Sparse signal representation and its applications in ultrasonic NDE

Many sparse signal representation (SSR) algorithms have been developed in the past decade. The advantages of SSR such as compact representations and super resolution lead to the state of the art performance of SSR for processing ultrasonic non-destructive evaluation (NDE) signals. Choosing a suitable SSR algorithm and designing an appropriate overcomplete dictionary is a key for success. After a brief review of sparse signal representation methods and the design of overcomplete dictionaries, this paper addresses the recent accomplishments of SSR for processing ultrasonic NDE signals. The advantages and limitations of SSR algorithms and various overcomplete dictionaries widely-used in ultrasonic NDE applications are explored in depth. Their performance improvement compared to conventional signal processing methods in many applications such as ultrasonic flaw detection and noise suppression, echo separation and echo estimation, and ultrasonic imaging is investigated. The challenging issues met in practical ultrasonic NDE applications for example the design of a good dictionary are discussed. Representative experimental results are presented for demonstration.     

Simulation of laser-generated ultrasonic wave propagation in solid media and air with application to NDE

Ultrasonic methods are well known as powerful and reliable tool for defect detection. In the previous decades focus and interest have been directed to non-contact sensors and methods, showing many advantages over contact techniques where inspection depends on contact conditions (pressure, coupling medium, contact area). The non-contact hybrid ultrasonic method described here is of interest for many applications, requiring periodic inspection in service or after manufacturing. Despite the potential impact of laser-generated ultrasound in many areas of industry, robust tools for studying the phenomenon are lacking and thus limit the design and optimization of non-destructive testing and evaluation techniques. Here a specific numerical method is presented to efficiently and accurately solve ultrasound wave propagation problems with frequencies in the MHz range traveling in relatively large bodies and through air. This work improves a previous numerical model where propagation of the acoustic waves through air had not been considered, allowing us to simulate the presence of a non-contact transducer in reception in order to simulate numerically the complete experimental setup. It is very important to limit the amount of air to be considered in the FE analyses; otherwise the computational cost would often exceed the resources available. A way to solve the problem is to implement non-reflecting boundary conditions. A non-reflecting boundary condition allows all outgoing waves to exit the domain at the boundary where they have been imposed without reflection; thus, it is possible to model only the portion of air between the non-contact transducer and the solid under testing. Several numerical and experimental analyses were conducted on a 136 lb AREMA rail; here we study in detail two fully non-contact testing configurations for the rail head and web. The information that can be acquired is very valuable for choosing the right setup and configuration when performing non-contact hybrid ultrasonic inspection.     

The propagation of ultrasound in porous media

The equations of Ying and Truell, and Waterman and Truell, describing the propagation of ultrasound in two-phase materials are solved numerically for porous solids, and are found to give unphysical results for high porosity. A new self-consistent theory, which can be solved analytically, is presented and is shown to have reasonable behaviour at high porosity.     

Mode propagation of ultrasound in hollow waveguides

It has previously been shown that there is close agreement between theoretical and experimental behaviour of pulses of ultrasound propagating in solid cylindrical waveguides. Waveguides are used in a number of areas of medical ultrasonics and it is therefore important to be able to model sound propagation in them accurately. This paper extends the analysis of guided wave propagation to hollow waveguides. In particular, frequency spectra of modes of progagation are given and theoretical group velocity curves are compared with experimental results. Signal strengths of modes propagating in both solid and hollow stainless steel waveguides of similar cross-sectional area are also compared.     

Nonlinear propagation of ultrasound in superfluid3He

After introducing the physics of sound propagation in normal and superfluid³He, nonlinear phenomena are discussed. These bear close resemblance to optical effects, including saturation of the absorption, amplitude dependence of the group velocity, pulse break-up, and pulse compression. Preliminary evidence indicates that above an input power threshold the sound pulses propagate in a solitonlike fashion. A naive sine-Gordon model does not explain the observations.     

The propagation of ultrasound in an austenitic weld

The propagation of ultrasound through an austenitic weld is investigated experimentally as well as in a numerical simulation. The weld is insonified at normal incidence to the fusion line with a longitudinal contact transducer. In order to experimentally trace the ultrasound through the weld, slices of different thicknesses from the original weld have been fabricated. Through-transmission A-scans have then been produced for each weld slice and compared with the corresponding numerical simulation. A comparison of the direction of ultrasound propagation through the weld for the two approaches shows quite good agreement. However, attenuation due to scattering at grain boundaries in the weld is poorly modelled in the simulation. In order to improve this, a better model of the weld is needed.     

On the possibility of suppression of self-focusing of a femtosecond laser pulse during its propagation in a cubic nonlinear medium

Based on a computer simulation, the self-focusing of an axially symmetric beam in a cubic nonlinear medium under the anomalous dispersion conditions is studied with the account for the time dispersion of nonlinear response, which manifests for femtosecond pulses. It is shown that, at a certain value of the parameter of linear modulation of the pulse (or of its chirp), the dispersion of nonlinear response can lead either to the suppression of formation of a nonlinear focus and to the possibility of formation of optical shock waves in time or even to a change in the regime of the beam self-action owing to the action of the local response, i.e., to the change from the self-focusing of the beam to the regime of its defocusing.     

Theoretical and experimental investigation of fluid rheology effects on modulated ultrasound propagation

A mathematical model is developed and presented to capture the effect of viscoelastic nature of a material on modulated ultrasound (US) pulses. The model is established by considering perturbation of material elements subject to modulated US pulses and by introducing the exponential relaxation of the perturbed fluid elements with a spectrum of time constants. Both the model and experimental findings revealed that consecutive perturbation of a material via the modulated US pulses enabled to probe the relaxation times of similar order of magnitudes to the frequency of the US modulation while filtering out the impact of other relaxation times on the US measurement. The US experimental results were verified by those of a conventional rheometer. Hence carrying out measurements at different US modulation frequencies in the Hz ranges seems to allow one to obtain the relaxation time spectrum of the investigated material in the time scales of milliseconds to seconds.     

Anisotropic field of background internal waves on a sea shelf and its effect on low-frequency sound propagation

The space-time spectral characteristics of the field of background internal waves (IW) are obtained for two oceanic shelf regions (the Atlantic shelf of the United States and the Kamchatka shelf) and analyzed. Within the framework of a numerical experiment, it is shown that the observed anisotropy of the IW field may considerably affect the low-frequency sound fluctuations in the aforementioned regions and, in particular, may change the interference invariant of the sound field.     

固体隔声层对超声波传播的影响实验研究

介绍了一种可用于实验教学的测量固体隔声层对超声波传播发生影响的实验装置,并进行了实际测量,理论和实验结果相符较好。     

Modeling of interaction between therapeutic ultrasound propagation and cavitation bubbles

In medical applications of high intense focused ultrasound the mechanism of interaction between ultrasound waves and cavitation bubbles is responsible for several therapeutic effects as well as for undesired side effects. Based on a two-phase continuum approach for bubbly liquids, in this paper a numerical model is presented to simulate these interactions. The numerical results demonstrate the influence of the cavitation bubble cloud on ultrasound propagation. In the case of a lithotripter pulse an increased bubble density leads to significant changes in the tensile part of the pressure waveform. The calculations are verified by measurements with a fiber optical hydrophone and by experimental results of the bubble cloud dynamics.     

Modeling of nonlinear ultrasound propagation in tissue from array transducers

A computationally efficient model capable of simulating finite-amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described. It is based on a second-order operator splitting approach [Tavakkoli et al., J. Acoust. Soc. Am. 104, 2061-2072 (1998)], with a fractional step-marching scheme, whereby the effects of diffraction, attenuation, and nonlinearity can be computed independently over incremental steps. This approach is an extension to that of Christopher and Parker [J. Acoust. Soc. Am. 90, 507-521; 90, 488-499 (1991)], wherein linear and nonlinear effects are propagated separately over incremental steps, and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources. Results of the model are compared with published data. Predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented.     

The possibility of superluminal sources and their Doppler effect

From the Special Relativity Theory, the existence of Superluminal reference-frames and faster-than-light objects can be inferred, when its validity is not arbitrarily confined to subluminal velocities. The ‘Extended Theory of Relativity’ allows in particular extending the Doppler effect formulae to Superluminal sources. This point is here explored, due to its possible astrophysical interest. Some other questions are briefly considered, regarding the possibility of ‘radio contact’ between subluminal and Superluminal objects.     

The measurements of anisotropy of ultrasound propagation and magnetic susceptibility in viscous ferrofluid

Results of experimental study of anisotropy of ultrasound propagation and anisotropy of magnetic susceptibility in a ferrofluid of considerable viscosity are reported. The dependence of the propagation velocity and absorption coefficient of ultrasonic wave on the angle between the direction of measurement and that of the magnetic field provides important information on the ferrofluid structure in a magnetic field. The results show that the ultrasonic absorption coefficient of a wave propagating in a viscous ferrofluid in a DC magnetic field depends mainly on the rotational degree of freedom. Measurements of the anisotropy of the magnetic susceptibility of a ferrofluid bring the information on the magnetic moment of the magnetic particles and their mean radius.     

Differential geometry of ray surfaces in anisotropic solids and its contribution to NDE: modelling and experiment

Point-source/point-receiver techniques are one of the most widely used methods for nondestructive evaluation of anisotropic materials. The group velocities resulting from these techniques must be, for further inverse evaluation of elastic coefficients, geometrically converted into corresponding phase velocities. On the other hand, the phase velocities can be determined from a material's response to a line source. But, due to the anisotropy, the short line sources generated by cylindrical lenses are insufficient for reliable determination of the phase velocity. In this paper, a long line source is approximated by a set of linearly arranged point sources. As it follows from the differential geometry of ray surfaces, information obtained from such set of sources is sufficient for determination of phase velocities of both the quasi-transverse and the quasi-longitudinal modes of propagation. Moreover, this approach can be generalized for any arbitrary set of point sources only by employing a proper time-base transformation. The applicability of the presented approaches is illustrated on transversely isotropic and tetragonal fibrous composite materials.     

A single-pole model for the propagation of ultrasound in soft tissue

A minimum-phase function, which characterizes the velocity dispersion in tissue was calculated from measured attenuation. This function was incorporated into a causal tissue model. Predictions of attenuation using the minimum-phase function with just a single pole matched measured attenuation in the 1- to 10-MHz range within a few percent. Dispersion of phase velocity predicted by the single-pole model was comparable to measured dispersion. The frequency associated with the single pole, which is a relaxation frequency, decreased with hemoglobin concentration and collagen content but increased with temperature. The electrical equivalent circuit for this model is a delay coupled with a low-pass filter which can be configured as a resistance in series with a parallel combination of resistance and capacitance.