Analysis on accuracy improvement of rotor–stator rubbing localization based on acoustic emission beamforming method

This paper attempts to introduce an improved acoustic emission (AE) beamforming method to localize rotor–stator rubbing fault in rotating machinery. To investigate the propagation characteristics of acoustic emission signals in casing shell plate of rotating machinery, the plate wave theory is used in a thin plate. A simulation is conducted and its result shows the localization accuracy of beamforming depends on multi-mode, dispersion, velocity and array dimension. In order to reduce the effect of propagation characteristics on the source localization, an AE signal pre-process method is introduced by combining plate wave theory and wavelet packet transform. And the revised localization velocity to reduce effect of array size is presented. The accuracy of rubbing localization based on beamforming and the improved method of present paper are compared by the rubbing test carried on a test table of rotating machinery. The results indicate that the improved method can localize rub fault effectively.     

Nonlinear Kalman Filtering for acoustic emission source localization in anisotropic panels

Nonlinear Kalman Filtering is an established field in applied probability and control systems, which plays an important role in many practical applications from target tracking to weather and climate prediction. However, its application for acoustic emission (AE) source localization has been very limited. In this paper, two well-known nonlinear Kalman Filtering algorithms are presented to estimate the location of AE sources in anisotropic panels: the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). These algorithms are applied to two cases: velocity profile known (CASE I) and velocity profile unknown (CASE II). The algorithms are compared with a more traditional nonlinear least squares method. Experimental tests are carried out on a carbon-fiber reinforced polymer (CFRP) composite panel instrumented with a sparse array of piezoelectric transducers to validate the proposed approaches. AE sources are simulated using an instrumented miniature impulse hammer. In order to evaluate the performance of the algorithms, two metrics are used: (1) accuracy of the AE source localization and (2) computational cost. Furthermore, it is shown that both EKF and UKF can provide a confidence interval of the estimated AE source location and can account for uncertainty in time of flight measurements.     

基于双传声器对的多声源二维定位跟踪算法

提出一种房间混响声场环境下的多声源二维定位跟踪算法。研究了基于盲源分离的时延估计,以及联合空间分布的多个传声器对的定位算法。用高斯似然函数解决在多源、多维情况下声源定位的时延匹对模糊问题,使之能够用双传声器对实现对多个声源的二维定位,结合粒子滤波算法实现对多个运动声源的跟踪。仿真实验验证了提出算法的有效性。      

FLEXURAL INTENSITY MEASUREMENT ON FINITE PLATES USING MODAL SPECTRUM IDEAL FILTERING

Flexural intensities on various plate-like structures with arbitrary boundary conditions are calculated using measured and FEM yielded mobility. In doing so, a two-dimensional spatial Fourier transform has been implemented along with a refined k-spectral filtering concept. Intensity is decomposed into individual contributions from bending moments, twisting moments and shear forces. The source and energy sink localization and energy flow have been analyzed through these contributions. The effect of reflections from the plate edges and that of the uncorrelated noise, on the intensity, are discussed. It is shown that the width of the k -filters may have a non-negligible influence on the shape of the intensity field. Damping in the structure can efficiently control the edge reflections and therefore help to localize the energy sources and sinks. A link has been found, at certain excitation conditions, between the radiated acoustic intensity and the active flexural intensity. It is also observed that the classical method of studying the vibration transmission, using vibration amplitude measurements, does not reflect the transmitted vibration energy but rather provides information on non-propagating, reactive energy. The FEM study, further explains some of the experimental observations and suggests the possibility of applying intensity to complex analytical models.     

Acoustic source localization in anisotropic plates

The conventional triangulation technique cannot locate the acoustic source in an anisotropic plate because this technique requires the wave speed to be independent of the propagation direction which is not the case for an anisotropic plate. All methods proposed so far for source localization in anisotropic plates require either the knowledge of the direction dependent velocity profile or a dense array of sensors. In this paper for the first time a technique is proposed to locate the acoustic source in large anisotropic plates with the help of only six sensors without knowing the direction dependent velocity profile in the plate. Experimental results show that the proposed technique works for both isotropic and anisotropic structures. For isotropic plates the required number of sensors can be reduced from 6 to 4.     

Velocity vector measurement based on correlation process between low coherence interference outputs

Velocity vector measurement by using fiber-optic low coherence interferometers is proposed and demonstrated. The interference outputs between the reference and backscattered light from the probing points in the flow are correlation processed. The probing points can be specified and are set on the x-, y-, and z-axis in the flow by using the fiber-optic low coherence interferometers. The direction (angles from each axis) and absolute value of the flow velocity can be measured from peak positions of correlations.     

Temperature gradient mechanism in laser forming of thin plates

To obtain further insight into the deformation of a plate in the laser forming process, the temperature gradient mechanism (TGM) is studied. Through the investigation, it can be found that, under the processing conditions of TGM, the plate not only bends about the x-axis but also about the y-axis. An analytical model estimate of the bending angle about the y-axis is constructed based on the theories of heat transfer and the mechanics of elastoplasticity. Numerical simulations are carried out to investigate the deformation of the plate about the y-axis by choosing the different process parameters. The analytically based estimate is used to suggest suitable starting values for the simulation process of calculated results. The study of the bending about the y-axis may describe more fully the deformation of a plate, which is helpful in high-precision forming.     

Beamforming array techniques for acoustic emission monitoring of large concrete structures

This paper introduces a novel method of acoustic emission (AE) analysis which is particularly suited for field applications on large plate-like reinforced concrete structures, such as walls and bridge decks. Similar to phased-array signal processing techniques developed for other non-destructive evaluation methods, this technique adapts beamforming tools developed for passive sonar and seismological applications for use in AE source localization and signal discrimination analyses. Instead of relying on the relatively weak P-wave, this method uses the energy-rich Rayleigh wave and requires only a small array of 4–8 sensors. Tests on an in-service reinforced concrete structure demonstrate that the azimuth of an artificial AE source can be determined via this method for sources located up to 3.8 m from the sensor array, even when the P-wave is undetectable. The beamforming array geometry also allows additional signal processing tools to be implemented, such as the VESPA process (VElocity SPectral Analysis), whereby the arrivals of different wave phases are identified by their apparent velocity of propagation. Beamforming AE can reduce sampling rate and time synchronization requirements between spatially distant sensors which in turn facilitates the use of wireless sensor networks for this application.     

Comparison of subwavelength focusing properties of diffraction and Fresnel zone plate plasmonic planar lenses

The subwavelength focusing properties of diffractive plasmonic planar lenses (DPLs) and Fresnel zone plate plasmonic planar lenses (FZPs) have been compared in this paper. To that end, we use the same lens material, incident wavelength, thickness and focal length for comparison. Both DPLs and FZPs consist of central circular slits surrounded by transparent and opaque zones and can get clear focusing performances. By using the rigorous electromagnetic numerical method, the fields in the focal region are analyzed in detail, and our results demonstrate that FZP can generate higher transmission efficiency, and higher peak field intensity at the focal plane. Focusing polarization properties of the lens illuminated by linearly polarized state, are calculated and analyzed also. The numerical results show that both the DPL and the FZP produce asymmetrical focal spot distributions with a low f-number. To the FZP, the full-width at half-maximum (FWHM) varies from 256 nm (along y-axis) to 516 nm(along x-axis) and to the DPL, the FWHM varies from 256 nm(along y-axis) to 580 nm(along x-axis), respectively. But for a high f-number, the asymmetrical performance of the focal spot will be reduced due to complicated electromagnetical field interferences and micro waveguide effect. Otherwise, the DPL can get a higher depolarization effect than the FZP does.     

Love wave propagation in functionally graded piezoelectric material layer

An exact approach is used to investigate Love waves in functionally graded piezoelectric material (FGPM) layer bonded to a semi-infinite homogeneous solid. The piezoelectric material is polarized in z-axis direction and the material properties change gradually with the thickness of the layer. We here assume that all material properties of the piezoelectric layer have the same exponential function distribution along the x-axis direction. The analytical solutions of dispersion relations are obtained for electrically open or short circuit conditions. The effects of the gradient variation of material constants on the phase velocity, the group velocity, and the coupled electromechanical factor are discussed in detail. The displacement, electric potential, and stress distributions along thickness of the graded layer are calculated and plotted. Numerical examples indicate that appropriate gradient distributing of the material properties make Love waves to propagate along the surface of the piezoelectric layer, or a bigger electromechanical coupling factor can be obtained, which is in favor of acquiring a better performance in surface acoustic wave (SAW) devices.     

A method for phase reconstruction in the optical three-dimensional shape measurement

In the optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid the phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing the numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

Near-field beamforming analysis for acoustic emission source localization

This paper attempts to introduce a near-field acoustic emission (AE) beamforming method to estimate the AE source locations by using a small array of sensors closely placed in a local region. The propagation characteristics of AE signals are investigated based on guided wave theory to discuss the feasibility of using beamforming techniques in AE signal processing. To validate the effectiveness of the AE beamforming method, a series of pencil lead break tests at various regions of a thin steel plate are conducted. The potential of this method for engineering applications are explored through rotor-stator rubbing tests. The experimental results demonstrate that the proposed method can effectively determine the region where rubbing occurs. It is expected that the work of this paper may provide a helpful analysis tool for near-field AE source localization.     

Propagation of astigmatic stochastic electromagnetic beams in oceanic turbulence

In this paper, we investigate the characteristics of astigmatic stochastic electromagnetic beams through oceanic turbulence. Taking the electromagnetic Gaussian Schell-model (GSM) beam as an example, the analytic expressions for the spectral density and the spectral degree of polarization of the beam propagating the oceanic turbulence are derived. It is indicated that the spectral density along the z-axis of the GSM beam in the oceanic turbulence is severely influenced by the source correlation properties, as well as by the sea-related parameters. We show that the characteristics of the spectral density along the x-axis, y-axis and z-axis of astigmatic electromagnetic GSM beams passing through the oceanic turbulence are qualitatively different. Furthermore, we find that as the astigmatic coefficient becomes larger, the maximum value of the spectral density along the z-axis increases rapidly and the width of the spectral density becomes shorter rapidly. Finally, the results have shown that different strengths of astigmatism have different effects on the spectral degree of polarization.     

复合材料板声发射源定位的时间差映射方法

针对复合材料板内可能出现的纤维断裂、基体开裂等缺陷以及声波在不同传播方向的传播速度不一致且波速差异较大等问题,提出一种改进的时间差映射方法实现对复合材料板的声发射源定位。该方法采用的是预构建数据库方法,不需考虑波在板中的传播速度不一致以及波的传播模态等问题,而且实验对传感器在板中的布置没有严格要求。首先,为了快速准确地选择和删除采集的大量声发射数据中存在的伪声发射事件,采用聚类算法自动识别和选择每个网格节点上高度相关性的声发射事件并构建时间差训练数据库;其次,为了提高网格分辨率,采用插值补偿算法增加网格密度;最后,针对测试区域验证实际声源的位置,使用加权差分算法实现声源的定位。理论分析和实验结果表明:声源位置的定位平均实际误差从26.5 mm(采用传统的时间差映射方法)降至18.0 mm(采用改进后的时间差映射方法),对应的平均相对误差从5.3%降至3.6%;并且整体运行时间从5 h减少到16.87 s。研究表明改进后的时间差映射方法可有效快速地提高声源的定位结果及精度。      

The effect of metastable states of the impurities on quantized acoustoelectric current

We report a detailed experimental study of the fluctuations of acoustoelectric (AE) current induced by surface acoustic waves in a shallow-etched quantum point contact defined in a GaAs/Al_xGa_1?xAs heterostructure at 1.7 K. We observe that current fluctuations between two AE current plateaus are more obvious than those at the plateaus. Switching the metastable states of the impurities is considered as the physical origin of the current fluctuations.     

A new type of acoustic modes of vibration of thin piezoelectric plates: Quasi-longitudinal normal modes

Using ST-cut quartz crystal plates as an example, a new type of normal modes of acoustic vibrations is described. The modes propagate along the x axis with a velocity close or equal to that of longitudinal bulk waves propagating in the same direction and have a longitudinal component of elastic displacement no less than two orders of magnitude greater than the two other components (the shear-horizontal and shear-vertical ones) throughout the whole plate thickness. The domain of existence of the quasi-longitudinal modes consists of a set of limited zones that contain the “allowed” values of the plate thickness H/λ (H is the plate thickness and λ is the wavelength) and are separated by “forbidden” zones corresponding to common Lamb modes. The closeness (or coincidence) of the velocities of a quasi-longitudinal mode in the plate and a longitudinal bulk wave in an unbounded crystal is a necessary but not sufficient condition for the existence of the aforementioned type of modes in ST,x quartz.     

Acoustic properties of ZrS3−xSex compounds

In the anisotropic ZrSe_3?xSe_x compounds, the velocity of acoustic waves propagating in a direction parallel to the fibers decreases linearly as the Selenium content is progressively increased for 0 < x < 2; in this region of composition two acoustic waves with different velocities are observed. For x > 2, following an increase of velocity, only one acoustic wave is likely to be propagated with a nearly constant velocity. This behavior is tentatively explained by a possible structural transformation taking place at x ～ 2.     

近场子空间聚焦的碰摩故障声发射定位方法

针对宽带多源声发射信号的相干、多模态和能量衰减快问题,提出一种近场多重相干信号子空间聚焦的定位算法用于碰摩故障声发射源的定位检测。首先,为滤除干扰模态波、减小频散效应,采用基于模态声发射传播特性分析的小波分解滤波方法,从碰摩初期的声发射信号中获取零阶模态波及波速用于定位计算;其次,为实现信号解相干,提出基于双边相关变换(TCT)的近场聚焦矩阵估计方法;最后,针对声发射信号的能量衰减快问题,利用近场基于特征分解的多重信号分类(N-MUSIC)的空间谱估计方法来实现声源的精确定位。理论分析和实验结果表明:该方法定位精度高、计算复杂度低、稳定性强,能有效识别多个相干碰摩声源。相比传统相干子空间算法(CSM),该方法减少了信号初值和聚焦频点的计算量,对双声源的分辨概率较现有修正近场多重信号分类算法提高了17%,是一种有效的碰摩故障源检测方法。      

Vibrations of heated plates with two opposite edges simply supported

Vibration analysis of the family of rectangular plates with two opposite sides simply supported can be simplified by assuming mode shapes. In the present paper a vibration analysis of such plates which are heated so as to have a temperature varying in the direction parallel to these sides is presented. A steady state temperature which satisfies the Laplace equation is considered. Due to the assumption of mode shapes the governing plate differential equation, which in general is a function of the x and y co-ordinates, becomes a function of one co-ordinate. This equation is analyzed by a finite difference method and solved by a standard simultaneous iteration technique. The accuracy of the method is ascertained by comparing the results for some well known boundary conditions when there is no temperature effect with the standard solutions available in the literature. From the results an attempt has been made to correlate the natural frequency with the temperature. Plates of uniform thickness with different length to breadth ratios have been analyzed. The assumed linear temperature distribution satisfies the Laplace equation and the plate is free to expand in its plane at its edges so that no thermal stresses will be induced.