Modal identification based on continuous wavelet transform and ambient excitation tests

This paper deals with the use of the continuous wavelet transform for modal identification from ambient vibration tests. The wavelet analysis of the free responses of a linear mechanical system has been used to estimate its natural frequencies, viscous damping ratios, and mode shapes, using either the modulus or the phase of the wavelet transform with “ridge” and “skeleton” notions. This technique is extended in this paper, to the response from ambient excitation tests based on the equivalent formulation between the free response and the correlation function of a linear mechanical system under stationary stochastic excitation. The main novelties involve the new formulation of continuous wavelet transform and the use of the singular value decomposition algorithm for ridges and skeleton detection under the noisy conditions of ambient vibration tests. A complete procedure for modal identification of ambient response, including these new formulations, is presented and then applied to numerical examples and experimental test to illustrate its validity.     

Accurate identification of the frequency response functions for the rotor-bearing-foundation system using the modified pseudo mode shape method

In this paper, an identification technique in the dynamic analyses of rotor-bearing-foundation systems called the pseudo mode shape method (PMSM) was improved in order to enhance the accuracy of the identified dynamic characteristic matrices of its foundation models. Two procedures, namely, phase modification and numerical optimisation, were proposed in the algorithm of PMSM to effectively improve its accuracy. Generally, it is always necessary to build the whole foundation model in studying the dynamics of a rotor system through the finite element analysis method. This is either unfeasible or impractical when the foundation is too complicated. Instead, the PMSM uses the frequency response function (FRF) data of joint positions between the rotor and the foundation to establish the equivalent mass, damping, and stiffness matrices of the foundation without having to build the physical model. However, the accuracy of the obtained system's FRF is still unsatisfactory, especially at those higher modes. In order to demonstrate the effectiveness of the presented methods, a solid foundation was solved for its FRF by using both the original and modified PMSM, as well as the finite element (ANSYS) model for comparisons. The results showed that the accuracy of the obtained FRF was improved remarkably with the modified PMSM based on the results of the ANSYS. In addition, an induction motor resembling a rotor-bearing-foundation system, with its housing treated as the foundation, was taken as an example to verify the algorithm experimentally. The FRF curves at the bearing supports of the rotor (armature) were obtained through modal testing to estimate the above-mentioned equivalent matrices of the housing. The FRF of the housing, which was calculated from the equivalent matrices with the modified PMSM, showed satisfactory consistency with that from the modal testing.     

Critical earthquake load inputs for multi-degree-of-freedom inelastic structures

The problem of modeling earthquake ground motions as design inputs for multi-degree-of-freedom inelastic structures is studied. The earthquake acceleration is expressed as a Fourier series modulated by an envelope function. The coefficients of the series representation are calculated such that the structure inelastic deformation is maximized subjected to predefined constraints. These constraints are taken to reflect known characteristics of recorded earthquakes such as upper bounds on the energy and peak values of the ground acceleration, velocity and displacement and upper and lower limits on the Fourier spectra of the ground acceleration. The material stress-strain behavior is modeled using bilinear and elastic-plastic relations. The resulting nonlinear optimization problem is solved by using the sequential quadratic optimization method. Issues related to various forms of energy dissipated by the inelastic structure are explored. The study also examines the effect of nonlinear damping models and the influence of the strain hardening ratio (ratio of the post-yield stiffness to the pre-yield stiffness) on the derived optimal earthquake and associated inelastic deformation. The formulation is demonstrated for a two-storey inelastic building frame with nonlinear damping.     

DSWT-FTIR-RBFNN鉴别罂粟和虞美人

采用水平衰减全反射傅里叶红外光谱法(HATR-FTIR)测定罂粟和虞美人的FTIR,由于两者为同科同属中药材,所含化学成分较为相近,为了更好地突出罂粟和虞美人在FTIR上的差异,并据此进行正确分类识别,利用离散平稳小波变换(DSWT)分别对罂粟和虞美人的种皮和种仁的FTIR进行若干尺度的变换,从中选择2个最具代表性的尺度作为特征提取的尺度空间.根据罂粟和虞美人的FTIR分布情况,确定将DSWT域内2个尺度的FTIR分别划分为2个特征区域并以每个区域内的光谱能量作为特征参数.从而构造一个包含8个特征参数的特征向量,将这个特征向量输入到径向基函数神经网络(RBFNN)进行训练,从而达到正确识别罂粟和虞美人的目的.实验中共取罂粟和虞美人的FTIR数据128对,其中训练样本78对,测试样本50对.实验结果表明利用文章的方法对罂粟和虞美人的正确识别率分别为99.8%和99.9%,从而验证了方法的有效性.     

Estimation of structural system parameters from stationary and non-stationary ambient vibrations: An exploratory-confirmatory analysis

The natural frequency and damping parameters of a building structure are estimated from a long ambient vibration record that shows considerable non-stationarity. The long record is segmented into 57 approximately independent one minute duration stationary time series segments. Each segment is low pass filtered to reject unwanted higher frequency modes and is analyzed by a 2SLS (two stage least squares) time domain parametric model procedure. The scatter diagrams of the estimates of the natural frequency and damping parameters exhibit considerable variability. Estimates of the natural frequency and damping parameters and coefficient of variation expressions of their reliability are obtained by an exploratory-confirmatory data analysis of those 57 vibration time series. A procedure that can obtain the structural parameter estimates with the reliability that is available from stationary analysis from a long and not necessarily stationary record is indicated.     

Estimation of damping from response spectra

In this paper procedures for estimating damping ratio from response spectra are examined. The study is restricted to an evaluation of bias and random errors introduced by signal processing requirements. A second order system is used in the study, and a Gaussian white noise input is assumed. It is shown that, due to bias errors in estimating the response spectra, calculations of damping ratio by the peak response and half-power bandwidth methods give overestimates. The bias errors of the damping ratio estimates are a function of the true damping of the system and the ratio of analysis bandwidth to resonant frequency. The bias error for the half-power bandwidth method is three times that for the peak response method. It is also shown for large ranges of damping ratio and bandwidth ratio that zero bias response occurs at a point where the response is approximately 80% of the peak response. Numerical results obtained by simulation studies are used to verify the expressions for normalized bias error. Expressions for random error associated with damping ratio estimates are also developed. Random error can be minimized by maintaining a high coherence between the system input and response.     

基于图像二维小波多尺度分解傅里叶变换轮廓术

应用傅里叶变换轮廓术测量物体三维面形时,当被测物体形状复杂或是被噪声严重污染时,导致频谱分布展宽,发生频谱混叠现象,基频提取困难,无法准确恢复物体的三维面型.提出了基于小波分解的傅里叶变换轮廓术,采用小波变换的方法对变形条纹图进行二维多尺度分解,重构被测物的背景图像,滤出图像的零频成分,得到相对变形条纹.运用小波变换与傅里叶变换轮廓术相结合的方法,只需拍摄一幅变形条纹图,将被测物体与背景分离,不受背景成分的影响,且易于基频信息的提取,降低了对滤波器的要求.实验证明该方法较好地防止了频谱的混叠问题,提高了测量范围与解相精度.     

Damping characteristics of a spray-deposited shape memory alloy beam

The damping characteristics of an Ni–Ti shape memory alloy (SMA) beam are theoretically and experimentally studied with interest in identifying an appropriate damping model for the material. The SMA beam is manufactured by a spray deposition method followed by heat treatment and found to have nanocrystalline structure in which damping capacity is high. The beam is then tested to obtain an impulse response and the frequency response function (FRF). By using the Hilbert transform technique it is shown that damping of the beam is almost amplitude independent in the tested range of displacement. It is also shown from the FRF that the damping of the spray-deposited shape memory alloy beam is well represented by a model including both linear viscous and hysteretic dampings.     

Intensity analysis methods for transient signals

Conventionally, the Fourier transform is applied for sound intensity analysis of stationary signals, but this method can be applied for analyzing non-stationary transient signals. Instead of the Fourier transform analysis, instantaneous spectrum analysis methods such as the Wigner-Ville distribution and the wavelet transform are proposed. By using the mathematical example as a transient signal, advantages and disadvantages of these methods including the short-time Fourier transform are compared. From calculation results, it is considered that the STFT method is the most suitable for the accurate measurement of sound intensity levels, but the WT method is also recommended from its higher resolution of transient signals.     

利用声信号对滚动轴承进行故障诊断的研究

旋转机械在运行过程中产生的声信号包含了滚动轴承的运行状态信息,且可采用非接触式测量,本文应用它对滚动轴承进行故障诊断。基于morlet小波变换的包络分析对采集的声信号进行降噪及包络处理,然后变换到频域,提取出特征频率并经过转换后作为线性神经网路的输入向量,辨识滚动轴承的状态。实验表明,本方法对滚动轴承故障诊断是有效的。     

Improved grid-noise removal in single-frame digital moiré 3D shape measurement

A single-frame grid-noise removal technique was developed for application in single-frame digital-moiré 3D shape measurement. The ability of the stationary wavelet transform (SWT) to prevent oscillation artifacts near discontinuities, and the ability of the Fourier transform (FFT) applied to wavelet coefficients to separate grid-noise from useful image information, were combined in a new technique, SWT-FFT, to remove grid-noise from moiré-pattern images generated by digital moiré. In comparison to previous grid-noise removal techniques in moiré, SWT-FFT avoids the requirement for mechanical translation of optical components and capture of multiple frames, to enable single-frame moiré-based measurement. Experiments using FFT, Discrete Wavelet Transform (DWT), DWT-FFT, and SWT-FFT were performed on moiré-pattern images containing grid noise, generated by digital moiré, for several test objects. SWT-FFT had the best performance in removing high-frequency grid-noise, both straight and curved lines, minimizing artifacts, and preserving the moiré pattern without blurring and degradation. SWT-FFT also had the lowest noise amplitude in the reconstructed height and lowest roughness index for all test objects, indicating best grid-noise removal in comparison to the other techniques.     

A non-linear fluid force model for vortex-induced vibration of an elastic cylinder

Even under the assumption of a sinusoidal lift and drag force at a single frequency for a stationary cylinder in a cross flow, higher harmonics that represent non-linearity in the fluid-structure interaction process are present. This fact is considered in the formulation of a non-linear fluid force model for a freely vibrating cylinder in a cross flow. The force model is developed based on an iterative process and the modal analysis approach. The fluid force components in the model can be evaluated from measured vibration data with the help of the auto-regressive moving averaging (ARMA) technique. An example is used to illustrate that non-linear (higher order) force components are present at resonance, even for a case with relatively weak fluid-structure interaction. Further analysis reveals that the fluid force components are dependent on structural damping and mass ratio. The non-linear fluid force model is further modified by taking these considerations into account and is used to predict the dynamic characteristics of a freely vibrating cylinder over a range of Reynolds numbers, mass and structural damping ratios. On comparison with measurements obtained from four different experiments and predictions made by previous single-degree-of-freedom model, good agreement is found over a wide range of these parameters.     

Adaptive bistable stochastic resonance and its application in mechanical fault feature extraction

Stochastic resonance (SR) is an important approach to detect weak vibration signals from heavy background noise. In order to increase the calculation speed and improve the weak feature detection performance, a new bistable model has been built. With this model, an adaptive and fast SR method based on dyadic wavelet transform and least square system parameters solving is proposed in this paper. By adding the second-order differential item into the traditional bistable model, noise utilization can be increased and the quality of SR output signal can be improved. The iteration algorithm for implementing the adaptive SR is given. Compared with the traditional adaptive SR method, this algorithm does not need to set up the searching range and searching step size of the system parameters, but only requires a few iterations. The proposed method, discrete wavelet transform and the traditional adaptive SR method are applied to analyzing simulated vibration signals and extracting the fault feature of a rotor system. The contrastive results verify the superiority of the proposed method, and it can be effectively applied to weak mechanical fault feature extraction.     

Simulation of random envelope processes

Efficient and practical methods of simulating stationary and nonstationary random envelope processes are presented. The stationary envelope processes are simulated by using the fast Fourier transform while the nonstationary envelope processes are simulated as the square root of the sum of a series of cosine functions and a series of sine functions with random phase angles. Typical applications of the envelope simulation are the simulations of peaks and troughs which play an important role in the analyses of the first excursion probability, fatigue and crack propagation. In particular, applications to the crack propagation under random loadings are demonstrated in detail.     

Continuous wavelet transform and exactly solvable model of nonstationary signals

An analytic expression for a continuous wavelet transform (CWT) is obtained for a nonstationary signal with spectral properties varying with time. As a model of the nonstationary signal, a superposition of elementary nonstationary signals is considered, each of which is the product of the Gaussian-shape envelope and an oscillating function. To obtain the CWT, the mother Morlet wavelet is used. The result is compared with the window Fourier transform (Gabor transform).The advantages of the CWT are illustrated by concrete examples. The applications of the exactly solvable model of nonstationary signals for simulating transient processes in physics are considered.     

瞬态位移干涉仪信号处理新方法

利用短时傅里叶变换计算速度快的特点,先对瞬态位移干涉仪信号进行预处理,得到速度的轮廓范围.据此估计小波变换中尺度因子的范围,然后用连续小波变换的方法对信号再次进行处理,用此方法分析计算机模拟出的位移干涉信号,恢复的速度相对误差小于2%.对高速爆轰实验中的位移干涉信号分别采用短时傅立叶变换、小波变换和二者相结合的方式进行分析,并记录三者的计算速度.实验表明,第三种方法能准确地恢复出物体的速度历史,计算误差在系统要求的范围内.本文综合计算速度和计算误差两方面的考虑,选择了适合于瞬态位移干涉信号处理的方法.     

基于多尺度总体最小二乘的图像去噪

提出了一种基于多尺度总体最小二乘的图像去噪算法.采用平稳小波变换对噪音图像进行分解,分别对各个分解层的高频子带,通过总体最小二乘算法估计信号小波系数|并且考虑到不同尺度小波系数之间的相关性,将尺度相关性约束到总体最小二乘算法中,进而准确估计各高频子带信号小波系数,再由估计的信号小波系数通过小波逆变换得到去噪图像.实验结果表明,考虑尺度间相关性的总体最小二乘平稳小波变换图像去噪算法能有效去除图像噪音,在信噪比和视觉质量上有了较大改善.     

Two-dimensional multiscale windowed Fourier transform based on two-dimensional wavelet transform for fringe pattern demodulation

A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown.     

小波变换在载频条纹相位分析法中的应用研究

为了克服在非平稳信号分析中傅里叶变换的全局性缺陷,以及窗口傅里叶分析的单一分辨率和伸缩窗口傅里叶分析的尺度不确定性问题,采用伽博解析小波变换技术对空间载频光栅条纹进行相位分析,有效地提取出相对于载频条纹基频的完整相位信息,从本质上解决了上述问题。以三维轮廓术为例,与傅里叶分析进行了对比研究,给出了小波分析应用在空间载频条纹相位分析中详细而完整的理论推导证明、计算机模拟以及实验验证结果。