时频域独立元分析方法实现超声兰姆波的多模式分离

为方便兰姆波信号分析与模式定征,提出一种将短时傅里叶变换(Short-Time Fourier Transform,STFT)与独立元分析(Independent Component Analysis,ICA)相结合的多模式超声兰姆波识别方法。首先通过STFT将兰姆波时域信号投影至时频域,基于各模式信号在时频域相对独立的特点,利用ICA实现混叠模式分离。根据分离模式时频能量脊提取各模式群速度曲线,进而估计板厚。将方法运用于时域有限差分(Finite-Difference Time-Domain,FDTD)法仿真与钢板实验,分离得到A0、A1和S0三种模式。仿真与实验中平均群速度估计误差约为1.5%和2.0%,板厚估计误差约为0.3%和2.0%。仿真结果表明,在信噪比(Signal-to-Noise Ratio,SNR)不小于0 dB的情况下,时频域独立元分析方法均可实现兰姆波多模式分离、群速度曲线提取及板厚估计。      

The propagation of Lamb waves in a plate bordered with layers of a liquid.

The influence of liquid layers on the propagation of Lamb waves in a plate of finite thickness is studied theoretically. The dispersion equations of Lamb waves in a plate bordered with layers of liquids are derived. Numerical solutions of the equations show that the phase velocity of Lamb waves changes with the thickness of the liquid layers. For the lowest antisymmetrical mode of very thin plates, the numerical results calculated from the dispersion equations are compared with those derived from the bending wave acoustic impedance approach. The limitation of the latter is discussed. Applications of Lamb waves pertinent to biosensing are also presented.     

Measurements of dispersion curves of leaky Lamb waves using a lensless line-focus transducer.

This paper presents a new method of measuring dispersion curves of leaky Lamb waves propagating in a thin plate. The measurement system is based on a lens-less line-focus transducer and its defocusing measurement technique. A new waveform processing method known as V(f, z) method is introduced for analyzing the measured waveforms and for extracting the dispersion relation. For two thin-plate samples, namely a 150 microm thick alumina plate and a 320 microm thick stainless steel plate, the dispersion curves of several lower order modes of leaky Lamb waves have been experimentally determined in the frequency range of few to 25 MHz. The experimental dispersion curves have then been compared with the theoretical ones. Excellent agreement is observed. It is then verify that this method indeed provides a convenient and accurate way for experimentally measuring dispersion curves of leaky Lamb waves of thin-plate samples.     

兰姆波检测信号的匹配追踪时频分析

为有效去除兰姆波检测信号中的冗余信息和识别多个模态,应用匹配追踪方法对兰姆波信号进行处理。在Chirplet原子基础上添加弯曲算子进行改进,以更好地匹配频散和多模式兰姆波信号的特征。由改进的Chirplet原子组成过完备字典,使用基于遗传算法的匹配追踪(GAMP)信号稀疏分解方法,从过完备字典中选出与待分析信号相匹配的最佳原子,利用最佳匹配原子和对应的分解系数进行信号重构和时频分析。研究结果表明,改进后的Chirplet原子更能反映出兰姆波信号的非线性时频变化特征,得到的时频分布与频散曲线的弯曲特性能很好的吻合。采用改进后的Chirplet原子匹配追踪方法可以获取更加精确的走时信息,为后续兰姆波损伤定位成像奠定基础。      

Normal mode expansion method for laser-generated ultrasonic Lamb waves in orthotropic thin plates

A quantitative theory for modeling the laser-generated transient ultrasonic Lamb waves, which propagates along arbitrary directions in orthotropic plates, is presented by employing an expansion method of generalized Lamb wave modes. The displacement field is expressed by a summation of the symmetric and antisymmetric modes in the surface stress-free orthotropic plate, and therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin plates because one needs only to evaluate several lower modes. The transient waveforms excited by the thermoelastic expansion and the oil-coating evaporation are analyzed for a transversely isotropic thin plate. The results show that the theory provides a quantitative analysis to characterize anisotropic elastic stiffness properties of orthotropic plates by laser-generated Lamb wave detection.     

Nondestructive testing in human teeth using a leaky Lamb wave device

A Lamb wave interdigital transducer mounted on a layered substrate composed of two plates, a thin piezoelectric ceramic plate and an acrylic plate, operating at a liquid-solid boundary, is investigated for ultrasonic nondestructive testing of the layer thickness in human teeth. A higher-order mode having a phase velocity higher than the longitudinal wave velocity in the human teeth can be used for nondestructive testing. In the combination of the two layers, the fourth mode of leaky Lamb wave is most favorable for a frequency-controllable radiation angle of an ultrasound beam into a water layer as an acoustic coupler. In the configuration of an acoustic delay line, the layer-thickness measurement in vivo, evaluated from the time interval between two reflected ultrasound echoes, is successfully realized under a thin water layer as the acoustic coupler.     

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.     

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.     

Mode separation of Lamb waves based on dispersion compensation method

Ultrasonic Lamb modes typically propagate as a combination of multiple dispersive wave packets. Frequency components of each mode distribute widely in time domain due to dispersion and it is very challenging to separate individual modes by traditional signal processing methods. In the present study, a method of dispersion compensation is proposed for the purpose of mode separation. This numerical method compensates, i.e., compresses, the individual dispersive waveforms into temporal pulses, which thereby become nearly un-overlapped in time and frequency and can thus be extracted individually by rectangular time windows. It was further illustrated that the dispersion compensation also provided a method for predicting the plate thickness. Finally, based on reversibility of the numerical compensation method, an artificial dispersion technique was used to restore the original waveform of each mode from the separated compensated pulse. Performances of the compensation separation techniques were evaluated by processing synthetic and experimental signals which consisted of multiple Lamb modes with high dispersion. Individual modes were extracted with good accordance with the original waveforms and theoretical predictions.     

Localization of notches with Lamb waves

A time-frequency representation (TFR) is used to analyze the interaction of a multimode and dispersive Lamb wave with a notch, and then serves as the basis for a correlation technique to locate the notch. The experimental procedure uses a laser source and a dual-probe laser interferometer to generate and detect Lamb waves in a notched plate. The high fidelity, broad-bandwidth, point-like and noncontact nature of laser ultrasonics are critical to the success of this study, making it possible to experimentally measure transient Lamb waves without any frequency biases. A specific TFR, the reassigned spectrogram, is used to resolve the dispersion curves of the individual modes of the plate, and then the slowness-frequency representation (SFR) of the plate is calculated from this reassigned spectrogram. By considering the notch to be an additional (second) source, the reflected and transmitted contributions of each Lamb mode are automatically identified using the SFRs. These results are then used to develop a quantitative understanding of the interaction of an incident Lamb wave with a notch, helping to identify mode conversion. Finally, two complementary, automated localization techniques are developed based on this understanding of scattering of Lamb waves.     

用于储罐底板缺陷检测的超声兰姆波模式研究

从超声兰姆波的声场方程出发,得到板材表面离面位移(法向位移)为零的条件,即当超声兰姆波的相速度等于板材介质的纵波声速时,在板材表面的离面位移为零。在给定适当频厚积的条件下,分别数值模拟了仅有切向位移而无离面位移的A1、S1、A2和S2兰姆波模式在有液体负载的单层钢板中的传播情形。结果表明:离面位移为零的S2模式频散较小且对板中缺陷更为敏感。     

铝板中Lamb波检测的实验研究

Lamb波在传播过程中具有频散及多模态特性,若相关参数选择不当,会导致在实际应用中信号相互叠加而无法识别。本文基于Lamb波的频散曲线是其频散方程实数解分布的特点,采用二分法绘制了铝板中Lamb波的频散曲线、波结构曲线和入射角曲线。根据曲线选择S0模态的Lamb波对1mm厚铝板中不同类型的缺陷进行检测。实验结果表明,S0模态的Lamb波对裂纹型缺陷和贯穿型缺陷十分敏感,但对于裂纹型缺陷,其幅值变化并不与缺陷大小成线性关系,并且S0模态Lamb波的声场指向性十分集中,在偏离声束轴线时无法检测到缺陷。     

两侧有固体层负载时板中Lamb波的传播

本文研究了薄板二面有固体导负载时板中Ｌａｍｂ波的传播，从弹性波理论出发并结合应的边界条件，导出板中Ｌａｍｂ波的色散方程，数值计算表示，不管作为自由状态时板中Ｌａｍｂ波相速（板厚取定时）是大于或小于外层固体的声表面波波速，板中对称及反对称模式的Ｌａｍｂ波相速都随着外层固体层厚度增加而变化并且渐近于外层固体的声表面波波速，数值计算又表明，对很薄的板，板中对称及反对称模式的相速均随负载板的厚度呈线性变化     

基于模式分离的兰姆波逆时偏移成像

应用频率域逆时偏移方法实现各向同性和各向异性板中缺陷的兰姆波成像.由于缺陷引起的多模态散射信号会在重建图像中形成伪像,根据基本导波模式振动对称性的差别进行了模式分离预处理.基于多元阵列超声技术,开展了铝板和复合板内缺陷频率域逆时偏移超声成像方法的数值仿真研究.首先,建立有限元模型,采用环形传感器数值采集由缺陷引起的兰姆波散射信号,然后,将采集到的多模式散射信号进行模式分离处理,再将模式分离后的兰姆波散射信号经时间反转后并在相应的接收器处重新激励,在频域中运用格林函数反向传播兰姆波散射信号,获取监测区域的声场信息,与正向传播声场进行互相关,重建缺陷图像.首先对铝板中单缺陷以及复合材料板中相邻的两个相同缺陷进行数值仿真,对比有无模式分离处理的缺陷逆时偏移成像效果,体现出模式分离的重要性.在此基础上,采用逆时偏移方法对复合板材内位置邻近、深度不同的双缺陷进行识别.数值结果表明,模式分离预处理后的缺陷重建图像能够有效去除多模式干扰产生的伪像.文中提出的成像方法对各向同性板和各向异性板内缺陷的检测和成像具有很好的发展潜力,可以准确地探测多个缺陷的形状、尺寸和深度.     

Guided waves propagating in sandwich structures made of anisotropic,viscoelastic, composite materials

The propagation of Lamb-like waves in sandwich plates made of anisotropic and viscoelastic material layers is studied. A semi-analytical model is described and used for predicting the dispersion curves (phase velocity, energy velocity, and complex wave-number) and the through-thickness distribution fields (displacement, stress, and energy flow). Guided modes propagating along a test-sandwich plate are shown to be quite different than classical Lamb modes, because this structure does not have the mirror symmetry, contrary to most of composite material plates. Moreover, the viscoelastic material properties imply complex roots of the dispersion equation to be found that lead to connections between some of the dispersion curves, meaning that some of the modes get coupled together. Gradual variation from zero to nominal values of the imaginary parts of the viscoelastic moduli shows that the mode coupling depends on the level of material viscoelasticity, except for one particular case where this phenomenon exists whether the medium is viscoelastic or not. The model is used to quantify the sensitivity of both the dispersion curves and the through-thickness mode shapes to the level of material viscoelasticity, and to physically explain the mode-coupling phenomenon. Finite element software is also used to confirm results obtained for the purely elastic structure. Finally, experiments are made using ultrasonic, air-coupled transducers for generating and detecting guided modes in the test-sandwich structure. The mode-coupling phenomenon is then confirmed, and the potential of the air-coupled system for developing single-sided, contactless, NDT applications of such structures is discussed.     

Model-based analysis of dispersion curves using chirplets

Time-frequency representations, like the spectrogram or the scalogram, are widely used to characterize dispersive waves. The resulting energy distributions, however, suffer from the uncertainty principle, which complicates the allocation of energy to individual propagation modes (especially when the dispersion curves of these modes are close to each other in the time-frequency domain). This research applies the chirplet as a tool to analyze dispersive wave signals based on a dispersion model. The chirplet transform, a generalization of both the wavelet and the short-time Fourier transform, enables the extraction of components of a signal with a particular instantaneous frequency and group delay. An adaptive algorithm identifies frequency regions for which quantitative statements can be made about an individual mode's energy, and employs chirplets (locally adapted to a dispersion curve model) to extract the (proportional) energy distribution of that single mode from a multimode dispersive wave signal. The effectiveness of this algorithm is demonstrated on a multimode synthetic Lamb wave signal for which the ground-truth energy distribution is known for each mode. Finally, the robustness of this algorithm is demonstrated on real, experimentally measured Lamb wave signals by an adaption of a correlation technique developed in previous research.     

Wideband dispersion removal and mode separation of Lamb waves based on two-component laser interferometer measurement

Ultrasonic Lamb waves are considered as a sensitive and effective tool for nondestructive testing and evaluation of plate-like or pipe-like structures. The nature of multimode and dispersion causes the wave packets to spread, and the modes overlap in both time and frequency domains as they propagate through the structures. By using a two-component laser interferometer technique, in combination with a priori knowledge of the dispersion characteristics and wave structure information of Lamb wave modes, a two-component signal processing technique is presented for implementing dispersion removal and mode separation simultaneously for two modes mixture signals of Lamb waves. The proposed algorithm is first processed and verified using synthetic Lamb wave signals. Then, the two-component displacements test experiment is conducted using different aluminum plate samples. Moreover, we confirm the effectiveness and robustness of this method.     

Mode selection of Lamb waves for the evaluation of solid plates with liquid loading

This paper studies the mode selection of Lamb waves for evaluating solid plates with liquid loading. For this purpose, the Lamb wave selected should have the features such as zero normal displacement components at the plate surface in contact with liquid, small dispersion, and maximum group velocity. It is found that when the phase velocity of Lamb wave is equal to the longitudinal wave velocity of the plate material, its normal displacement at the plate surface is always zero. Through the numerical analyses, the specific S₂ Lamb wave that has zero normal displacement component at the plate surface, small dispersion and maximum group velocity compared with the other Lamb waves has been found. With respect to the specific S₂ Lamb wave, some experimental examinations have been carried out. It is found that the liquid loading on the plate surface has less influence on the specific S₂ Lamb wave signal but it can effectively eliminate the other signals. Moreover, the specific S₂ Lamb wave selected exhibits the capability of detecting multiple defects in the solid plate with the liquid loading. It can be concluded that the specific S₂ Lamb wave selected is suitable for the evaluation of solid plates with liquid loading.     

基于频散特征的单水听器模式特征提取及距离深度估计研究

针对浅海环境中低频宽带水声脉冲信号, 研究基于频散特征结合时频分析的单水听器距离和深度估计方法. 以简正波理论为依据, 将单水听器上的接收信号表示成一系列传播模式之和的形式, 分析了经典波导环境下的频散现象, 采用自适应径向高斯核函数的时频分析方法来表征接收信号的频散特征. 为提高时频分辨率, 采用自适应径向高斯核函数的时频分布来提取频散关系曲线中传播模式的到达时间差, 利用模式的到达时间差估计声源的距离. 采用多模式联合匹配的方式, 通过二值掩模滤波的时频滤波方法, 提取所需的模式. 通过计算实际提取出的模式能量与预测的模式能量之间的误差, 建立代价函数, 并通过模式能量匹配的方式, 确定声源的深度. 通过对基于Pekeris波导模型的浅海环境进行仿真验证, 结果表明: 自适应径向高斯核函数的时频分析方法能够很好地反映信号本身的频散特征, 具有较高的时频分辨率, 克服了传统短时傅里叶变换时频表征的限制, 使得模式在时频域更加容易辨识和分离; 从测距效果来看, 不同模式组合下的距离估计结果不同, 采用在时频面上具有较高能量的模式, 可得到较为准确的距离估计; 选用高能量的模式所得的距离估计的相对误差小于2%. 在定深方面, 参与联合匹配的模式个数越多, 代价函数的峰值更加地尖锐, 同时具有低的伪峰, 深度估计的性能会进一步有所提升. 该工作对于研究低频水声脉冲信号的分离和提取具有重大意义. 关键词： 频散信道 时频分析 单水听器 定位     

轨道板中超声兰姆波传播的有限元计算和实验*

该文针对我国高速铁路轨道板缺陷的非接触动态检测问题,研究了空气耦合超声兰姆波在轨道板中的传播规律。首先,给出了轨道板中超声兰姆波的相速度和群速度频散曲线,结果表明:随着频厚积的增加,频散现象越明显,并且A0相速度收敛于Rayleigh波的波速。然后,建立轨道板中波传播的有限元模型,计算得到兰姆波传播的群速度为2220 m/s,且二维傅里叶变换系数的较大值沿Rayleigh波的频散曲线分布。最后,在沪杭高铁嘉兴南站进行了现场测试,以8.8°倾斜角向轨道板激励产生超声兰姆波,激发产生的兰姆波模态群速度为2325 m/s,且二维傅里叶变换分析其系数的较大值沿Rayleigh波的频散曲线分布。有限元计算结果和实验结果均与理论计算结果一致。该研究为后续轨道板缺陷的非接触动态检测提供了理论依据和实验方法。