非最小相位线性非高斯序列的替代数据检验

替代数据法作为检验时间序列非线性和混沌的统计方法获得了广泛应用.常用的替代数据法的零假设为“原序列来自(经过单调静态非线性变换的)平稳线性高斯随机过程”.拒绝此假设,并不能说明序列必然来自确定性的非线性动力系统,非最小相位的线性非高斯序列也会导致基于相位随机化的替代数据检验拒绝此假设 关键词： 替代数据 时间序列分析 非线性 非最小相位     

热超声键合换能系统动力学特性的非线性检验

根据实际超声换能系统的振动测试，提出了热超声键合换能系统动力学特性的非线性检验方法，利用基于相空间重构的替代数据法，通过对换能杆末端的实测数据进行正确替代，并用非线性动力学的理论来检验其是否具有非线性.通过实验对超声换能杆末端轴向、俯仰、横向的振动时间序列的关联维数进行了准确的计算，从而清晰地描述了上述三个方向的动力学特性.所提出的方法有利于更好地认识超声键合换能系统，为建立更加合理的非线性动力学模型奠定良好的理论基础，有很好的应用价值. 关键词： 超声键合 时间序列 相位随机化 替代数据     

一种新的时间序列确定性辨识方法

提出一种新的基于辛几何谱的时间序列确定性检测方法，通过计算原始时间序列及其替代数据的辛几何谱，利用非参数Mann-Whitney 秩和检验方法，可有效地辨别确定性混沌过程和随机过程.通过对常见的随机过程，Lorenz，Rssler，Mackey-Glass，高维耦合方程的仿真检验，说明了方法的有效性. 并通过用Santa Fe测试集中两个序列检验了其对实际时间序列的适用性，最后研究不同数据长度和不同强度噪声对该方法性能的影响说明了其鲁棒性.     

连续动力系统时间序列的非线性检验

用相位随机化的替代数据方法，研究了连续混沌动力系统时间序列的非线性检验判定.研究发现，在不同的采样情况下，混沌时间序列的非线性特性检验有所差异，尤其对于过采样时间序列，往往会出现虚假的判断结果.针对过采样时间序列，最好采用能够反映非线性特征的参数，作为检验统计量进行检验判断. 关键词： 替代数据 关联维数 连续时间序列 非线性检验     

一种时间序列的弱非线性检验方法

时间序列的非线性是判定该时间序列具有混沌特性的必要条件.提出一种基于线性和非线性AR模型归一化多步预测误差比值的非线性检验量δ_NAR,采用替代数据法来检测时间序列中的弱非线性.以Lorenz时间序列为例,分析了估计非线性检验量δ_NAR时各相关参数对弱非线性检测性能的影响.通过混沌时间序列非线性检测试验,对4种混沌时间序列中的3种,非线性检验量δ_NAR都表现出比基于AIC模型选择准则的非线性检验量相似文献   

高斯势垒/阱作用下非局域矢量光孤子 的传输特性

非局域非线性介质中高斯势垒或势阱作用下矢量光孤子的传输特性,由具有高斯型线性势的耦合非局域非线性薛定谔方程描述,通过平方算子法对方程进行数值计算,并利用分步法仿真矢量光孤子的传输.在非局域非线性大块介质中,异相位矢量孤子的分量总是自发地分离,高斯势垒可以抑制分量间的排斥作用;同相位矢量孤子的分量则总是自发地融合,高斯势阱可以抑制分量间的吸引作用.通过定量分析势垒高度(或势阱深度)或宽度与矢量孤子两个分量在归一化传输距离为500处的间距之间的关系,发现如果势垒(或势阱)的高度(或深度)及宽度太大或太小,高斯线性势都不能抑制这一过程,甚至会恶化矢量光孤子的传输.对于异相位孤子,最有效抑制分量分离过程的高斯势垒设置是高度为1.10,宽度为1.00;对于同相位孤子,最有效抑制分量融合过程的高斯势阱应设置是深度为-1.50,宽度为1.00.研究结果可为全光开关、光逻辑门、光计算等光控光技术提供参考.     

基于脉冲对的交叉相位调制脉冲压缩中离散效应的抑制

提出一种新的抑制离散效应的方法——非对称脉冲对法，并对采用该方法和采用非同步耦合法在基于脉冲对交叉相位调制对脉冲进行压缩过程中，对离散效应影响的抑制效果进行了研究.数值模拟的结果显示：对于峰值功率为10mW、半极大全宽度为5ps的高斯入射脉冲，采用非对称脉冲对法，可以获得压缩比为137、基座能量比为0122、峰值功率为116mW的压缩脉冲. 关键词： 交叉相位调制 离散效应 非同步耦合法 非对称脉冲对法     

不同非局域程度条件下空间光孤子的传输特性

光束在非局域非线性介质中传输由非局域非线性薛定谔方程描述.讨论了在不同非局域程度 条件下，空间光孤子的传输特性.提出了一个基于分步傅里叶算法数值求解孤子波形和分布 的迭代算法.假定介质的非线性响应函数为高斯型，得出了在不同非局域程度条件下空间光 孤子的数值解，并数值证明了它们的稳定性.结果表明，不论非局域程度如何，光束都能以 光孤子态在介质中稳定传输.光孤子的波形是从强非局域时的高斯型过渡到局域时的双曲正 割型，形成孤子的临界功率随非局域程度的减弱而减小，光孤子相位随距离线性增大，相位 的变化率随非局域程度的减弱而减小. 关键词： 非局域非线性薛定谔方程 空间光孤子 临界功率 相位     

面向语音增强的约束序贯高斯混合模型噪声功率谱估计

提出了一种基于极大似然的噪声对数功率谱估计方法,采用高斯混合模型对每一个频带上的功率谱包络构建统计模型,将时序包络划分为语音和非语音类,它们分别对应于高斯混合模型的两个高斯分量,描述语音和非语音的统计分布,其中非语音高斯分量的均值即为噪声功率谱的最优估计.采用序贯学习的方法,在极大似然准则下逐帧更新模型参数,并逐帧给出噪声功率谱的最优估计值。此外,由于序贯更新过程中语音信号长时缺失,容易导致模型失稳,提出了一种在线的最小描述长度准则(MDL)来判断语音信号是否长时缺失,从而保证了模型的稳定性.实验表明,算法性能整体优于经典的MS和IMCRA算法。      

利用光强分布设计多波长频率转换器件

对获得多波长同时产生的可调控的频率转换器件进行了研究。通过分析非线性晶体中耦合光强随传播距离的变化,提出了一种基于晶体中光强分布获得非线性结构的方法。针对和频过程,利用MATLAB软件进行仿真,设计出了6个和频过程同时发生的非周期结构。为灵活调控各个非线性过程的输出强度,得到任意形状的目标功率谱,提出在设计过程中引入权重系数。对和频及倍频产生的研究表明:获得的非线性结构不仅实现了多波长的同时输出,而且可以任意调节输出光功率谱。该设计方法速度快、效率高,可以为实际制作非线性光学器件提供理论指导。     

Testing the assumptions of linear prediction analysis in normal vowels

In this paper we develop an improved surrogate data test to show experimental evidence, for all the simple vowels of U.S. English, for both male and female speakers, that Gaussian linear prediction analysis, a ubiquitous technique in current speech technologies, cannot be used to extract all the dynamical structure of real speech time series. The test provides robust evidence undermining the validity of these linear techniques, supporting the assumptions of either dynamical nonlinearity and/or non-Gaussianity common to more recent, complex, efforts at dynamical modeling speech time series. However, an additional finding is that the classical assumptions cannot be ruled out entirely, and plausible evidence is given to explain the success of the linear Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian dynamics. This supports the use of appropriate hybrid linear/nonlinear/non-Gaussian modeling. With a calibrated calculation of statistic and particular choice of experimental protocol, some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance.     

Test your surrogate data before you test for nonlinearity

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT, which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies, we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions against the use of the AAFT algorithm.     

Detection of coupling between oscillators with analytic tests for significance

To detect coupling between two oscillators from a time series, we suggest a method based on the estimation of the phase increments correlation with an analytic test for significance. With exemplary oscillators, we show that the suggested method complements a widely used approach based on the estimation of the mean phase coherence. In particular, the suggested method allows efficient detection of a non-synchronizing coupling and, due to a less restrictive null hypothesis, it is applicable to a wider range of situations, including arbitrarily strong phase nonlinearities.     

Correlation dimension: A pivotal statistic for non-constrained realizations of composite hypotheses in surrogate data analysis

Currently surrogate data analysis can be used to determine if data is consistent with various linear systems, or something else (a nonlinear system). In this paper we propose an extension of these methods in an attempt to make more specific classifications within the class of nonlinear systems.

In the method of surrogate data one estimates the probability distribution of values of a test statistic for a set of experimental data under the assumption that the data is consistent with a given hypothesis. If the probability distribution of the test statistic is different for different dynamical systems consistent with the hypothesis, one must ensure that the surrogate generation technique generates surrogate data that are a good approximation to the data. This is often achieved with a careful choice of surrogate generation method and for noise driven linear surrogates such methods are commonly used.

This paper argues that, in many cases (particularly for nonlinear hypotheses), it is easier to select a test statistic for which the probability distribution of test statistic values is the same for all systems consistent with the hypothesis. For most linear hypotheses one can use a reliable estimator of a dynamic invariant of the underlying class of processes. For more complex, nonlinear hypothesis it requires suitable restatement (or cautious statement) of the hypothesis. Using such statistics one can build nonlinear models of the data and apply the methods of surrogate data to determine if the data is consistent with a simulation from a broad class of models. These ideas are illustrated with estimates of probability distribution functions for correlation dimension estimates of experimental and artificial data, and linear and nonlinear hypotheses.     

A suggested statistical test for measuring bivariate nonlinear dependence

We devise a new asymptotic statistical test to assess independence in bivariate continuous distributions. Our approach is based on the Cramér–von Mises test, in which the empirical process is viewed as the Kullback–Leibler divergence, that is, as the distance between the data under the independence hypothesis and the data empirically observed. We derive the theoretical characteristic function of the limit distribution of the test statistic and find the critical values through computer simulation. A Monte Carlo experiment is considered as assessing the validation and power performance of the test by assuming a bivariate nonlinear dependence structure with fat tails. Two extra examples, respectively, consider stationary and conditionally nonstationary series. Results confirm that our suggested test is consistent and powerful in the presence of bivariate nonlinear dependence even if the environment is non-Gaussian. Our case is illustrated with high-frequency data from stocks listed on the NYSE that recently experienced so-called mini-flash crashes.     

Fractional diffusion and reflective boundary condition

Scaling analysis of the magnitude series (volatile series) has been proposed recently to identify possible non-linear/multifractal signatures in the given data [Y. Ashkenazy, et al. Phys. Rev. Lett. 86 (2001) 1900; Y. Ashkenazy, et al. Physica A 323 (2003) 19; T. Kalisky, Y. Ashkenazy, S. Havlin. Phys. Rev. E 72 (2005) 011913]. In this article, correlations of volatile series generated from stationary first-order linear feedback process with Gaussian and non-Gaussian innovations are investigated. While volatile correlations corresponding to Gaussian innovations exhibited uncorrelated behavior across all time scales, those of non-Gaussian innovations showed significant deviation from uncorrelated behavior even at large time scales. The results presented raise the intriguing question whether non-Gaussian innovations can be sufficient to realize long-range volatile correlations.     

The delay vector variance method for detecting determinism and nonlinearity in time series

A novel ‘delay vector variance’ (DVV) method for detecting the presence of determinism and nonlinearity in a time series is introduced. The method is based upon the examination of local predictability of a signal. Additionally, it spans the complete range of local linear models due to the standardisation to the distribution of pairwise distances between delay vectors. This provides consistent and easy-to-interpret diagrams, which convey information about the nature of a time series. In order to gain further insight into the technique, a DVV scatter diagram is introduced, which plots the DVV curve against that for a globally linear model (surrogate data). This way, the deviation from the bisector line represents a qualitative measure of nonlinearity, which can be used additionally for constructing a quantitative measure for statistical testing. The proposed method is compared to existing methods on synthetic, as well as standard real-world signals, and is shown to provide more consistent results overall, compared to other, established nonlinearity analysis methods.     

From nonlinearity to causality: statistical testing and inference of physical mechanisms underlying complex dynamics

Principles and applications of statistical testing as a tool for inference of underlying mechanisms from experimental time series are discussed. The computational realizations of the test null hypothesis known as the surrogate data are introduced within the context of discerning nonlinear dynamics from noise, and discussed in examples of testing for nonlinearity in atmospheric dynamics, solar cycle and brain signals. The concept is further generalized for detection of directional interactions, or causality in bivariate time series.