An elastodynamic computational time-reversal method for shape reconstruction of traction-free scatterers

This study proposes an elastodynamic time-reversal imaging method for the shape reconstruction of flaws with the traction-free boundary. The proposed method is a generalization of the synthetic aperture focusing technique (SAFT) implemented with the aid of time-reversal back-propagation computation. The reconstruction formula is derived from the boundary condition applied on the flaw boundary without using a diffraction theory yielding an inherently normalized objective function. No restriction is imposed on the wave source or the material properties as long as the wave medium is linearly elastic and lossless. There are two major advantages with the proposed method. First, it is free from ray tracing. The method can thus work with an arbitrary source and the wave modes including inhomogeneous waves. Second, signal conditioning is not required to focus a scattered field to the correct location in the reconstructed image. Numerical examples are presented to demonstrate the performance and benefits of the proposed method. In the numerical examples, the shape of cavities and cracks in an elastic layer is reconstructed from synthetic data. The results show that the method works well with the reverberating incident fields in which inhomogeneous and body waves coexist. Also demonstrated is that the curvature of the cavities is resolved well at the scale of the incident wave length. Through the numerical examples, the method is shown to be a versatile imaging method potentially useful for ultrasonic nondestructive characterization of small flaws.     

Direct numerical modeling of time-reversal acoustic subwavelength focusing

Focusing waves back to their original source position is possible both experimentally and numerically thanks to time reversal mirrors (TRM). For a TRM placed in the far field of the source, the focusing spot of the reversed wavefield is subject to the diffraction limit and cannot be smaller than half the minimum wavelength, even for a very small source. Yet, numerous time reversal experiments in resonating media have shown subwavelength focusing. In this work, we show that it is possible to model these subwavelength focusing observations with simple physics, only the 2-D standard acoustic wave equation, and with specific fine scale heterogeneity. Our work is based on the spectral element method to solve the wave equation and to model time reversal experiments. Such a method makes it possible to propagate very long time series in complex and strongly discontinuous media with high accuracy. The acoustic wave equations are solved at the fine scale in media with one or more split rings of size much smaller than the wavelength. Such split rings produce a Helmholtz resonance effect as well as propagation band-gaps. We show that, in such media, even with a single split ring resonator, subwavelength focusing down to 1/13th of the minimum wavelength can be observed.     

Discriminating linear from nonlinear elastic damage using a nonlinear time reversal DORT method

The DORT method is a selective detection and focusing technique originally developed to detect defects and damages which induce linear changes of the elastic moduli. It is based on the time reversal (TR) where a signal collected from an array of transducers is time reversed and then back-propagated into the medium to obtain focusing on selected targets. TR is based on the principle of spatial reciprocity. Attenuation, dispersion, multiple scattering, mode conversion, etc. do not break spatial reciprocity. The presence of defects or damage, may cause materials to show nonlinear elastic wave propagation behavior that will break spacial reciprocity. Therefore the DORT method will not allow focusing on nonlinear elastic scatterers. This paper presents a new method for the detection and identification of multiple linear and nonlinear scatterers by combining nonlinear elastic wave spectroscopy, time reversal and DORT method. In the presence of nonlinear hysteretic elastic scatterers, forcing the solid with a harmonic excitation, the time reversal operator can be obtained not only at the fundamental frequency of excitation, but also at the odd harmonics. At the fundamental harmonic, either inhomogeneities and linear damages can be individually selected but only at odd harmonics nonlinear hysteretic elastic damages exist. A procedure was developed where by decomposing the operator at the odd harmonics, it was possible to focus on nonlinear scatterers and to differentiate them from the linear inhomogeneities. A complete mathematical nonlinear DORT formulation for 1 and 2D structures is presented. To model the presence of nonlinear elastic hysteretic scatterers a Preisach–Mayergoyz (PM) material constitutive model was used. Results relative to 1 and 2 dimensional structures are reported showing the capability of the method to focus and discern selectively linear and nonlinear scatterers. Furthermore, an analysis was conducted to study the influence of the number of sources and their location on the imaging process showing that using a higher numbers of sensors does not automatically bring to a minor uncoupled behaviour between the nonlinear targets.     

基于多通道时间反转Lamb波的铝板小缺陷检测

超声Lamb波具有传播距离远、衰减小等特点,广泛应用于板结构的无损检测。将Lamb波检测技术与时间反转理论相结合,能提高铝板中小缺陷的检测能力。采用多通道时间反转板中Lamb波聚焦方法对1mm厚的铝板中直径0.8mm通孔缺陷进行检测,检测结果显示多通道时间反转检测信号中形成了两处明显的聚焦,即直达波和缺陷回波聚焦,证明此方法有效提高了检测分辨铝板小缺陷的能力。最后通过直达波、缺陷回波两处聚焦的时间差和Lamb波S_0模态群速度,准确实现了铝板中小缺陷的定位。多通道时间反转Lamb波聚焦方法不仅得到了缺陷检测回波,而且准确实现了缺陷的定位,达到了提高铝板中小缺陷检测能力的目的。     

Time reversal super resolution in randomly layered media

In this paper we extend previous work on time reversal in randomly layered media [J.-P. Fouque, J. Garnier, A. Nachbin, K. Sølna, Time reversal refocusing for point source in randomly layered media, Wave Motion 42 (2005) 238–260]. We consider first the case of an active source embedded below the surface in a finely layered random medium. We carry out time reversal with a time reversal mirror placed at the surface and we consider here the case where this mirror is larger than the carrier wavelength. In contrast with the situation addressed in our previous paper, where the size of the mirror was comparable to the wavelength, we show that multi-pathing dramatically enhances the effective aperture of the mirror so that super resolution at the location of the source can be obtained. In other words, the focal spot radius of the refocused field obtained in the case of a multiply scattering medium is much smaller than the spot size obtained in the case of a homogeneous medium. This super resolution effect is obtained by time-reversing the long incoherent waves generated by the multiple scattering due to the thin layers. We also give an application to the problem of focusing on a passive scatterer buried in the random medium and illuminated by a source at the surface.     

Numerical simulation of ultrasonic time reversal on defects in carbon fibre reinforced polymer

An ultrasonic non-destructive testing method is under development for detecting small scale damage in carbon fibre reinforced polymer. This method relies on signal processing to detect the presence of nonclassical nonlinear signature of microcracking or delamination in the material. Using reciprocal time reversal with nonlinear spectroscopy, the ultrasound can be focused on defect which is in unknown location in test object and may be far from the sending or the receiving transducer. With spectral analysis of defect and delayed time reversal input, the defect can be excited to larger displacement amplitudes by using its resonance. The study is conducted using finite element simulations in two dimensions for carbon fibre composite plate.     

Time reversal super resolution in randomly layered media

In this paper we extend previous work on time reversal in randomly layered media [J.-P. Fouque, J. Garnier, A. Nachbin, K. Sølna, Time reversal refocusing for point source in randomly layered media, Wave Motion 42 (2005) 238–260]. We consider first the case of an active source embedded below the surface in a finely layered random medium. We carry out time reversal with a time reversal mirror placed at the surface and we consider here the case where this mirror is larger than the carrier wavelength. In contrast with the situation addressed in our previous paper, where the size of the mirror was comparable to the wavelength, we show that multi-pathing dramatically enhances the effective aperture of the mirror so that super resolution at the location of the source can be obtained. In other words, the focal spot radius of the refocused field obtained in the case of a multiply scattering medium is much smaller than the spot size obtained in the case of a homogeneous medium. This super resolution effect is obtained by time-reversing the long incoherent waves generated by the multiple scattering due to the thin layers. We also give an application to the problem of focusing on a passive scatterer buried in the random medium and illuminated by a source at the surface.     

Rattle noise source localization through the time reversal of dispersive vibration signals on a road vehicle

This paper proposes a localization method to identify the source of impulsive rattle generation on a road vehicle. The proposed method makes use of numerical time reversal for dispersive vibrations on the vehicle frames that consist of multi-linked paths with junctions. The vibrations propagated to the vehicle were analyzed in the time and frequency domains via the spectral element method (SEM). The vibration interactions resulted from structural spans of the vehicle were examined in terms of the propagated pathways with the junctions. The multi-node time reversal was proposed to implement re-emission procedures from all independent nodes. The modified spectral matrices of the proposed procedure enabled the multi-node time reversal under consideration of the structural spans of the vehicle. The proposed method was verified by an actual vehicle test. The combination of the SEM and the multi-node time reversal allows effective localization of rattle noise sources in vehicles.     

基于时间反转法的Lamb波检测技术的研究进展

Lamb波具有传播距离远、衰减小等特点,已被广泛应用于大型板类结构的损伤检测。时间反转是实现超声波聚焦的有效方法之一。本文回顾并总结了近20年来时间反转方法在Lamb波检测领域中的研究进展。针对Lamb波固有的频散和多模态等传播特性,详细论述了时间反转法在板结构Lamb波检测中的应用。最后对基于时间反转法的免基准信号Lamb波损伤检测方法进行了总结,分析其存在的问题并对其应用前景进行了展望。     

Quantitative guided wave testing by applying the time reversal principle on dispersive waves in beams

A method for the localization and characterization of defects in waveguide-like structures is presented in this paper. In contrast to traditional ultrasound and guided wave techniques, a broadband signal is used to enforce strong dispersion of the flexural wave mode. Since dispersion is well compensated in a time reversal experiment we use a time reversal numerical simulation to identify the origin and the original shape of the flexural wave excited at a local non-uniformity due to mode conversion. Limitations of the time reversal process for broadband signals due to multimode and evanescent behavior of guided waves are discussed and eliminated using a Timoshenko beam model. The resulting novel process which uses both flexural and longitudinal wave information allows detection, localization and size estimation of several defects in a beam with only a single measurement. The method proposed is experimentally validated on rectangular solid beams and cylindrical hollow beams with notches of different sizes and positions. Up to three notches could be localized from one measurement, with a maximum error of 3% with respect to the propagation distance. The size was accurately predicted for notches as small as 0.5 mm depth or 8.3% of the cross section, using a generalized spring model of a crack.     

混凝土损伤识别中的时间逆转成像方法

时间逆转成像技术具有定位准确和操作简单之特点,本文将其运用于混凝土结构损伤的检测．通过提取各换能器单元的发射信号和损伤散射信号构建超声波传播的传递矩阵然后对其进行奇异值分解,获得包含损伤信息的奇异向量;采用多重信号分类(multiple signal classification, MUSIC)算法,分别基于数值模拟数据和实验实测数据对混凝土结构内部损伤进行成像,实现了准确的损伤定位,并将成像结果与偏移成像法进行对比．此工作探索了将时间逆转成像技术应用于混凝土结构内部损伤实际工程检测可行性,为无损检测技术人员定性或定量分析混凝土结构的内部缺陷提供理论参考．     

相位谱线性重构法去除Lamb波频散研究

Lamb波广泛应用于板壳结构的损伤检测,而Lamb波的频散效应使得板结构中损伤散射信号的渡越时间信息难以准确提取,因而影响了阵列波束成形损伤成像算法对损伤成像定位的效果和精度.提出的相位谱线性重构法,在中心频率处通过对相位谱展开,进行线性化处理,有效地去除了激励信号中的频散效应.该方法保证了中心频率下的信号分量不变,为研究阵列波束成形损伤成像算法对损伤精确成像奠定了基础.采用数值模拟和实验手段,验证所提出的相位谱线性重构法去除频散的效果,进而结合阵列波束成形损伤成像方法分析损伤成像定位的效果和精度.结果 表明,采用的频散去除方法能够提高损伤散射信号的信噪比,提升阵列波束成形损伤成像方法对损伤成像定位的效果和精度.     

机械振动信号盲源分离的时域方法

介绍盲源信号分离基本原理,分析了瞬态混叠模型和卷积混叠模型的特征,给出两个源信号独立性的评判准则,研究了盲分离正确性的评价误差函数,进行数值仿真,并用时域卷积瞬态混叠模型对实际机械振动信号进行源信号的盲分离。数值仿真和实际信号的分离效果较好,说明所用方法在机械振动信号盲源分离中的适用性。文中还分析了多源信号分离中所用方法的收敛性。     

A fractal reconstruction method for LDV spectral analysis

An unequally spaced fractal interpolation method is developed to reconstruct the low data rate laser Doppler velocimetry (LDV) signal for better spectral results. The reconstructed result not only augments the data points to improve the statistics but also retains the turbulent fractal dimension of the flow. In other words, the interpolated data are flow turbulence-correlated data which are physically reasonable. This method is demonstrated on the LDV spectral measurements in the shear layer of a jet flow and the results are compared against the hot-wire spectral data. When the data rate of the LDV signal is low, the fractal interpolation method can suitably restore the major spectral peaks while the conventional sample-and-hold fails. Effects of the data rate, data record length, sampling rate and the fractal dimension on the accuracy of the spectral reconstruction are also discussed. A version of this paper was presented at the 4th International Symposium on Transport Phenomena in Heat and Mass Transfer, July 14–18, 1991, Sydney, Australia     

基于惯导及声学浮标辅助的水下航行器导航定位系统

针对纯惯导系统误差发散和无线电信号在水下衰减快从而无法精确定位的问题,设计了一种基于声学浮标辅助惯导的水下定位系统,该系统由惯导系统和声学定位系统组成,其中声学定位系统由若干个浮标构成水听器阵,浮标的经纬度坐标由GPS提供,浮标完成对接收到的声源信号的处理,利用互相关测时延差的方法来进行定位。由于水下噪声、混响等因素会造成接收到的多路声信号出现模糊互相关峰,因此对接收信号应进行频域加权处理。最后利用声学系统的定位信息来校正惯导的误差。仿真结果表明:与基本互相关方法相比,加权处理能有效提高时延差的精度,所提出的惯导和声学浮标辅助设备导航系统能够使定位误差小于2 m,保证了水下航行器能够长时间在水下航行。     

Force reconstruction based on the union of singular spectral analysis and regularization method

Abstract

To overcome the problem of some ill-posed inverse problem of force reconstruction, which is caused by the noise in the measured responses and small singular values of the structure, a technology of force reconstruction based on a hybrid method of singular spectral analysis (SSA) and the Landweber regularization method is proposed in this study for the first time. The SSA is used to filter the structural response before using Landweber regularization. A new choice method of phase space reconstruction dimension is theoretically proposed, and the minimum embedding dimension is determined by the concept of optimizing difference spectrum theory. The feasibility of this method was demonstrated through three kinds of force reconstructions. The numerical simulation results and an acoustic vibration experiment demonstrated that the proposed method is more effective than the traditional method.

Communicated by Wei-Chau Xie.     

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

A new interface reconstruction method in 3D is presented. The method involves a conservative level‐contour reconstruction coupled to a cubic‐Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second‐order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required. Copyright © 2008 John Wiley & Sons, Ltd.     

Noise processing of flaw reconstruction by wavelet transform in ultrasonic guided SH waves

The ultrasonic guided wave technique is a potential and useful tool for nondestructive testing. The scattered or reflected wave from a flaw can give its qualitative or even quantitative information such as location, size and severity. However, in experiments and in situ tests, the noises always exist together with signals. In this paper, we propose a wavelet-transform based noise processing approach for reflected wave signals to the quantitative reconstruction of surface flaws on a plate using guided SH waves. We suggest two different denoising methods based on wavelet transform (WT) in time and wavenumber domains respectively. Numerical results show that wavenumber-domain WT operation gives a better denoising effect than direct time-domain WT denoising. Using the former, one can successfully perform the inverse reconstruction of flaw by reflected signals with signal noise ratio as high as ?5 dB. This research can act as a theoretical reference for practical applications of ultrasonic guided SH waves in quantitative nondestructive evaluation.     

爆破振动持时分析及微差爆破延期时间优选

爆破振动持续时间以及微差爆破延期时间分别是爆破振动危害客观评价与主动控制的重要指标,对振动持时影响因素和延期时间优选方法进行深入探究极为必要。结合量纲分析理论,探讨了爆破振动持时影响因素,推导出爆破振动持时预测公式,该公式线性相关性达到89.7%;基于地震波线性叠加原理,通过MATLAB 7.0编程,计算得到毫秒微差爆破不同爆心距处合理延时区间。结果表明,爆破振动信号能量与振动持续时间相关性高,在振动持时预测公式中引入信号能量,可提高预测精度;振动持续时间与比例速度负相关,与比例药量正相关;合理孔间延期时间往往不是某一具体值,而是一个或多个时间区间;不同爆心距处合理延期时间值不同。工程应用表明,给出的爆破振动持时预测公式与微差爆破延时优选方法切实可行。