Nonlinear Time Series Analysis Methods Research Articles

Efficient scheduling of power communication resources based on fuzzy weighted constraint equalisation

Resources in the power communication system are affected by crosstalk between power grid subnets during scheduling, resulting in a poor equalisation of resource allocation. In order to improve equalisation allocation of resources in the power communication system, an efficient scheduling method of power communication system resources based on fuzzy weighted constraint equalisation is proposed. In this method, the nonlinear time series analysis method is used to construct an information flow model of power communication system resource data and the channel equalisation control is carried out in transmission links of the power communication system; the fuzzy weighted constraint equalisation method is used to implement adaptive baud-spaced equalisation handling during resource scheduling and the fuzzy mesh-based clustering algorithm is used to carry out pairing of classification attribute weights of power resources, so as to achieve efficient clustering of resources and to improve the link equalisation in resource scheduling. Simulation results show that with this method, the average data recall rate during resource scheduling reaches about 90% and the equalisation curve changes very smoothly, which fully indicates that with this method, the data recall rate and scheduling efficiency are high and the equalisation capability of communication channels is strong.

Characterizing continuously rotating detonation via nonlinear time series analysis

The sampled pressure signals in continuously rotating detonation combustors have the inherence of nonlinear dynamics. To dig out more information on combustion modes, the nonlinear time series analysis method is thus applied to the pressure-time series obtained at a hydrogen/air rotating detonation combustor by using the phase space reconstruction and wavelet entropy algorithm. The variation of wavelet entropy is approved to be associated with the periodicity variation of pressure signals. Different structures of attractor as well as wavelet entropy distribution in the phase diagram can distinguish the deflagration mode from the unstable and stable detonation modes under the conditions of different air flow rates. The limit-cycle oscillation is exhibited in the phase space diagram with a very low flow rate, here 25 g/s. The mean wavelet entropy of pressure-time series can be a quantitative index of different combustion modes occurring in the combustor. The present study is expected to enhance the understanding of the physical mechanism of continuously rotating detonation and contribute on the development of detonation propulsion technology.

Reconstructed Dynamics of the Imaging Photoplethysmogram.

Human photoplethysmogram (PPG) is one of the signals widely applied for health monitoring. Development of the new techniques made possible evolution of traditional contact PPG which was measured at red and near-infrared light (NIR) to the contactless, imaging PPG (iPPG) that can be recorded at various light wavelengths, including ambient visible light. However, despite the numerous advantages of iPPG its applications demonstrated so far are quite limited. The NIR PPG was previously found to be useful for various applications in the area of physiological and mental health monitoring by utilizing advanced methods of nonlinear time-series analysis applied on its reconstructed dynamics. The main purpose of this study is to demonstrate data-driven approach with time-delay-reconstructed attractor obtained from the iPPG. The results of this study demonstrated that the iPPG dynamics can be reconstructed with fine data resolution, and its time-delay-reconstructed trajectory is almost deterministic, though contains noise. The obtained results might be useful for further applied studies on the iPPG.

Searching for Chaos Evidence in Eye Movement Signals.

Most naturally-occurring physical phenomena are examples of nonlinear dynamic systems, the functioning of which attracts many researchers seeking to unveil their nature. The research presented in this paper is aimed at exploring eye movement dynamic features in terms of the existence of chaotic nature. Nonlinear time series analysis methods were used for this purpose. Two time series features were studied: fractal dimension and entropy, by utilising the embedding theory. The methods were applied to the data collected during the experiment with “jumping point” stimulus. Eye movements were registered by means of the Jazz-novo eye tracker. One thousand three hundred and ninety two (1392) time series were defined, based on the horizontal velocity of eye movements registered during imposed, prolonged fixations. In order to conduct detailed analysis of the signal and identify differences contributing to the observed patterns of behaviour in time scale, fractal dimension and entropy were evaluated in various time series intervals. The influence of the noise contained in the data and the impact of the utilized filter on the obtained results were also studied. The low pass filter was used for the purpose of noise reduction with a 50 Hz cut-off frequency, estimated by means of the Fourier transform and all concerned methods were applied to time series before and after noise reduction. These studies provided some premises, which allow perceiving eye movements as observed chaotic data: characteristic of a space-time separation plot, low and non-integer time series dimension, and the time series entropy characteristic for chaotic systems.

Local noise sensitivity: Insight into the noise effect on chaotic dynamics.

Noise contamination in experimental data with underlying chaotic dynamics is one of the significant problems limiting the application of many nonlinear time series analysis methods. Although numerous studies have been devoted to the investigation of different aspects of noise-nonlinear dynamics interactions, the effects produced by noise on chaotic dynamics are not fully understood. This study sought to analyze the local effects produced by noise on chaotic dynamics with a smooth attractor. Local Wayland test translation errors were calculated for noise-induced Lorenz and Rössler chaotic models, and for experimental green light photoplethysmogram data. Results demonstrated that under noise induction, local regions on the chaotic attractor with high values of local translation error can be observed. This phenomenon was defined as the local noise sensitivity. It was found that for both models, local noise-sensitive regions were located close to the system's equilibrium points. Additionally, it was found that the reconstructed dynamics represent well the local noise sensitivity of the original dynamics. The concept of local noise sensitivity is expected to contribute to various applied studies, as it reveals regions of chaotic attractors that are sensitive to the presence of noise.

Identification of Dynamic Patterns of Speech-Evoked Auditory Brainstem Response Based on Ensemble Empirical Mode Decomposition and Nonlinear Time Series Analysis Methods

The speech-evoked auditory brainstem response (sABR) shows how complex sounds such as speech and music are processed in the auditory system. Speech-ABR could be used to evaluate particular impairments and improvements in auditory processing system. Many researchers used linear approaches for characterizing different components of sABR signal, whereas nonlinear techniques are not applied so commonly. The primary aim of the present study is to examine the underlying dynamics of normal sABR signals. The secondary goal is to evaluate whether some chaotic features exist in this signal. We have presented a methodology for determining various components of sABR signals, by performing Ensemble Empirical Mode Decomposition (EEMD) to get the intrinsic mode functions (IMFs). Then, composite multiscale entropy (CMSE), the largest Lyapunov exponent (LLE) and deterministic nonlinear prediction are computed for each extracted IMF. EEMD decomposes sABR signal into five modes and a residue. The CMSE results of sABR signals obtained from 40 healthy people showed that 1st, and 2nd IMFs were similar to the white noise, IMF-3 with synthetic chaotic time series and 4th, and 5th IMFs with sine waveform. LLE analysis showed positive values for 3rd IMFs. Moreover, 1st, and 2nd IMFs showed overlaps with surrogate data and 3rd, 4th and 5th IMFs showed no overlap with corresponding surrogate data. Results showed the presence of noisy, chaotic and deterministic components in the signal which respectively corresponded to 1st, and 2nd IMFs, IMF-3, and 4th and 5th IMFs. While these findings provide supportive evidence of the chaos conjecture for the 3rd IMF, they do not confirm any such claims. However, they provide a first step towards an understanding of nonlinear behavior of auditory system dynamics in brainstem level.

Dynamic characterization and predictability analysis of wind speed and wind power time series in Spain wind farm

The renewable energy resources such as wind power have recently attracted more researchers’ attention. It is mainly due to the aggressive energy consumption, high pollution and cost of fossil fuels. In this era, the future fluctuations of these time series should be predicted to increase the reliability of the power network. In this paper, the dynamic characteristics and short-term predictability of hourly wind speed and power time series are investigated via nonlinear time series analysis methods such as power spectral density analysis, time series histogram, phase space reconstruction, the slope of integral sums, the ��− �� method, the recurrence plot and the recurrence quantification analysis. Moreover, the interactive behavior of the wind speed and wind power time series is studied via the cross correlation, the cross and joint recurrence plots as well as the cross and joint recurrence quantification analyses. The results imply stochastic nature of these time series. Besides, a measure of the short-term mimic predictability of the wind speed and the underlying wind power has been derived for the experimental data of Spain’s wind farm.

Failure of Arm Movement Control in Stroke Patients, Characterized by Loss of Complexity.

We study the mechanism of human arm-posture control by means of nonlinear dynamics and quantitative time series analysis methods. Utilizing linear and nonlinear measures in combination, we find that pathological tremors emerge in patient dynamics and serve as a main feature discriminating between normal and patient groups. The deterministic structure accompanied with loss of complexity inherent in the tremor dynamics is also revealed. To probe the underlying mechanism of the arm-posture dynamics, we further analyze the coupling patterns between joints and components, and discuss their roles in breaking of the organization structure. As a result, we elucidate the mechanisms in the arm-posture dynamics of normal subjects responding to the gravitational force and for the reduction of the dynamic degrees of freedom in the patient dynamics. This study provides an integrated framework for the origin of the loss of complexity in the dynamics of patients as well as the coupling structure in the arm-posture dynamics.

Search for the 531-day-period wobble signal in the polar motion based on EEMD

Abstract. In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531-day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM series (1962–1977), but cannot be found in the recent PM series (1978–2013) using conventional analysis approaches. By virtue of the demodulation feature of EEMD, the 531 dW can be confirmed to be present in PM based on the differences of the amplitudes and phases between different intrinsic mode functions. Results from three sub-series divided from the EOP C04 series show that the period of the 531 dW is subject to variations, in the range of 530.9–524 days, and its amplitude is also time-dependent (about 2–11 mas). Synthetic tests are carried out to explain why the 531 dW can only be observed in recent 30-year PM time series after using EEMD. The 531 dW is also detected in the two longest available superconducting gravimeter (SG) records, which further confirms the presence of the 531 dW. The confirmation of the 531 dW existence could be significant in establishing a more reasonable Earth rotation model and may effectively contribute to the prediction of the PM and its mechanism interpretation.

Application of photoplethysmogram for detecting physiological effects of tractor noise

This study sought to investigate the effect of tractor noise on the cardiovascular system of farm workers by the photoplethysmographic technique, which was used to derive signal reflecting features of cardiovascular system performance. Fourier transform and nonlinear time-series analysis methods, such as time-delay embedding and the Wayland test, were applied to the photoplethysmogram signal to analyze differences in cardiovascular system performance arising upon exposure to levels of tractor noise corresponding to low, medium and high tractor engine speeds. Results showed that the ratio of two significant component frequencies obtained by Fourier analysis and Wayland test translation error can distinguish differences in photoplethysmogram signal arising under noise exposure. Additionally, the translation error was less dependent on the subject than the frequency ratio, which may make it useful index for application to real-time health monitoring of farmers.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations.

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior.

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh—Rose neuron model

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh—Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

Extraction of nonlinear characteristics from eddy current magnetic field of Al-alloy weld and their classification

GMR (giant magneto resistance) sensor can be used to measure the eddy current magnetic field of the Al-alloy weld. The nonlinear time series analysis method is introduced to study the signals from the eddy current magnetic field of the weld in three different states, which include good, lack of penetration, and clustered blowhole weld. Several nonlinear characteristic parameters, such as Lyapunov exponent and correlation dimension etc., are extracted. The results show that the eddy current magnetic field of the Al-alloy weld has distinguished chaotic features. Analysis of the Lempel-Ziv complexity and approximate entropy for different signals leads to the conclusion that these two complex measures are sensitive to the eddy current magnetic field of the weld zone. Through these methods, nonlinear characteristics of eddy current magnetic field of the weld can be obtained for identifying and classifying the type of the weld, which will serve as an efficient supplementary diagnostic tool to reveal different patterns of the welds.

Nonlinear time series analysis of snapping shrimp sounds

Snapping shrimp produce sounds through cavitation bubbles generated by the rapid closing of their claws. These sounds are a primary source of ambient noise in sub-tropical, shallow water environments. Though seasonal and daily variations of snapping shrimp sound levels have been reported, comprehensive studies of short time series have been limited. We investigate the respective spectral characteristics from acoustic arrays recordings at various locations in Oahu, HI, over hourly, daily and weekly periods. Nonlinear time series analysis methods encompassing recurrence plots are used to investigate the acoustic time series together with bivariate and cross recurrence plot analysis with that of tidal and sunlight cycles. Signal entropy and determinism are investigated and transient acoustic ship sounds are located

Characterizing atmospheric surface layer turbulence using chaotic return map analysis

Nonlinear time series analysis methods are used to investigate the dynamics of mechanical and convective turbulences in the atmospheric surface layer flow. Using dynamical invariant analysis (e.g. correlation dimension, Lyapunov exponent and mutual information) along with recurrence quantification analysis (e.g. recurrent rate, determinism, average diagonal length of recurrence plot, etc.) of the vertical wind component data, it is confirmed that a convective turbulence is a lower order manifold in its phase space exhibiting higher degree of organization than a mechanical turbulence. Applying a quasi-one-dimensional chaotic return map technique, the topological differences between the mechanical and convective turbulences are explored. These quasi-one-dimensional return maps are produced using the local maxima of the first principal component of the reconstructed turbulence data. A comparison of the probability distribution of the local maxima of a forced Lorenz model with the turbulence data indicates the possible existence of a stable fixed point for both type of turbulences. Furthermore, dynamically the mechanical turbulence is found to resemble an unforced Lorenz model whereas the convective turbulence resembles a forced Lorenz model.

Algorithm and Simulation of the Feature Extraction for Rotating Machinery Signal in Fault Status

The nonlinear feature of the rotating machinery signal in fault situation was extracted and researched based on the collected the vibration signal. And the extraction algorithm was researched. On the basis of the phase space reconstitution the recurrence plot (RP) algorithm was researched with the nonlinear time series analysis method. The inner feature of the recurrence plots was analyzed quantitatively, the feature called recurrence rate was extracted finally. Simulation result shows that the extracted feature has the function and property diagnosis of the machinery faults based on the RP and recurrence quantification analysis (RQA) methods and also with nice engineering application value.

ANOMALOUS LOW STATES AND LONG-TERM VARIABILITY IN THE BLACK HOLE BINARY LMC X-3

Rossi X-ray Timing Explorer observations of the black hole binary LMC X-3 reveal an extended very low X-ray state lasting from 2003 December 13 until 2004 March 18, unprecedented both in terms of its low luminosity (>15 times fainter than ever before seen in this source) and long duration (~3 times longer than a typical low/hard state excursion). During this event little to no source variability is observed on timescales of ~hours-weeks, and the X-ray spectrum implies an upper limit of 1.2x10^35 erg s^-1. Five years later another extended low state occurs, lasting from 2008 December 11 until 2009 June 17. This event lasts nearly twice as long as the first, and while significant variability is observed, the source remains reliably in the low/hard spectral state for the ~188 day duration. These episodes share some characteristics with the "anomalous low states" in the neutron star binary Her X-1. The average period and amplitude of the variability of LMC X-3 have different values between these episodes. We characterize the long-term variability of LMC X-3 before and after the two events using conventional and nonlinear time series analysis methods, and show that, as is the case in Her X-1, the characteristic amplitude of the variability is related to its characteristic timescale. Furthermore, the relation is in the same direction in both systems. This suggests that a similar mechanism gives rise to the long-term variability, which in the case of Her X-1 is reliably modeled with a tilted, warped precessing accretion disk.

Autonomic mediation of the interdependence between variability signals of heart rate and blood pressure in the lizard Gallotia galloti

Autonomic nervous system (ANS) involvement in the mediation of the synchronization between beat-to-beat RR interval variability (RRIV) and systolic blood pressure variability (SBPV) signals of the lizard Gallotia galloti (Oudart, 1839) was investigated through linear and nonlinear time series analysis methods in a pharmacological blockade context. The ANS blockers used were atropine, prazosin, and propranolol. The interdependence between the signals was quantified by means of the magnitude-squared coherence (MSC), which measures amplitude and phase linear synchronization; the phase lag index (PLI), which evaluates the phase synchronization; and the index L, which quantifies the generalized linear and nonlinear synchronization. Atropine decreased the PLI in the low-frequency (LF: 0.01–0.05 Hz) range; prazosin decreased the MSC in the medium-frequency (MF: 0.06–0.15 Hz) range; and propranolol did not alter any of the interdependence measures. It is suggested that (i) the cholinoceptor activity mediates the phase cardiovascular synchronization in the LF range; (ii) the α1-adrenoceptor activity mediates the amplitude and phase linear cardiovascular synchronization in the MF range; and (iii) the β-adrenoceptor activity plays no role in mediating any dynamics of cardiovascular synchronization in the studied frequency range. When comparing these results with those in mammals, a lesser overall autonomic involvement in the mediation of the studied cardiovascular interdependences is seen in reptiles.

Dynamical Reconstruction of Road Longitudinal Profiles: A Theoretical and Experimental Study

This paper presents a theoretical and experimental study dealing with the dynamical reconstruction of longitudinal road profiles. The non-linear time series analysis method is used; it is based on the concept of deterministic chaos to detect anomalies. For this purpose, attractors, recurrence plots and recurrence quantification analysis are performed to detect anomalies on road pavements. In particular, modification of attractor and presence of vertical and horizontal lines in recurrence plots allow us to detect the above-mentioned local irregularities. Therefore, on the basis of the available database, it is possible to detect local irregularities to design and perform pavement rehabilitation and/or maintenance.

Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series

The complexity of the short-term cardiovascular control prompts for the introduction of multivariate (MV) nonlinear time series analysis methods to assess directional interactions reflecting the underlying regulatory mechanisms. This study introduces a new approach for the detection of nonlinear Granger causality in MV time series, based on embedding the series by a sequential, non-uniform procedure, and on estimating the information flow from one series to another by means of the corrected conditional entropy. The approach is validated on short realizations of linear stochastic and nonlinear deterministic processes, and then evaluated on heart period, systolic arterial pressure and respiration variability series measured from healthy humans in the resting supine position and in the upright position after head-up tilt.