visualized by the Schardin-Cranz schlieren method.     

A new multichannel time reversal focusing method for circumferential Lamb waves and its applications for defect detection in thick-walled pipe with large-diameter

This paper proposes a new multichannel time reversal focusing (MTRF) method for circumferential Lamb waves which is based on modified time reversal algorithm and applies this method for detecting different kinds of defects in thick-walled pipe with large-diameter. The principle of time reversal of circumferential Lamb waves in pipe is presented along with the influence from multiple guided wave modes and propagation paths. Experimental study is carried out in a thick-walled and large-diameter pipe with three artificial defects, namely two axial notches on its inner and outer surface respectively, and a corrosion-like defect on its outer surface. By using the proposed MTRF method, the multichannel signals focus at the defects, leading to the amplitude improvement of the defect scattered signal. Besides, another energy focus arises in the direct signal due to the partial compensation of dispersion and multimode of circumferential Lamb waves, alongside the multichannel focusing, during MTRF process. By taking the direct focus as a time base, accurate defect localization is implemented. Secondly, a new phenomenon is exhibited in this paper that defect scattered wave packet appears just before the right boundary of truncation window after time reversal, and to which two feasible explanations are given. Moreover, this phenomenon can be used as the theoretical basis in the determination of defect scattered waves in time reversal response signal. At last, in order to detect defects without prior knowing their exact position, a large-range truncation window is used in the proposed method. As a result, the experimental operation of MTRF method is simplified and defect detection and localization are well accomplished.     

Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding

The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.     

Acoustic waves propagating in a fluid-filled spherical shell placed in a liquid

Acoustic waves arising in a fluid-filled elastic spherical shell placed in a liquid are considered. It is demonstrated that, in general, none of the four types of waves possible in such a system (subsonic and supersonic antisymmetric Lamb waves, symmetric Lamb waves, and whispering galleries) is realized separately, but an interaction between the waves of different types takes place.     

Automatic determination of the number of targets present when using the time reversal operator

Acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources. The DORT method is a derivation of the time reversal process, which allows for focusing on multiple targets. An important step in this process is the determination of the number of targets or sources present. This is achieved by examining the eigenvalues of the time reversal operator (TRO). The number of significant eigenvalues is then chosen as the number of sources present. However, as mentioned in [N. Mordant, C. Prada, and M. Fink, J. Acoust. Soc. Am. 105, 2634-2642 (1999) and C. Prada, M. Tanter, and M. Fink, in Proceedings of the IEEE Symposium, 1997, pp. 679-683], factors such as low signal to noise ratio (SNR), small data sample, array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues. This paper proposes a robust method of automatically determining the number of targets even in the presence of a small number of snapshots. For white Gaussian noise, the profile of the ordered eigenvalues is seen to fit an exponential law. The observed eigenvalues are then compared to this model and a mismatch is detected between the observed profile and the noise-only model. The index of the mismatch gives the number of scatterers present.     

Scattering characteristics of Lamb waves from debondings at structural features in composite laminates

This article investigates the scattering characteristics of Lamb waves from a debonding at a structural feature in a composite laminate. This study specifically focuses on the use of the low frequency fundamental antisymmetric (A(0)) Lamb wave as the incident wave for debonding detection. Three-dimensional finite element (FE) simulations and experimental measurements are used to investigate the scattering phenomena. Good agreement is obtained between the FE simulations and experimental results. Detailed parameter studies are carried out to further investigate the relationship between the scattering amplitudes and debonding sizes. The results show that the amplitude of the scattered A(0) Lamb wave is sensitive to the debonding size, which indicates the potential of using the low frequency A(0) Lamb wave as the interrogating wave for debonding detection and monitoring. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques and optimize transducer networks.     

Time reversed reverberation focusing in a waveguide

Time reversal mirrors have been applied to focus energy at probe source locations and point scatterers in inhomogeneous media. In this paper, we investigate the application of a time reversal mirror to rough interface reverberation processing in a waveguide. The method is based on the decomposition of the time reversal operator which is computed from the transfer matrix measured on a source-receiver array [Prada et al., J. Acoust. Soc. Am. 99, 2067-2076 (1996)]. In a similar manner, reverberation data collected on a source-receiver array can be filtered through an appropriate temporal window to form a time reversal operator. The most energetic eigenvector of the time reversal operator focuses along the interface at the range corresponding to the filter delay. It is also shown that improved signal-to-noise ratio measurement of the time reversal operator can be obtained by ensonifying the water column with a set of orthogonal array beams. Since these methods do not depend upon a priori environmental information, they are applicable to complex shallow water environments. Numerical simulations with a Pekeris waveguide demonstrate this method.