Atangana-Baleanu分数阶双稳系统的随机共振现象

针对基于常用分数阶微积分对随机共振现象的研究存在奇异性的问题,提出了基于Atangana-Baleanu分数阶微积分的双稳系统随机共振现象的研究方法。首先,根据Atangana-Baleanu分数阶微积分的定义构造了用于描述随机共振系统的Langevin方程;其次,通过改进的Oustaloup算法对其近似化求解;最后,编写仿真程序,利用控制单一变量法研究参数变化对随机共振的影响。仿真结果表明:噪声强度一定时改变分数阶求导阶次,分数阶求导阶次与输出信号的功率谱值呈非线性关系且存在一个最佳分数阶求导阶次使系统产生随机共振;分数阶求导阶次一定时改变噪声强度,噪声强度与输出信号的功率谱值呈非线性关系且存在一个最佳噪声强度使系统产生随机共振。     

基于包络解调随机共振和CEEMD的机械早期微弱故障诊断方法研究

针对噪声背景下机械振动信号早期故障特征提取难题,提出一种基于包络解调随机共振和互补总体经验模态分解的机械早期微弱故障提取及诊断新方法。首先对含噪声机械故障信号进行包络解调处理,然后对包络信号进行变尺度随机共振输出,使故障特征信号得到增强,最后对处理后的信号进行互补总体经验模态分解(CEEMD),得到机械振动信号故障特征分量,实现故障特征提取及诊断。对机械故障诊断实例表明,该方法不仅能增强信号幅值,同时减少了虚假分量,提高了CEEMD算法的精度,有效提取出被噪声淹没的微弱故障信号,提高了机械早期故障诊断效果。     

Phase synchronization of switchings in stochastic and chaotic bistable systems

We study synchronization of switching processes in stochastic and chaotic bistable systems driven by a periodic signal in terms of phase synchronization. By introduction of instantaneous phases of transitions between metastable states and of the periodic forcing we show explicitly the effect of phase locking. The dynamics of phase difference appears to be qualitatively equivalent to that of a synchronized classical self-sustained oscillator. We have found that the degree of phase coherence between the input signal and the response estimated employing the effective diffusion constant is maximal at an optimal noise level in a stochastic bistable system or at an optimal value of a control parameter in a purely deterministic case. We also consider the effect of mutual synchronization of the switching processes in coupled stochastic and chaotic bistable systems.     

基于VMD和变尺度多稳随机共振的微弱故障信号特征提取方法

针对强噪声背景下旋转机械早期故障诊断的难题,提出一种基于变分模态分解与变尺度多稳随机共振的微弱故障信号特征提取方法。首先应用参数优化的变分模态分解(variational mode decomposition, VMD)算法对微弱故障信号进行分解, 得到若干本征模态分量(intrinsic mode function, IMF);然后通过峭度准则筛选出其中峭度最大的IMF分量;最后对该IMF分量进行变尺度多稳随机共振, 实现微弱故障信号的增强。实例表明:在强噪声背景下,利用参数优化VMD分解与变尺度多稳随机共振相结合的方法,可以有效提取出微弱信号特征频率,实现旋转机械故障状态的准确判断。     

双稳系统随机共振效应的数值分析

以绝热近似随机共振理论为基础,分析了双稳系统随机共振模型,研究系统参数、噪声强度、信号幅值和频率变化对双稳系统随机共振效应的影响。通过分析得出,输入信号和系统参数一定时,系统发生随机共振所需要的噪声存在一个最佳强度;信号幅值的增大有利于随机共振效应的产生;信号频率的增大将使输出功率谱信号频率处谱峰逐渐离开噪声能量集中的低频区,且谱峰幅度逐渐减小,随机共振效应逐渐弱化消失。针对信号幅值、频率、噪声强度超出绝热近似理论的小参数要求而成为大参数,对变尺度方法实现大参数信号的随机共振进行分析和评述。     

基于EEMD的振动信号自适应降噪方法

摘 要：应用集合经验模式分解（Ensemble empirical mode decomposition ,EEMD）能有效抑制模态混叠的特性,根据白噪声经经验模式分解（Empirical mode decomposition, EMD）后其固有模式函数（intrinsic mode functions ,IMF）分量的能量密度与其平均周期的乘积为一常量这一特点设计了自动选择IMF分量重构信号的算法,提出了基于EEMD的振动信号自适应降噪方法。对仿真信号和滚动轴承振动信号的降噪结果表明了该降噪方法的可行性和有效性。     

Mechanical-thermal noise in MEMS gyroscopes

We derive expressions for the effect of mechanical thermal noise on a vibrational microelectromechanical system gyroscope, including the angle of random walk, the noise equivalent rotation rate, and the spectral density of the noise component of the rate measurement. We explicitly calculate and compare the output signal due to rotation and the output due to noise. We avoid several ambiguities in the literature concerning bandwidth and correctly observe a factor of two reduction in noise power due to synchronous demodulation. We use stochastic averaging to obtain an approximate "slow" system that clarifies the effect of thermal noise and shows the effect of frequency mismatch between the drive and sense axes. We compute the noise equivalent rate for both open-loop and force-to-rebalance operation of the gyroscope.     

基于变尺度多稳随机共振的微弱信号检测研究

针对强噪声背景下微弱信号难以检测的难题,提出基于变尺度多稳随机共振的微弱信号检测方法。多稳随机共振系统比双稳随机共振系统具有更好的微弱信号检测能力,为强噪声背景下微弱信号的检测提供了新方法。首先对大频率信号进行尺度变换使之满足随机共振条件,将频率压缩后的信号通过多稳系统,调整参数使其发生随机共振得到信号的频谱特征,并与双稳随机共振方法得到的特征频率进行比较,仿真和实例结果均表明:相同条件下,多稳随机共振方法比双稳随机共振方法得到的频率准确,可以增强信号的幅值,有效地检测出被噪声淹没的微弱信号。     

基于自适应随机共振的齿轮微弱冲击故障信号增强提取方法研究

针对强背景噪声下冲击信号难以检测的问题,提出一种基于自适应随机共振的齿轮微弱冲击故障信号增强提取方法。首先,利用峭度指标和互相关系数构造修正峭度指标作为随机共振检测冲击信号的测度函数;其次,利用滑动窗将多冲击分量信号分割成多个单冲击分量信号作为随机共振的系统输入,并借助遗传算法实现系统参数的自适应选取;最后,将提出的方法应用于电力机车走行部齿轮箱故障诊断,结果显示该方法可有效实现微弱冲击特征的增强提取。     

Nonstationary weak signal detection based on normalization stochastic resonance with varying parameters

The nonlinear stochastic resonance system possesses the ability of taking advantage of background noise to enhance the weak signal. It provides a new approach to detect the weak signal embedded with heavy noise. This study proposes a new varying parameter stochastic resonance employing the fourth-order Runge–Kutta numerical method as well as the normalized transformation of a bistable stochastic resonance system. The model performs well in the detection of a time-varying signal with background noise for denoising and signal recovery. We take the fitness coefficient and cross-correlation coefficient as the criteria and analyze the influence of different parameters. The simulating results indicate its availability, validity and that it generates a better performance than the traditional stochastic resonance. The method develops the area of time-varying signal detection with stochastic resonance and presents new strategy for detection and denoising of a time-varying signal. It can be expected to be widely used in the areas of aperiodic signal processing, radar communication, etc.     

基于非线性耦合双稳态随机共振的轴承微弱故障信号增强检测方法研究

针对滚动轴承微弱故障信号难以检测的难题,提出一种基于新型非线性耦合双稳态随机共振模型的轴承微弱故障信号增强检测方法。噪声背景下,随机共振可以实现微弱信号的增强输出,提高微弱信号特征的检测。提出的非线性耦合双稳态系统是由两个单一双稳态系统经非线性方式耦合而成,通过分析耦合系数、阻尼系数随着噪声强度改变的信噪改善比响应特性曲线图研究了不同参数对随机共振现象的影响。结果表明,耦合双稳系统比单一双稳态系统具有更强随机共振现象的产生。最后采用模型对轴承故障微弱信号进行了增强检测应用,所提出的非线性耦合双稳态随机共振能够实现在复杂的噪声背景下对微弱故障信号的检测。     

Interferometric data analysis based on Markov nonlinear filtering methodology

For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting techniques, a whole interferometric data series is required. We propose a new interferometric data processing methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the parameters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the condition that the noise component be a Markov stochastic process realization. The accuracy and stability of the recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic solution of the phase unwrapping problem.     

中值与小波消噪集成的转子振动信号滤波方法研究

对受强脉冲随机噪声干扰转子振动信号的滤波方法进行了研究。提出了一种将中值滤波与小波消噪算法集成的混合滤波器。其中,中值滤波用于滤除信号的强脉冲噪声分量,小波消噪平滑线性叠加在中值系列中的平稳随机噪声。结果表明,实施的滤波方法对该类信号的处理效果好,获取的转子本质振动信号保持了信号的光滑性。     

Improving performance of neurons by adding colour noise

Noise is not always an interfering signal which perturbs the system. On the contrary, noise signals can enhance the performance of some non‐linear systems such as stochastic resonance (SR). These systems can detect the weak input signal when it is added to the noise signal. According to this property, SR models play a significant role in the functioning of the brain for detecting weak input signals and synchronisation of neural connections. In this study, the authors model neurons as SR systems where different types of noise, i.e. white noise and pink noise, are employed to amplify the weak nervous signals. They demonstrate colour noise, in particular, pink noise enhances the performance of the SR system to amplify the input signal. Furthermore, pink noise has a wider range of optimum values in comparison to white noise. Therefore, they can conclude that neurons are more sensitive to detect the signals that carry pink noise than signals with white noise or without noise. Hence, the retrieving ability of neurons can be improved by adding pink noise.Inspec keywords: stochastic processes, white noise, neural nets, brain, noise, neurophysiologyOther keywords: interfering signal, particular noise, colour noise, weak nervous signals, pink noise, white noise, SR system, authors model neurons, SR models, noise signal, weak input signal, nonlinear systems     

非线性分数阶双稳系统逻辑随机共振的研究

在整数阶逻辑随机共振的郎之万方程基础上构建了分数阶情况下的郎之万方程。对该方程描述的非线性分数阶双稳系统进行了仿真验证,分析分数阶阶次和系统参数的改变对逻辑随机共振现象的影响。结果表明当分数阶阶次小于临界值时,即使没有外加高斯白噪声或微弱周期信号也能观察到逻辑随机共振现象;当分数阶阶次大于临界值时,需要外加高斯白噪声或微弱周期信号才能实现逻辑随机共振,选择合适的噪声强度、微弱周期信号振幅、频率等可以提高逻辑输出的成功率。     

A stochastic model of the time-of-flight noise in airborne sonarranging systems

A stochastic model is developed for describing the statistical properties of the noise present in the time-of-flight (TOF) measurements made by in-air ultrasonic (US) transducers. The proposed method of analysis decomposes the TOF noise into three components with different physical origin and properties: a deterministic time-varying mean, a correlated random process and an uncorrelated random process. The physics of US waves propagating in air and the operating mode of typical sonar ranging systems are considered in orienting the choice of the model structure. The time-varying mean correlates with global thermal changes and drafts affecting the environment. The de-trended data are assumed to result from the sum of a correlated random component, due to inhomogeneities in the medium, such as temperature gradients and air turbulence, and an uncorrelated random component, mainly due to the wide band electronic noise superimposed on the echo signal. Autoregressive-moving average (ARMA) modelling techniques are used to capture the correlation structure with exponential decay of the piecewise stationary correlated random process. A method of adaptive segmentation allows to test for weak stationarity of this component. Kalman filtering techniques are used for its estimation. The adequacy of the representation in typical indoor environments is demonstrated by analyzing experimental data from Polaroid sensors     

基于周期势函数的自适应二阶欠阻尼随机共振信号增强方法

针对滚动轴承微弱故障振动信号在噪声环境下故障特征难以提取的问题,提出一种基于周期势函数的自适应二阶欠阻尼随机共振信号增强方法。采用粒子群算法对系统参数和阻尼系数的自适应匹配,实现对多个拟增强频段的随机共振,更加适用于工程实际中多故障信号提取。数据库考题检验和工程实验验证表明:1)该方法明显提高了输出信噪比,故障特征频率处主峰突出,边带干扰少,方便故障的机器判读,误判率低;2)随着噪声强度的增加,虽然输出信噪比有所降低,但该方法的检测效果仍优于基于周期势函数的自适应一阶随机共振方法的检测效果;3)该方法对噪声的适应性更强,在噪声环境下对于微弱故障信号的提取有着明显优势。     

Characterization and modeling of drift noise in Fourier transform spectroscopy: implications for signal processing and detection limits

A theoretical analysis of long-term drift noise in Fourier transform spectroscopy is presented. Theoretical predictions are confirmed by experiment. Fractional Brownian motion is employed as a stochastic process model for drift noise. A formulation of minimum detectable signal is given that properly accounts for drift noise. The spectral exponent of the low-frequency drift noise is calculated from experimental data. A frequency-dependent optimal spectrum averaging time is found to exist beyond which the minimum detectable signal increases indefinitely. It is also shown that the minimum detectable signal in an absorbance or transmission measurement degrades indefinitely with the time elapsed since background spectrum acquisition.     

Uncertainty of signal reconstruction in the case of jittery andnoisy measurements

Time domain measurements are distorted by the measurement system if the bandwidth of the system is not sufficiently high compared to that of the signal to be measured. If the distortion is known the measured signal can be compensated for it (inverse filtering or deconvolution). Since the measurement is always corrupted by noise, the reconstruction is an estimation task, i.e., the reconstructed signal may vary depending on the actual noise record. Our aim is to investigate the errors related to the signal reconstruction, and to provide an error bound around the reconstructed time domain waveform. Based on their nature we can distinguish between systematic and stochastic errors. In this paper, we investigate the stochastic type of errors and suggest a method to calculate the uncertainty (variance) of the reconstruction. We developed a method for the calibration of high-speed sampling systems. Both stationary and jitter noises will be investigated     

Algorithms for the Optimum Estimation of the Parameters of a Radio Signal in a Measurement Time of Less Than a Period and a Nonmultiple of a Period in Which the Result Is Tied to the Beginning of the Measurement Interval

Optimum estimates of the parameters of a noisy (white noise) sinusoidal radio signal of known frequency are considered, based on an investigation of the likelihood function, when the measurement time is less than a period and a nonmultiple of a period. Estimates are presented for the phase shift and the amplitude in the presence (absence) of a constant component and nonlinear distortions when the result is tied to the beginning of the measurement interval.