scholarly journals A Refinement of Recurrence Analysis to Determine the Time Delay of Causality in Presence of External Perturbations

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 865
Author(s):  
Emmanuele Peluso ◽  
Teddy Craciunescu ◽  
Andrea Murari
Keyword(s):  
Time Series ◽  
Recurrence Plot ◽  
Recurrence Plots ◽  
Recurrence Analysis ◽  
External Perturbations ◽  
New Type ◽  
Periodic Signals ◽  
Alternative Techniques ◽  
Definition Of ◽  
The Right

This article describes a refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable. The methodology is based on the definition of a new type of recurrence plots, the Conditional Joint Recurrence plot. The potential of the proposed approach resides in the great flexibility of recurrence plots themselves, which allows extending the technique to more than three quantities. Autoregressive time series, both linear and nonlinear, with different couplings and percentage of additive Gaussian noise have been investigated in detail, with and without outliers. The approach has also been applied to the case of synthetic periodic signals, representing realistic situations of synchronization experiments in thermonuclear fusion. The results obtained have been very positive; the proposed Conditional Joint Recurrence plots have always managed to identify the right interval of the causal influences and are very competitive with alternative techniques such as the Conditional Transfer Entropy.

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.

DEFINITION OF DISTANCE FOR MARKED POINT PROCESS DATA AND ITS APPLICATION TO RECURRENCE PLOT-BASED ANALYSIS OF EXCHANGE TICK DATA OF FOREIGN CURRENCIES

2010 ◽  
Vol 20 (11) ◽  
pp. 3699-3708 ◽  
Author(s):  
SATOSHI SUZUKI ◽  
YOSHITO HIRATA ◽  
KAZUYUKI AIHARA
Keyword(s):  
Point Process ◽  
Foreign Exchange ◽  
Marked Point ◽  
Recurrence Plot ◽  
Marked Point Process ◽  
Recurrence Plots ◽  
Process Data ◽  
Tick Data ◽  
Point Process Data ◽  
Definition Of

Recurrence plots are effective in analyzing nonstationary time series. Further, it is desirable to make the recurrence plot-based analysis applicable to marked point process data such as foreign exchange tick data. In this paper, we define a distance for marked point process data and establish the basis for further analyses. We also show that foreign exchange tick data have serial dependence using recurrence plots and the random shuffle surrogate method.

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>

Defects detection from time series of cutting force in composite milling process by recurrence analysis

2020 ◽  
Vol 39 (23-24) ◽  
pp. 890-901
Author(s):  
Krzysztof Ciecieląg ◽  
Krzysztof Kecik ◽  
Kazimierz Zaleski
Keyword(s):  
Time Series ◽  
Milling Time ◽  
Milling Process ◽  
Minimal Size ◽  
Indicator Values ◽  
Recurrence Plots ◽  
Defect Depth ◽  
Recurrence Analysis ◽  
Nonlinear Methods ◽  
Different Diameters

The article presents possibility of defects detection from milling time series using nonlinear methods: recurrence plots and recurrence quantifications. The defects are modeled as the holes with different diameters and depths. This allows estimation of the minimal size of defect possible to detect. Based on the conducted research, it has been shown that some of the recurrence indicators enable detection of defects. These recurrence indicators have been tested on the reals damage. Additionally, we show influence of the defect depth on the recurrence indicator values.

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.

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>

Analysis of time series recurrence and cross recurrence in the relationship of climate with Coffee Leaf Rust

2021 ◽  
Author(s):  
Ana M. Tarquis ◽  
Emmanuel Lasso ◽  
Juan Carlos Corrales ◽  
Elias de Melo
Keyword(s):  
Time Series ◽  
Leaf Rust ◽  
Central America ◽  
Financial Support ◽  
Weather Conditions ◽  
Production Costs ◽  
Recurrence Plots ◽  
Recurrence Analysis ◽  
Coffee Rust ◽  
Coffee Leaf Rust

<p>Agroindustry in South and Central America is positioned as a traditional production sector, where exists a need for integration of processes for the implementation of contingency measures in a timely manner against events that create a risk for crops. Diseases affecting agricultural sectors are often closely related to weather conditions and crop management. In particular, for the coffee production, the Coffee Leaf Rust (CLR) is a disease that affects quality and production costs for farmers greatly. </p><p>Detecting the patterns that affect the disease can lead to early actions that lessen its impact. In this sense, some researchers in the sector have focused their efforts on determining over time the relationships between weather conditions and agronomic properties of crops with episodes of epidemics of diseases as coffee rust. </p><p>Different natural processes, such as the climate, can have different and recurrent behaviors in time. Despite its periodicity, climate change has impacted on recurring events, both in their temporality and intensity. Thus, climate variables have properties of dynamic deterministic or nonlinear systems. The recurrence analysis of states in these systems is one of the solutions to carry out a study of their behavior in the time-domain.  Eckmann et al. proposed the Recurrence Plots (RP) for the visualization of state recurrence, allowing to see the space phase trajectories in a bidimensional representation. This analysis, initially applied to a single time series and its recurrence with itself, can also be extended to compare two time series by Cross Recurrence Plots (CRP) and find the recurrence between them. Moreover, the elements of PR and CRP can be quantified, obtaining direct elements of comparison between series or pairs of time series.</p><p>The aim of this analysis was to find the times and conditions in which the time series of the climatic variables present events related to anomalies or extreme values in the CLRI time series. In addition, the recurrence analysis allows to know the time delay for which each climatic variable affects the disease.</p><p><strong>References</strong></p><p> J. Avelino et al., «The coffee rust crises in Colombia and Central America (2008–2013): impacts, plausible causes and proposed solutions», Food Secur.,  7(2), 303-321, 2015.</p><p> J. M. Waller, M. Bigger, y R. J. Hillocks, Coffee pests, diseases and their management. CABI, 2007.</p><p> A. C. Kushalappa y A. B. Eskes, «Advances in coffee rust research», Annu. Rev. Phytopathol., 27(1), 503–531, 1989.</p><p> E. Lasso, D. C. Corrales, J. Avelino, E. de Melo Virginio Filho, y J. C. Corrales, «Discovering weather periods and crop properties favorable for coffee rust incidence from feature selection approaches», Comput. Electron. Agric., 176, 105640, 2020.</p><p> J. P. Eckmann, S. O. Kamphorst, y D. Ruelle, «Recurrence plots of dynamical systems», World Sci. Ser. Nonlinear Sci. Ser. A, 16, 441–446, 1995.</p><p><strong>Acknowledgements</strong></p><p>Technical support of Telematics Engineering Group (GIT) of the University of Cauca, the Tropical Agricultural Research and Higher Education Center (CATIE) and the InnovAccion Cauca project of the Colombian Science, Technology, and Innovation Fund (SGR- CTI) for PhD scholarship granted to MSc. Lasso is acknowledge. Financial support by Fundación Premio Arce (ETSIAAB, UPM) financial support under contract FPA18PPMAT08 is greatly appreciated.</p>

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.

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