scholarly journals Cross recurrence plot based synchronization of time series

2002 ◽  
Vol 9 (3/4) ◽  
pp. 325-331 ◽  
Author(s):  
N. Marwan ◽  
M. Thiel ◽  
N. R. Nowaczyk
Keyword(s):  
Time Series ◽  
Sediment Cores ◽  
Real Data ◽  
Recurrence Plot ◽  
Magnetic Data ◽  
Data Series ◽  
Recurrence Plots ◽  
Makarov Basin ◽  
The Cross ◽  
Cross Recurrence Plot

Abstract. The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series. This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS). A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of them is compressed or stretched) so that they are synchronized. An application of this method to geophysical sediment core data illustrates its suitability for real data. The rock magnetic data of two different sediment cores from the Makarov Basin can be adjusted to each other by using this method, so that they are comparable.

scholarly journals Encoding Time Series as Multi-Scale Signed Recurrence Plots for Classification Using Fully Convolutional Networks

Sensors ◽  
2020 ◽  
Vol 20 (14) ◽  
pp. 3818
Author(s):  
Ye Zhang ◽  
Yi Hou ◽  
Shilin Zhou ◽  
Kewei Ouyang
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Recurrence Plot ◽  
The State ◽  
Recurrence Plots ◽  
Convolutional Networks ◽  
Multi Scale ◽  
Fully Convolutional Networks ◽  
Benchmark Datasets ◽  
Visualization Evaluation

Recent advances in time series classification (TSC) have exploited deep neural networks (DNN) to improve the performance. One promising approach encodes time series as recurrence plot (RP) images for the sake of leveraging the state-of-the-art DNN to achieve accuracy. Such an approach has been shown to achieve impressive results, raising the interest of the community in it. However, it remains unsolved how to handle not only the variability in the distinctive region scale and the length of sequences but also the tendency confusion problem. In this paper, we tackle the problem using Multi-scale Signed Recurrence Plots (MS-RP), an improvement of RP, and propose a novel method based on MS-RP images and Fully Convolutional Networks (FCN) for TSC. This method first introduces phase space dimension and time delay embedding of RP to produce multi-scale RP images; then, with the use of asymmetrical structure, constructed RP images can represent very long sequences (>700 points). Next, MS-RP images are obtained by multiplying designed sign masks in order to remove the tendency confusion. Finally, FCN is trained with MS-RP images to perform classification. Experimental results on 45 benchmark datasets demonstrate that our method improves the state-of-the-art in terms of classification accuracy and visualization evaluation.

Recurrence Plot based entropies and their ability to detect transitions

2020 ◽  
Author(s):  
K. Hauke Kraemer ◽  
Norbert Marwan ◽  
Karoline Wiesner ◽  
Jürgen Kurths
Keyword(s):  
Time Series ◽  
Shannon Entropy ◽  
Recurrence Plot ◽  
Climate Dynamics ◽  
Value Distribution ◽  
Tipping Points ◽  
Recurrence Plots ◽  
The Past ◽  
Entropy Measures ◽  
Regime Transitions

<p>Many dynamical processes in Earth Sciences are the product of many interacting components and have often limited predictability, not least because they can exhibit regime transitions (e.g. tipping points).To quantify complexity, entropy measures such as the Shannon entropy of the value distribution are widely used. Amongst other more sophisticated ideas, a number of entropy measures based on recurrence plots have been suggested. Because different structures, e.g. diagonal lines, of the recurrence plot are used for the estimation of probabilities, these entropy measures represent different aspects of the analyzed system and, thus, behave differently. In the past, this fact has led to difficulties in interpreting and understanding those measures. We review the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.</p><p>Finally, we illustrate their potential in an application on paleoclimate time series. Using the presented entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.</p>

Dynamical assessment of physiological systems and states using recurrence plot strategies

1994 ◽  
Vol 76 (2) ◽  
pp. 965-973 ◽  
Author(s):  
C. L. Webber ◽  
J. P. Zbilut
Keyword(s):  
Time Series ◽  
Physiological State ◽  
Original Description ◽  
Recurrence Plot ◽  
External Noise ◽  
Multidimensional Space ◽  
Recurrence Plots ◽  
Time Correlations ◽  
The One ◽  
Physiological Systems

Physiological systems are best characterized as complex dynamical processes that are continuously subjected to and updated by nonlinear feedforward and feedback inputs. System outputs usually exhibit wide varieties of behaviors due to dynamical interactions between system components, external noise perturbations, and physiological state changes. Complicated interactions occur at a variety of hierarchial levels and involve a number of interacting variables, many of which are unavailable for experimental measurement. In this paper we illustrate how recurrence plots can take single physiological measurements, project them into multidimensional space by embedding procedures, and identify time correlations (recurrences) that are not apparent in the one-dimensional time series. We extend the original description of recurrence plots by computing an array of specific recurrence variables that quantify the deterministic structure and complexity of the plot. We then demonstrate how physiological states can be assessed by making repeated recurrence plot calculations within a window sliding down any physiological dynamic. Unlike other predominant time series techniques, recurrence plot analyses are not limited by data stationarity and size constraints. Pertinent physiological examples from respiratory and skeletal motor systems illustrate the utility of recurrence plots in the diagnosis of nonlinear systems. The methodology is fully applicable to any rhythmical system, whether it be mechanical, electrical, neural, hormonal, chemical, or even spacial.

Recurrence based coupling analysis between event-like data and continuous data

2021 ◽  
Author(s):  
Abhirup Banerjee ◽  
Bedartha Goswami ◽  
Norbert Marwan ◽  
Bruno Merz ◽  
Juergen Kurths
Keyword(s):  
Time Series ◽  
Soil Moisture ◽  
Heavy Precipitation ◽  
Recurrence Plot ◽  
Coupled Systems ◽  
Prototype System ◽  
Flood Events ◽  
Recurrence Plots ◽  
Coupling Analysis ◽  
Distance Method

<p>Extreme events such as earthquakes, tsunamis, heat weaves, droughts, floods, heavy precipitation, or tornados -- affect the human communities and cause tremendous loss of property and wealth, but can be related to multiple and complex sources. For example, a flood is a natural event caused by many drivers such as extreme precipitation, soil moisture, or temperature. We are interested in understanding the direct and indirect coupling between flood events with different climatological and hydrological drivers such as soil moisture and temperature.</p><p>We use multivariate recurrence plot and recurrence quantification analysis as a powerful framework to study the couplings between the different systems, especially the direction of coupling. The standard delay-embedding method is not a suitable for the recurrence analysis of event-like data. Therefore, we apply the novel edit-distance method to compute recurrence plots of time series of flood events and use the standard recurrence plot method for the continuous varying time series such as soil moisture and temperature. The coupling analysis is performed using the mean conditional probabilities of recurrence derived from the different recurrence plots. We demonstrate this approach on a prototype system and apply it on the hydrological data. Using this approach we are able to indicate the coupling direction and lag between the different coupled systems.</p>

scholarly journals Small Order Patterns in Big Time Series: A Practical Guide

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 613 ◽  
Author(s):  
Christoph Bandt
Keyword(s):  
Time Series ◽  
Variance Components ◽  
Brain Activity ◽  
Real Data ◽  
Speech Analysis ◽  
Permutation Entropy ◽  
Data Series ◽  
Autocorrelation Functions ◽  
Wide Range ◽  
Theoretical Side

The study of order patterns of three equally-spaced values x t , x t + d , x t + 2 d in a time series is a powerful tool. The lag d is changed in a wide range so that the differences of the frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, and outliers and missing data do not matter. On the theoretical side, we study the properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

scholarly journals Condition Monitor System for Rotation Machine by CNN with Recurrence Plot

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3221 ◽  
Author(s):  
Hsueh ◽  
Ittangihala ◽  
Wu ◽  
Chang ◽  
Kuo
Keyword(s):  
Time Series ◽  
Failure Modes ◽  
Time Series Data ◽  
Induction Motors ◽  
Recognition Task ◽  
Recurrence Plot ◽  
Operating Conditions ◽  
Series Data ◽  
Recurrence Plots ◽  
Preprocessing Method

Induction motors face various stresses under operating conditions leading to some failure modes. Hence, health monitoring for motors becomes essential. In this paper, we introduce an effective framework for fault diagnosis of 3-phase induction motors. The proposed framework mainly consists of two parts. The first part explains the preprocessing method, in which the time-series data signals are converted into two-dimensional (2D) images. The preprocessing method generates recurrence plots (RP), which represent the transformation of time-series data such as 3-phase current signals into 2D texture images. The second part of the paper explains how the proposed convolutional neural network (CNN) extracts the robust features to diagnose the induction motor’s fault conditions by classifying the images. The generated RP images are considered as input for the proposed CNN in the texture image recognition task. The proposed framework is tested on the dataset collected from different 3-phase induction motors working with different failure modes. The experimental results of the proposed framework show its competitive performance over traditional methodologies and other machine learning methods.

scholarly journals A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Vibration ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 332-368 ◽  
Author(s):  
Bedartha Goswami
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Nonlinear Time Series ◽  
Recurrence Plot ◽  
Series Data ◽  
Nonlinear Time Series Analysis ◽  
Recurrence Plots ◽  
Series Analysis ◽  
Wide Range ◽  
Dynamical Features

Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated.

scholarly journals Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

2021 ◽  
Author(s):  
Tobias Braun ◽  
Vishnu R. Unni ◽  
R. I. Sujith ◽  
Juergen Kurths ◽  
Norbert Marwan
Keyword(s):  
Time Series ◽  
Empirical Data ◽  
Acoustic Pressure ◽  
Pressure Fluctuations ◽  
Recurrence Plot ◽  
Dynamical Regime ◽  
Recurrence Plots ◽  
Dynamical Complexity ◽  
Recurrence Quantification ◽  
Regime Transitions

AbstractWe propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.

scholarly journals Finding recurrence networks' threshold adaptively for a specific time series

2014 ◽  
Vol 1 (1) ◽  
pp. 803-822
Author(s):  
D. Eroglu ◽  
N. Marwan ◽  
S. Prasad ◽  
J. Kurths
Keyword(s):  
Time Series ◽  
Recurrence Plot ◽  
Adaptive Threshold ◽  
Model System ◽  
Recurrence Plots ◽  
Sediment Record ◽  
Novel Method ◽  
Prototypical Model ◽  
Analyze Time Series ◽  
Selection Of

Abstract. Recurrence plot based recurrence networks are an approach to analyze time series using complex networks theory. In both approaches, recurrence plots and recurrence networks, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.

Recurrence Density Enhanced Complex Networks for Nonlinear Time Series Analysis

2018 ◽  
Vol 28 (01) ◽  
pp. 1850008 ◽  
Author(s):  
Diego G. de B. Costa ◽  
Barbara M. da F. Reis ◽  
Yong Zou ◽  
Marcos G. Quiles ◽  
Elbert E. N. Macau
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Logistic Map ◽  
Fluid Flows ◽  
Nonlinear Time Series ◽  
Recurrence Plot ◽  
Recurrence Plots ◽  
Statistical Measures ◽  
Set Of Points ◽  
Experimental Fluid

We introduce a new method, which is entitled Recurrence Density Enhanced Complex Network (RDE-CN), to properly analyze nonlinear time series. Our method first transforms a recurrence plot into a figure of a reduced number of points yet preserving the main and fundamental recurrence properties of the original plot. This resulting figure is then reinterpreted as a complex network, which is further characterized by network statistical measures. We illustrate the computational power of RDE-CN approach by time series by both the logistic map and experimental fluid flows, which show that our method distinguishes different dynamics sufficiently well as the traditional recurrence analysis. Therefore, the proposed methodology characterizes the recurrence matrix adequately, while using a reduced set of points from the original recurrence plots.

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