基于变分模式分解和微积分增强能量算子的滚动轴承故障诊断

针对滚动轴承故障振动信号的特点,考虑变分模式分解在复杂信号分解及微积分增强能量算子在瞬态成分检测方面的优势,提出基于变分模式分解和微积分增强能量算子的滚动轴承故障诊断方法.首先利用变分模式分解将复杂信号分解为多个本质模式函数,以削弱背景噪声的影响和满足能量算子对信号单分量的要求;然后根据提出的敏感分量选取原则,从本质模式函数中选出包含主要故障信息的本质模式函数为敏感分量;最后利用微积分增强能量算子强化敏感分量中的瞬态冲击,并根据敏感分量瞬时能量的时域波形及Fourier频谱诊断滚动轴承故障.分析结果表明该方法能够有效诊断滚动轴承故障.      

Nonlinear Signal Analysis: Time-Frequency Perspectives

Recently, there has been growing utilization of time-frequency transformations for the analysis and interpretation of nonlinear and nonstationary signals in a broad spectrum of science and engineering applications. The continuous wavelet transform and empirical mode decomposition in tandem with Hilbert transform have been commonly utilized in such applications, with varying success. This study evaluates the performance of the two approaches in the analysis of a variety of classical nonlinear signals, underscoring a fundamental difference between the two approaches: the instantaneous frequency derived from the Hilbert transform characterizes subcyclic and supercyclic nonlinearities simultaneously, while wavelet-based instantaneous frequency captures supercyclic nonlinearities with a complementary measure of instantaneous bandwidth characterizing subcyclic nonlinearities. This study demonstrates that not only is the spectral content of the wavelet instantaneous bandwidth measure consistent with that of the Hilbert instantaneous frequency, but in the case of the R?ssler system, produces identical oscillatory signature.     

基于EEMD的轧辊偏心补偿控制

针对傅里叶变换、小波算法等传统信号处理方法在非线性信号的提取与重构中存在的缺陷,提出了基于聚合经验模态分解的轧辊偏心信号提取新方法。另外,针对传统自动厚度控制系统(AGC)在偏心补偿控制中的不足,设计了有偏心补偿环节的 AGC系统。新方法将轧制力信号分解为多个不同特征模态函数,从中提取表征偏心信号的特征模态函数,并用此重构偏心信号,最后将新方法重构的偏心信号投入到此系统中控制轧件厚度。仿真及实验结果表明,利用聚合经验模态分解方法重构得到的轧辊偏心模型可以很大程度减小厚度波动,补偿效果优于小波算法。     

Performance of Wavelet Transform and Empirical Mode Decomposition in Extracting Signals Embedded in Noise

Time-frequency transformations have gained increasing attention for the characterization of nonstationary signals in a broad spectrum of science and engineering applications. This study evaluates the performance of two popular transformations, the continuous wavelet transform and empirical mode decomposition with Hilbert transform (EMD+HT), in estimating instantaneous frequency (IF) in the presence of noise. The findings demonstrate that under these conditions wavelets seeking harmonic similitude at various scales produce lower variance IF estimates than EMD+HT. The shortcomings of the latter approach are attributed to its empirical, envelope-dependent nature, leading to bases that are themselves derived from noise.     

Use of intrinsic modes in biology: examples of indicial response of pulmonary blood pressure to +/- step hypoxia

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero "local mean," and a final nonoscillatory mode. With this device, we obtain a set of "mean trends," each of which represents a "mean" in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of "indicial response function" is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.     

Visual system-response functions and estimating reflectance

The almost-illuminant-independent achromatic variable zeta [J. Opt. Soc. Am A 11, 1003 (1994)] is supplemented by two achromatic variables, both almost illuminant-independent. The results are numerically verified and obtained by means of so-called (human) visual system-response functions, defined as those linear combinations of the color-matching functions that constitute the best possible approximations to delta functions. It is argued that they and not the cone sensitivities are basic to understanding the visual system as a color-constant signal detection system. The three variables solve the color-constancy problem and define a chromatic adaptation transform for blackbody radiators of temperature T. The generalization of the results to arbitrary well-behaved illuminants is discussed.     

Critical Analysis of Different Hilbert-Huang Algorithms for Pavement Profile Evaluation

Pavement profile analysis is a major component in pavement infrastructure management decision making for maintenance and rehabilitation. This paper takes an in-depth look at pavement profile characterization and evaluation, taking into account the inherent nature of road profile data, i.e., nonstationary and non-Gaussian. Although there have been several studies aimed at the analysis and characterization of pavement profile, the bulk have been limited to applying relatively conventional signal processing techniques, such as the Fourier analysis. Using this approach, only the average condition of the local conditions can be represented. Most transient and changing signals will not be handled well due to the averaging effect of the technique. The Hilbert-Huang transform operates at the scale of every oscillation, an extremely important property for obtaining localized profile information. In this paper, the different algorithms of the Hilbert-Huang transform: empirical mode decomposition (EMD), ensemble EMD, and complex EMD (CEMD) have been discussed and implemented to extract useful information from road profile data. The robustness of the algorithms is compared based on its ability to produce physically meaningful intrinsic mode functions (IMFs) which truly characterize the underlying process. The results show that although all the methodologies yielded similar residual trends, the CEMD produced physically meaningful and trusted IMFs whose information at the various levels of decomposition could be used to extract profile information such as the extent of deterioration and localized roughness information.     

Hilbert-Huang Transform Analysis of Dynamic and Earthquake Motion Recordings

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.     

Control of epilepsy associated with cerebral arteriovenous malformations after radiosurgery

The autocorrelation function pertaining to spatial distributions of ultrasonic scatterers in soft tissue is believed to contain useful information related to tissue morphology. A simple processing method applied to radio-frequency echo signals estimates this function for a sample having isotropic scattering conditions. It utilizes backscattered echo signals from the sample and echo signals from a reference object having defined scattering properties. The ratio of the echo signal power spectrum from the sample to the echo signal power spectrum from the reference object is obtained, and corrected for attenuation differences between the two media. This yields a "form factor" for the sample, whose inverse Fourier transform is the autocorrelation function. The method was tested using tissue-mimicking samples for which spatial autocorrelation functions could be modeled from the dimensions of embedded scatterers. The shapes of the measured autocorrelation functions were in reasonable agreement with those estimated, although measured functions overestimated the function at small lag distances. Scatterer diameters estimated from the zeros of the autocorrelation function agreed to within 6% of expected values when the measurement system bandwidth satisfied minimal criteria.     

Efficacy of Hilbert and Wavelet Transforms for Time-Frequency Analysis

Two independently emerging time-frequency transformations in Civil Engineering, namely, the wavelet transform and empirical mode decomposition with Hilbert transform (EMD+HT), are discussed in this study. Their application to a variety of nonstationary and nonlinear signals has achieved mixed results, with some comparative studies casting significant doubt on the wavelet’s suitability for such analyses. Therefore, this study shall revisit a number of applications of EMD+HT in the published literature, offering a different perspective to these commentaries and highlighting situations where the two approaches perform comparably and others where one offers an advantage. As this study demonstrates, much of the differing performance previously observed is attributable to EMD+HT representing nonlinear characteristics solely through the instantaneous frequency, with the wavelet relying on both this measure and the instantaneous bandwidth. Further, the resolutions utilized by the two approaches present a secondary factor influencing performance.     

Evolutionary Spectra Estimation Using Wavelets

A wavelets-based method is developed to estimate the evolutionary power spectral density (EPSD) of nonstationary stochastic processes. The method relies on the property that the continuous wavelet transform of a nonstationary process can be treated as a stochastic process with EPSD given in terms of the EPSD of the process in a closed form. This yields an equation in the frequency domain relating the instantaneous mean-square value of the wavelet transform to the EPSD of the process. A number of these equations are considered, each related to a certain scale of the wavelet transform, in conjunction with representing the target EPSD as a sum of time-independent shape functions modulated by time-dependent coefficients; the squared moduli of the Fourier transforms of the wavelets associated with the selected scales are taken as shape functions. This leads to a linear system of equations which is solved to determine the unknown time-dependent coefficients; the same system matrix applies for all time instances. Numerical examples demonstrate the accuracy and computational efficiency of the proposed method.     

提高轧辊偏心信号频谱分析精度的方法

针对目前冷轧生产中因轧辊偏心引起带材厚度波动的问题，提出了一种提高轧辊偏心信号频谱分析精度的方法。该方法综合应用伪点剔除技术、抗混滤波技术和平滑趋势技术对原始轧辊偏心信号进行预处理，再使用改进的快速傅立叶变换算法对预处理后的信号进行分析，其频谱分辨率明显提高。现场测试表明，经该方法分析ABB压头采集到的轧辊偏心信号，其频谱分辨精度明显高于以往用快速傅立叶变换算法的分辨精度，从而可以快速准确地诊断轧辊偏心所造成的影响。     

冲击信号的频谱分析

通过对轧机的冲击信号特征频率进行分析,比较了几种常用频谱(或时频)分析方法(傅立叶变换、短时傅立叶及小波分析)在此类分析中的适用性及各自的特点,得出短时傅立叶在轧机冲击信号特征频率估计中占有一定的优势。     

迭代广义短时Fourier变换在行星齿轮箱故障诊断中的应用

短时Fourier变换(STFT)在分析非平稳信号的过程中,受调制系数的影响,时频分布图中的能量扩散至主导频率的周围,降低了时频分布的可读性.运用STFT分析瞬时频率缓变或恒定的信号时,调制系数的影响较小甚至可以忽略不计,而得到能量聚集程度很高的时频分布.根据这一特点,提出了迭代广义短时Fourier变换(IG-STFT),该方法有效改善了时频图的可读性.首先运用迭代广义解调分离出频率恒定的单分量成分,然后运用STFT分析信号的时频分布,最后依据STFT的分析结果和相位函数得到原信号的时频分布.通过行星齿轮箱仿真信号和实验信号分析,验证了该方法在分析非平稳信号中的有效性,准确诊断了齿轮故障.      

Estimation of Laboratory Wave Reflection by a Transfer Function Method

A theory of transfer function method for separating two-dimensional wave data obtained in laboratory experiments into incident and reflected waves is presented in this paper. Based on the linear wave assumption, specific transfer functions are derived from mathematical manipulations of the composite wave field, and the corresponding impulse response functions are obtained by implementing the inverse Fourier transform of transfer functions. These response functions are used to perform convolution integrals with time series data measured by fixed wave gauges at different locations in a wave flume and then to separate the incident and reflected waves. Compared with other available methods, the phase difference between two wave signals is considered in the transfer functions. Thus, the separation of waves does not involve the phase calculation and the corresponding error is avoided. The validity of the present method is examined through numerical examples and laboratory experiments of physical models carried out in a wave flume. A comparison of results from physical experiments shows that the present method gives much better estimates of incident and reflected waves than other methods available in the literature.     

Antiplane (SH) Waves Diffraction by a Semicircular Cylindrical Hill Revisited: An Improved Analytic Wave Series Solution

An improved accurate closed-form wave function analytic solution of two-dimensional scattering and diffraction of antiplane SH waves by a semicircular cylindrical hill on an elastic half space is presented. In the previous solution, stress and displacement residual auxiliary functions were defined at the circular interface above and below the circular hill. The method of weighted residues (moment method) was used to solve for the unknown scattered and transmitted waves by requiring each term of Fourier series expansion of these auxiliary residual functions to vanish. It was found that the stress residual amplitudes on both (left and right) rims of the hill (ideally should be zero) are not numerically insignificant, irrespective of how many terms used. It was pointed out that the shear stress at the rim is infinite, and that the stress auxiliary function is discontinuous at both rims of the hill, exhibiting a problem for the numerical solution that is more complicated than Gibbs’ phenomenon. The problem with the overshoot of the stress residual amplitudes at the rim was most likely numerical. In this paper, all displacement and stress waves were expressed as cosine functions, and the solution of the circular hill problem was reformulated in this paper, and, for the solution to be correct, the computed stress and displacement residual amplitudes were shown to be numerically negligible everywhere, including those at both rims of the hill. Displacements at higher frequencies are also computed.     

Dynamical models for psychological assessment: Phase space functions.

This article examines the implications of phase space functions for psychological assessment. Behavior problems, causal variables, and causal relationships are dynamic and demonstrate complex nonlinear and discontinuous relationships. Measuring the temporal, dynamic, and nonlinear dimensions of variables can enhance the accuracy of predictions of the future time course of variables and of the strength of causal relationships for behavior problems. Cross-sectional, longitudinal, and time series research designs are prone to inferential errors because they often fail to consider the dynamic time course functions of variables. The value of a variable (its state) coupled with the current direction and rate of change of the variable (its phase), at a single measurement point, is its phase state. Equal state values across persons on a variable dimension does not mean that those persons are in equal phases on that variable dimension. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Simulation of Nonstationary Stochastic Processes by Spectral Representation

This paper presents a rigorous derivation of a previously known formula for simulation of one-dimensional, univariate, nonstationary stochastic processes integrating Priestly’s evolutionary spectral representation theory. Applying this formula, sample functions can be generated with great computational efficiency. The simulated stochastic process is asymptotically Gaussian as the number of terms tends to infinity. This paper shows that (1) these sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number of terms in the cosine series is large, i.e., the ensemble averaged evolutionary power spectral density function (PSDF) or autocorrelation function approaches the corresponding target function as the sample size increases, and (2) the simulation formula, under certain conditions, can be reduced to that for nonstationary white noise process or Shinozuka’s spectral representation of stationary process. In addition to derivation of simulation formula, three methods are developed in this paper to estimate the evolutionary PSDF of a given time-history data by means of the short-time Fourier transform (STFT), the wavelet transform (WT), and the Hilbert-Huang transform (HHT). A comparison of the PSDF of the well-known El Centro earthquake record estimated by these methods shows that the STFT and the WT give similar results, whereas the HHT gives more concentrated energy at certain frequencies. Effectiveness of the proposed simulation formula for nonstationary sample functions is demonstrated by simulating time histories from the estimated evolutionary PSDFs. Mean acceleration spectrum obtained by averaging the spectra of generated time histories are then presented and compared with the target spectrum to demonstrate the usefulness of this method.