动力调谐陀螺静态漂移的非线性时间序列建模

动力调谐陀螺仪受陀螺仪自身工艺及各种电气因素影响,其随机漂移往往表现出非线性性质,利用线性随机建模方法并不能表现出随机漂移的非线性。作者通过传统的24位置测试获得动力调谐陀螺仪的静态漂移数据,然后对数据进行预处理(如,去除野点,进行数据平滑并利用小波分解提取趋势项),提取出随机漂移数据,并采用非线性AR时间序列方法对处理后的这些漂移数据进行建模。模型适用性检验结果表明,所建立的非线性AR模型可以很好地拟合动力调谐陀螺随机漂移,适用于描述动力调谐陀螺仪随机漂移特性。     

Nonlinear analysis of near-wall turbulence time series

We present the results of the nonlinear analysis of a near-wall turbulence signal, measured using a Laser Doppler Anemometer. Despite being preliminary in part, the results highlight some interesting aspects of the dynamics of coherent structures. Careful reconstruction of the dynamics from the scalar time series highlight particular phases of the bursting cycle, corresponding to the VITA detections, immersed in the overall high-dimension dynamics: the possibility to distinguish these trajectories in the embedding space provides indications for conditional sampling techniques on the reconstructed attractor. The application of nonlinear prediction to a system of high-dimension produces forecasts of rapidly decreasing quality over time, with no consequences for practical applications. Much more interesting instead is the analysis of the forecast errors for very short forecast intervals, where we observed a greater difficulty to predict the beginning of coherent structure instability probably due to the quasi-random forcing of the outer flow.     

Topology identification of complex networks from noisy time series using ROC curve analysis

As it is known, there is various unknown information in most real world networks, such as uncertain topological structure and node dynamics. Thus how to identify network topology from dynamical behaviors is an important inverse problem for physics, biology, engineering, and other science disciplines. Recently, with the help of noise, a method to predict network topology has been proposed from the dynamical correlation matrix, which is based on a general, one-to-one correspondence between the correlation matrix and the connection matrix. However, the success rate of this prediction method depends on the threshold, which is related to the coupling strength and noise intensity. Different coupling strength and noise intensity result in different success rate of prediction. To deal with this problem, we select a desirable threshold to improve the success rate of prediction by using Receiver Operating Characteristic (ROC) curve analysis. By the technique of ROC curve analysis, we find that the accuracy and efficiency of topology identification is mainly determined by coupling strengths. The success rate of estimation will be reduced if the coupling is too weak or too strong. The presence of noise facilitates topology identification, but the noise intensity is not always crucial to the effectiveness of topology identification.     

Novel techniques for improving NNetEn entropy calculation for short and noisy time series

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N = 19,625 elements that must be filled with the given data. A substantial number of practical time series have fewer elements than 19,625. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series of any length 5 ≤ N ≤ 19,625. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short-time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. In addition to external noise, the hyperparameter (bias) used in entropy calculation also plays a critical role. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal-to-Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise.

     

Nonlinear dynamical stability analysis of the circular three-dimensional frame

The three-dimensional frame is simplified into flat plate by the method of quasiplate. The nonlinear relationships between the surface strain and the midst plane displacement are established. According to the thin plate nonlinear dynamical theory, the nonlinear dynamical equations of three-dimensional frame in the orthogonal coordinates system are obtained. Then the equations are translated into the axial symmetry nonlinear dynamical equations in the polar coordinates system. Some dimensionless quantities different from the plate of uniform thickness are introduced under the boundary conditions of fixed edges, then these fundamental equations are simplified with these dimensionless quantities. A cubic nonlinear vibration equation is obtained with the method of Galerkin. The stability and bifurcation of the circular three-dimensional frame are studied under the condition of without outer motivation. The contingent chaotic vibration of the three-dimensional frame is studied with the method of Melnikov. Some phase figures of contingent chaotic vibration are plotted with digital artificial method.     

Nonlinear dynamical modeling in ECG analysis: a heuristic guideline

We highlight some of the pitfalls involved in the analysis of electrocardiogram data (ECG) when the correlation dimension (CD) estimates are used to discriminate between various states of the human heart or to distinguish healthy dynamics from different types of arrhythmia. It is argued that due to the PQRST complex, high autocorrelation and/or short data sets, the CD estimates would be distorted when continuously sampled ECG voltage data are used instead of beat-to-beat (RR) interval series.     

Weighted multifractal analysis of financial time series

In this paper, we propose the weighted multifractal analysis based on variance-weighted partition function (WMA), to evaluate the fractals of nonlinear time series containing amplitude information. The reliability of the proposed WMA is supported by simulations on generated and real-world financial volatility data. Numerical simulations with synthesized data show that WMA is comparative to the classic partition function-based standard multifractal analysis (SMA) and the multifractal detrending moving average analysis. More importantly, empirical analyses of Chinese stock indices illustrate that WMA outperforms SMA in distinguishing Hang Seng Index form SSE Composite Index and SZSE Component Index qualitatively and quantitatively, showing the power of WMA in discriminating series with distinctive amplitudes.     

Process pathway inference via time series analysis

Motivated by recent experimental developments in functional genomics, we construct and test a numerical technique for inferring process pathways, in which one process calls another process, from time series data. We validate using a case in which data are readily available and we formulate an extension, appropriate for genetic regulatory networks, which exploits Bayesian inference and in which the present-day undersampling is compensated for by prior understanding of genetic regulation.     

Adaptation of dynamical properties of time series data and its applications in deep brain stimulation

Nonlinear Dynamics - The chaotic nature of the brain can be observed by electroencephalogram signals. This chaotic behavior can be affected by the progressive nature of neurodegenerative disorders...     

Multiscale time irreversibility analysis of financial time series based on segmentation

Time irreversibility is a subject of increasing interest in an unbalanced system of various time series. Taking into account dynamic basic concepts, we provide multiscale time irreversibility analysis of financial time series based on segmentation which quantifies the time asymmetry in multiscales and is applied to several different forms of financial time series. Specifically, we adopt four distinct time irreversibility indices—Porta’s, Guzik’s and Ehler’s indices (P%, G% and E) and \(\gamma _{2,1} (k)\), respectively, derived from data segments on various timescales. We investigate the performance of our statistical tests for local financial time series from segmented series system with known time reversal properties and find out that it can help classify the partially representative financial markets finally. Particularly, the smaller the scale factor L is the better the ability to distinguish data. Statistical analysis shows a close relationship between G% and E. On the contrary, the connection between P% and G% or P% and E is not proven. In addition, we define a new metric \(\gamma _{2,1} (k)\) to measure the degree of time irreversibility. By further observing the results of the proposed method for computing the degree of irreversibility of the time series, we confirm that the asymmetry is an inherent property of the financial time series, which can be extended to a wide range of scales. Finally, we apply this method to the recurrence plot and multiscale recurrence quantification analysis, to compare effectiveness of the segmentation method.     

基于时间序列分析的自适应联邦滤波算法

以信息源的视角审视联邦滤波信息分配系数的问题,提出基于时间序列分析的自适应联邦滤波算法。通过引入导航传感器历史数据作为信息基础,以自回归滑动平均模型对其进行分析,使信息分配系数与导航传感器工作状态和环境状态相适应,提高系统性能。将此算法应用于组合导航系统,通过仿真实验对比,新的算法比经典联邦滤波算法定位精度提高40%,比其他的自适应联邦滤波算法位置误差标准差、速度误差标准差分别平均提高19.74%和30.67%,说明该算法具有良好性能。     

Vibration time series analysis of bubbling and turbulent fluidization

A non-intrusive vibration monitoring technique was used to study the hydrodynamics of a gas–solid fluidized bed. Experiments were carried out in a 15 cm diameter fluidized bed using 226, 470 and 700 μm sand particles at various gas velocities, covering both bubbling and turbulent regimes. Auto correlation function, mutual information function, Hurst exponent analysis and power spectral density function were used to analyze the fluidized bed hydrodynamics near the transition point from bubbling to turbulent fluidization regimes. The first pass of the autocorrelation function from one half and the time delay at which it becomes zero, and also the first minimum of the mutual information, occur at a higher time delay in comparison to stochastic systems, and the values of time delays were maximum at the bubbling to turbulent transition gas velocity. The maximum value of Hurst exponent of macro structure occurred at the onset of regime transition from bubbling to turbulent. Further increase in gas velocity after that regime transition velocity causes a decrease in the Hurst exponent of macro structure because of breakage of large bubbles to small ones. The results showed these methods are capable of detecting the regime transition from bubbling to turbulent fluidization conditions using vibration signals.     

A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar's cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincar's global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.     

Complexity analysis of the time series using inverse dispersion entropy

Nonlinear Dynamics - The primary object of this study is to measure the complexity of different types of signals. We undertake the experiment to support the hypothesis of inverse dispersion entropy...     

Nonlinear dynamical behavior of shallow cylindrical reticulated shells

By using the method of quasi-shells,the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral tri- angle cell are founded.By using the method of the separating variable function,the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support.The tensile force is solved out from the compati- ble equations,a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin.The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function.The existence of the chaotic motion of the single-layer shallow cylin- drical reticulated shell is approved by using the digital simulation method and Poincarémapping.     

Nonlinear dynamical characteristics of piles under horizontal vibration

The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So,the effect of the axis force on the pile is considered.