Velocity measurement by vibro-acoustic Doppler

We describe the theoretical principles of a new Doppler method, which uses the acoustic response of a moving object to a highly localized dynamic radiation force of the ultrasound field to calculate the velocity of the moving object according to Doppler frequency shift. This method, named vibro-acoustic Doppler (VAD), employs two ultrasound beams separated by a slight frequency difference, Δf, transmitting in an X-focal configuration. Both ultrasound beams experience a frequency shift because of the moving objects and their interaction at the joint focal zone produces an acoustic frequency shift occurring around the low-frequency (Δf) acoustic emission signal. The acoustic emission field resulting from the vibration of the moving object is detected and used to calculate its velocity. We report the formula that describes the relation between Doppler frequency shift of the emitted acoustic field and the velocity of the moving object. To verify the theory, we used a string phantom. We also tested our method by measuring fluid velocity in a tube. The results show that the error calculated for both string and fluid velocities is less than 9.1%. Our theory shows that in the worst case, the error is 0.54% for a 25° angle variation for the VAD method compared with an error of -82.6% for a 25° angle variation for a conventional continuous wave Doppler method. An advantage of this method is that, unlike conventional Doppler, it is not sensitive to angles between the ultrasound beams and direction of motion.     

On the Feasibility of Shearographic Imaging of Acoustic Cross‐Modulation

Abstract: The detectability of defects as well as their detection contrast have significantly increased in recent years because of the use of nonlinear variants of the classical non‐destructive acoustic methods. The non‐uniformity of stiffness and hysteresis around the area of a defect results in strong non‐classical acoustic nonlinearity, which can be used to effectively distinguish the presence of defects. Motivated by the latest advances in nonlinear laser Doppler vibrometry and nonlinear ultrasonics, we investigated the potential of shearography to detect the so‐called cross‐modulation effect. This effect arises when a strong, low‐frequency pump wave dynamically changes the elastic response of a defect, so that the amplitude of a weak, high‐frequency probing wave passing through the defect is modulated. As a result, the frequency spectrum of the response contains mixed frequency components, which are directly attributed to the underlying defect.     

基于生成微分方程的行星齿轮箱故障振动信号解调分析

行星齿轮箱振动信号具有明显的调制特点,幅值解调和频率解调分析能够有效提取其中的故障信息。生成微分方程(GDE)方法可以估计调制信号的幅值包络和瞬时频率,实现解调分析,但该方法需要信号满足单分量要求。实际行星齿轮箱振动信号通常由复杂多分量成分组成,为实现信号的幅值解调和频率解调分析,应用经验模式分解(EMD)将信号分解为单分量本质模式函数,基于生成微分方程计算瞬时频率和幅值包络,根据瞬时频率的波动特点选择本质模式函数作为敏感分量,由敏感分量的包络谱和瞬时频率的Fourier频谱识别故障特征频率。通过行星齿轮箱故障模拟实验数据分析验证了解调分析方法的效果。     

Modeling ultrasound imaging as a linear, shift-variant system

Wo solve the equation that governs acoustic wave propagation in an inhomogeneous medium to show that the radio-frequency (RF) ultrasound signal can he expressed as the result of filtering the scatterer field with a point-spread function. We extend the analysis to make the link between the RF ultrasound signal and the representation of ultrasound scatterers as vectors with small magnitude and random phase in the complex plane. Others have previously performed parts of this analysis. The contribution of the present paper is to provide a single, coherent treatment emphasizing the assumptions that have to be made and the physical consequences of the models derived. This leads to insights into the interaction of monopole and dipole scattering, useful techniques for simulating and analyzing speckle statistics in the complex plane and a new expression for the normalized covariance of the analytic RF ultrasound signal in terms of the complex envelope of the point-spread function.     

Real and complex Doppler effects in lossy media

The theory of the Doppler effect in the presence of lossy media and moving scatterers is investigated. Essentially two kinds of phenomena emerge, which are not distinguishable in the conventional case of lossless media. When the scatterers move uniformly, or the equation of motion involves a slowly varying velocity, it is shown that propagation in lossy media involves complex Doppler effects. The complications introduced by the received complex frequency signal are discussed. It is shown that spectrum broadening occurs, and that, in certain cases, by using judiciously chosen temporal filters, the spectral degradation of the received signal can be counteracted. The second class of phenomena is associated with periodic and harmonic motion, when the scatterer is vibrating around a fixed location. In this case the incident wave is frequency modulated by the moving scatterer, giving rise to sidebands of real frequencies.     

基于双曲调频距离误差的目标跟踪修正算法

双曲调频信号的多普勒不变性可使运动目标匹配滤波输出的能量损失达到最小，在运动目标检测与参数估计中具有独特优势，已广泛应用于新型主动声呐。然而其多普勒不变性在提高检测能力的同时，会引入目标距离估计误差，从而影响主动声呐跟踪性能。文章在分析双曲调频信号距离估计误差的基础上，提出了目标跟踪算法的误差修正方法，通过将距离估计误差公式与传统观测方程及滤波算法进行融合，实现目标跟踪算法的误差补偿，显著提高了算法的跟踪性能，尤其是对快速运动目标的跟踪性能。     

基于能量重心法的列车轴承多普勒畸变故障声信号校正诊断研究

由麦克风采集的运动声源信号存在多普勒畸变现象,这极大的增加了对信号分析的难度,针对这一问题,本文提出了一种基于能量重心法的多普勒畸变校正方法,并将其应用在列车轴承故障诊断中。首先由基于能量重心法的瞬时频率（IF）估计（IFE）来获取IF向量,在莫尔斯声学理论的基础上,对IF向量进行非线性拟合,进而得到在时域进行重采样的时间间隔序列,再对原信号进行重采样处理,即可实现多普勒畸变的消除。最后本文做了一个仿真和列车轴承内外圈故障声信号的实验,分析的结果验证了此种方法的有效性。     

水下高速目标航行参数遥测技术研究

对于高速、强机动的水下目标来说,其航行参数信息的实时遥测具有重要意义。水声信号的多普勒频移估计与补偿是水声遥测的关键技术之一,它直接影响着水声遥测的效果与性能。针对双曲线调频信号及线性调频信号进行仿真分析,对比在相同情况下的多普勒频偏可补偿性,仿真实验证明双曲线调频信号具备较高的多普勒容限,其时延值估计精度可达到1μs。结合工程实际,采用双曲调频信号与单频信号组合的方式进行水声遥测,充分发挥双曲线调频信号的多普勒不变性和单频信号对多普勒频移的敏感性,在获得较高定位精度的同时,也具备高精度的水声遥测功能。该组合信标信号经过湖上试验验证,具有遥测精度高、误码率低、易于实现等优点,可直接应用于相关水声工程中。     

超声波测振信号的能量算子解调方法

连续超声波束遇到振动物体表面会产生多普勒效应,反射超声波信号是受振动信号调制的非线性调相信号。对反射波信号求导获得调幅调频信号,再采用能量算子对称差分法,求取该调幅调频信号的瞬时幅值及瞬时频率。鉴于超声波反射回波信号存在幅值衰减现象,而超声波频率不易受外界干扰,故通过调幅调频信号的瞬时频率提取被测物体的振动速度,并由振动速度求导得到振动加速度。同时,从幅值及频率两个方面探讨振动测量范围。仿真及实验结果表明:基于能量算子的超声波测振信号解调方法能有效地提取振动信号,与传统的相位解调方法相比,具有更大的测量范围。     

Real-time tracking of time-varying velocity using a self-mixing laser diode

A new method is proposed for estimating the time-varying velocity of a moving target with a low-cost laser sensor using optical feedback interferometry. A new algorithm is proposed to track velocity variations from real-time analysis of the output signal of a self-mixing laser diode. This signal is strongly corrupted by a multiplicative noise caused by the speckle effect, which occurs very often with noncooperative targets used in many industrial applications. The proposed signal processing method is based on a second order adaptive linear predictor filter, which enables us to track the digital instantaneous Doppler frequency, which is proportional to the velocity. A model of the laser diode output signal is proposed, and it is shown that the sensor and its associated algorithm have a global first-order lowpass transfer function with a cutoff frequency expressed as a function of the speckle perturbations, the signal to noise ratio and the mean Doppler frequency. Numerical as well as experimental results illustrate the properties of this sensor.     

Designing waveforms for temporal encoding using a frequency sampling method

In this paper a method for designing waveforms for temporal encoding in medical ultrasound imaging is described. The method is based on least squares optimization and is used to design nonlinear frequency modulated signals for synthetic transmit aperture imaging. By using the proposed design method, the amplitude spectrum of the transmitted waveform can be optimized, such that most of the energy is transmitted where the transducer has large amplification. To test the design method, a waveform was designed for a BK8804 linear array transducer. The resulting nonlinear frequency modulated waveform was compared to a linear frequency modulated signal with amplitude tapering, previously used in clinical studies for synthetic transmit aperture imaging. The latter had a relatively flat spectrum which implied that the waveform tried to excite all frequencies including ones with low amplification. The proposed waveform, on the other hand, was designed so that only frequencies where the transducer had a large amplification were excited. Hereby, unnecessary heating of the transducer could be avoided and the signal-to-noise ratio could be increased. The experimental ultrasound scanner RASMUS was used to evaluate the method experimentally. Due to the careful waveform design optimized for the transducer at hand, a theoretic gain in signal-to-noise ratio of 4.9 dB compared to the reference excitation was found, even though the energy of the nonlinear frequency modulated signal was 71% of the energy of the reference signal. This was supported by a signal-to-noise ratio measurement and comparison in penetration depth, where an increase of 1 cm was found in favor for the proposed waveform. Axial and lateral resolutions at full-width half-maximum were compared in a water phantom at depths of 42, 62, 82, and 102 mm. The axial resolutions of the nonlinear frequency modulated signal were 0.62, 0.69, 0.60, and 0.60 mm, respectively. The corresponding axial resolutions for the reference waveform were 0.58, 0.65, 0.62, and 0.60 mm, respectively. The compression properties of the matched filter (mismatched filter for the linear frequency modulated signal) were tested for both waveforms in simulation with respect to the Doppler frequency shift occurring when probing moving objects. It was concluded that the Doppler effect of moving targets does not significantly degrade the filtered output. Finally, in vivo measurements are shown for both methods, wherein the common carotid artery on a 27-year-old healthy male was scanned.     

Elastodynamic Doppler effects by a moving stress-free edge

Wave reflection by a uniformly moving stress-free edge is discussed for all three types of incident plane SH, P and SV-waves, and the Rayleigh surface wave on the moving edge is also discussed. Focusing on the Doppler effect and ray angles for the reflected wave, all frequency shifts and reflection angles are expressed in the closed form of simple algebraic equations. It is found that the Rayleigh surface wave on the moving stress-free edge has its complex velocity. This complex velocity means that the Rayleigh wave decays when the edge is expanding, but grows exponentially when the edge is shrinking. This is a completely new result.     

A fiber optic phase modulator with an optical frequency shift of up to 20 GHz

A fiber optic phase modulator is described in which the phase of a light wave traveling in an optical fiber is modulated by a composite electromechanical resonator with Q≌1000. The instantaneous frequency of the wave at the modulator output varies according to a harmonic law. The interval of tuning of the instantaneous light wave frequency achieved in the experiment is 20 GHz, which corresponds to a modulation index of ≌10⁶. It is demonstrated that a maximum value of the frequency tuning range is determined by the elastic limit of the resonator material.     

Analysis and extraction of stepped frequency radar signature for micro-motion structure

Radar signature produced by micro-motion structures contains movement and structure information which is useful for radar target recognition. For stepped frequency (SF) radar, the Doppler modulation is coupled with the stepped carrier frequency. It shifts and smears the high-resolution range profile and makes it difficult to analyse and extract the micro-motion information from the range profile directly. The authors propose to comprehend the SF radar as a special pulse Doppler radar, and the range profile as a Doppler profile for the convenience of motion analysis. The signature of moving targets for SF radar is analysed from this point of view and the equivalent instantaneous Doppler frequency (EIDF) is introduced. Then, a typical micro-motion, rotation, is taken as an example. The sinusoidal vibration of the peaks in the range profile sequence is explained in detail, especially the relationship between the sinusoid parameters and the rotation parameters. An approach to extract the rotation parameters from the range profile or EIDF spectrum sequence is proposed based on the Hough transform. Simulated and experimental results validate the theoretical analysis and the feature extraction method.     

Phase noise and phase modulation in optical coherence tomography

The signal in optical coherence tomography is often modulated either in phase or by use of the Doppler modulation generated by a depth-scanning mechanism. The effect of each type of modulation on the signal's amplitude is evaluated. The advantages of each type of modulation in terms of immunity to phase noise and penetration depth are discussed in relation to two envelope detection schemes, i.e., lock-in detection and rms-to-dc conversion. Phase noise due to drifts and demodulation instabilities causes distortion of the signal envelope and can be responsible in part for the speckle appearance of the image.     

Transient surface velocity measurements in a liquid by an active ultrasonic probe

A high sensitive ultrasonic method for measuring the surface velocity in a liquid is described. This method is based on the detection of the phase of a high frequency continuous ultrasonic wave (probe beam) reflected from the moving surface. The analysis shows that the main phenomenon is the interaction, through the acoustic nonlinearity parameter B/A of the fluid, between the reflected carrier wave and the low frequency pressure wave transmitted by the moving surface in the liquid. This interaction produces a phase-shift of the carrier proportional to the surface velocity and to the time delay undergone by the probe beam. Results of experiments carried out in water with a 30-MHz focused transducer probe are in good agreement with the analysis. Surface velocity smaller than 0.04 mm/s (i.e., mechanical displacements down to 3 pin) can be detected in a 5 MHz bandwidth. Lateral resolution of 0.5 mm has been achieved. Compared to optical techniques, this method has the advantages of compactness and of a low sensitivity to surface roughness.     

一种新的相位编码信号多普勒补偿算法研究

相位编码信号是一种多普勒频率敏感信号,而且码长越大,对多普勒频率越敏感,严重影响了雷达对高径向速度目标和远距离目标探测的能力。该文在分析伪码序列与多普勒容限关系的基础上,提出一种新的伪码调相准连续波雷达的多普勒补偿算法。该算法将回波信号取平方后送到动目标检测(MTD)滤波器中,通过提取回波信号中的多普勒频率信息,进行多普勒补偿。从仿真结果可以看出,该算法能够有效地降低多普勒频率对脉冲压缩结果的影响,验证了方法的可行性。     

宽带多普勒测速技术中跨周期模糊问题的研究

宽带声学多普勒流速剖面仪,利用伪随机编码调制发射脉冲信号以及复相关算法计算各水层反射回波的多普勒频移,进而达到测速的目的。复相关算法中,在排除模糊速度干扰的情况下,测速精度与脉冲信号的长度存在正比的关系。而脉冲宽度越长,所用来调制发射脉冲信号的编码阶数也越高,随之带来的便是速度模糊的问题。在复相关测频算法的基础上,针对长编码脉冲信号出现的周期性测频模糊情况,利用短编码脉冲信号的测频结果作为判别标准,选取恰当的周期性频偏作为计算结果,既提高了测速精度,又解决了精度提高所带来的周期性速度模糊问题,并且在实际应用中,提高了低信噪比条件下的测速精度。     

利用Radon-Wigner变换的空间目标测距算法

针对雷达对运动目标的测距问题,根据运动目标在宽带线性调频脉冲照射下的回波特点,提出了一种采用Radon-Wigner变换进行运动目标测距的方法。该方法首先研究了运动目标多散射点回波信号经Stretch处理的数学模型,然后针对处理后回波的叠加性和线性调频特点,利用Radon-Wigner变换的时频聚集特性,对其进行调频参数的估计,进而实现匀速运动目标的测距。仿真结果表明,该方法对运动目标的测距是有效的。     

The local mean decomposition and its application to EEG perception data

This paper describes the local mean decomposition (LMD), a new iterative approach to demodulating amplitude and frequency modulated signals. The new method decomposes such signals into a set of functions, each of which is the product of an envelope signal and a frequency modulated signal from which a time-varying instantaneous frequency can be derived. The LMD method can be used to analyse a wide variety of natural signals such as electrocardiograms, functional magnetic resonance imaging data, and earthquake data. The paper presents the results of applying LMD to a set of scalp electroencephalogram (EEG) visual perception data. The LMD instantaneous frequency and energy structure of the EEG is examined, and compared with results obtained using the spectrogram. The nature of visual perception is investigated by measuring the degree of EEG instantaneous phase concentration that occurs following stimulus onset over multiple trials. The analysis suggests that there is a statistically significant difference between the theta phase concentrations of the perception and no perception EEG data.