Nonlinear Time Series Analysis Research Articles

Characterization of homogeneous nucleation of superheated liquid droplets by nonlinear analysis

The homogeneous bubble nucleation in superheated liquid droplets can be initiated by energetic particles or radiation. The nonlinearity in the heat transfer introduces chaos in the temperature time series of a boiling system. In the present study, the acoustical pulses from the homogeneous nucleation of superheated liquid droplets by neutrons and gamma-rays have been collected. Nonlinear time series analysis methods like 3D attractor reconstruction and Fast Fourier transformation (FFT) have been performed on the collected pulses. The analysis predicts the possibility of the existence of chaos, and the positive value of the largest Lyapunov exponent confirms it. The nonlinearity in the energy deposition by both the recoil nuclei and electrons from the neutrons and gamma-rays respectively, introduce chaos. A qualitative difference has been observed in the 3D attractor and Rescaled Range (R/S) plots between the neutron and gamma-ray-induced pulses, and the present differences are useful for the identification of these pulses.

Seismic Analysis of the Soil Behavior and Titling of the Building

The mechanism of this yielding and its behavior under seismic loading of soil are the primary focus of this investigation. Nonlinear analysis is taken into account to see the real behavior of soil. In order to analyze soil, we employ both its solid mass and its lumped mass. In this study, the Finite Element Model (FEM) forms the basis for the mathematical formulas. Soil analysis in the case of a lumped mass takes into account the soil's one DOF, two DOF, and multi DOF degrees of freedom. In order to determine soil characteristics for MDOF, a soil bore log must be employed. In the instance of MDOF, the soil is composed of 12 distinct layers. SAP 2000 is used to do linear and nonlinear analysis of time series for this research. According to the findings, solid and lumped soil mass displacements are almost identical. Therefore, it is possible to get insight into the behavior of soil mass during an earthquake by studying lumped soil mass. The soil's nonlinear behavior is investigated using a variety of linear completely plastic hysteretic loops. Soil characteristics are shown to be crucial in this regard. Inadequate soil stiffness may result in persistent deformation, which in turn can lead structures to lean out of alignment. It is also noted that near the soil's surface, amplification is greatest.

Nonlinear Dynamic Analysis of Seafloor Pressure Time Series with and without Internal Waves

Ocean internal wave as a nonlinear process oscillates within ocean interior rather than the surface. Internal waves have significant influences on the transport of material, energy and even global climate. The generation, transmission and attenuation of internal wave play a significant role in the ocean dynamics owing to the exchange of the energy within each process. In this paper, reduced complexity of seafloor pressure time series induced by internal wave in the southern Taiwan bank has been investigated using nonlinear dynamic analysis. Cao method has been used to distinguish between the pressure signal with internal wave and the random signal without internal wave. The reconstructed phase spaces and correlation dimensions of the time series with and without internal wave are compared. Internal wave leads the seafloor pressure time series to produce a more regular phase space reconstruction and more low dimensional dynamics. Our study suggests that nonlinear dynamic analysis could be a valuable and promising method in real-time ocean internal wave detection.

An ecological network approach for detecting and validating influential organisms for rice growth.

How to achieve sustainable food production while reducing environmental impacts is a major concern in agricultural science, and advanced breeding techniques are promising for achieving such goals. However, rice is usually grown under field conditions and influenced by surrounding ecological community members. How ecological communities influence the rice performance in the field has been underexplored despite the potential of ecological communities to establish an environment-friendly agricultural system. In the present study, we demonstrate an ecological-network-based approach to detect potentially influential, previously overlooked organisms for rice (Oryza sativa). First, we established small experimental rice plots, and measured rice growth and monitored ecological community dynamics intensively and extensively using quantitative environmental DNA metabarcoding in 2017 in Japan. We detected more than 1000 species (including microbes and macrobes such as insects) in the rice plots, and nonlinear time series analysis detected 52 potentially influential organisms with lower-level taxonomic information. The results of the time series analysis were validated under field conditions in 2019 by field manipulation experiments. In 2019, we focused on two species, Globisporangium nunn and Chironomus kiiensis, whose abundance was manipulated in artificial rice plots. The responses of rice, namely, the growth rate and gene expression patterns, were measured before and after the manipulation. We confirmed that, especially in the G. nunn-added treatment, rice growth rate and gene expression pattern were changed. In the present study, we demonstrated that intensive monitoring of an agricultural system and the application of nonlinear time series analysis were helpful to identify influential organisms under field conditions. Although the effects of the manipulations were relatively small, the research framework presented here has future potential to harness the ecological complexity and utilize it in agriculture. Our proof-of-concept study would be an important basis for the further development of field-basis system management.

An ecological network approach for detecting and validating influential organisms for rice growth

How to achieve sustainable food production while reducing environmental impacts is a major concern in agricultural science, and advanced breeding techniques are promising for achieving such goals. However, rice is usually grown under field conditions and influenced by surrounding ecological community members. How ecological communities influence the rice performance in the field has been underexplored despite the potential of ecological communities to establish an environment-friendly agricultural system. In the present study, we demonstrate an ecological-network-based approach to detect potentially influential, previously overlooked organisms for rice (Oryza sativa). First, we established small experimental rice plots, and measured rice growth and monitored ecological community dynamics intensively and extensively using quantitative environmental DNA metabarcoding in 2017 in Japan. We detected more than 1000 species (including microbes and macrobes such as insects) in the rice plots, and nonlinear time series analysis detected 52 potentially influential organisms with lower-level taxonomic information. The results of the time series analysis were validated under field conditions in 2019 by field manipulation experiments. In 2019, we focused on two species, Globisporangium nunn and Chironomus kiiensis, whose abundance was manipulated in artificial rice plots. The responses of rice, namely, the growth rate and gene expression patterns, were measured before and after the manipulation. We confirmed that, especially in the G. nunn-added treatment, rice growth rate and gene expression pattern were changed. In the present study, we demonstrated that intensive monitoring of an agricultural system and the application of nonlinear time series analysis were helpful to identify influential organisms under field conditions. Although the effects of the manipulations were relatively small, the research framework presented here has future potential to harness the ecological complexity and utilize it in agriculture. Our proof-of-concept study would be an important basis for the further development of field-basis system management.

Nexus between renewable energy and economic growth in G7 countries: New insight from nonlinear time series and panel cointegration analysis

This study aims to investigate the impact of renewable energy consumption on the economic growth of G7 countries and explore the potential nonlinear relationship between the two variables. Initially, the NARDL model is employed to analyze the G7 countries, allowing for the control of nonlinear relationships and considering asymmetric effects. The findings of the NARDL model reveal an asymmetric long run cointegration relationship between renewable energy consumption and economic growth in Canada and the US, while other countries show different dynamics. Subsequently, a causal dynamic impact analysis is conducted to gain further insights into the relationship between renewable energy consumption and economic growth. In the next step, the advantage of panel data analysis is utilized to investigate the overall impact across all G7 countries. For this purpose, the study extends the NARDL model to the PNARDL (Panel Nonlinear Autoregressive Distributed Lag) model, which facilitates the control of asymmetric effects and nonlinearity in the panel data model. In this context, this study is one of the first studies to control the nonlinearity in panel data analysis. The results from the PNARDL model demonstrate that renewable energy has a positive long-term relationship with economic growth in G7 countries; however, this relationship is statistically insignificant.

Dryland sensitivity to climate change and variability using nonlinear dynamics

Primary productivity response to climatic drivers varies temporally, indicating state-dependent interactions between climate and productivity. Previous studies primarily employed equation-based approaches to clarify this relationship, ignoring the state-dependent nature of ecological dynamics. Here, using 40 y of climate and productivity data from 48 grassland sites across Mongolia, we applied an equation-free, nonlinear time-series analysis to reveal sensitivity patterns of productivity to climate change and variability and clarify underlying mechanisms. We showed that productivity responded positively to annual precipitation in mesic regions but negatively in arid regions, with the opposite pattern observed for annual mean temperature. Furthermore, productivity responded negatively to decreasing annual aridity that integrated precipitation and temperature across Mongolia. Productivity responded negatively to interannual variability in precipitation and aridity in mesic regions but positively in arid regions. Overall, interannual temperature variability enhanced productivity. These response patterns are largely unrecognized; however, two mechanisms are inferable. First, time-delayed climate effects modify annual productivity responses to annual climate conditions. Notably, our results suggest that the sensitivity of annual productivity to increasing annual precipitation and decreasing annual aridity can even be negative when the negative time-delayed effects of annual precipitation and aridity on productivity prevail across time. Second, the proportion of plant species resistant to water and temperature stresses at a site determines the sensitivity of productivity to climate variability. Thus, we highlight the importance of nonlinear, state-dependent sensitivity of productivity to climate change and variability, accurately forecasting potential biosphere feedback to the climate system.

Nonlinear Time Series Analysis and Prediction of General Aviation Accidents Based on Multi-Timescales

General aviation accidents have complex interactions and influences within them that cannot be simply explained and predicted by linear models. This study is based on chaos theory and uses general aviation accident data to conduct research on different timescales (HM-scale, ET-scale, and EF-scale). First, time series are constructed by excluding seasonal patterns from the statistics of general aviation accidents. Secondly, the chaotic properties of multi-timescale series are determined by the 0–1 test and Lyapunov exponent. Finally, by introducing the sparrow search algorithm and tent chaotic mapping, a CSSA-LSSVM prediction model is proposed. The accident data of the National Transportation Safety Board (NTSB) of the United States in the past 15 years is selected for case analysis. The results show that the phase diagram of the 0–1 test presents Brownian motion characteristics, and the maximum Lyapunov exponents of the three scales are all positive, proving the chaotic characteristics of multi-timescale series. The CSSA-LSSVM prediction model’s testing results illustrate its superiority in time series predicting, and when the timescale declines, the prediction error reduces gradually while the fitting effect strengthens and then decreases. This study uncovers the nonlinear chaotic features of general aviation accidents and demonstrates the significance of multi-timescale research in time series analysis and prediction.

Stage 2: Visual information and communication context as modulators of interpersonal coordination in face-to-face and videoconference-based interactions

Interpersonal coordination of body movement—or similarity in patterning and timing of body movement between interaction partners—is well documented in face-to-face (FTF) conversation. Here, we investigated the degree to which interpersonal coordination is impacted by the amount of visual information available and the type of interaction conversation partners are having. To do so within a naturalistic context, we took advantage of the increased familiarity with videoconferencing (VC) platforms and with limited visual information in FTF conversation due to the COVID-19 pandemic. Pairs of participants communicated in one of three ways: FTF in a laboratory setting while socially distanced and wearing face masks; VC in a laboratory setting with a view of one another's full movements; or VC in a remote setting with a view of one another's face and shoulders. Each pair held three conversations: affiliative, argumentative, and cooperative task-based. We quantified interpersonal coordination as the relationship between the two participants' overall body movement using nonlinear time series analyses. Coordination changed as a function of the contextual constraints, and these constraints interacted with coordination patterns to affect subjective conversation outcomes. Importantly, we found patterns of results that were distinct from previous research; we hypothesize that these differences may be due to changes in the broader social context from COVID-19. Taken together, our results are consistent with a dynamical systems view of social phenomena, with interpersonal coordination emerging from the interaction between components, constraints, and history of the system.

System dynamics monitoring using PIC micro-controller-based PLSE

The permutation largest slope entropy (PLSE) algorithm has been shown to be effective to distinguish between regular and non-regular dynamics from time series analysis. However, as it is the case for many non-linear time series analysis algorithms, such a characterization is locally made and does not allow one to capture some micro-phenomena, such as intermittency, that may occur in the system behavior. This paper presents a PIC micro-controller based implementation of the PLSE for a real-time monitoring of system dynamics. The PLSE algorithm is optimized to fit the program and data memory of low-end processors using the XC8 compiler and the MPLAB X IDE. The resulting algorithm is implemented on the PIC16F18446 and deployed on the Explorer 8 development board. The effectiveness of the developed tool is validated by considering an electrical circuit of the Duffing oscillator that can generate both periodic and chaotic dynamics. By comparing the PLSE values with the phase portraits and previous results on the Duffing oscillator circuit, the developed tool efficiently allows one to monitor the behavior of dynamical systems.

Characterising the variability in ocean data using fractal and correlation dimension analysis

Understanding the variability of ocean data is essential for predicting its behaviour in time domain. This study aims to examine the usability of several nonlinear time series analysis techniques for diagnosing the complexity of the underlying dynamics of various ocean data. For such purpose, one-year data from an offshore platform and two-year data from a weather buoy were collected and analysed. The results indicate that all the ocean data considered here are chaotic in nature, reflected by the unfolded structure in the reconstructed phase space. In general, the surface currents speed possess the largest fractal dimension (or lowest Hurst exponent) and correlation dimension, while the significant wave height has the lowest values. This implies that the dynamics associated with surface currents speed tend to be the most complex, which can lead to more random and unpredictable temporal behaviour. The fractal analysis shows that the fluctuation of these ocean data are mostly persistent, and the dependence of fractal properties on window length appears to vary amongst different ocean data. Overall, the results derived from various analysis techniques are consistent, which confirms the potential of using chaotic time series analysis technique for characterizing ocean data variability.

Induced Relaxation Enhances the Cardiorespiratory Dynamics in COVID-19 Survivors.

Most COVID-19 survivors report experiencing at least one persistent symptom after recovery, including sympathovagal imbalance. Relaxation techniques based on slow-paced breathing have proven to be beneficial for cardiovascular and respiratory dynamics in healthy subjects and patients with various diseases. Therefore, the present study aimed to explore the cardiorespiratory dynamics by linear and nonlinear analysis of photoplethysmographic and respiratory time series on COVID-19 survivors under a psychophysiological assessment that includes slow-paced breathing. We analyzed photoplethysmographic and respiratory signals of 49 COVID-19 survivors to assess breathing rate variability (BRV), pulse rate variability (PRV), and pulse-respiration quotient (PRQ) during a psychophysiological assessment. Additionally, a comorbidity-based analysis was conducted to evaluate group changes. Our results indicate that all BRV indices significantly differed when performing slow-paced breathing. Nonlinear parameters of PRV were more appropriate for identifying changes in breathing patterns than linear indices. Furthermore, the mean and standard deviation of PRQ exhibited a significant increase while sample and fuzzy entropies decreased during diaphragmatic breathing. Thus, our findings suggest that slow-paced breathing may improve the cardiorespiratory dynamics of COVID-19 survivors in the short term by enhancing cardiorespiratory coupling via increased vagal activity.

Identification of Electrical Tree Aging State in Epoxy Resin Using Partial Discharge Waveforms Compared to Traditional Analysis.

Electrical treeing is one of the main degradation mechanisms in high-voltage polymeric insulation. Epoxy resin is used as insulating material in power equipment such as rotating machines, power transformers, gas-insulated switchgears, and insulators, among others. Electrical trees grow under the effect of partial discharges (PDs) that progressively degrade the polymer until the tree crosses the bulk insulation, then causing the failure of power equipment and the outage of the energy supply. This work studies electrical trees in epoxy resin through different PD analysis techniques, evaluating and comparing their ability to identify tree bulk-insulation crossing, the precursor of failure. Two PD measurement systems were used simultaneously-one to capture the sequence of PD pulses and another to acquire PD pulse waveforms-and four PD analysis techniques were deployed. Phase-resolved PD (PRPD) and pulse sequence analysis (PSA) identified tree crossing; however, they were more sensible to the AC excitation voltage amplitude and frequency. Nonlinear time series analysis (NLTSA) characteristics were evaluated through the correlation dimension, showing a reduction from pre- to post-crossing, and thus representing a change to a less complex dynamical system. The PD pulse waveform parameters had the best performance; they could identify tree crossing in epoxy resin material independently of the applied AC voltage amplitude and frequency, making them more robust for a broader range of situations, and thus, they can be exploited as a diagnostic tool for the asset management of high-voltage polymeric insulation.

Package AdvEMDpy: Algorithmic variations of empirical mode decomposition in Python

AbstractThis work presents a $\textsf{Python}$ EMD package named AdvEMDpy that is both more flexible and generalises existing empirical mode decomposition (EMD) packages in $\textsf{Python}$ , $\textsf{R}$ , and $\textsf{MATLAB}$ . It is aimed specifically for use by the insurance and financial risk communities, for applications such as return modelling, claims modelling, and life insurance applications with a particular focus on mortality modelling. AdvEMDpy both expands upon the EMD options and methods available, and improves their statistical robustness and efficiency, providing a robust, usable, and reliable toolbox. Unlike many EMD packages, AdvEMDpy allows customisation by the user, to ensure that a broader class of linear, non-linear, and non-stationary time series analyses can be performed. The intrinsic mode functions (IMFs) extracted using EMD contain complex multi-frequency structures which warrant maximum algorithmic customisation for effective analysis. A major contribution of this package is the intensive treatment of the EMD edge effect which is the most ubiquitous problem in EMD and time series analysis. Various EMD techniques, of varying intricacy from numerous works, have been developed, refined, and, for the first time, compiled in AdvEMDpy. In addition to the EMD edge effect, numerous pre-processing, post-processing, detrended fluctuation analysis (localised trend estimation) techniques, stopping criteria, spline methods, discrete-time Hilbert transforms (DTHT), knot point optimisations, and other algorithmic variations have been incorporated and presented to the users of AdvEMDpy. This paper and the supplementary materials provide several real-world actuarial applications of this package for the user’s benefit.

Temporary disruption in language processing reflected as multiscale temporal discoordination in a recurrent network

By juxtaposing time series analyses of activity measured from a fully recurrent network undergoing disrupted processing and of activity measured from a continuous meta-cognitive report of disruption in real-time language comprehension, we present an opportunity to compare the temporal statistics of the state-space trajectories inherent to both systems. Both the recurrent network and the human language comprehension process appear to exhibit long-range temporal correlations and low entropy when processing is undisrupted and coordinated. However, when processing is disrupted and discoordinated, they both exhibit more short-range temporal correlations and higher entropy. We conclude that by measuring human language comprehension in a dense-sampling manner similar to how we analyze the networks, and analyzing the resulting data stream with nonlinear time series analysis techniques, we can obtain more insight into the temporal character of these discoordination phases than by simply marking the points in time at which they peak.

Temporary disruption in language processing reflected as multiscale temporal discoordination in a recurrent network

By juxtaposing time series analyses of activity measured from a fully recurrent network undergoing disrupted processing and of activity measured from a continuous meta-cognitive report of disruption in real-time language comprehension, we present an opportunity to compare the temporal statistics of the state-space trajectories inherent to both systems. Both the recurrent network and the human language comprehension process appear to exhibit long-range temporal correlations and low entropy when processing is undisrupted and coordinated. However, when processing is disrupted and discoordinated, they both exhibit more short-range temporal correlations and higher entropy. We conclude that by measuring human language comprehension in a dense-sampling manner similar to how we analyze the networks, and analyzing the resulting data stream with nonlinear time series analysis techniques, we can obtain more insight into the temporal character of these discoordination phases than by simply marking the points in time at which they peak.

Lyapunov exponents for temporal networks.

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network and construct a measure to estimate the network maximum Lyapunov exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low- and high-dimensional chaos and finally discuss potential applications.

Nonlinear features in whistles produced by the short-beaked common dolphin (Delphinus delphis) off southeastern Brazil.

Animal vocalizations have nonlinear characteristics responsible for features such as subharmonics, frequency jumps, biphonation, and deterministic chaos. This study describes the whistle repertoire of a short-beaked common dolphin (Delphinus delphis) group at Brazilian coast and quantifies the nonlinear features of these whistles. Dolphins were recorded for a total of 67 min around Cabo Frio, Brazil. We identify 10 basic categories of whistle, with 75 different types, classified according to their contour shape. Most (45) of these 75 types had not been reported previously for the species. The duration of the whistles ranged from 0.04 to 3.67 s, with frequencies of 3.05-29.75 kHz. Overall, the whistle repertoire presented here has one of the widest frequency ranges and greatest level of frequency modulation recorded in any study of D. delphis. All the nonlinear features sought during the study were confirmed, with at least one feature occurring in 38.4% of the whistles. The frequency jump was the most common feature (29.75% of the whistles) and the nonlinear time series analyses confirmed the deterministic chaos in the chaotic-like segments. These results indicate that nonlinearities are a relevant characteristic of these whistles, and that are important in acoustic communication.

Characterizing the statistical complexity of nonlinear time series via ordinal pattern transition networks

Complex network approaches have lately emerged as innovative and complementary notions of nonlinear time series analysis, capable of revealing numerous aspects that more classic analytic methods fail to reveal. In this paper, we concentrate on ordinal pattern transition networks (OPTN) to characterize the statistical complexity of time series by considering each pattern as a network node and the probability of transition between patterns as a directed weighted edge between nodes. The traditional complexity measures of time series, permutation entropy (PE) and transition entropy (TE), have been first explained via OPTN, and a new statistical complexity technique termed permutation weighted statistical transition entropy (PWSTE) is suggested to address some drawbacks of some existing complexity measures. In the context of OPTN, the proposed PWSTE enhances PE and TE by taking into account both static information (i.e., network node probability distributions) and dynamic information (i.e., time series transition probabilities represented by nodes). It combines with the imbalance of OPTN, which enables a more accurate measurement of the statistical complexity of nonlinear time series. The suggested new technique for assessing statistical complexity is thoroughly described based on the simulated time series, and the findings demonstrate that the proposed algorithm is more sensitive and effective in identifying dynamic changes. When the proposed algorithm is used to medical data, the EEG time series of epileptic patients are examined to define the changes in EEG data over various stages. The findings demonstrate that the proposed PWSTE algorithm outperforms conventional methods in identifying the stage in which a patient’s EEG data is located.

Challenges and perspectives in recurrence analyses of event time series

The analysis of event time series is in general challenging. Most time series analysis tools are limited for the analysis of this kind of data. Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series. Here, the basic concept is introduced, the challenges are discussed, and the future perspectives are summarized.