Dependent variables in broad band continuous time series

In this paper we continue our development of new methods for the analysis of broad band time series by deriving quantities which are able to indicate deterministic dependence of an element in one time series on elements in other time series. These methods are very broadly applicable and are particularly well suited to the study of continuous time series, in which the value of the function may depend on derivatives of the function itself, or on other quantities. We apply our methods to a number of mathematical examples including the Lorentz equation, the Hénon-Heiles equations, the forced Brusselator and the Mackey-Glass equation. We show that our methods are very successful at indicating deterministic dependencies in these systems, even if the time series are highly chaotic. Statistical aspects of our procedure are discussed, as are a number of interesting and surprising epistomological implications.     

基于递归量化分析与支持向量机的癫痫脑电自动检测方法

癫痫脑电信号的自动检测对癫痫的临床诊断与治疗具有重要意义.基于递归图(recurrence plot)的递归量化分析(recurrence quantification analysis,RQA)重现了非线性时间序列的动力学行为,分析了其递归特性,本文提出了基于RQA的癫痫脑电信号特征提取方法.实验结果表明:直接基于RQA特征的癫痫脑电的检测准确率较高,其中直接基于确定率DET的分类准确率可达到90.25%.本文还把提取的RQA特征值和变化系数、波动指数相结合组成特征向量,输入到SVM分类器,实现癫痫脑电信号的自动检测;实验结果表明:该方法的分类准确率可达到99%.     

Investigation of determinism in heart rate variability

The article searches for the possible presence of determinism in heart rate variability (HRV) signals by using a new approach based on NARMA (nonlinear autoregressive moving average) modeling and free-run prediction. Thirty-three 256-point HRV time series obtained from Wistar rats submitted to different autonomic blockade protocols are considered, and a collection of surrogate data sets are generated from each one of them. These surrogate sequences are assumed to be nondeterministic and therefore they may not be predictable. The original HRV time series and related surrogates are submitted to NARMA modeling and prediction. Special attention has been paid to the problem of stationarity. The results consistently show that the surrogate data sets cannot be predicted better than the trivial predictor-the mean-while most of the HRV control sequences are predictable to a certain degree. This suggests that the normal HRV signals have a deterministic signature. The HRV time series derived from the autonomic blockade segments of the experimental protocols do not show the same predictability performance, albeit the physiological interpretation is not obvious. These results have important implications to the methodology of HRV analysis, indicating that techniques from nonlinear dynamics and deterministic chaos may be applied to elicit more information about the autonomic modulation of the cardiovascular activity. (c) 2000 American Institute of Physics.     

Practical implementation of nonlinear time series methods: The TISEAN package

We describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos. A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters. Computer programs that implement the resulting strategies are publicly available as the TISEAN software package. The use of each algorithm will be illustrated with a typical application. As to the theoretical background, we will essentially give pointers to the literature. (c) 1999 American Institute of Physics.     

统一气体动理学方法研究进展

在临近空间高超声速飞行器气动载荷、航天飞行器变轨/调姿、微尺度元器件传质/传热等科学和工程实践中，存在着大量的时序多流域（多尺度）流动问题以及位于单一流场中的复杂多流域问题（局部稀薄问题），对数值预测工作提出挑战.因此，近年来从介观气体动理学基础上发展出了一大类将连续流与稀薄流进行统一计算的高效数值方法，包括确定论形式的UGKS，GKUA和DUGKS方法，以及粒子形式的USP-BGK和UGKWP方法.文章围绕着确定论和统计粒子两类统一方法的最新研究进展进行回顾和分析，重点关注在每种方法中全流域统一性质的来源与实现方式、目前已取得的关键进展以及该方法的扩展性和应用价值.      

Statistical modelling of the backscattered field in a one-dimensional non-stationary stochastic problem

Within the framework of an exact wave approach in the spatial-time domain, the one-dimensional stochastic problem of sound pulse scattering by a layered random medium is considered. On the basis of a unification of methods which has been developed by the authors, previously applied to the investigation of non-stationary deterministic wave problems and stochastic stationary wave problems, an analytical-numerical simulation of the behaviour of the backscattered field stochastic characteristics was carried out. Several forms of incident pulses and signals are analysed. We assume that random fluctuations of a medium are described by virtue of the Gaussian Markov process with an exponential correlation function. The most important parameters appearing in the problem are discussed; namely, the time scales of diffusion, pulse durations, the medium layer thickness or the largest observation time scale in comparison with the time scale of one correlation length for the case of a half-space. An exact pattern of the pulse backscattering processes is obtained. It is illustrated by the behaviour of the backscattered field statistical moments for all observation times which are of interest. It is shown that during the time interval when the main part of the pulse energy leaves the medium, the backscattered field is a substantially non-stationary process, having a non-zero mean value and an average intensity that decays according to a power law. There are various power indices for the different duration incident pulses, however, they are not the same as those of previous papers, which were obtained on the basis of an approximate and asymptotic analysis. We have also verified that the Gaussian law is valid for the probability density function of the backscattered field in the case of any incident pulse duration.     

一种基于非完整二维相空间分量置换的混沌检测方法

由于混沌时间序列和随机过程具有很多类似的性质, 因而在实际中很难将两者区分开来. 混沌信号检测与识别是混沌时间序列分析中一个重要的课题. 混沌信号是由确定性的混沌映射或混沌系统产生的, 相比于高斯白噪声序列, 其在非完整的二维相空间中表现出更加丰富的结构特性. 本文通过研究混沌时间序列和高斯白噪声序列在非完整二维相空间中的分布特性, 利用混沌信号的非线性动力学特性, 提出了一种基于非完整二维相空间分量置换的混沌信号检测方法. 该方法首先由接收序列得到非完整的二维相空间, 基于第一维分量大小关系实现对第二维分量的置换与分组, 进一步求得F检验统计量. 然后利用混沌系统的局部特性, 获取非完整二维相空间的动力学结构信息, 实现对混沌序列的有效检测. 在高斯白噪声条件下对多种混沌信号进行了信号检测的数值仿真. 仿真结果表明: 相比置换熵检测, 本文所提算法所需数据量小、计算简单以及具有更低的时间复杂度, 同时对噪声具有更好的鲁棒性.     

Recurrence quantification analysis of electrostatic fluctuations in fusion plasmas

We have investigated plasma turbulence at the edge of a tokamak plasma using data from electrostatic potential fluctuations measured in the Brazilian tokamak TCABR. Recurrence quantification analysis has been used to provide diagnostics of the deterministic content of the series. We have focused our analysis on the radial dependence of potential fluctuations and their characterization by recurrence-based diagnostics. Our main result is that the deterministic content of the experimental signals is most pronounced at the external part of the plasma column just before the plasma radius. Since the chaoticity of the signals follows the same trend, we have concluded that the electrostatic plasma turbulence at the tokamak plasma edge can be partially explained by means of a deterministic nonlinear system.     

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is "bleached"), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.     

HELS法在循环平稳声场全息重建中的理论与实验研究

Helmholtz 方程最小二乘法利用一组球面波基函数拟合声源产生的声场,根据重建和实际声压的误差最小原则,利用最小二乘法确定基函数展开的项数以及对应的权重系数,该方法具有计算效率高和需要测点少的优点,在实际工程中有很大的实用性.Helmholtz 方程最小二乘法和其他近场声全息方法一样都是针对平稳声场,对非平稳声场的分析很少.对于实际工程中经常遇到的一类特殊非平稳声场——循环平稳声场,现有的技术多以单通道信号分析为主,其高阶统计量在故障诊断领域应用较广.分析了循环平稳声场中Helmholtz方程最小二乘 关键词： 声全息 循环平稳 Helmholtz 方程 球面波     

Statistical modelling of the backscattered field in a one-dimensional non-stationary stochastic problem

Abstract

Within the framework of an exact wave approach in the spatial-time domain, the one-dimensional stochastic problem of sound pulse scattering by a layered random medium is considered. On the basis of a unification of methods which has been developed by the authors, previously applied to the investigation of non-stationary deterministic wave problems and stochastic stationary wave problems, an analytical-numerical simulation of the behaviour of the backscattered field stochastic characteristics was carried out. Several forms of incident pulses and signals are analysed. We assume that random fluctuations of a medium are described by virtue of the Gaussian Markov process with an exponential correlation function. The most important parameters appearing in the problem are discussed; namely, the time scales of diffusion, pulse durations, the medium layer thickness or the largest observation time scale in comparison with the time scale of one correlation length for the case of a half-space. An exact pattern of the pulse backscattering processes is obtained. It is illustrated by the behaviour of the backscattered field statistical moments for all observation times which are of interest. It is shown that during the time interval when the main part of the pulse energy leaves the medium, the backscattered field is a substantially non-stationary process, having a non-zero mean value and an average intensity that decays according to a power law. There are various power indices for the different duration incident pulses, however, they are not the same as those of previous papers, which were obtained on the basis of an approximate and asymptotic analysis. We have also verified that the Gaussian law is valid for the probability density function of the backscattered field in the case of any incident pulse duration.     

Nonlinear time series analysis of electrocardiograms

In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's "dimension." We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three "normal" subjects and three "heavy smokers" at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics. (c) 1995 American Institute of Physics.     

On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis

The question whether the human cardiac system is chaotic or not has been an open one. Recent results in chaos theory have shown that the usual methods, such as saturation of correlation dimension D(2) or the existence of positive Lyapunov exponent, alone do not provide sufficient evidence to confirm the presence of deterministic chaos in an experimental system. The results of surrogate data analysis together with the short-term prediction analysis can be used to check whether a given time series is consistent with the hypothesis of deterministic chaos. In this work nonlinear dynamical tools such as surrogate data analysis, short-term prediction, saturation of D(2) and positive Lyapunov exponent have been applied to measured ECG data for several normal and pathological cases. The pathology presently studied are PVC (Premature Ventricular Contraction), VTA (Ventricular Tachy Arrhythmia), AV (Atrio-Ventricular) block and VF (Ventricular Fibrillation). While these results do not prove that ECG time series is definitely chaotic, they are found to be consistent with the hypothesis of chaotic dynamics. (c) 1998 American Institute of Physics.     

基于时间序列符号化模式表征的有向加权复杂网络

时间序列复杂网络分析近些年已发展成为非线性信号分析领域的一个国际热点课题.为了能更有效地挖掘时间序列(特别是非线性时间序列)中的结构特征,同时简化时间序列分析的复杂度,提出了一种新的基于时间序列符号化结合滑窗技术模式表征的有向加权复杂网络建网方法.该方法首先按照等概率区段划分的方式将时间序列做符号化处理,结合滑窗技术确定不同时刻的符号化模式作为网络的节点;然后将待分析时间序列符号化模式的转换频次和方向作为网络连边的权重和方向,从而建立时间序列有向加权复杂网络.通过对Logistic系统不同参数设置对应的时间序列复杂网络建网测试结果表明,相比经典的可视图建网方法,本文方法的网络拓扑能更简洁、直观地展示时间序列的结构特征.进而,将本文方法应用于规则排列采集的自然风场信号分析,其网络特性指标能较准确地预测采集信号的排布规律,而可视图建网方法的网络特性指标没有任何规律性的结果.     

异常心电节律VT和VF信号的复杂性分析

在替代随机数据假设检验的基础上,提出了针对确定性混沌信号的改进非线性算法,并应用于心脏中的异常节律心电信号分析.指出：室性心动过速(VT)和心室纤颤(VF)是不同于随机信号的,是具有复杂非线性特性的混沌信号.进而在信号定性分析的基础上,从非线性动力学的角度,提出新的复杂度和复杂率的定义和相关的检测方法,对VT和VF进行了定量分析.结果表明,异常心电节律VT和VF信号的定性和定量分析是客观的和准确可靠的. 关键词： 复杂离散度 Lempel-Ziv复杂度 复杂率 平均复杂度 复杂饱和度     

Characterizing pseudoperiodic time series through the complex network approach

Recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network [J. Zhang, M. Small, Phys. Rev. Lett. 96 (2006) 238701]. Essentially, this is a transformation from the time domain to the network domain, which allows for the dynamics of the time series to be studied via organization of the network. In this paper, we focus on the deterministic chaotic Rössler time series and stochastic noisy periodic data that yield substantially different structures of networks. In particular, we test an extensive range of network topology statistics, which have not been discussed in previous work, but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles. Our goal is to find out how they reflect and quantify different aspects of specific dynamics, and how they can be used to distinguish different dynamical regimes. For example, we find that the joint degree distribution appears to fundamentally characterize spatial organizations of cycles in phase space, and this is quantified via an assortativity coefficient. We applied network statistics to electrocardiograms of a healthy individual and an arrythmia patient. Such time series are typically pseudoperiodic, but are noisy and nonstationary and degrade traditional phase-space based methods. These time series are, however, better differentiated by our network-based statistics.     

Using short curved vertical arrays in ocean acoustic tomography

We consider the possibility of reconstructing the ocean mode structure based on measurements with short (not covering the entire ocean waveguide) arrays curved in an unknown way by ocean currents, which corresponds to the conditions of a real experiment. We have developed an algorithm for estimating the arrival times of various mode signals by solving a system of linear equations. The mode reconstruction accuracy as a function of the array length and profile curvature is investigated. The cases of using both the ocean noise field and deterministic signals as a sound source are considered. Comparison with the commonly used mode filtering method is made.     

Analogical model for mechanical vibrations in flue organ pipes inferred by independent component analysis

Several experiments have been performed to investigate the mechanical vibrations associated with an organ pipe. The measurements have been made by using laser Doppler vibrometry, a well-known not-invasive optical measurement technique that is very widely used in structural dynamics. The recorded signals are analyzed by using a well-established decomposition method in time domain, i.e., independent component analysis. Asymptotic dynamics methods to recognize low-dimensional dynamic system associated with this wave field is then considered. The full-toned recorded signals appear decomposed into three independent components. The independent components are nonlinear due to the fractal dimension of the attractor. These results for the mechanic vibrational field are compared with those of the acoustic one. It is interesting to note that the two fields have many common characteristics. Finally, a low-dimensional dynamic system that reproduces the main characteristics of the mechanical wave field in the time and frequency domains is introduced.     

Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence

Spectroscopic techniques are increasingly used for field laser applications in industry and research. Under field conditions complex gas sensors cannot be considered as stable and therefore drift characterization is a key issue to distinguish between sample data and sensor drift. In this paper the history of von Neumann’s two-sample variance and Allan variance stability investigations in the field of frequency metrology and the relationship to wavelet analysis are reviewed. The concept has been used to characterize accuracy and precision of spectroscopic data in the time domain and practical guidelines for the interpretation of σ/τ plots are presented. Two topics relevant for spectroscopic measurements are discussed: First, the optical fringe effect, which is present in any spectrometer, limits the precision and accuracy of spectroscopic measurements by forming time dependent background structures superimposed to the signal under investigation. The two-sample variance is used to characterize optical etalons and long-term drift using σ/τ plots. Second, the short-term instrument stability characteristic in the presence of atmospheric turbulence is discussed. This is important for laser-based gas monitors measuring the turbulent transport of trace gases between the biosphere and the atmosphere using the eddy-covariance technique. It will be shown how the spectral characteristics of turbulence in the Kolmogorov inertial subrange can be identified in the time domain and how the effect of optical fringes can be separated from atmospheric signals.     

Stochastic analysis of recurrence plots with applications to the detection of deterministic signals

Recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems, denoising, as well as detection of deterministic signals embedded in noise. Though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise. Computations using examples from harmonic processes, autoregressive models, and outputs from nonlinear systems are shown to illustrate this relationship. Finally, the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test. Results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub-optimal when compared to well-known detectors based on the likelihood ratio.